Method and device for predicting rigidity of defect-containing composite material
By using softening inclusion method and combined interface units to simulate the manufacturing defects of composite materials in the composite stiffness prediction, establish a single-cell finite element model and apply periodic boundary conditions, the problem of difficult to effectively deal with manufacturing defects in composite stiffness prediction in the prior art is solved, and the prediction accuracy is improved.
Patent Information
- Application Number
- CN202510243112.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-03
- Publication Date
- 2025-06-20
Smart Images
Figure CN120180703A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the technical field of composite material analysis, and particularly relates to a method and device for predicting the stiffness of composite materials with defects. Background Art
[0002] Composite materials are widely used in the aerospace field due to their excellent mechanical properties. During the manufacturing process of composite materials, damages at the mesoscopic scale such as pores, fiber / matrix debonding, etc. are inevitable. Therefore, analyzing the influence of manufacturing defects such as pores and fiber / matrix debonding on mechanical properties has high engineering value. Currently, when using unit cells to characterize macro-mesoscopic mechanical properties, either manufacturing defects are ignored, or holes are dug in the matrix to simulate pores, and the fiber / matrix interface is directly cut to simulate initial debonding. This makes the model very complex and difficult to apply periodic boundary conditions. Summary of the Invention
[0003] To solve the above problems, this application provides a method and device for predicting the stiffness of composite materials with defects. The softening inclusion method is used to simulate matrix pores, and combined interface elements are used to simulate the debonding of the composite material fiber / matrix interface. A unit cell finite element model is established, periodic boundary conditions are set, and axial stress is applied to obtain the stiffness performance of a unidirectional laminate of composite materials with pores and fiber / matrix interface debonding.
[0004] The first aspect of this application provides a method for predicting the stiffness of composite materials with defects, mainly including:
[0005] Step S1: Determine the size parameters and periodic boundary conditions of the unit cell model of the composite material in a rectangular coordinate system. The periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model;
[0006] Step S2: Determine the ranges of the pore region of the matrix and the fiber / matrix debonding region of the matrix in the rectangular coordinate system;
[0007] Step S3: For the pore region, assign a set first smaller value to the matrix elastic modulus. For the debonding region, use interface elements to simulate, and assign a set second smaller value to the interface normal shear modulus. At the same time, for the debonding region, if the interface normal displacement is greater than or equal to 0, assign a set third smaller value to the interface normal elastic modulus;
[0008] Step S4: Update the strain of the unit cell model based on the matrix elastic modulus, interface direction shear modulus, and normal elastic modulus, and update the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
[0009] Preferably, in step S1, the periodic boundary conditions are expressed as:
[0010]
[0011] Among them, is the displacement of a point on a part of the boundary of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume-averaged strain of the unit cell, is the coordinate difference of the corresponding boundary points.
[0012] Preferably, the first smaller value is 10 -8 times the matrix elastic modulus of the initial undamaged matrix, and the second smaller value is 10 -8 times the interface normal shear modulus of the initial undamaged interface element, and the third smaller value is 10 -8 times the interface normal elastic modulus of the initial undamaged interface element.
[0013] The second aspect of the present application provides a stiffness prediction device for a defective composite material, mainly including:
[0014] A periodic boundary condition determination module for determining the size parameters and periodic boundary conditions of the unit cell model of the composite material in a rectangular coordinate system, where the periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model;
[0015] A damage area determination module for determining the range of the pore area and the matrix fiber debonding area of the matrix in the rectangular coordinate system;
[0016] A damage area stiffness setting module for, for the pore area, assigning the matrix elastic modulus with a set first smaller value, for the debonding area, simulating with interface elements, and assigning the interface normal shear modulus with a set second smaller value. At the same time, for the debonding area, if the interface normal displacement is greater than or equal to 0, assigning the interface normal elastic modulus with a set third smaller value;
[0017] A strain and displacement difference update module for updating the strain of the unit cell model based on the matrix elastic modulus, interface direction shear modulus, and normal elastic modulus, and updating the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
[0018] Preferably, in the periodic boundary condition determination module, the periodic boundary conditions are expressed as:
[0019]
[0020] Among them, is the displacement of a point on a part of the boundary of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume-averaged strain of the unit cell, is the coordinate difference of the corresponding boundary points.
