A method for compressive-shear failure analysis of laminates considering the competition between buckling and first-layer failure

Abstract

The present invention discloses a method for analyzing the compression-shear failure of laminates considering the competition between buckling and first-layer failure, comprising the following steps: (1) calculating an initial load based on a load ratio; (2) solving the buckling load of the laminate based on the Rayleigh-Ritz method; (3) predicting the first-layer failure load of the laminate based on a Hashin failure criterion; (4) comparing the buckling load and the first-layer failure load to determine the failure load and failure mode of the laminate; (5) fitting the failure load and failure mode under multiple load ratios to obtain a compression-shear failure curve of the laminate, which is used to judge the failure condition of the laminate under any load ratio. The present invention predicts the buckling load and first-layer failure load of the laminate under different compression-shear loads based on a theoretical method, establishes a method for analyzing the compression-shear failure of laminates considering the competition between buckling and first-layer failure, and further provides a compression-shear failure curve of the laminate, which can significantly improve the efficiency of structural design and reduce the cost of testing.

Description

Technical Field

[0001] The present invention relates to the field of failure analysis of composite laminates, and in particular to a laminate compression-shear failure analysis method that considers the competition between buckling and first-layer failure. Background Art

[0002] Laminates are one of the most widely used structural forms of fiber-reinforced composites in aircraft structures. Due to their excellent in-plane mechanical properties, they are often used in aerospace structures such as aircraft and rockets. Existing design guidelines for composite laminate structures include some that prohibit buckling of structures such as skins under allowable loads, while others prohibit static damage and degradation of the material. Considering that both buckling and overstress damage can reduce the structural load-bearing capacity and affect structural safety, structural design must simultaneously avoid both behaviors to ensure that the structure does not fail during use.

[0003] The study found that the order in which buckling and structural static damage occur is not fixed, and there is a competitive relationship between the two. Existing structural failure studies mostly use experimental methods or numerical calculation methods, both of which require a high time and economic cost, making it impossible to carry out systematic research. This leads to a lack of comprehensive understanding and in-depth exploration of the competitive phenomenon in existing research, which seriously restricts the structural design efficiency in engineering practice and the performance utilization of laminate structures in the overall structure of aircraft. In comparison, theoretical methods have simple models and small computational complexity, and scholars have conducted a large number of theoretical-based studies on the buckling and static damage of composite laminates. However, few scholars have used theoretical methods to simultaneously study the buckling and static damage behaviors of laminates, and a theoretical-based research method for the competitive relationship between buckling and static damage has yet to be established.

[0004] Therefore, predicting the competitive relationship between buckling and static damage in laminate structures based on fast and efficient theoretical methods is an important part of composite laminate structure design and failure analysis, and has important guiding value for the efficient application of composite materials in aircraft structures. It is within this context that this method proposes a compressive-shear failure analysis method for laminates that considers the competitive relationship between buckling and first-ply failure. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: to overcome the shortcomings of the existing technology, and based on theories such as the Rayleigh-Ritz method, the Hashin failure criterion and the first-layer failure criterion, provide a laminate compression-shear failure analysis method that considers the competition between buckling and first-layer failure, realize the compression-shear buckling and first-layer failure sequence prediction of laminates based on theoretical methods, improve the failure analysis efficiency of laminates, and reduce the time and economic costs in structural design.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a laminate compression-shear failure analysis method considering the competition between buckling and first-layer failure, comprising the following steps:

[0007] 1. A method for analyzing laminate compression-shear failure considering the competition between buckling and first-layer failure, characterized by comprising the following steps:

[0008] Step A: Calculate the initial load based on the load ratio. The specific implementation process is as follows:

[0009] (A1) Given shear load N xy With compression load N x The ratio of load ratio η:

[0010] (A2) Given the initial compressive load:

[0011]

[0012] Then the initial shear load is calculated:

[0013] N xy0 =ηN x0 (2)

[0014] Step B, solve the buckling load of the laminate based on the Rayleigh-Ritz method. The specific implementation process is as follows:

[0015] (B1) Based on the Rayleigh-Ritz method, the out-of-plane displacement field of the laminate is assumed to be an expression with unknown coefficients:

