One-dimensional interface fracture driving force pure modal distribution method based on double-cantilever camber beam

Abstract

The invention discloses a one-dimensional interface fracture driving force pure modal distribution method based on a double-cantilever camber beam. The method comprises the following steps: defining a geometric configuration and a load condition of a double-cantilever camber beam model according to an application scene of a composite material; according to the geometrical configuration and the load condition, calculating interlayer shearing force and interlayer opening force of the non-cracking area of the double-cantilever camber beam; calculating an equivalent load of the crack tip of the double-cantilever camber beam model by combining an equivalent superposition principle based on the interlayer shearing force and the interlayer opening force; according to the equivalent load of the crack tip of the double-suspension-arm camber beam model, the total energy release rate of the double-suspension-arm camber beam model is calculated; and distributing the one-dimensional interface fracture driving force mode into a pure I type and a pure II type based on the total energy release rate in combination with the equivalent load of the crack tip of the double-cantilever camber beam model. According to the method, the energy of each component can be quickly and accurately predicted, finite element analysis is not needed, and the time cost is saved.

Description

Technical Field

[0001] This invention belongs to the field of composite material technology in solid mechanics and fracture mechanics, and particularly relates to a pure mode allocation method for one-dimensional interface fracture driving force based on double cantilever beams. Background Technology

[0002] Bending composite structures are widely used in various fields due to their excellent material properties, such as wind turbine blades, turbine blades, and aerospace fuselages. Despite their many advantages, composite materials also have certain limitations. Compared to conventional materials, composite materials are more sensitive to defects such as cracks. Their structures are typically formed by bonding layers of material together with adhesives, which can easily lead to adhesive failure under load, resulting in fracture. Such fractures often exhibit a mixed mode of Type I (opening) and Type II (shear) fractures, causing the component to lose its integrity and affecting its normal use.

[0003] In studying the initiation and propagation behavior of this type of failure, the double cantilever beam model is often used. This model mainly consists of two or more layers of materials bonded together, with cantilever beams at both ends. Each layer can have different physical and mechanical properties, thus effectively simulating the deformation of layered composite materials under edge loads and the failure of the bond layer. Energy release rate ( G This is commonly used to assess crack initiation; when its value exceeds the material's fracture toughness, the crack begins to propagate. In mixed modes, fracture toughness is not a simple summation of single-mode values, but is load-related; therefore, it is necessary to know the mixed-mode ratio under a specific loading condition.

[0004] Currently, the finite element method can be used to calculate the distribution of fracture modes. However, fine meshing is required in the crack tip region, which significantly increases computational costs. Furthermore, the choice of element type affects the magnitude of the error, making it difficult to guarantee computational accuracy and resulting in a long overall computation time. Therefore, there is an urgent need to propose a pure mode distribution method for one-dimensional interface fracture driving force based on a double cantilever beam. Summary of the Invention

[0005] To address the aforementioned technical issues, this invention proposes a one-dimensional interface fracture driving force pure mode allocation method based on a double cantilever beam. This method can quickly and accurately characterize the energy release rate under mixed modes, thereby significantly reducing the time cost incurred by using finite element calculations.

[0006] To achieve the above objectives, this invention provides a pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam, comprising: Define the geometric configuration and load conditions of the double cantilever bending beam model according to the application scenario of composite materials; Based on the geometric configuration and load conditions, calculate the interlayer shear force and interlayer opening force in the uncracked region of the double cantilever beam. Based on interlaminar shear force and interlaminar tension, the equivalent load at the crack tip of the double cantilever beam model is calculated using the principle of equivalent superposition. Calculate the total energy release rate of the double cantilever beam model based on the equivalent load at the crack tip. Based on the total energy release rate and the equivalent load at the crack tip of the double cantilever beam model, the one-dimensional interface fracture driving force modes are classified into pure type I and pure type II.

[0007] Optionally, calculating the interlaminar shear force and interlaminar tension in the uncracked region of the double cantilever beam includes: selecting a micro-element of the uncracked part of the double cantilever beam, and establishing an equilibrium equation based on the condition that the micro-element has consistent deformation and continuous curvature at the bonding interface. Solving the equilibrium equations yields the interlaminar shear force along the interface tangentially and the interlaminar opening force perpendicular to the interface.

