Method for evaluating joint strength

Abstract

This invention provides a method for evaluating joint strength that makes it possible to evaluate the joint strength of adhesive joints expressed by adhesive joint parameters that deviate from the assumptions of the theoretical formula. [Solution] The method for evaluating joint strength comprises: an evaluation position identification step, which identifies an evaluation position, which is the position from the end of the adhesive where the stress generated in the adhesive is evaluated, using a first finite element analysis model that represents the adhesive joint with first adhesive joint parameters and a predetermined theoretical formula based on material mechanics; a first stress acquisition step, which obtains a first stress at the evaluation position corresponding to the input load to the adhesive, using a second finite element analysis model that represents the adhesive joint with second adhesive joint parameters different from the first adhesive joint parameters; a second stress acquisition step, which obtains a second stress at the evaluation position corresponding to the tensile strength of the adhesive; and an evaluation step, which evaluates the joint strength with respect to cohesive failure based on the magnitude relationship between the first stress and the second stress on a plane with shear stress and normal stress as axes.

Description

Technical Field

[0001] The present disclosure relates to a method for evaluating joint strength.

Background Art

[0002] Conventionally, there is known a method for evaluating joint strength having a step of obtaining the shear stress of a double-lap joint by the finite element method for a double-lap joint in which three plate members including a plate member are overlapped and side-constrained (for example, Patent Document 1).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] As a method for evaluating the joint strength of an adhesive joint bonded using an adhesive, generally, a method for evaluating the average shear stress by a so-called single-lap shear test is known. The value of this average shear stress may be described in the adhesive catalog. However, since the type of the member material is specified in the value described in the catalog, when using different types of materials, it is necessary to individually conduct a single-lap shear test. On the other hand, as a method for evaluating the joint strength by calculation, a method for calculating the maximum stress generated in the adhesive using a theoretical formula corresponding to the single-lap shear test is known. However, since there are prerequisite conditions for various adhesive joint parameters in the theoretical formula, for example, when the member is a thin plate and other conditions deviate greatly from the prerequisite conditions, the maximum stress may not be calculated appropriately.

[0005] The present disclosure describes a method for evaluating joint strength that enables evaluation of the joint strength of an adhesive joint represented by adhesive joint parameters deviating from the prerequisite conditions of the theoretical formula. [Means for solving the problem]

[0006] One aspect of the present disclosure is a method for evaluating the joint strength of an adhesive joint bonded using an adhesive, comprising: an evaluation position identification step of identifying an evaluation position, which is the position from the end of the adhesive where the stress generated in the adhesive is evaluated, using a first finite element analysis model representing the adhesive joint with first adhesive joint parameters and a predetermined theoretical formula based on material mechanics; a first stress acquisition step of obtaining a first stress at the evaluation position corresponding to the input load to the adhesive, using a second finite element analysis model representing the adhesive joint with second adhesive joint parameters different from the first adhesive joint parameters; a second stress acquisition step of obtaining a second stress at the evaluation position corresponding to the tensile strength of the adhesive; and an evaluation step of evaluating the joint strength with respect to cohesive failure based on the magnitude relationship between the first stress and the second stress on a plane with shear stress and normal stress as axes.

[0007] In a method for evaluating joint strength according to one aspect of this disclosure, the evaluation location is identified in the evaluation location identification step using a first finite element analysis model and a predetermined theoretical formula based on material mechanics. In the first stress acquisition step and the second stress acquisition step, a first stress obtained using a second finite element analysis model and a second stress corresponding to the tensile strength of the adhesive are obtained as stresses at the evaluation location. In the evaluation step, the joint strength is evaluated with respect to cohesive failure based on the relationship between the magnitudes of the first stress and the second stress on a plane with shear stress and normal stress as axes. For example, the evaluation location is identified such that the analytical stress value obtained from the first finite element analysis model representing the adhesive joint with first adhesive joint parameters is a stress value with a small error compared to the theoretical formula. By focusing on the first stress at the evaluation location in the analytical stress value obtained from the second finite element analysis model representing the adhesive joint with second adhesive joint parameters, the joint strength is evaluated using a value with high accuracy from the distribution of analytical stress values ​​of the finite element analysis model. Therefore, even with a second adhesive joint parameter that deviates significantly from the preconditions of the theoretical formula, the accuracy of evaluating the joint strength can be improved. Accordingly, according to one aspect of the present disclosure, the method for evaluating the joint strength of an adhesive joint, expressed by an adhesive joint parameter that deviates from the preconditions of the theoretical formula, makes it possible to evaluate the joint strength of an adhesive joint.

[0008] In one embodiment, the evaluation position identification step may specify the evaluation position as a position from the end of the adhesive such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula. In this case, by specifying the evaluation position such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula, it becomes possible to evaluate the joint strength using a more accurate value from the distribution of analytical stress values ​​of the finite element analysis model.

[0009] In one embodiment, the evaluation position identification step may use a first finite element analysis model that does not consider geometric nonlinearity and a theoretical formula that applies to steel plates with a thickness of 9 mm or more. In this case, the error between the analyzed stress value and the theoretical value can be reduced by using the first finite element analysis model and a predetermined theoretical formula based on material mechanics, making it possible to identify the evaluation position more reliably.

[0010] In one embodiment, the first stress acquisition step may use a second finite element analysis model that takes geometric nonlinearity into account. In this case, the analytical stress values ​​of the second finite element analysis model can be calculated with high accuracy, for example, under conditions such as the member being a thin plate.

