Warpage analysis method, warpage analysis device, and warpage analysis program of resin molding, and recording medium

Abstract

To provide a warpage analysis method, a warpage analysis device, and a warpage analysis program of a resin molding, and a recording medium, which improve prediction accuracy by fully considering a crystallinity behavior of a resin in a molding process.SOLUTION: A warpage analysis method of a resin molding includes a crystallinity calculation step of calculating the temporal change of the crystallinity of the resin, on the basis of temporal changes of a temperature and a pressure in a resin solidification shrinkage process, and a specific volume calculation step of calculating the temporal change of the specific volume of the resin, on the basis of the temporal change of the temperature, the temporal change of the pressure and the temporal change of the crystallinity, where the crystallinity calculation step calculates the temporal change of the crystallinity by considering the crystallinity behavior of the resin in a molding temperature region obtained by high speed differential scanning calorimetry, and the specific volume calculation step calculates the temporal change of the specific volume, on the basis of a predetermined expression.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present disclosure relates to a method for analyzing warpage of a resin molded product, a warpage analysis apparatus, a warpage analysis program, and a recording medium.

Background Art

[0002] Conventionally, for the purpose of improving accuracy, efficiency, and cost reduction in product design and the like of resin molded products, the behavior of resin in a mold and warpage deformation of the finally obtained product have been analyzed using CAE (Computer-Aided-Engineering).

[0003] Here, in the current CAE analysis, generally, the temperature information and pressure information of the resin obtained by resin flow analysis or the like are used as input information, the specific volume is calculated using the Tait equation as the governing equation, and finally the shrinkage amount of the molded product is calculated.

[0004] However, in the case of crystalline resins, when the temperature of the resin decreases to a certain temperature during the molding process, crystallization starts and the rate of decrease in specific volume increases. The temperature at which this crystallization starts varies depending on the cooling rate of the resin. Since the above-mentioned Tait equation is a model in which one specific volume V is obtained from the pressure P and the temperature T, the cooling rate dependence in the crystallization behavior of the resin cannot be considered. That is, in the current general CAE analysis, changes in resin physical properties based on the crystallization behavior of the resin during the molding process cannot be considered, and there is a problem from the viewpoint 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 to 3).

[0006] Patent Document 1 discloses a method for calculating the PVT curve and the specific volume of a resin according to the crystallization behavior during molding by using data on the resin temperature, pressure, and crystallinity during the molding process and a method for obtaining the PVT characteristics of the resin at an arbitrary crystallinity, and further predicting the shrinkage rate. A molding shrinkage process simulation method for a crystalline resin molded product is disclosed.

[0007] In Patent Document 2, while measuring the specific volume characteristics (PVT characteristics) of the crystalline material corresponding to the pressure and temperature in the molten and solidified states of the crystalline material or in a state close to the thermal equilibrium state thereof at a first temperature change rate from a high temperature to a low temperature, the crystallization behavior of the crystalline material is determined, a crystallization parameter representing the growth degree of the crystal nuclei of the crystalline material is determined based on the crystallization behavior, a first degree of crystallization in a thermally non-equilibrium state corresponding to the pressure, temperature, and a second temperature change rate from a high temperature to a low temperature faster than the first temperature change rate is analytically determined using the crystallization parameter, and a method for predicting the physical properties of a crystalline material in a thermally non-equilibrium state is disclosed, which is characterized by predicting the PVT characteristics in the thermally non-equilibrium state using the PVT characteristics and the first degree of crystallization.

[0008] In Patent Document 3, in the crystallization process simulation of a crystalline resin molded product, there are a data input unit for inputting at least data on the resin temperature, pressure, and shear stress during the molding process, a nucleation rate and crystal growth rate analysis unit for determining the nucleation rate and crystal growth rate during molding, a relative degree of crystallization calculation unit for predicting the relative degree of crystallization and spherulite size distribution using Avrami's equation, and a crystallization process simulation method and apparatus for predicting the change over time of the degree of crystallization X during molding using the achieved degree of crystallization.

Prior Art Documents

Patent Documents

[0009]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0010] However, in the examples of Patent Document 1 above, although there is a disclosure regarding the use of crystallization simulation based on the Avrami equation for the crystallinity of the molded product, the details are not mentioned.

[0011] On the other hand, Patent Documents 2 and 3 above describe that the change in crystallinity with respect to temperature is experimentally determined by changing the cooling rate using a normal differential scanning calorimeter (DSC) and used for analysis. However, with a normal DSC, it is substantially impossible to reproduce measurements in a high-speed cooling environment such as 3°C / s or more, particularly 10°C / s or more, which is achieved during actual molding. Also, with a normal DSC, it is substantially impossible to measure the crystallization behavior during the isothermal process, particularly in the low-temperature range of a general molding temperature range (e.g., 25°C to 300°C).

[0012] Thus, in the prior art, there has been a problem that it is difficult to sufficiently consider the crystallization behavior of the resin during the molding process in CAE analysis because the crystallization behavior at the cooling rate during actual molding and in the particularly low-temperature range of the molding temperature range cannot be experimentally observed.

[0013] Therefore, in the present disclosure, in the warpage analysis method, warpage analysis apparatus, warpage analysis program, and recording medium for resin molded products, an object is to improve the prediction accuracy by sufficiently considering the crystallization behavior of the resin during the molding process.

Means for Solving the Problems

[0014] To solve the above problems, the warpage analysis method for resin molded products disclosed herein is a method for performing warpage analysis of resin molded products by computer simulation, a crystallinity calculation step of calculating the change over time of the crystallinity of the resin based on at least the change over time of the temperature during the solidification shrinkage process of the resin, a specific volume calculation step of calculating the change over time of the specific volume of the resin based on the change over time of the temperature, the change over time of the pressure during the solidification shrinkage process of the resin, and the change over time of the crystallinity, and In the crystallinity calculation step, the time-dependent change in the crystallinity is calculated in consideration of the crystallization behavior of the resin within the molding processing temperature range obtained in advance by high-speed differential scanning calorimetry. In the specific volume calculation step, the time-dependent change in the specific volume is calculated based on the following formula (1).

[0015]

Number

[0016] (However, in formula (1), T is temperature, p is pressure, t is time, v is specific volume, v c is the specific volume of the crystalline part, v m is the specific volume of the amorphous part, Xc is the crystallinity, m 1 ~m 3 、c 1 ~c 3 are coefficients.) It is characterized by this.

[0017] A fast scanning calorimeter (Fast Scanning Calorimetry, hereinafter also referred to as "FSC") can perform non-isothermal heat measurements at a heating and cooling rate of 3 °C / s or more, preferably 10 °C / s or more, and isothermal heat measurements in which the sample temperature is set to a desired temperature at a heating and cooling rate of 100 °C / s or more, preferably 1000 °C / s or more and 10000 °C or less and maintained at the desired temperature. That is, with FSC, measurements that reproduce the high-speed cooling environment (for example, 3 °C / s or more, particularly 10 °C / s or more) achieved during actual molding processing, and the crystallization behavior during the isothermal process in the general molding processing temperature range (for example, 25 °C to 300 °C, and in the case of polypropylene, for example, 40 °C to 120 °C) can be measured.