[0008] Optionally, the equivalent load at the crack tip of the double cantilever beam model, calculated using the principle of equivalent superposition, includes: Superimpose a crack-free model with the same geometry as the double cantilever beam model, and apply a bending moment equal to and opposite to the original load at the neutral axis of the crack-free model; By superposition processing, the load at the end of the crack-free model is transformed into a form driven by the equivalent bending moment and equivalent axial force at the crack tip.

[0009] Optionally, the double cantilever beam model can be either a top-thick and bottom-thick model or a top-thick and bottom-thin model.

[0010] Optionally, the equivalent load at the crack tip of the thin-top-thick-bottom model is calculated as follows: ; ; ; in, , , , These represent the equivalent bending moment and axial force of the upper and lower beams, respectively. and Indicates interlaminar tension and shear force. and Indicates the radius of curvature at the centroidal axis of the upper and lower beams. and These represent the thicknesses of the upper and lower beams, respectively. Indicates the unit angle.

[0011] Optionally, the equivalent load at the crack tip of the top-thick, bottom-thin model is calculated as follows: ; ; in, , These represent the equivalent bending moments of the lower beam and the upper beam, respectively. and Indicates the radius of curvature at the centroidal axis of the lower and upper beams. and These represent the thickness of the lower beam and the upper beam, respectively.

[0012] Optionally, calculating the total energy release rate of the double cantilever beam model includes: ; in, This represents the radius of curvature at the crack interface. Indicates the model thickness. This indicates the Young's modulus of the material. This represents the coefficient resulting from the non-coincidence between the neutral axis and the centroidal axis.

[0013] Optionally, the one-dimensional interface fracture driving force modes can be classified into pure Type I and pure Type II modes, including: ; ; in, , This represents the combination of corresponding coefficients in the formula. and This represents the modal phase angle used for assignment.

[0014] Technical effects of the invention: The invention discloses a pure mode allocation method for one-dimensional interface fracture driving force based on double cantilever beams, which can quickly and accurately characterize the energy release rate under mixed modes, thereby significantly reducing the time cost caused by using finite element calculation. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam according to an embodiment of the present invention. Figure 2 This is a structural schematic diagram provided in Embodiment 1 of the present invention; Figure 3 This is a comparison chart of results provided in Example 1 of the present invention; Figure 4 This is a structural schematic diagram provided for Embodiment 2 of the present invention; Figure 5 This is a comparison chart of results provided for Example 2 of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] This embodiment provides a pure mode allocation method for the one-dimensional interface fracture driving force based on a double cantilever beam, including: Define the geometric configuration and load conditions of the double cantilever bending beam model according to the application scenario of composite materials; Based on the geometric configuration and load conditions, calculate the interlayer shear force and interlayer opening force in the uncracked region of the double cantilever beam. Based on interlaminar shear force and interlaminar tension, the equivalent load at the crack tip of the double cantilever beam model is calculated using the principle of equivalent superposition. Calculate the total energy release rate of the double cantilever beam model based on the equivalent load at the crack tip. Based on the total energy release rate and the equivalent load at the crack tip of the double cantilever beam model, the one-dimensional interface fracture driving force modes are classified into pure type I and pure type II.

[0019] Furthermore, based on the application scenario of composite materials, the geometric configuration and load conditions of the double cantilever beam model are defined, specifically including: setting the radius of curvature of the lower beam centroidal axis as... The radius of curvature of the centroidal axis of the upper beam is A complete beam is The bonding interface is The thickness at the lower beam is... The thickness of the upper beam is A bending moment is applied at the end of the beam. and At the crack tip, it transforms into and It is used to drive crack propagation.

[0020] Furthermore, based on the aforementioned geometric configuration and load conditions, the inter-layer shear force and inter-layer opening force in the uncracking region of the double cantilever beam are calculated, specifically including: We select a micro-element of the uncracked portion of a double cantilever beam, where end A is the crack tip and end B is the region affected by crack mechanics. The crack propagation direction is from A to B. Since end B is in an uncracked state, the beam deformation is uniform and the curvature remains continuous at this location, resulting in: ; in, , and It is the bending moment at end B of the uncracked region. , describes the coefficients that arise from the non-coincidence between the neutral axis and the centroidal axis.