[0011] In one embodiment, the first stress acquisition step may use a second finite element analysis model in which the plate material thickness is 2 mm or less. In this case, it becomes possible to evaluate the joint strength of adhesive joints, which cannot be adequately evaluated by theoretical formulas that target plate materials with a thickness of 9 mm or more. [Effects of the Invention]

[0012] According to this disclosure, it is possible to evaluate the bonding strength of an adhesive joint represented by adhesive joint parameters that deviate from the assumptions of the theoretical formula. [Brief explanation of the drawing]

[0013] [Figure 1] This flowchart illustrates a method for evaluating joint strength according to the embodiment. [Figure 2] (a) is a plan view of the adhesive joint test specimen. (b) is a side view of the adhesive joint test specimen. (c) is a plan view of the adhesive joint test specimen from (a) as seen from the back. [Figure 3] This figure illustrates the difference in analytical stress values ​​when any of the adhesive joint parameters are changed. [Figure 4](a) is a side view of an adhesive joint when the thickness of the plate material is 0.675 mm. (b) is a side view of an adhesive joint when the thickness of the plate material is 1.35 mm. (c) is a side view of an adhesive joint when the thickness of the plate material is 2.7 mm. (d) is a side view of an adhesive joint when the thickness of the plate material is 5.4 mm. [Figure 5] This is a side view of a model showing an example of analysis conditions for finite element analysis. [Figure 6] This figure shows the first example of the principal stress distribution from the end of the adhesive in a bonded joint and the evaluation location when the plate material thickness is 5.4 mm. [Figure 7] This figure shows a second example of the principal stress distribution from the end of the adhesive in a bonded joint and the evaluation location when the plate thickness is 5.4 mm. [Figure 8] This figure shows a third example of the principal stress distribution from the edge of the adhesive in a bonded joint and the evaluation location when the plate material thickness is 5.4 mm. [Figure 9] This is a plane graph with shear stress and normal stress as axes, showing the relationship between the magnitudes of the first stress and the second stress calculated by the joint strength evaluation method according to the embodiment. [Figure 10] This is a graph of a plane with shear stress and normal stress as axes, showing the relative magnitudes of the first stress and the second stress calculated using a predetermined theoretical formula based on material mechanics. [Modes for carrying out the invention]

[0014] The embodiments of this disclosure will be described below with reference to the drawings.

[0015] The method for evaluating joint strength according to this embodiment is for evaluating the joint strength of adhesive joints bonded using an adhesive. An adhesive joint is a part that is integrated by connecting members or parts that constitute a structure or machine, etc., using an adhesive. Adhesive joints can also be used to connect dissimilar materials. In the method for evaluating joint strength according to this embodiment, the joint strength is considered to be determined by the strength of the adhesive alone, and the method targets adhesive joints that undergo cohesive failure.

[0016] Generally, since the strength of an adhesive joint is lower than that of the adhesive alone, it is conceivable to calculate the average shear stress by means of a Single Lap Shear (SLS) test and evaluate the bonding strength of the adhesive joint. The average shear stress is a value obtained by dividing the breaking load by the bonding area. The value of the average shear stress may be described in the adhesive catalog. The values described in the adhesive catalog are specified for each type of material of the adherend of the adhesive joint (for example, steel, aluminum alloy, etc.). Therefore, when using a material different from the specified type in the catalog, it is necessary to individually conduct a single lap shear test.

[0017] In addition, a method of evaluating the bonding strength of an adhesive joint using a predetermined theoretical formula based on the mechanics of materials is known. Examples of the predetermined theoretical formula include the stress calculation formula of the Guidelines for Repair and Strengthening of Structures by FRP Bonding (hereinafter, also simply referred to as the "JSCE Guidelines"). The stress calculation formula of the JSCE Guidelines gives the maximum stress generated according to the position from the end of the adhesive of the adhesive joint in the single lap shear test. Since the stress calculation formula of the JSCE Guidelines inputs the dimensions, longitudinal elastic modulus, etc. of the adherend of the adhesive joint, it is possible to evaluate the bonding strength even when the dimensions and materials of the adherend are different.

[0018] However, there are various preconditions for the dimensions, longitudinal elastic modulus, etc. of the adherend. Examples of the preconditions include conditions such as the adherend of the joint having a thickness of 9 mm or more and being a steel plate with a width of 50 mm or more in the short side direction of the adherend. Therefore, for example, in the case where the adherend is a thin plate, etc., when the conditions deviate significantly from the preconditions, it may not be possible to appropriately evaluate the strength of the adhesive joint by simply using a predetermined theoretical formula based on the mechanics of materials.

[0019] Furthermore, to evaluate the strength of adhesive joints of thin plate adherends for which the stress calculation formulas of the Japan Society of Civil Engineers guidelines are unsuitable, it is possible to analyze using the finite element method (FEM). The finite element method can also take into account geometric nonlinearity, a condition in which nonlinearity appears in the analysis. However, at the ends of the adhesive in an adhesive joint, the actual stress is infinite, which is difficult to represent computationally using the finite element method.

[0020] In light of these drawbacks, the joint strength evaluation method according to this embodiment evaluates joint strength by using a predetermined theoretical formula based on material mechanics and a finite element analysis model in combination. Below, an example of the joint strength evaluation method will be described with reference to the flowchart in Figure 1.