[0018] In this configuration, in the crystallinity calculation step, the time-dependent change in the crystallinity is calculated in consideration of the crystallization behavior of the resin within the molding processing temperature range obtained by FSC measurement. As a result, it becomes possible to perform a warp analysis that more accurately considers the cooling rate dependence of the PVT curve based on the actual phenomenon, so the prediction accuracy of the warp analysis is improved.

[0019] The degree of crystallinity is the relative degree of crystallinity, The change over time φ(t) of the relative degree of crystallinity is calculated using the Nakamura model represented by the following formula (2),

[0020] [Number]

[0021] (However, in formula (2), φ(t) is the change over time of the relative degree of crystallinity, K(T) is a value related to the rate constant of crystal growth, and n is the Avrami exponent.) It is preferable that the K(T) and the n are determined in consideration of the crystallization behavior obtained by the high-speed differential scanning calorimetry.

[0022] According to this configuration, since the value K(T) related to the rate constant of crystal growth and the Avrami exponent n are determined in consideration of the crystallization behavior obtained by FSC measurement, the prediction accuracy of the warpage analysis is improved.

[0023] It is preferable that the crystallization behavior obtained by the high-speed differential scanning calorimetry is obtained by at least one of isothermal measurement at an arbitrary temperature within the molding processing temperature range and non-isothermal measurement in a temperature range including the arbitrary temperature.

[0024] According to this configuration, the prediction accuracy of the warpage analysis is improved.

[0025] In one embodiment, the molding processing temperature range is 25°C or higher and 300°C or lower.

[0026] Since the molding processing temperature range of a general resin molding process is the above temperature range, according to this configuration, by using the measurement results in the above temperature range obtained by FSC, the prediction accuracy of the warpage analysis is improved.

[0027] The degree of crystallinity is the absolute degree of crystallinity, The degree of crystallinity calculation step is a relative degree of crystallinity calculation step for calculating the change over time of the relative degree of crystallinity of the resin, An absolute crystallinity calculation step of calculating the change over time of the absolute crystallinity of the resin based on the change over time of the relative crystallinity, is preferable.

[0028] According to this configuration, since the influence of the cooling rate can be considered more accurately, the prediction accuracy of the warpage analysis is improved.

[0029] Preferably, the change over time Φ(t) of the absolute crystallinity is represented by the following formula (3).

[0030]

Number

[0031] (However, in formula (3), φ is the relative crystallinity, f c (T) is the degree of crystallinity reached upon isothermal crystallization or non-isothermal crystallization at temperature T (crystallization peak temperature), f 1 ~f 6 is a coefficient.) The time derivative of φ(t) in formula (3) represents the rate of change of the change over time of the relative crystallinity (also referred to as the "progress rate of the relative crystallinity"). By performing a time integration of the product of the time derivative of φ(t) and the degree of crystallinity reached upon isothermal crystallization or non-isothermal crystallization at the temperature T at that time t (indicating up to what maximum degree of crystallinity can be reached at that temperature T based on the melting enthalpy of the crystal shown in the literature value), the absolute crystallinity at that time t and temperature T can be calculated. According to this configuration, since the influence of the cooling rate can be considered more accurately, the prediction accuracy of the warpage analysis is improved.

[0032] One aspect of the warpage analysis device for resin molded products disclosed herein is a device that performs warpage analysis of resin molded products by computer simulation, a crystallinity calculation unit that calculates the change over time of the crystallinity of the resin based on at least the change over time of the temperature in the solidification shrinkage process of the resin, A specific volume calculation unit that calculates the change over time of the specific volume of the resin based on the change over time of the temperature, the change over time of the pressure during the solidification shrinkage process of the resin, and the change over time of the crystallinity. The crystallinity calculation unit calculates the change over time of the crystallinity in consideration of the crystallization behavior of the resin within the molding processing temperature range obtained in advance by high-speed differential scanning calorimetry measurement. The specific volume calculation unit calculates the change over time of the specific volume based on the following formula (1).

[0033]

Equation

[0034] (However, in formula (1), T is temperature, p is pressure, t is time, v is specific volume, v c is the specific volume of the crystalline part, v m is the specific volume of the amorphous part, Xc is the crystallinity, m 1 ~m 3 , c 1 ~c 3 are coefficients.) It is characterized by this.

[0035] According to this configuration, since warpage analysis can be performed with higher accuracy by more accurately considering the cooling rate dependence of the PVT curve based on the actual phenomenon, the prediction accuracy of warpage analysis is improved.

[0036] Also, one aspect of the warpage analysis program for resin molded products disclosed here is to cause a computer to execute at least Procedure A for calculating the change over time of the crystallinity of the resin based on at least the change over time of the temperature during the solidification shrinkage process of the resin, and Procedure B for calculating the change over time of the specific volume of the resin based on the change over time of the temperature, the change over time of the pressure during the solidification shrinkage process of the resin, and the change over time of the crystallinity. In Procedure A, the change over time of the crystallinity is calculated in consideration of the crystallization behavior of the resin within the molding processing temperature range obtained in advance by high-speed differential scanning calorimetry measurement. In the said Procedure B, based on the following formula (1), the change over time of the said specific volume is calculated

[0037]

Number

[0038] (However, in formula (1), T is temperature, p is pressure, t is time, v is specific volume, v c is the specific volume of the crystalline part, v m is the specific volume of the amorphous part, Xc is the crystallinity, m 1 ~m 3 , c 1 ~c 3 are coefficients.) It is characterized by this.

[0039] According to this configuration, since it becomes possible to perform a warp analysis that more accurately takes into account the cooling rate dependence of the PVT curve based on the actual phenomenon, the prediction accuracy of the warp analysis is improved.

[0040] One aspect of the recording medium disclosed herein is a computer-readable recording medium on which the above-described warp analysis program for a resin molded product is recorded.

Effects of the Invention

[0041] As described above, according to the present disclosure, since it becomes possible to perform a warp analysis that more accurately takes into account the cooling rate dependence of the PVT curve based on the actual phenomenon, the prediction accuracy of the warp analysis is improved.

Brief Description of the Drawings

[0042]

Figure 1

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Figure 10

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Figure 15

Figure 16

Embodiments for Carrying Out the Invention

[0043] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. The following description of the preferred embodiments is merely exemplary in nature and is in no way intended to limit the present disclosure, its applications, or its uses.

[0044] (Embodiment 1) <Molding of Resin and Resin Molded Product> The technology of the present disclosure can be applied to all molding methods using a mold made of a resin material as a raw material. Specific examples of the molding method include injection molding, transfer molding, plunger molding, press molding, blow molding, vacuum molding, pressure-air molding, and the like. In this specification, the terms "resin" and "resin material" mean a resin composition containing a resin raw material and, if necessary, any optional additive.

