Residual stress prediction method and residual stress prediction program

Abstract

To predict residual stress generated in a resin molded article with high accuracy.SOLUTION: A stress prediction method includes a step of acquiring a physical property value of a thermoplastic resin, a step of creating an analysis model of an injection-molded article, a step of acquiring a temperature distribution and a pressure distribution of the analysis model, a step of calculating a temperature load distribution on the basis of the temperature distribution and the pressure distribution, a step of calculating an elastic constant matrix distribution, and a step of using the temperature load distribution and the elastic constant matrix distribution to perform: At least one of the step of calculating the temperature load distribution and the step of calculating the elastic constant matrix distribution corrects the temperature load distribution or the elastic constant matrix distribution in accordance with a difference in volume change due to the shape of the thermoplastic resin.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present disclosure relates to a residual stress prediction method and a residual stress prediction program. [Background technology]

[0002] Injection molding is commonly used to manufacture parts with complex shapes using thermoplastic resins, but resin molded products obtained by injection molding can sometimes have residual stress.

[0003] Residual stress occurs during injection molding of thermoplastic resins when the thermoplastic resin is injected in a molten state and then cooled and solidified. In particular, if the thermoplastic resin is a crystalline resin, the molecular chains, which were random immediately after filling the mold, become oriented (folded and aligned) as a result of crystallization, resulting in a decrease (shrinkage) in volume compared to the volume immediately after filling the mold (mold dimensions), which can lead to the effects of thermal stress and non-uniform deformation.

[0004] The generation of large residual stresses can cause warpage during injection molding, resulting in reduced dimensional accuracy of the product. Furthermore, when a resin product is immersed in oil, such as gasoline, large residual stresses can occur, raising concerns about dimensional changes and reduced strength due to these residual stresses. For these reasons, there is a need for improved technology to predict the residual stresses that will occur in resin molded products.

[0005] For example, Patent Document 1 describes a method for calculating residual stress in a metal material by determining parameters that minimize the difference between calculated values ​​and measured values ​​using finite element analysis. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Publication No. 2019-190990 Summary of the Invention [Problem to be solved by the invention]

[0007] However, there is a problem in that it is difficult to predict the residual stress with sufficient accuracy for resin molded products. That is, when calculating the residual stress of a resin material, it is necessary to deal with various materials, shapes, and molding conditions. For example, calculating the residual stress in the same way as for metal materials described in Patent Document 1 requires a great deal of effort and calculation costs.

[0008] Furthermore, in the case of resin molded products, the locations where residual stress can be measured are limited, so even if a residual stress analysis method is established, the calculation results from this analysis method will not be sufficiently verified, raising concerns about the accuracy of the analysis.In fact, for example, it is possible to obtain calculation results for residual stress distribution using commercially available injection molding analysis software, but there tends to be a large discrepancy between the calculated values ​​and the measured values, and even when using analysis software, the accuracy of residual stress prediction is not sufficient.

[0009] The technology disclosed herein has been made in consideration of the above points, and aims to provide a residual stress prediction method and a residual stress prediction program that can predict residual stresses that occur in resin molded products with high accuracy. [Means for solving the problem]

[0010] a step of acquiring physical property values ​​of the thermoplastic resin; a step of creating an analytical model in which the injection-molded product is divided into a plurality of elements; a step of acquiring temperature and pressure distributions of the analytical model during a molding process of the thermoplastic resin; a step of calculating a temperature distribution of the analytical model during a cooling process after demolding using the temperature and pressure distributions; a step of calculating a temperature load distribution of the analytical model based on the temperature and pressure distributions during the molding process and the temperature distribution during the cooling process; a step of calculating an elastic constant matrix distribution that indicates a relationship between a strain vector and a stress vector in the thermoplastic resin; and a step of calculating strain and stress generated in each element of the analytical model by structural analysis using the temperature load distribution and the elastic constant matrix distribution, wherein at least one of the steps of calculating the temperature load distribution and the elastic constant matrix distribution corrects the temperature load distribution or the elastic constant matrix distribution according to differences in volume change due to a shape of the thermoplastic resin.