[0016]

[0017] Where w is the out-of-plane (z-direction) displacement field at any point in the neutral plane of the laminate, W ij is the unknown coefficient in the expression, f(x,y,i,j) is the shape function of the layer plate, and I and J control the number of shape functions used to simulate the displacement field;

[0018] (B2) Combined with classical laminate theory, the total strain energy U of the entire laminate, the external work K and the total potential energy Π of the laminate are obtained;

[0019] Π=U+K (4)

[0020] (B3) Substitute the assumed displacement field into the total potential energy expression, and take the total potential energy as the goal to minimize, and let the total potential energy Π for each unknown coefficient W ij Calculate the variation and transform the problem into a set of linear equations as shown in formula (5), and further solve the buckling eigenvalue of the structure;

[0021]

[0022] (B4) Take the minimum value of each buckling eigenvalue of the laminate as the critical buckling eigenvalue λ of the laminate cr , further calculate the buckling load of the laminate under the current load ratio:

[0023]

[0024]

[0025] in and are the compression load and shear load when the laminate buckles, respectively.

[0026] Step C, predicting the failure load of the first layer of the laminate based on the Hashin failure criterion. The specific implementation process is as follows:

[0027] (C1) Determine the stress of each layer in the main direction of the material based on the relationship between load, strain and stress

[0028]

[0029] Among them, k is the serial number of each layer, T k is the coordinate transformation matrix of each layer, is the elastic coefficient matrix of each layer in the reference coordinate system, A is the tensile stiffness matrix of the laminate, and N0 is the initial load vector of the laminate;

[0030] (C2) Using the modified two-dimensional Hashin criterion, the material failure mode of each single layer is judged:

[0031] Fiber stretching:

[0032] Fiber Compression:

[0033] Matrix stretching:

[0034] Matrix compression:

[0035] Fiber base shearing:

[0036] in are the failure state variables of each single layer, σ1, σ2 and τ 12 for The three components of X T 、X C 、Y T 、Y C and S 12 They are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength and in-plane shear strength of the material;

[0037] (C3) Use the first layer failure criterion to judge the failure of the laminate. When , it is judged that static damage occurs in the structure;

[0038] (C4) Define the load factor based on the linear relationship between load and stress

[0039]

[0040] Further, the minimum value of the load coefficient corresponding to different single layers and different failure modes is taken as the first layer failure load coefficient R of the structure. cr :

[0041]

[0042] (C5) by R cr The first layer failure load of the laminate is calculated as follows:

[0043]

[0044]

[0045] in and are the compression load and shear load when the first layer of the laminate fails, respectively.

[0046] Step D: Compare the buckling load and the first-layer failure load to determine the failure load and failure mode of the laminate. The specific implementation process is as follows:

[0047] (D1) When It is assumed that the laminate buckles preferentially under the current load ratio, and the compression and shear buckling loads in equations (6a) and (6b) are the failure loads;

[0048] (D2) When It is assumed that the first layer failure occurs first under the current load ratio, and the first layer failure load in compression and shear in formulas (11a) and (11b) is the failure load;

[0049] Step E: The compression-shear failure curve of the laminate is obtained by fitting the failure load and failure mode under multiple load ratios within the range of η∈(-∞,+∞). This curve is used to determine the failure condition of the laminate under any load ratio. The specific implementation process is as follows:

[0050] (E1) Select multiple load ratios within the range of η∈(-∞,+∞) and solve the failure load and failure mode of the same laminate structure under different load ratios according to the above steps AD;

[0051] (E2) Using the compression load as the abscissa and the shear load as the ordinate, plot the points corresponding to each failure load in a rectangular coordinate system. Fit the points to multiple buckling curves and the first-layer failure curve according to the failure form. Then, combine the curves to obtain the compression-shear failure curve of the laminate structure in the range of η∈(-∞,+∞);

[0052] (E3) For any given load ratio η*, N xy / N x =η* can form a ray in the rectangular coordinate system. The horizontal and vertical coordinates corresponding to the intersection of the ray and the compression-shear failure curve are the compression and shear loads of the laminate failure under this load ratio. If the intersection of the ray and the compression-shear failure curve falls on the buckling curve, then the failure mode of the structure under this load ratio is buckling; if the intersection of the ray and the compression-shear failure curve falls on the first-layer failure curve, then the failure mode of the structure under this load ratio is first-layer failure.

