CN113515835A - Stress-strain response calculation method of metal matrix composite under spectral load - Google Patents

Stress-strain response calculation method of metal matrix composite under spectral load Download PDF

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CN113515835A
CN113515835A CN202110284300.7A CN202110284300A CN113515835A CN 113515835 A CN113515835 A CN 113515835A CN 202110284300 A CN202110284300 A CN 202110284300A CN 113515835 A CN113515835 A CN 113515835A
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孙志刚
姚旭博
牛序铭
肖瀚民
刘炎
宋迎东
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a stress-strain response calculation method of a metal matrix composite under spectral load, which is characterized by solving the stress born by a composite matrix and fibers at a crack plane of a unit cell model based on the unit cell model with the crack length of the matrix; dividing the substrate and the fiber of the unit cell model with the cracks into n units; establishing a friction slip model containing the length of the matrix crack; determining the yield condition of the SiC/Ti composite material matrix, judging whether the matrix enters plastic yield, and solving the stress born by the composite material matrix and the fibers at the crack plane after the single cell model with the cracks enters the plastic yield; solving the interface shear stress and the fiber and matrix stress strain when the matrix non-boundary unit yields; carrying out strain coordination judgment on the matrix and the fiber; solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material; and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model containing the crack length of the matrix and the plastic yield of the matrix in the step.

