Method for analyzing resin molded products, analysis apparatus, analysis program, and recording medium.

Abstract

In the analysis method, analysis apparatus, analysis program, and recording medium for resin molded products, the crystallization behavior of the resin is considered more accurately based on the actual phenomenon, thereby improving the prediction accuracy of the analysis. [Solution] The method for analyzing a resin molded product is a method for analyzing a resin molded product by computer simulation, and the analysis utilizes the change over time of the total absolute crystallinity Φ, taking into account the primary crystallization behavior and secondary crystallization behavior of the resin during a non-isothermal process, and comprises: a relative crystallinity calculation step S311 that calculates the change over time of the relative crystallinity φ of the resin based on the change over time of at least the temperature during the solidification shrinkage process of the resin; a primary absolute crystallinity calculation step S312 that calculates the change over time of the primary absolute crystallinity Φ1, taking into account the primary crystallization behavior of the resin, based on the change over time of the relative crystallinity φ; and a total absolute crystallinity calculation step S313 that calculates the change over time of the total absolute crystallinity Φ based on the change over time of the primary absolute crystallinity Φ1 and a predetermined formula.

Description

[Technical Field]

[0001] This disclosure relates to a method for analyzing resin molded products, an analysis apparatus, an analysis program, and a recording medium. [Background technology]

[0002] Conventionally, in order to improve the accuracy, efficiency, and cost reduction of product design for resin molded products, the behavior of resin within the mold and the warping deformation of the final product have been analyzed using CAE (Computer-Aided Engineering).

[0003] For example, when performing a warpage deformation analysis of resin in injection molding, general-purpose CAE software typically uses temperature and pressure information of the resin obtained from resin flow analysis as input information, calculates the specific volume using the Tait equation as the governing equation, and finally calculates the shrinkage amount of the molded product.

[0004] However, in the case of crystalline resins, when the resin temperature decreases during the molding process and reaches a certain temperature, crystallization begins, and the rate of decrease in specific volume increases. The temperature at which this crystallization begins varies depending on the cooling rate of the resin. The Tait equation mentioned above is a model that derives one specific volume V from pressure P and temperature T, and therefore cannot consider the cooling rate dependence of the crystallization behavior of the resin. In other words, current general CAE analysis cannot take into account the changes in resin properties based on the crystallization behavior of the resin during the molding process, which poses a problem from the standpoint of improving prediction accuracy.

[0005] Therefore, attempts have been made to consider the crystallization behavior of the resin during the molding process in CAE analysis (see, for example, Patent Documents 1 and 2).

[0006] Patent Document 1 discloses a crystallization process simulation method and apparatus for a crystalline resin molded product, comprising: a data input unit for inputting data on resin temperature, pressure, and shear stress during the molding process; a nucleation rate and nucleation growth rate analysis unit for determining the nucleation rate and nucleation growth rate during molding; a relative crystallization degree calculation unit for predicting the relative crystallization degree and spherulite size distribution using Avrami's equation; and a crystallization process simulation method and apparatus for predicting the change in crystallization degree X during molding over time using the attained crystallization degree.

[0007] Patent Document 2 discloses an apparatus and method for simulating the processing history of a material, characterizing the morphology of the material using a two-phase structure description, and predicting the physical properties of the processed material using the morphology characterization. The document describes an example in which the morphology characterization includes an index of relative crystallinity, and the two-phase structure description includes a crystallization rate model, an amorphous phase model, and a semi-crystalline phase model. [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 10-138312 [Patent Document 2] Special Publication No. 2006-523351 [Overview of the project] [Problems that the invention aims to solve]

[0009] Incidentally, it is generally known that there are two types of crystallization processes in resins: primary crystallization and secondary crystallization. Primary crystallization is the process in which spherulites are formed, consisting of a layered structure (lamellar structure) of crystalline layers created by the folding of polymer chains and amorphous layers sandwiched between adjacent crystalline layers. Secondary crystallization is the process of further thickening and growth of the crystalline layers in the lamellar structure created in primary crystallization, and the completion of the lamellar structure.

[0010] While the technologies described in Patent Documents 1 and 2 consider the crystallization behavior of the resin during the molding process in CAE analysis, they do not adequately consider the primary and secondary crystallization processes mentioned above, and there is room for improvement from the standpoint of improving prediction accuracy.

[0011] Therefore, this disclosure aims to improve the prediction accuracy of analysis by more accurately considering the crystallization behavior of resin based on real-world examples in an analysis method, analysis apparatus, analysis program, and recording medium for resin molded products. [Means for solving the problem]

[0012] To solve the above problems, one aspect of the method for analyzing resin molded products disclosed herein is: A method for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallization behaviors of the resin during a non-isothermal process. A relative crystallinity calculation step that calculates the change in the relative crystallinity φ of the resin over time based on at least the change in temperature over time during the solidification shrinkage process of the resin, A primary absolute crystallinity calculation step that calculates the change in primary absolute crystallinity Φ1 over time, taking into account the primary crystallinity behavior of the resin, based on the change in relative crystallinity φ over time, The system comprises a total absolute crystallinity calculation step, which calculates the change in the total absolute crystallinity Φ over time based on the change in the primary absolute crystallinity Φ1 over time and the following formula (1).

[0013]

number

[0014] (However, in equation (1), Φ(t j ) is any time step t j Total absolute crystallinity progression, Φ1(t j ) is any time step t j The amount of primary absolute crystallinity progression in X jis any arbitrary time step t j , the ratio of the total absolute crystallinity development amount to the primary absolute crystallinity development amount at, a(T) is a constant dependent on the material and temperature, T is temperature, τ is the characteristic time until the onset of secondary crystallization behavior, i 1 / 2 is the half-crystallization time t 1 / 2 is the order of the time step at which is reached.) characterized in that:

[0015] According to the present configuration, analysis that considers the crystallization behavior of resin with higher accuracy based on actual phenomena can be achieved, thus improving the prediction accuracy of the analysis. In addition, calculation costs can be reduced. In the present specification, the term "crystallinity development amount" means the development amount of crystallinity for each time step.

[0016] In one aspect, in the primary absolute crystallinity calculation step, the temporal change of said primary absolute crystallinity Φ1 is calculated based on the following formula (2)

[0017] [Math.]]

[0018] (where, in formula (2), ΔΦ1(t i ) is the primary absolute crystallinity development amount at any arbitrary time step t i , Δφ(t i ) is the relative crystallinity development amount at any arbitrary time step t i that developed at temperature T(t i ), Φ 1,∞ (T(t i )) is the achieved crystallinity of primary crystallization when isothermally crystallized at temperature T(t i )).) The configuration can be formed as follows.

[0019] According to the present configuration, it is advantageous for improving the prediction accuracy of analysis.

[0020] In one embodiment, the specific volume calculation step is further provided, which calculates the change in the specific volume of the resin over time based on the change in temperature over time, the change in pressure over time during the solidification shrinkage process of the resin, and the change in the total absolute crystallinity Φ over time. The specific volume calculation step can be configured to calculate the change in the specific volume over time based on the following formula (3).

[0021]

number

[0022] (However, in equation (3), T is temperature, p is pressure, t is time, v is specific volume, v c v is the specific volume of the crystalline part. m (where m1~m3 and c1~c3 are coefficients, where m1 is the specific volume of the amorphous region and c1~c3 is the coefficient.) This configuration allows for more accurate analysis that considers the cooling rate dependence of the PVT curve based on the actual phenomenon, thereby improving the prediction accuracy of the analysis.

[0023] In one embodiment, any time step t n A physical property information acquisition process to acquire physical property information of the resin used in the calculation, Based on the aforementioned physical property information, the time step t n A resin properties calculation step in which the resin properties, including the temperature of the resin, are calculated, The aforementioned time step t n The system further comprises a property information modification step for modifying the property information of the resin based on the total absolute crystallinity Φ calculated in the total absolute crystallinity calculation step, Next time step t n+1 In the process of acquiring the physical property information, the modified physical property information is acquired as the physical property information of the resin. It can be configured as follows.

[0024] This configuration allows for analysis that more accurately considers the crystallization behavior of the resin based on the actual phenomenon, thereby improving the prediction accuracy of the analysis.

[0025] In one embodiment, the physical property information includes the shear viscosity of the resin. In the resin property calculation step, the shear rate of the resin is calculated as a resin property based on the shear viscosity. In the aforementioned physical property information correction process, the shear viscosity is corrected to the shear viscosity calculated by the following formula (B1): |η|=Φ|η c |+(1-Φ)|η m | ···(B1) (However, in formula (B1), η is shear viscosity, η c η is the shear viscosity of the crystalline region. m (This is the shear viscosity of the amorphous region.) The next timestep t n+1 In the resin properties calculation step, the shear rate is calculated based on the corrected shear viscosity. It can be configured as follows.

[0026] Conventional analyses use resin shear rate data to perform flow calculations. In these analyses, it is assumed that flow uniformly stops when a set temperature is reached during the cooling process, and the shear viscosity, which is the basis for calculating the shear rate, is kept constant below that temperature. However, the cooling rate of the resin varies depending on the molding conditions, for example, so the flow stop temperature also changes. Consequently, conventional flow analyses that uniformly define the flow stop temperature lack sufficient accuracy in predicting shear rate, and cannot guarantee sufficient prediction accuracy in predicting, for example, flow length.

[0027] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B1), the following time step t n+1 The shear viscosity used in the calculations is calculated. This allows for the reproduction of the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute degree of crystallinity Φ. Furthermore, by correcting the shear viscosity, the flow stop temperature can be effectively set to be variable according to the cooling rate, thereby improving the accuracy of shear rate prediction and the accuracy of predictions such as flow length.

[0028] In one embodiment, the physical property information includes the specific volume of the resin. In the resin property calculation step, the pressure of the resin is calculated as a resin property based on the specific volume. In the aforementioned physical property information correction step, the specific volume is corrected to the specific volume calculated by the following formula (B2): |v|=Φ|v c |+(1-Φ)|v m | ···(B2) (However, in formula (B2), v is specific volume, v c v is the specific volume of the crystalline part. m (This is the specific volume of the amorphous region.) The next timestep t n+1 In the resin properties calculation step, the pressure is calculated based on the corrected specific volume. It can be configured as follows.

[0029] Conventional analyses use resin pressure data for calculations. In this case, the specific volume, which is the premise for pressure calculations, is calculated using the resin temperature and pressure as input information and the Tait equation as the governing equation. However, in the case of crystalline resins, when the resin temperature decreases during the molding process and reaches a certain temperature, crystallization begins, and the rate of decrease in specific volume increases. The temperature at which this crystallization begins changes depending on the cooling rate of the resin. The Tait equation mentioned above is a model that derives one specific volume V from pressure P and temperature T, so it cannot take into account the cooling rate dependence of the specific volume in the crystallization behavior of the resin. In other words, current general CAE analyses cannot take into account the changes in resin properties based on the crystallization behavior of the resin during the molding process, and there is room for improvement from the perspective of improving prediction accuracy.

[0030] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B2), the following time step t n+1The specific volume used in the calculation is calculated. This allows for the reproduction of the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute degree of crystallinity Φ. Furthermore, by correcting the specific volume, it becomes possible to perform an analysis that more accurately considers the cooling rate dependence of the specific volume based on the real phenomenon, thereby improving the prediction accuracy of the analysis.

[0031] In one embodiment, the physical property information includes the thermal conductivity of the resin. In the resin property calculation step, the temperature of the resin is calculated as a resin property based on the thermal conductivity. In the aforementioned physical property information correction step, the thermal conductivity is corrected to the thermal conductivity calculated by the following formula (B3): |λ|=Φ|λ c |+(1-Φ)|λ m | ···(B3) (However, in equation (B3), λ is the thermal conductivity, λ c λ is the thermal conductivity of the crystalline part. m (This is the thermal conductivity of the amorphous region.) The next timestep t n+1 In the resin properties calculation step, the temperature is calculated based on the modified thermal conductivity. It can be configured as follows.

[0032] Conventional analyses use resin temperature data for calculations. In these analyses, the thermal conductivity of the resin, which is the basis for the temperature calculation, is assumed to change from a molten state to a solid state during the cooling process, for example, when it reaches an arbitrarily set temperature. The analysis is set so that the thermal conductivity changes uniformly from that of the molten state to that of the solid state at that time. However, in actual molding processes, the resin may be in a state where it is a mixture of molten and solid states, and the thermal conductivity is thought to change continuously depending on the degree of crystallinity of the resin. In this case, conventional analyses that set the thermal conductivity to change uniformly from the value of the molten state to that of the solid state lack sufficient accuracy in predicting temperature, and cannot guarantee sufficient prediction accuracy in the analysis.

