Composite material fatigue life prediction method

Abstract

To provide a method for accurately predicting the fatigue life of a fiber-reinforced composite material that repeatedly receives loads from a plurality of directions.SOLUTION: The present invention is a method for predicting the fatigue life of a composite material that includes reinforced fiber oriented in a base material and receives loads from a plurality of different directions. The fatigue life (Nf) is predicted as the sum (Nf=Ni+Np) of the occurrence life (Ni) until the occurrence of damage in the composite material and the progress life (Np) from the occurrence of damage until rupture of the composite material. The occurrence time of damage is specified on the basis of the degree of damage (D) determined from a change in rigidity of the composite material occurring due to the repetition of the loads. The occurrence life is represented by an occurrence life prediction formula determined through regression analysis with at least the loads and the physical properties of the composite material as explanatory variables. The progress life is represented by a progress life prediction formula determined through regression analysis with at least the loads and the degree of damage as explanatory variables.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for predicting the fatigue life of a fiber-reinforced composite material. [Background technology]

[0002] Composite materials, which contain reinforcing fibers (carbon fiber, glass fiber, etc.) in a base material (matrix) such as resin, are lightweight, high-strength, have excellent specific strength, and are easy to mold and process, so they are used in a variety of products in various fields.

[0003] To expand the applications of composite materials, it is important to understand their fatigue life (fatigue strength) in addition to general mechanical properties such as tensile strength and elongation. However, there is a limit to the amount of time that can be spent to perform fatigue tests under various conditions. Therefore, a relatively simple method for predicting (estimating) the fatigue life of composite materials is required, and a related description is found in the following Non-Patent Document 1. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] "Study on fatigue life estimation of woven fiber reinforced composite laminates considering four-layer lamination" (Fujimoto et al., Graduate School of Osaka University, Journal of Smart Processing Society, Vol. 11, No. 3 (2022), pp. 141-146) [Patent documents]

[0005] [Patent Document 1] Patent No. 4581758 [Patent Document 2] Patent No. 6582753 Summary of the Invention [Problem to be solved by the invention]

[0006] Non-Patent Document 1 predicts the fatigue life (fatigue strength) of woven glass fiber reinforced epoxy resin laminates, which are unidirectional fiber reinforced plastics (UD-FPR), when subjected to uniaxial loading. However, as can be seen from the SN diagram published in the document, despite the use of FEM analysis and complex fracture and damage laws, the prediction accuracy is low, with an error range of up to 50%.

[0007] Generally, composite materials are anisotropic materials whose mechanical properties differ between the orientation direction of the reinforcing fibers and the direction intersecting (perpendicular) it. Furthermore, components formed by alternately stacking (e.g., cross-stacking) layered composite materials are often subjected to loads from the opposite direction. For this reason, the fatigue life prediction under uniaxial loading, as in Non-Patent Document 1, does not reflect the actual situation.

[0008] Although Patent Documents 1 and 2 also describe methods for predicting fatigue life, they are not directed to fiber-reinforced composite materials, and these documents contain no description or suggestion related to this.

[0009] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a new method for predicting the fatigue life of a fiber-reinforced composite material. [Means for solving the problem]

[0010] As a result of extensive research, the inventors have discovered that by focusing on the change in stiffness (degree of damage) of fiber-reinforced composite materials subjected to loads from multiple directions, it is possible to predict their fatigue life as the sum of the fatigue life at initiation and the fatigue life at progressive failure. By expanding on this finding, the present inventors have completed the present invention, which will be described below.

[0011] <<Fatigue life prediction method for composite materials>> The present invention provides a method for predicting the fatigue life of a composite material that contains reinforcing fibers oriented in a matrix and is subjected to loads from a plurality of different directions, wherein the fatigue life (Nf) is predicted as the sum (Nf = Ni + Np) of the initiation life (Ni) until damage occurs in the composite material and the progression life (Np) from the damage occurrence to the fracture of the composite material, and the time of damage occurrence is specified based on the damage level (D) obtained from the change in stiffness of the composite material caused by the repeated load. The initiation life is expressed by an initiation life prediction formula determined by regression analysis using at least the load and the physical properties of the composite material as explanatory variables, and the progression life is expressed by a progression life prediction formula determined by regression analysis using at least the load and the damage level as explanatory variables.

