Method for generating crack propagation resistance curve for bridged toughened biomimetic helical structure

Abstract

The application discloses a crack propagation resistance curve generation method for bridged toughening biomimetic spiral structure and belongs to the field of composite material design. The prediction method comprises the following steps: acquiring geometric and material parameters of the biomimetic spiral structure; constructing a crack bridging fracture mechanics theoretical model of the biomimetic spiral structure; given a crack propagation length, solving a crack tip opening displacement by using a Newton iteration method; obtaining a fracture toughness by using the crack tip opening displacement; judging whether a steady state propagation stage is entered, if yes, obtaining a crack propagation resistance curve; and if not, increasing the crack propagation length. The application can quickly obtain fracture parameters such as the crack tip opening displacement and the crack propagation resistance curve by comprehensively considering structural heterogeneity, anisotropy and three-dimensional characteristics of the fiber spiral structure, and provides a technical approach for the toughening design of the biomimetic spiral structure.

Description

Technical Field

[0001] This invention relates to the field of biomimetic composite material design, specifically to a method for generating crack propagation resistance curves for bridging and toughening biomimetic helical structures. Background Technology

[0002] In traditional engineering materials, strength and toughness often exhibit contradictory properties. Materials typically dissipate localized stress through plastic deformation within a certain range, thereby improving toughness. This results in high-strength materials often being more brittle, while low-strength materials, due to their ease of deformation, possess better toughness. Good toughness allows materials to undergo a certain degree of deformation before failure, effectively releasing stress concentration and preventing sudden brittle fracture of the structure.

[0003] Through long-term natural evolution, organisms have developed many structural materials that combine lightweight, high strength, high toughness, and excellent impact resistance. These materials are primarily composed of hard inorganic minerals and soft organic polymers. Through multi-scale hierarchical assembly and complex interfacial bonding, they maintain high strength while achieving toughness several orders of magnitude higher than their constituent components, overcoming the traditional limitation that strength and toughness are difficult to achieve simultaneously. In particular, the biomimetic helical structures discovered in biological systems such as skeletons, mantis shrimp predatory hammers, and fish scales, due to their outstanding mechanical properties, provide effective biomimetic design ideas for the development of novel strong and tough composite materials.

[0004] However, accurately predicting the crack propagation resistance curve of biomimetic helical structures is a major challenge limiting their application. Biomimetic helical structures exhibit significant anisotropy at both the micro and macro scales. Furthermore, when fibers near the crack tip are pulled out, not only are in-plane closing forces perpendicular to the crack surface generated, but out-of-plane shear stresses may also occur. Therefore, considering the three-dimensional configuration and anisotropy of biomimetic helical structures, it is necessary to establish a method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures to provide technical support for their optimized design. Summary of the Invention

[0005] The purpose of this invention is to propose a method for generating crack propagation resistance curves for bridging toughened biomimetic helical structures. This method can quickly predict the fracture toughness of the structure and provide technical support for its optimized design.

[0006] The objective of this invention is achieved through the following technical solution: a method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures, comprising the following steps:

[0007] S1, obtain the geometric and equivalent material parameters of the biomimetic spiral structure;

[0008] S2, Constructing a theoretical model of crack bridging fracture mechanics for a biomimetic spiral structure;

[0009] S3, given the crack propagation length, the crack tip opening displacement equations are solved iteratively using Newton's method to obtain the crack tip opening displacement;

[0010] S4, using the crack tip opening displacement to determine the fracture toughness;

[0011] S5, Determine if the crack has entered the steady-state propagation stage: If not, increase the crack propagation length and repeat steps S3-S5; if yes, proceed to step S6.

[0012] S6 yields the crack propagation resistance curve.

[0013] Preferably, the biomimetic spiral structure comprises two component materials: a rigid fiber phase and a soft matrix phase. It is formed by stacking single-layer structures with the same fiber orientation along the thickness direction, with a certain twist angle between the layers.

[0014] Preferably, the geometric parameters of the biomimetic spiral structure in step S1 include fiber length. fiber radius The thickness of a single-layer board is helix angle The number of monolayers in a unit cell structure unit cell thickness The equivalent material parameters of the biomimetic spiral structure described in step S1 include the equivalent elastic modulus along the in-plane direction. In-plane equivalent Poisson ratio Anisotropic fracture parameters and Matrix fracture toughness .