[0045] -Injection Molding of Resin- As an example of the molding method, an overview of injection molding will be described. FIG. 1 is a diagram for explaining each step in the injection molding of resin and a graph showing an example of the pressure and temperature history of the resin.

[0046] As shown in FIG. 1, the injection molding of resin includes an injection step S51, a holding pressure step S52, and a cooling step S53.

[0047] First, a molten resin material heated to temperature T is injected into the cavity formed by clamping molds M1 and M2 (injection step S51). 1 When the resin is filled throughout the cavity, in order to reduce the excessive shrinkage amount of the resin due to temperature drop, additional resin filling injection is started (time A1). Then, a pressure exceeding atmospheric pressure P is applied to the resin in the cavity. And while adjusting the additional resin filling amount, the resin pressure is maintained around the set predetermined pressure P (holding pressure step S52).

[0048] 0 1

[0049] When a certain amount of additional resin has been filled in for a certain period of time, the filling of the additional resin is stopped (time A2). As a result, the pressure of the resin in the cavity is P 1 and gradually decreases until it eventually reaches atmospheric pressure P 0 (time A3). After the molded product is cooled in the mold, it is demolded by mold opening and then air-cooled (cooling step S53).

[0050] Although not shown in FIG. 1, the molded product thus obtained is cooled to room temperature T 0 and then becomes a product through post-processing such as deburring.

[0051] In the injection step S51, molecular orientation of the polymer chains occurs due to the shear flow of the resin. In the pressure holding step S52, crystallization proceeds as the temperature decreases in the molecular orientation state, and volume shrinkage due to crystallization occurs. In the mold cooling of the cooling step S53, although the shrinkage of the resin proceeds, residual stress is generated in the molded product due to mold restraint. In the air cooling of the cooling step S53, the residual stress is released by demolding, resulting in deformation of the molded product.

[0052] Note that, not limited to injection molding, it is generally known that there are two types of crystallization processes in the crystallization of resins: primary crystallization and secondary crystallization. In this specification, "primary crystallization" means crystallization in which spherulites composed of a laminated structure (lamellar structure) of crystal layers formed by folding of polymer chains and amorphous layers sandwiched between adjacent crystal layers are formed. Also, "secondary crystallization" refers to further thickening growth of the crystal layers in the lamellar structure generated by primary crystallization and the completion of the lamellar structure.

[0053] In addition, as a result of intensive research, the inventors of the present application have found that the crystallization of the resin that proceeds from the pressure holding step S52 to the mold cooling of the cooling step S53 in injection molding is mainly primary crystallization in a non-isothermal process, but in addition, secondary crystallization in a non-isothermal process also proceeds. Further crystallization occurs during the air cooling in the cooling step S53, and the crystallization is mainly secondary crystallization in an isothermal process.

[0054] -Resin Molded Product- The resin molded product is not particularly limited as long as it is a resin molded product manufactured by the above-described various molding methods. Specific examples of the resin molded product include, for example, parts for automobiles, parts for rockets, aircraft, etc., and sports goods. Preferably, plate-shaped molded products such as interior and exterior members of vehicles are included. Note that the resin molded product may be an insert molded product.

[0055] As the resin raw material, well-known crystalline resins can be targeted. Specifically, for example, polypropylene resin, polyethylene resin, polyacetal resin, polyamide (PA) resin, etc. can be mentioned. These resins can be used alone or in a mixture of two or more.

[0056] The resin may contain additives such as reinforcing fibers, fillers, pigments, dyes, impact resistance improvers, UV absorbers, etc. The reinforcing fibers are not particularly limited, and well-known fibers can be used. Specifically, for example, glass fibers, carbon fibers, cellulose nanofibers, etc. can be mentioned. These fibers can be used alone or in a mixture of two or more. The fiber diameter, fiber length, content, etc. of the reinforcing fibers, and the specifications, content, etc. of other additives are not particularly limited and can be set to generally used conditions. These additives can be added alone or in a plurality of types.

[0057] <Warp analysis device for resin molded products> Fig. 2 shows a configuration example of a warp analysis device 100 for a resin molded product according to the present embodiment (hereinafter, also referred to as "analysis device 100"). The analysis device 100 is a CAE (Computer Aided Engineering) system having a computer 110 as a basic configuration. The analysis device 100 is a device that performs warp analysis of a resin molded product manufactured by the above-described various molding methods using the finite element method by computer simulation. Note that the analysis device 100 is merely an example of a warp analysis device for a resin molded product according to the present disclosure, and the configuration of the warp analysis device is not limited to this example. Hereinafter, the case where the analysis device 100 is applied to warp analysis of a resin injection molded product will be described as an example.

[0058] The analysis device 100 includes a storage unit 120 composed of, for example, a ROM, a RAM, a hard disk, etc., and a processor 130 composed of, for example, a CPU, etc. Further, the analysis device 100 includes a display unit 140 composed of, for example, a display, an input unit 150 composed of a keyboard, etc., and a reading unit 160 for acquiring information stored in various recording media 170. Information such as a program for arithmetic processing and various analysis data is stored in the storage unit 120 and / or the recording media 170. The processor 130 performs various arithmetic processes based on the information stored in the storage unit 120, the information input via the input unit 150, and the information acquired from the recording media 170 via the reading unit 160. Note that the analysis device 100 is configured to be communicable with an external device via an interface (not shown).

[0059] The analysis device 100 creates a fluid analysis model and a structural analysis model by dividing shape data such as 3D CAD data defining the cavity of a mold into a plurality of minute elements by a model creation unit 131. Note that the fluid analysis model is a finite element model used for fluid analysis described later. The structural analysis model is a finite element model used for structural analysis described later. As the fluid analysis model and the structural analysis model, the same model may be used or different models may be used.

[0060] As the model creation unit 131, commercially available automatic mesh generation software or the like can be used. Specifically, for example, 3D TIMON (registered trademark)-Pre / Post manufactured by Toray Engineering D Solutions Co., Ltd., FEMAP (registered trademark) manufactured by NST Co., Ltd., Patran (registered trademark) manufactured by MSC Software Corporation, Hyper mesh (registered trademark) manufactured by Altair, etc. CAE preprocessors can be used. Note that the shape and size of the elements are not particularly limited and are appropriately set according to product specifications, material composition, calculation efficiency, and calculation accuracy levels. Also, a finite element model of the mold may be created and used for analysis. When creating a finite element model of the mold, for example, a finite element model of only the surface forming the cavity of the mold or a part of the mold including the surface may be created.

[0061] Analysis conditions are set based on material property data regarding the type, formulation, additives, various physical property values, etc. of the resin, and boundary condition data describing molding conditions such as injection speed and resin temperature during injection.