[0033] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B3), the following time step t n+1 The thermal conductivity used in the calculations is calculated. This allows us to reproduce the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute crystallinity Φ. Furthermore, because the crystallinity dependence of thermal conductivity can be considered in accordance with the real phenomenon, the accuracy of temperature prediction is improved, and the accuracy of the analysis is improved.

[0034] In one embodiment, the physical property information includes the temperature of the resin. In the resin property calculation step, the temperature of the resin is calculated as the resin property based on the temperature of the resin as physical property information and the modified heat conduction equation represented by the following formula (D1).

[0035]

number

[0036] (However, in equation (D1), ρ is density, Cv is specific heat, T is temperature, λ is thermal conductivity, η is viscosity, γ dot is shear rate, ΔHc is crystallization exothermic term, ΔΦ(t n ) is time step t n Total absolute degree of crystallinity progression, h c (This is a constant and represents the total amount of enthalpy change [J / g] when the resin crystallizes.) In the aforementioned physical property information modification step, the temperature of the resin as physical property information is modified to the temperature of the resin calculated as a resin characteristic. The next timestep t n+1 In the resin property calculation step, the temperature of the resin as a resin property is calculated based on the corrected temperature. It can be configured as follows.

[0037] In equation (D1), a crystallization exothermic term ΔHc is added to the conventional heat conduction equation, taking into account the exothermic reaction of crystallization. This crystallization exothermic term ΔHc is then expressed as the total enthalpy change h when the resin crystallizes. cand total absolute crystallinity progression ΔΦ(t n This is expressed as the product of ( ). With this configuration, the crystallization behavior of the resin can be taken into consideration when calculating the temperature change of the resin over time, thus improving the prediction accuracy of the analysis.

[0038] The specific heat Cv is given by the following equation (D2). Cv=g1T 5 +g2T 4 +g3T 3 +g4T 2 +g5T+g6···(D2) (However, in equation (D2), g1 to g6 are coefficients and are input parameters that depend on the material.) It is preferable.

[0039] This configuration is advantageous for improving the prediction accuracy of the analysis.

[0040] The analysis is at least one of the flow analysis and warpage analysis of the resin molded product. It is preferable.

[0041] Applying this analysis method to fluid dynamics analysis improves the prediction accuracy of fluid dynamics analysis. Furthermore, applying this analysis method to warpage analysis improves the prediction accuracy of warpage analysis.

[0042] One embodiment of the resin molding analysis apparatus disclosed herein is: A device for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallization behaviors of the resin during a non-isothermal process. A relative crystallinity calculation unit calculates the change in the relative crystallinity φ of the resin over time based on at least the change in temperature over time during the solidification shrinkage process of the resin, A primary absolute crystallinity calculation unit calculates the change in primary absolute crystallinity Φ1 over time, taking into account the primary crystallization behavior of the resin, based on the change in relative crystallinity φ over time. The system comprises a total absolute crystallinity calculation unit that calculates the change in the total absolute crystallinity Φ over time based on the change in the primary absolute crystallinity Φ1 over time and the following formula (1),

[0043]

number

[0044] (However, in equation (1), Φ(t j ) is any time step t j Total absolute crystallinity progression, Φ1(t j ) is any time step t j The amount of primary absolute crystallinity progression in X j is any time step t j The ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression, a(T) is a constant that depends on the material and temperature, T is the temperature, τ is the characteristic time until secondary crystallinity behavior begins, i 1 / 2 The semi-crystallization time t is 1 / 2 This is the order of the time steps to reach that point. It is characterized by the following:

[0045] This configuration allows for analysis that more accurately considers the crystallization behavior of the resin based on the actual phenomenon, thereby improving the prediction accuracy of the analysis.

[0046] One aspect of the resin molding analysis program disclosed herein is: A program for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallization behaviors of the resin during a non-isothermal process. At least, Procedure A for calculating the change over time of the relative crystallinity φ of the resin based on at least the change over time of temperature during the solidification shrinkage process of the resin, Procedure B for calculating the change over time of the primary absolute crystallinity Φ1, taking into account the primary crystallization behavior of the resin, based on the change over time of the relative crystallinity φ, The procedure C for calculating the change in the total absolute crystallinity Φ over time based on the change in the primary absolute crystallinity Φ1 and the following formula (1) is performed in this order.

[0047]

number

[0048] (However, in equation (1), Φ(t j ) is any time step t j Total absolute crystallinity progression, Φ1(t j ) is any time step t j The amount of primary absolute crystallinity progression in X j is any time step t j The ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression, a(T) is a constant that depends on the material and temperature, T is the temperature, τ is the characteristic time until secondary crystallinity behavior begins, i 1 / 2 The semi-crystallization time t is 1 / 2 This is the order of the time steps to reach that point. It is characterized by the following:

[0049] This configuration allows for analysis that more accurately considers the crystallization behavior of the resin based on the actual phenomenon, thereby improving the prediction accuracy of the analysis.

[0050] One aspect of the recording medium disclosed herein is: This is a computer-readable recording medium that stores the analysis program for the aforementioned resin molded product. [Effects of the Invention]

[0051] As described above, according to this disclosure, the analysis method, analysis apparatus, analysis program, and recording medium for resin molded products enable analysis that takes into account the crystallization behavior of the resin with greater accuracy based on the actual phenomena, thereby improving the prediction accuracy of the analysis. [Brief explanation of the drawing]

[0052] [Figure 1] Diagrams illustrating each step in resin injection molding, and graphs showing an example of the resin pressure and temperature history. [Figure 2] This figure shows an example of the configuration of a warpage analysis device for resin molded products in this disclosure. [Figure 3] A flowchart illustrating an example of a method for analyzing the warpage of a resin molded product according to this disclosure. [Figure 4] A diagram illustrating the difference between relative crystallinity and absolute crystallinity. [Figure 5] A flowchart illustrating an example of the crystallinity calculation process. [Figure 6] A diagram illustrating the method for determining the Avrami index n and rate constant k using an Avrami plot. [Figure 7] An example of the results of calculating the Avrami index n and rate constant k based on isothermal crystallization measurement results by FSC and Avrami plots. [Figure 8] This graph shows the measured relative crystallinity results obtained by non-isothermal measurements of FSCs and the calculated relative crystallinity results obtained using the Nakamura model. [Figure 9] This graph shows the relationship between the Ozawa index n and temperature, calculated using the Ozawa plot and a reinterpreted Ozawa plot, for a real sample used as a reference example. [Figure 10] A diagram illustrating the discretization of non-isothermal processes. [Figure 11] This graph shows the time course of absolute crystallinity obtained by isothermal measurement using FSC for the actual sample used as a reference example. The solid lines represent the fitting results of the Zhuravlev model for the time course at each temperature. [Figure 12] A graph showing the relationship between absolute crystallinity and temperature for a real sample used as a reference. [Figure 13] This graph shows the measured results of absolute crystallinity and the simulation results obtained using Model B and Model C. [Figure 14] This graph shows the measured results of absolute crystallinity and the simulation results obtained using Model A and Model B. [Figure 15]This graph shows the PVT characteristics of the reference resin material when cooled at a rate of 1°C / s with p0 = 10 MPa. [Figure 16] A graph showing an example of a model plane for the specific volume vc(T,p) of the crystalline region. [Figure 17] A graph showing an example of a model plane for the specific volume vm(T,p) of the amorphous region. [Figure 18] A diagram showing an example configuration of the analysis device for resin molded products according to Embodiment 2. [Figure 19] A flowchart showing an example of a method for analyzing a resin molded product according to Embodiment 2. [Figure 20] A graph showing the relationship between the temperature and crystallization enthalpy of a real resin sample used as a reference example. [Figure 21] This graph shows the measured and simulated results of crystallization exothermic activity at various cooling rates for a real resin sample used as a reference example. [Figure 22] A graph showing the relationship between temperature and specific heat of a real resin sample used as a reference example. [Modes for carrying out the invention]

[0053] Embodiments of the present disclosure will be described in detail below with reference to the drawings. The following description of preferred embodiments is illustrative in nature and is not intended to limit the present disclosure, its applications, or its uses in any way.

[0054] (Embodiment 1) <Resin molding and resin molded products> The technology disclosed herein can be applied to all molding methods using molds made from resin materials. Specific examples of molding methods include injection molding, transfer molding, plunger molding, press molding, blow molding, vacuum molding, and pressure molding.

[0055] In this specification, the terms "resin" and "resin material" mean a resin composition containing resin raw materials and, if necessary, optional additives.

[0056] -Injection molding of resin- As an example of a molding method, an overview of injection molding will be described. Figure 1 is a diagram illustrating each step in resin injection molding, as well as a graph showing an example of the resin pressure and temperature history.

[0057] As shown in Figure 1, resin injection molding comprises an injection step S51, a holding pressure step S52, and a cooling step S53.

[0058] First, molten resin material heated to temperature T1 is injected into the cavity formed by the clamping of molds M1 and M2 (injection step S51).

[0059] Once the resin has filled the entire cavity, additional resin injection is started to reduce excessive shrinkage of the resin due to the decrease in temperature (time Q1). This applies a pressure to the resin in the cavity that exceeds atmospheric pressure P0. Then, while adjusting the amount of additional resin added, the resin pressure is maintained at a predetermined pressure P1 (pressure holding process S52).

[0060] After a certain period of time or after a certain amount of additional resin has been added, the addition of additional resin is stopped (time Q2). As a result, the resin pressure in the cavity gradually decreases from P1 and eventually reaches atmospheric pressure P0 (time Q3). After cooling in the mold, the molded product is demolded by opening the mold and then cooled to the atmosphere (cooling process S53).

[0061] The molded product obtained in this way, although not shown in Figure 1, is cooled to room temperature T0 and then undergoes post-processing such as deburring to become a finished product.

[0062] In the injection process S51, molecular orientation of polymer chains occurs due to the shear flow of the resin. In the holding pressure process S52, crystallization progresses as the temperature decreases in the molecularly oriented state, and volume shrinkage occurs due to crystallization. In the cooling process S53, although resin shrinkage progresses during mold cooling, residual stress is generated in the molded product due to mold constraint. In the cooling process S53, air cooling releases the residual stress through demolding, causing deformation of the molded product.

[0063] It should be noted that, not limited to injection molding, it is generally known that there are two types of crystallization processes for resins, as described above: primary crystallization and secondary crystallization. In this specification, "primary crystallization" refers to the crystallization in which spherulites are formed, consisting of a laminated structure (lamellar structure) of crystalline layers created by the folding of polymer chains and amorphous layers sandwiched between adjacent crystalline layers. "Secondary crystallization" refers to the further thickening growth of the crystalline layers in the lamellar structure formed in primary crystallization and the completion of the lamellar structure.

[0064] Furthermore, the inventors of this application have diligently researched and found that, as a result of their research, the crystallization of the resin in injection molding, particularly from the holding pressure process S52 to the mold cooling process S53, is mainly primary crystallization in a non-isothermal process, but in addition, secondary crystallization in a non-isothermal process also occurs. Moreover, further crystallization occurs during atmospheric cooling in the cooling process S53, but this crystallization is mainly secondary crystallization in an isothermal process.

[0065] -Resin molded products- The resin molded product is not particularly limited as long as it is manufactured by the various molding methods described above. Specific examples of resin molded products include, for example, automobile parts, rocket and aircraft parts, and sporting goods. Preferably, plate-shaped molded products such as interior and exterior components for vehicles are used. The resin molded product may also be an insert molded product.

[0066] As resin raw materials, well-known crystalline resins can be used, but specifically, examples include polypropylene resin, polyethylene resin, polyacetal resin, and polyamide (PA) resin. These resins can be used individually or in mixtures of two or more.

[0067] The resin may contain additives such as reinforcing fibers, fillers, pigments, dyes, impact modifiers, and UV absorbers. The reinforcing fibers are not particularly limited, and well-known fibers can be used, but specific examples include glass fibers, carbon fibers, and cellulose nanofibers. These fibers may be used individually or in combination of two or more. The fiber diameter, fiber length, and content of the reinforcing fibers, as well as the specifications and content of other additives, are not particularly limited and can be those of commonly used conditions. These additives may be added individually or in combination.

