Apparatus for evaluating the joint strength of a single lap joint and its program

Abstract

To appropriately evaluate the joint strength of connecting materials forming a single-lap joint structure. [Solution] The joining material 10, which forms a single-lap joint structure by overlapping and joining the one ends of the first and second flake members 11 and 12 vertically, is equipped with a calculation processing unit that has a formula pre-stored based on the energy release rate associated with crack propagation at the joining interface. When the same tensile load is applied to each flake member 11 and 12 in an outward direction from the other end, the calculation processing unit considers the thermal residual stress of the joint 23, separates the energy release rate for in-plane opening type and in-plane shear type failure modes, and is configured to evaluate the joint strength characteristics by numerical analysis based on the failure conditions when a crack generated in the joint 23 propagates from one flake member 11 to the other flake member 12.

Description

[Technical Field]

[0001] The present invention relates to a joint strength evaluation device and program for evaluating the joint strength characteristics of a joint material that forms a single-lap joint structure by overlapping and joining one end of a first and second piece-shaped member vertically. [Background technology]

[0002] To lighten the weight of aircraft fuselages and the structures of transportation equipment such as automobiles, and to improve fuel efficiency, dissimilar joining technologies are being developed to join components made of different materials. Numerous technologies for evaluating the interfacial properties of dissimilar joining materials have been studied. Various JIS test methods have been standardized to measure the energy release rate, which is the fracture toughness value that represents the energy per unit area required for crack propagation in a material, as an indicator of fracture toughness at the joint interface. These JIS test methods include the double cantilever beam test (DCB test) and the end-face notched bending test (ENF test). The DCB test is a test concerning a mode I, in-plane opening type crack deformation state, performed with a load applied to cause the crack to open vertically. The ENF test is a test concerning a mode II, in-plane shear type crack deformation state, performed with a load applied along the crack extension direction (length direction) from the crack tip side. In particular, it is known that exact solutions based on linear elasticity theory at the crack tip of a joint interface between dissimilar materials exhibit oscillations in the stress and displacement fields, and, except in special cases, the stress intensity factors cannot be separated between Mode I and Mode II. Therefore, when evaluating the fracture toughness of a joint interface between dissimilar materials, the ratio of the energy release rates in Mode I and Mode II is used as a parameter. On the other hand, the single-lap joint test (Non-Patent Literature 1) is often used as a method for evaluating the joint strength of a material interface, which is a trade-off with fracture toughness. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] JIS K6850 "Adhesives - Test method for tensile shear bond strength of rigid adherends" (1999) [Overview of the project] [Problems that the invention aims to solve]

[0004] In the aforementioned single-lap joint test, the apparent shear strength, obtained by dividing the fracture load by the joint area, is evaluated as the joint strength. However, in reality, the joint strength is affected by the stress singularity at the joint ends and the bending resulting from the asymmetry of the test specimens made of dissimilar materials, making it difficult to say that the joint strength is being properly evaluated. Here, methods for evaluating the joint strength of a single-lap joint test include evaluation using stress-strain criteria and evaluation using fracture mechanics parameters. In the former case, the brittleness and ductility properties of the adhesive and adherend are considered, and stress and strain criteria at the joint ends are applied. Generally, joint strength improves as the thickness of the adhesive decreases, but in stress analysis, the stress at the joint ends increases, so joint strength may not be accurately predicted using only fracture criteria of stress and strain at the joint ends. Furthermore, in the latter method using fracture mechanics parameters, numerical analysis using a bonding force model is employed, but it is difficult to understand which material parameters are the dominant factors influencing the strength characteristics and to determine the optimal combination of materials in order to understand the joining mechanism. Therefore, the inventors have diligently researched a method for evaluating joint strength characteristics from a mechanical model based on fracture mechanics. As a result, we devised a new model that allows for the numerical evaluation of joint strength characteristics by considering the bending deformation unique to single-lap joints and the effects of thermal residual stress generated during joining, and by deriving the energy release rate associated with crack propagation at the joint interface in a closed form through mode separation.

