Interaction integration method for decoupling macro and micro breaking strength factors of chiral material

Abstract

The invention discloses an interaction integral method for decoupling macro and micro breaking strength factors of a chiral material, which comprises the following steps of: firstly, obtaining a J integral expression represented by the macro and micro strength factors according to a control equation of the chiral material and an expression of an auxiliary field; secondly, extracting an interaction part of a real field and an auxiliary field of the chiral material to obtain a linear integral form of an interaction integral; thirdly, substituting the definition of the auxiliary field and the control equation of the real field into the interaction integral to obtain an interaction integral form considering the chiral microstructure; line integrals along the material interface are then derived to eliminate the effects of chiral material interface integrals. And finally, according to a J integral expression, obtaining a relationship between the interaction integral and the macro and micro intensity factors, and separating the macro and micro intensity factors by selecting an auxiliary intensity factor. According to the method, the macroscopic stress intensity factor and the microscopic even stress intensity factor of the chiral material can be decoupled, and the fracture behavior of the material can be accurately analyzed.

Description

Technical Field

[0001] The invention belongs to the technical field of fracture mechanics and relates to an interaction integration method capable of decoupling macroscopic and microscopic fracture mode intensity factors of chiral materials. Background Art

[0002] Biological microstructures tend to adopt chiral shapes, which is even considered to be a unifying structural principle in biology. There are various complex chiral microstructures in nature, such as the Bouligand structure in the crab exoskeleton, the nanorod bundle microstructure in the limpet teeth, and the triple helix structure of collagen fibers in tendons. These chiral microstructures usually give materials excellent mechanical properties, including high strength, toughness and impact resistance.

[0003] Chirality in materials usually manifests itself as coupling of mechanical deformations, such as tension-twist coupling or bending-twist coupling. Due to the unique deformation characteristics of chiral microstructures, chiral microstructures control the fracture and mechanical properties of materials. For example, chiral tissues can induce couple stresses, thereby significantly reducing stress concentration near the crack tip. In addition, chiral tissues can hinder crack propagation, thereby enhancing the fracture toughness of biomaterials to a certain extent. Therefore, for such materials, it is crucial to establish a correct fracture mechanics analysis model to gain a deep understanding of their underlying deformation mechanisms for the design of high-performance biomimetic composite materials.

[0004] In linear elastic fracture mechanics, the stress intensity factor and energy release rate near the crack tip are important parameters for evaluating the fracture behavior of materials. The main methods for solving the stress intensity factor include displacement method, stress method, J integral and interaction integral. For the coupling between macroscopic and microscopic fracture modes of chiral materials, the interaction integral can well separate the intensity factors of different fracture modes.

[0005] However, there is currently a lack of means to decouple the macroscopic stress intensity factor and microscopic couple stress intensity factor of chiral materials. Therefore, in order to study the fracture mechanics properties of such materials and guide the bionic optimization design of composite materials, it is of great engineering significance to establish an interaction integral that decouples the macroscopic and microscopic fracture strength factors of chiral materials. Summary of the invention

[0006] In order to solve the current lack of means to decouple the macroscopic stress intensity factor and microscopic couple stress intensity factor of chiral materials, the present invention takes into account the coupled deformation between the volume strain and micro-rotation of chiral materials, and derives the interaction integral expression of the macroscopic and microscopic fracture intensity factors of decoupled chiral materials through strict J-integral theory, and then proposes an interaction integral method for decoupling the macroscopic and microscopic fracture intensity factors of chiral materials. This method can achieve the decoupling of the macroscopic stress intensity factor and microscopic couple stress intensity factor of chiral materials, and accurately analyze the fracture behavior of materials.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A method for decoupling the interaction integration of macroscopic and microscopic fracture strength factors of chiral materials comprises the following steps:

[0009] Step 1: Considering the influence of tension-torsion coupling and deformation, the J-integral theory of chiral materials is established according to the control equation of chiral materials and the expression of auxiliary fields. By deducing and simplifying, the J-integral expression characterized by macro-micro intensity factors is obtained;

[0010] Step 2: By extracting the interaction part between the real field and the auxiliary field of the chiral material, the line integral form of the interaction integral of the chiral material is obtained;

[0011] Step 3: Convert the line integral into the area integral through the divergence theorem, and divide the line integral form of the chiral material interaction integral into two terms. Substitute the definition of the auxiliary field and the control equation of the real field into the chiral material interaction integral for derivation, and obtain the chiral material interaction integral form considering the chiral microstructure;

[0012] Step 4: In view of the structural characteristics of complex material interfaces in biomaterials, the integral region is divided into different material parts. By setting the material interface to have good bonding characteristics, based on the curvilinear coordinate system and using the chain rule to derive the line integral along the material interface, the influence of the chiral material interface integral is eliminated.