[0068] <Analysis device for resin molded products> Figure 2 shows an example of the configuration of the resin molded product analysis device 100 (hereinafter also referred to as "analysis device 100") according to this embodiment. The analysis device 100 is a CAE (Computer Aided Engineering) system with a computer 110 as its basic configuration. The analysis device 100 is a device that performs analysis of resin molded products manufactured by the various molding methods described above using the finite element method through computer simulation. Note that the analysis device 100 is merely one example of a resin molded product analysis device according to this disclosure, and the configuration of the analysis device is not limited to this example. In this embodiment, the case in which the analysis device 100 is mainly applied to the warpage analysis of resin injection molded products will be described as an example.

[0069] The analysis device 100 includes a storage unit 120 consisting of, for example, ROM, RAM, or a hard disk, and a processor 130 consisting of, for example, a CPU. The analysis device 100 also includes a display unit 140 consisting of, for example, a display, an input unit 150 consisting of, for example, a keyboard, and a reading unit 160 for acquiring information stored on various recording media 170. The storage unit 120 and / or recording media 170 store information such as programs for calculation processing and various analysis data. The processor 130 performs various calculation processing based on the above information stored in the storage unit 120, information input via the input unit 150, and information acquired from the recording media 170 via the reading unit 160. The analysis device 100 is configured to communicate with external devices via an interface not shown.

[0070] The analysis device 100 uses a model creation unit 131 to divide shape data, such as 3D CAD data defining the cavity of the mold, into multiple minute elements to create a model for fluid analysis and a model for structural analysis. The model for fluid analysis is a finite element model used for fluid analysis, which will be described later. The model for structural analysis is a finite element model used for structural analysis, which will be described later. The same model may be used for both the fluid analysis model and the structural analysis model, or different models may be used.

[0071] The model creation unit 131 can use commercially available automatic mesh generation software, etc. Specifically, the model creation unit 131 can use CAE preprocessors such as 3D TIMON(registered trademark)-Pre / Post from Toray Engineering D Solutions Co., Ltd., FEMAP(registered trademark) from NST Corporation, Patran(registered trademark) from MSC Software Corporation, and Hyper mesh(registered trademark) from Altair. The shape and size of the elements are not particularly limited and are set appropriately according to the product specifications, material composition, calculation efficiency and calculation accuracy levels. Furthermore, a finite element model of the mold may also be created and used for analysis. When creating a finite element model of a mold, for example, a finite element model may be created for only the surface forming the cavity of the mold or for a part of the mold including said surface.

[0072] Analysis conditions are set based on material property data such as resin type, compound, additives, and various physical properties, as well as boundary condition data that describes molding conditions such as injection speed and resin temperature during injection.

[0073] The fluid analysis unit 133 uses the above-described fluid analysis model to perform a fluid analysis to analyze the behavior of the resin during the injection process S51, the holding pressure process S52, and the cooling process S53. The fluid analysis unit 133 then calculates various data, including resin properties such as temperature information (temperature change over time), pressure information (pressure change over time), and shear rate information (shear rate change over time), for each element and for each minute-time interval. The calculated data is stored in the storage unit 120. For the fluid analysis unit 133, injection molding CAE software such as 3D TIMON® manufactured by Toray Engineering D Solutions Co., Ltd. can be used. Note that the minute-time interval is the analysis unit time for fluid analysis and structural analysis, and is not particularly limited; it is set appropriately according to the product specifications, material composition, calculation efficiency, and calculation accuracy level.

[0074] The structural analysis unit 134 uses the aforementioned structural analysis model and, based on the temperature and pressure information of the resin calculated by the fluid analysis unit 133, performs a structural analysis of the resin, i.e., calculates the shrinkage behavior, to determine the amount of resin shrinkage, and finally calculates the deformation shape and amount of deformation of the molded product. The structural analysis unit 134 can be based on solvers such as Abaqus from Dassault Systèmes K.K. or 3D TIMON®-WARP from Toray Engineering D Solutions Co., Ltd.

[0075] The structural analysis unit 134 includes, for example, a crystallinity calculation unit 135, a specific volume calculation unit 136, a shrinkage amount calculation unit 137, and a deformation calculation unit 138. Details will be described later, but each unit has the following functions.

[0076] The crystallinity calculation unit 135 calculates the crystallinity information of the resin for each element and for each minute of time (change in crystallinity over time) based on at least the temperature information obtained by the above flow analysis.

[0077] The crystallinity calculation unit 135 comprises a relative crystallinity calculation unit 135A, a primary absolute crystallinity calculation unit 135B, and a total absolute crystallinity calculation unit 135C.

[0078] The specific volume calculation unit 136 calculates the specific volume information of the resin for each element and for each minute of time (change in specific volume over time) based on temperature information, pressure information, and crystallinity information.

[0079] The shrinkage amount calculation unit 137 calculates the amount of resin shrinkage for each element and for each minute of time based on the specific volume information.

[0080] The deformation calculation unit 138 calculates the deformation shape and deformation amount from the design shape of the molded product obtained by accumulating the above shrinkage amounts.

[0081] Crystallinity information such as relative crystallinity φ, primary absolute crystallinity Φ1, and total absolute crystallinity Φ obtained from structural analysis, as well as specific volume information, shrinkage amount information, and deformation shape / deformation amount information, are also stored in the memory unit 120.

[0082] <Method for analyzing resin molded products> The analysis method for resin molded products according to this embodiment (hereinafter also referred to as "this analysis method") is a method for analyzing resin molded products manufactured by the various molding methods described above using the finite element method through computer simulation. This analysis method is performed, for example, using the analysis apparatus 100 described above. In this embodiment, the case in which this analysis method is applied to the warpage analysis of a resin injection molded product will be explained as an example.

[0083] Figure 3 is a flowchart showing an example of this analysis method. As shown in Figure 3, this analysis method comprises, for example, a model creation step S1, a fluid analysis step S2, and a structural analysis step S3.

[0084] First, in the model creation process S1, as described above, the model creation unit 131 divides the shape data of the mold cavity, etc., created using 3D CAD, etc., into minute elements for numerical analysis, and creates a model for fluid analysis and a model for structural analysis. The method of model creation is not particularly limited, and generally known methods can be adopted.

[0085] Next, in the flow analysis step S2, analysis conditions such as material property data and boundary condition data are set, and flow analysis is performed using the flow analysis model described above. In this way, temperature information and pressure information for each element and minute time interval of the resin are obtained for each step in the resin injection molding process, namely the injection step S51, the holding pressure step S52, and the cooling step S53.

[0086] Furthermore, the method of flow analysis is not particularly limited, and generally known methods can be employed. Specifically, for example, the initial flow velocity (injection velocity) of the resin, the kinematic viscosity coefficient of the resin material, boundary conditions, etc., are used as input information, and the Navier-Stokes equations, the continuity equation, etc., are used as governing equations to obtain pressure information and flow velocity information for each element and for each minute time in the flow solidification process of the resin. In addition to the shear rate information of the resin based on the flow velocity information, the initial temperature (injection temperature) of the resin, the specific heat, density, and thermal conductivity of the resin material are used as input information, and the heat conduction equation is used as the governing equation to obtain temperature information for each element and for each minute time in the flow solidification process of the resin.

[0087] Then, using the structural analysis model described above, the shrinkage behavior of the resin is calculated based on the temperature and pressure information obtained in the flow analysis step S2, and the amount of resin shrinkage in the holding pressure step S52 and the cooling step S53 is calculated. Finally, the deformation shape and amount of deformation of the molded product are calculated (structural analysis step S3).

[0088] Specifically, the structural analysis step S3 comprises a crystallinity calculation step S31, a specific volume calculation step S32, a shrinkage amount calculation step S33, and a deformation calculation step S34.

[0089] The amount of resin shrinkage can be calculated based on the volume change due to temperature changes, the volume change due to pressure changes, and the degree of crystallinity. Specifically, the specific volume for each element and each minute time period is determined based on the temperature and pressure information for each element and each minute time period obtained in the flow analysis step S2 (degree of crystallinity calculation step S31 and specific volume calculation step S32). Then, the amount of shrinkage for each element and each minute time period is calculated based on the temperature information, pressure information, and specific volume information for each element and each minute time period (shrinkage amount calculation step S33). Finally, the final amount of warpage and the warpage shape of the molded product are calculated using equations such as generalized Hooke's law, based on the amount of shrinkage, elastic modulus, stress, etc. (deformation calculation step S34).

[0090] Conventionally, when calculating specific volume information based on the temperature and pressure information mentioned above, the governing equation has been a state equation such as the Tait equation. The Tait equation is generally expressed as V = V0{1 - 0.0894 × ln(1 + P / B)} + V1, and the coefficients included in B are determined by the least squares method or similar based on PVT characteristic data obtained separately using experimental methods such as the piston method for resin materials.

[0091] As mentioned above, the crystallization behavior of crystalline resins changes depending on the cooling rate of the resin. However, the Tait equation does not include a term related to time, and can only consider the PVT characteristics at the cooling rate used in experiments such as the piston method, so it cannot consider the cooling rate dependence of the crystallization behavior.

[0092] In this analysis method, the change in crystallinity over time is calculated in the crystallinity calculation step S31, based at least on temperature information. Then, in the specific volume calculation step S32, the specific volume of the entire resin is calculated using the two-phase model described later, based on temperature information, pressure information, and crystallinity information. This makes it possible to calculate specific volume information that takes into account the cooling rate dependence of the crystallization behavior.

[0093] [Crystallization Calculation Process] In the crystallinity calculation step S31, the crystallinity information of the resin is calculated based on at least the change in temperature over time during the solidification shrinkage process of the resin. At this time, as will be described later, a model equation that takes into account the primary and secondary crystallinity behaviors of the resin during the non-isothermal process is used. With this configuration, it becomes possible to perform analysis that takes into account the crystallinity behavior of the resin with greater accuracy based on the actual situation, thereby improving the prediction accuracy of the analysis.

[0094] Furthermore, in this specification, the degree of crystallinity X c These are the relative crystallinity φ and absolute crystallinity Φ shown in Figure 4. a It is used in a sense that includes both (also called "achievable degree of crystallinity") and absolute crystallinity Φ. a This concept includes the primary absolute crystallinity Φ1 and the total absolute crystallinity Φ, which will be described later.

[0095] While the enthalpy of melting of crystalline resin materials is known from literature, in most cases, the resin material of a molded product does not reach a crystalline state with the enthalpy of melting of the literature value after the molding process is completed. This is because the crystallization behavior is highly dependent on molding conditions. Absolute crystallinity indicates how far crystallization has progressed relative to the enthalpy of melting of the crystalline material shown in the literature. On the other hand, relative crystallinity indicates how far crystallization has progressed relative to the absolute crystallinity that can be achieved depending on the molding conditions, i.e., the achievable crystallinity.

[0096] Crystallinity can be determined, for example, by measuring the heat of fusion of the crystal using DSC. In this case, "relative crystallinity" refers to the crystallinity when the total enthalpy change H(∞) of the crystallization exothermic peak is set to 1. Absolute crystallinity is the enthalpy of fusion of the crystal (literature value) ΔH f This represents the degree of crystallinity when set to 1.

[0097] Crystallinity X calculated in crystallinity calculation step S31 c From the perspective of improving prediction accuracy, the absolute crystallinity Φ, which is temperature-dependent, is important. aIn particular, the inventors of this application have conducted diligent research and found that the absolute crystallinity Φ a Therefore, we have derived a model for calculating the time-dependent change in total absolute crystallinity Φ, which is the absolute crystallinity that takes into account both the primary and secondary crystallinity behaviors of the resin during a non-isothermal process. The model for calculating the time-dependent change in total absolute crystallinity Φ will be described in detail below. In this specification, in order to distinguish it from the total absolute crystallinity Φ mentioned above, the absolute crystallinity that takes into account only the primary crystallinity behavior of the resin will be referred to as primary absolute crystallinity Φ1.

[0098] As shown in Figure 5, the crystallinity calculation step S31 comprises a relative crystallinity calculation step S311, a primary absolute crystallinity calculation step S312, and a total absolute crystallinity calculation step S313.

[0099] -Relative crystallinity calculation process- Specifically, the relative crystallinity φ(t) at a given time t can be described using the Nakamura model, which is expressed by the following equation (A1).

[0100]

number

[0101] In equation (A1), K(T) is a value related to the crystal growth rate constant k(T), for example, K(T) = k(T) 1 / n Furthermore, n is the Avrami index (also called the "Ozawa index" in the Ozawa plot) relating to the shape (dimension) of the crystal. k(T) or K(T) and n can be determined using the Avrami plot (isothermal crystallization measurement), the Ozawa plot (non-isothermal crystallization measurement), the reinterpreted Ozawa plot (non-isothermal crystallization measurement), and kinetic models of crystallization such as the Hoffman-Lauritzen theory.