[0005] The present invention is based on the inventors' knowledge and aims to provide a joint strength evaluation device and program that can appropriately evaluate the joint strength of a jointing material forming a single lap joint structure. [Means for solving the problem]

[0006] In order to achieve the above object, the present invention mainly provides a joint strength evaluation apparatus for evaluating the joint strength characteristics of a joint material having a single lap joint structure in which one end side of the first and second sheet members are overlapped and joined vertically. The apparatus includes an arithmetic processing unit in which a mathematical formula based on the energy release rate associated with crack propagation at the joint interface of the joint material is stored in advance. When the same tensile load is applied to each of the other end sides of the sheet members in the outward direction, the arithmetic processing unit takes into account the thermal residual stress at the joint of the joint material, separates the energy release rate in each of the in-plane opening mode and the in-plane shear mode, and is configured to be able to evaluate the joint strength characteristics by numerical analysis based on the fracture condition when the crack generated at the joint progresses from one side of the sheet member to the other side of the sheet member.

Effect of the Invention

[0007] According to the present invention, by considering the bending deformation peculiar to the single lap joint structure and the influence of the thermal residual stress generated during joining, separating the energy release rate associated with crack propagation at the joint interface by mode, and deriving it in a closed form, the joint strength characteristics can be appropriately evaluated. That is, even in the case of joining different materials, by arbitrarily specifying various shape sizes and material properties, the joint strength characteristics at that time can be evaluated by numerical analysis. Therefore, without conducting a single lap joint test, it is possible to easily estimate various combinations of sizes and materials that are optimal for joining members required during actual use. [[ID=了]]

Brief Description of the Drawings

[0008] [Figure 1] It is a perspective view of a joint material of a single lap joint structure used as a model in the present embodiment. [Figure 2] It is a diagram for explaining the shape size, etc. of the joint material. [Figure 3] It is a diagram including a free body diagram (FBD) for explaining the axial force distribution, etc. around the first crack in the joint material. [Figure 4]This figure includes a free-body diagram (FBD) for explaining the axial force distribution around the second crack in the aforementioned joint material. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings.

[0010] The bonding strength evaluation apparatus according to the present invention consists of hardware and software, comprising a processing unit such as a CPU, a storage device such as memory or a hard disk, and program modules that enable these devices to function, and has the following program installed to function as the processing unit.

[0011] The aforementioned calculation processing unit formulates the forces and moments acting on the joint ends of the single-lap joint structure shown in Figures 1 and 2, enabling the evaluation of the joint strength characteristics of the joining materials forming the single-lap joint structure. In other words, this calculation processing unit has a formula pre-stored based on the energy release rate associated with crack propagation at the joint interface of the single-lap joint structure. As will be described later, this formula allows, for example, the shape, size, and material properties of the members constituting the joining material to be set to predetermined values, and when either the critical energy release rate or the joint strength (critical fracture load) of each fracture mode in the joining material (in-plane opening type and in-plane shear type) is taken as an input value, the other can be derived as an output value for each crack length.

[0012] As shown in Figure 1, the model joint 10 has a single lap joint structure in which the ends of first and second piece-shaped members 11 and 12, which are made of elongated plate material having the same width B as each other, are joined by overlapping them vertically.

[0013] The first and second flake members 11 and 12 are stacked on top of each other so as not to shift in the width direction. As shown in Figure 2, in the overlapping portion 14, the first and second cracks 21 and 22 (delamination portions) are located at both ends in the length direction, which is the extension direction of each flake member 11 and 12, and the remaining portion is the joint portion 23, which is the joining region of each flake member 11 and 12. In the following description, the boundary portions between the first and second cracks 21 and 22 and the joint portion 23 will be referred to as the first and second crack tips 21A and 22A.