[0021] At the bonding interface, circumferential stress will be generated. and radial stress The resultant forces are shear forces along the tangential direction of the interface. and the normal opening force perpendicular to the interface Assuming the shear force at the bond interface of the upper beam... Horizontal to the right, opening force Vertically downwards, the direction of the corresponding force on the lower beam is opposite. According to the equilibrium condition of the force system, the sum of all internal forces is zero, thus establishing the equilibrium equations: ; ; For the top-thick and bottom-thick model, combining the continuity condition with the equilibrium equations yields the interlayer shear force. Zhang Kaili The result is: ; ; Furthermore, based on interlaminar shear force and interlaminar tension, and combined with the principle of equivalent superposition, the equivalent load at the crack tip of the double cantilever beam model is calculated, specifically including: A model of the same size and without cracks is superimposed on top of the model. An equal and opposite bending moment is applied at the neutral axis. After this treatment, the model's ends no longer bear bending moments; instead, the initiation and propagation of cracks are driven by the equivalent force and moment at the crack tip. According to the equilibrium equations and internal forces, the equivalent load at the crack tip of the model with a thinner top and thicker bottom is: ; ; ; in, , , , These represent the equivalent bending moment and axial force of the upper and lower beams, respectively.

[0022] The equivalent load at the crack tip in the top-thick, bottom-thin model is: ; ; in, , These represent the equivalent bending moments of the lower beam and the upper beam, respectively.

[0023] At this point, it is stipulated that the equivalent bending moment direction of both the upper and lower beams is positive; the axial force at the upper beam is positive, and the axial force direction of the lower beam is negative.

[0024] Furthermore, based on the equivalent load at the crack tip of the double cantilever beam model, the total energy release rate of the double cantilever beam model is calculated, specifically including: ; Furthermore, based on the total energy release rate and the equivalent load at the crack tip of the double cantilever beam model, the one-dimensional interface fracture driving force modes are classified into pure Type I and pure Type II, specifically including: The thinner beam is defined as beam 1, and the main bending moment is defined on beam 1. The bending moment on beam 2 is According to axial force The calculation formula yields: ; Based on the total energy release rate and the above formula, the energy release rate formula can be rewritten as follows: ; Among them, coefficient , and The formula for total energy release rate is used. and The transformation relationship between them yields , and The coefficients are combined as follows. When the model is thinner at the top and thicker at the bottom, the coefficients are: ; ; ; When the model is thicker at the top and thinner at the bottom, its coefficients are: ; ; ; Based on the above allocation coefficients and using the combined stress intensity factor of Suo and Hutchinson for allocation, the energy release rates of the single fracture modes are obtained as follows: ; ; in, and The phase angle parameter of the model is obtained by Suo and Hutchinson in solving the integral equation of the plane elasticity problem. The specific formula is as follows: ; Specific application examples of this invention are as follows: like Figure 1 As shown, a pure mode allocation method for the one-dimensional interface fracture driving force of a double cantilever beam includes: S1.1 Based on the real-world application scenarios of composite materials, the geometric configuration of the double cantilever beam is defined and its load conditions are determined through a theoretical model. S1.2 Based on the geometry and loading conditions of the double cantilever beam model, calculate the inter-story internal forces in the uncracked region. and ; S1.3 Based on interlayer internal forces and And by combining the principle of equivalent superposition, the equivalent force and moment at the tip of the double cantilever beam are calculated; S1.4 Calculate the total energy release rate of the model based on the equivalent force and moment at the tip of the double cantilever beam; Based on the total energy release rate of the model and the force system at the crack tip, S1.5 uses the Suo and Hutchinson method to classify the mixed fracture modes into pure Type I and pure Type II.

[0025] Case 1 The following implementation case 1 uses a double cantilever curved beam as an example to calculate and allocate the energy release rate of the hybrid mode. The model is as follows... Figure 2 As shown, the radius of curvature of the crack interface The thickness of the upper beam is The thickness of the lower beam is Material properties: Young's modulus Poisson's ratio The top and bottom loading are respectively... and .