[0021] First, the evaluation position identification step (steps S10 to S12) will be explained. The evaluation position identification step is a step in which the evaluation position, which is the position from the end of the adhesive where the stress generated in the adhesive is evaluated, is identified using a first finite element analysis model that represents the adhesive joint with first adhesive joint parameters and a predetermined theoretical formula based on material mechanics. The end of the adhesive refers to, for example, the position inside the adhesive in the longitudinal direction of the adherend, with the constrained end side of the adhesive joint in the analysis model (the left side in the example of Figure 5) as the origin.

[0022] The first adhesive joint parameter is a parameter related to the adhesive joint that minimizes the error between the analytical stress value obtained from the first finite element analysis model and the theoretical value obtained from a predetermined theoretical formula based on material mechanics. Examples of adhesive joint parameters in the case of a single-lap shear test include the width of the adhesive along the short direction of the adherend (adhesion width), the thickness of the adherend (plate thickness), the Young's modulus of the adherend, the length of the adherend in the longitudinal direction (length of the adherend), and the length of the adhesive along the longitudinal direction of the adherend (adhesion length).

[0023] In this embodiment, in order to investigate whether joint strength can be evaluated for different adhesive joint parameters, the sensitivity of the stress calculation formula of the Japan Society of Civil Engineers (JSCE) guidelines is examined. As an example, for an adhesive joint with an adhesive width of 25.4 mm, a adherend thickness of 2.7 mm, a Young's modulus of elasticity of Ti64 material as the adherend value, a adherend length of 63.5 mm, and an adhesive length of 12.7 mm, the experimental principal stress at fracture in a single-lap shear test is 118.6 MPa. Using this value as a reference, the theoretical values ​​calculated using the JSCE guidelines stress calculation formula when the adhesive width, adherend thickness, and adhesive length are doubled are plotted in Figure 3. The theoretical values ​​calculated using the JSCE guidelines stress calculation formula when the adhesive width, adherend thickness, and adhesive length are halved are also plotted in Figure 3. Figure 3 plots the theoretical values ​​calculated using the stress calculation formula of the Japan Society of Civil Engineers (JSCE) guidelines when the Young's modulus is the value for the A2024 material used for the adherend. Figure 3 also plots the theoretical values ​​calculated using the JSCE guidelines for adherend lengths of 1 / 4, 1 / 2, 2, and 4 times the original length. Note that each calculation result was obtained by adjusting the input load so that the principal stress at failure matches.

[0024] Figure 3 illustrates the difference in analytical stress values ​​when any of the adhesive joint parameters are changed. In Figure 3, the vertical axis represents shear stress, and the horizontal axis represents normal stress. The curve in Figure 3 is the curve between the normal stress σ and the shear stress τ obtained by substituting the tensile strength of the adhesive alone into σp in equation (1) below.

number

[0025] As shown in Figure 3, the plots of calculation results when the thickness of the adherend is changed show a greater change in position than the reference plot (circle) than the plots of calculation results when other adhesive joint parameters are changed. In other words, the thickness of the adherend is highly sensitive to changes in stress in response to dimensional changes. Therefore, in this embodiment, we focus on the thickness of the adherend as an example of an adhesive joint parameter.

[0026] In the evaluation location identification step, the stress distribution from the end of the adhesive is calculated using a first finite element analysis model that represents the adhesive joint with first adhesive joint parameters (step S10).

[0027] In step S10, a first finite element analysis model is used in which the adhesive joint is represented with a thickness of 5.4 mm (first adhesive joint parameter), which is chosen to minimize the error between the analytical stress value obtained from the first finite element analysis model and the theoretical value obtained from a predetermined theoretical formula based on material mechanics. The adhesive joint parameter of the analysis model is the same as that of the adhesive joint 100 used for testing to verify whether the evaluation results of the joint strength evaluation method are valid, except for the thickness of the adhesive.

[0028] Here, we will explain the configuration of the adhesive joint 100 used for testing, while also describing the analysis model.

[0029] As shown in Figures 2(a) to 2(c) and Figure 4, test specimens of the adhesive joint 100 for testing may be prepared with a thickness of 2.7 mm multiplied by 1 / 4 (0.675 mm), 1 / 2 (1.35 mm), and 2 (5.4 mm). Figure 2(a) is a plan view of the adhesive joint test specimen. The adhesive joint 100 consists of two test specimens: an upper test specimen 10 and a lower test specimen 20. The upper test specimen 10 and the lower test specimen 20 are rectangular plates with a length of 108 mm in the longitudinal direction and a width of 25.4 mm in the transverse direction. The length of the adherend is 63.5 mm. The material of the plate is, for example, Ti64. The Young's modulus can be the value for Ti64.

[0030] The bonding area has, for example, a certain size. The end 11 of the upper test piece 10 and the end 21 of the lower test piece 20 are joined via an adhesive. The adhesive is, for example, an epoxy adhesive. The bonding width is, for example, 25.4 mm. The bonding length is, for example, 12.7 mm. A plate 13 made of the same material as the upper test piece 10 is bonded to the end 12 of the upper test piece 10 for a length of 31.8 mm in the longitudinal direction. A plate 23 made of the same material as the lower test piece 20 is bonded to the end 22 of the lower test piece 20 for a length of 31.8 mm in the longitudinal direction.