[0102] Specifically, for example, the Avrami plot can be represented by the following equation (A2).

[0103] φ(t)=1-exp[-kt n ] ···(A2) By transforming equation (A2), we obtain the following equation (A3).

[0104] log[-ln(1-φ)]=logk+nlogt ···(A3) In other words, when plotting time (logt) on the horizontal axis and log[-ln(1-φ)] on the vertical axis, the slope of the line corresponds to the Avrami exponent n, and the intercept corresponds to the velocity constant logk.

[0105] Using a high-speed differential scanning calorimetry (FSC), the temperature of a molten sample is rapidly reduced to the measurement temperature, and once the measurement temperature is reached, the temperature is kept constant. The change in heat flow over time is then measured, for example, as shown in the upper part of Figure 6. The change in crystallinity over time during the isothermal process at the desired measurement temperature is then calculated. The data for the change in crystallinity over time at each temperature are graphed as shown in the lower part of Figure 6, and the Avrami index n and rate constant k are determined based on equation (A3).

[0106] Figure 7 shows an example of the results of calculating the Avrami index n and rate constant k based on isothermal crystallization measurement results by FSC and Avrami plots. In Figure 7, digital microscope images of the sample after isothermal crystallization measurement by FSC at 50°C and 100°C are shown above the graph.

[0107] From the results in Figure 7, the Avrami exponent n and the rate constant k can be approximated by a fifth-degree polynomial in temperature T, as shown in equations (A4) and (A5) below.

[0108] n(T) = a1T 5 +a2T 4 +a3T 3 +a4T 2 +a5T+a6···(A4) k(T) = b1T 5 +b2T 4 +b3T 3 +b4T 2 +b5T+b6···(A5) In equations (A4) and (A5), a1 to a6 and b1 to b6 are material-dependent coefficients.

[0109] Substituting equations (A4) and (A5) above into the Nakamura model in equation (A1) above, the relative crystallinity φ(t) is calculated as shown in Figure 8. In Figure 8, the measured results from non-isothermal measurements of FSC are shown by solid lines, and the calculated results obtained using the Nakamura model are shown by dashed lines. From Figure 8, it can be seen that the relative crystallinity model using the Nakamura model can reproduce the cooling rate dependence of the crystallization behavior.

[0110] The Avrami index n and the rate constant k may also be determined using the Ozawa plot, which is represented by the following equation (A6).

[0111]

number

[0112] When using the Ozawa plot, the crystallization behavior in a non-isothermal process is measured when the sample is cooled at a constant cooling rate using FSC. The log[-ln(1-φ)] values ​​for each cooling rate at a given temperature are extracted and plotted with logβ on the x-axis and log[-ln(1-φ)] on the y-axis. The slope of the regression line for each temperature obtained from the resulting graph is the Ozawa exponent n, and the intercept is the rate constant logX(T).

[0113] Furthermore, the reinterpreted Ozawa plot shown by equations (A7) and (A8) below (A. Toda: Thermochimica Acta, 707, 179086 (2022), ibid. 713, 179244, (2022)) may also be used.

[0114] φ(T,β i ) = 1 - exp[-φ0] ···(A7)

[0115]

number

[0116] The primary crystallization behavior in a non-isothermal process at a constant scanning rate β can be evaluated based on the Kolmogorov-Johnson-Mehl-Avrami model using the reinterpreted Ozawa plots shown in equations (A7) and (A8). Here, φ(T,β i ) is the rate of cooling β i The relative crystallinity at temperature T is shown, φ0 indicates the case of heterogeneous nucleation, N0 is the initial nucleus number density, g is the geometric coefficient, G is the linear growth rate, and n is the Ozawa exponent.

[0117] When using the reinterpreted Ozawa plot, the K(T) term of the Nakamura model is expressed by the following equation (A9).

[0118]

number

[0119] β peak (T) is determined from the relationship between the cooling rate and the exothermic peak temperature, and includes information on the growth rate G. The horizontal axis is log(β). peak (T)) By finding the slope of the regression line of the data plotted with log[1-exp(-φ0)] on the vertical axis, each β i The Ozawa index can be calculated using this method.

[0120] Figure 9 shows the Ozawa index n calculated using the Ozawa plot and the reinterpreted Ozawa plot for the actual samples in the reference example described later. As shown in Figure 9, when using the reinterpreted Ozawa plot, the same number of n as the number of measurement data points are obtained, thus improving the reliability of the data compared to the Ozawa plot.

[0121] Although details will be omitted here, the Hoffman-Lauritzen theory, shown in equation (A10) below, can also be used to define the K(T) term in the Nakamura model.

[0122]

number

[0123] In formula (A10), Tg is the glass transition temperature, T m is the melting point. By using formula (A10), the pressure dependence of the melting point and the glass transition temperature, which are temperatures related to the temperature at which crystallization starts, can be taken into consideration.

[0124] - Primary absolute crystallinity calculation step- In the primary absolute crystallinity calculation step S312, the temporal change in the primary absolute crystallinity Φ1 of a resin is calculated based on the temporal change in the relative crystallinity φ calculated in the above relative crystallinity calculation step S311.

[0125] First, for the kinetics of relative crystallinity in general non-isothermal processes, for example, the Nakamura model of the above formula (A1) can be applied. Next, in order to consider the absolute value of primary crystallization in a non-isothermal process, as shown in Fig. 10, consider a case where the non-isothermal process is discretized by time Δt. By discretizing the temperature profile with time Δt, the progress of crystallization can be considered as an isothermal process within each time step. For this reason, the ultimate crystallinity Φ of primary crystallization at any temperature T 1,∞ (T) is known, then for each time step t i at temperature T(t i ), the progress amount Δφ(t i ) of relative crystallinity progressed at i ) and the ultimate crystallinity Φ of primary crystallization when isothermal crystallization is performed at temperature T(t 1,∞ (T(t i )) by taking the product of these, the progress amount ΔΦ1(t i ) of the primary absolute crystallinity at each time step t i ) can be obtained. Then, by taking the sum of the progress amounts ΔΦ1(t i ) of the primary absolute crystallinity at each time step t i ) for all time steps up to any time t, the primary absolute crystallinity Φ1(t) at time t can be obtained. That is, the primary absolute crystallinity Φ1(t) can be expressed by the model of the following formula (2) (sometimes referred to as "Model C").

[0126]

Mathematical Expression

[0127] However, in equation (2), ΔΦ1(t i ) is any time step t i The amount of primary absolute crystallinity progression in Δφ(t i ) is any time step t i Temperature T(t i The amount of relative crystallinity progression that occurred, Φ 1,∞ (T(t i )) is temperature T(t i This is the degree of crystallinity achieved during primary crystallization when isothermal crystallization is carried out using ).

[0128] Model C in equation (2) is, in other words, a model for calculating the change over time of the primary absolute crystallinity Φ1, which is the absolute crystallinity that considers only the primary crystallinity behavior.

[0129] Here, the degree of crystallinity Φ achieved when isothermal crystallization is performed at any temperature is the degree of crystallinity attained in primary crystallization. 1,∞ This can be determined by fitting the plot of absolute crystallinity and crystallization time obtained from isothermal crystallization experiments using equation (4) below. Equation (4) is the Zhuravlev model, which is obtained by adding a secondary crystallization term for an isothermal process progressing on a logarithmic time scale to the Kolmogorov-Johnson-Mehl-Avrami model (also called the "KJMA model"), which represents the primary crystallization behavior in a non-isothermal process at a constant scanning speed (E. Zhuravlev, et al., Eur. Polym. J. 52 (2014) 1.).

[0130]

number

[0131] However, in equation (4), Φ(t) is the change over time of the total absolute crystallinity, Φ2(t) is the change over time of the secondary absolute crystallinity, Φ 1,∞ t is the degree of crystallinity achieved when isothermal crystallization is performed at temperature T. 1 / 2τ is the semi-crystallization time, n is the Avrami index, A is a constant that depends on the material and temperature, and τ is the characteristic time until secondary crystallization behavior begins.

[0132] Then, Φ obtained in the same manner under each temperature condition 1,∞ By plotting temperature on the x-axis and fitting it using a polynomial, the degree of crystallinity achieved in primary crystallization Φ can be determined. 1,∞ Temperature dependence Φ 1,∞ (T) is obtained.

[0133] Specific examples are shown using Figures 11 and 12. Figure 11 is a graph showing the change in absolute crystallinity over time for the actual sample of the reference example described later, obtained by isothermal measurements at each temperature using FSC as described later. The Zhuravlev model of equation (4) above is fitted to the change in absolute crystallinity over time at each temperature in Figure 11, and the crystallinity Φ achieved in primary crystallization at each temperature is obtained. 1,∞ The value of is obtained. Note that the degree of crystallinity Φ obtained is on the regression curve of the Zhuravlev model. 1,∞ The crystallization time that yields the value is the characteristic time τ described above. The degree of crystallinity achieved in the primary crystallization is Φ. 1,∞ When the value of is plotted against temperature, it looks like the black dots in Figure 12. When a fifth-degree polynomial is fitted to the plot of black dots in Figure 12, as shown by the solid line, the degree of crystallinity achieved in primary crystallization Φ 1,∞ Temperature dependence Φ 1,∞ (T) is obtained.

[0134] Note that the plots indicated by circles in Figure 12 represent the absolute crystallinity Φ obtained by non-isothermal measurement. a The value of is plotted with the crystallization exothermic peak temperature on the x-axis. As shown in Figure 12, the absolute crystallinity Φ obtained from non-isothermal measurements a The value (○) represents the degree of crystallinity achieved in primary crystallization, Φ, calculated from the results of isothermal measurements. 1,∞It can be seen that the value is higher than the value (●). This indicates that under non-isothermal process conditions such as from the pressure holding step S52 to the mold cooling in the cooling step S53 in the molding process, the achieved crystallinity at any time and any temperature is higher than the achieved crystallinity of primary crystallization in an isothermal process. That is, it shows that under such non-isothermal process conditions, secondary crystallization further proceeds in addition to primary crystallization. From this, it can be seen that in order to improve the analysis accuracy of resin molded products, it is necessary to more accurately consider the primary crystallization behavior and secondary crystallization behavior in the non-isothermal process.

[0135] -Total Absolute Crystallinity Calculation Step- In the total absolute crystallinity calculation step S313, the temporal change in the total absolute crystallinity Φ is calculated based on the temporal change in the primary absolute crystallinity Φ1 calculated in the primary absolute crystallinity calculation step S312 described above.

[0136] First, dividing both sides of equation (4) by Φ1(t) gives equation (5).

[0137]

Mathematical Expression

[0138] Next, for the case of t≧t 1 / 2 , if A = a×ln10, equation (6) is obtained.

[0139]

Mathematical Expression

[0140] Then, time differentiation of equation (6) gives equation (7) as a differential equation having a solution indicating the temporal change in crystallinity.

[0141]

Mathematical Expression

[0142] In a non-isothermal process, the coefficient a depends on temperature. Also, since the crystal growth rate strongly depends on temperature, t 1 / 2 To determine this, it is necessary to sequentially calculate the time evolution of primary crystallization. Therefore, the crystallization behavior in a non-isothermal process can be expressed by the discretization equation (8) below (also called "Model A"), which describes the progress of secondary crystallization using the differential equation (7).

[0143]

number

[0144] However, in equation (8), Φ(t j ) is any time step t j Total absolute crystallinity progression, Φ1(t i ) is any time step t i The amount of primary absolute crystallinity progression in X i,j is time step t i In this case, the ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression is given by a(T), where a(T) is a constant dependent on the material and temperature, T is the temperature, and τ is the characteristic time until secondary crystallinity behavior begins.

[0145] Model A in equation (8) is a two-dimensional array equation, indicating that only primary crystallization is calculated at timesteps where j=i, and calculations including secondary crystallization are performed in the range of timesteps where j>i. In other words, timestep t i For the primary crystallized component produced, the next time step t i+1 Subsequently, the progress of secondary crystallization is calculated, and the amount of progress is added based on the differential equation (7). Then, the time step t j The total absolute crystallinity reached is calculated from time step t0 to t. j It is obtained by summing the crystallinity up to that point. Equation (8) sequentially calculates the total amount of progress in absolute crystallinity at each time step.

[0146] If we adopt Model A from Equation (8) as the model equation for calculating the change in total absolute crystallinity Φ over time, we can calculate the total absolute crystallinity Φ by considering the primary and secondary crystallinity behaviors in a non-isothermal process, thereby improving prediction accuracy.

