JP7156119B2 - Method for Predicting Stress-Strain Properties of Fiber Reinforced Resin Molded Products - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Act September 11, 2018, Article 43 published on the website (http://www.jscm.gr.jp/schedule/2018/43CMsympo/login.php) Presented in the proceedings of the Composite Materials Symposium. [Publications, etc.] Announced at the 43rd Composite Materials Symposium on September 14, 2018.

The present disclosure relates to a method for predicting stress-strain characteristics of fiber-reinforced resin molded articles.

Conventionally, the mechanical properties of fiber-reinforced resin materials have been predicted by CAE (Computer Aided Engineering) (see Patent Document 1, for example).

In addition, it is known that the mechanical properties of fiber-reinforced resin materials can be influenced by fiber-resin interface properties (see, for example, Non-Patent Document 1).

JP 2013-36897 A

J. Rosenthal: Polym. Compo. , 13, 6 (1992), p462-p466

However, although Patent Document 1 mentions using the interfacial strength of the interface between the fiber and the resin contained in the fiber-reinforced resin material as one of the input parameters used for analysis, a specific method has not been disclosed.

Therefore, an object of the present disclosure is to provide a method for accurately predicting the stress-strain characteristics of a fiber-reinforced resin molded product while suppressing the amount of calculation.

In order to solve the above problems, the stress-strain characteristic prediction method of a fiber reinforced resin molded product according to the first technology disclosed herein includes image data of a sample of a fiber reinforced resin molded product that serves as a reference, and the sample creating a representative volume element based on the fiber length data and orientation data of the fiber contained in the representative volume element, and for each of the fiber, the resin, and the fiber-resin interface, the total number of elements of the representative volume element is a predetermined number of elements A finite element mesh is created by the finite element method so that the following is obtained, and the functions indicating the stresses of the fibers, the resin, and the fiber-resin interface are added according to their content ratios, and the representative a step of creating a model function that indicates the stress-strain characteristics of the entire volume element; material characteristic values of the fiber and the resin; It is characterized by comprising a step of obtaining a regression formula by regressing a model function, and a step of predicting the stress-strain characteristics of an arbitrary fiber reinforced resin molded product based on the regression formula.

According to this technology, the measured data of the interfacial strength of the fiber-resin interface is regressed to the model function to obtain the regression equation, so that the model function that takes into account the interfacial strength of the fiber-resin interface can be identified. Volume elements can be divided into three types, fiber, resin, and fiber-resin interface, and each can be modeled by mesh division by the finite element method. Thus, it is possible to accurately predict the stress-strain characteristics of fiber-reinforced resin moldings.

A second technique is characterized in that, in the first technique, the function indicating the stress at the fiber-resin interface is described using a bonding force model.

The cohesive force model is a function called CZM (Cohesive Zone Model), and can directly consider the interfacial strength. According to the present technology, since the interface strength can be directly considered, the stress-strain characteristics of the fiber-reinforced resin molded product can be predicted with high accuracy.

A third technique is characterized in that, in the first or second technique, the measured data of the interfacial strength of the fiber-resin interface is measured by a nanoindentation method.

The nanoindentation method can more accurately measure the strength of the interface between the resin portion and the fiber portion of the sample piece by pressing the fiber portion of the sample piece cut out from the molded product with a fine probe. According to the present technology, since the regression equation is obtained using the measured data of the interfacial strength measured by the nanoindentation method, the stress-strain characteristics of the fiber-reinforced resin molded product can be predicted with higher accuracy.

A fourth technique is characterized in that, in any one of the first to third techniques, the fiber-reinforced resin molded product is an injection molded product.

The fiber reinforced resin molded product obtained by injection molding has a random fiber length and fiber orientation of the fibers contained in the resin, and the content ratio and orientation may differ depending on the part of the molded product. Formulation of the model function is difficult, and analysis by CAE can be difficult. According to this technology, even in a fiber-reinforced resin molded product obtained by injection molding, a function indicating the stress-strain characteristics of fiber, resin, and fiber-resin interface is added according to the content ratio, Since a model function representing the stress-strain characteristics of is created, it is possible to accurately predict the stress-strain characteristics of fiber reinforced resin molded products.

