Calculation method and system for high temperature tensile constitutive model of braided ceramic matrix composites

Abstract

The present invention provides a method and system for calculating a high-temperature tensile constitutive model of a woven ceramic-based composite material, wherein the method includes constructing a finite element model of the woven ceramic-based composite material; determining a reduction coefficient of a unit elastic parameter in a preparation process; determining an average thermal deformation when the material expands freely at high temperature; substituting a yarn high-temperature tensile constitutive curve into the finite element model to determine an initial high-temperature tensile constitutive curve of the woven ceramic-based composite material; interpolating the strain corresponding to zero stress based on the initial high-temperature tensile constitutive curve, extracting points where stress is greater than zero in the initial high-temperature tensile constitutive curve, and obtaining a high-temperature tensile constitutive curve of the woven ceramic-based composite material. The constitutive model constructed by the present invention does not need to consume a lot of time and test pieces, and has a high degree of applicability for establishing a constitutive model for woven ceramic-based composite materials, and considers the initial thermal stress between yarns caused by preparation reasons, so as to realize the prediction of the constitutive behavior of woven ceramic-based composite materials at high temperatures.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical analysis of composite materials, and in particular relates to a calculation method and system for a high-temperature tensile constitutive model of a woven ceramic-based composite material. Background Art

[0002] Braided ceramic matrix composites have higher modulus and strength in high temperature environments, and can better resist ablation and thermal shock. They are an ideal material that can replace high-temperature alloys and are a better choice for making hot end components of aircraft engines. In order to better apply braided ceramic matrix composites to engineering practice, it is necessary to study its various mechanical properties based on the high-temperature constitutive model of braided ceramic matrix composites. Braided ceramic matrix composites have complex micro-geometric structures, and the preparation process and high-temperature environment cause complex thermal stresses inside them. In addition, the damage mode during the tensile process is complex. Therefore, it is technically difficult to accurately simulate the high-temperature tensile constitutive behavior of braided ceramic matrix composites.

[0003] Patent application No. 201910245966.4 discloses a multi-scale prediction method for the strength of woven ceramic matrix composites. A parametric method is used to establish a unit cell model of woven ceramic matrix composites, which includes yarns and a matrix, and performs periodic meshing. Subsequently, the mechanical behavior of the yarn unit is simulated by the mesomechanics method, and the yarn unit stiffness matrix is ​​converted from the local coordinate system to the global coordinate system by using the strain conversion matrix. Finally, by applying incremental periodic boundary conditions, the mesoscopic stress and strain field of the unit cell are calculated. The volume averaging method is used to obtain the macroscopic stress and strain of the woven ceramic matrix composite. If a failure unit band is formed that passes through the unit cell, it is considered that the woven ceramic matrix composite has failed, and the average stress of the unit cell at this time is the strength of the woven ceramic matrix composite. Patent application No. 201910113899.0 discloses a method for predicting the stress-strain response and strength of woven ceramic-based composite materials, which is characterized in that a matrix fiber bundle with the same in-situ performance as the woven CMCs is prepared, a single-cell finite element model is established for the matrix fiber bundle, and finite element calculation is performed on the single-cell finite element model to obtain the stress-strain response of the matrix fiber bundle. The maximum stress on the stress-strain curve is the strength of the woven CMCs.

[0004] However, the above-mentioned existing technologies do not take into account the initial thermal stress between yarns caused by preparation reasons, and the prediction method mainly focuses on the room temperature mechanical properties of woven ceramic matrix composites, and cannot realize the prediction of the constitutive behavior of woven ceramic matrix composites at high temperatures. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a calculation method and system for a high-temperature tensile constitutive model of a braided ceramic matrix composite material.

[0006] In a first aspect, the present invention provides a method for calculating a high temperature tensile constitutive model of a woven ceramic matrix composite material, comprising:

[0007] Based on XCT slices of the microstructure of woven ceramic matrix composites, a finite element model of the microstructure of woven ceramic matrix composites was constructed;

[0008] Cut the finite element model to obtain the minimum representative volume unit;

[0009] Determine the reduction factor of elastic parameters of the smallest representative volume unit in the process of fabricating woven ceramic matrix composites;

[0010] Determine the average thermal deformation of the braided ceramic matrix composite during free expansion at high temperature and obtain the high-temperature tensile constitutive curve of the yarn;

[0011] Substitute the yarn high temperature tensile constitutive curve into the finite element model, and determine the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit;

[0012] Based on the initial high temperature tensile constitutive curve of the woven ceramic matrix composite material, the strain corresponding to zero stress is interpolated as the initial thermal strain;

[0013] Extract the nodes with stress greater than zero in the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material;

[0014] According to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain, the high temperature tensile constitutive curve of the braided ceramic matrix composite material is determined.