[0013] Step 5: According to the J-integral expression characterized by the macro-micro intensity factors, the relationship between the interaction integral and the macro-micro intensity factors is obtained, and the macro-micro intensity factors are decoupled by selecting auxiliary intensity factors.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. For the first time, the J-integral expression characterized by macro- and micro-intensity factors was completely derived, and based on the J-integral theory, an interaction integral method for separating the macro- and micro-intensity factors of chiral materials was proposed, which expanded the application scope of the interaction integral method.

[0016] 2. The present invention eliminates the influence of material interface integrals through rigorous theoretical derivation, so that the interaction integral is still applicable to biomaterials containing complex material interfaces, and can realize fracture mechanics analysis of biomaterials with different structural characteristics, such as the nanorod bundle microstructure in limpet teeth.

[0017] 3. The method of the present invention has good applicability and can be combined with existing numerical calculation methods such as finite element, extended finite element, interaction integration method, etc. to achieve the decoupling of macro and micro fracture modes of chiral biomaterials, and can be developed into a commercial program to flexibly adapt to changes in the required problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A flowchart for deriving the interaction integral of the macro-micro fracture strength factors of decoupled chiral materials;

[0019] Figure 2 is a schematic diagram of the integration region bounded by a closed loop;

[0020] Figure 3 Schematic diagram of the integration domain A being divided into two domains A1 and A2 by the material interface;

[0021] Figure 4 Schematic diagram of a two-dimensional auxetic chiral elastic solid with plane cracks under mixed-mode loading conditions;

[0022] Figure 5 It is a schematic diagram of the curvilinear coordinate system on the material interface;

[0023] Figure 6 It is a square plate of chiral material and finite element mesh diagram;

[0024] Figure 7 is the stress intensity factor and couple stress intensity factor diagram at different chiral angles;

[0025] Figure 8 are the errors of stress intensity factor and couple stress intensity factor decoupled from different integration regions. DETAILED DESCRIPTION

[0026] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0027] The present invention provides an interaction integral method for decoupling the macro-micro fracture strength factors of chiral materials. The method takes into account the constitutive relationship of the coupling between the volume strain and micro-rotation of chiral materials. First, based on the control equation of the chiral material and the expression of the auxiliary field, the J-integral expression characterized by the macro-micro intensity factor is obtained through derivation and simplification; secondly, the line integral form of the interaction integral is obtained by extracting the interaction part between the real field and the auxiliary field of the chiral material; thirdly, the definition of the auxiliary field and the control equation of the real field are substituted into the interaction integral for derivation to obtain the interaction integral form that takes into account the chiral microstructure. Subsequently, based on the curvilinear coordinate system and using the chain rule, the line integral along the material interface is derived to eliminate the influence of the interface integral of the chiral material. Finally, based on the J-integral expression characterized by the macro-micro intensity factor, the relationship between the interaction integral and the macro-micro intensity factor is obtained, and the macro-micro intensity factor is separated by selecting the auxiliary intensity factor. Figure 1 As shown, the specific steps include:

[0028] Step 1: Considering the influence of tension-torsion coupling and deformation, the J-integral theory of chiral materials is established according to the control equation of chiral materials and the expression of auxiliary fields. By derivation and simplification, the J-integral expression characterized by macro-micro intensity factors is obtained. The specific steps are as follows:

[0029] Step 1. Establish the control equation of chiral materials:

[0030] Balanced equation:

[0031]

[0032] Geometric equations:

[0033]

[0034] Constitutive equation:

[0035]