[0062] The flow analysis unit 133 performs a flow analysis to analyze the behavior of the resin in the injection process S51, the holding pressure process S52, and the cooling process S53 using the above-described flow analysis model. Then, the flow analysis unit 133 calculates various data including temperature information (temporal change in temperature) and pressure information (temporal change in pressure) of the resin for each element and for each minute time through the flow analysis. The calculated various data are stored in the storage unit 120. As the flow analysis unit 133, for example, injection molding CAE software such as 3D TIMON (registered trademark) manufactured by Toray Engineering D Solutions Co., Ltd. can be used. Note that the minute time is the analysis unit time for flow analysis and structural analysis, and is not particularly limited and is appropriately set according to product specifications, material composition, calculation efficiency, and calculation accuracy levels.

[0063] The structural analysis unit 134 uses the above-described structural analysis model to perform a structural analysis of the resin, that is, a shrinkage behavior calculation, based on the temperature information and pressure information of the resin calculated by the flow analysis unit 133, calculates the shrinkage amount of the resin, and finally calculates the deformed shape and deformation amount of the molded product. As the structural analysis unit 134, for example, solvers such as Abaqus manufactured by Dassault Systèmes, 3D TIMON (registered trademark)-WARP manufactured by Toray Engineering D Solutions Co., Ltd. can be customized and utilized.

[0064] 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. Although details will be described later, each unit has the following functions.

[0065] The crystallinity calculation unit 135 calculates the crystallinity information (change in crystallinity over time) of the resin for each element and for each minute time based on the temperature information and pressure information obtained by the above flow analysis.

[0066] The specific volume calculation unit 136 calculates the specific volume information (change in specific volume over time) of the resin for each element and for each minute time based on the temperature information, pressure information, and crystallinity information.

[0067] The shrinkage amount calculation unit 137 calculates the shrinkage amount of the resin for each element and for each minute time based on the specific volume information.

[0068] The deformation calculation unit 138 calculates the deformed shape and deformation amount from the designed shape of the molded product finally obtained by integrating the above shrinkage amount.

[0069] The crystallinity information, specific volume information, shrinkage amount information, deformed shape / deformation amount information, etc. obtained by the structural analysis are also stored in the storage unit 120.

[0070] <Method for analyzing warpage of resin molded product> FIG. 3 is a flowchart showing an example of a method for analyzing warpage of a resin molded product according to the present embodiment (hereinafter also referred to as "the present analysis method"). The present analysis method is a method for analyzing warpage of a resin molded product manufactured by the above-described various molding methods using the finite element method by computer simulation, and is performed, for example, using the above-described analysis apparatus 100. Hereinafter, a case where the present analysis method is applied to warpage analysis of a resin injection molded product will be described as an example.

[0071] As shown in FIG. 3, the present analysis method includes, for example, a model creation step S1, a flow analysis step S2, and a structural analysis step S3.

[0072] First, in the model creation step S1, as described above, the model creation unit 131 divides the shape data of the cavity of the mold created using 3D CAD or the like into minute elements for numerical analysis, and creates a flow analysis model and a structural analysis model. The method for creating the model is not particularly limited, and generally known methods can be adopted.

[0073] 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 above-described flow analysis model. Then, temperature information and pressure information for each element and for each minute time in each step of resin injection molding, that is, the injection step S51, the holding pressure step S52, and the cooling step S53, are acquired.

[0074] Note that the method of flow analysis is not particularly limited, and generally known methods can be adopted. Specifically, for example, the initial flow velocity (injection velocity) of the resin, the kinematic viscosity coefficient of the resin material, boundary conditions, etc. are input information, and the Navier-Stokes equation, 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 resin flow and solidification process. In addition to information on the shear rate of the resin based on the flow velocity information, information such as the initial temperature (injection temperature) of the resin, the specific heat, density, and thermal conductivity of the resin material is 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 resin flow and solidification process.

[0075] Then, using the above-described model for structural analysis, based on the temperature information and pressure information obtained in the flow analysis step S2, the shrinkage behavior of the resin is calculated, and the shrinkage amounts of the resin in the pressure holding step S52 and the cooling step S53 are calculated. Then, the deformation shape and deformation amount of the finally obtained molded product are calculated (structural analysis step S3).

[0076] Specifically, the structural analysis step S3 includes a crystallinity calculation step S31, a specific volume calculation step S32, a shrinkage amount calculation step S33, and a deformation calculation step S34.

[0077] The shrinkage amount of the resin can be calculated based on the volume change amount accompanying the change in the temperature of the resin, the volume change amount accompanying the change in the pressure of the resin, and the crystallinity. That is, based on the temperature information and pressure information for each element and for each minute time obtained in the flow analysis step S2, the specific volume for each element and for each minute time is obtained (crystallinity calculation step S31 and specific volume calculation step S32). Then, based on the temperature information, pressure information, and specific volume information for each element and for each minute time, the shrinkage amount for each element and for each minute time is calculated (shrinkage amount calculation step S33). Then, finally, based on the shrinkage amount, elastic modulus, stress, etc., using an equation such as the generalized Hooke's law, the final warpage deformation amount and warpage deformation shape of the molded product are calculated (deformation calculation step S34).

[0078] Here, this analysis method is characterized by the crystallinity calculation step S31 and the specific volume calculation step S32.

[0079] Conventionally, when calculating specific volume information based on the above-described temperature information and pressure information, as the governing equation, for example, an equation of state such as the Tait equation has been used. The Tait equation is generally expressed as V = V 0 {1 - 0.0894×ln(1 + P / B)} + V 1 and is used by determining the coefficient included in B by the least squares method or the like based on the PVT characteristic data obtained by using an experimental method such as the piston method separately for the resin material.

[0080] As described above, the crystallization behavior of the crystalline resin varies greatly 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 during experiments such as the piston method, so the dependence of the crystallization behavior on the cooling rate cannot be considered.

[0081] In the present disclosure, based on temperature information and pressure information, the change over time of the degree of crystallinity is calculated using a crystallization model. Then, based on the temperature information, pressure information, and degree of crystallinity information, a two-phase model, that is, a model of the specific volume of each of the crystalline part and the amorphous part, is created, and these models are added together based on the degree of crystallinity, that is, the ratio of the crystalline part in the entire resin, to calculate the specific volume of the entire resin.

[0082] [Crystallinity calculation step] In the crystallinity calculation step S31, the crystallinity information of the resin is calculated based on at least the above-mentioned temperature information. Also, depending on the model formula used, the crystallinity information of the resin is calculated based on the above-mentioned temperature information and pressure information. At this time, the crystallization behavior of the resin within the molding processing temperature range obtained in advance by FSC measurement is considered.

[0083] In this specification, the degree of crystallinity X c is used in a meaning that includes both the relative degree of crystallinity φ and the absolute degree of crystallinity Φ (also referred to as "achieved degree of crystallinity") shown in FIG. 4.