[0053] The advantages of the present invention compared with the prior art are:

[0054] 1. Existing academic research and engineering applications lack methods for analyzing the competitive behavior of composite laminate buckling and first-ply failure, hindering the ability to quickly and economically predict the failure modes and loads of laminates under different combined compression and shear loads. This paper proposes a theoretical analysis method. This method features a simple model and fast computational speed, effectively predicting the failure behavior of the same structure under different load ratios, providing a reference and basis for composite aircraft design.

[0055] 2. The present invention proposes a laminate compression-shear failure analysis method that takes into account the competition between buckling and first-layer failure, which can reduce the experimental and computational workload in composite laminate structure design and failure analysis, and significantly reduce the time and economic costs of testing and calculation.

[0056] 3. Prior to this study, no theoretical analysis method that simultaneously considers both buckling and static failure had been proposed. The buckling analysis and first-layer failure analysis methods proposed in this study are both well-established methods that have been extensively documented. The predicted results are highly consistent with theoretical analysis, experimental, and numerical results provided in the literature, demonstrating the validity of the proposed analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is an implementation flow chart of the present invention.

[0058] Figure 2a It is a schematic diagram of the geometric parameters of the laminate.

[0059] Figure 2b Schematic diagram of the laminate loads and boundary conditions.

[0060] Figure 3a is the compression-shear failure curve of Graphite / Epoxy laminates.

[0061] Figure 3b is the compression shear failure curve of Glass / Epoxy laminate.

[0062] Figure 3c is the compression-shear failure curve of Aramid / Epoxy laminates.

[0063] Figure 3d is the compression-shear failure curve of Boron / Epoxy laminates. DETAILED DESCRIPTION

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] The present invention is a laminate compression-shear failure analysis method considering the competition between buckling and first-layer failure. The implementation process is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0066] Example 1: Compression-shear failure analysis of a four-sided simply supported symmetric laminate considering the competition between buckling and first-layer failure

[0067] like Figure 2a As shown in , consider a rectangular laminate with geometric dimensions of a (length) × b (width) × t (thickness), and a total number of layers n. Figure 2b As shown in Figure 3, the plate is simply supported on four sides and bears axial compression load in the x-direction and in-plane shear load.

[0068] Step A: Calculate the initial load based on the load ratio. The specific implementation process is as follows:

[0069] (A1) Given the current load ratio as η.

[0070] (A2) Compression load is Shear load is N xy0 =ηN x0 .

[0071] Step B, solve the buckling load of the laminate based on the Rayleigh-Ritz method. The specific implementation process is as follows:

[0072] (B1) Buckling analysis of the structure is performed, and the out-of-plane displacement field assumption of the four-sided simply supported laminate is given:

[0073]

[0074] (B2) Combining the ply and load characteristics of the laminate, the total strain energy U of the entire laminate, the external work K exerted on the laminate, and the total potential energy Π can be obtained:

[0075]

[0076] Where A is the area of ​​the laminate, D ij is the bending stiffness coefficient of the structure;

[0077]

[0078] Π=U+K (4)

[0079] (B3) Substitute the assumed displacement field into the total potential energy expression, and take the total potential energy as the goal to minimize, and let the total potential energy Π for each unknown coefficient W ij The variation is calculated and the problem is transformed into a set of linear equations as shown in formula (5), and the buckling eigenvalue of the structure is further solved.

[0080]

[0081] (B4) Take the minimum value of each buckling eigenvalue of the laminate as the critical buckling eigenvalue λ of the laminate cr , further calculate the buckling load of the laminate under the current load ratio:

[0082]

[0083]

[0084] Step C, predicting the failure load of the first layer of the laminate based on the Hashin failure criterion. The specific implementation process is as follows:

[0085] (C1) Determine the stress of each layer in the main direction of the material based on the relationship between load, strain and stress

[0086]

[0087] (C2) Using the modified two-dimensional Hashin criterion, the material failure mode of each single layer is judged:

[0088] Fiber stretching:

[0089] Fiber Compression:

[0090] Matrix stretching:

[0091] Matrix compression:

[0092] Fiber base shearing:

[0093] (C3) Use the first layer failure criterion to judge the failure of the laminate. When , it is judged that static damage occurs in the structure.