[0012] According to the fatigue life prediction method (also simply referred to as the "prediction method") of the present invention, the fatigue life of a fiber-reinforced composite material subjected to repeated loads from multiple directions (e.g., biaxial or triaxial directions) can be predicted with high accuracy.

[0013] System / Program The present invention may be understood as a system or program (including a recording medium) that executes the above-described prediction method on a computer. For example, the present invention may be understood as a Finite Element Method (FEM), Computer Aided Engineering (CAE), Computer Aided Design (CAD), or the like that incorporates the above-described method for predicting the fatigue life of a composite material as a tool (program). Note that the "step" in this specification may be read as "means" to refer to a component element related to the system or program.

[0014] "others" Unless otherwise specified, "x to y" in this specification includes a lower limit of x and an upper limit of y. Any numerical value included in the various numerical values ​​or numerical ranges described in this specification can be used as a new lower limit or upper limit to create a new range such as "a to b." [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a diagram illustrating an example of a processing procedure (flowchart) for identifying a prediction formula for the fatigue life of a fiber-reinforced composite material. [Figure 2] 1 is an SN diagram obtained in a fatigue test of a fiber-reinforced composite material, and a graph showing the relationship between the number of cycles (N) and the degree of damage (D). [Figure 3] FIG. 10 is a scatter diagram showing the relationship between the measured and predicted values ​​of the damage occurrence life (Ni). [Figure 4] This is an SN diagram comparing the measured and predicted values ​​of fatigue life (Nf). [Figure 5A] Formulas for predicting fatigue life (Nf) and initiation life (Ni). [Figure 5B] This is a mathematical formula for predicting the progressive life (Np). DETAILED DESCRIPTION OF THE INVENTION

[0016] The contents described in this specification may apply not only to the prediction method but also to a system or program using the same. One or more components arbitrarily selected from this specification may be added to the components of the present invention described above. Which embodiment is best depends on the target, required performance, etc.

[0017] 《Composite materials》 A composite material has oriented reinforcing fibers and a matrix material containing the fibers. The composite material preferably has anisotropic mechanical properties when viewed at least microscopically or layer-by-layer. The mechanical properties of the composite material as a whole or a member made of the composite material as a whole may be isotropic when viewed macroscopically.

[0018] The specific materials and volume ratios (occupancy rates) of the reinforcing fibers and matrix are not important. Examples of reinforcing fibers include carbon fibers and glass fibers. The reinforcing fibers may be short fibers, long fibers, continuous fibers, etc. The matrix may be resin, metal, etc. The resin may be a thermoplastic resin or a thermosetting resin. Typical composite materials include tapes (UD (uni-directional) tapes, etc.) and sheets (UD prepregs, etc.) in which continuous fibers (bundles, knits, etc.) aligned in one direction are filled or impregnated with resin (e.g., polyamide (PA), polyphenylene sulfide (PPS), etc.).

[0019] 《Stiffness / Damage》 When composite materials are subjected to repeated loads, internal damage (defects) can occur, reducing their rigidity (R). If the shape (cross-section) of a composite material is roughly maintained until just before fracture, its rigidity can essentially be indicated by its elastic modulus. The elastic modulus (longitudinal elastic modulus E, transverse elastic modulus G) can also be determined as the rate of change of stress (σ, τ) versus strain (ε, γ), or the slope of the tangent in a load-displacement diagram or stress-strain diagram. For convenience, in this specification, the change in the rigidity (elastic modulus) of a composite material is normalized and treated as the damage level (D) shown in Equation (2) of Figure 5A.