[0147] Note that in equation (8), ΔΦ1(t i )X i,j It is necessary to store each element for the number of time steps, which can increase computational costs. In the crystallization process of resin, secondary crystallization proceeds after primary crystallization occurs, so Model A in equation (8) is a model that is more in line with the principle of the crystallization process, but from the viewpoint of suppressing computational load, it is desirable to adopt a simpler model.

[0148] Therefore, we obtained equation (1) (also called "Model B") as an approximation of Model A in equation (8). Equation (1) is roughly equivalent to the final ΔΦ1(t) in equation (8). j )X i,j This model omits the process of summing up the values ​​and instead sequentially calculates the progress of secondary crystallization based on the crystallinity of the previous time step.

[0149]

number

[0150] However, in equation (1), Φ(t j ) is any time step t j Total absolute crystallinity progression, Φ1(t j ) is any time step t j The amount of primary absolute crystallinity progression in X j is any time step t j The ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression, a(T) is a constant that depends on the material and temperature, T is the temperature, τ is the characteristic time until secondary crystallinity behavior begins, i 1 / 2 The semi-crystallization time t is 1 / 2 This is the order of the time steps to reach that point.

[0151] In Model B of formula (1), the progress term of secondary crystallization is a discretized formula based on a differential equation, so for each time step t j , to calculate the progress of crystallinity, it is only necessary to know the information X of crystallinity at the immediately preceding time step t j-1 at j-1 only. Therefore, when Model B of formula (1) is adopted as a model formula for calculating the temporal change in total absolute crystallinity Φ, the calculation cost can be greatly reduced while maintaining excellent prediction accuracy compared with the case where Model A of formula (8) is adopted.

[0152] -Experiment 1- FIG. 13 shows the cooling rate dependence of the total absolute crystallinity Φ calculated using Model B of formula (1) and the absolute crystallinity Φ₁ calculated using Model C of formula (2). Note that the crosses represent measured values obtained by non-isothermal measurement using FSC.

[0153] As shown in FIG. 13, it can be seen that the primary absolute crystallinity Φ₁ calculated by considering only primary crystallization behavior using Model C has a difference from the measured value. In contrast, it can be seen that the total absolute crystallinity Φ calculated by considering both the primary crystallization behavior and the secondary crystallization behavior in the non-isothermal process using Model B matches the measured value with high accuracy. This shows that Model B of formula (1) can accurately reproduce the crystallization behavior in a non-isothermal process.

[0154] -Experiment 2- FIG. 14 shows the results of calculating the temporal change in total absolute crystallinity Φ based on Model A of formula (8) and Model B of formula (1). Note that the crosses represent measured values obtained by non-isothermal measurement using FSC.

[0155] As shown in FIG. 14, it can be seen that Model A of formula (8) can accurately reproduce the cooling rate dependence of the absolute crystallinity Φ a observed in the measured values indicated by the crosses. It can also be seen that Model B of formula (1) also has prediction accuracy comparable to that of Model A.

[0156] Furthermore, while the calculation time using Model A was approximately 88 minutes, the calculation time using Model B was approximately 0.89 seconds. In other words, it was found that the calculation time could be reduced by 99.98% by adopting Model B instead of Model A. The specifications of the computer used for the calculation were: Processor: Intel(R) Core(TM) i5-10310U CPU@1.70GHz 2.21GHz, Installed RAM: 16.0GB (15.8GB usable).

[0157] [Specific volume calculation process] In the specific volume calculation step S32, the specific volume information is calculated based on the temperature information, pressure information, and crystallinity information mentioned above, as well as the following formula (3).

[0158]

number

[0159] However, in equation (3), T is temperature, p is pressure, t is time, v is specific volume, v c v is the specific volume of the crystalline part. m is the specific volume of the amorphous region, and m1~m3 and c1~c3 are coefficients.

[0160] Equation (3) gives the specific volume v of the crystalline portion. c and specific volume v of the amorphous region m This is a two-phase model obtained by multiplying each of the two phases by the proportion of the crystalline part Φ and the proportion of the amorphous part 1-Φ, respectively, based on the total absolute crystallinity Φ, and then adding the two together. Hereinafter, v c , v m The derivation method will be explained.

[0161] First, a capillary rheometer (a known piston method) is used to cool a molten sample at a constant cooling rate under a pressure p0, and the PVT properties are measured. Figure 15 shows an example of PVT properties. The PVT properties indicated by the symbol × in Figure 15 are those of the resin material in the reference example described later, when cooled at p0 = 10 MPa and a cooling rate of 3°C / min.

[0162] The PVT characteristics decrease linearly in the liquid phase, but decrease rapidly when the temperature drops below the temperature at which crystallization of the resin material begins. The amorphous region can basically be considered as the liquid phase, and the specific volume v of the amorphous region at pressure P0. m (T,p0) can be modeled by a straight line including the dashed portion obtained as the regression equation for the high-temperature portion of the PVT characteristics (Figure 15 (i)).

[0163] Next, the sample is removed after the PVT characteristics measurement is complete, and the absolute crystallinity Φ is determined by DSC, XRD, etc. a Measure (Figure 15 (ii)).

[0164] Furthermore, the specific volume v of the crystalline portion at pressure p0 c (T,p0) is calculated from equation (3). Specifically, the specific volume v of the amorphous region. m (T,p0) is obtained as a regression equation for the high-temperature portion of the PVT characteristics, as described above. Also, the absolute crystallinity Φ a These have also been obtained by measurement. Furthermore, the specific volume v(T,p0) of the resin material at pressure p0 is known information from the results of PVT characteristic measurement using the piston method. m (T,p0), Φ a Substitute the value of v(T,p0) into equation (3) and get v c (T,p0) can be determined (Figure 15 (iii)).

[0165] The above PVT characteristic measurement and steps (i) to (iii) are repeated while changing the pressure p0. Finally, v c (T,p), v m Model (T,p).

[0166] As a result, the specific volume v of the crystalline part c (T,p) has a linear relationship with respect to temperature T and pressure p, respectively, and can be modeled by a plane as shown in Figure 16, i.e., the second row of equation (3) above. c1, c2, and c3 are material-dependent coefficients.

[0167] Also, the specific volume v of the amorphous region m(T, p) has a linear relationship with respect to each of temperature T and pressure p, and can be modeled by a plane as shown in Figure 17, that is, the formula in the third line of the above formula (3). m1, m2 and m3 are coefficients dependent on the material.

[0168] After calculating the specific volume by the above formula (3), the deformed shape and deformation amount of the finally obtained molded product are obtained through the shrinkage amount calculation step S33 and the deformation calculation step S34.

[0169] The above structural analysis has been described on the assumption that it is applied to in-mold shrinkage behavior in a non-isothermal process (from the pressure holding step S52 to mold cooling in the cooling step S53), but it can also be applied to out-of-mold shrinkage behavior in an isothermal process (after demolding in the cooling step S53).

[0170] <On FSC Measurement> The actually measured value of crystallinity considered in the crystallinity calculation step S31 can be measured using Differential Scanning Calorimetry (DSC), Fast Scanning Calorimetry (FSC), or the like, preferably FSC. In particular, FSC enables non-isothermal thermal measurement at a temperature increase / decrease rate of 3°C / s or more, preferably 10°C / s or more, and isothermal thermal measurement in which the sample temperature is set to a desired temperature at a temperature increase / decrease rate of 100°C / s or more, preferably 1000°C / s or more and 10000°C / s or less, and held at the desired temperature. That is, with FSC, it is possible to perform measurements that reproduce the high-speed cooling environment achieved during actual molding processing (for example, 3°C / s or more, particularly 10°C / s or more), and measure the crystallization behavior in an isothermal process in a general molding processing temperature range (for example, 25°C to 300°C, and for polypropylene, for example, 40°C to 120°C).

[0171] In the present configuration, in the crystallinity calculation step S31, the temporal change in the total absolute crystallinity Φ is calculated in consideration of the crystallization behavior of the resin within the molding processing temperature range obtained by DSC or FSC, preferably FSC. This enables warpage analysis that considers the cooling rate dependence of the PVT curve more accurately based on actual phenomena, thereby improving the prediction accuracy of warpage analysis.

[0172] Furthermore, for isothermal measurements at any temperature (measurement temperature) within the molding temperature range specified by FSC, it is preferable to use a temperature profile in which the sample temperature is lowered to the measurement temperature at a cooling rate of preferably 100°C / s or more, more preferably 1000°C / s or more and 10000°C / s or less, and then held at the measurement temperature for a predetermined time.

[0173] Furthermore, for non-isothermal measurements within a temperature range including the above-mentioned arbitrary temperature (measurement temperature), it is preferable to use a temperature profile that reduces the sample temperature at a cooling rate of preferably 1°C / s to 1000°C / s, more preferably 1°C / s to 320°C / s, and preferably at a constant cooling rate.

[0174] For measuring the absolute (achievable) crystallinity of a sample by reheating it after isothermal or non-isothermal measurement, it is preferable to use a temperature profile that raises the sample temperature at a heating rate of preferably 100°C / s or more and 10000°C / s or less, more preferably 500°C / s or more and 2000°C / s or less, preferably at a constant heating rate.

[0175] With the above configuration, crystallization behavior can be observed with high precision.

[0176] <Analysis program for resin molded products and its recording medium> At least a portion of each step of the above analysis method is programmed as an analysis program for resin molded products manufactured by the various molding methods described above. That is, the analysis program for resin molded products according to this embodiment is a program that causes a computer to execute at least the steps of the crystallinity calculation step S31, i.e., at least step A of the relative crystallinity calculation step S311, step B of the primary absolute crystallinity calculation step S312, and step C of the total absolute crystallinity calculation step S313, in this order. The program may also be configured to execute the entire procedure of the structural analysis step S3, i.e., in addition to the above procedure, the steps of the specific volume calculation step S32, the shrinkage amount calculation step S33, and the deformation calculation step S34. Furthermore, the program may be configured to execute the steps of the model creation step S1 and the flow analysis step S2 in addition to the entire procedure of the structural analysis step S3. This analysis program is stored in, for example, the memory unit 120 and can be executed by the processor 130. Furthermore, the analysis program is not limited to being stored in the memory unit 120; it can also be recorded on various well-known computer-readable recording media, such as optical discs or magnetic tape media. By inserting such a recording media into the reading unit 160 and reading the analysis program, the program can be executed.

[0177] (Example of experiment) The above reference examples, Experiment 1, and Experiment 2 will be explained in detail.

[0178] <Reference example> [material] As an actual sample, we used isotactic polypropylene (manufactured by Sun Aroma Co., Ltd., M w = 20.6 × 10 4 M w / M n =7.5, MFR (230℃, load: 2.16kg (JIS K 7210-1:2014)): 31g / 10min, stereoregularity ( 13A 1C-NMR spectrum (97.8 mm / mm) was used. The enthalpy of melting of the crystalline material (literature value) is 206.75 J / g (B. Wunderlich: Thermal Analysis of Polymeric Materials, Springer, Berlin (2005)).

[0179] [High-speed differential scanning calorimetry] The crystallization behavior of resin materials was evaluated using a high-speed differential scanning calorimeter (Mettler-Toledo, Flash DSC1).

[0180] -Non-isothermal measurement- The sample was heated to 230°C and then cooled at a constant rate of 1 to 320°C / s. Subsequently, the enthalpy of fusion (J / g) was calculated from the melting curve when the sample was reheated at a rate of 1000°C / s, and the absolute (achievable) crystallinity was determined by dividing this value by the enthalpy of fusion value from the above-mentioned literature.

[0181] -Isothermal measurement- The sample was heated to 230°C, then cooled at a constant rate of 1000°C / s, and maintained isothermally within the temperature range of 0 to 110°C for 0.015 to 500 seconds. Subsequently, the enthalpy of melting (J / g) was calculated from the melting curve when the sample was reheated at a rate of 1000°C / s, and the absolute (achieved) crystallinity was determined by dividing this value by the enthalpy of melting from the above-mentioned literature value.

[0182] -Estimation of Mass- The size of the solidified sample after cooling was approximately 30–150 μm square and approximately 10–20 μm thick. The mass m of the sample was determined by the specific heat C of the liquid phase of the sample, measured using a standard DSC. p Based on the heat flow dq / dt of the liquid phase of the sample measured by FSC, the mass was estimated using the following equation (9). For example, the mass of the 100°C isothermal crystal could be estimated to be 55.2 ng.

[0183]

number

[0184] [PVT characteristic measurement] Using a commercially available capillary rheometer, the temperature of a molten sample was lowered from 230°C to 70°C at a constant cooling rate of 3°C / min under a pressure P0 (10 MPa), and the PVT characteristics were measured.