[0031] Figure 2(b) is a side view of a test specimen of an adhesive joint. The upper specimen 10 and the lower specimen 20 have equal and constant thicknesses. The thickness of the adherends, the upper specimen 10 and the lower specimen 20, is, for example, 2.7 mm. The thickness of the adhesive is uniformly distributed throughout the joint. The thickness of the adhesive is, for example, 0.2 mm.

[0032] Figure 2(c) is a plan view of the adhesive joint test specimen from Figure 2(a), seen from the back. As shown in Figures 2(a) and 2(c), a total of six strain gauges 30 are placed in the longitudinal direction, 10 mm away from the end 11 of the upper test specimen 10 and 10 mm away from the end 21 of the lower test specimen 20. In the example of Figure 2(a), the strain gauges 30 are placed in the center of the short-side of the upper test specimen 10 and the lower test specimen 20. In the example of Figure 2(c), the strain gauges 30 are placed 2.7 mm from both ends of the short-side of the upper test specimen 10 and the lower test specimen 20. As shown in Figure 4, the thicknesses of the adherends are 0.675 mm, 1.35 mm, 2.7 mm, and 5.4 mm.

[0033] Returning to the explanation of step S10, for example, in the analysis model in Figure 5, the analysis is performed using the Abaqus 2022 solver and 4-node first-order strain elements to calculate the stress distribution. In the analysis, one end of the adhesive joint 100 of the analysis model (the left side in the example of Figure 5) is completely constrained. The other end of the adhesive joint 100 of the analysis model (the right side in the example of Figure 5) is pulled along the X direction in Figure 5 under predetermined load conditions. In this first finite element analysis model, for example, geometric nonlinearity is not considered. In the first finite element analysis model, the load conditions are, for example, 17.2kN as the first load, 17.2kN as the second load, and 17.3kN as the third load, and the stress distribution from the end of the adhesive of the adhesive joint is calculated.

[0034] Next, the stress distribution from the end of the adhesive is calculated using a predetermined theoretical formula based on material mechanics (step S11). In step S11, the stress calculation formula from the Japan Society of Civil Engineers guidelines is used as the predetermined theoretical formula based on material mechanics. The stress calculation formula from the Japan Society of Civil Engineers guidelines may be applied to steel plates with a thickness of 9 mm or more.

[0035] In step S11, the stress distribution is calculated by applying the thickness value of the adherend material, which is the thickest plate in the analysis model at 5.4 mm (the first adhesive joint parameter), and the load conditions of 17.2 kN for the first finite element analysis model in this case, the first 17.2 kN, the second 17.2 kN, and the third 17.3 kN, to the stress calculation formula of the Japan Society of Civil Engineers guidelines. In step S11, for example, geometric nonlinearity is not considered. The principal stress values ​​according to the stress calculation formula of the Japan Society of Civil Engineers guidelines are, for example, 143 MPa for the first load condition of 17.2 kN, 148 MPa for the second load condition of 17.2 kN, and 142 MPa for the third load condition of 17.3 kN.

[0036] Next, the evaluation position is identified, which is the position from the end of the adhesive where the stress generated in the adhesive is to be evaluated (step S12).

[0037] The evaluation position is the position from the end of the adhesive that minimizes the error between the analytical stress value obtained from the finite element analysis model and the theoretical value obtained from a predetermined theoretical formula based on material mechanics. The evaluation position can be determined by calculating the adhesive joint parameter (i.e., the first adhesive joint parameter) that minimizes the error between the analytical stress value and the theoretical value using the finite element analysis model and the predetermined theoretical formula based on material mechanics. In this way, by determining the evaluation position using the first adhesive joint parameter, it is possible to expect improved accuracy of the analytical stress value obtained from a second adhesive joint parameter different from the first adhesive joint parameter, compared to the analytical stress value obtained when it is difficult to express it computationally using the conventional finite element method analysis described above.

[0038] Specifically, in step S12, the position from the end of the adhesive is identified as the evaluation position such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula.

[0039] Figure 6 shows the first example of the principal stress distribution from the edge of the adhesive in an adhesive joint and the evaluation position when the plate material thickness is 5.4 mm. Figure 7 shows the second example of the principal stress distribution from the edge of the adhesive in an adhesive joint and the evaluation position when the plate material thickness is 5.4 mm. Figure 8 shows the third example of the principal stress distribution from the edge of the adhesive in an adhesive joint and the evaluation position when the plate material thickness is 5.4 mm. In Figures 6 to 8, the horizontal axis represents the distance from the edge of the adhesive, and the vertical axis represents the principal stress.

[0040] The triangular plots in Figure 6 show the analytical stress values ​​obtained from the first finite element analysis model, which does not consider geometric nonlinearity, for the first load condition of 17.2 kN in step S10. The circular plots in Figure 6 show the analytical stress values ​​obtained from the first finite element analysis model, which considers geometric nonlinearity, for the first load condition of 17.2 kN. The dashed line L1 in Figure 6 corresponds to the distance (0.774 mm) in the triangular plots that matches the principal stress value of 143 MPa obtained in step S11 using the stress calculation formula of the Japan Society of Civil Engineers guidelines.

[0041] The triangular plots in Figure 7 show the analytical stress values ​​obtained from the first finite element analysis model, which does not consider geometric nonlinearity, for the second load condition of 17.2 kN in step S10. The circular plots in Figure 7 show the analytical stress values ​​obtained from the first finite element analysis model, which considers geometric nonlinearity, for the second load condition of 17.2 kN. The dashed line L2 in Figure 7 corresponds to the distance (0.711 mm) in the triangular plots that matches the principal stress value of 148 MPa obtained in step S11 using the stress calculation formula of the Japan Society of Civil Engineers guidelines.