[0026] The specific steps are as follows: The model in step S1.1 is thinner at the top and thicker at the bottom, so the upper beam is defined as beam 1 and the lower beam as beam 2.

[0027] Assuming the deformation in the uncracked zone is consistent with that at the beam's neutral axis, and the curvature remains continuous, we obtain: ; in , and It is the bending moment at end B of the uncracked region. , describes the coefficients that arise from the non-coincidence between the neutral axis and the centroidal axis.

[0028] get , , .

[0029] Circumferential stress will be generated at the bonding interface. and radial stress The resultant forces generated by the internal stresses are shear forces along the tangential direction of the interface. Normal opening force perpendicular to the interface It is assumed that at the bonding interface of the upper beam, the shear force... Horizontal to the right, opening force Vertically downwards, the direction of the lower beam is opposite. According to the equilibrium condition of the force system, the sum of all internal forces is zero, thus establishing the equilibrium equations: ; ; Combining curvature continuity with the equilibrium equations, we obtain: , Further calculation of interlayer shear force Zhang Kaili get: ; ; Substitute interlaminar shear force Zhang Kaili Shear force was calculated Zhang Kaili .

[0030] Using the superposition method, a model of the same size but without cracks is superimposed. A bending moment of equal magnitude but opposite direction to that shown in the diagram is then applied on top of this superposition. The equivalent force and moment at the tip after superposition are calculated as follows: ; ; ; in , , , Let represent the equivalent bending moment and axial force of the upper and lower beams, respectively. Substituting these values ​​into the equivalent force at the tip, we obtain... , .

[0031] The total energy release rate is: ; Substituting the values ​​into the calculation, the result of the total energy release rate is: The FEM results are ; The model is thinner at the top and thicker at the bottom; the appropriate distribution coefficient is selected as follows: ; ; ; ; ; Substituting the model dimensions into the calculation results , , The modal phase angle is , .

[0032] The result of assigning the mixed mode to a single mode is: ; ; Substituting the values ​​yields the energy release rate for Mode I. Energy release rate of Mode II The proportion of Mode I in the total energy release rate .

[0033] The FEM results are , , The results were comparable to those of FEM.

[0034] Loading is achieved by fixing the upper beam. Change the load on the lower beam The value of will result in multiple sets of calculation results, such as Figure 3 As shown.

[0035] Case 2 The following uses a double cantilevered beam with a thicker upper section and a thinner lower section as an example to calculate and allocate the energy release rate in the hybrid mode. The model is as follows: Figure 4 As shown, the radius of curvature of the crack interface The thickness of the upper beam is The thickness of the lower beam is Material properties: Young's modulus Poisson's ratio The top and bottom loading are respectively... and .

[0036] The model is thicker at the top and thinner at the bottom, so the upper beam is defined as 2 beams and the lower beam as 1 beam. Curvature continuity is obtained as follows: ; in , and It is the bending moment at end B of the uncracked region. , describes the coefficients that arise from the non-coincidence between the neutral axis and the centroidal axis.

[0037] get , , ; Depend on Figure 2 The force analysis in the middle yielded the following results: ; ; Substituting into the curvature continuity formula yields , ; Interlaminar shear force and Zhang Kaili The calculation formula is: ; ; Substituting into the formula for interlayer internal forces, we get , ; Using the superposition method, a model of the same size but without cracks is superimposed. On top of this, a bending moment of equal magnitude but opposite direction to that shown in the diagram is applied. The equivalent force and moment at the tip after superposition are calculated as follows: ; ; ; in, , , , These represent the equivalent bending moment and axial force of the lower beam and upper beam, respectively.

[0038] Substituting into the formula for the equivalent effect at the tip, we get ; The total energy release rate is: ; Substituting the values ​​into the calculation, the total energy release rate is: The FEM results are .

[0039] The model is thicker at the top and thinner at the bottom, and the equivalent bending moment of the lower beam is defined as the principal bending moment. The coefficients used for the selected allocation are: ; ; ; ; ; Calculated , , The modal phase angle is , .

[0040] The allocation results of the mixed fracture modes are as follows: ; ; Substituting the values ​​yields the energy release rate for Mode I. Energy release rate of Mode II The proportion of Mode I in the total energy release rate .