[0015] Furthermore, the reduction coefficient of the elastic parameter of the minimum representative volume unit in the process of preparing the woven ceramic matrix composite material includes:

[0016] Construct periodic boundary conditions of finite element models; periodic boundary conditions include rigid body displacement constraints, line node displacement constraints, surface node displacement constraints and vertex node displacement constraints;

[0017] The rigid body displacement constraint is:

[0018] u x＝0,y＝0,z＝0 =v x＝0,y＝0,z＝0 =w x＝0,y＝0,z＝0 =0;

[0019] Among them, u, v, and w are the displacements of the finite element model in the x, y, and z directions respectively; the x direction is the warp direction, the y direction is the weft direction; the z direction is the thickness direction of the finite element model; u x＝0,y＝0,z＝0 v is the displacement of the node in the x direction with coordinates (0,0,0) in the spatial coordinate system; x＝0,y＝0,z＝0is the displacement of the node in the y direction with coordinates (0,0,0) in the spatial coordinate system; w x＝0,y＝0,z＝0 is the displacement in the z direction of the node with coordinates (0,0,0) in the spatial coordinate system;

[0020] Among the node displacement constraints on the line, the constraint parallel to the x direction is:

[0021]

[0022] Among the node displacement constraints on the line, the constraint parallel to the y direction is:

[0023]

[0024] Among the node displacement constraints on the line, the constraint parallel to the z direction is:

[0025]

[0026] Among them, L c , W c , H c are the lengths of the finite element model in the x, y, and z directions respectively; u y＝0,z＝0 v is the x-direction displacement of the node on the x-axis in the spatial coordinate system; y＝0,z＝0 is the y-direction displacement of the node on the x-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xz plane, z = H c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the z-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, y = W c , z=H c The x-direction displacement of the straight line node parallel to the x-axis; v z＝0,x＝0 is the y-direction displacement of the node on the y-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c The y-direction displacement of the straight line node parallel to the y-axis; w z＝0,x＝0is the z-direction displacement of the node on the y-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, x = L c , z=H c The y-direction displacement of the straight line node parallel to the y-axis; w x＝0,y＝0 is the z-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, y = W c The z-direction displacement of the straight line node parallel to the z-axis; u x＝0,y＝0 is the x-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, z = W c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the z-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, x = L c , y=W c And the z-direction displacement of the straight line nodes parallel to the z-axis;

[0027] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the x direction is:

[0028]

[0029] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the y direction is:

[0030]

[0031] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the z direction is:

[0032]

[0033] Among them, v x＝0is the y-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The y-direction displacement of the node on the plane; w x＝0 is the z-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The z-direction displacement of the node on the plane; w y＝0 is the z-direction displacement of the node on the xz plane in the spatial coordinate system; In the spatial coordinate system, y = W c The z-direction displacement of the node on the plane; u z＝0 is the x-direction displacement of the node on the xy plane in the spatial coordinate system; In the spatial coordinate system, at z = H c The x-direction displacement of the nodes on the plane;

[0034] The vertex node displacement constraint is:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] in, In the spatial coordinate system, the coordinates are (0,W c ,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (0,W c ,H c )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the x direction;

[0042] A temperature load is applied, and the reference temperature is set as the preparation temperature and the actual temperature load is set as room temperature. The process of cooling the woven ceramic matrix composite material from the preparation temperature to room temperature is simulated, and the thermal residual stress caused by the microstructure inhomogeneity and the anisotropy of material parameters during the cooling process is obtained; based on the thermal residual stress of the minimum representative volume unit and the room temperature constitutive curve of the yarn, the elastic parameters of the corrected minimum representative volume unit and their reduction coefficients relative to the initial elastic parameters are obtained; the same temperature and boundary conditions are applied for iterative calculation until the elastic parameters of the minimum representative volume unit are stable, and the reduction coefficients of the elastic parameters of the minimum representative volume unit are obtained.

[0043] Further, the method of determining the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature to obtain the high temperature tensile constitutive curve of the yarn includes:

[0044] The average value du of the x-direction displacement difference of the finite element model is calculated according to the following formula: x :

[0045]

[0046] Among them, n x is the number of nodes on a surface of the finite element model perpendicular to the x direction; x(i) is the coordinate value of node i in the x direction; L c is the length of the finite element model in the x direction; The x-coordinate value is L c u is the x-direction displacement of node i whose coordinate value in the x-direction is 0;

[0047] ix(i)=0

[0048] The average value dv of the y-direction displacement difference of the finite element model is calculated according to the following formula: y :

[0049]