[0042] The triangular plots in Figure 8 show the analytical stress values ​​obtained from the first finite element analysis model, which does not consider geometric nonlinearity, for the third load condition of 17.3 kN in step S10. The circular plots in Figure 8 show the analytical stress values ​​obtained from the first finite element analysis model, which considers geometric nonlinearity, for the third load condition of 17.3 kN. The dashed line L3 in Figure 8 corresponds to the distance (0.790 mm) in the triangular plots that matches the principal stress value of 142 MPa obtained in step S11 using the stress calculation formula of the Japan Society of Civil Engineers guidelines.

[0043] In this embodiment, the average value of the three evaluation positions identified from the examples in Figures 6 to 8, namely 0.774 mm, 0.711 mm, and 0.790 mm, is 0.758 mm, which is used to identify the evaluation position. Note that the method for identifying the evaluation position is not limited to this example, and the load conditions in step S10 may be other than three, and the calculation of the average value in step S12 is not mandatory.

[0044] Although it was explained that geometric nonlinearity does not need to be considered in step S10, the circular plots in Figures 6 to 8 are shown for reference to illustrate the difference from the triangular plots. In Figures 6 to 8, the circular plots show approximately the same principal stress distribution as the triangular plots. This means that the analytical stress values ​​without considering geometric nonlinearity are equivalent to the analytical stress values ​​with geometric nonlinearity considered. For example, in a finite element analysis that simply models a thin plate adherend, the error in the analytical stress values ​​may be large if geometric nonlinearity is not considered. Conversely, in a finite element analysis that models a thick plate adherend, for example, the error in the analytical stress values ​​is expected to be small even without considering geometric nonlinearity. Therefore, by using such a first adhesive joint parameter, the error between the analytical stress values ​​and the theoretical values ​​can be reduced in the first finite element analysis model and a predetermined theoretical formula based on material mechanics, making it possible to more reliably identify the evaluation position.

[0045] Next, the stress acquisition steps (steps S13 to S14) will be described. The stress acquisition steps are steps in which analytical stress values ​​at evaluation locations for evaluating the joint strength of adhesive joints are obtained using a finite element analysis model. The stress acquisition steps consist of a first stress acquisition step (step S13) and a second stress acquisition step (step S14).

[0046] First, a second finite element analysis model is used to represent the adhesive joint using second adhesive joint parameters that differ from the first adhesive joint parameters, and the first stress at the evaluation position corresponding to the input load on the adhesive is obtained (step S13). The first stress represents the value of the stress that is evaluated in the context of stress evaluation in the design of an actual part or component. The first stress is compared with the second stress, which will be described later.

[0047] The second adhesive joint parameter is different from the first adhesive joint parameter, and is such that the error between the analytical stress value and the theoretical value is larger compared to the analytical stress value calculated using the first adhesive joint parameter. Here, the second adhesive joint parameter corresponds to adherend thicknesses of 0.675 mm, 1.35 mm, and 2.7 mm, which are different from 5.4 mm. In the second finite element analysis model, the adhesive joint parameters other than the adherend thickness are set to the same values ​​as in the first finite element analysis model. The second finite element analysis model uses a finite element analysis model that takes geometric nonlinearity into account.

[0048] In step S13, for example, in the analysis model shown in Figure 5, the analysis is performed using the Abaqus 2022 solver and a 4-node first-order strain element to calculate the stress distribution. In the analysis, similar to step S10, one end of the adhesive joint 100 in the analysis model is completely constrained, and the other end is pulled by an input load to the adhesive. The input load to the adhesive refers to the load applied to the adhesive joint from the surrounding members in the context of stress evaluation in the design of actual parts or components. Here, for the purpose of explaining the method of evaluating joint strength, the input load to the adhesive is set to a load equal to the first to third load conditions described above.

[0049] In the second finite element analysis model, when the thickness of the adherend is 0.675 mm, the load conditions are, for example, 13.9 kN as the first load, 13.2 kN as the second load, and 13.5 kN as the third load, and the stress distribution from the end of the adhesive joint is calculated.

[0050] In the second finite element analysis model, when the thickness of the adherend is 1.35 mm, the load conditions are, for example, 13.1 kN as the first load, 13.1 kN as the second load, and 13.4 kN as the third load, and the stress distribution from the end of the adhesive of the bonded joint is calculated.

[0051] In the second finite element analysis model, when the thickness of the adherend is 2.7 mm, the load conditions are, for example, 15.2 kN as the first load, 15.2 kN as the second load, and 15.3 kN as the third load, and the stress distribution from the end of the adhesive joint is calculated.

[0052] The stress distribution calculated in step S13 is obtained as a graph, as shown in Figures 6 to 8, with principal stress values ​​corresponding to the thickness of each adherend. In the stress distribution calculated in step S13, we focus on the principal stress value with the evaluation position identified in step S13 as the position on the horizontal axis. This principal stress value corresponds to the first stress at the evaluation position corresponding to the input load to the adhesive.