[0020] In actual fatigue tests, for example, the damage level (D) gradually changes up to a certain number of cycles (Ni), after which D rises sharply (see Figure 2). This is thought to be because the fatigue failure mode of the composite material changes at Ni. Therefore, in this invention, the overall fatigue life (Nf) of a composite material is predicted as the sum of the initiation life (Ni) until dominant damage occurs and the propagation life (Np) until that damage progresses to fracture.

[0021] 《Generation Lifespan: Ni》 A Ni prediction formula can be established using external and internal factors that are highly correlated with Ni. External factors include repeatedly applied loads (stress, temperature, gas, etc.). Internal factors include the physical properties of the composite material, such as the properties of the matrix, the properties of the reinforcing fibers, and the properties at the interface between the matrix and the reinforcing fibers.

[0022] The physical properties of the matrix and reinforcing fibers are, for example, tensile strength, shear strength, fatigue strength, and other physical property values. The physical property at the interface between the matrix and reinforcing fibers is, for example, fatigue strength, which reflects the bondability and adhesion between the two. The fatigue strength at the interface includes, for example, fatigue strength when repeated stress acts in a direction perpendicular to the reinforcing fibers (referred to as "mode I"), and fatigue strength when repeated stress acts along (parallel to) the reinforcing fibers (referred to as "mode II").

[0023] By performing multiple regression analysis using actual measured values ​​on a prediction formula that assumes Ni as the dependent variable and the above-mentioned external factors (such as repeated stress) and internal factors (the physical properties of the composite material itself) as explanatory variables, it is possible to identify an effective prediction formula in which the dominant factors are extracted or selected.

[0024] In this case, a prediction formula may be determined by performing multiple regression analysis using a load (stress) that takes into account (i.e., corrected) stress concentrations that may occur due to initial defects contained in the composite material as explanatory variables.

[0025] 《Progressive life: Np》 The prediction formula for Np can be established according to the Paris law, which essentially shows the relationship between the crack growth rate (da / dN) and the stress intensity factor range (ΔK) in the crack growth region.

[0026] An effective prediction formula can be identified by performing a regression analysis of the prediction formula using at least the load and damage level as explanatory variables. If there is a section where the crack growth stagnates, for example, it is possible to identify prediction formulas before and after this section. Incidentally, the smaller the cyclic load, the more dominant Ni becomes and the smaller Np becomes.

[0027] The repeated stress load may vary depending on the usage environment, structure, form, etc. For example, if layers with different orientation directions of reinforcing fibers are alternately stacked and subjected to repeated loads from multiple directions (e.g., multiaxial stress), the shear stress acting between the layers (interlaminar shear stress) may become the dominant external factor (explanatory variable). [Example]

[0028] The present invention will be specifically described using as an example the case of predicting the biaxial tensile fatigue life of a cross-ply test piece made of carbon fiber reinforced resin.

[0029] [Create prediction formula] The procedure for creating a prediction formula for the fatigue life of fiber-reinforced composite materials is shown in the flowchart in Figure 1. The procedure will be explained below in order.

[0030] <<Fatigue test execution / Step S1>> Fatigue tests were actually conducted using test pieces (actual items). Specifically, the following procedures were carried out.

[0031] (1) Test piece Four pieces of UD tape, made of continuous, unidirectionally aligned carbon fiber bundles impregnated with epoxy resin (base material), were stacked alternately lengthwise and widthwise in a cross shape to prepare a test specimen (composite material). The cross-shaped UD tape pieces were heated and cured, including the straight sections extending from their intersections (centers), to form a shape. The test specimens were symmetrical from top to bottom and left to right, and were subjected to fatigue tests with the carbon fibers stretched in the longitudinal direction (tensile direction) (oriented state).

[0032] (2) Testing machine The test piece was attached to the test jig described in detail in JP 2022-107955 A (see Figures 1 and 4 of the patent publication). This test jig was then attached to an electrohydraulic material testing machine (fatigue testing machine) capable of applying repeated loads (tensile stress) in one axial direction (Y direction).