[0050] Among them, n y is the number of nodes on a surface of the finite element model perpendicular to the y direction; y(i) is the coordinate value of node i in the y direction; W c is the length of the finite element model in the y direction; The coordinate value in the y direction is W c The y-direction displacement of node i; v i y(i)＝0 is the y-direction displacement of node i whose coordinate value in the y-direction is 0;

[0051] The average value dw of the z-direction displacement difference of the finite element model is calculated according to the following formula: z :

[0052]

[0053] Among them, n z is the number of nodes on a surface of the finite element model perpendicular to the z direction; z(i) is the coordinate value of node i in the z direction; H c is the length of the finite element model in the z direction; The coordinate value in the z direction is H c The z-direction displacement of node i; w i|z(i)＝0 is the z-direction displacement of node i whose coordinate value in the z-direction is 0.

[0054] Furthermore, the high-temperature tensile constitutive curve of the yarn is substituted into the finite element model, and the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material is determined according to the reduction coefficient of the elastic parameter of the minimum representative volume unit, including:

[0055] Create a displacement boundary condition:

[0056]

[0057] in, In the spatial coordinate system, at x = L c The x-direction displacement of the node on the plane; u x＝0 is the x-direction displacement of the node on the yz plane in the spatial coordinate system; ε i represents the strain load of node i increasing from zero; du x is the average value of the x-direction displacement difference of the finite element model;

[0058] The average strain of the finite element model is calculated according to the following formula

[0059]

[0060] The average stress of the finite element model is calculated according to the following formula

[0061]

[0062] Among them, n e is the total number of the smallest representative volume unit; is the stress of the jth minimum representative volume unit; is the volume of the jth minimum representative volume unit;

[0063] The product of the yarn's high-temperature initial elastic parameter and the reduction coefficient of the minimum representative volume unit is taken as the initial elastic parameter of the minimum representative volume unit in the finite element model; the progressive damage analysis method is used to determine the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material based on the yarn's high-temperature tensile constitutive curve.

[0064] Further, the high temperature tensile constitutive curve of the braided ceramic matrix composite material is determined according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain, including:

[0065] The initial thermal strain is corrected according to the following formula:

[0066]

[0067] in, is the strain corresponding to the node where the stress is greater than zero in the initial high temperature tensile constitutive curve; is the corrected initial thermal strain;

[0068] The high temperature tensile constitutive curve of the woven ceramic matrix composite material is determined based on the corrected initial thermal strain.

[0069] In a second aspect, the present invention provides a high temperature tensile constitutive model calculation system for a braided ceramic matrix composite material, comprising:

[0070] Finite element model building module, used to build a finite element model of the mesostructure of woven ceramic matrix composite materials based on XCT slices of the mesostructure of woven ceramic matrix composite materials;

[0071] Model cutting module, used to cut the finite element model to obtain the minimum representative volume unit;

[0072] A reduction coefficient determination module, used to determine the reduction coefficient of the elastic parameters of the minimum representative volume unit in the preparation process of the woven ceramic matrix composite material;

[0073] The average thermal deformation determination module is used to determine the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature, and obtain the high-temperature tensile constitutive curve of the yarn;

[0074] An initial high-temperature tensile constitutive curve determination module is used to substitute the yarn high-temperature tensile constitutive curve into the finite element model and determine the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit;

[0075] An interpolation module is used to interpolate the strain corresponding to zero stress as the initial thermal strain based on the initial high-temperature tensile constitutive curve of the woven ceramic matrix composite material;

[0076] A node extraction module is used to extract nodes with stress greater than zero in the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material;

[0077] The high temperature tensile constitutive curve determination module is used to determine the high temperature tensile constitutive curve of the woven ceramic matrix composite material according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain.

[0078] The present invention provides a method and system for calculating a high-temperature tensile constitutive model of a woven ceramic-based composite material. The method can construct a constitutive model more efficiently without consuming a lot of time and test pieces, can effectively reduce the cost of constitutive model construction, and has a high degree of applicability for constitutive model establishment of woven ceramic-based composite materials. At the same time, the initial thermal stress between yarns caused by preparation reasons is taken into account, and the constitutive behavior prediction of woven ceramic-based composite materials at high temperatures can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0080] Figure 1 A flow chart of a method for calculating a high temperature tensile constitutive model of a woven ceramic matrix composite material provided by an embodiment of the present invention;

[0081] Figure 2 XCT slice diagram of the 2.5D woven ceramic matrix composite material provided by the embodiment of the present invention;

[0082] Figure 3 A schematic diagram of a finite element model reflecting the microstructure of a woven ceramic matrix composite material provided in an embodiment of the present invention;

[0083] Figure 4 Schematic diagram of a finite element model with displacement constraints provided in an embodiment of the present invention

[0084] Figure 5 A stress-strain curve of a small composite material provided by an embodiment of the present invention;

[0085] Figure 6 A high temperature constitutive curve of a woven ceramic matrix composite material provided by an embodiment of the present invention;

[0086] Figure 7 A structural diagram of a calculation system for a high-temperature tensile constitutive model of a woven ceramic matrix composite material provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0088] In one embodiment, if Figure 1 As shown, an embodiment of the present invention provides a method for calculating a high temperature tensile constitutive model of a woven ceramic matrix composite material, comprising:

[0089] Step 101, constructing a finite element model of the mesostructure of the woven ceramic matrix composite material based on XCT slices of the mesostructure of the woven ceramic matrix composite material.