[0185] [Differential Scanning Calorimetry] After the PVT characteristic measurement was completed, the sample was removed at 70°C and the degree of crystallinity was determined by DSC. c The following measurements were taken. Specifically, the solid sample after PVT characteristic measurement was cut using a microtome to create thin sections approximately 200 μm thick. These thin sections were punched to prepare a measurement sample with a diameter of 4.5 mm, a thickness of 200 μm, and a mass of 3.3 ± 0.1 mg. This measurement sample was subjected to DSC, and the heat of fusion was measured to calculate the degree of crystallinity.

[0186] <Calculation conditions and calculation parameters> Tables 1 and 2 show the calculation conditions and parameter values ​​used in Experiment 1 and Experiment 2, respectively. The Nakamura model of equation (A1) was used to calculate the change in relative crystallinity φ over time, and K(T) and n were determined using the reinterpreted Ozawa plots of equations (A7) to (A9) (where n is expressed as a 5th-degree polynomial in equation (A4)). Model C of equation (2) was used to calculate the change in primary absolute crystallinity Φ1 over time. Model B of equation (1) or Model A of equation (8) was used to calculate the change in total absolute crystallinity Φ over time. Experiment 1 compares the calculation results of Model B, the calculation results of Model C, and the measured values ​​(Figure 13). Experiment 2 compares the calculation results of Model B, the calculation results of Model A, and the measured values ​​(Figure 14).

[0187] [Table 1]

[0188] [Table 2]

[0189] Note that the β in formula (A9) shown in Table 2 peak(T), n in equation (A4), Φ in equation (2) 1,∞ (T) and a in equation (1) are expressed as a fifth-degree polynomial of temperature T. Therefore, these fifth-degree polynomials can be grouped together as "f(T) = b1T 5 +b2T 4 +b3T 3 +b4T 2 The expression is written as "+b5T+b6", and the coefficients of each term are shown as b1 to b6 in Table 2. Also, since τ in equation (1) is a constant, in Table 2, b1=b2=b3=b4=b5=0, and the value of τ is written in column b6.

[0190] (Embodiment 2) Other embodiments relating to this disclosure will be described in detail below. In the description of these embodiments, the same reference numerals are used for parts that are the same as in Embodiment 1, and detailed descriptions will be omitted.

[0191] <Analysis device for resin molded products> Figure 18 shows an example of the configuration of the analysis device 100 according to this embodiment. In this embodiment of the analysis device 100, the case in which the analysis device 100 is applied to the flow analysis of a resin injection molded product will be described as an example. The basic hardware configuration and functional configuration of the analysis device 100 can be the same as the configuration of the analysis device 100 of Embodiment 1. The analysis device 100 according to this embodiment may or may not include a structural analysis unit. If the analysis device 100 includes a structural analysis unit, it may have the same configuration as the structural analysis unit 134 of Embodiment 1, or it may be configured using a commercially available solver, for example, as exemplified as the base for the structural analysis unit 134 of Embodiment 1.

[0192] The fluid analysis unit 133 of the analysis device 100 comprises a physical property information acquisition unit 133k, a resin property calculation unit consisting of a pressure calculation unit 133a, a temperature calculation unit 133b, and a shear rate calculation unit 133c, a cooling rate calculation unit 133d, a crystallinity calculation unit 133f, and a physical property information correction unit 133q. Details will be described later, but each unit has the following functions.

[0193] The physical property information acquisition unit 133k uses a time step t nThe resin's physical property information is acquired for use in the calculation. The physical property information acquisition unit 133k then performs the next time step t n+1 In this process, the modified physical property information is obtained as the physical property information of the resin.

[0194] The physical property information of the resin includes information such as the shear viscosity, specific volume, and thermal conductivity of the resin.

[0195] The pressure calculation unit 133a calculates the time step t based on physical property information such as specific volume. n The resin pressure for each element is calculated.

[0196] The temperature calculation unit 133b calculates the time step t based on physical property information such as thermal conductivity. n The temperature of the resin for each element is calculated.

[0197] The shear rate calculation unit 133c calculates the time step t based on physical property information such as shear viscosity. n The shear rate of the resin for each element in the system is calculated.

[0198] The cooling rate calculation unit 133d calculates the time step t based on the temperature. n The cooling rate of the resin for each element is calculated. The cooling rate is the rate of change of temperature over time, with a time step of t. n t n+1 The temperature of the resin in each case is T n , T n+1 If we let the infinitesimal time be Δt, then the cooling rate ΔT / Δt = (T n+1 - Tn It is expressed as ) / Δt.

[0199] The crystallinity calculation unit 133f calculates the time step t based on the temperature and the cooling rate. n The crystallinity information (change in crystallinity over time) of the resin for each element is calculated.

[0200] The crystallinity calculation unit 133f comprises a relative crystallinity calculation unit 133fa, a primary absolute crystallinity calculation unit 133fb, and a total absolute crystallinity calculation unit 133fc.

[0201] The physical property information correction unit 133q corrects the physical property information of the resin based on the degree of crystallinity.

[0202] Information such as crystallinity (relative crystallinity φ, primary absolute crystallinity Φ1, total absolute crystallinity Φ, etc.), temperature, cooling rate (temperature change over time), pressure, shear rate, shear viscosity, specific volume, and thermal conductivity obtained during the flow analysis process is also stored in the memory unit 120.

[0203] <Methods for analyzing resin molding> Figure 19 is a flowchart showing an example of the analysis method according to this embodiment, illustrating an example of its application to the flow analysis of resin injection molding. The following explanation will use the application of this analysis method to the flow analysis of resin injection molding as an example. This analysis method is performed, for example, using the analysis device 100 described above. If the analysis device 100 is equipped with a structural analysis unit, structural analysis can be performed using resin property data obtained from the flow analysis as input information. The structural analysis method is not particularly limited, and the structural analysis method of Embodiment 1 may be adopted, or a generally known method may be adopted.

[0204] As shown in Figure 19, this analysis method comprises, for example, a model creation step SB1, an analysis condition setting step SB2, a time step setting step SB3, a physical property information acquisition step SB4, a resin property calculation step including a pressure calculation step SB5, a shear rate calculation step SB6, and a temperature calculation step SB7, a cooling rate calculation step SB8, a crystallinity calculation step SB9, a physical property information correction step SB10, and a determination step SB11. The outline of each step is as follows.

[0205] First, in the model creation process SB1, the model creation unit 131 divides the shape data of the mold cavity, etc., created using 3D CAD, etc., into minute elements for numerical analysis and creates a model for flow analysis. Next, in the analysis condition setting process SB2, analysis conditions such as material condition data and boundary condition data are set as initial data. Then, in the time step setting process SB3, time information is set to the previous time step t n-1The calculation is performed by advancing a small time interval Δt from the starting point (time step t). n Set to this.

[0206] In the physical property information acquisition process SB4, the time step t n Obtain the physical property information of the resin used in the calculation.

[0207] In the pressure calculation process SB5, the pressure of the resin for each element is calculated using input information such as the initial flow velocity (injection speed) of the resin, the kinematic viscosity coefficient of the resin material, boundary conditions, and specific volume, and governing equations such as the Navier-Stokes equation and the continuity equation.

[0208] Furthermore, in the shear rate calculation process SB6, the shear rate of the resin for each element is calculated using input information such as the shear viscosity and temperature of the resin, and the Navier-Stokes equations and the continuity equation as governing equations.

[0209] In the temperature calculation process SB7, for example, information such as the shear rate of the resin, the initial temperature of the resin (injection temperature), the specific heat, density, and thermal conductivity of the resin material are input, and the heat conduction equation is used as the governing equation to calculate the temperature of the resin for each element.

[0210] In the cooling rate calculation process SB8, the time step t n Temperature T n and the previous time step t n-1 Temperature T n-1 Based on, time step t n The cooling rate of the resin for each element in the system, ΔT / Δt, is calculated.

[0211] In the crystallinity calculation step SB9, the time step t is calculated based on the temperature and the cooling rate. n The degree of crystallinity of the resin is calculated.

[0212] In the physical property information correction process SB10, based on the degree of crystallinity of the resin calculated in the degree of crystallinity calculation process SB9, the time step t n Correct the physical property information of the resin used in the calculation.

[0213] Then, in the determination process SB11, time step t n The time step t is set as the end of the analysis. end Determine whether it is above or below the specified value. Time step t n ga t end If the result is less than (NO), return to the time step setting process SB3 and repeat processes SB3 to SB11.

[0214] And then, the next time step t n+1 In the physical property information acquisition process SB4, time step t n The physical property information corrected in the physical property information correction process SB10 is processed at time step t n+1 This information is obtained as the physical property information of the resin used in the calculation.

[0215] Furthermore, in the determination process SB11, the time step t n ga t end If the answer is YES, the fluid analysis will be terminated.

[0216] This analysis method is particularly characterized by the crystallinity calculation step SB9 and the physical property information correction step SB10.

[0217] [Crystallization Calculation Process] In the crystallinity calculation process SB9, the time step t n The total absolute degree of crystallinity Φ of the resin is calculated based on the temperature and cooling rate, i.e., based on the change in temperature over time.

[0218] Furthermore, the crystallinity calculation step SB9 in this embodiment can have the same configuration as the crystallinity calculation step S31 in Embodiment 1. That is, the crystallinity calculation step SB9 can be configured to include a relative crystallinity calculation step, a primary absolute crystallinity calculation step, and a total absolute crystallinity calculation step (see Figure 5).

[0219] [Physical property information correction process] In the physical property information correction process SB10, based on the total absolute crystallinity Φ of the resin calculated in the crystallinity calculation process SB9, the time step t n Correct the physical property information of the resin used in the calculation.

[0220] Examples of physical properties that are modified at this time include shear viscosity, specific volume, and thermal conductivity.

[0221] -Correction of shear viscosity- If the resin property calculation process is the shear rate calculation process SB6, then shear viscosity can be cited as a prerequisite for calculating the shear rate.

[0222] In this case, in the physical property information correction process SB10, the time step t n The shear viscosity used in the calculation is corrected to the shear viscosity calculated by the following formula (B1).

[0223] |η|=Φ|η c |+(1-Φ)|η m | ···(B1) (However, in formula (B1), η is shear viscosity, η c η is the shear viscosity of the crystalline region. m (This is the shear viscosity of the amorphous region.) And then, the next time step t n+1 In the shear rate calculation process, the shear rate is calculated based on the shear viscosity modified by equation (B1).

[0224] Conventional fluid analysis uses resin shear rate data to calculate fluid flow. In this method, it is assumed that the flow stops uniformly when a set temperature is reached during the cooling process, and the shear viscosity, which is the basis for calculating the shear rate, is kept constant below that temperature. However, the cooling rate of the resin varies depending on the molding conditions, for example, so the flow stop temperature also changes. Consequently, conventional fluid analysis, which uniformly sets the flow stop temperature, lacks sufficient accuracy in predicting the shear rate, and cannot guarantee sufficient prediction accuracy in predicting, for example, the flow length.

[0225] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B1), the following time step t n+1The shear viscosity used in the calculations is calculated. This allows for the reproduction of the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute degree of crystallinity Φ. Furthermore, by correcting the shear viscosity, the flow stop temperature can be effectively set to be variable according to the cooling rate, thereby improving the accuracy of shear rate prediction and the accuracy of predictions such as flow length.

[0226] Furthermore, when combining the flow analysis of this embodiment with the warpage analysis of Embodiment 1, the total absolute crystallinity Φ in equation (B1) may be changed to the relative crystallinity φ. That is, equation (B1) can be rewritten as the following equation (B4).

[0227] |η|=X c |η c |+(1-X c )|η m | ···(B4) (However, in formula (B4), X c φ is the relative crystallinity or total absolute crystallinity Φ, η is the shear viscosity, η c is the solid phase (X c =φ case) or crystal part (X c Shear viscosity (in the case of =Φ), η m (This is the shear viscosity of the amorphous region.) In equation (B4), the degree of crystallinity Xc may be either the relative degree of crystallinity φ or the total absolute degree of crystallinity Φ, but from the viewpoint of improving prediction accuracy, it is preferable to use the total absolute degree of crystallinity Φ.

[0228] - Correction of specific volume - If the resin property calculation process is the pressure calculation process SB5, then specific volume can be cited as material property information that is a prerequisite for calculating the pressure.

[0229] In this case, in the physical property information correction process SB10, the time step t n The specific volume used in the calculation is corrected to the specific volume calculated by the following formula (B2).