[0014] In the above model, the same tensile load P is applied to the first and second flake members 11 and 12, pulling them outward from the other end (free end) in the longitudinal direction, not the joint 23 side. Based on the fracture conditions when a crack propagates from the first flake member 11 to the second flake member 12, the joint strength characteristics can be evaluated. In other words, the calculation processing unit is configured to consider the thermal residual stress of the joint 23 using the formulas described later, separate the energy release rates for each fracture mode (in-plane opening type and in-plane shear type), and evaluate the joint strength characteristics by numerical analysis based on the fracture conditions when a crack generated in the joint 23 propagates from the first flake member 11 to the second flake member 12.

[0015] In the following explanation, the coordinate axes will be defined as follows: the length direction of each piece-shaped member 11, 12 will be the x-axis, and the thickness direction (vertical direction) of each piece-shaped member 11, 12, which is perpendicular to the x-axis, will be the z-axis. Furthermore, the angle θ of the direction of action of the tensile load P with respect to the x-axis in the plane of Figure 2 is determined according to the predetermined shape of the joint 10.

[0016] Furthermore, the shape and size of the first and second flake-shaped members 11 and 12 shall be expressed as follows: the thicknesses of the first and second flake-shaped members 11 and 12 shall be h1 and h2, respectively. The total length of the joining material 10 shall be L, the length of the joint 23 shall be l, and the lengths of the first and second cracks 21 and 22 shall be t, respectively. R , t LLet the lengths of the first and second sheet-like members 11 and 12, excluding the overlap portion 14, be l1 and l2, respectively. Therefore, the thicknesses h1 and h2, and the lengths L, l1, and l2 are constants specified according to the shapes of the respective sheet-like members 11 and 12, and the crack length t R , t L , and the length l of the joint 23 (l = L - (l1 + l2 + t R + t L )) are variables.

[0017] Also, in the following equations, elements with the letter "N" attached represent the force components in the x-axis direction, which is the horizontal direction, elements with the letter "Q" attached represent the force components in the z-axis direction, which is the vertical direction, and elements with the letter "M" attached represent the moment components.

[0018] The equations according to the model are as follows. Here, various combinations of different materials are assumed for the first and second sheet-like members 11 and 12, but the selection of the same material is also possible.

[0019] First, when the joint state of the first and second sheet-like members 11 and 12 is completely released and they separate from each other, the fracture condition equation is as follows. In this embodiment, the exponent part of Equation (1) is squared, but the present invention is not limited to this, and a value n fitted according to the material can be adopted, and usually n = 1 or 2 is used.

Equation

[0020]

number

[0021] Each internal force N C Q C It is calculated by the following formula.

number

[0022] The coefficients F1 and F2 in equations (6) and (7) above are obtained from the boundary conditions at both ends of the joint 23, and from Ci and a in equations (4) and (5) above. i , b i d i Using k, κ, etc., the following formulas can be used to determine the answer.

number

[0023] Here, N in equations (6) to (9) above e (l), M e (l), N c (0), Q c (0), M c (0) can be obtained by the following formulas.

number

number

[0024] Here, N in equations (16) to (18) and (23) to (25) above. 10Q 10 M 10 These are the horizontal internal force, vertical internal force, and moment acting near the first crack tip 21A in the first flake member 11, as shown in Figure 3, and can be calculated using the following equations. Note that N in equations (23) to (25) above 20 Q 20 M 20 These are the horizontal internal force, the vertical internal force, and the moment acting near the first crack tip 21A in the second flake member 12. However, since the tensile load on the second flake member 12 is borne by the second crack tip 22A, these forces do not bear any load and are therefore calculated as zero.

number

[0025] In the above-described joint strength evaluation device, predetermined values ​​are set based on the aforementioned shape, size, and material properties of the first and second flake members 11 and 12, and then the critical energy release rate G of each mode is evaluated. IC , G IIC By inputting this, the tensile load P at which the joint state of the joint 23 is completely released can be calculated based on the failure condition equation (1) above. The tensile load P at this time corresponds to the joint strength (critical failure load) of the single lap joint test and the length t of the cracks that occur on both the left and right sides of the overlap portion 14. R , t L This is required in response to the need for a specific solution. Therefore, without actually performing a single-lap joint test, the joint strength characteristics associated with crack propagation in single-lap joint structures made of various sizes of different or identical materials can be understood through numerical analysis, making it easy to identify the optimal size and material selection for joining members.