[0090] like Figure 2 As shown in the figure, a 2.5D woven ceramic matrix composite material was selected for slicing, and its internal structure was observed using XCT technology. The cross-sections in the warp and weft directions were photographed respectively. The warp direction can be regarded as a sine curve, and the weft direction can be regarded as a straight line. The cross-section is approximately an ellipse. The mesoscopic structural parameters such as the thickness, width, and wavelength of the warp and weft yarns can be obtained through the XCT slice diagram. Figure 3 As shown, the yarn cross section is simplified, and a finite element model reflecting the mesostructure of the woven ceramic matrix composite is established based on the observed mesostructure size.

[0091] Step 102, cut the finite element model to obtain the minimum representative volume element RVE (representative volume element). The minimum representative volume element is meshed, such as Figure 4 As shown, improved periodic boundary conditions are imposed on the finite element model, including rigid body displacement constraints, line node displacement constraints, surface node displacement constraints and vertex node displacement constraints.

[0092] Step 103, determining the reduction coefficient of the elastic parameter of the minimum representative volume unit in the process of preparing the woven ceramic matrix composite material.

[0093] Exemplarily, the rigid body displacement constraint is:

[0094] ux＝0,y＝0,z＝0 =v x＝0,y＝0,z＝0 =w x＝0,y＝0,z＝0 =0.

[0095] Among them, u, v, and w are the displacements of the finite element model in the x, y, and z directions respectively; the x direction is the warp direction, the y direction is the weft direction; the z direction is the thickness direction of the finite element model; u x＝0,y＝0,z＝0 v is the displacement of the node in the x direction with coordinates (0,0,0) in the spatial coordinate system; x＝0,y＝0,z＝0 is the displacement of the node in the y direction with coordinates (0,0,0) in the spatial coordinate system; w x＝0,y＝0,z＝0 is the displacement in the z direction of the node with coordinates (0,0,0) in the spatial coordinate system.

[0096] Among the node displacement constraints on the line (excluding vertex nodes), the constraints parallel to the x direction are:

[0097]

[0098] Among the node displacement constraints on the line, the constraint parallel to the y direction is:

[0099]

[0100] Among the node displacement constraints on the line, the constraint parallel to the z direction is:

[0101]

[0102] Among them, L c , W c , H c are the lengths of the finite element model in the x, y, and z directions respectively; the coordinate ranges of the finite element model are [0,L c ],[0,W c ],[0,H c ];u y＝0,z＝0 v is the x-direction displacement of the node on the x-axis in the spatial coordinate system; y＝0,z＝0 is the y-direction displacement of the node on the x-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xz plane, z = H c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the z-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, y = W c , z=H c The x-direction displacement of the straight line node parallel to the x-axis; v z＝0,x＝0 is the y-direction displacement of the node on the y-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c The y-direction displacement of the straight line node parallel to the y-axis; w z＝0,x＝0 is the z-direction displacement of the node on the y-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, x = L c , z=H c The y-direction displacement of the straight line node parallel to the y-axis; w x＝0,y＝0 is the z-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, y = W c The z-direction displacement of the straight line node parallel to the z-axis; u x＝0,y＝0 is the x-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, z = W c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the z-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, x = L c , y=W c And the z-direction displacement of the straight line node parallel to the z-axis.

[0103] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the x direction is:

[0104]

[0105] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the y direction is:

[0106]

[0107] Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the z direction is:

[0108]

[0109] Among them, v x＝0 is the y-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The y-direction displacement of the node on the plane; w x＝0 is the z-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The z-direction displacement of the node on the plane; w y＝0 is the z-direction displacement of the node on the xz plane in the spatial coordinate system; In the spatial coordinate system, y = W c The z-direction displacement of the node on the plane; u z＝0 is the x-direction displacement of the node on the xy plane in the spatial coordinate system; In the spatial coordinate system, at z = H c The x-direction displacement of a node on a plane.

[0110] The vertex node displacement constraint is:

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] in, In the spatial coordinate system, the coordinates are (0,W c ,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (0,W c ,Hc )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the x direction.