[0053] Next, a second stress is obtained at the evaluation position corresponding to the tensile strength of the adhesive (step S14). The second stress is the stress value that serves as the basis for evaluating the first stress. The second stress is, for example, the normal stress and shear stress obtained by substituting the tensile strength of the adhesive alone into σp in equation (1) above. The second stress may also be calculated by multiplying the normal stress and shear stress obtained by substituting the tensile strength of the adhesive alone into σp in equation (1) above by a predetermined coefficient to account for variations in joint strength. The predetermined coefficient may be, for example, around -15% to 15%. The tensile strength of the adhesive may be the value of the tensile strength listed in the adhesive catalog, etc.

[0054] Next, the evaluation steps (steps S15 to S19) will be explained. The evaluation steps are for evaluating the joint strength based on the acquired first and second stresses.

[0055] First, the first stress is plotted on a plane with shear stress and normal stress as axes (step S15). In step S15, for example, the first stress at the evaluation position calculated in step S13 is plotted on a plane where the vertical axis is shear stress and the horizontal axis is normal stress, for each thickness of the adherend and the input load to the adhesive. The first stress when the input load is the first load and the thickness of the adherend is 0.675 mm is plotted on the plane. The first stress when the input load is the second load and the thickness of the adherend is 0.675 mm is plotted on the plane. The first stress when the input load is the third load and the thickness of the adherend is 0.675 mm is plotted on the plane. Similarly, the first stress when the input load is the first to third loads and the thickness of the adherend is 1.35 mm is plotted on the plane. When the thickness of the adherend is 2.7 mm, the first stress when the input load is the 1st to 3rd load is plotted on the plane. When the thickness of the adherend is 5.4 mm, the first stress when the input load is the 1st to 3rd load may also be plotted on the plane.

[0056] Next, a curve of the second stress is drawn on a plane with shear stress and normal stress as axes (step S16). In step S16, for example, the second stress calculated in step S14 is drawn as a curve between normal stress and shear stress on a plane where the vertical axis is shear stress and the horizontal axis is normal stress. Alternatively, the second stress calculated by multiplying by a predetermined coefficient to account for variations in joint strength may be drawn as a curve between normal stress and shear stress.

[0057] Next, it is determined whether the first stress is located closer to the origin than the curve of the second stress (step S17). In step S17, for example, the position of the plot of the first stress is compared with the position of the curve of the second stress on a plane where the vertical axis is shear stress and the horizontal axis is normal stress. In the example in Figure 9, the origin is the point where both the normal stress and the shear stress are 0 MPa.

[0058] If the first stress is located closer to the origin than the curve of the second stress (Step S17: YES), the adhesive joint 100 with the configuration of the second adhesive joint parameter for which the first stress is calculated is evaluated as having a low risk of failure (Step S18). The joint strength evaluation method is then terminated.

[0059] On the other hand, if the first stress is not located closer to the origin than the curve of the second stress (i.e., the first stress is located further out from the origin than the curve of the second stress), then the adhesive joint 100 with the configuration of the second adhesive joint parameter for which the first stress is calculated is evaluated as having a high risk of failure (step S19). After that, the joint strength evaluation method is terminated.

[0060] Figure 9 is a graph of a plane with shear stress and normal stress as axes, showing the relationship between the magnitudes of the first stress and the second stress calculated by the joint strength evaluation method according to the embodiment. Figure 10 is a graph of a plane with shear stress and normal stress as axes, showing the relationship between the magnitudes of the first stress and the second stress calculated by a predetermined theoretical formula based on material mechanics. In Figures 9 and 10, the curves of the second stress (Avg. strength) are drawn with solid and dashed lines, respectively. The solid line corresponds to a value that does not take into account the variation in joint strength. The dashed line corresponds to a value that takes into account a variation in joint strength of -10% (Avg. strength -10%).

[0061] Figures 9 and 10 show several plots. The circular plot in Figure 9 is the plot of the first stress when the thickness of the adherend is 0.675 mm. The triangular plot in Figure 9 is the plot of the first stress when the thickness of the adherend is 1.35 mm. The rectangular plot in Figure 9 is the plot of the first stress when the thickness of the adherend is 2.7 mm. The X-shaped plot in Figure 9 is the plot of the first stress when the thickness of the adherend is 5.4 mm. The circular plot in Figure 10 is the plot of the theoretical value calculated using the stress calculation formula of the Japan Society of Civil Engineers guidelines when the thickness of the adherend is 0.675 mm. The triangular plot in Figure 10 is the plot of the theoretical value calculated using the stress calculation formula of the Japan Society of Civil Engineers guidelines when the thickness of the adherend is 1.35 mm. The rectangular plot in Figure 10 is the plot of the theoretical value calculated using the stress calculation formula of the Japan Society of Civil Engineers guidelines when the thickness of the adherend is 2.7 mm. The X-shaped plots in Figure 10 represent theoretical values ​​calculated using the stress calculation formula from the Japan Society of Civil Engineers guidelines for a substrate thickness of 5.4 mm.

[0062] In the examples shown in Figures 9 and 10, a single-lap shear test was separately conducted using the adhesive joints 100 for testing shown in Figures 2(a) to 2(c), and the results showed that all adhesive joints 100 of the thickness of the adherends fractured (failed) due to cohesive failure. By comparing these experimental results with the examples in Figures 9 and 10, we will verify whether the evaluation results of the joint strength evaluation method are valid.