[0084] The melting enthalpy of the crystal of the resin material is known information as a literature value, but in most cases, the resin material of the molded product does not substantially reach a crystal having the melting enthalpy of the literature value after the molding process. This is because the crystallization behavior greatly depends on the molding conditions and the like. The absolute degree of crystallinity indicates how far the crystallization has progressed based on the melting enthalpy of the crystal shown in the literature value. On the other hand, the relative degree of crystallinity indicates how far the crystallization has progressed based on the absolute degree of crystallinity that can be reached according to the molding conditions, that is, the achieved degree of crystallinity.

[0085] The degree of crystallinity can be determined, for example, by measuring the heat of fusion of crystals using DSC. At this time, the "relative degree of crystallinity" means the degree of crystallinity when the total enthalpy change amount H(∞) of the crystallization exothermic peak is set to 1. The absolute degree of crystallinity means the degree of crystallinity when the enthalpy of fusion (literature value) ΔH f of the crystal is set to 1.

[0086] The degree of crystallinity calculated in the crystallinity calculation step S31 may be either the relative degree of crystallinity or the absolute degree of crystallinity. Since the absolute degree of crystallinity has temperature dependence, from the viewpoint of improving prediction accuracy, it is preferable to use the absolute degree of crystallinity as the degree of crystallinity. As will be described later in Embodiment 2, a model for calculating the absolute degree of crystallinity (also referred to as the "absolute degree of crystallinity model") can be created using a model for calculating the relative degree of crystallinity (also referred to as the "relative degree of crystallinity model"). Therefore, in this embodiment, the case of using the relative degree of crystallinity model will be described.

[0087] Specifically, the relative degree of crystallinity φ(t) at a certain time t can be described using the Nakamura model represented by the following formula (2).

[0088]

Equation

[0089] In the formula (2), K(T) is a value related to the rate constant k(T) of crystal growth. For example, K(T)=k(T) 1 / n is. Also, n is the Avrami exponent related to the shape (dimension) of the crystal (also referred to as the "Ozawa exponent" in the Ozawa plot). k(T) or K(T) and n can be determined using a kinetics model of crystallization such as the Avrami plot (isothermal crystallization measurement), the Ozawa plot (non-isothermal crystallization measurement), the reinterpreted Ozawa plot (non-isothermal crystallization measurement), and the Hoffman-Lauritzen theory.

[0090] Specifically, for example, the Avrami plot is represented by the following formula (4).

[0091] φ(t) = 1 - exp[-kt n ···(4) When Equation (4) is transformed, the following Equation (4A) is obtained.

[0092] log[-ln(1 - φ)] = logk + nlogt ···(4A) That is, when plotted with the horizontal axis being time (logt) and the vertical axis being log[-ln(1 - φ)], the slope of the straight line corresponds to the Avrami exponent n and the intercept corresponds to the rate constant logk.

[0093] Using FSC, the temperature of the molten sample is rapidly decreased to the measurement temperature, and when the measurement temperature is reached, the temperature is kept constant, and the change in heat flow over time as shown in the upper diagram of FIG. 5, for example, is measured. Then, the change in crystallinity over time during the isothermal process at the desired measurement temperature is calculated. For the data on the change in crystallinity over time at each temperature, it is graphed as shown in the lower diagram of FIG. 5, and the Avrami exponent n and the rate constant k are determined based on Equation (4A).

[0094] FIG. 6 is an example of the result of calculating the Avrami exponent n and the rate constant k based on the isothermal crystallization measurement result by FSC and the Avrami plot. In FIG. 6, digital micrographs of the samples after the isothermal crystallization measurement by FSC at 50 °C and 100 °C are shown above the graph.

[0095] From the results in FIG. 6, the Avrami exponent n and the rate constant k can be approximated by fifth-degree polynomials of temperature T as shown in the following Equations (5) and (6).

[0096] n(T) = a 1 T 5 + a 2 T 4 + a 3 T 3 + a 4 T 2 + a 5 T + a 6 ···(5) k(T) = b 1 T 5 + b 2 T4 +b 3 T 3 +b 4 T 2 +b 5 T + b 6 ···(6) In equations (5) and (6), a 1 ~a 6 and b 1 ~b 6 are coefficients that depend on the material.

[0097] Substituting the above equations (5) and (6) into the Nakamura model of the above equation (2) and calculating the relative crystallinity φ(t) gives the result shown in Figure 7. In Figure 7, the solid line shows the measured results from the non-isothermal measurement of FSC, and the dashed line shows the calculated results obtained using the Nakamura model. It can be seen from Figure 7 that the relative crystallinity model using the Nakamura model can reproduce the cooling rate dependence of the crystallization behavior with high accuracy.

[0098] Note that the determination of the Avrami exponent n and the rate constant k may also be performed using the Ozawa plot represented by the following equation (7).

[0099]

Equation

[0100] When using the Ozawa plot, measure the crystallization behavior in the non-isothermal process when the sample is cooled at a constant cooling rate using FSC. Extract the value of log[-ln(1 - φ)] for each cooling rate at a certain temperature, and plot with the horizontal axis as logβ and the vertical axis as log[-ln(1 - φ)]. The slope of the regression line for each temperature of the graph thus obtained is determined as the Ozawa exponent n, and the intercept is determined as the rate constant logX(T).

[0101] Furthermore, the reinterpreted Ozawa plot (A. Toda: Thermochimica Acta, 707, 179086(2022), ibid. 713, 179244, (2022)) represented by the following equations (8) and (9) may also be used.

[0102] φ(T, β i ) = 1 - exp[-φ 0 ···(8)

[0103]

Math

[0104] The primary crystallization behavior in the non-isothermal process at a certain scanning speed β can be evaluated by the reinterpreted Ozawa plot shown in Eqs. (8) and (9) based on the Kolmogorov-Johnson-Mehl-Avrami model. Here, φ(T, β i ) is the relative crystallinity at the cooling rate β i and temperature T, and φ in Eq. (9) 0 represents the case of heterogeneous nucleation, where N 0 is the initial nucleus density, g is the geometric coefficient, G is the linear growth rate, and n is the Ozawa exponent.

[0105] When using the reinterpreted Ozawa plot, the K(T) term of the Nakamura model is represented by the following Eq. (10).

[0106]

Math

[0107] 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. By obtaining the slope of the regression line of the data plotted with the horizontal axis as log(β peak (T)) and the vertical axis as log[1 - exp(-φ 0 )], the Ozawa exponent at each β i can be calculated.

[0108] For the actual samples in the reference example described later, the Ozawa plot and the Ozawa exponent n calculated using the reinterpreted Ozawa plot are shown in Fig. 8. As shown in Fig. 8, when using the reinterpreted Ozawa plot, the same number of n as the number of measurement data can be obtained, so the reliability of the data is improved compared to the Ozawa plot.