[0015] Preferably, the crack bridging fracture mechanics theoretical model of the biomimetic spiral structure described in step S2 is as follows:

[0016] ;

[0017] In the formula, To achieve the true fracture toughness of the biomimetic helical structure, The equivalent stress intensity factor for the bridged region (Type I). The matrix elastic modulus. For the matrix Poisson's ratio, For the type III equivalent stress intensity factor of the bridging region, we have:

[0018] ;

[0019] In the formula, The length of the crack bridging region. Let X be the in-plane closed normal stress generated by fiber pull-out in the bridging zone, and X be the coordinates of the bridging zone. Then:

[0020] ;

[0021] In the formula, This refers to the out-of-plane shear force generated during fiber pull-out in the bridging zone.

[0022] Preferably, the crack bridging fracture mechanics theoretical model incorporates the influence of the in-plane closed normal stress and out-of-plane shear force generated by fiber pull-out in the bridging region on the total fracture toughness. The in-plane closed normal stress generated by fiber pull-out in the bridging region... Represented as:

[0023] ;

[0024] In the formula For Dirichlet functions, The coordinates of the fiber location in the bridging zone, for fiber twist angle at the location, for The crack tip at that location opens and shifts. This refers to the cohesive force generated by the shear deformation of the soft matrix;

[0025] The out-of-plane shear force generated by fiber pull-out in the bridging region Represented as:

[0026] ;

[0027] in, The number of fibers in the bridging zone;

[0028] Cohesion generated by shear deformation of soft matrix The expression is as follows:

[0029] ;

[0030] In the formula It refers to the shear strength of soft matrix materials. , It is the characteristic critical displacement. This represents the shear deformation of the matrix.

[0031] Preferably, the equation set of equations for the crack tip opening displacement in step S3 is expressed as follows:

[0032] ;

[0033] In the formula ( X' represents the coordinates of the discrete bridging force's position, and X' is the integration variable. This is Cauchy's principal value integral.

[0034] Preferably, the Newton's method described in step S3 specifically includes sub-steps S31 to S36:

[0035] S31, the vector form of the crack tip opening displacement equation set is:

[0036] ;

[0037] In the formula, As the independent variable, we have:

[0038] ;

[0039] For vector functions, we have:

[0040] ;

[0041] S32, Construct the iterative formula:

[0042] ;

[0043] In the formula For difference quotient;

[0044] ;

[0045] In the formula The Jacobian matrix is ​​represented as follows:

[0046] ;

[0047] in, Let be an N-dimensional fundamental unit vector, where the i-th fundamental unit vector is denoted as... ;

[0048] S33, Select initial value Given a precision level ;

[0049] S34, Calculation and ;

[0050] S35, find the independent variable for the (k+1)th iteration:

[0051] ;

[0052] S36, Determine the iteration termination condition Check if the condition is met. If so, stop the iteration and output the result. If not satisfied, repeat sub-steps S34~S36.

[0053] Preferably, the method for determining fracture toughness using crack tip opening displacement in step S4 is as follows:

[0054] .

[0055] Preferably, the steady-state crack propagation stage described in step S5 is defined as follows: when the fiber at the end of the crack wake region is completely pulled out or fails due to breakage, the length of the bridging zone no longer increases with crack propagation, and the toughening effect of the bridging zone reaches its limit; the criteria for the steady-state crack propagation stage are as follows:

[0056] ;

[0057] In the formula For fiber tensile strength, It represents the tensile force of a single fiber.

[0058] Preferably, in step S6, the horizontal axis of the crack propagation resistance curve represents the crack propagation length, and the vertical axis represents the total fracture toughness.

[0059] Compared with the prior art, the effective gain of the present invention is as follows: by adopting the crack propagation resistance curve generation method for bridging and toughening biomimetic spiral structures proposed in the present invention, which comprehensively considers the heterogeneity, anisotropy, and three-dimensional structural characteristics of the biomimetic spiral structure and torsional fibers, the crack propagation resistance curve of the biomimetic spiral structure can be accurately and quickly predicted. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0061] Figure 1 A flowchart of the method provided by the present invention;

[0062] Figure 2 This is a schematic diagram of the biomimetic spiral structure bridging and toughening provided by the present invention;

[0063] Figure 3 This is a schematic diagram of fiber extraction provided by the present invention;

[0064] Figure 4 A schematic diagram of the crack propagation resistance curve provided by the present invention;

[0065] Figure 5 This is a schematic diagram of the critical opening displacement of the crack tip provided by the present invention. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0067] This invention designs a method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures, such as... Figure 1 As shown, the steps and technical principles are as follows:

[0068] Step S1: Obtain the geometric and equivalent component material parameters of the biomimetic spiral structure.