[0033] The angle between the links of the test jig was adjusted so that the ratio (load ratio) of the load Px acting in the X direction (horizontal direction) of the test piece to the load Py acting in the Y direction (vertical direction) of the test piece was Px / Py = 2. The load ratio (Px / Py) may be changed within a range of, for example, 1 to 3 or 1 to 5.

[0034] Incidentally, by using the test jig disclosed in JP 2024-8330 A, triaxial load fatigue life tests can be performed using the fatigue testing machine described above, and the corresponding fatigue life predictions for composite materials can also be made. The contents of these publications are incorporated herein by reference as appropriate and constitute a part of this specification.

[0035] (3) Fatigue test Using the test fixture and testing machine described above, a biaxial tensile fatigue test was conducted in which the test specimen was repeatedly subjected to tensile stress in two orthogonal axial directions. The tensile stress (cyclic stress) was varied in a pulsating manner along a sinusoidal waveform (minimum stress / maximum stress: 0.1).

[0036] Fatigue tests were performed multiple times, varying the cyclic stress (amplitude or maximum stress). Figure 2 shows the SN diagram of the specimen obtained in this way. The vertical axis (cyclic stress) is the nominal interlaminar shear stress τiL applied to the intersection of the specimen, normalized by the relative value obtained by dividing it by the static strength (100%). The nominal interlaminar shear stress τiL was calculated by dividing the combined load of the maximum load (Px)max in the X direction and the maximum load (Py)max in the Y direction cyclically applied to the specimen by the area ((n-1)A) of the intersection of the specimen before testing, as shown in equation (3) in Figure 5A. Here, n is the number of layers at the intersection (n = 4 in this example).

[0037] During the fatigue test, the stiffness (R) at the intersection of the specimen was measured after each cycle, and the change (R - R) relative to the initial stiffness (R) was also observed. As shown in equation (2) in Figure 5A, the stiffness change (R - R) was converted (normalized) into damage (D), which is the ratio of the stiffness change (R - R) up to just before fracture (the final cycle). The change in damage (D) over time (change for each specified number of cycles) is also shown in Figure 2.

[0038] The stiffness (R) was defined as the slope ΔP / Δδ (ΔP: total amplitude of the load, Δδ: amplitude of the piston displacement in the y direction of the testing machine) of the load-displacement diagram obtained for each cycle of the fatigue test.

[0039] (4) Features As can be seen from Figure 2, the damage level (D) calculated from the change in stiffness increased gradually when the number of cycles (N) was small, and increased rapidly as the number of cycles (N) increased. Furthermore, when the cyclic stress was large, there was a tendency for D to decrease just before the sudden increase, but the point at which the sudden increase in D began (when damage occurred) could be clearly identified in all cases.

[0040] Moreover, when the cyclic stress was large, the phenomenon that D stagnates after the start of a rapid increase (the rate of change (slope) of D relative to N becomes gentler) was clearly observed.

[0041] <<Acquisition of measured values ​​(Nf, Ni, Np, D) / Step S2>> Based on the SN diagram shown in Figure 2 and the change in D, the actual measured values ​​(Nf, Ni, Np, D) for each fatigue test were obtained. Ni was taken as the number of cycles at which D changed suddenly relative to N (when damage occurred). Although it is not necessarily important to specify this point precisely, if necessary, the point of intersection between the approximation line (regression line) for the region where D changes gradually relative to N and the approximation line for the region where D changes suddenly relative to N may be taken as the time when damage occurred. The approximation line can be determined, for example, by the least squares method.

[0042] Once Ni is determined, Np is calculated from the actual fatigue life (Nf) obtained in the fatigue test as Nf-Ni (difference). In this way, multiple measured values ​​(Nf, Ni, Np, D) were obtained from the actual fatigue test.

[0043] {Prediction formula for occurrence life / Steps S31 to S33} A prediction formula for the occurrence life (Ni) was created in accordance with steps S31 to S33 (collectively referred to as "step S3") shown in Fig. 1. Specifically, it is as follows.

[0044] (1) Establishing a prediction formula (step S31) First, we extracted external factors (cyclic loads applied to the composite material) and internal factors (physical properties of the composite material) that may have a significant effect on the initiation life (Ni), which accounts for the majority of the total fatigue life (Nf), and formulated a tentative prediction equation (40) (see Fig. 5A).