[0021] Preferably, the first smaller value is 10 times the matrix elastic modulus of the initial undamaged matrix, -8 the second smaller value is 10 times the interface normal shear modulus of the initial undamaged interface element, -8 the third smaller value is 10 times the interface normal elastic modulus of the initial undamaged interface element. -8 times.
[0022] This application reduces the geometric complexity of the unit cell model, ensures the regularity of the unit cell grid, and improves the stiffness prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0023] Figure 1 is a flowchart of a preferred embodiment of the method for predicting the stiffness of a defective composite material according to this application.
[0024] Figure 2 is a schematic structural diagram of the unit cell model.
[0025] Figure 3 is a schematic diagram of the matrix pore defect.
[0026] Figure 4 is a schematic diagram of the fiber-matrix debonding defect. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0027] To make the purpose, technical solutions, and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings in the embodiments of this application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions throughout. The described embodiments are some, but not all, of the embodiments of this application. The embodiments described below by referring to the drawings are exemplary and are intended to explain this application and should not be construed as limiting this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of this application without creative efforts shall fall within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the drawings.
[0028] The first aspect of this application provides a method for predicting the stiffness of a defective composite material, as Figure 1 shown, mainly including:
[0029] Step S1, determining the size parameters and periodic boundary conditions of the unit cell model of the composite material in the rectangular coordinate system, where the periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model;
[0030] Step S2: Determine the ranges of the pore region and the matrix fiber debonding region of the matrix in the rectangular coordinate system;
[0031] Step S3: For the pore region, assign a set first smaller value to the matrix elastic modulus. For the debonding region, simulate using interface elements and assign a set second smaller value to the interface normal shear modulus. At the same time, for the debonding region, if the interface normal displacement is greater than or equal to 0, assign a set third smaller value to the interface normal elastic modulus;
[0032] Step S4: Update the strain of the unit cell model based on the matrix elastic modulus, the interface direction shear modulus, and the normal elastic modulus, and update the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
[0033] First, in Step S1, the unit cell model constructed in this application is as Figure 2 shown, including the fiber in the middle and the cubic matrix coating the fiber. In the rectangular coordinate system xyz, the unit cell length is L, parallel to the x-axis, the width is W, parallel to the y-axis, the height is H, parallel to the z-axis, and the radius of the central fiber is r, with the axial direction along the x-axis.
[0034] Therefore, the fiber volume content is as follows:
[0035]
[0036] In some alternative embodiments, in Step S1, the periodic boundary conditions are expressed as:
[0037]
[0038] where, is the displacement of a point on a part of the boundary of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume average strain of the unit cell, is the coordinate difference of the corresponding boundary point.
[0039] To prevent overconstraint and underconstraint, the periodic boundary conditions defined by Equation (2) should be applied to the faces, edges, and vertices respectively. For example, the periodic displacement boundary conditions for the two faces perpendicular to the x-axis are as follows:
[0040]
[0041] That is:
[0042]
[0043] Step S2 is used to perform the defect area, and step S3 is used to perform finite element modeling on the defect area, mainly including matrix pore defect simulation and debonding defect simulation between fibers and the matrix.
[0044] For the matrix pore defect simulation, taking the spherical matrix pore defect as an example for illustration, the schematic diagram is shown in Figure 3 , the pore center coordinates are (x0, y0, z0), and the radius is R.
[0045] Therefore, the state variable SDV3 characterizing the non-damaged area and the pore defect area can be determined from the element center coordinates (x, y, z) according to equation (5):
[0046]
[0047] Then in step S3, the matrix elastic modulus E can be determined according to the state variable SDV3 m (The theoretical elastic modulus of the pore area is zero. To avoid errors in finite element analysis, it is set to a small value):
[0048]
[0049] For the debonding defect simulation between fibers and the matrix, taking the debonding defect as shown in Figure 4 as an example for illustration, the x-axis coordinate range of the defect area is a to b, and the included angle range between the connection line of the defect boundary and the fiber center and the y-axis is T1 to T2.