[0118] The above boundary conditions satisfy the structural symmetry while allowing the free expansion of the structure, reducing the structural stress concentration caused by unnecessary constraints.

[0119] A temperature load was applied, and the reference temperature was set to the preparation temperature (1100℃), and the actual temperature load was set to room temperature (22℃). The process of cooling the woven ceramic matrix composite material from the preparation temperature to room temperature was simulated, and the thermal residual stress caused by the microstructure inhomogeneity and the anisotropy of material parameters during the cooling process was obtained; based on the thermal residual stress of the minimum representative volume unit and the room temperature constitutive curve of the yarn, the elastic parameters of the corrected minimum representative volume unit and their reduction coefficients relative to the initial elastic parameters were obtained; the same temperature and boundary conditions were applied for iterative calculation until the elastic parameters of the minimum representative volume unit were stable, and the reduction coefficients of the elastic parameters of the minimum representative volume unit were obtained.

[0120] Step 104, determining the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature, and obtaining a high temperature tensile constitutive curve of the yarn.

[0121] Exemplarily, the average value du of the x-direction displacement difference of the finite element model is calculated according to the following formula: x :

[0122]

[0123] Among them, n x is the number of nodes on a surface of the finite element model perpendicular to the x direction; x(i) is the coordinate value of node i in the x direction; L c is the length of the finite element model in the x direction; The x-coordinate value is L c u is the x-direction displacement of node i whose coordinate value in the x-direction is 0.

[0124] ix(i)=0

[0125] The average value dv of the y-direction displacement difference of the finite element model is calculated according to the following formula: y :

[0126]

[0127] Among them, n y is the number of nodes on a surface of the finite element model perpendicular to the y direction; y(i) is the coordinate value of node i in the y direction; W c is the length of the finite element model in the y direction; The coordinate value in the y direction is W c The y-direction displacement of node i; v i y(i)＝0 is the y-direction displacement of node i whose coordinate value in the y-direction is 0.

[0128] The average value dw of the z-direction displacement difference of the finite element model is calculated according to the following formula: z :

[0129]

[0130] Among them, n z is the number of nodes on a surface of the finite element model perpendicular to the z direction; z(i) is the coordinate value of node i in the z direction; H c is the length of the finite element model in the z direction; The coordinate value in the z direction is H c The z-direction displacement of node i; w i|z(i)＝0 is the z-direction displacement of node i whose coordinate value in the z-direction is 0.

[0131] Step 105 , substituting the yarn high temperature tensile constitutive curve into the finite element model, and determining the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit.

[0132] For example, the temperature load is reapplied to the finite element model again, and the reference temperature is the preparation temperature, and the average thermal deformation of the material during free expansion at high temperature is calculated. The high-temperature tensile stress-strain curve of the fiber bundle material is obtained through the experiment, corresponding to the yarn of the woven ceramic matrix composite material, and the stress-strain curve of the small composite material, such as Figure 5 shown.

[0133] Create a displacement boundary condition:

[0134]

[0135] Among them, u x＝Lc In the spatial coordinate system, at x = L c The x-direction displacement of the node on the plane; u x＝0 is the x-direction displacement of the node on the yz plane in the spatial coordinate system; ε i represents the strain load of node i increasing from zero; du x is the average value of the x-direction displacement difference of the finite element model.

[0136] The average strain of the finite element model is calculated according to the following formula

[0137]

[0138] The average stress of the finite element model is calculated according to the following formula

[0139]

[0140] Among them, n e is the total number of the smallest representative volume unit; is the stress of the jth minimum representative volume unit; is the volume of the jth minimum representative volume unit.

[0141] The product of the yarn's high-temperature initial elastic parameter and the reduction coefficient of the minimum representative volume unit is taken as the initial elastic parameter of the minimum representative volume unit in the finite element model; the progressive damage analysis method is used to determine the initial high-temperature tensile constitutive curve of the woven ceramic matrix composite material based on the yarn's high-temperature tensile constitutive curve; wherein, when the displacement load increases and the stress decreases or the unit failure that penetrates the cross-section occurs in the finite element model, it is considered that the structure has reached the failure strength and the calculation is terminated.

[0142] Step 106 , based on the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material, interpolate the strain corresponding to the node with zero stress as the initial thermal strain.

[0143] Step 107 , extracting nodes with stress greater than zero in the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material.

[0144] Step 108 , determining a high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain.

[0145] Exemplarily, the initial thermal strain is corrected according to the following formula:

[0146]

[0147] in, is the strain corresponding to the node where the stress is greater than zero in the initial high temperature tensile constitutive curve; is the corrected initial thermal strain.