[0026] Furthermore, according to experiments conducted by the inventors, single-lap joint tests were performed on first and second flap-shaped members 11 and 12 having predetermined shapes, sizes, and material properties. The results showed that the apparent shear strength obtained from the tests was in good agreement with the shear strength calculated from the critical load of fracture based on numerical analysis results using the joint strength evaluation device of the present invention, demonstrating the accuracy of the joint strength evaluation device.

[0027] Furthermore, according to the failure condition equation (1) above, improving either the critical energy release rate of mode I or mode II will satisfy the failure condition for either mode I or mode II. Therefore, in order to improve joint strength, it is necessary to devise ways to improve the fracture toughness of both fracture modes. In this regard, by using the tensile load P assumed as the critical load of fracture for a single lap joint structure as the input value, the apparent critical energy release rate G that can be taken according to equation (1) above can be determined. IC , G IIC The interrelationships between them are understood, and based on these interrelationships, the highest critical energy release rate G between them is determined. IC , G IIC This makes it possible to explore combinations of these factors. This also makes it possible to comparatively evaluate fracture toughness based on differences in the joining morphology of the joint 23 (engagement due to irregularities, spikes, etc.).

[0028] Furthermore, by arranging the first and second flake-shaped members 11 and 12 inverted vertically and performing numerical analysis with the joint strength evaluation device, it becomes possible to evaluate the situation under which a crack propagates from the second flake-shaped member 12 to the first flake-shaped member 11. By comparing this with the energy release rate when a crack propagates from the first flake-shaped member 11 to the second flake-shaped member 12, it becomes easier to determine which direction the crack will propagate, as a higher value indicates easier crack propagation. [Explanation of Symbols]

[0029] 10 Bonding material 11 First flake-shaped member 12 Second flake-shaped member 14 Overlapping section 21 First crack 22 Second crack 23 Joint

Claims

1. In a joint strength evaluation device for evaluating the joint strength characteristics of a joint material that forms a single-lap joint structure by overlapping and joining the one ends of the first and second piece-shaped members vertically, The system includes a calculation processing unit in which a mathematical formula based on the energy release rate associated with crack propagation at the bonding interface of the aforementioned bonding material is pre-stored. The single lap joint joint strength evaluation device is characterized in that the calculation processing unit is configured to evaluate the joint strength characteristics by numerical analysis based on the failure conditions when a crack generated in the joint propagates from one of the flake members to the other flake member, taking into account the thermal residual stress at the joint of the joining material when the same tensile load is applied outward from the other end of each flake member.

2. The single-lap joint strength evaluation device according to claim 1, characterized in that, when the shape size and material properties of each flake member and the critical energy release rate of each fracture mode are input values ​​to the formula, the critical fracture load under tensile load is derived as an output value for each length of the crack.

3. The single-lap joint strength evaluation device according to claim 1, characterized in that, when the shape size and material properties of each flake member and the critical failure load under the tensile load are taken as input values ​​in the formula, the critical energy release rate of each failure mode is derived as an output value for each length of the crack.

4. In a program for a joint strength evaluation device that evaluates the joint strength characteristics of a joint material forming a single-lap joint structure in which the ends of first and second piece-shaped members are joined by overlapping them vertically, The computer functions as a calculation processing unit in which a mathematical formula based on the energy release rate associated with crack propagation at the bonding interface of the aforementioned bonding material is pre-stored. The program for evaluating the joint strength of a single lap joint is characterized in that the calculation processing unit is configured to evaluate the joint strength characteristics by numerical analysis based on the failure conditions when a crack generated in the joint propagates from one of the flake members to the other flake member, taking into account the thermal residual stress at the joint of the joining material when the same tensile load is applied outward from the other end of each flake member.

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