As described above, according to the present disclosure, the measured data of the interfacial strength of the fiber-resin interface is regressed to the model function to obtain the regression equation, so the model function that takes into account the interfacial strength of the fiber-resin interface is identified. The representative volume elements can be divided into three types, fiber, resin, and fiber-resin interface, and each of them can be modeled by mesh division by the finite element method. Thus, it is possible to accurately predict the stress-strain characteristics of fiber-reinforced resin moldings.

It is a flow for explaining a stress-strain characteristic prediction method according to one embodiment. It is a perspective view which shows an example of a fiber reinforced resin molding. It is a microfocus X-ray CT image of a fiber-reinforced resin molded product. FIG. 3 is a perspective view showing a portion of a meshed representative volume element (RVE); It is a figure for demonstrating cutting of the test piece used in a nanoindentation method. It is a figure for demonstrating the measurement procedure of a nanoindentation method. 4 is a graph showing the relationship between displacement and load of a microprobe measured using the nanoindentation method. It is a graph which shows the result of the tensile test of a PP molded article. 4 is a graph showing the distribution of fiber lengths obtained in a fiber length measurement test. FIG. 10 is a diagram plotting interface shear strength values against the MA content ratio in the resin for test materials 3 to 8. FIG. 2 is a graph comparing tensile test results and CAE calculation results for stress-strain characteristics of test materials 1 and 2. FIG.

Hereinafter, embodiments of the present disclosure will be described in detail based on the drawings. The following description of preferred embodiments is merely exemplary in nature and is in no way intended to limit the disclosure, its applicability or its uses.

(one embodiment)
<Fiber-reinforced resin molded product>
The stress-strain characteristic prediction method according to the present embodiment is preferably applied to fiber-reinforced resin molded articles (hereinafter also simply referred to as "molded articles"). .

-resin-
The resin is a base material for forming the skeleton of the molded product, and is a thermosetting resin or a thermoplastic resin. Specific examples of resins include polyolefin resins such as polypropylene resin (PP) and maleic anhydride-modified polypropylene (MAHPP), epoxy resins (hereinafter sometimes referred to as "epoxy"), phenolic resins, unsaturated Polyester resin, vinyl ester resin, polycarbonate resin, polyester resin, polyamide (PA) resin, liquid crystal polymer resin, polyether sulfone resin, polyether ether ketone resin, polyarylate resin, polyphenylene ether resin, polyphenylene sulfide (PPS) resin , polyacetal resins, polysulfone resins, polyimide resins, polyetherimide resins, polystyrene resins, modified polystyrene resins, AS resins (copolymers of acrylonitrile and styrene), ABS resins (copolymers of acrylonitrile, butadiene and styrene), modified ABS resins, Examples include MBS resin (methyl methacrylate, butadiene and styrene copolymer), modified MBS resin, polymethyl methacrylate (PMMA) resin, modified polymethyl methacrylate resin, and the like. These may be used singly or in combination of two or more.

-fiber-
Fibers are materials added to resins mainly for the purpose of improving the strength of fiber-reinforced resin molded articles. Examples include silicon carbide fiber, boron fiber, silicon carbide fiber, and the like. Examples of CF include polyacrylonitrile (PAN-based), pitch-based, cellulose-based, vapor-grown carbon fibers using hydrocarbons, and graphite fibers. As GF, E glass, S glass, or the like is used. These may be used singly or in combination of two or more.

Although the fiber diameter r is not intended to be limited, the average diameter such as a catalog value is, for example, 5 nm or more and 100 μm or less. Although the fiber length L is not intended to be limited, the fiber length obtained in the fiber length measurement test described later is, for example, 10 nm or more and 5000 μm or less. Moreover, the aspect ratio (L/r) obtained by dividing the fiber length L by the fiber diameter r is not intended to be limited, but is, for example, 5 or more, preferably 5 or more and 500 or less.