[0045] The internal factors are the physical properties of the base material (resin), the reinforcing fibers (carbon fibers: CF), the physical properties of their interfaces, etc. The inventors previously performed non-destructive measurements of microscopic fatigue damage in composite materials using synchrotron radiation, etc., and based on these results, extracted and selected the nine parameters (correlated factors / explanatory variables) shown in prediction equation (40).

[0046] τiI and τiII shown in the prediction formula (40) are the fatigue strengths at the interface between the matrix (resin) and the reinforcing fiber (CF). τiI is the interfacial fatigue strength in the direction perpendicular to the CF extension direction (mode I), and τiII is the interfacial fatigue strength in the CF extension direction (mode II).

[0047] In addition, α, β, γ, η, and λ shown in the prediction equation (40) are undetermined constants. λ is called the “virtual crack length” and is a correction term for the initial defect size.

[0048] (2) Multiple regression analysis (step S32) 10 in biaxial tensile fatigue tests 6 Using the results of seven experiments in which the specimens broke in less than 1000 cycles, a multiple regression analysis (Ni: objective variable, each factor: explanatory variable) based on the prediction formula (40) was performed. In this case, it was assumed that the specimens had no initial defects, and a0 = 0. In this example, the analysis was performed using the free statistical analysis software "R." Of course, general-purpose analysis tools (for example, spreadsheet software such as Microsoft Excel) may also be used.

[0049] Multiple regression analysis showed that τiII / τm and σft / σf could be excluded from the explanatory variables. In addition, as can be seen from the analysis results shown in Table 1, the adjusted R 2 The adjusted multiple correlation coefficient was 0.793, and the F value, which indicates significance, was 0.019. These results also show that regression equation (41) is statistically significant.

[0050] In addition, the P value of the explanatory variable τmw / τiL related to resin shear fatigue and interlaminar shear stress was the smallest at 0.015 in all the multiple regression analysis results, and the coefficient α was also sufficiently significant.

[0051] (3) Determining the prediction formula (step S33) Based on the results of this multiple regression analysis, regression equation (41) was used as the prediction equation for the occurrence life. Figure 3 shows the results of comparing Ni calculated from prediction equation (41) with the actually measured Ni assuming no initial defects (a0 = 0). As can be seen from Figure 3, it was verified that the occurrence life can be predicted with high accuracy, with an error of within ±1 digit, when prediction equation (41) is used. Thus, it became clear that the occurrence life (Ni) can be predicted based on prediction equation (41).

[0052] Incidentally, τmw in prediction formula (41) can be calculated as τmw=σmw / √3 from the von Mises yield condition using the tensile fatigue strength σmw of the resin, which is easy to measure. Also, τiI can be calculated simply by a fatigue test in which uniaxial tensile stress is applied to a unidirectional laminate (UD tape) in the direction perpendicular to the CF.

[0053] 《Progression Life Prediction Formula / Steps S41~S43》 A prediction formula for the propagation life (Np) was created in accordance with steps S41 to S43 (collectively referred to as "step S4") shown in Fig. 1. Specifically, it is as follows.

[0054] (1) Establishment of a prediction formula (step S41) First, based on the Paris law, we formulated the prediction formula (50) (see FIG. 5B) expressed as a differential equation.

[0055] As shown in Fig. 2, a stagnation region was observed in the range where damage progressed within the composite material. Taking this into consideration, the prediction equation (50) was divided into the interval [Di, Da] and the interval [Da, Dc], and the prediction equation (51) for Np was established by integrating the prediction equation (50).

[0056] In addition, the subscript 1 in the prediction formula (51) indicates the region before stagnation (the range from when damage occurs to when stagnation starts), and the subscript 2 indicates the region after stagnation (the range from when stagnation ends to when fracture occurs). Di indicates the damage level at the time of damage occurrence. Dc indicates the damage level at the time of fracture, where Dc = 1. For convenience of calculation, Da was set to the damage level midway between when stagnation starts and when stagnation ends (when propagation resumes).