[0148] like Figure 6 As shown, the high temperature tensile constitutive curve of the woven ceramic matrix composite is determined according to the corrected initial thermal strain.

[0149] The high-temperature tensile constitutive model calculation method for woven ceramic-based composite materials provided by the embodiment of the present invention can construct the constitutive model more efficiently without consuming a lot of time and test pieces, can effectively reduce the cost of constitutive model construction, and has high applicability for the establishment of constitutive models for woven ceramic-based composite materials. At the same time, the initial thermal stress between yarns caused by preparation reasons is taken into account, and the constitutive behavior prediction of woven ceramic-based composite materials at high temperatures can be achieved.

[0150] Based on the same inventive concept, an embodiment of the present invention also provides a system for calculating a high-temperature tensile constitutive model of a woven ceramic-based composite material. Since the principle of solving the problem by this system is similar to the calculation method for the high-temperature tensile constitutive model of a woven ceramic-based composite material, the implementation of this system can refer to the implementation of the calculation method for the high-temperature tensile constitutive model of a woven ceramic-based composite material, and the repeated parts will not be repeated.

[0151] In another embodiment, a high temperature tensile constitutive model calculation system for a braided ceramic matrix composite material is provided in an embodiment of the present invention. Figure 7 As shown, including:

[0152] The finite element model building module 10 is used to build a finite element model of the mesostructure of the woven ceramic matrix composite material based on the XCT slices of the mesostructure of the woven ceramic matrix composite material.

[0153] The model cutting module 20 is used to cut the finite element model to obtain the minimum representative volume unit.

[0154] The reduction coefficient determination module 30 is used to determine the reduction coefficient of the elastic parameter of the minimum representative volume unit in the process of preparing the woven ceramic matrix composite material.

[0155] The average thermal deformation determination module 40 is used to determine the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature, and obtain the high-temperature tensile constitutive curve of the yarn.

[0156] The initial high temperature tensile constitutive curve determination module 50 is used to substitute the yarn high temperature tensile constitutive curve into the finite element model and determine the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit.

[0157] The interpolation module 60 is used to interpolate the strain corresponding to zero stress as the initial thermal strain based on the initial high temperature tensile constitutive curve of the woven ceramic matrix composite material.

[0158] The node extraction module 70 is used to extract nodes with stress greater than zero in the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material.

[0159] The high temperature tensile constitutive curve determining module 80 is used to determine the high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain.

[0160] For more specific working processes of the above modules, please refer to the corresponding contents disclosed in the above embodiments, which will not be repeated here.

[0161] The present invention has been described in detail above in conjunction with specific implementations and exemplary examples, but these descriptions cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, a variety of equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its implementation methods, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be subject to the attached claims.

Claims

1. A method for calculating the high temperature tensile constitutive model of a woven ceramic matrix composite material, characterized in that: include: Based on XCT slices of the microstructure of woven ceramic matrix composites, a finite element model of the microstructure of woven ceramic matrix composites was constructed; Cut the finite element model to obtain the minimum representative volume unit; Determine the reduction factor of elastic parameters of the smallest representative volume unit in the process of fabricating woven ceramic matrix composites; The reduction coefficient for determining the elastic parameters of the minimum representative volume unit in the process of preparing the woven ceramic matrix composite material includes: Construct periodic boundary conditions of finite element models; periodic boundary conditions include rigid body displacement constraints, line node displacement constraints, surface node displacement constraints and vertex node displacement constraints; Apply temperature load, set the reference temperature as preparation temperature, and the actual temperature load as room temperature, simulate the process of cooling the woven ceramic matrix composite material from preparation temperature to room temperature, and obtain the thermal residual stress caused by microstructure inhomogeneity and material parameter anisotropy during the cooling process; based on the thermal residual stress of the minimum representative volume unit and the room temperature constitutive curve of the yarn, obtain the elastic parameters of the modified minimum representative volume unit and its reduction coefficient relative to the initial elastic parameters; apply the same temperature and boundary conditions for iterative calculation until the elastic parameters of the minimum representative volume unit are stable, and obtain the reduction coefficient of the elastic parameters of the minimum representative volume unit; Determine the average thermal deformation of the braided ceramic matrix composite during free expansion at high temperature and obtain the high-temperature tensile constitutive curve of the yarn; Substitute the yarn high temperature tensile constitutive curve into the finite element model, and determine the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit; Based on the initial high temperature tensile constitutive curve of the woven ceramic matrix composite, the strain corresponding to the node with zero stress is interpolated as the initial thermal strain; Extract the nodes with stress greater than zero in the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material; According to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain, the high temperature tensile constitutive curve of the braided ceramic matrix composite material is determined.