The shape of the cross section perpendicular to the longitudinal direction of the fiber is not particularly limited, but may be circular, elliptical, rectangular, polygonal, or any other shape. In other words, the shape of the fiber is treated as a cylindrical shape, an elliptical columnar shape, a square columnar shape, a polygonal columnar shape, or the like.

Moreover, the content ratio of the fibers in the molded article is, for example, 1% by mass or more and 50% by mass or less, preferably 5% by mass or more and 20% by mass or less.

－Modifiers and surface treatments－
From the viewpoint of improving the adhesiveness between the resin and the fiber, if necessary, a modifier may be added to the resin, or the fiber may be surface-treated. Examples of resin modifiers include maleic anhydride-modified polypropylene (MAHPP) and the like. The surface treatment of fibers includes plasma treatment, strong acid oxidation treatment, and the like. Addition of these modifiers and surface treatment methods may be carried out singly, or two or more of them may be used in combination.

-Other additives-
Fiber-reinforced resin molded articles may contain additives such as fillers, pigments, dyes, impact modifiers, and UV absorbers from the viewpoint of improving moldability, strength, design, functionality, etc. . These additives may be added singly or in combination.

When additives, etc. are contained in the fiber-reinforced resin molded product, the content ratio of the additive is, for example, 5% by mass in the molded product from the viewpoint of improving moldability, strength, design, functionality, etc. You can:

-Molding-
Applications of the molded product to which the method for predicting the stress-strain characteristics of a fiber-reinforced resin molded product according to the present embodiment is preferably applied include automobile parts, rockets, aircraft parts, sporting goods, and the like.

-Molding method-
The molding method is not particularly limited, and may be various known molding methods. Specific examples include injection molding, extrusion molding, vacuum molding, compression molding, autoclave molding, and resin transfer molding (RTM).

In addition, the stress-strain characteristics prediction method according to the present embodiment can efficiently predict even if there are variations in the fiber length, fiber diameter, orientation, etc. of the fiber, so the stress-strain characteristics of the injection molded product can be used particularly preferably for prediction of The fiber reinforced resin molded product obtained by injection molding has a random fiber length and fiber orientation of the fibers contained in the resin, and the content ratio and orientation may differ depending on the part of the molded product. Formulation of the model function is difficult, and analysis by CAE can be difficult. According to this technology, even in a fiber-reinforced resin molded product obtained by injection molding, a function indicating the stress-strain characteristics of fiber, resin, and fiber-resin interface is added according to the content ratio, Since a model function representing the stress-strain characteristics of is created, it is possible to accurately predict the stress-strain characteristics of fiber reinforced resin molded products.

<Method for predicting stress-strain characteristics>
FIG. 1 shows the flow of the stress-strain characteristic prediction method according to this embodiment. The stress-strain characteristic prediction method includes an RVE creation step S1, a finite element mesh creation step S2, a model function creation step S3, a regression analysis step S4, and a prediction step S5. In the following steps, commercially available CAE software such as Digimat (manufactured by e-Xtreme engineering Co., Ltd., Simpleware (manufactured by Synopsys), J-OCTA (manufactured by JSOL Co., Ltd.), Abaqus (manufactured by Intermesh Japan Co., Ltd.), etc. can be performed using

- RVE creation process -
In the RVE creation step S1, based on the image data of a sample cut out from a fiber-reinforced resin molded product as a reference, the fiber length data and orientation data of the fibers contained in the sample, and the content ratio of the fibers contained in the sample, It is the step of creating a representative volume element (RVE), a geometric model of the microstructure of the sample.

Specifically, for example, as shown in FIG. 2, a sample 100 of a molded product that serves as a reference is prepared by a manufacturing method such as injection molding. Sample 100 is, for example, a standard ISO dumbbell specimen for tensile testing.