[0057] Also, when no stagnant region is observed (e.g., N≧10 5 When Da = Dc, the prediction formula (51) is naturally integrated in a definite interval [Di, Dc] (Da = Dc).

[0058] (2) Regression analysis (step S42) Next, as can be seen from Figure 2, a proportional (linear function) relationship is observed between the repeated stress τiL and the damage levels Di and Da. Therefore, when a linear regression analysis was performed with τiL as the explanatory variable and Di or Da as the response variable, the regression equation shown in Equation (52) or Equation (53) was obtained.

[0059] (3) Determining the prediction formula (step S43) In this way, a prediction formula for the progressive fatigue life (Np) was obtained, consisting of equations (51), (52), and (53). Verification of this prediction formula was replaced by verification of the total fatigue life (Nf) as follows.

[0060] <Fatigue life prediction / Step S5> Based on the above results, the fatigue life (Nf) of the composite material was predicted for any cyclic stress (τiL) as Nf = Ni + Np (Equation (1) in Figure 5A).

[0061] A comparison of the predicted and measured values ​​of Nf is shown in Figure 4. The predicted values ​​of Ni obtained from equation (41) are also shown in Figure 4. The solid line in Figure 4 is an SN diagram that approximates the measured values ​​of Nf in semi-logarithmic display, and the dashed line indicates the ±10% error range along the vertical axis.

[0062] As is clear from Figure 4, the predicted values ​​(◇ marks) of the biaxial tensile fatigue strength (fatigue life) of the composite material were within ±10% of the actual measured values ​​(■ marks), with a maximum error of approximately 8%.

[0063] From the above, it was confirmed that the prediction equation consisting of equations (1), (41), and (51) to (53) can predict the fatigue life of a composite material for an arbitrary repeated stress (τiL) with high accuracy.

[0064] [Table 1]

Claims

1. A method for predicting the fatigue life of a composite material containing reinforcing fibers oriented in a matrix and subjected to loads from different directions, comprising: The fatigue life (Nf) is predicted as the sum of the initiation life (Ni) until damage occurs in the composite material and the propagation life (Np) from the damage occurrence until the composite material breaks (Nf = Ni + Np), The occurrence of the damage is identified based on a damage degree (D) calculated from a change in stiffness of the composite material caused by the repeated loading, the occurrence life is expressed by an occurrence life prediction formula determined by regression analysis using at least the load and the physical properties of the composite material as explanatory variables; A method for predicting the fatigue life of a composite material, wherein the progressive life is expressed by a progressive life prediction formula determined by regression analysis using at least the load and the damage level as explanatory variables.

2. 2. The method for predicting a fatigue life of a composite material according to claim 1, wherein the physical properties of the composite material include at least a fatigue strength of the base material and a fatigue strength at an interface between the base material and the reinforcing fibers.

3. 3. The method for predicting a fatigue life of a composite material according to claim 2, wherein the fatigue strength at the interface is a fatigue strength in a direction perpendicular to the orientation direction of the reinforcing fibers.

4. 2. The method for predicting a fatigue life of a composite material according to claim 1, wherein the load in the initiation life prediction formula is corrected taking into account stress concentration that may occur due to an initial defect.

5. 2. The method for predicting a fatigue life of a composite material according to claim 1, wherein the progression life prediction formula takes into account a damage level (Da) when the progression of damage in the composite material stagnates.

6. The composite material is formed by laminating layers in which the reinforcing fibers are oriented in different directions, The method for predicting a fatigue life of a composite material according to claim 1 , wherein the load includes a shear stress acting between the layers.

7. 2. The method for predicting a fatigue life of a composite material according to claim 1, wherein the fatigue life (Nf) is a biaxial tensile fatigue life.

8. the base material is a resin, The method for predicting a fatigue life of a composite material according to any one of claims 1 to 7, wherein the reinforcing fibers are continuous fibers.

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