[0230] |v|=Φ|v c |+(1-Φ)|v m | ···(B2) (However, in formula (B2), v is specific volume, v c v is the specific volume of the crystalline part. m (This is the specific volume of the amorphous region.) And then, the next time step t n+1 In the pressure calculation step SB5, the pressure is calculated based on the specific volume modified by equation (B2).

[0231] Note that formula (B2) may also be written as formula (3) in Embodiment 1.

[0232] Conventional fluid analysis uses resin pressure data to perform fluid calculations. In this case, the specific volume, which is the premise for the pressure calculation, is calculated using the resin temperature and pressure as input information and the Tait equation as the governing equation. However, in the case of crystalline resins, when the resin temperature decreases during the molding process and reaches a certain temperature, crystallization begins, and the rate of decrease in specific volume increases. The temperature at which this crystallization begins changes depending on the cooling rate of the resin. The Tait equation mentioned above is a model that derives one specific volume V from pressure P and temperature T, so it cannot take into account the cooling rate dependence of the specific volume in the crystallization behavior of the resin. In other words, current general CAE analysis cannot take into account the changes in resin properties based on the crystallization behavior of the resin during the molding process, and there is room for improvement from the perspective of improving prediction accuracy.

[0233] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B2), the following time step t n+1 The specific volume used in the calculation is calculated. This allows for the reproduction of the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute degree of crystallinity Φ. By correcting the specific volume in this way, it becomes possible to perform flow analysis that more accurately considers the cooling rate dependence of the specific volume based on the real phenomenon, thereby improving the prediction accuracy of the flow analysis.

[0234] v c , v m The method for deriving this can be the same as the method used in the specific volume calculation step S32 of Embodiment 1.

[0235] Furthermore, when combining the flow analysis of this embodiment with the warpage analysis of Embodiment 1, the total absolute crystallinity Φ in equation (B2) may be changed to the relative crystallinity φ. That is, equation (B2) can be rewritten as the following equation (B5).

[0236] |v|=X c |v c |+(1-X c )|v m | ···(B5) (However, in formula (B5), X c φ is the relative crystallinity or total absolute crystallinity Φ, v is the specific volume, v c is the solid phase (X c =φ case) or crystal part (X c Specific volume (in the case of Φ), v m (This is the specific volume of the amorphous region.) In equation (B5), the crystallinity Xc may be either the relative crystallinity φ or the total absolute crystallinity Φ, but from the viewpoint of improving prediction accuracy, it is preferable to use the total absolute crystallinity Φ.

[0237] -Correction of thermal conductivity- If the resin property calculation process is the temperature calculation process SB7, then thermal conductivity can be cited as a prerequisite for calculating the temperature.

[0238] In this case, in the physical property information correction process SB10, the time step t n The thermal conductivity used in the calculation is corrected to the thermal conductivity calculated by the following formula (B3).

[0239] |λ|=Φ|λ c |+(1-Φ)|λ m | ···(B3) (However, in equation (B3), λ is the thermal conductivity, λ c λ is the thermal conductivity of the crystalline part. m (This is the thermal conductivity of the amorphous region.) And then, the next time step t n+1 In the temperature calculation process, the temperature is calculated based on the thermal conductivity modified by equation (B3).

[0240] Conventional fluid dynamics analysis uses resin temperature data to perform fluid dynamics calculations. In this case, the thermal conductivity of the resin, which is the premise for temperature calculations, is assumed to change from a molten state to a solid state during the cooling process, for example, when it reaches an arbitrarily set temperature, and the thermal conductivity is set to change uniformly from the thermal conductivity of the molten state to the thermal conductivity of the solid state at that timing. However, in the actual molding process, the resin may be in a state where it is a mixture of molten and solid states, and the thermal conductivity is thought to change continuously depending on the degree of crystallinity of the resin. In that case, conventional fluid dynamics analysis, which is set to change uniformly from the value of the molten state to the value of the solid state, has insufficient temperature prediction accuracy and cannot guarantee sufficient prediction accuracy for fluid dynamics analysis.

[0241] In this configuration, the total absolute crystallinity Φ, which takes into account the primary and secondary crystallinity behavior of the resin in a non-isothermal process, is used, and based on the above formula (B3), the following time step t n+1 The thermal conductivity used in the calculations is calculated. This allows us to reproduce the real phenomenon where a semi-crystalline state exists, in which molten and solid resins coexist, based on the total absolute crystallinity Φ. In this way, the crystallinity dependence of thermal conductivity can be considered in accordance with the real phenomenon, improving the accuracy of temperature prediction and thus the accuracy of flow analysis prediction.

[0242] Furthermore, when combining the flow analysis of this embodiment with the warpage analysis of Embodiment 1, the total absolute crystallinity Φ in equation (B3) may be changed to the relative crystallinity φ. That is, equation (B3) can be rewritten as the following equation (B6).

[0243] |λ|=X c |λ c |+(1-X c )|λ m | ···(B6) (However, in formula (B6), X c Φ is the relative crystallinity or total absolute crystallinity, λ is the thermal conductivity, λ c is the solid phase (X c =φ case) or crystal part (X c Thermal conductivity (in the case of Φ), λ mis the thermal conductivity of the amorphous region.) The crystallinity Xc in formula (B6) may be either the relative crystallinity φ or the total absolute crystallinity Φ, and from the viewpoint of improving prediction accuracy, it is preferably the total absolute crystallinity Φ.

[0244] <On FSC Measurement> As described above, in the present configuration, in the crystallinity calculation step SB9, the temporal change of the total absolute crystallinity Φ is calculated using Model B that accounts for the primary crystallization behavior and secondary crystallization behavior of the resin in a non-isothermal process. This enables flow analysis that considers the cooling rate dependence of the PVT curve more accurately based on actual phenomena, thereby improving the prediction accuracy of flow analysis.

[0245] For the conditions and the like of FSC measurement, the same conditions and the like as those in Embodiment 1 can be employed.

[0246] <Analysis Program for Resin Molded Article and Recording Medium Therefor> The analysis program for a resin molded article according to the present embodiment can be a program that causes a computer to execute at least the procedure of the crystallinity calculation step SB9 among the procedures of the above steps. Further, the analysis program may be a program that causes the computer to execute, among the procedures of the above steps, the procedure BA of the physical property information acquisition step SB4, the procedure BB of the resin characteristic calculation step (at least one of the pressure calculation step SB5, the shear rate calculation step SB6, and the temperature calculation step SB7), the procedure BC of the cooling rate calculation step SB8, the procedure BD of the crystallinity calculation step SB9, and the procedure BE of the physical property information correction step SB10. Further, the program may be configured to cause the computer to execute the procedures of the entire analysis step, that is, the procedures of other steps in addition to the above procedures BA to BE.

[0247] (Embodiment 3) As the governing equation used for calculating temperature information in the flow analysis step S2 in the above-mentioned Embodiment 1, or as the governing equation used in the temperature calculation step SB7 in Embodiment 2, a modified heat conduction equation represented by the following formula (D3) may be used.

[0248]

number

[0249] (However, in equation (D3), ρ is density, Cv is specific heat, T is temperature, λ is thermal conductivity, η is viscosity, γ dot is shear rate, X c φ is the relative crystallinity or total absolute crystallinity Φ, ΔHc is the exothermic crystallization term, ΔX c (t n ) is time step t n Crystallization progress, ΔH c (T) is the enthalpy of crystallization [J / g] (X) when isothermal crystallization occurs at temperature T. c In the case of =φ, h1~h6 are coefficients (input parameters that depend on the material) or h c (X c =Φ case. h c is a constant, representing the total amount of enthalpy change [J / g] during the crystallization of the resin. Below, crystallinity X c We will explain using the case where relative crystallinity φ is used and applied to the temperature calculation step SB7 in Embodiment 2 as an example.

[0250] The resin temperature is calculated in the temperature calculation process SB7 for each time step, using the temperature information from the previous time step as one of the input pieces. That is, time step t n The physical property information acquired in the physical property information acquisition process SB4 includes the previous time step t n-1 The resin temperature T calculated in the temperature calculation process SB7 n-1 It includes.

[0251] And then, time step t n In the temperature calculation process SB7, the temperature of the resin is used as physical property information. n-1 Based on the modified heat conduction equation expressed in equation (3), the resin properties are defined as time step t. n The temperature of the resin in T n Calculate.

[0252] In the physical property information modification process SB10, the temperature of the resin as physical property information T n-1This is the resin temperature T calculated as a resin property. n It will be corrected to:

[0253] Next time step t n+1 In the physical property information acquisition process SB4, the corrected temperature T is used as physical property information. n Obtain it.

[0254] Then, the next time step t n+1 In the temperature calculation process SB7, the corrected temperature T n Based on this, the temperature T of the resin as a resin property n+1 Calculate.

[0255] <Exothermic crystallization> For example, as shown in Figure 4, when the temperature of a molten resin is lowered using a DSC or similar device and the change in heat flow is measured, the heat flow increases as crystallization occurs. This phenomenon is due to a phase transition occurring as the resin crystallizes, generating latent heat (also called "crystallization exothermic reaction"), which then manifests as heat flow.

[0256] In equation (D3), a crystallization exothermic term ΔHc is added to the conventional heat conduction equation, taking into account the exothermic reaction of crystallization. This crystallization exothermic term ΔHc is then used to express the crystallization enthalpy ΔH when isothermal crystallization occurs at temperature T. c (T) and crystallization progress ΔX c (t n It is expressed as the product of ).

[0257] Note that crystallization enthalpy ΔH c (T) is modeled based on actual tests. Specifically, materials are isothermally crystallized at a constant temperature using DSC, FSC, etc., and the crystallization enthalpy for each temperature is calculated from the obtained heat flow change data. Then, as shown in Figure 20, the x-axis is plotted with temperature and the y-axis with crystallization enthalpy, and the total amount of crystallization heat generated for each temperature is fitted with a 5th-order polynomial. The coefficients h1 to h6 of the resulting 5th-order polynomial are material-dependent input parameters and can be set for each material, for example, based on actual tests. For example, in the example in Figure 20, the values ​​shown in Table 3 were obtained as coefficients h1 to h6.

[0258] [Table 3]

[0259] Thus, crystallization enthalpy ΔH c (T) is the amount of crystallinity evolution ΔX c (t n By multiplying by (D3), the amount of crystallization heat generated at each time step can be expressed. Furthermore, by using equation (D3) as the governing equation, the change in temperature over time can be simulated while taking into account the amount of crystallization heat, thus improving the prediction accuracy of the analysis.

[0260] In practice, the crystallization enthalpy was calculated based on equation (D3) using the coefficients h1 to h6 in Table 3, and the change in heat flow with respect to temperature was calculated for each cooling rate of 5°C / s, 10°C / s, 20°C / s, and 50°C / s. The results are shown in Figure 21. As shown in Figure 21, the calculation results generally reproduce the measured results for each cooling rate measured using DSC, and it was found that the cooling rate dependence of crystallization exothermic reaction can be reproduced with high accuracy by using equation (D3).

[0261] <Specific heat> The specific heat Cv in equation (D3) is not particularly limited and may be a constant value, for example, but it may also be given by equation (D2) below.

[0262] Cv=g1T 5 +g2T 4 +g3T 3 +g4T 2 +g5T+g6···(D2) (However, in equation (D2), g1 to g6 are coefficients and are input parameters that depend on the material.) Equation (D2) is modeled based on actual tests. Specifically, by lowering the temperature of the resin using DSC or similar methods and measuring the change in specific heat, data like that shown in Figure 22 is obtained. The specific heat change data is then fitted with a fifth-degree polynomial, for example, by excluding latent heat. The coefficients g1 to g6 of the resulting fifth-degree polynomial are material-dependent input parameters and can be set for each material, for example, based on actual tests.

[0263] This configuration allows for the simulation of the time-dependent change in resin temperature by considering the temperature change in specific heat, which is advantageous for improving the accuracy of predictions in the analysis.

[0264] Note that the degree of crystallinity X in formula (D3) c For this, either the relative crystallinity φ or the total absolute crystallinity Φ may be used, but from the viewpoint of improving prediction accuracy, it is preferable to use the total absolute crystallinity Φ. In this case, equation (D3) can be rewritten as equation (D1).

[0265]

number

[0266] (However, in equation (D1), ρ is density, Cv is specific heat, T is temperature, λ is thermal conductivity, η is viscosity, γ dot is shear rate, ΔHc is crystallization exothermic term, ΔΦ(t n ) is time step t n Total absolute degree of crystallinity progression, h c (This is a constant and represents the total amount of enthalpy change [J / g] when the resin crystallizes.) Furthermore, the above-described modified heat conduction equation can be appropriately incorporated into the analysis program of the above embodiment.