Then, for the sample 100, as shown in FIG. 2, an end portion 101 opposite to the gate side of the dumbbell parallel portion is cut out, and a microfocus X-ray CT image (image data) shown in FIG. 3 is taken. The image data is not limited to microfocus X-ray CT images, and may be images such as FIB-SEM.

In addition, data such as the fiber length, fiber diameter, fiber content ratio, fiber orientation, etc. of the fibers contained in the molded product are obtained. Specifically, for example, the fiber length may be obtained using catalog values or obtained experimentally. As an experimental method, a part of the sample 100 is cut out, the resin component is removed by incineration, the fiber length is measured for a predetermined number of fibers, and the weight average fiber length _Lw is calculated by the following formula (1). method.

L _w = (Σ _{i Ni Li} ² )/(Σ _{i Ni Li} ) (i = 1, 2, ..., I) (1)
where N _i is the number of fibers with length L _i and I is the number of fibers with different fiber lengths.

Further, the fiber diameter may be obtained using a catalog value or obtained experimentally. Experimentally, for example, a predetermined number of fibers obtained as described above are observed under a microscope, and the average diameter is calculated. For the fiber content ratio, the charged value when the sample 100 is manufactured may be used. It should be noted that, as a constraint, it is desirable to place the fibers in the RVE such that the fiber cross-sections are not placed on the RVE surface due to convergence issues in later regression analysis.

Further, the fiber orientation data is obtained by, for example, using the CT image shown in FIG. 3, measuring the angles θ and φ shown in FIG. 2 for each fiber, and calculating the orientation tensor A represented by the following formula (2) Obtainable.

Then, from the image data, fiber length, fiber diameter, fiber content ratio, fiber orientation, and constraint conditions obtained in this manner, RVE is created, for example, assuming that the fibers are cylindrical.

-Finite element mesh creation process S2-
The RVE created in the RVE creation step S1 is divided into finite element meshes by the finite element method. At this time, the regions of the fibers, the resin, and the fiber-resin interface are individually mesh-divided. Specifically, it is desirable to perform mesh division so that the number of elements in the entire RVE is equal to or less than a predetermined number of elements, ie, one million elements or less, preferably 600,000 elements or less.

A portion of the meshed RVE is shown in FIG. 4 (reference numeral 200). For example, the fiber and resin regions can be divided by tetrahedral primary elements.

The region of the fiber-resin interface can be described using, for example, a contact sharing model, an interface layer model, a contact model, a bonding force model, and the like. A contact-sharing model is a model in which only one material property is changed. The interfacial layer model is a model in which a mesh with a constant thickness is cut around the fiber and the material properties are changed here. A contact model is a model in which fibers and resin are divided into separate meshes, and contact is defined at the boundary between them using a coefficient of friction and the like. The cohesive force model is a function called CZM (Cohesive Zone Model), and can directly consider interface strength as described later. Therefore, from the viewpoint of enabling highly accurate stress-strain property prediction, it is desirable to describe using a binding force model that can directly consider interfacial strength.

At this time, the model function indicating the stress-strain characteristics of the entire RVE uses the finite element mesh described above, and uses a function that indicates the stress of the fiber, a function that indicates the stress of the resin, and a function that indicates the stress at the fiber-resin interface. , is added according to the content ratio (mass ratio) of the fiber, resin, and fiber-resin interface in RVE.

Specifically, the function representing the stress σ of the entire RVE can be described as the following equation (3).
σ=σ ^E +σ ^P (3)
However, in Equation (3), σ ^E is the stress in the elastic region of the composite material, and σ ^P is the stress in the plastic region of the composite material.

σ ^E can be described as follows, for example, using compound velocity.
σ ^E = ασ ^E _f V _f + σ ^E _m (1−V _f ) (4)
where α is the orientation coefficient of the fiber, σ ^E _f and σ ^E _m are the elastic stresses of the fiber and matrix, respectively, and V _f is the volume fraction of the fiber. Equivalent one-property theory or the like may be used here.