[0109] Figure 9 shows the heat flow curve (actual measurement) obtained by non-isothermal measurement using FSC for the actual sample of the reference example described later, and the simulation result of the heat flow curve obtained by differentiating the relative crystallinity calculated using the relative crystallinity model of Equation (3) under the conditions of the example with respect to temperature. In the crystallinity calculation step, the Ozawa plot was re-interpreted to obtain the n and K(T) terms. As shown in Figure 9, it can be seen that the predicted values are in good agreement with the measured values.

[0110] Also, although details are omitted, as the method for giving the K(T) term of the Nakamura model, the Hoffman-Lauritzen theory represented by the following Equation (11) may be used.

[0111]

Equation

[0112] In Equation (11), Tg is the glass transition temperature, and T m is the melting point. By using Equation (11), the pressure dependencies of the melting point and the glass transition temperature, which are temperatures related to the temperature at which crystallization starts, can be considered.

[0113] [Specific Volume Calculation Step] In the specific volume calculation step S32, specific volume information is calculated based on the above-described temperature information, pressure information, and crystallinity information, and the following Equation (1).

[0114]

Equation

[0115] (However, in Equation (1), T is temperature, p is pressure, t is time, v is specific volume, v c is the specific volume of the crystalline part, v m is the specific volume of the amorphous part, Xc is crystallinity, m 1 ~m 3 、c 1 ~c 3 are coefficients.) Hereinafter, v c, v m The derivation method of

[0116] First, using a capillary rheometer (known piston method), lower the temperature of the molten sample at a constant cooling rate under pressure p 0 and measure the PVT characteristics. An example of the PVT characteristics is shown in FIG. 10. The PVT characteristics indicated by the symbol × in FIG. 10 are for the resin material of the reference example described later, when the temperature is lowered at p 0 = 10 MPa and a cooling rate of 3°C / min.

[0117] 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 starts. The amorphous part can be basically considered as a liquid phase, and the specific volume v 0 of the amorphous part at pressure P m (T, p 0 ) can be modeled by a straight line including the dashed line part obtained as a regression equation of the data in the high-temperature part of the PVT characteristics (i in FIG. 10).

[0118] Next, take out the sample after the measurement of the PVT characteristics is completed, and measure the crystallinity X c using DSC, XRD, etc. (ii in FIG. 10).

[0119] Furthermore, calculate the specific volume v 0 of the crystalline part at pressure p c (T, p 0 ) from Equation (1). Specifically, the specific volume v m (T, p 0 ) of the amorphous part has been obtained as a regression equation of the data in the high-temperature part of the PVT characteristics as described above. Also, the crystallinity X c has also been obtained by measurement. Furthermore, the specific volume v(T, p 0 ) of the resin material at pressure p 0 is known information from the results of the PVT characteristic measurement by the piston method. Substitute the values of these v m (T, p 0 ), X c and v(T, p 0 ) into Equation (1) to obtain v c (T, p0 ) can be obtained (see (iii) in FIG. 10).

[0120] The above PVT characteristic measurement and the operations (i) to (iii) are repeated while changing the pressure p. 0 In this way, finally, v c (T, p) and v m (T, p) are modeled.

[0121] The specific volume v m (T, p) of the amorphous part is linearly related to each of the temperature T and the pressure p, and it was found that it can be modeled by a plane as shown in FIG. 11, that is, the above formula (13). m 1 , m 2 and m 3 are coefficients depending on the material. For the material whose PVT characteristics were measured in FIG. 10, m 1 = 0.701786, m 2 = -1.1009, m 3 = 1166.315, and a very good correlation with the coefficient of determination R 2 = 0.99 was obtained (see Table 2 described later).

[0122] The specific volume v c (T, p) of the crystalline part is linearly related to each of the temperature T and the pressure p, and it was found that it can be modeled by a plane as shown in FIG. 12, that is, the above formula (12). c 1 , c 2 and c 3 are coefficients depending on the material. For the material whose PVT characteristics were measured in FIG. 10, c 1 = 0.207416, c 2 = -0.72424, c3 = 1008.499, and a good correlation with the coefficient of determination R 2 = 0.92 was obtained (see Table 2 described later).

[0123] Using the formula (1) of the specific volume model thus obtained, the reproducibility of the cooling temperature dependence of the PVT characteristics was verified.

[0124] Figure 13 shows the simulation results of the PVT characteristics of the comparative examples and examples described later. In the crystallinity calculation step, n and k(t) were obtained using an Avrami plot, and the relative crystallinity was calculated as the crystallinity. It can be seen that when the two-domain Tait model of the comparative example is used, only the PVT characteristics at the cooling rate (3 °C / min) used in the experiment can be simulated. On the other hand, when the new model of Equation (1) is used, it was found that the cooling rate dependence of the PVT characteristics in which crystallization occurs at a lower temperature as the cooling rate increases can be reproduced.

[0125] After calculating the specific volume according to the above Equation (1), through the shrinkage amount calculation step S33 and the deformation calculation step S34, the deformation shape and deformation amount of the finally obtained molded product are obtained.

[0126] Note that the above structural analysis was described assuming application to the in-mold shrinkage behavior of the non-isothermal process (from the pressure holding step S52 to the mold cooling in the cooling step S53), but it can also be applied to the out-of-mold shrinkage behavior of the isothermal process (after demolding in the cooling step S53).

[0127] <Regarding FSC measurement> As described above, in this configuration, in the crystallinity calculation step S31, the time-dependent change in crystallinity is calculated in consideration of the crystallization behavior of the resin in the molding processing temperature range obtained by FSC measurement. Thereby, since it becomes possible to perform a warp analysis that more accurately considers the cooling rate dependence of the PVT curve based on the actual phenomenon, the prediction accuracy of the warp analysis is improved.

[0128] Note that for the isothermal measurement at an arbitrary temperature (measurement temperature) within the molding processing temperature range by FSC, it is preferable to use a temperature profile in which the sample temperature is cooled 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 held at the measurement temperature for a predetermined time.

[0129] In addition, for non-isothermal measurement within a temperature range including the above arbitrary temperature (measurement temperature), it is preferable to use a temperature profile in which the sample temperature is decreased at a cooling rate of preferably 1 °C / s or more and 1000 °C / s or less, more preferably 1 °C / s or more and 320 °C / s or less, and preferably at a constant cooling rate.

[0130] For measurement of the absolute (attained) crystallinity by reheating the sample after completion of isothermal measurement or non-isothermal measurement, it is preferable to use a temperature profile in which the sample temperature is increased 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, and preferably at a constant heating rate.

[0131] According to the above configuration, the crystallization behavior can be accurately observed.