[0094] (C4) Calculation of load factor and the first-floor failure load factor R cr :

[0095]

[0096]

[0097] (C5) is further cr The first layer failure load of the laminate is calculated as follows:

[0098]

[0099]

[0100] Step D: Compare the buckling load and the first-layer failure load to determine the failure load and failure mode of the laminate. The specific implementation process is as follows:

[0101] (D1) When It is assumed that the laminate buckles preferentially under the current load ratio, and the compression and shear buckling loads in equations (6a) and (6b) are the failure loads;

[0102] (D2) When It is assumed that the first layer failure occurs first under the current load ratio, and the first layer failure load in compression and shear in formulas (10a) and (10b) is the failure load.

[0103] Step E: The compression-shear failure curve of the laminate is obtained by fitting the failure loads and failure modes under multiple load ratios, which is used to determine the failure condition of the laminate under any load ratio. The specific implementation process is as follows:

[0104] (E1) According to the above process, the four material systems of Graphite / Epoxy, Glass / Epoxy, Aramid / Epoxy and Boron / Epoxy are tested respectively, [±45] s For a composite laminate with a layup and dimensions of a:b:t = 50:50:1 (mm), multiple load ratios were selected within the range η∈(-∞,+∞). Following steps A to D, the failure load and failure mode of each material laminate structure at different load ratios were calculated. The corresponding performance parameters for each material system are listed in Table 1. The load ratios selected in the analysis varied across the material systems and were determined based on the needs of the curve fit.

[0105] Table 1 Performance parameters of various material systems

[0106]

[0107] (E2) With compression load as the horizontal coordinate and shear load as the vertical coordinate, draw the corresponding points of each failure load in the rectangular coordinate system. According to the failure form, fit the points into multiple buckling curves and the first layer failure curve. Then, combine the curves to obtain the compression-shear failure curve of the laminate structure in the range of η∈(-∞,+∞). The failure curve of the Graphite / Epoxy laminate is as follows: Figure 3a As shown in Figure 2, the failure curve of the Glass / Epoxy laminate is as follows: Figure 3b As shown in Figure 2, the failure curve of Aramid / Epoxy laminate is as follows: Figure 3c As shown, the failure curve of Boron / Epoxy laminate is as follows Figure 3d The areas exceeding the failure load in the figure are divided according to the distribution of the buckling curve and the first-story failure curve. The light gray area indicates that the structure buckles first within this load ratio range, while the dark gray area indicates that the first-story failure occurs first.

[0108] (E3) For each material of the laminate structure, the failure load and failure mode of the structure under a given load ratio η* can be determined by the failure curve. xy / N x =η* can form a ray in the rectangular coordinate system. The horizontal and vertical coordinates corresponding to the intersection of the ray and the compression-shear failure curve are the compression and shear loads of the laminate failure under this load ratio. If the intersection of the ray and the compression-shear failure curve falls on the buckling curve, then the failure mode of the structure under this load ratio is buckling; if the intersection of the ray and the compression-shear failure curve falls on the first-layer failure curve, then the failure mode of the structure under this load ratio is first-layer failure.

[0109] Some parts of the present invention are well known to those skilled in the art and are not described in detail.