σ ^P can be written as follows.
σ ^P =σ ^P _m ×f(α, L, τ _if ) (5)
Here, σ ^P _m is the stress in the plastic region of the resin, L is the fiber length, and τ _if is the interfacial strength between the fiber and the resin.

From the above, the stress of the composite material can be described as follows.
σ= ^ασE _f V _f +σ ^E _m (1−V _f )+σ ^P _m ×f(α, L, τ _if ) (6)
-Data acquisition step S3-
Data are acquired as material characteristic values to be input to the above equation (6). The data are the Young's modulus E _f of the fiber, the Young's modulus E _m of the resin, the stress-strain relationship of the resin, and the interfacial strength τ _if of the fiber-resin interface.

Literature values can be used for the Young's modulus E _f of the fiber and the Young's modulus E _m of the resin. The stress-strain relationship of the resin can be obtained experimentally as measured data (material characteristic values) by, for example, performing a tensile test on a molded product manufactured only from a resin that does not contain fibers, as described later. The interfacial strength τ _if of the fiber-resin interface can be obtained experimentally as measured data (material characteristic values) using, for example, a nanoindentation method, a microdroplet method, or the like, as described later.

In the nanoindentation method, as shown in FIGS. 5 and 6, for example, by pressing a fiber portion 12 of a thin sample piece 13 cut out from a molded product 100 with a microprobe 2, the resin portion 11 of the sample piece 13 is pushed. and the strength of the interface with the fiber portion 12 is measured. Specifically, as shown in FIG. 7, the relationship between the displacement of the microprobe 2 and the load is plotted. Calculate

τ _if =P/(πdL) (7)
However, in the formula (7), P is the load, d is the fiber diameter of the fiber portion 12, and L is the fiber length of the fiber portion 12. Reference numerals (a) to (d) in FIGS. 6 and 7 correspond to each other.

In this way, the nanoindentation method directly measures the strength of the interface between the resin portion 11 and the fiber portion 12 in the sample piece 13 actually cut out from the molded product, so the interface strength τ _if of the fiber-resin interface can be calculated as follows. can be measured accurately. Therefore, it is desirable to obtain measured data of the interfacial strength τ _if of the fiber-resin interface by the nanoindentation method.

-Regression analysis step S4-
The above-mentioned material characteristic values of the fiber and resin, the strain of the resin, and the measured data (material characteristic values) of the interfacial strength of the fiber-resin interface are regressed to the model function of the above formula (6), and these material characteristic values are the best Determine and identify each coefficient of equation (6) as shown. Then, the regression formula of the following formula (8) is finally obtained.

σ=Kε (8)
However, in equation (8), K is the stiffness matrix and ε is the strain of the entire RVE.

-Prediction step S5-
In the prediction step S5, the stress-strain characteristics of an arbitrary fiber-reinforced resin molded product are predicted based on the regression formula (8) above.

As described above, the function representing the stress at the fiber-resin interface is defined, and the measured data of the interface strength at the fiber-resin interface is regressed to the model function to obtain the regression equation. A model function considering strength can be identified, and representative volume elements can be divided into three types, fiber, resin, and fiber-resin interface, and each can be modeled by mesh division by the finite element method. Thus, it is possible to accurately predict the stress-strain characteristics of fiber-reinforced resin moldings.

(Other embodiments)
Other embodiments according to the present disclosure will be described in detail below. In the description of these embodiments, the same parts as in the above embodiment are denoted by the same reference numerals, and detailed description thereof will be omitted.

To reflect the presence or absence of surface treatment on the fiber surface, for example, τ _if may be expressed by the following equation (9).

τ _if =a+b(1−e ^cx ) (9)
However, in formula (9), a is the friction coefficient of the resin surface, b is the binding tensor, c is the degree of bonding between the maleic anhydride-modified polypropylene and the surface-treated resin surface, and x is the maleic anhydride-modified polypropylene. content ratio.