[0050] Therefore, the state variable SDV3 characterizing the non-damaged area and the debonding defect area can be determined from the element center coordinates according to the following formula:
[0051]
[0052] Among them, the included angle θ between the connection line of the defect boundary and the fiber center and the y-axis is calculated as follows:
[0053]
[0054] Both the non-damaged area and the debonding area are simulated by a layer of interface elements, and different material properties are set. The interface normal elastic modulus E N and the shear modulus E S (The theoretical shear elastic modulus of the debonding area is zero, the normal direction is in a tensile state, and the normal modulus is also zero. To avoid errors in finite element analysis, both are set to small values): The interface normal displacement 33
[0055]
[0056] In the above formula, δ 33 is the interface normal displacement.
[0057] In some alternative embodiments, the first smaller value is the matrix elastic modulus of the initial undamaged matrix multiplied by 10 -8 times, the second smaller value is the interface normal shear modulus of the initial undamaged interface element multiplied by 10 -8 times, and the third smaller value is the interface normal elastic modulus of the initial undamaged interface element multiplied by 10 -8 times.
[0058] This application simulates the matrix pore defects of the composite material based on the softened inclusion method, and uses the combined interface element to simulate the fiber / matrix interface debonding of the composite material, reducing the geometric complexity of the unit cell model and ensuring the regularity of the unit cell grid.
[0059] Taking the prediction of the elastic constants of the T300 / BSL914C composite material unidirectional plate as an example for specific illustration. The elastic constants of the T300 fiber are as follows: the longitudinal modulus E 11 is 230 GPa, the transverse modulus E 22 is 28 GPa, the Poisson's ratio ν 12 is 0.25, the shear modulus G 12 is 35 GPa, and the transverse shear modulus G 23 is 11.2 GPa. The matrix elastic modulus of BSL914C is 4 GPa, and the Poisson's ratio is 0.35. The fiber volume fraction is 60%.
[0060] The elastic constants of the T300 / BSL914C composite material unidirectional plate obtained by experimental tests are as follows: the longitudinal modulus E 11 is 138 GPa, the transverse modulus E 22 is 11 GPa, the Poisson's ratio ν 12 is 0.28, and the shear modulus G 12 is 5.5 GPa.
[0061] Based on the provided material property parameters and damage geometric parameters, stiffness analysis is carried out on the unit cell model constructed according to this application. L = W = H = 100 mm, and the number of one-eighth circular elements is set to 10. The center coordinates of the matrix pores are (50 mm, 75 mm, 75 mm), and the radius is 20 mm; the geometric parameters of the interface debonding area are: a = 30 mm, b = 30 mm, T1 = 30°, T2 = 70°.
[0062] The prediction results of the elastic constants of the T300 / BSL914C composite material unidirectional plate are shown in Table 1. It can be seen that the prediction accuracy of the transverse elastic modulus is significantly improved after introducing defects, the prediction accuracy of the longitudinal modulus and Poisson's ratio is slightly improved, while the prediction accuracy of the shear modulus is relatively low.
[0063] Table 1 Prediction Results of Elastic Constants of T300 / BSL914C Composite Material Unidirectional Plate
[0064]
[0065] The second aspect of the present application provides a device for predicting the stiffness of a composite material with defects corresponding to the above method, mainly including:
[0066] A periodic boundary condition determination module, configured to determine the size parameters and periodic boundary conditions of the unit cell model of the composite material in a rectangular coordinate system, where the periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model;
[0067] A damage area determination module, configured to determine the ranges of the pore area of the matrix and the matrix-fiber debonding area in the rectangular coordinate system;
[0068] A damage area stiffness setting module, for the pore area, assigning a set first smaller value to the matrix elastic modulus, for the debonding area, simulating with interface elements and assigning a set second smaller value to the interface normal shear modulus, and at the same time, for the debonding area, if the interface normal displacement is greater than or equal to 0, assigning a set third smaller value to the interface normal elastic modulus;
[0069] A strain and displacement difference update module, configured to update the strain of the unit cell model based on the matrix elastic modulus, the interface direction shear modulus, and the normal elastic modulus, and update the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
[0070] In some alternative embodiments, in the periodic boundary condition determination module, the periodic boundary conditions are expressed as:
[0071]
[0072] Wherein, is the displacement of a point on a part of the boundary of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume-averaged strain of the unit cell, is the coordinate difference of the corresponding boundary points.