[0036] The above formula uses tensor component notation, and the value range of each subscript i, j, k, l is 1 to 2 and follows the Einstein summation convention: the variable marked with the symbol subscript i, j, k, l is a component of a vector or tensor. When a subscript appears only once, it is called a "free index" and all values ​​of the subscript must be traversed; in the same item, if a subscript appears in pairs, it is called a "dummy index", which means that the sum is traversed over its value range. As long as the free indexes on the left and right sides of the equation can correspond, the specific letters used do not change the meaning of the equation. Among them, σ ij is the stress component, ε kk , ε lk , ε ij and ε jiis the strain component, m i3 is the couple stress component, χ i3 is the curvature component. e ij3 、e 3ij and e 3lk is the Levitra symbol. ij is the Kronecker symbol. The comma in the subscript indicates that the partial derivative is taken with respect to the corresponding coordinate component, that is, u j is the displacement component, φ3 is the micro-rotation, x i is the coordinate component. is the stress component without considering the chirality effect, is the stress component considering the chirality. λ, μ, κ and γ are elastic constants. A is the chiral material parameter that characterizes the coupling between body strain and micro-rotation. The relationship between Young's modulus E, shear modulus G, Poisson's ratio ν and coupling number N is as follows:

[0037]

[0038] The expressions of each parameter are as follows:

[0039]

[0040] Where ω represents the slenderness ratio of the ligament's in-plane thickness to its length, E s ′ represents the plane elastic modulus, when E s ′=E s When , it indicates plane stress, when When , it represents plane strain, where E s and v s are Young’s modulus and Poisson’s ratio of the underlying chiral lattice material, respectively. s represents the distance between the centers of the circles. β represents the chirality angle, where β>0 represents positive chirality and β<0 represents negative chirality.

[0041] Step 1 and 2: The auxiliary field stress field of the chiral material can be expressed as:

[0042]

[0043]

[0044] The auxiliary field displacement field of the chiral material can be expressed as:

[0045]

[0046]

[0047] The auxiliary field strain field of chiral materials can be expressed as:

[0048]

[0049] in and represents the auxiliary stress, and represents the auxiliary displacement. r,θ represents the polar coordinates of the crack tip, and denote the auxiliary strain and curvature, respectively. and denote the auxiliary stress component and the couple stress component, respectively. Indicates auxiliary micro rotation. ijkl and B i3k3 is the material stiffness of the chiral elastic body. Where ξ=A / (λ+μ) is a dimensionless parameter with a value range of The material parameter S can be expressed as:

[0050]

[0051] In the case of plane stress, Poisson's ratio v needs to be replaced by v / (1+v). Macro stress intensity factor K I and K II , microscopic couple stress intensity factor K VI They can be defined as:

[0052]

[0053] Among them, r and θ represent the cylindrical coordinate components, lim represents the limit symbol, and K I and K II denote the macroscopic type I and type II stress intensity factors, K VI represents the microscopic type VI stress intensity factor, σ 22 and σ 21 represents the stress component, m 23 represents the couple stress component.

[0054] For a two-dimensional inhomogeneous chiral elastic body, the J-integral is defined as follows:

[0055]

[0056] Where Γ0 represents an arbitrary integral path, and a circular integral path is taken, in which case Γ = rdθ. i represents the unit external normal vector of the integration path, such as Figure 2 As shown. jk and σ ij represents the stress component, m j3 Indicates m i3 Couple stress component, u j,1 represents the displacement component, φ 3,1 represents the micro-rotation component, χj3 represents the curvature component, ε jk Represents the strain component. δ i1 is the Kronecker symbol. ∫ represents the integral symbol.

[0057] Substituting the expression of the auxiliary field at the crack tip into the definition of the J integral, through derivation and simplification, we can obtain the J integral expression expressed by two macroscopic stress intensity factors and one microscopic couple stress intensity factor:

[0058]

[0059] Step 2: By extracting the interaction between the real field and the auxiliary field of the chiral material, the line integral form of the chiral material interaction integral is obtained. The specific steps are as follows:

[0060] Step 21: Convert the J integral (formula (13)) in step 1 into a closed loop integral, such as Figure 2 As shown in Figure 2, it is assumed that there is no stress and couple stress on the crack surface. At this time, the J integral can be expressed as the integrand multiplied by a weight function:

[0061]

[0062] Among them, ω i It is a contour line The unit external normal vector, Γ1, represents the integration path, Γ B Represented by the integral path Γ1, A closed loop, such as Figure 2 As shown in Figure 1, q is an arbitrary smooth weight function whose value is 1 on Γ0 and 0 on Γ1.