[0063] As a comparative example, in Figure 10, the circular plot and the triangular plot are located closer to the origin than the dashed curve. Therefore, in the evaluation plotted using the stress calculation formula of the Japan Society of Civil Engineers guidelines, the risk of failure is evaluated as low when the thickness of the adherend is 0.675 mm and when the thickness of the adherend is 1.35 mm. However, these evaluations are inconsistent with the experimental result that the test adhesive joint 100 fractured. Since the stress calculation formula of the Japan Society of Civil Engineers guidelines does not take into account the geometric nonlinearity that has a greater impact when the thickness of the adherend is relatively thin, it can be considered that the theoretical stress was underestimated in the circular plot and the triangular plot in Figure 10.

[0064] In contrast, in Figure 9, the circular plots are not located closer to the origin than the dashed curve (they are located outside the origin relative to the dashed curve). The triangular plots are not located closer to the origin than the solid curve (they are located outside the origin relative to the solid curve). Therefore, in the evaluation plotting the analytical stress values ​​obtained from the second finite element analysis model, the risk of failure is assessed as high when considering a -10% variation in joint strength for a workpiece thickness of 0.675 mm. For a workpiece thickness of 1.35 mm, the risk of failure is assessed as high without considering the variation in joint strength.

[0065] Thus, these evaluations are consistent with the experimental result that the test adhesive joint 100 fractured. In addition to considering the geometric nonlinearity, which has a significant impact when the thickness of the adherend is relatively thin, in the second finite element analysis model, by focusing on the first stress at the evaluation position where the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula, it can be considered that the evaluation was made using a highly accurate value from the stress distribution of the analytical stress value of the finite element analysis model.

[0066] As described above, in the joint strength evaluation method according to this embodiment, the evaluation location is identified in the evaluation location identification step (steps S10 to S12) using the first finite element analysis model and the stress calculation formula of the Japan Society of Civil Engineers guidelines. In the first stress acquisition step and the second stress acquisition step (steps S13 to S14), the stress at the evaluation location is obtained as the first stress obtained using the second finite element analysis model and the second stress corresponding to the tensile strength of the adhesive. In the evaluation step (steps S15 to S19), the joint strength is evaluated with respect to cohesive failure based on the magnitude relationship between the first stress and the second stress on a plane with shear stress and normal stress as axes. For example, the evaluation location is identified such that the analytical stress value obtained from the first finite element analysis model representing the adhesive joint with the first adhesive joint parameters is equal to the theoretical value of the stress calculation formula of the Japan Society of Civil Engineers guidelines. By focusing on the first stress at the evaluation location in the analytical stress value obtained from the second finite element analysis model representing the adhesive joint with the second adhesive joint parameter, the joint strength is evaluated using the value with the highest accuracy from the distribution of analytical stress values ​​in the finite element analysis model. Therefore, even if the second adhesive joint parameter deviates significantly from the preconditions of the stress calculation formula in the Japan Society of Civil Engineers guidelines, the accuracy of the joint strength evaluation can be improved. Accordingly, the joint strength evaluation method according to this embodiment makes it possible to evaluate the joint strength of an adhesive joint represented by an adhesive joint parameter that deviates from the preconditions of the stress calculation formula in the Japan Society of Civil Engineers guidelines.

[0067] In the joint strength evaluation method according to this embodiment, in the evaluation position identification step (step S12), the evaluation position is identified as a position from the end of the adhesive such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the stress calculation formula of the Japan Society of Civil Engineers guidelines. By identifying the evaluation position in such a way that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the stress calculation formula of the Japan Society of Civil Engineers guidelines, it becomes possible to evaluate the joint strength using a more accurate value from the distribution of analytical stress values ​​of the finite element analysis model.

[0068] In the joint strength evaluation method according to this embodiment, the evaluation position identification step (steps S10, S11) uses a first finite element analysis model that does not consider geometric nonlinearity and a stress calculation formula from the Japan Society of Civil Engineers guidelines that applies to steel plates with a plate thickness of 9 mm or more. This makes it possible to reduce the error between the analyzed stress value and the theoretical value by using the first finite element analysis model and the predetermined stress calculation formula from the Japan Society of Civil Engineers guidelines based on material mechanics, thereby enabling more reliable identification of the evaluation position.

[0069] In the joint strength evaluation method according to this embodiment, the first stress acquisition step (step S13) uses a second finite element analysis model that takes geometric nonlinearity into account. This makes it possible to accurately calculate the analytical stress values ​​of the second finite element analysis model, for example, under conditions such as when the member is a thin plate.

[0070] In the joint strength evaluation method according to this embodiment, the first stress acquisition step (step S13) uses a second finite element analysis model in which the plate material thickness is 2 mm or less. This makes it possible to evaluate the joint strength of adhesive joints that cannot be adequately evaluated by the stress calculation formula of the Japan Society of Civil Engineers guidelines, which is intended for plate materials with a thickness of 9 mm or more.

[0071] Furthermore, according to the joint strength evaluation method of this embodiment, since the thickness of the adherend is more sensitive to the stress calculation formula than the Young's modulus of the adherend, the strength can be evaluated even when the adherends are made of different materials, as long as the materials do not undergo plastic deformation. In addition, it is possible to evaluate the joint strength of adhesive joints used for thin plate members such as the body of a railway vehicle.

[0072] While embodiments of this disclosure have been described above, this disclosure is not limited to the embodiments described above. This disclosure can be implemented in various forms, including the embodiments described above, with various modifications and improvements based on the knowledge of those skilled in the art.