[0073] In some alternative embodiments, the first smaller value is 10 -8 times the matrix elastic modulus of the initially undamaged matrix, the second smaller value is 10 -8 times the interface normal shear modulus of the initially undamaged interface element, and the third smaller value is 10 -8 times the interface normal elastic modulus of the initially undamaged interface element.
[0074] As described above, it is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claimed rights.
Claims
1. A method for predicting the stiffness of defective composite materials, characterized in that: include: Step S1, determining the size parameters and periodic boundary conditions of a unit cell model of the composite material in a rectangular coordinate system, wherein the periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model; Step S2, determining the range of the pore area of the matrix and the debonding area of the matrix fibers in the rectangular coordinate system; Step S3, for the pore area, use the set first smaller value to assign the matrix elastic modulus, for the debonding area, use the interface unit simulation, and use the set second smaller value to assign the interface normal shear modulus, and at the same time, for the debonding area, if the interface normal displacement is greater than or equal to 0, use the set third smaller value to assign the interface normal elastic modulus; Step S4: updating the strain of the unit cell model based on the matrix elastic modulus, the interface direction shear modulus and the normal elastic modulus, and updating the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
2. The method for predicting stiffness of defective composite materials according to claim 1, characterized in that: In step S1, the periodic boundary condition is expressed as: in, is the displacement of a point on the boundary of a part of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume average strain of the unit cell, is the coordinate difference of the corresponding boundary points.
3. The method for predicting stiffness of defective composite materials according to claim 1, characterized in that: The first smaller value is 10 of the elastic modulus of the matrix of the initial undamaged matrix. -8 times, and the second smallest value is 10 of the normal shear modulus of the initial undamaged interface element -8 times, and the third smallest value is 10 of the interface normal elastic modulus of the initial undamaged interface unit. -8 times.
4. A device for predicting the stiffness of defective composite materials, characterized in that: include: A periodic boundary condition determination module, used to determine the size parameters and periodic boundary conditions of the unit cell model of the composite material in a rectangular coordinate system, wherein the periodic boundary conditions include the relationship between the displacement difference and strain of two corresponding points of the unit cell model; A damage region determination module, used to determine the range of the matrix pore region and the matrix fiber debonding region in the rectangular coordinate system; A damage area stiffness setting module, for assigning a value to the matrix elastic modulus using a set first smaller value for the pore area, for simulating the debonding area using an interface unit, and for assigning a value to the interface normal shear modulus using a set second smaller value, and for the debonding area, if the interface normal displacement is greater than or equal to 0, assigning a value to the interface normal elastic modulus using a set third smaller value; The strain and displacement difference updating module is used to update the strain of the unit cell model based on the matrix elastic modulus, the interface direction shear modulus and the normal elastic modulus, and to update the displacement difference according to the strain of the unit cell model and the periodic boundary conditions.
5. The device for predicting stiffness of defective composite materials according to claim 4, characterized in that: In the periodic boundary condition determination module, the periodic boundary condition is expressed as: in, is the displacement of a point on the boundary of a part of the unit cell model, is the displacement of the corresponding point on the boundary, is the volume average strain of the unit cell, is the coordinate difference of the corresponding boundary points.
6. The device for predicting stiffness of defective composite materials according to claim 4, characterized in that: The first smaller value is 10 of the elastic modulus of the matrix of the initial undamaged matrix. -8 times, and the second smallest value is 10 of the normal shear modulus of the initial undamaged interface element -8 times, and the third smallest value is 10 of the interface normal elastic modulus of the initial undamaged interface unit. -8 times.