2. The calculation method of the high temperature tensile constitutive model of the woven ceramic matrix composite material according to claim 1 is characterized in that: The constrained rigid body displacement constraint is: u x＝0,y＝0,z＝0 =v x＝0,y＝0,z＝0 =w x＝0,y＝0,z＝0 =0; Among them, u, v, and w are the displacements of the finite element model in the x, y, and z directions respectively; the x direction is the warp direction, the y direction is the weft direction; the z direction is the thickness direction of the finite element model; u x＝0,y＝0,z＝0 v is the displacement of the node in the x direction with coordinates (0,0,0) in the spatial coordinate system; x＝0,y＝0,z＝0 is the displacement of the node in the y direction with coordinates (0,0,0) in the spatial coordinate system; w x＝0,y＝0,z＝0 is the displacement in the z direction of the node with coordinates (0,0,0) in the spatial coordinate system; Among the online node displacement constraints, the constraint parallel to the x direction is: Among the node displacement constraints on the line, the constraint parallel to the y direction is: Among the node displacement constraints on the line, the constraint parallel to the z direction is: Among them, L c , W c , H c are the lengths of the finite element model in the x, y, and z directions respectively; u y＝0,z＝0 v is the x-direction displacement of the node on the x-axis in the spatial coordinate system; y＝0,z＝0 is the y-direction displacement of the node on the x-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xz plane, z = H c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the x-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, on the xy plane, y = W c And the z-direction displacement of the straight line nodes parallel to the x-axis; In the spatial coordinate system, y = W c , z=H c The x-direction displacement of the straight line node parallel to the x-axis; v z＝0,x＝0 is the y-direction displacement of the node on the y-axis in the spatial coordinate system; w y＝0,z＝0 is the z-direction displacement of the node on the x-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c The y-direction displacement of the straight line node parallel to the y-axis; w z＝0,x＝0 is the z-direction displacement of the node on the y-axis in the spatial coordinate system; In the spatial coordinate system, on the xy plane, x = L c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the y-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, on the yz plane, z = H c And the z-direction displacement of the straight line nodes parallel to the y-axis; In the spatial coordinate system, x = L c , z=H c The y-direction displacement of the straight line node parallel to the y-axis; w x＝0,y＝0 is the z-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, y = W c The z-direction displacement of the straight line node parallel to the z-axis; u x＝0,y＝0 is the x-direction displacement of the node on the z-axis in the spatial coordinate system; In the spatial coordinate system, on the yz plane, z = W c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the z-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, on the xz plane, x = L c And the x-direction displacement of the straight line nodes parallel to the z-axis; In the spatial coordinate system, x = L c , y=W c And the z-direction displacement of the straight line nodes parallel to the z-axis; Among the surface node displacement constraints, the constraint between the front and back faces perpendicular to the x direction is: Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the y direction is: Among the node displacement constraints on the surface, the constraint between the front and back surfaces perpendicular to the z direction is: Among them, v x＝0 is the y-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The y-direction displacement of the node on the plane; w x＝0 is the z-direction displacement of the node on the yz plane in the spatial coordinate system; In the spatial coordinate system, at x = L c The z-direction displacement of the node on the plane; w y＝0 is the z-direction displacement of the node on the xz plane in the spatial coordinate system; In the spatial coordinate system, y = W c The z-direction displacement of the node on the plane; u z＝0 is the x-direction displacement of the node on the xy plane in the spatial coordinate system; In the spatial coordinate system, at z = H c The x-direction displacement of the nodes on the plane; The vertex node displacement constraint is: in, In the spatial coordinate system, the coordinates are (0,W c ,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (0,W c ,H c )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,0,H c )’s node displacement in the x direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in z direction; In the spatial coordinate system, the coordinates are (L c ,W c ,0)’s node displacement in the y direction; In the spatial coordinate system, the coordinates are (L c ,W c ,H c )’s node displacement in the x direction.

3. The calculation method of the high temperature tensile constitutive model of the woven ceramic matrix composite material according to claim 1 is characterized in that: The method of determining the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature to obtain the high temperature tensile constitutive curve of the yarn comprises: The average value du of the x-direction displacement difference of the finite element model is calculated according to the following formula: x : Among them, n x is the number of nodes on a surface of the finite element model perpendicular to the x direction; x(i) is the coordinate value of node i in the x direction; L c is the length of the finite element model in the x direction; The x-coordinate value is L c The x-direction displacement of node i; u i|x(i)＝0 is the x-direction displacement of node i whose coordinate value in the x-direction is 0; The average value dv of the y-direction displacement difference of the finite element model is calculated according to the following formula: y : Among them, n y is the number of nodes on a surface of the finite element model perpendicular to the y direction; y(i) is the coordinate value of node i in the y direction; W c is the length of the finite element model in the y direction; The coordinate value in the y direction is W c The y-direction displacement of node i; v i|y(i)＝0 is the y-direction displacement of node i whose coordinate value in the y-direction is 0; The average value dw of the z-direction displacement difference of the finite element model is calculated according to the following formula: z : Among them, n z is the number of nodes on a surface of the finite element model perpendicular to the z direction; z(i) is the coordinate value of node i in the z direction; H c is the length of the finite element model in the z direction; The coordinate value in the z direction is H c The z-direction displacement of node i; w i|z(i)＝0 is the z-direction displacement of node i whose coordinate value in the z-direction is 0.