[0011] According to another aspect of the present disclosure, a residual stress prediction program causes a computer to execute the residual stress prediction method described above. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a diagram illustrating the injection molding process. [Figure 2] FIG. 2 is a diagram showing a specific example of PVT data for a thermoplastic resin. [Figure 3] FIG. 3 is a flow diagram showing a residual stress prediction method according to one embodiment. [Figure 4] FIG. 4 is a diagram showing a specific example of the shape of a resin molded product. [Figure 5] FIG. 5 is a diagram showing a specific example of the analytical model. [Figure 6] FIG. 6 is a diagram illustrating a strain measurement method. [Figure 7] FIG. 7 is a diagram showing an analytical quarter model according to the embodiment. [Figure 8] FIG. 8 is a diagram showing the temperature load distribution according to the first embodiment. [Figure 9] FIG. 9 is a diagram showing constraint conditions for structural analysis. [Figure 10] FIG. 10 is a diagram illustrating the stress distribution in the resin portion according to the first embodiment. [Figure 11] FIG. 11 is a diagram illustrating the stress distribution in the resin portion according to the second embodiment. [Figure 12] FIG. 12 is a diagram illustrating the stress distribution in the resin part according to the third embodiment. [Figure 13] FIG. 13 is a diagram showing the stress distribution in the resin part according to the comparative example. [Figure 14] FIG. 14 is a diagram showing a list of prediction results for the examples and comparative examples. [Figure 15] FIG. 15 is a block diagram illustrating an example of the hardware configuration of an information processing device. DETAILED DESCRIPTION OF THE INVENTION

[0013] Before describing an embodiment of the present disclosure, a general injection molding process will be described. Fig. 1 is a diagram for explaining each step of injection molding. Fig. 1 shows a timeline of molding, focusing on one mold.

[0014] Injection molding begins by injecting resin into the mold cavity through a gate. Immediately after injection, the resin delivery speed is controlled, but when, for example, 99% of the preset amount of resin has been filled, the process switches to resin pressure control (holding pressure). Even after the switch, injection continues while maintaining pressure.

[0015] Gate sealing is one indicator for obtaining stable injection-molded products. Gate sealing is a phenomenon in which the resin at the gate solidifies and stops flowing, and the time it takes for the resin at the gate to solidify and stop flowing is called the gate sealing time. If the dwell pressure is stopped before the gate sealing time, the molten resin will flow back through the gate into the injection molding machine, resulting in poor filling and weight loss. On the other hand, if the dwell pressure is stopped after the gate sealing time, the gate will have solidified and the resin will not flow back, resulting in a stable injection-molded product. For this reason, the gate sealing time is an indicator that is always measured at the molding site.

[0016] The gate sealing time may be determined as the time at which the weight of the injection-molded product is maximized, after the molding conditions are set so as to minimize the time until gate sealing occurs. In this case, the time until gate sealing occurs and the weight of the injection-molded product may be obtained by experiment (weighing). Alternatively, the time until gate sealing occurs and the weight of the injection-molded product may be obtained by simulation using flow analysis instead of experiment.

[0017] Alternatively, the gate seal time is the time when the temperature at the center of the gate reaches the flow stop temperature T S At this time, the temperature at the center of the gate reaches the flow stop temperature T S The time point at which the value of the saturation voltage Vs reaches the threshold value Vs may be obtained by experiment or may be determined by simulation.

[0018] Flow stop temperature T S may be the inflection point when the resin is cooled at a cooling rate in the range of 1°C / min to 50°C / min in specific heat measurement.

[0019] Or, the flow stop temperature T S may be calculated by the following formula (1) using data fitting coefficients b5 and b6 of the 2-DOMAIN TAIT PVT model for PVT data showing the relationship between pressure, volume, and temperature of the resin. TS =b5+b6×P (1) T S :Flow stop temperature P: Pressure b5, b6: Coefficients

[0020] FIG. 2 shows specific examples of PVT data for a thermoplastic resin. The relationship between pressure, specific volume, and temperature for the resin is shown in FIG. 2. As shown in FIG. 2, coefficient b5 is the temperature at the inflection point when the pressure is 0 MPa. That is, the slope of the relationship between temperature and specific volume at a pressure of 0 MPa changes with the point where the temperature is equal to coefficient b5 as the inflection point, indicating a solid-liquid phase transition. Also, as shown in FIG. 2, coefficient b6 can be determined from the pressure dependence of the inflection point. That is, coefficient b6 is the slope of the line connecting the inflection points for each pressure.

[0021] Following dwelling, the injection-molded product is cooled within the mold for a predetermined cooling time (in-mold cooling). After the cooling time has elapsed, the mold is opened and the injection-molded product is pushed out of the mold by the ejector pins and released. The mold is then closed again to form a mold cavity, and the next injection-molded product can be obtained. The released injection-molded product can then be cooled outside the mold (ex-mold cooling). Ex-mold cooling can continue, for example, until the injection-molded product reaches room temperature.

[0022] Residual stress may occur in injection-molded products obtained by such injection molding, but there is a problem in that it is difficult to predict the residual stress with sufficient accuracy. Therefore, an object of the present disclosure is to provide a residual stress prediction method and a residual stress prediction program that can predict the residual stress occurring in a resin molded product with good accuracy.

[0023] Hereinafter, an embodiment according to the present disclosure will be described with reference to the accompanying drawings. The embodiment described below is an example and should not be construed as being limited by this description.

[0024] [Method for predicting residual stress generation behavior] 3 is a flow diagram showing a residual stress prediction method according to one embodiment of the present invention, which performs coupled analysis in which the results of flow analysis are applied to structural analysis.