[0132] <Program for Warpage Analysis of Resin Molded Products and Recording Medium Thereof> At least a part of each step of the above warpage analysis method is programmed as a program for warpage analysis of a resin molded product manufactured by the above various molding methods. That is, the program for warpage analysis of a resin molded product according to the present embodiment is a program that causes a computer to execute at least, among the procedures of the above respective steps, procedure A of the crystallinity calculation step S31 and procedure B of the specific volume calculation step S32. Note that the program may be configured to cause the computer to execute the procedures of the entire structure analysis step S3, that is, in addition to the above procedures A and B, the procedure of the shrinkage amount calculation step S33 and the procedure of the deformation calculation step S34. Further, the program may be configured to cause the computer to execute, in addition to the procedures of the entire structure analysis step S3, the procedures of the model creation step S1 and the flow analysis step S2. This warpage analysis program is stored, for example, in the storage unit 120 and can be executed by the processor 130. Further, the warpage analysis program is not limited to being stored in the storage unit 120, and can be recorded on various well-known computer-readable recording media such as optical disk media and magnetic tape media. Then, by mounting such a recording medium on the reading unit 160 and reading out the warpage analysis program, the program can be executed.

[0133] (Embodiment 2) Hereinafter, other embodiments according to the present disclosure will be described in detail. In the description of these embodiments, the same parts as those in Embodiment 1 are denoted by the same reference numerals, and detailed description thereof will be omitted.

[0134] In Embodiment 1, the case where the relative crystallinity φ is used as the crystallinity X c was described. In Embodiment 2, the crystallinity calculation step S31 when the absolute crystallinity Φ is used as the crystallinity X c will be described.

[0135] First, the time-dependent change φ(t) of the relative crystallinity is calculated by the method of Embodiment 1 above (relative crystallinity calculation step).

[0136] Then, based on the relative crystallinity φ(t), the time-dependent change Φ(t) of the absolute crystallinity of the resin is calculated (absolute crystallinity calculation step).

[0137] For example, the time-dependent change Φ(t) of the absolute crystallinity can be described by the following formula (3).

[0138] [Number]

[0139] In formula (3), the time derivative of φ(t) is the progress rate of the relative crystallinity (the rate of change of the time-dependent change), f c (T) is the achieved crystallinity when isothermally crystallized or non-isothermally crystallized at the temperature T (crystallization peak temperature), f 1 ~f 6 represents coefficients depending on the material.

[0140] Figure 14 shows the absolute crystallinity measured using FSC for the actual samples of the reference examples described later. The circles in Figure 14 represent the isothermal measurement results, and the black dots represent the non-isothermal measurement results. The isothermal measurement results were fitted using the KJMA model represented by the following formula (12), and the values of the achieved crystallinity in the primary crystallization obtained were plotted. Note that the horizontal axis is the crystallization peak temperature. As shown in Figure 14, it can be seen that the absolute crystallinity tends to be higher in the non-isothermal measurement results than in the isothermal measurement results. This indicates that under the conditions of the non-isothermal process from the pressure holding step S52 to the mold cooling in the cooling step S53 during the molding process, the achieved crystallinity at a certain time and temperature is higher than that in the isothermal process.

[0141]

Number

[0142] (However, in formula (12), φ 1 (t) is the primary absolute crystallinity at time t, ΔH f 1st is the achieved crystallinity in the primary crystallization, and t 1 / 2 represents the half crystallization time.) That is, the absolute crystallinity obtained by the isothermal measurement is considered to be the achieved crystallinity at the completion of the primary crystallization. And the results in Figure 14 are considered to indicate that in the non-isothermal process, in addition to the primary crystallization, secondary crystallization is also progressing.

[0143] When fitting is performed for each of the isothermal measurement and non-isothermal measurement data in Figure 14, it can be approximated by a fifth-degree polynomial. The approximation formula is the above f c (T) (the obtained values of f 1 ~f 6 are shown in Table 1 described later).

[0144] Figure 15 is based on the relative crystallinity obtained by the calculation of formula (3) in Figure 9, f c (T) obtained by isothermal measurement and f cThis is the result of calculating the absolute crystallinity based on (T). The isothermal measurement is shown by the dashed line, and the non-isothermal measurement is shown by the solid line. Also, the x marks indicate the measured values by FSC.

[0145] As shown in Fig. 15, it can be seen from the measured values of the x marks that the absolute crystallinity depends on the cooling rate. When f c (T) obtained by isothermal measurement is used, it is difficult to reproduce the cooling rate dependence of the absolute crystallinity. On the other hand, when f c (T) obtained by non-isothermal measurement is used, it was found that the cooling rate dependence of the absolute crystallinity can be reproduced.

[0146] Fig. 16 shows the result of predicting the PVT characteristics by applying the calculated result of the absolute crystallinity based on the non-isothermal measurement in Fig. 15 to the crystallinity X c in Equation (1). Note that the Tait model in Fig. 16 is the simulation result of the comparative example described later. As shown in Fig. 16, when the new model of Equation (1) is used, it is suggested that the cooling rate dependence of the PVT characteristics can be reproduced, and the prediction accuracy can be further improved by using the absolute crystallinity.

[0147] (Experimental Example) Next, the specific experimental examples will be described.

[0148] <Reference Example> [Materials] As the actual sample, isotactic polypropylene (manufactured by Sun Allomer Co., M w = 20.6×10 4 , M w / M n = 7.5, MFR (230 °C, load: 2.16 kg (JIS K 7210-1:2014)): 31 g / 10 min, stereoregularity ( 13 C-NMR): 97.8 mmmm) was used. The melting enthalpy (literature value) of the crystal of this material is 206.75 J / g (B. Wunderlich: Thermal Analysis of Polymeric Materials, Springer, Berlin (2005)).

[0149] [Measurement of PVT characteristics] Using a commercially available capillary rheometer, the temperature of the molten sample was decreased from 230 °C to 70 °C at a constant cooling rate of 3 °C / min under pressures P 0 (10 MPa, 20 MPa, 30 MPa, 40 MPa), and the PVT characteristics were measured.

[0150] [Differential scanning calorimetry measurement] After the measurement of the PVT characteristics, the sample at 70 °C was taken out, and the crystallinity X c was measured by DSC. Specifically, the solid sample after the PVT characteristics measurement was cut using a microtome and made into a thin slice with a thickness of about 200 μm. This thin slice sample was 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 crystallinity.

[0151] [High-speed differential scanning calorimetry measurement] The crystallization behavior of the resin material was evaluated using a high-speed differential scanning calorimeter (manufactured by Mettler-Toledo, Flash DSC1).

[0152] -Non-isothermal measurement- After the sample was heated to 230 °C, it was cooled at a constant rate in the range of cooling rates from 1 to 100 °C / s. Then, if necessary, the enthalpy of fusion J / g was calculated from the melting curve when reheating at a heating rate of 2000 °C / s, and the absolute (attained) crystallinity was determined by dividing by the enthalpy of fusion of the above literature value.

[0153] -Isothermal measurement- After the sample was heated to 230 °C, it was cooled at a constant rate of 1000 °C / s and held isothermally for 0.015 to 500 s in the temperature range of 0 to 110 °C. Then, if necessary, the enthalpy of fusion J / g was calculated from the melting curve when reheating at a heating rate of 1000 °C / s, and the absolute (attained) crystallinity was determined by dividing by the enthalpy of fusion of the above literature value.