[0267] (Other embodiments) When combining the warpage analysis of Embodiment 1 and the flow analysis of Embodiment 2, and using at least one of equations (B1) to (B3) in the flow analysis of Embodiment 2, the primary absolute crystallinity calculation step S312 and the total absolute crystallinity calculation step S313 may be omitted in the crystallinity calculation step S31 of the warpage analysis of Embodiment 1.

[0268] Furthermore, when combining the warpage analysis of Embodiment 1 and the analysis of Embodiment 3, and when formula (D1) is used in the analysis of Embodiment 3, the primary absolute crystallinity calculation step S312 and the total absolute crystallinity calculation step S313 may be omitted in the crystallinity calculation step S31 of the warpage analysis of Embodiment 1.

[0269] In these embodiments, the total absolute crystallinity Φ in equation (3) can be replaced with the relative crystallinity φ. That is, equation (3) can be rewritten as the following equation (E3).

[0270]

number

[0271] (However, in formula (E3), X c φ is the relative crystallinity or total absolute crystallinity Φ, T is temperature, p is pressure, t is time, v is specific volume, v c is the solid phase (X c =φ case) or crystal part (X c Specific volume (in the case of Φ), v m (where m1~m3 and c1~c3 are coefficients, where m1 is the specific volume of the amorphous region and c1~c3 is the coefficient.) Furthermore, when combining the flow analysis of Embodiment 2 and the analysis of Embodiment 3, if equation (D1) is used in the analysis of Embodiment 3, then at least one of equations (B4) to (B6) may be used in the flow analysis of Embodiment 2, and the analysis may be performed using the relative crystallinity φ. [Industrial applicability]

[0272] This disclosure is extremely useful because it allows for improved prediction accuracy in a resin molded product analysis method, analysis apparatus, analysis program, and recording medium, by taking into account the crystallization behavior of the resin during the molding process. [Explanation of Symbols]

[0273] 100 Analysis device for resin molded products 131 Model Creation Department 133 Flow Analysis Department 133k Physical property information acquisition section 133a Pressure calculation unit 133b Temperature calculation section 133c Shear rate calculation unit 133d Cooling rate calculation section 133f Crystallinity calculation part 133fa Relative Crystallinity Calculation Unit 133fb Primary absolute crystallinity calculation unit 133fc Total Absolute Crystallinity Calculation Unit 133q Physical property information correction section 134 Structural Analysis Department 135 Crystallinity calculation section 135A Relative crystallinity calculation unit 135B Primary absolute crystallinity calculation unit 135C Total Absolute Crystallinity Calculation Unit 136 Specific volume calculation section 137 Contraction Amount Calculation Unit 138 Deformation Calculation Unit 170 recording media S1 Model Creation Process S2 Flow analysis process S3 Structural analysis process S31 Crystallinity calculation process S311 Relative crystallinity calculation process S312 Primary absolute crystallinity calculation process S313 Total absolute crystallinity calculation process S32 Specific volume calculation process S33 Shrinkage Amount Calculation Process S34 Deformation Calculation Process S51 Injection process S52 Pressure holding process S53 Cooling process SB4 Physical property information acquisition process SB5 Pressure Calculation Process SB6 Shear Rate Calculation Process SB7 Temperature calculation process SB8 Cooling rate calculation process SB9 Crystallinity Calculation Process SB10 Physical property information correction process

Claims

1. A method for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallinity behaviors of the resin during a non-isothermal process. A relative crystallinity calculation step that calculates the change in the relative crystallinity φ of the resin over time based on at least the change in temperature over time during the solidification shrinkage process of the resin, Based on the change in the relative crystallinity φ over time, the primary absolute crystallinity Φ of the resin is determined considering its primary crystallization behavior. １ A primary absolute crystallinity calculation process for calculating the change over time, The aforementioned primary absolute crystallinity Φ １ The system comprises a total absolute crystallinity calculation step that calculates the change in total absolute crystallinity Φ over time based on the change in the following formula (1) and [Mathematical Formula 1] (However, in formula (1), Φ(t ｊ ) represents the total absolute crystallinity development amount at any time step t ｊ , Φ １ (t ｊ ) represents the primary absolute crystallinity development amount at any time step t ｊ , X ｊ is the ratio of the total absolute crystallinity development amount to the primary absolute crystallinity development amount at any time step t ｊ , a(T) is a constant dependent on the material and temperature, T is temperature, τ is the characteristic time until the onset of secondary crystallization behavior, i １／２ is the order of the time step at which the half-crystallization time t １／２ is reached.) A method for analyzing resin molded products, characterized by the features described herein.

2. In claim 1, In the primary absolute crystallinity calculation step, the primary absolute crystallinity Φ １ The change over time is calculated based on the following formula (2). [Math 2] (However, in equation (2), ΔΦ １ (t ｉ ) is any time step t ｉ The amount of primary absolute crystallinity progression in Δφ(t) ｉ ) is any time step t ｉ Temperature T(t) ｉ The amount of relative crystallinity progression that occurred, Φ １，∞ (T(t ｉ )) is temperature T(t ｉ This is the degree of crystallinity achieved during primary crystallization when isothermal crystallization is carried out. A method for analyzing resin molded products, characterized by the features described herein.

3. In claim 1, The system further comprises a specific volume calculation step for calculating the change in the specific volume of the resin over time based on the change in temperature over time, the change in pressure over time during the solidification shrinkage process of the resin, and the change in the total absolute crystallinity Φ over time. In the specific volume calculation step, the change in the specific volume over time is calculated based on the following formula (3). [Math 3] (However, in equation (3), T is temperature, p is pressure, t is time, v is specific volume, v ｃ v is the specific volume of the crystalline part. ｍ The specific volume of the amorphous region is m １ ~m ３ , c １ ~c ３ (This is a coefficient.) A method for analyzing resin molded products, characterized by the features described herein.

4. In claim 1 or claim 2, Any time step t ｎ A physical property information acquisition process to acquire physical property information of the resin used in the calculation, Based on the aforementioned physical property information, the time step t ｎ A resin properties calculation step in which the resin properties, including the temperature of the resin, are calculated, The aforementioned time step t ｎ The system further comprises a property information modification step for modifying the property information of the resin based on the total absolute crystallinity Φ calculated in the total absolute crystallinity calculation step, Next time step t ｎ＋１ In the process of acquiring the physical property information, the modified physical property information is acquired as the physical property information of the resin. A method for analyzing resin molding, characterized by the following features.

5. In claim 4, The aforementioned physical property information includes the shear viscosity of the resin. In the resin property calculation step, the shear rate of the resin is calculated as a resin property based on the shear viscosity. In the aforementioned physical property information correction step, the shear viscosity is corrected to the shear viscosity calculated by the following formula (B1): |η|=Φ|η ｃ |+(1-Φ)|η ｍ |・・・(B1) (However, in formula (B1), η is shear viscosity, η ｃ η is the shear viscosity of the crystalline region. ｍ (This is the shear viscosity of the amorphous region.) The next timestep t ｎ＋１ In the resin properties calculation step, the shear rate is calculated based on the corrected shear viscosity. A method for analyzing resin molding, characterized by the following features.

6. In claim 4, The aforementioned physical property information includes the specific volume of the resin, In the resin property calculation step, the pressure of the resin is calculated as a resin property based on the specific volume. In the aforementioned physical property information correction step, the specific volume is corrected to the specific volume calculated by the following formula (B2): |v|=Φ|v ｃ |+(1-Φ)|v ｍ | ・・・(B2) (However, in formula (B2), v is specific volume, v ｃ v is the specific volume of the crystalline part. ｍ (This is the specific volume of the amorphous region.) The next timestep t ｎ＋１ In the resin properties calculation step, the pressure is calculated based on the corrected specific volume. A method for analyzing resin molding, characterized by the following features.

7. In claim 4, The aforementioned physical property information includes the thermal conductivity of the resin. In the resin property calculation step, the temperature of the resin is calculated as a resin property based on the thermal conductivity. In the aforementioned physical property information correction step, the thermal conductivity is corrected to the thermal conductivity calculated by the following formula (B3): |λ|=Φ|λ ｃ |+(1-Φ)|λ ｍ | ・・・(B3) (However, in equation (B3), λ is the thermal conductivity, λ ｃ λ is the thermal conductivity of the crystalline part. ｍ (This is the thermal conductivity of the amorphous region.) The next timestep t ｎ＋１ In the resin properties calculation step, the temperature is calculated based on the modified thermal conductivity. A method for analyzing resin molding, characterized by the following features.

8. In claim 4, The aforementioned physical property information includes the temperature of the resin, In the resin property calculation step, the temperature of the resin is calculated as the resin property based on the temperature of the resin as physical property information and the modified heat conduction equation represented by the following formula (D1). [Math 4] (However, in equation (D1), ρ is density, Cv is specific heat, T is temperature, λ is thermal conductivity, η is viscosity, γ dot is shear rate, ΔHc is crystallization exothermic term, ΔΦ(t ｎ ) is the time step t ｎ Total absolute degree of crystallinity progression, h ｃ (This is a constant and represents the total amount of enthalpy change [J / g] when the resin crystallizes.) In the aforementioned physical property information modification step, the temperature of the resin as physical property information is modified to the temperature of the resin calculated as a resin characteristic. The next timestep t ｎ＋１ In the resin property calculation step, the temperature of the resin as a resin property is calculated based on the corrected temperature. A method for analyzing resin molded products, characterized by the features described herein.

9. In claim 8, The specific heat Cv is given by the following formula (D2). Cv=g １ T ５ +g ２ T ４ +g ３ T ３ +g ４ T ２ +g ５ T+g ６ ・・・(D2) (However, in formula (D2), g １ ~g ６ (This is a coefficient, and it is an input parameter that depends on the material.) A method for analyzing resin molded products, characterized by the features described herein.

10. In claim 1 or claim 2, The analysis is at least one of the flow analysis and warpage analysis of the resin molded product. A method for analyzing resin molded products, characterized by the features described herein.

11. A device for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallinity behaviors of the resin during a non-isothermal process. A relative crystallinity calculation unit calculates the change in the relative crystallinity φ of the resin over time based on at least the change in temperature over time during the solidification shrinkage process of the resin, Based on the change in the relative crystallinity φ over time, the primary absolute crystallinity Φ of the resin is determined considering its primary crystallization behavior. １ A primary absolute crystallinity calculation unit that calculates the change over time, The aforementioned primary absolute crystallinity Φ １ The system comprises a total absolute crystallinity calculation unit that calculates the change in total absolute crystallinity Φ over time based on the change over time of and the following formula (1), [Math 5] (However, in formula (1), Φ(t ｊ ) is any time step t ｊ Total absolute degree of crystallinity progression, Φ １ (t ｊ ) is any time step t ｊ The amount of primary absolute crystallinity progression in X ｊ is any time step t ｊ The ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression, a(T) is a constant that depends on the material and temperature, T is the temperature, τ is the characteristic time until secondary crystallinity behavior begins, i １／２ The semi-crystallization time t is １／２ This is the order of the time steps to reach that point. An analytical device for resin molded products, characterized by the following features.

12. A program for analyzing resin molded products using computer simulation, The aforementioned analysis utilizes the time-dependent change in total absolute crystallinity Φ, taking into account the primary and secondary crystallinity behaviors of the resin during a non-isothermal process. At least, Procedure A for calculating the change over time of the relative crystallinity φ of the resin based on at least the change over time of temperature during the solidification shrinkage process of the resin, Based on the change in the relative crystallinity φ over time, the primary absolute crystallinity Φ of the resin is determined considering its primary crystallization behavior. １ Procedure B for calculating the change over time, The aforementioned primary absolute crystallinity Φ １ The procedure C for calculating the change in total absolute crystallinity Φ over time based on the change over time of the following equation (1) is performed in this order. [Math 6] (However, in formula (1), Φ(t ｊ ) is any time step t ｊ Total absolute degree of crystallinity progression, Φ １ (t ｊ ) is any time step t ｊ The amount of primary absolute crystallinity progression in X ｊ is any time step t ｊ The ratio of the total absolute crystallinity progression to the primary absolute crystallinity progression, a(T) is a constant that depends on the material and temperature, T is the temperature, τ is the characteristic time until secondary crystallinity behavior begins, i １／２ The semi-crystallization time t is １／２ This is the order of the time steps to reach that point. An analysis program for resin molded products characterized by the following features.

13. A computer-readable recording medium that stores an analysis program for a resin molded product as described in claim 12.

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