[0025] As shown in FIG. 3, the residual stress prediction method according to one embodiment includes the steps of acquiring physical property values ​​for analysis (step S101), creating an analytical model (step S102), calculating the temperature distribution and pressure distribution in the process of injecting and molding a thermoplastic resin (injection molding process) (step S103), calculating the temperature distribution in the cooling process after demolding (step S104), calculating the temperature load distribution (step S105), calculating the elastic constant matrix (step S106), and calculating the residual stress (step S107).

[0026] [Acquisition of physical properties for analysis (Step S101)] In the step of acquiring physical property values ​​for analysis (step S101), the physical property values ​​of the thermoplastic resin are acquired. Specifically, for example, a viscoelasticity measuring device is used to acquire the Young's modulus of the thermoplastic resin. Furthermore, PVT data representing the relationship between the pressure, volume, and temperature of the thermoplastic resin is acquired by actual measurement. Furthermore, the Poisson's ratio of the thermoplastic resin is acquired based on the Young's modulus and the PVT data.

[0027] [Creating an analytical model (step S102)] In the step of creating an analytical model (step S102), the shape of the injection-molded product is divided into tiny elements, and a model to be used in running the simulation is created. Here, the shape of the injection-molded product (which may be the design shape of the injection-molded product or the shape of the mold, etc. The shape of the mold also includes conditions such as the position, number, and size of runners and gates) is input into a computer using, for example, a 3D shape measurement or CAD system. Next, the shape input into the computer is divided into multiple 3D elements using an element division preprocessor or the like, and an analytical model is created.

[0028] FIG. 4 shows a specific example of the shape of a resin molded product. In FIG. 4, the upper figure is a perspective view of the resin molded product, and the lower figure is a plan view of the resin molded product. As shown in this figure, the resin molded product may be, for example, an insert-molded product obtained by inserting a cylindrical metal insert member 12 into a resin member 10. The resin member 10 shown in FIG. 4 has an inner diameter of 25 mm, an outer diameter of 39 mm, and a height of 30 mm, while the metal insert member 12 has an inner diameter of 21 mm, an outer diameter of 25 mm, and a height of 45 mm. The resin member 10 can be formed, for example, using Polyplastics' Duracon (registered trademark) POM M90-44 (unfilled material), and the metal insert member 12 can be formed, for example, using titanium.

[0029] A specific example of an analytical model of such a resin molded product is shown in FIG. 5. In the analytical model shown in FIG. 5, the resin portion and the metal insert portion corresponding to the resin member 10 and the metal insert member 12 in FIG. 4 are divided into elements using tetrahedral elements, respectively. The shape of the elements may be selected from, for example, tetrahedral primary elements, secondary elements, hexahedral primary elements, secondary elements, etc. High calculation accuracy can be obtained by increasing the number of element divisions and making each element sufficiently fine, but a large number of element divisions results in a long calculation time. Therefore, it is preferable to adopt an appropriate number of element divisions taking into consideration the calculation accuracy, calculation time, etc.

[0030] In this embodiment, an example will be described in which the same analysis model is carried over from the flow analysis to the structural analysis in the coupled analysis of the flow analysis and the structural analysis. However, the analysis may be performed by preparing a flow analysis model and a separate structural analysis model.

[0031] [Calculation of temperature distribution and pressure distribution (step S103)] In the step of calculating the temperature distribution and pressure distribution in the injection molding process of the thermoplastic resin (step S103), a flow analysis (simulation) of the injection molding is performed using the created analytical model. That is, the flow analysis calculates the temperature and pressure of each element of the analytical model in the process of injecting and molding the thermoplastic resin (which may include the in-mold cooling process). This makes it possible to calculate the temperature distribution and pressure distribution of the analytical model in the injection molding process.

[0032] When performing a flow analysis, the physical property values ​​of the thermoplastic resin used in injection molding are input. The physical property values ​​used in the flow analysis include PVT data, thermal conductivity data, specific heat data, etc.

[0033] The specific heat of a thermoplastic resin can be measured, for example, by a differential scanning calorimetry (DSC). The thermal conductivity of a thermoplastic resin can be determined, for example, by the AC steady-state method (ISO 22007-3). Methods for measuring thermal conductivity include the AC steady-state method, the hot-wire method, and the hot-disk method, but the AC steady-state method can determine thermal conductivity with good accuracy.

[0034] After entering the physical property values, the analysis conditions for thermoplastic resin flow analysis are entered. Molding conditions include resin (cylinder) temperature, mold temperature, injection speed, dwell pressure, and dwell time. The mold temperature may be set to be equal to the cooling water temperature or heater set temperature.