[0063] Step 22: Superimpose the real field and the auxiliary field to obtain the superposition state J act+aux integral:

[0064]

[0065] Among them, J act+aux represents the superposition state of the real field and the auxiliary field, J act+aux The integral can be divided into three partsJ act+aux =J act +J aux +I, where J act is the J-integral form of the real field, J aux is the J-integral form of the auxiliary field, and is the real field stress component without considering the chirality effect, and is the real field stress component considering the chirality effect. and is the auxiliary field stress component, and is the auxiliary field couple stress component, is the auxiliary field strain component, is the auxiliary field curvature component, is the auxiliary field displacement component, To assist the field micro-rotation, the comma in the subscript indicates the partial derivative with respect to the corresponding coordinate component, that is, ∮ represents the integral symbol, I represents the line integral form of the chiral material interaction integral, and the line integral form of the chiral material interaction integral can be expressed as:

[0066]

[0067] Step 3: Convert the line integral into the area integral through the divergence theorem, and divide the line integral form of the chiral material interaction integral into two terms. Substitute the definition of the auxiliary field and the control equation of the real field into the chiral material interaction integral for derivation, and obtain the chiral material interaction integral form considering the chiral microstructure. The specific steps are as follows:

[0068] Step 3.1. The line integral form of the chiral material interaction integral can be converted into the regional integral form through the divergence theorem:

[0069]

[0070] Step 3.2: Consider that the auxiliary constitutive equation is consistent with the real field constitutive equation, so the relationship between the auxiliary field and the real field can be expressed as According to the definition of auxiliary field, there is the following relationship:

[0071]

[0072] in and Represents the constant amount of material at the crack tip.

[0073] Step 3: According to the definition of the auxiliary field and the control equation of the real field, the interaction integral can be simplified to a form without the chiral material derivative term, and the chiral material interaction integral form considering the chiral microstructure is obtained:

[0074]

[0075] Step 4: In view of the structural characteristics of biomaterials with complex material interfaces, the integral region is divided into different material parts. By setting the material interface to have good bonding characteristics, based on the curve coordinate system and using the chain rule to derive the line integral along the material interface, the influence of the chiral material interface integral is eliminated. The specific steps are as follows:

[0076] Step 41. Consider chiral materials with ideal bonding interfaces to discuss the effects of material interfaces, e.g. Figure 3 As shown in Figure 1, an integration domain A is divided into two domains A1 and A2 by the material interface. A1 is a closed integral domain. Surrounded by Γ B1 ,Γ interface ,Γ B3 , Both represent integral paths, and A2 is a closed integral Surrounded by Representation and Γ interface The integration path in the opposite direction, Γ B2 represents the integral path. The material properties of these two regions show diversity, but remain continuous but differentiable, ensuring a smooth transition between different properties. At this point, the chiral material interaction integral considering the chiral microstructure in step 3 can be decomposed into two loop integrals and and an interface integral I interface :

[0077]

[0078] The interface integral can be expressed as:

[0079]

[0080] The superscript It means that they are located in areas A1 and A2 respectively, and take the material properties in areas A1 and A2 respectively.

[0081] Step 4.2: The definition of auxiliary field stipulates the continuity of auxiliary stress, couple stress, displacement, micro-spin and their derivatives on the interface. Therefore, the auxiliary field satisfies the following relationship:

[0082]

[0083] Step 43: Set the interface to be in equilibrium, which necessarily means that the resultant force and the resultant force acting on the interface are both zero:

[0084]

[0085] Step 4. Bringing the continuity condition of the auxiliary field and the interface equilibrium condition into the interface integral, we can obtain:

[0086]

[0087] Step 4 and 5: Figure 4 As shown, a curvilinear coordinate system (ξ1,ξ2) is defined, and a point on the curvilinear coordinate system satisfies the relationship and In addition, the Cartesian coordinate system and the curvilinear coordinate system have the following relationship:

[0088]

[0089] Step 4 and 5: Under the premise of complete interface bonding, the displacement, micro-rotation and their derivatives on both sides of the interface must be equal.