4. The method for calculating the high temperature tensile constitutive model of a woven ceramic matrix composite material according to claim 1, characterized in that: Substituting the yarn high temperature tensile constitutive curve into the finite element model and determining the initial high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit includes: Create a displacement boundary condition: in, In the spatial coordinate system, at x = L c The x-direction displacement of the node on the plane; u x＝0 is the x-direction displacement of the node on the yz plane in the spatial coordinate system; ε i represents the strain load of node i increasing from zero; du x is the average value of the x-direction displacement difference of the finite element model; The average strain of the finite element model is calculated according to the following formula The average stress of the finite element model is calculated according to the following formula Among them, n e is the total number of the smallest representative volume unit; is the stress of the jth minimum representative volume unit; is the volume of the jth minimum representative volume unit; The product of the yarn's high-temperature initial elastic parameter and the reduction coefficient of the minimum representative volume unit is taken as the initial elastic parameter of the minimum representative volume unit in the finite element model; the progressive damage analysis method is used to determine the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material based on the yarn's high-temperature tensile constitutive curve.

5. The method for calculating the high temperature tensile constitutive model of a woven ceramic matrix composite material according to claim 4, characterized in that: The step of determining the high temperature tensile constitutive curve of the braided ceramic matrix composite material according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain comprises: The initial thermal strain is corrected according to the following formula: in, is the strain corresponding to the node where the stress is greater than zero in the initial high temperature tensile constitutive curve; is the corrected initial thermal strain; The high temperature tensile constitutive curve of the woven ceramic matrix composite material is determined based on the corrected initial thermal strain.

6. A high temperature tensile constitutive model calculation system for braided ceramic matrix composite materials, characterized in that: include: Finite element model building module, used to build a finite element model of the mesostructure of woven ceramic matrix composite materials based on XCT slices of the mesostructure of woven ceramic matrix composite materials; Model cutting module, used to cut the finite element model to obtain the minimum representative volume unit; A reduction coefficient determination module, used to determine the reduction coefficient of the elastic parameters of the minimum representative volume unit in the preparation process of the woven ceramic matrix composite material; The reduction coefficient for determining the elastic parameters of the minimum representative volume unit in the process of preparing the woven ceramic matrix composite material includes: Construct periodic boundary conditions of finite element models; periodic boundary conditions include rigid body displacement constraints, line node displacement constraints, surface node displacement constraints and vertex node displacement constraints; Apply temperature load, set the reference temperature as preparation temperature, and the actual temperature load as room temperature, simulate the process of cooling the woven ceramic matrix composite material from preparation temperature to room temperature, and obtain the thermal residual stress caused by microstructure inhomogeneity and material parameter anisotropy during the cooling process; based on the thermal residual stress of the minimum representative volume unit and the room temperature constitutive curve of the yarn, obtain the elastic parameters of the modified minimum representative volume unit and its reduction coefficient relative to the initial elastic parameters; apply the same temperature and boundary conditions for iterative calculation until the elastic parameters of the minimum representative volume unit are stable, and obtain the reduction coefficient of the elastic parameters of the minimum representative volume unit; The average thermal deformation determination module is used to determine the average thermal deformation of the braided ceramic matrix composite material during free expansion at high temperature, and obtain the high-temperature tensile constitutive curve of the yarn; An initial high-temperature tensile constitutive curve determination module is used to substitute the yarn high-temperature tensile constitutive curve into the finite element model and determine the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material according to the reduction coefficient of the elastic parameter of the minimum representative volume unit; An interpolation module is used to interpolate the strain corresponding to the node with zero stress as the initial thermal strain based on the initial high-temperature tensile constitutive curve of the woven ceramic matrix composite material; A node extraction module is used to extract nodes with stress greater than zero in the initial high-temperature tensile constitutive curve of the braided ceramic matrix composite material; The high temperature tensile constitutive curve determination module is used to determine the high temperature tensile constitutive curve of the woven ceramic matrix composite material according to the strain corresponding to the point where the stress is greater than zero and the initial thermal strain.

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