[0069] The geometric parameters of the biomimetic helical structure include fiber length. fiber radius The thickness of a single-layer board is helix angle The number of monolayers in a unit cell structure unit cell thickness The equivalent material parameters of the biomimetic spiral structure described in step S1 include the equivalent elastic modulus along the in-plane direction. In-plane equivalent Poisson ratio Anisotropic fracture parameters and Matrix fracture toughness .

[0070] Step S2: Construct a theoretical model of crack bridging fracture mechanics for a biomimetic spiral structure.

[0071] The morphology of the bridging region in the biomimetic spiral structure is as follows Figure 2 As shown, the theoretical model of crack bridging fracture mechanics is as follows:

[0072] ;

[0073] In the formula, To achieve the true fracture toughness of the biomimetic helical structure, The matrix elastic modulus. The equivalent stress intensity factor for the bridged region is... For the matrix Poisson's ratio, The equivalent stress intensity factors for Type III bridging regions are:

[0074] ;

[0075] In the formula, The length of the crack bridging region. Let X be the in-plane closed normal stress generated by fiber pull-out in the bridging zone, and X be the coordinates of the bridging zone. Then:

[0076] ;

[0077] In the formula, The out-of-plane shear force generated by fiber pull-out in the bridging zone, such as Figure 3 As shown.

[0078] The in-plane closed normal stress generated by fiber pull-out in the bridging zone It can be represented as:

[0079] ;

[0080] In the formula For Dirichlet functions, The coordinates of the fiber location in the bridging zone, for fiber twist angle at the location, for The crack tip at that location opens and shifts. This refers to the cohesive force generated by the shear deformation of the soft matrix;

[0081] The out-of-plane shear force generated by fiber pull-out in the bridging region It can be represented as:

[0082] ;

[0083] in, The number of fibers in the bridging zone;

[0084] Cohesion generated by shear deformation of soft matrix The expression is as follows:

[0085] ;

[0086] In the formula It refers to the shear strength of soft matrix materials. , It is the characteristic critical displacement. This represents the shear deformation of the matrix.

[0087] Step S3: Given the crack propagation length, use Newton's method to iteratively solve the crack tip opening displacement equations to obtain the crack tip opening displacement.

[0088] The equations for the crack tip opening displacement are expressed as follows:

[0089] ;

[0090] In the formula ( X' represents the coordinates of the discrete bridging force's position, and X' is the integration variable. This is Cauchy's principal value integral.

[0091] The step S3, which involves using Newton's method to solve the equations for the crack tip opening displacement, specifically includes the following sub-steps S31 to S36:

[0092] Sub-step S31, the vector form of the crack tip opening displacement equations is:

[0093] ;

[0094] In the formula, As the independent variable, we have:

[0095] ;

[0096] In the formula, For vector functions, we have:

[0097] ;

[0098] Sub-step S32, construct the iterative formula:

[0099] ;

[0100] In the formula For difference quotient;

[0101] ;

[0102] In the formula The Jacobian matrix can be represented as follows:

[0103] ;

[0104] in, Let be an N-dimensional fundamental unit vector, where the i-th fundamental unit vector is denoted as... ;

[0105] Sub-step S33: Select initial value Given a precision level ;

[0106] Sub-step S34, calculate and ;

[0107] Sub-step S35: Calculate the independent variable for the (k+1)th iteration.

[0108] ;

[0109] S36, Determine the iteration termination condition If the condition is met, stop iterating and output the result. If not satisfied, repeat sub-steps S34~S36.

[0110] Step S4: Calculate fracture toughness using crack tip opening displacement.

[0111] The method for determining fracture toughness using crack tip opening displacement is as follows:

[0112] .

[0113] Step S5: Determine whether the crack has entered the steady-state propagation stage. If not, increase the crack propagation length and repeat steps S3-S5. If yes, proceed to step S6.

[0114] The steady-state crack propagation stage is defined as follows: when the fiber at the end of the crack wake region is completely pulled out or fails due to fracture, the length of the bridging zone no longer increases with crack propagation, and the toughening effect of the bridging zone reaches its limit. The criteria for the steady-state crack propagation stage are as follows:

[0115] ;

[0116] Step S6 yields the crack propagation resistance curve.

[0117] The specific implementation process of this invention is explained below using a typical biomimetic spiral structure as an example:

[0118] (1) Biomimetic spiral structure such as Figure 2 As shown, fiber radius Fiber length Single-layer board thickness helix angle 15°, equivalent elastic modulus Equivalent Poisson ratio Matrix elastic modulus Matrix Poisson's ratio Matrix fracture toughness .