Formula (9) is an approximate formula obtained from the measured data of the interfacial strength of the fiber-resin interface obtained by the above-described nanoindentation method, microdroplet method, or the like.

The surface treatment of the fiber surface means, for example, in the case of glass fiber, introducing a functional group such as a COOH group to the surface of the glass fiber, or in the case of carbon fiber, treating the fiber surface with a sizing agent or plasma treatment. It refers to adjusting the degree of adhesion to resin etc. The values of a, b, and c may change depending on the presence or absence of surface treatment.

By introducing the above equation (9) into the above equation (6) of the first embodiment, it becomes possible to predict the stress-strain characteristics considering the presence or absence of surface treatment.

[Experimental example]
Next, a concrete experimental example will be described.

<Test material>
As the resin, homopolypropylene (MA1B manufactured by Japan Polypropylene Co., Ltd., hereinafter also referred to as "PP") and maleic anhydride-modified PP (Umex 1001 manufactured by Sanyo Chemical Industries, Ltd., hereinafter also referred to as "MA") were used. ) was blended so that the content ratio in the total resin was 0% by mass, 5% by mass, and 10% by mass. As fibers, commercially available glass fibers with a diameter of 17 μm (hereinafter also referred to as “GF”), glass fibers subjected to surface treatment A (introduction of CN groups), and glass fibers subjected to surface treatment B (introduction of COOH groups). was added so that the fiber content ratio in the molded article was 10% by mass, and a total of 8 types of molded articles shown in Table 1 were produced by injection molding.

<Tensile test>
A standard ISO dumbbell sample (4 mm thick) for tensile testing was molded by a Japan Steel Works, Ltd. electric horizontal 220t injection molding machine (J220AD-2M460H/30) equipped with a low-shear screw (see Figure 2). There are four types of samples: a PP molded product with only resin (with or without MA) for obtaining material characteristic values to be input in the calculation, and a PP/GF molded product (with/without MA) used for verification of the calculation. Got ready. According to JIS K7161, a universal testing machine (manufactured by Instron) was used to measure the stress-strain curve at a chuck distance of 115 mm and a test speed of 1 mm/min. The double-headed arrow shown in FIG. 2 indicates the tensile direction by the universal testing machine. FIG. 8 shows the stress-strain curve of the PP molding.

<Fiber length measurement test>
Cut out a part of the untested molded product, heat it at 625 ° C. for 4 hours using an electric furnace to burn off the PP, then measure the fiber length of 1000 GFs and use the above formula (1) was used to calculate the weight average fiber length (Lw). FIG. 9 shows the measured fiber length distribution.

<Fiber orientation measurement test>
The end of the dumbbell parallel portion shown in FIG. 2 on the side opposite to the gate was cut off, and an image was taken with a resolution of 4 μm using a microfocus X-ray CT apparatus (Tohken-skyscan 2011 manufactured by Token Co., Ltd.). Based on this image, φ and θ shown in FIG. 2 are measured for each fiber with TRI/3D-FBR64 manufactured by Ratoc System Engineering Co., Ltd., and the orientation tensor A represented by the above formula (2) is calculated. did. Table 2 shows the calculation results of the orientation tensor A.

<Fiber-resin interface strength measurement>
Using a nanoindenter (manufactured by Toyo Technica), GF was extruded from a thin film (thickness: about 200 μm) obtained by cutting the molded product of FIG. It was measured as interface strength. Table 2 shows the measurement results of the interfacial strength of test materials 1 and 2. FIG. 10 shows the measurement results of the interfacial strength of test materials 3 to 8.

<Calculation>
From the CT image obtained by fiber orientation measurement, the fiber content ratio of 10% by mass, and the measurement results of fiber length and fiber orientation by the above method, Digimat 2016.1 (e-Xtreme engineering) was used to obtain RVE ( 3.1 mm x 0.6 mm x 0.6 mm).