[0073] In the above embodiment, the stress calculation formula in the Japan Society of Civil Engineers guidelines was given as an example of a predetermined theoretical formula based on material mechanics, but the invention is not limited to this example. Any other theoretical formula that can calculate the stress distribution in an adhesive based on material mechanics may be used.

[0074] In the above embodiment, when identifying the evaluation position, the end of the adhesive was defined as a position inside the adhesive in the longitudinal direction of the adherend, with the constrained end side of the adhesive joint in the analysis model (left side in Figure 5) as the origin. However, the embodiment is not limited to this example. The end of the adhesive may be, for example, a position from the free end side of the adhesive joint in the analysis model.

[0075] In the above embodiment, the evaluation position was identified such that the analytical stress value obtained from the first finite element analysis model and the theoretical stress value obtained from the theoretical formula were equal. However, the invention is not limited to this example. For example, the evaluation position may be identified such that the analytical stress value obtained from the first finite element analysis model and the theoretical stress value obtained from the theoretical formula fall within a predetermined equivalent range.

[0076] In the above embodiment, geometric nonlinearity was not considered in the first finite element analysis model, but it may be considered. A theoretical formula was used for steel plates with a thickness of 9 mm or more, but the model is not limited to this example. Various other conditions may be used as preconditions for the theoretical formula. A second finite element analysis model was used for plates with a thickness of 2 mm or less, but the model is not limited to this example. Various other adhesive joint parameters may be used as adhesive joint parameters that deviate from the preconditions of the theoretical formula. Adhesive joint parameters other than the thickness of the plate may also be used.

[0077] In the above embodiment, geometric nonlinearity was considered in the second finite element analysis model, but the model is not limited to this example. For example, if the impact of not considering geometric nonlinearity is small and the error can be reduced by specifying the evaluation position, then geometric nonlinearity may not be considered in the second finite element analysis model.

[0078] The constituent elements of various aspects of this disclosure are described below. [1] A method for evaluating the joint strength of adhesive joints bonded using an adhesive, An evaluation position identification step involves identifying an evaluation position, which is the position from the end of the adhesive where the stress generated in the adhesive is evaluated, using a first finite element analysis model representing the adhesive joint with first adhesive joint parameters and a predetermined theoretical formula based on material mechanics. A first stress acquisition step involves obtaining a first stress at the evaluation position corresponding to the input load on the adhesive, using a second finite element analysis model that represents the adhesive joint with second adhesive joint parameters different from the first adhesive joint parameters, A second stress acquisition step to obtain a second stress at the evaluation position corresponding to the tensile strength of the adhesive, A method for evaluating joint strength, comprising: an evaluation step of evaluating the joint strength with respect to cohesive failure based on the relationship between the magnitudes of the first stress and the second stress on a plane with shear stress and normal stress as axes. [2] The method for evaluating joint strength according to [1], wherein in the step of identifying the evaluation position, the evaluation position is identified as a position from the end of the adhesive such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula. [3] The method for evaluating joint strength according to [1] or [2], wherein the evaluation position identification step uses the first finite element analysis model that does not consider geometric nonlinearity and the theoretical formula that applies to steel plates with a thickness of 9 mm or more. [4] The method for evaluating joint strength described in any one of [1] to [3] uses the second finite element analysis model that takes geometric nonlinearity into account in the first stress acquisition step. [5] The method for evaluating joint strength described in any one of [1] to [4], wherein the first stress acquisition step uses the second finite element analysis model in which the thickness of the plate material is 2 mm or less. [Explanation of Symbols]

[0079] 10 Upper test specimen 11 End 12 End 13 board 20 Lower test specimens 21 End 22 End 23 board 30 strain gauges 100 adhesive joints L1 Dashed line L2 dashed line L3 dashed line

Claims

1. A method for evaluating the joint strength of adhesive joints bonded using an adhesive, An evaluation position identification step involves identifying an evaluation position, which is the position from the end of the adhesive where the stress generated in the adhesive is evaluated, using a first finite element analysis model representing the adhesive joint with first adhesive joint parameters and a predetermined theoretical formula based on material mechanics. A first stress acquisition step is performed to obtain a first stress at the evaluation position corresponding to the input load to the adhesive, using a second finite element analysis model that represents the adhesive joint with second adhesive joint parameters different from the first adhesive joint parameters, A second stress acquisition step to obtain a second stress at the evaluation position corresponding to the tensile strength of the adhesive, A method for evaluating joint strength, comprising: an evaluation step of evaluating the joint strength with respect to cohesive failure based on the relationship between the magnitudes of the first stress and the second stress on a plane with shear stress and normal stress as axes.

2. The method for evaluating joint strength according to claim 1, wherein in the evaluation position identification step, the evaluation position is identified as a position from the end of the adhesive such that the analytical stress value obtained from the first finite element analysis model is equal to the theoretical stress value obtained from the theoretical formula.

3. The method for evaluating joint strength according to claim 1 or 2, wherein the evaluation position identification step uses the first finite element analysis model that does not consider geometric nonlinearity and the theoretical formula that applies to steel plates with a thickness of 9 mm or more.

4. The method for evaluating joint strength according to claim 3, wherein the first stress acquisition step uses the second finite element analysis model that takes geometric nonlinearity into consideration.

5. The method for evaluating joint strength according to claim 4, wherein in the first stress acquisition step, the second finite element analysis model is used in which the thickness of the plate material is 2 mm or less.

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