[0090] Step 46: Substitute the expressions obtained in steps 45 and 46 Substituting equation (26) into the interface integral expression, we can obtain I interface = 0. This indicates that the expression of the interaction integral obtained in step 3 is still applicable to chiral materials with complex interfaces. Steps 3 and 4 prove that the interaction integral proposed by the present invention for the fracture characteristics of chiral microstructures does not require the derivative of material parameters, and is also applicable to the structural characteristics of complex material interfaces in biomaterials.

[0091] Step 5: According to the J-integral expression characterized by the macro-micro intensity factor, the relationship between the interaction integral and the macro-micro intensity factor is obtained, and the macro-micro intensity factor is decoupled by selecting the auxiliary intensity factor. The specific steps are as follows:

[0092] Step 51: According to the J-integral expression of formula (14) in step 1, considering the superposition of the real field and the auxiliary field, the J-integral expression expressed by the auxiliary field intensity factor and the real field intensity factor can be obtained:

[0093]

[0094] in, and denote the auxiliary field macroscopic type I and type II stress intensity factors, respectively, represents the auxiliary field microscopic type VI stress intensity factor.

[0095] Step 52: From the interaction between the real state and the auxiliary state, the interaction integral expressed in terms of two macroscopic stress intensity factors and one microscopic couple stress intensity factor can be derived:

[0096]

[0097] Step 5.3. By using the vector composed of three auxiliary intensity factors Taking the values ​​[1 0 0], [0 1 0] and [0 0 1] respectively, we can obtain the intensity factor expressed as the interaction integral:

[0098]

[0099] Among them, the material parameters S, μ, κ, and γ need to be replaced by inhomogeneous chiral material parameters at the crack tip.

[0100] Step 54: By solving the problem, we can get the macroscopic stress intensity factor and microscopic couple stress intensity factor of the chiral material.

[0101] In order to illustrate the applicability of the above technical solution of the present invention, the stress intensity factor and the couple stress intensity factor are first decoupled below, and then different material functions are selected to verify that the present invention is still applicable to chiral materials containing material interfaces.

[0102] Example 1: Decoupling two macroscopic stress intensity factors and one couple stress intensity factor.

[0103] like Figure 5 As shown in Figure 1, a square plate of homogeneous chiral material with length 2W = 2 and central crack length 2a = 1 is studied. The upper and lower edges of the chiral plate are subjected to stress σ0 and couple stress m0. Figure 5 The corresponding finite element mesh for a homogeneous square plate of chiral material is given in . All numerical examples given in the results use normalized intensity factors. Figure 6 The results show that the present invention can easily decouple two macroscopic stress intensity factors and one microscopic couple stress intensity factor, which proves that the method of the present invention is effective in decoupling the fracture strength factor of chiral materials.

[0104] Example 2: Applicability of interaction integrals for interfaces with complex materials.

[0105] like Figure 7 As shown, a material function is selected. Figure 5 The chiral material plate in is divided into a uniform material region and an inhomogeneous material region. Ten integration regions (10, 25, 50, 100, 150, 200, 250, 300, 350 and 400) are selected. Figure 8 The errors of the decoupled stress intensity factors and couple stress intensity factors for different integration regions are shown in . Figure 8 It can be found that the errors of all intensity factors are less than 0.2%. This example proves that for chiral biomaterials with complex interfaces, the interaction integral proposed by the present invention is not affected and is still applicable.

Claims

1. A method for decoupling the interaction integration of the macroscopic and microscopic fracture strength factors of chiral materials, characterized in that The method comprises the following steps: Step 1: Considering the influence of tension-torsion coupling and deformation, the J-integral theory of chiral materials is established according to the control equation of chiral materials and the expression of auxiliary fields. By deducing and simplifying, the J-integral expression characterized by macro-micro intensity factors is obtained; Step 2: By extracting the interaction part between the real field and the auxiliary field of the chiral material, the line integral form of the interaction integral of the chiral material is obtained; Step 3: Convert the line integral into the area integral through the divergence theorem, and divide the line integral form of the chiral material interaction integral into two terms. Substitute the definition of the auxiliary field and the control equation of the real field into the chiral material interaction integral for derivation, and obtain the chiral material interaction integral form considering the chiral microstructure; Step 4: In view of the structural characteristics of complex material interfaces in biomaterials, the integral region is divided into different material parts. By setting the material interface to have good bonding characteristics, based on the curvilinear coordinate system and using the chain rule to derive the line integral along the material interface, the influence of the chiral material interface integral is eliminated. Step 5: According to the J-integral expression characterized by the macro-micro intensity factors, the relationship between the interaction integral and the macro-micro intensity factors is obtained, and the macro-micro intensity factors are decoupled by selecting auxiliary intensity factors.

2. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 1, characterized in that The specific steps of step one are as follows: Step 1. Establish the control equation of chiral materials: Balanced equation: s ji,j =0, m i3,i +e ij3 s ij =0. Geometric equations: ε ij =u j,i -e ij3 φ3, x i3 =φ 3,i 。 Constitutive equation: m i3 =gx i3 , Among them, σ ij is the stress component, ε kk , ε lk , ε ij and ε ji is the strain component, m i3 is the couple stress component, χ i3 is the curvature component, e ij3 、e 3ij and e 3lk is the Levitra symbol, δ ij is the Kronecker symbol. The comma in the subscript indicates the partial derivative with respect to the corresponding coordinate component. j is the displacement component, φ3 is the micro-rotation, x i are the coordinate components, is the stress component without considering the chirality effect, To consider the stress component affected by chirality, λ, μ, κ and γ are elastic constants, and A is the chiral material parameter that characterizes the coupling between body strain and microrotation; Step 1 and 2: The auxiliary field stress field of the chiral material is expressed as: The auxiliary field displacement field of the chiral material is expressed as: The auxiliary field strain field of the chiral material is expressed as: in, and represents the auxiliary stress, and represents the auxiliary displacement, r,θ represents the polar coordinates of the crack tip, and denote the auxiliary strain and curvature respectively, and denote the auxiliary stress component and the couple stress component, respectively. A stands for auxiliary micro-rotation, ijkl and B i3k3 is the material stiffness of the chiral elastic body, where ξ=A / (λ+μ) is a dimensionless parameter with a value range of S is the material parameter, K I and K II is the macro stress intensity factor, K VI is the microscopic couple stress intensity factor; For a two-dimensional inhomogeneous chiral elastic body, the J-integral is defined as follows: where Γ0 represents an arbitrary integration path, n i represents the unit external normal vector of the integration path, σ jk and σ ij represents the stress component, m j3 Indicates m i3 Couple stress component, u j,1 represents the displacement component, φ 3,1 represents the micro-rotation component, χ j3 represents the curvature component, ε jk represents the strain component, δ i1 is the Kronecker symbol, ∫ represents the integral symbol; The expression of the auxiliary field at the crack tip is brought into the definition of the J integral. Through derivation and simplification, the J integral expression expressed by two macroscopic stress intensity factors and one microscopic couple stress intensity factor is obtained:

3. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 2, characterized in that The Young's modulus E, shear modulus G, Poisson's ratio ν and coupling number N of the chiral material are expressed as:

4. The interactive integration method for decoupling the macroscopic and microscopic fracture strength factors of chiral materials according to claim 2 or 3, characterized in that The expressions of λ, μ, κ, γ, and A are as follows: Where ω represents the slenderness ratio of the ligament’s in-plane thickness to its length, E s ′ represents the plane elastic modulus, when E s ′=E s When , it indicates plane stress, when When , it represents plane strain, where E s and v s are Young’s modulus and Poisson’s ratio of the underlying chiral lattice material, a s represents the distance between the centers of the circles, and β represents the chirality angle, where β>0 represents positive chirality and β<0 represents negative chirality.

5. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 2, characterized in that The material parameter S is expressed as: Macro stress intensity factor K I and K II , microscopic couple stress intensity factor K VI They are defined as: Among them, lim represents the limit symbol, K I and K II denote the macroscopic type I and type II stress intensity factors, K VI represents the microscopic type VI stress intensity factor, σ 22 and σ 21 represents the stress component, m 23 represents the couple stress component.

6. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 2, characterized in that The specific steps of step 2 are as follows: Step 2:

1. Convert the J integral in step 1 into a closed loop integral. Assume that there is no stress and couple stress on the crack surface. At this time, the J integral is expressed as the integrand multiplied by a weight function: Among them, ω i It is a contour line The unit outward normal vector of represents the integration path, Γ B Represented by the integral path The closed loop is composed of , q is an arbitrary smooth weight function, whose value is 1 on Γ0 and 0 on Γ1; Step 22: Superimpose the real field and the auxiliary field to obtain the superposition state J act+aux integral: Among them, J act+aux represents the superposition state of the real field and the auxiliary field, J act+aux The integral is divided into three partsJ act+aux =J act +J aux +I, where J act is the J-integral form of the real field, J aux is the J-integral form of the auxiliary field, and is the real field stress component without considering the chirality effect, and To consider the real field stress component affected by chirality, and is the auxiliary field stress component, and is the auxiliary field couple stress component, is the auxiliary field strain component, is the auxiliary field curvature component, is the auxiliary field displacement component, To assist the field micro-rotation, the comma in the subscript represents the partial derivative with respect to the corresponding coordinate component, ∮ represents the integral sign, and I represents the line integral form of the chiral material interaction integral.

7. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 6, characterized in that The line integral form of the chiral material interaction integral is expressed as:

8. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 6, characterized in that The specific steps of step three are as follows: Step 3.

1. Convert the line integral form of the chiral material interaction integral into the regional integral form by using the divergence theorem: Step 3.2: Consider that the auxiliary constitutive equation is consistent with the real field constitutive equation, so the relationship between the auxiliary field and the real field is expressed as According to the definition of auxiliary field, there is the following relationship: in and represents the constant amount of material at the crack tip; Step 3: According to the definition of the auxiliary field and the control equation of the real field, the interaction integral is simplified to a form without the chiral material derivative term, and the chiral material interaction integral form considering the chiral microstructure is obtained:

9. The interactive integration method for decoupling the macroscopic and microscopic fracture strength factors of chiral materials according to claim 8, characterized in that The specific steps of step 4 are as follows: Step 41: An integration domain A is divided into two domains A1 and A2 by the material interface, where A1 is obtained by closed integration Surrounded by Both represent integral paths, and A2 is a closed integral Surrounded by Representation and Γ interface The integration path in the opposite direction, Γ B2 represents the integral path. At this time, the chiral material interaction integral considering the chiral microstructure in step 3 is decomposed into two loop integrals and and an interface integral I interface : The interface integral is expressed as: The superscript It means that they are located in regions A1 and A2, respectively, and the material properties in regions A1 and A2 are taken respectively; Step 42: The auxiliary field satisfies the following relationship: Step 43: Set the interface to be in equilibrium, then the resultant force and the resultant force acting on the interface are both zero: Step 4. Substitute the continuity condition of the auxiliary field and the interface equilibrium condition into the interface integral to obtain: Step 4.5: Define a curvilinear coordinate system (ξ1,ξ2), where a point on the curvilinear coordinate system satisfies the relationship and The Cartesian coordinate system and the curvilinear coordinate system have the following relationship: Step 4 and 5: Under the premise of complete interface bonding, the displacement, micro-rotation and their derivatives on both sides of the interface must be equal. Step 46: Substitute the expressions obtained in steps 45 and 46 into the interface integral expression to obtain I interface =0.

10. The interactive integration method for decoupling the macro-micro fracture strength factors of chiral materials according to claim 9, characterized in that The specific steps of step five are as follows: Step 51: Based on the J-integral expression in step 1, considering the superposition of the real field and the auxiliary field, the J-integral expression expressed by the auxiliary field intensity factor and the real field intensity factor is obtained: in, and denote the auxiliary field macroscopic type I and type II stress intensity factors, respectively, represents the auxiliary field microscopic type VI stress intensity factor; Step 52: From the interaction between the true state and the auxiliary state, derive the interaction integral expressed in terms of two macroscopic stress intensity factors and one microscopic couple stress intensity factor: Step 5.

3. By using the vector composed of three auxiliary intensity factors Taking the values ​​[100], [010] and [001] respectively, we obtain the intensity factor expressed as the interaction integral: Step 54: By solving, the macroscopic stress intensity factor and microscopic couple stress intensity factor of the chiral material are obtained.

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