[0035] The molding conditions also include the specification of the time start and end points of the flow analysis. The start point of the flow analysis can be, for example, the time when the thermoplastic resin starts to be injected from the mold gate into the cavity. On the other hand, the end point of the flow analysis can be, for example, the time when the cooling time ends after the molten thermoplastic resin is injected into the mold cavity and before the resin is released from the mold. In particular, the end point of the flow analysis can be the time when the resin is released from the mold. The time when the resin is released in the flow analysis can be the time when a predetermined time has elapsed since the start of injection (which may be determined based on the time until the resin is released in the actual process).

[0036] [Calculation of temperature distribution during cooling process after demolding (step S104)] In the step of calculating the temperature distribution in the cooling process after demolding (outside-mold cooling) (step S104), the temperature distribution of each element of the analytical model in the cooling process after demolding (outside-mold cooling) is calculated using the temperature distribution calculated in step S103. This step S104 can be realized by analysis using structural analysis software.

[0037] The time starting point for an out-of-mold cooling analysis can be, for example, the time of mold release. For an analysis of the inside of the mold, a finite element model of the mold is used to model the mold itself in addition to the injection-molded part and to consider the interaction between the injection-molded part and the mold. On the other hand, for an analysis of the outside of the mold, a model of the mold itself is not necessary, so the model and boundary conditions of the injection-molded part are significantly changed.

[0038] The time end point of the out-of-mold cooling analysis can be, for example, the time when the injection-molded product reaches room temperature outside the mold. Here, the time when the injection-molded product reaches room temperature outside the mold can be specified, for example, according to the time from the start of injection in an actual process until the injection-molded product reaches room temperature outside the mold. Alternatively, for example, the time when the temperature of the injection-molded product reaches room temperature in the out-of-mold cooling analysis can be determined. Generally, the time when a predetermined time has elapsed since the start of injection can be set as the end point of the out-of-mold cooling analysis.

[0039] [Calculation of temperature load distribution (step S105)] In the step of calculating the temperature load distribution (step S105), the temperature load distribution of the injection-molded product is calculated using the temperature distribution and pressure distribution calculated in steps S103 and S104. Here, the volumetric shrinkage distribution of the injection-molded product is obtained from the temperature distribution and pressure distribution, and the temperature load distribution is obtained by converting the change in volume into a temperature difference based on the volumetric shrinkage distribution.

[0040] The volumetric shrinkage distribution of an injection molded product is calculated as follows. First, the temperature (T1) and pressure (P1) at a certain point before shrinkage are determined from the temperature and pressure distributions obtained by flow analysis. These temperature (T1) and pressure (P1) are then applied to the PVT data of the thermoplastic resin to convert them into the volume before shrinkage (V1).

[0041] For example, in the PVT data shown in Figure 2, when the temperature is 200°C and the pressure is 50 MPa, the specific volume is approximately 0.82 cm 3 / g. In other words, at a certain point before shrinkage, the volume per unit weight (1 g) of a thermoplastic resin with T1 = 200 °C and P1 = 50 MPa is V1 = approximately 0.82 cm 3 is.

[0042] Similarly, the temperature (T2) and pressure (P2) at a certain point after shrinkage can be determined from the temperature and pressure distributions obtained by flow analysis. These temperature (T2) and pressure (P2) are then applied to the PVT data of the thermoplastic resin to convert them into the volume after shrinkage (V2). Note that this certain point after shrinkage may be specified as the point when a predetermined time has elapsed since the start of injection (for example, it may be determined by comparing it with the time it takes for the injection-molded product to reach the mold temperature in an actual process).

[0043] For example, in the PVT data shown in Figure 2, when the temperature is 40°C and the pressure is 50 MPa, the specific volume is approximately 0.70 cm 3 / g. In other words, if a point after shrinkage is the point at which the thermoplastic resin is cooled to 40°C, and T2 = 40°C and P2 = 50 MPa, the volume per unit weight (1 g) of the thermoplastic resin at this point is V2 = approximately 0.70 cm 3 is.

[0044] Next, the volumetric shrinkage rate ΔV of each element is calculated from the volume (V1, V2) of each element before and after shrinkage using the following formula (2), and the distribution of the volumetric shrinkage rate ΔV is obtained.

number

[0045] In other words, when the pressure is constant at 50 MPa (P1 = P2 = 50 MPa) and the temperature is cooled from T1 = 200°C to T2 = 40°C, the volumetric shrinkage rate ΔV can be calculated as (0.70 - 0.82) / 0.70 = -0.146, or -14.6%.

[0046] Even if the pressure before and after shrinkage is not constant, the temperature (T1) and pressure (P1) of each element before shrinkage and the temperature (T2) and pressure (P2) of each element after shrinkage are calculated by flow analysis, so the volumetric shrinkage rate ΔV of each element can be calculated from the temperatures (T1, T2) at the pressures (P1, P2) before and after shrinkage and the PVT data.