[0154] -Estimation of mass- The size of the solidified sample after cooling was approximately 30 to 150 μm square and about 10 to 20 μm thick. The mass m of the sample was estimated by the following formula (13) based on the specific heat C of the liquid phase of the sample measured by normal DSC p and the heat flow dq / dt of the liquid phase of the sample measured by FSC. For example, the mass of the 100 °C isothermal crystallization could be estimated to be 55.2 ng.

[0155]

Equation

[0156] <Example> The PVT characteristics were predicted using the above formulas (1) to (3).

[0157] Table 1 shows the calculation conditions and the values of the calculation parameters used in the crystallinity calculation step.

[0158]

Table 1

[0159] Table 2 shows the calculation conditions and the values of the calculation parameters used in the specific volume calculation step.

[0160]

Table 2

[0161] <Comparative Example> The PVT characteristics were predicted using the two-domain Tait model represented by the following formula (14).

[0162]

Equation

[0163] Table 3 shows the values of the calculation parameters used for the calculation of the specific volume.

[0164]

Table 3

Industrial Applicability

[0165] The present disclosure is extremely useful because it can improve the prediction accuracy by sufficiently considering the crystallization behavior of the resin in the molding process in a method for analyzing warpage of a resin molded product, a warpage analysis apparatus, a warpage analysis program, and a recording medium.

Description of Reference Numerals

[0166] 100 Warpage analysis apparatus for resin molded product 131 Model creation unit 133 Flow analysis unit 134 Structural analysis unit 135 Crystallinity calculation unit 136 Specific volume calculation unit 137 Shrinkage amount calculation unit 138 Deformation calculation unit 170 Recording medium S1 Model creation step S2 Flow analysis step S3 Structural analysis step S31 Crystallinity calculation step S32 Specific volume calculation step S33 Shrinkage amount calculation step S34 Deformation calculation step S51 Injection step S52 Pressure holding step S53 Cooling step

Claims

1. A method for analyzing warpage of a resin molded product by computer simulation, comprising the steps of: a crystallinity calculation step of calculating a change in crystallinity of the resin over time based on at least a change in temperature over time during a solidification and shrinkage process of the resin; A specific volume calculation step of calculating a change in a specific volume of the resin over time based on the change in temperature over time, the change in pressure over time during the solidification and shrinkage process of the resin, and the change in crystallinity over time, In the crystallinity calculation step, the change in the crystallinity over time is calculated in consideration of the crystallization behavior of the resin within a molding temperature range previously obtained by high speed differential scanning calorimetry; In the specific volume calculation step, the change in the specific volume over time is calculated based on the following formula (1): [0010] (In formula (1), T is temperature, p is pressure, t is time, v is specific volume, v ｃ is the specific volume of the crystalline part, v ｍ is the specific volume of the amorphous part, Xc is the degree of crystallinity, m １ ~m ３ , c １ ~c ３ is the coefficient.) A method for analyzing warpage of a resin molded product comprising:

2. In claim 1, The crystallinity is a relative crystallinity, The change in the relative crystallinity over time φ(t) is calculated using the Nakamura model represented by the following formula (2): [0025] (In formula (2), φ(t) is the change in relative crystallinity over time, K(T) is a value related to the rate constant of crystal growth, and n is the Avrami index.) The K(T) and n are determined taking into consideration the crystallization behavior obtained by the high-speed differential scanning calorimetry. A method for analyzing warpage of a resin molded product comprising:

3. In claim 1 or 2, The crystallization behavior obtained by the high speed differential scanning calorimetry is obtained by at least one of isothermal measurement at an arbitrary temperature within the molding temperature range and non-isothermal measurement in a temperature range including the arbitrary temperature. A method for analyzing warpage of a resin molded product comprising:

4. In claim 1 or 2, The molding temperature range is 25° C. or higher and 300° C. or lower. A method for analyzing warpage of a resin molded product comprising:

5. In claim 1 or 2, The crystallinity is the absolute crystallinity, The crystallinity calculation step includes: A relative crystallinity calculation step of calculating a change in the relative crystallinity of the resin over time; and an absolute crystallinity calculation step of calculating a change in absolute crystallinity of the resin over time based on the change in relative crystallinity over time. A method for analyzing warpage of a resin molded product comprising:

6. In claim 5, The change in absolute crystallinity over time Φ(t) is represented by the following formula (3): [0030] (In formula (3), φ is the relative crystallinity, f ｃ (T) is the degree of crystallinity achieved when isothermal or non-isothermal crystallization is performed at temperature T (crystallization peak temperature), f １ ~f ６ is the coefficient.) A method for analyzing warpage of a resin molded product comprising:

7. An apparatus for performing warpage analysis of a resin molded product by computer simulation, a crystallinity calculation unit that calculates a change in crystallinity of the resin over time based on at least a change in temperature over time during a solidification and shrinkage process of the resin; a specific volume calculation unit that calculates a change in a specific volume of the resin over time based on the change in temperature over time, the change in pressure over time during the solidification and shrinkage process of the resin, and the change in the crystallinity over time, The crystallinity calculation unit calculates the change in the crystallinity over time in consideration of the crystallization behavior of the resin within a molding temperature range previously obtained by high speed differential scanning calorimetry, The specific volume calculation unit calculates the change in the specific volume over time based on the following formula (1): [0045] (In formula (1), T is temperature, p is pressure, t is time, v is specific volume, v ｃ is the specific volume of the crystalline part, v ｍ is the specific volume of the amorphous part, Xc is the degree of crystallinity, m １ ~m ３ , c １ ~c ３ is the coefficient.) The warpage analysis device for a resin molded product is characterized in that

8. A program for performing warpage analysis of a resin molded product by computer simulation, At a minimum, the computer A step A of calculating a change in crystallinity of the resin over time based on at least a change in temperature over time during a solidification and shrinkage process of the resin; and step B of calculating a change in specific volume of the resin over time based on the change in temperature over time, the change in pressure over time during the solidification and shrinkage of the resin, and the change in crystallinity over time, In the step A, the change in the crystallinity over time is calculated in consideration of the crystallization behavior of the resin within a molding temperature range previously obtained by high speed differential scanning calorimetry; In the step B, the change in the specific volume over time is calculated based on the following formula (1): [0050] (In formula (1), T is temperature, p is pressure, t is time, v is specific volume, v ｃ is the specific volume of the crystalline part, v ｍ is the specific volume of the amorphous part, Xc is the degree of crystallinity, m １ ~m ３ , c １ ~c ３ is the coefficient.) A program for analyzing warpage of resin molded products.

9. 9. A computer-readable recording medium having recorded thereon the program for analyzing warpage of a resin molded product according to claim 8.

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