Using Abaqus 6.14-3 (manufactured by Dassault Systèmes, Inc.), the fiber and resin portions of the RVE were divided by tetrahedral primary elements (mesh size 40 μm). In addition, the fiber-resin interface was modeled with a bonding force model. The total number of elements in the RVE was approximately 600,000 elements.

Then, using Abaqus 6.14-3, input the catalog values as material property values of fibers and resins, the results of tensile tests of PP molded products, and the measurement results of the interfacial strength of the fiber-resin interface, and use the regression equation asked for

<Comparison between experimental results and calculation results>
For test materials 1 and 2, the apparent stress of the PP / GF molded product (with / without MA) obtained in the above-described tensile test - CAE using the regression equation (8) identified by the above method. Calculation results are shown in FIG.

As shown in FIG. 11, it can be seen that the experimental values of the stress-strain characteristics of the test materials 1 and 2 and the CAE calculation results are both substantially in agreement. In the experimental values, there is no difference between with and without MA in the elastic region, but after yielding, the stress value with MA (test material 2) is higher than that without MA (test material 1). there is In the CAE calculation results, the difference in stress values after yielding can also be simulated, suggesting that this difference can be expressed quantitatively in CAE by considering the fiber-resin interface strength in the above formula (6). was done.

<Effect of surface treatment on fiber surface>
When the interfacial strength was measured for test materials 3 to 8, as shown in Table 1 and FIG. It can be seen that the interfacial strength is higher and the adhesive strength between the fiber and the resin is higher when the GF to which A (CN group is introduced) is included. On the other hand, in test materials 4, 5, 7, and 8 containing MA, interfacial strength is higher when GF subjected to surface treatment B (introduction of COOH group) is included than in surface treatment A (introduction of CN group). It can be seen that the adhesive strength between the fiber and the resin is high. From this, it is considered that the interaction between COOH and MA is strong and the adhesive strength is improved. In addition, FIG. 10 suggests that when the content of MA exceeds 5% by mass, the difference in interfacial strength between the surface treatments A and B becomes smaller. In this way, the approximated curve of FIG. 11 is obtained from the measured data of the interface strength, and the approximated curve is represented by the above equation (9). The coefficients a, b and c of the approximation formula for surface treatment A are 5.3, 9.65 and 0.19, respectively, and the coefficients a, b and c of the approximation formula for surface treatment B are 4.6 and 4.6, respectively. 10.2, 0.37.

100 samples, molded products (fiber reinforced resin molded products)
101 Opposite gate side end 11 Resin part 12 Fiber part 15 Fiber-resin interface 200 Part (of representative volume element, RVE)

Claims (4)

a step of creating a representative volume element based on image data of a sample of a fiber-reinforced resin molded product that serves as a reference, and fiber length data and orientation data of fibers contained in the sample;
For each of the fibers, the resin and the fiber-resin interface, a finite element mesh is created by the finite element method so that the total number of elements of the representative volume elements is equal to or less than a predetermined number of elements, and the fibers, the resin and the a step of creating a model function indicating the stress-strain characteristics of the entire representative volume element by adding together functions indicating the stresses of the fiber-resin interfaces according to their content ratios;
obtaining a regression formula by regressing the material characteristic values of the fiber and the resin and the measured data of the interfacial strength of the fiber-resin interface obtained experimentally in advance against the model function;
A method for predicting stress-strain characteristics of a fiber-reinforced resin molded product, comprising a step of predicting the stress-strain characteristics of an arbitrary fiber-reinforced resin molded product based on the regression equation. In claim 1,
A method for predicting stress-strain characteristics of a fiber-reinforced resin molded product, wherein the function indicating the stress at the fiber-resin interface is described using a bonding force model. In claim 1 or claim 2,
A method for predicting stress-strain characteristics of a fiber-reinforced resin molded product, wherein the measured data of the interfacial strength of the fiber-resin interface is measured by a nanoindentation method. In any one of claims 1 to 3,
A stress-strain characteristic prediction method for a fiber reinforced resin molded product, wherein the fiber reinforced resin molded product is an injection molded product.

Images