[0047] Once the volumetric shrinkage rate is calculated, the volumetric shrinkage rate of each element is divided by the volumetric expansion rate of the thermoplastic resin to convert it into a temperature difference, thereby calculating the temperature load (temperature difference). The volumetric expansion rate is the coefficient β in the relational equation ΔV / V = βΔT when the original volume V changes by ΔV due to a temperature rise ΔT, and is a value that indicates the rate of volume change per unit temperature. While the volumetric expansion rate is generally calculated from PVT data, if the thermoplastic resin is isotropic, the volumetric expansion rate is three times the linear expansion rate. Therefore, the volumetric expansion rate of a thermoplastic resin may be obtained from a previously measured linear expansion rate instead of from PVT data. The volumetric expansion rate and linear expansion rate (sometimes collectively referred to as the "thermal expansion rate") may be temperature-dependent.

[0048] The temperature load refers to the "temperature difference before and after shrinkage" of a thermoplastic resin, and is distinct from the difference between the "temperature at a certain point before shrinkage" and the "temperature at a certain point after shrinkage" used in the process of calculating the volumetric shrinkage distribution. The difference between the "temperature at a certain point before shrinkage" and the "temperature at a certain point after shrinkage" mentioned above is calculated simply from the temperature. In contrast, the temperature load is calculated using temperature and pressure, not just temperature, because the volume is first calculated from temperature and pressure using PVT data, and then the calculated volume is converted back to temperature using the volumetric expansion coefficient. Therefore, the temperature load is a temperature difference that takes into account the effect of pressure on a thermoplastic resin during actual molding, and is therefore different from a temperature difference calculated simply as a temperature difference.

[0049] In this embodiment, the temperature load calculated as above is corrected by a temperature load correction coefficient. That is, since the resin portion during molding is constrained by the mold, the volumetric shrinkage rate of this resin portion is smaller than the volumetric shrinkage rate calculated using the temperature and pressure as described above, and the temperature load is also smaller. Therefore, the temperature load of the resin being injection molded is corrected using the temperature load correction coefficient μ according to the following equation (3):

number

[0050] Since the rate at which the volumetric shrinkage rate of the resin part during molding decreases is thought to depend on the shape of the resin part, the temperature load correction coefficient μ is a value that indicates the difference in volume change depending on the shape of the thermoplastic resin. Such a temperature load correction coefficient μ is calculated from the ratio of the volumetric shrinkage rate of a resin in a shape that can shrink freely, such as a flat plate or strip-shaped test piece, to the volumetric shrinkage rate of a resin in a shape that has steps and is restricted by the mold.

[0051] When the elastic constant matrix is ​​corrected as described later, the temperature load does not need to be corrected using the temperature load correction coefficient μ.

[0052] [Calculation of Elastic Constant Matrix (Step S106)] In the step of calculating the elastic constant matrix (step S106), an elastic constant matrix, which is a proportional constant between the stress vector and the strain vector, is calculated. Generally, the relationship between the stress vector [σ] and the strain vector [ε] is expressed by the following equation (4) using the elastic constant matrix [D]. [σ] = [D][ε] (4) [σ]: stress vector [D]: Elastic constant matrix [ε]: strain vector

[0053] When the thermoplastic resin is isotropic, the elastic constant matrix [D] is as shown in the following equation (5).

number

[0054] Here, since the elastic constant matrix [D] is temperature dependent, the residual stress changes depending on the ambient temperature. Normally, residual stress is measured at room temperature, so the value at room temperature is often used for the elastic constant matrix [D], and in the following, the residual stress will be the value in the room temperature environment. The stress of the resin changes over time from when the injection-molded resin starts to shrink until it reaches room temperature, and this amount of change in stress is called stress relaxation. When calculating residual stress, it is preferable to take stress relaxation into consideration. Therefore, in this embodiment, the elastic constant matrix correction coefficient K, which corresponds to stress relaxation, is used. relx The elastic constant matrix used to calculate the residual stress is calculated by correcting the elastic constant matrix at room temperature using the formula: In other words, the elastic constant matrix [D'] used to calculate the residual stress is calculated using the following formula (6). [D']=[D(T rt )]×K relx ···(6) [D']: Elastic constant matrix after correction [D(T rt )]: Elastic constant matrix at room temperature K relx : Elastic constant matrix correction coefficient

[0055] Elastic constant matrix correction factor K relx is a value that indicates the difference in volume change due to the shape of the thermoplastic resin, similar to the temperature load correction coefficient μ mentioned above. Therefore, the elastic constant matrix correction coefficient K relx is calculated from the ratio of the volumetric shrinkage rate of a resin in a shape that can shrink freely, such as a flat plate or strip-shaped test piece, to the volumetric shrinkage rate of a resin in a shape that has a step and whose shrinkage is restricted by a mold.