[0119] (2) Based on the above parameters, the crack tip opening displacement is obtained by iteratively solving using Newton's method under different fiber lengths, as shown in the figure. Figure 4 As shown.

[0120] (3) Substituting the crack tip opening displacement under different fiber lengths of the biomimetic helical structure into step 4, the fracture toughness under different crack propagation lengths can be obtained. The crack propagation resistance curves for different fiber lengths are shown in Figure 4. Figure 5 As shown.

[0121] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures, characterized in that, Includes the following steps: S1, obtain the geometric and equivalent material parameters of the biomimetic spiral structure; The geometric parameters of the biomimetic helical structure include fiber length. fiber radius The thickness of a single-layer board is helix angle The number of monolayers in a unit cell structure Unit cell thickness The equivalent material parameters of the biomimetic spiral structure include the equivalent elastic modulus along the in-plane direction. In-plane equivalent Poisson ratio Anisotropic fracture parameters and Matrix fracture toughness ; S2, Constructing a theoretical model of crack bridging fracture mechanics for a biomimetic spiral structure; The crack bridging fracture mechanics theoretical model of the biomimetic helical structure is as follows: ； In the formula, To achieve the true fracture toughness of the biomimetic helical structure, The equivalent stress intensity factor for the bridged region (Type I). The elastic modulus of the matrix. For the matrix Poisson's ratio, For the type III equivalent stress intensity factor of the bridging region, we have: ； In the formula, The length of the crack bridging region. Let X be the in-plane closed normal stress generated by fiber pull-out in the bridging zone, and X be the coordinates of the bridging zone. Then: ； In the formula, The out-of-plane shear force generated during fiber pull-out in the bridging zone; Among them, the out-of-plane shear force generated by fiber pull-out in the bridging region Represented as: ； in, The number of fibers in the bridging region; where For Dirichlet functions, The coordinates of the fiber location in the bridging zone, for fiber twist angle at the location, for The crack tip at that location opens and shifts. This refers to the cohesive force generated by the shear deformation of the soft matrix; S3, given the crack propagation length, the crack tip opening displacement equations are solved iteratively using Newton's method to obtain the crack tip opening displacement; The equations for the crack tip opening displacement described in step S3 are as follows: ； In the formula Let be the coordinates of the location where the discrete bridging force acts, where X' is the integration variable. This is the Cauchy principal value integral; S4, using the crack tip opening displacement to determine the fracture toughness; S5, Determine if the crack has entered the steady-state propagation stage: If not, increase the crack propagation length and repeat steps S3-S5; if yes, proceed to step S6. S6 yields the crack propagation resistance curve.

2. The method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures as described in claim 1, characterized in that, The crack bridging fracture mechanics theoretical model incorporates the influence of in-plane closed normal stress and out-of-plane shear force generated by fiber pull-out in the bridging region on the overall fracture toughness. The in-plane closed normal stress generated by fiber pull-out in the bridging region... Represented as: ； Cohesion generated by shear deformation of soft matrix The expression is as follows: ； In the formula It refers to the shear strength of soft matrix materials. , It is the characteristic critical displacement. This represents the shear deformation of the matrix.

3. The method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures as described in claim 1, characterized in that, Step S3, Newton's method, specifically includes sub-steps S31 to S36: S31, the vector form of the crack tip opening displacement equation set is: ； In the formula, As the independent variable, we have: ； For vector functions, we have: ； S32, Construct the iterative formula: ； In the formula For difference quotient; ； In the formula The Jacobian matrix is ​​represented as follows: ； in, Let be an N-dimensional fundamental unit vector, where the i-th fundamental unit vector is denoted as... ; S33, Select initial value Given a precision level ; S34, Calculation and ; S35, find the independent variable for the (k+1)th iteration: ； S36, Determine the iteration termination condition Check if the condition is met. If so, stop the iteration and output the result. If not satisfied, repeat sub-steps S34~S36.

4. The method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures as described in claim 1, characterized in that, The method for determining fracture toughness using crack tip opening displacement described in step S4 is as follows: 。 5. The method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures as described in claim 1, characterized in that, The criteria for the steady-state crack propagation stage described in step S5 are as follows: ； In the formula For fiber tensile strength, It represents the tensile force of a single fiber.

6. The method for generating crack propagation resistance curves for bridging-toughened biomimetic helical structures as described in claim 1, characterized in that, The crack propagation resistance curve described in step S6 has the crack propagation length on the horizontal axis and the total fracture toughness on the vertical axis.

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