[0110] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A laminate compression-shear failure analysis method considering the competition between buckling and first-layer failure, characterized by: The following steps are involved: Step A, calculating the initial load according to the load ratio; Step B, solving the buckling load of the laminate based on the Rayleigh-Ritz method; Step C, predicting the failure load of the first layer of the laminate based on the Hashin failure criterion; Step D, comparing the buckling load and the first layer failure load to determine the failure load and failure mode of the laminate; Step E, fitting the failure load and failure mode under multiple load ratios within the range of η∈(-∞,+∞) to obtain the compression-shear failure curve of the laminate, which is used to determine the failure condition of the laminate under any load ratio; Among them, in step A, the specific implementation process is: (A1) Given shear load N xy With compression load N x The ratio of load ratio η: (A2) Given the initial compressive load: Then the initial shear load is calculated: N xy0 =ηN x0 (2) Among them, in step B, the specific implementation process is: (B1) Based on the Rayleigh-Ritz method, the out-of-plane displacement field of the laminate is assumed to be an expression with unknown coefficients: Where w is the out-of-plane (z-direction) displacement field at any point in the neutral plane of the laminate, W ij is the unknown coefficient in the expression, f(x,y,i,j) is the shape function of the layer plate, and I and J control the number of shape functions used to simulate the displacement field; (B2) Combined with classical laminate theory, the total strain energy U of the entire laminate, the external work K and the total potential energy Π of the laminate are obtained; Π=U+K (4) (B3) Substitute the displacement field into the total potential energy expression, and take the total potential energy as the goal to minimize, and let the total potential energy π for each unknown coefficient W ij Calculate the variation, transform the problem into a system of linear equations as shown in formula (5), and solve the buckling eigenvalue of the structure; (B4) Take the minimum value of each buckling eigenvalue of the laminate as the critical buckling eigenvalue λ of the laminate cr , calculate the buckling load of the laminate under the current load ratio: in, and are the compression load and shear load when the laminate buckles; Among them, in step E, the specific implementation process is: (E1) Select multiple load ratios within the range of η∈(-∞,+∞) and solve the failure load and failure mode of the same laminate structure under different load ratios according to the above steps AD; (E2) Using the compression load as the abscissa and the shear load as the ordinate, plot the points corresponding to each failure load in a rectangular coordinate system. Fit the points to multiple buckling curves and the first-layer failure curve according to the failure form. Then, combine the curves to obtain the compression-shear failure curve of the laminate structure in the range of η∈(-∞,+∞); (E3) For any given load ratio η*, N xy / N x =η* form a ray in the rectangular coordinate system. The horizontal and vertical coordinates of the intersection of the ray and the compression-shear failure curve are the failure compression and shear loads of the laminate under this load ratio. Among them, if the intersection of the ray and the compression-shear failure curve falls on the buckling curve, then the failure mode of the structure under this load ratio is buckling; if the intersection of the ray and the compression-shear failure curve falls on the first-floor failure curve, then the failure mode of the structure under this load ratio is first-floor failure.

2. The method for analyzing laminate compression-shear failure considering the competition between buckling and first-layer failure according to claim 1, characterized in that: In step C, the specific implementation process is: (C1) Determine the stress of each layer in the main direction of the material based on the relationship between load, strain and stress Among them, k is the serial number of each layer, T k is the coordinate transformation matrix of each layer, is the elastic coefficient matrix of each layer in the reference coordinate system, A is the tensile stiffness matrix of the laminate, and N0 is the initial load vector of the laminate; (C2) Using the modified two-dimensional Hashin criterion, the material failure mode of each single layer is judged: in, is the failure state variable of each single layer, m=1,2,…,5; σ1, σ2 and τ 12 for The three components of X T 、X C 、Y T 、Y C and S 12 They are the longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength and in-plane shear strength of the material; (C3) Use the first layer failure criterion to judge the failure of the laminate. When , it is judged that static damage occurs in the structure; (C4) Define the load factor based on the linear relationship between load and stress Take the minimum value of the load coefficient corresponding to different single layers and different failure modes as the first layer failure load coefficient R of the structure cr : (C5) by R cr The first layer failure load of the laminate is calculated as follows: in, and are the compression load and shear load when the first layer of the laminate fails, respectively.

3. The method for analyzing laminate compression-shear failure considering the competition between buckling and first-layer failure according to claim 2, characterized in that: In step D, the specific implementation process is: (D1) When It is assumed that the laminate buckles preferentially under the current load ratio, and the compression and shear buckling loads in equations (6a) and (6b) are the failure loads; (D2) When It is assumed that the first layer failure occurs first under the current load ratio, and the first layer failure load in compression and shear in formulas (11a) and (11b) is the failure load.

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