[0056] In addition, when the temperature load correction coefficient μ is used to correct the temperature load, the elastic constant matrix correction coefficient K relx The elastic constant matrix correction coefficient K relx When it is difficult to identify the elastic constant matrix correction factor K relxWithout using relx In other words, when calculating the residual stress of an injection-molded product, calculations are performed on the process of cooling the molten resin, so the elastic constant matrix correction coefficient K relx In order to measure the actual shrinkage, it is necessary to consider the effect of shrinkage due to cooling, and the elastic constant matrix correction coefficient K relx In such cases, the change in the elastic constant matrix due to stress relaxation can be expressed by temperature correction, taking advantage of the fact that the Young's modulus included in the elastic constant matrix is ​​temperature dependent, and the corrected temperature T relx The elastic constant matrix corresponding to the above may be used as the corrected elastic constant matrix [D']. [D']=[D(T relx )] ···(7) [D']: Elastic constant matrix after correction [D(T)]: Elastic constant matrix at temperature T T relx : Corrected temperature

[0057] The corrected temperature T relx In setting the temperature load correction coefficient μ, the temperature at which the ratio of Young's modulus at room temperature to the temperature load correction coefficient μ is determined is called the corrected temperature T relx It may also be possible to use the following.

[0058] In this way, in the temperature load distribution calculation step (step S105) and the elastic constant matrix calculation step (step S106), at least one of the temperature load and the elastic constant matrix is ​​corrected and calculated. This correction takes into account the volumetric shrinkage in the mold during the cooling process of the injection-molded resin, and the temperature load and the elastic constant matrix that reflect the actual volumetric shrinkage can be calculated by the correction. Then, by calculating the residual stress using such a temperature load and elastic constant matrix, the accuracy of the residual stress prediction can be improved.

[0059] [Calculation of residual stress (step S107)] In the step of calculating the residual stress (step S107), the elastic constant matrix [D] at room temperature or the corrected elastic constant matrix [D'] and the temperature load T before or after correction are calculated. L A structural analysis is performed using the above and the strain and stress generated in each element of the analytical model are calculated. Since the temperature load or elastic constant matrix is ​​corrected taking into account the volumetric shrinkage in the mold, the residual stress can be calculated with good accuracy based on the temperature load and elastic constant matrix.

[0060] Next, examples of the residual stress prediction method according to the present embodiment (hereinafter also referred to simply as the "improved method") and comparative examples of the conventional method will be shown to specifically explain the residual stress prediction according to the present disclosure. Note that the technology of the present disclosure is not limited to these examples.

[0061] (Product shape and molding material) In the following example, we will explain how to predict residual stress in a resin molded product shown in Figure 4. As described above, the resin molded product shown in Figure 4 has a resin member 10 and a metal insert member 12. The resin member 10 has an inner diameter of 25 mm, an outer diameter of 39 mm, and a height of 30 mm, and the metal insert member 12 has an inner diameter of 21 mm, an outer diameter of 25 mm, and a height of 45 mm. The resin member 10 is made of Polyplastics' Duracon POM M90-44 (unfilled material), and the metal insert member 12 is made of titanium. The specific heat of the molding material was measured using a differential scanning calorimeter (DSC), and the thermal conductivity was determined using a thermal conductivity measurement method called the AC steady-state method (ISO 22007-3).

[0062] Furthermore, to measure the residual stress of the resin molded product, the strain of the metal insert member 12 was measured. Specifically, as shown in Fig. 6, a strain gauge 14 was attached to the inner surface of the cylindrical metal insert member 12, and the strain gauge 14 was connected to a strain measuring device (not shown) using a cable 16. The strain gauge 14 used was KFU-2-120-D17-11 manufactured by Kyowa Electronics Co., Ltd.

[0063] For the flow analysis in the examples and comparative examples, Autodesk's Moldfrow (registered trademark) Insight 2023 (3D solid model) (hereinafter referred to as "Moldfrow") was used. For the out-of-mold cooling analysis and structural analysis in the examples, ADVENTURECluster 2021 (hereinafter referred to as "ADVC") from Allied Engineering Co., Ltd. was used. For the calculation of the temperature load distribution and elastic constant matrix distribution in the examples (steps S105 and S106), a conversion program created by ourselves using Visual Basic (registered trademark) was used.

[0064] Example 1 The molding conditions for the actual molded products were set as follows: barrel temperature 200°C, cooling water temperature 80°C, injection speed 20 mm / s, dwell pressure 50 MPa, dwell time 26 seconds, and cycle time 47 seconds, and test samples were obtained under these molding conditions.

[0065] From the difference between the value of the strain gauge 14 before injection molding and the value of the strain gauge 14 when the strain reaches equilibrium after injection molding, the strain of the metal insert member 12 is −4.2×10 -4 A negative strain value indicates a compression state.