[0041] The FEM results are , ; .

[0042] Loading is achieved by fixing the upper beam. Change the load on the lower beam Different values ​​of were used to obtain multiple sets of calculation results, such as Figure 5 As shown.

[0043] This invention provides a pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam, comprising: defining a model according to the actual application scenario; calculating the interlayer internal forces in the uncracked region under pure bending state based on the loading model and geometric dimensions; superimposing the interlayer internal forces using the principle of equivalent superposition to calculate the equivalent force and moment at the crack tip; and calculating the energy release rate and mode allocation under fracture modes based on the equivalent force and moment, combined with energy release rate calculation and the Suo and Hutchinson phase angle models.

[0044] Compared with existing technologies, the method of this invention fully considers the relative size relationships of the model, interlaminar stress distribution, and crack tip effect. Therefore, this method can be applied to the failure prediction of most curved components, providing important theoretical support and technical guidance for the design of composite material interface properties and the safety assessment of complex structures.

[0045] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A pure mode distribution method for one-dimensional interface fracture driving force based on a double cantilever beam, characterized in that, include: Define the geometric configuration and load conditions of the double cantilever bending beam model according to the application scenario of composite materials; Based on the geometric configuration and load conditions, calculate the interlayer shear force and interlayer opening force in the uncracked region of the double cantilever beam. Based on interlaminar shear force and interlaminar tension, the equivalent load at the crack tip of the double cantilever beam model is calculated using the principle of equivalent superposition. Calculate the total energy release rate of the double cantilever beam model based on the equivalent load at the crack tip. Based on the total energy release rate and the equivalent load at the crack tip of the double cantilever beam model, the one-dimensional interface fracture driving force modes are classified into pure type I and pure type II.

2. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 1, characterized in that, The calculation of interlaminar shear force and interlaminar opening force in the uncracked region of a double cantilever beam includes: selecting a micro-element of the uncracked part of the double cantilever beam, and establishing an equilibrium equation based on the condition that the micro-element has consistent deformation and continuous curvature at the bonding interface. Solving the equilibrium equations yields the interlaminar shear force along the interface tangentially and the interlaminar opening force perpendicular to the interface.

3. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 1, characterized in that, The equivalent load at the crack tip of the double cantilever beam model, calculated using the principle of equivalent superposition, includes: Superimpose a crack-free model with the same geometry as the double cantilever beam model, and apply a bending moment equal to and opposite to the original load at the neutral axis of the crack-free model; By superposition processing, the load at the end of the crack-free model is transformed into a form driven by the equivalent bending moment and equivalent axial force at the crack tip.

4. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 1, characterized in that, The double cantilever curved beam model is either a top-thin, bottom-thick model or a top-thick, bottom-thin model.

5. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 4, characterized in that, The equivalent load at the crack tip in the top-thicker-bottom model is calculated as follows: ； ； ； in, , , , These represent the equivalent bending moment and axial force of the upper and lower beams, respectively. and Indicates interlaminar tension and shear force. and Indicates the radius of curvature at the centroidal axis of the upper and lower beams. and These represent the thicknesses of the upper and lower beams, respectively. Indicates the unit angle.

6. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 4, characterized in that, The equivalent load at the crack tip in the top-thick, bottom-thin model is calculated as follows: ； ； in, , These represent the equivalent bending moments of the lower beam and the upper beam, respectively. and Indicates the radius of curvature at the centroidal axis of the lower and upper beams. and These represent the thickness of the lower beam and the upper beam, respectively.

7. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 1, characterized in that, The calculation of the total energy release rate of the double cantilever beam model includes: ； in, This represents the radius of curvature at the crack interface. Indicates the model thickness. This indicates the Young's modulus of the material. This represents the coefficient resulting from the non-coincidence between the neutral axis and the centroidal axis.

8. The pure mode allocation method for one-dimensional interface fracture driving force based on a double cantilever beam as described in claim 1, characterized in that, The driving force modes of one-dimensional interface fracture are classified into pure Type I and pure Type II, including: ； ； in, , This represents the combination of corresponding coefficients in the formula. and This represents the modal phase angle used for assignment.

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