[0066] The Young's modulus of the thermoplastic resin at room temperature was measured according to ISO 527-1 and ISO 527-2, and was found to be 2500 MPa. The Poisson's ratio of the thermoplastic resin at room temperature was determined from the strain in the tensile direction and the perpendicular direction using a strain gauge soldered to a test piece for Young's modulus measurement, and was found to be 0.35. The viscosity of the thermoplastic resin at each temperature was determined using a Toyo Seiki Capillograph 1D with an orifice length of 20 mm and an orifice diameter of 1 mm.

[0067] In Example 1, the volumetric shrinkage distribution of the injection-molded product (interior and surface) was calculated using a conversion program based on the temperature distributions obtained by the injection, pressure-holding, and in-mold cooling analyses and the temperature distribution obtained by the out-mold cooling analysis. The temperature load was then corrected by setting the temperature load correction coefficient μ in Equation (3) to 0.16, and the obtained temperature load was set in the 1 / 4 model for structural analysis shown in Figure 7. The temperature load distribution according to Example 1 is shown in Figure 8.

[0068] The constraint conditions during structural analysis are shown in Figure 9. As shown in Figure 9, the resin part and part of the metal insert part were constrained in the direction perpendicular to the surface, and the upper end of the metal insert part was constrained in the side direction.

[0069] In Example 1, the elastic constant matrix correction coefficient K relx was set to 1, and the elastic constant matrix [D'] after correction in equation (6) above was set. As a result of performing a structural analysis calculation under the above conditions, the strain in the metal insert was -4.2 × 10 -4 The stress distribution in the resin part according to Example 1 is shown in FIG.

[0070] Example 2 In Example 2, the temperature load correction coefficient μ is set to 1, and the elastic constant matrix correction coefficient K relx was set to 0.16, and the elastic constant matrix [D'] after correction in the above formula (6) was set. The other conditions were the same as in Example 1, and as a result of performing a structural analysis calculation, the strain in the metal insert part was -4.2 × 10 -4 The stress distribution in the resin part according to Example 2 is shown in FIG.

[0071] Example 3 In Example 3, the temperature load correction coefficient μ is set to 1, and the corrected temperature T relx The temperature was set to 122°C, and the elastic constant matrix [D'] after correction of the above formula (7) was set. The other conditions were the same as in Example 1, and as a result of performing a structural analysis calculation, the strain in the metal insert part was -4.2 × 10-4 The stress distribution in the resin part according to Example 3 is shown in FIG.

[0072] (Comparative Example) In the comparative example relating to the conventional method, flow analysis was performed using Autodesk Moldflow Insight 2023 for the same analytical model as in Examples 1 to 3. The strain in the metal insert was -2.1 × 10 -9 The stress distribution in the resin part of the comparative example is shown in FIG.

[0073] FIG. 14 is a diagram showing a list of Examples 1 to 3 and a Comparative Example. As shown in the figure, in Example 1, the temperature load was corrected using a temperature load correction coefficient, in Example 2, the elastic constant matrix was corrected using an elastic constant matrix correction coefficient, and in Example 3, the elastic constant matrix was corrected using the corrected temperature. As a result, in each Example, values ​​calculated for the strain occurring in the metal insert portion were nearly identical to the measured values, whereas in the Comparative Example, values ​​calculated for the strain occurring in the metal insert portion were significantly smaller than the measured values. Furthermore, in the Comparative Example, the maximum stress in the resin portion was 88 MPa, which is greater than the tensile strength of 62 MPa for Duracon POM M90-44. Therefore, although fracture was predicted from the analysis results, fracture was not observed in the actual molded product. In this regard, in Examples 1 to 3, the stress in the resin portion was less than the tensile strength of the actual thermoplastic resin, resulting in results consistent with the fracture state of the actual molded product.

[0074] The residual stress prediction method according to the present disclosure can be executed by an information processing device. Fig. 15 is a block diagram showing an example of the hardware configuration of an information processing device 100 that executes the residual stress prediction method. As shown in Fig. 15, the information processing device 100 includes a processor 101, a main memory device 102, an auxiliary memory device 103, an I / O (Input / Output) interface 104, and a network interface (hereinafter abbreviated as "NW interface") 105.

[0075] The processor 101 includes, for example, a central processing unit (CPU), a field programmable gate array (FPGA), or a digital signal processor (DSP), and controls the entire information processing device 100 and executes various types of arithmetic processing.

[0076] The main storage device 102 includes, for example, a random access memory (RAM) or a read only memory (ROM), and stores information used in the arithmetic processing executed by the processor 101.

[0077] The auxiliary storage device 103 includes, for example, a hard disk drive (HDD) or a solid state drive (SSD), and stores various programs and data.

[0078] The I / O interface 104 is an interface through which a user inputs information and outputs information to a user, and may include, for example, a keyboard, a display, a touch panel, a microphone, or a speaker.

[0079] The NW interface 105 is an interface for connecting to a network via wire or wirelessly.

[0080] The information processing device 100 acquires analytical property values, such as Young's modulus and PVT data, measured using a test piece, via the I / O interface 104 and the NW interface 105. The processor 101 then executes a program stored in the auxiliary storage device 103 while using the main storage device 102 to create an analytical model and perform flow analysis and structural analysis. Furthermore, the processor 101 calculates the volumetric shrinkage rate and temperature load of the analytical model from the results of the flow analysis and structural analysis, and calculates an elastic constant matrix. The processor 101 then predicts residual stress based on the calculated temperature load and elastic constant matrix.

[0081] The processes executed by the information processing device 100 can also be written as a computer-executable program. In this case, the program can be stored on a computer-readable, non-transitory recording medium and installed on the computer. Examples of such recording media include portable recording media such as CD-ROMs, DVD discs, and USB memory, as well as semiconductor memories such as flash memories. [Explanation of symbols]

[0082] 101 processors 102 Main storage 103 Auxiliary storage device 104 I / O Interface 105 Network Interface

Claims

1. A residual stress prediction method for predicting residual stress generated in an injection-molded product obtained by injection molding a thermoplastic resin into a mold, comprising: acquiring physical property values ​​of the thermoplastic resin; creating an analytical model in which the injection-molded product is divided into a plurality of elements; acquiring a temperature distribution and a pressure distribution of the analysis model in a molding process of the thermoplastic resin; calculating a temperature distribution of the analysis model during a cooling process after demolding using the temperature distribution and the pressure distribution; calculating a temperature load distribution of the analysis model based on the temperature distribution and pressure distribution in the forming process and the temperature distribution in the cooling process; Calculating an elastic constant matrix distribution that indicates a relationship between a strain vector and a stress vector in the thermoplastic resin; and calculating strain and stress generated in each element of the analysis model by structural analysis using the temperature load distribution and the elastic constant matrix distribution, At least one of the step of calculating the temperature load distribution and the step of calculating the elastic constant matrix distribution includes: The temperature load distribution or the elastic constant matrix distribution is corrected in accordance with a difference in volume change due to the shape of the thermoplastic resin. Residual stress prediction method.

2. The step of calculating the elastic constant matrix distribution includes: Elastic constant matrix correction coefficient K corresponding to the difference in volume change due to the shape of the thermoplastic resin relx Correct the elastic constant matrix distribution using formula (A) The residual stress prediction method according to claim 1 . [D’]=[D(T rt )]×K relx ・・・(A) [D']: Elastic constant matrix after correction [D(T rt ) ]: Elastic constant matrix at room temperature K relx : Elastic constant matrix correction coefficient

3. The step of calculating the elastic constant matrix distribution includes: The corrected temperature T is set according to the difference in volume change due to the shape of the thermoplastic resin. relx Correct the elastic constant matrix distribution using equation (B) The residual stress prediction method according to claim 1 . [D’]=[D(T relx )] ・・・(B) [D']: Elastic constant matrix after correction [D(T)]: Elastic constant matrix at temperature T T relx : Corrected temperature

4. The step of calculating the temperature load distribution includes: The temperature load distribution is corrected by the formula (C) using a temperature load correction coefficient μ corresponding to the difference in volume change due to the shape of the thermoplastic resin. The residual stress prediction method according to claim 1 . [Equation 1] T L : Temperature load after correction μ: Temperature load correction coefficient ΔV: volumetric shrinkage rate β: Volume expansion rate

5. The step of calculating the temperature load distribution includes: A step of calculating a volumetric shrinkage rate ΔV with the gate seal time as the time start point and the time point when a predetermined time has elapsed since the start of injection as the time end point. The residual stress prediction method according to claim 4 .

6. The gate seal time is In the flow analysis of the analytical model, molding conditions are set so that the time until gate sealing occurs is minimized, and the time is determined as the time when the weight of the injection molded product reaches its maximum. The residual stress prediction method according to claim 5 .

7. The gate seal time is Determined as the time until the temperature at the center of the gate reaches the temperature at which the flow stops. The residual stress prediction method according to claim 5 .

8. The flow stop temperature is For the PVT data showing the relationship between the pressure, volume, and temperature of the resin, the data fitting coefficient b of the 2-DOMAIN TAIT PVT model is 5 and b 6 Using the formula (D), The residual stress prediction method according to claim 7. T S =b 5 +b 6 ×P ・・・(D) T S Flow stopping temperature P: Pressure b 5 , b 6 :coefficient

9. The flow stop temperature is In specific heat measurement, this is the inflection point when cooling a thermoplastic resin at a cooling rate ranging from 1°C / min to 50°C / min. The residual stress prediction method according to claim 7.

10. The step of acquiring the temperature distribution and the pressure distribution includes: The thermal conductivity obtained by the thermal conductivity measurement method using the AC steady-state method (ISO22007-3) is used in the calculation. The residual stress prediction method according to claim 1 .

11. A residual stress prediction program that causes a computer to execute the residual stress prediction method according to claim 1.

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