Description

Stress-strain response calculation method of metal matrix composite under spectral load
Technical Field
The invention belongs to the technical field of materials, and particularly relates to a stress-strain response calculation method of a metal matrix composite under spectral load.
Background
Continuous silicon carbide fiber reinforced Titanium Matrix Composites (hereinafter referred to as SiC/Ti) have high specific strength and high specific stiffness, and are mainly used for aircraft engine rotor components. When the SiC/Ti structure is subjected to centrifugal stress, tensile load is usually borne, and in a practical service environment, the tensile load is irregular and complex, so that the fatigue performance of the SiC/Ti composite material under spectral load needs to be researched. By researching the interfacial micromechanics property of the metal matrix composite and analyzing the influencing factors, the deformation and fracture mechanism of the metal matrix composite can be further understood, which has important significance for researching the fatigue property of the metal matrix composite. In order to more reliably apply the metal matrix composite to a practical structure, it is necessary to study the stress-strain behavior thereof. The metal matrix composite material as a composite material can generate complex microscopic damage failure under the action of spectral load, and the stress-strain behavior of the material shows obvious nonlinearity. Therefore, it is necessary to develop research on a calculation method of stress-strain behavior of the metal matrix composite under spectral load, and a good foundation is laid for researching the fatigue life of the composite in a service environment.
In the prior art, patent CN 111400922A, "method for calculating stress-strain behavior under any loading and unloading of unidirectional ceramic matrix composite material" proposes a friction slip model and a method for calculating stress-strain behavior under any loading and unloading of unidirectional ceramic matrix composite material based on the model, the model simulates a method for calculating stress-strain behavior of composite material when matrix cracks of ceramic matrix composite material are through cracks, however, the matrix of metal matrix composite material is elastic and plastic material, and matrix cracks are not through cracks and can continuously expand along with loading in loading process, so the method can not be used for analyzing stress-strain behavior of metal matrix composite material under any loading and unloading. The literature "hysteris loop model of unidentional carbon fiber-reinforced ceramic matrix composites under an arbitrary cyclic load" proposes a mesomechanics model of a unidirectional fiber reinforced ceramic matrix composite based on a friction theory, and the model realizes the simulation of the complex load history stress-strain response of the unidirectional fiber reinforced ceramic matrix composite, however, the cracking of the metal matrix of the SiC/Ti composite is a slow expansion process, not the through crack of the brittle matrix of the ceramic matrix composite, and moreover, the metal matrix is an elastic-plastic material and can generate plastic yield in the loading process. At present, a series of SiC/Ti composite material mesoscopic mechanical models are developed at home and abroad, but most of the models adopt a shear lag theory to solve the stress-strain response of the composite material, and the traditional shear lag model can only analyze the stress-strain response under simple load and cannot analyze the stress-strain response under any loading and unloading.
In view of the foregoing, there is a need for a method for efficiently calculating the stress-strain response of a metal matrix composite under spectral loading.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a stress-strain response calculation method of a metal matrix composite under spectral load by considering non-through cracks of the SiC/Ti composite and plastic yield of a matrix, establishes a mesoscopic mechanical model of the unidirectional fiber reinforced metal matrix composite, and realizes the simulation of the stress-strain response of the SiC/Ti composite under the spectral load.
In order to achieve the purpose, the invention adopts the following technical scheme:
a stress-strain response calculation method of a metal matrix composite under spectral load comprises the following steps:
the method comprises the following steps: solving the stress born by the composite material matrix and the fiber at the crack plane of the unit cell model based on the unit cell model with the matrix crack length;
step two: dividing the substrate and the fiber of the unit cell model with the cracks into n units;
step three: establishing a friction slip model containing the length of the matrix crack based on the first step and the second step;
step four: determining the yield condition of the SiC/Ti composite material matrix, judging whether the matrix enters plastic yield, and solving the stress born by the composite material matrix and the fibers at the crack plane after the single cell model with the cracks enters the plastic yield;
step five: based on the third step, the fourth step is to solve the interface shear stress and the fiber and matrix stress strain when the matrix non-boundary unit yields;
step six: carrying out strain coordination judgment on the matrix and the fiber;
step seven: solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material;
step eight: and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model containing the crack length of the matrix and the plastic yield of the matrix in the step.
Further, the specific steps of the first step are as follows:
based on the metal-based composite material unit cell model with the crack length, solving the stress born by the matrix and the fiber at the crack plane of the metal-based composite material unit cell model;
assuming that the stress borne by the matrix is in linear relation with the cross-sectional area of the matrix, when the two ends of the composite material are subjected to tensile load with the size of sigma, the stress sigma borne by the intact matrix at the crack planem1In order to realize the purpose,
Figure BDA0002979792480000021
wherein: emModulus of elasticity of the matrix, EcIs the elastic modulus of the composite material, sigma denotes the applied stress, according toMixing ratio Ec＝VfEf+VmEm，EfIs the modulus of elasticity, V, of the fiberf,VmVolume fraction, V, of the fibres and matrix, respectivelym＝1-Vf；r0To average crack length, rfIs the radius of the fiber, rmThe radius of the matrix is, and Q is the ratio of the intact matrix at the crack plane of the matrix to the whole area of the matrix;
balanced by the axial stress at the crack plane,
σπrm 2＝σf1πrf 2+σm1π(rm 2-r0 2)
wherein: pi is the circumferential ratio, sigmaf1The stress borne by the fibers in the plane of the matrix cracks,
the stress of the fibres at the crack plane is obtained as,
Figure BDA0002979792480000022
wherein: p is an intermediate quantity, the purpose of which is to simplify the formula without any substantial meaning;
Figure BDA0002979792480000023
Figure BDA0002979792480000024
further, the second step comprises the following specific steps:
dividing a matrix and fibers in a unit cell model with the matrix crack length into n units, sequentially numbering the n units as 1,2,3, …, i, … n, wherein i represents the ith unit, and connecting the units by springs; wherein the unit cell length L/2 is half of the distance L between two adjacent cracks, and each unit cell length
Figure BDA0002979792480000025
Compliance between substrates cfComprises the following steps:
Figure BDA0002979792480000026
compliance between fibres cmComprises the following steps:
Figure BDA0002979792480000031
further, the third step comprises the following specific steps:
the slippage treatment of the fiber and the matrix in the loading process is a quasi-static balance process, and the process is divided into a balance state and an increment state; when an additional stress increment delta sigma is applied to the composite material, if the matrix yields at the crack plane, the matrix and the fibers bear the stress increment delta sigmam1、Δσf1Respectively, are as follows,
Δσm1＝σm(max)-σm
Figure BDA0002979792480000032
wherein: sigmam(max) is the maximum axial stress that the matrix can bear, σmIs the stress born by the matrix due to the external load;
the incremental force borne by the fibres at this point
Figure BDA0002979792480000033
Incremental force borne on the substrate
Figure BDA0002979792480000034
In equilibrium, the fiber and matrix of the ith cell satisfy the equilibrium equation of force:
Figure BDA0002979792480000035
wherein: i denotes the cell number, j denotes the number of load steps, Ff(i, j) represents the axial tension to which the fibre of the ith unit is subjected, Fm(i, j) represents the axial tension to which the matrix of the ith cell is subjected, fi,jDenotes the interfacial shear force of the i-th cell, Ff(i +1, j) is an axial tension to which the fiber representing the (i + 1) th unit is subjected, Fm(i +1, j) represents the axial tension to which the matrix of the (i + 1) th unit is subjected;
when an incremental force deltaf is applied in an incremental state, the fiber and matrix also produce a corresponding force increment, when the fiber and matrix of the ith cell satisfy the force balance equation:
ΔFf(i,j)＝Δfi,j+ΔFf(i+1,j)
ΔFm(i,j)＝-Δfi,j+ΔFm(i+1,j)
wherein: Δ Ff(i，j)，ΔFm(i, j) represents the force increment, Δ F, experienced by the fiber and the matrix of the ith cell, respectivelyf(i+1,j)，ΔFm(i +1, j) represents the force increment experienced by the fiber and matrix of the (i + 1) th cell, respectively, Δ fi,jThe increase in interfacial shear of the ith cell, wherein: Δ fi,jSubscript i of (a) denotes a cell number,. DELTA.fi,jThe subscript j of (a) denotes the number of load steps;
according to the displacement superposition principle, the displacement increment of the unit n is as follows:
Figure BDA0002979792480000036
Figure BDA0002979792480000037
wherein:
Figure BDA0002979792480000041
indicating the incremental force that the fiber is subjected to,
Figure BDA0002979792480000042
representing the incremental force borne by the matrix, Δ σ representing the incremental applied stress exerted on the composite, k representing the kth unit, Δ fk,jDenotes the increase in interfacial shear force, Δ u, of the k-th cellm(i,j)，Δuf(i, j) represents the displacement increment of the matrix and the fiber of the ith cell, respectively, Delauuf(i+1,j)，Δum(i +1, j) represents displacement increments of the fiber and matrix of the (i + 1) th cell, respectively;
since in the incremental state, the displacement produced by the unit fibers and the matrix, which are not slipped, is equal:
Δuf(i,j)＝Δum(i, j), i ∈ { units where no slip occurred }
Solving to obtain:
Figure BDA0002979792480000043
for the solved i-th unit interfacial shear force increment delta fi,jBased on the maximum shear stress criterion, once the shear stress of the unit is greater than the shear strength of the interface, the interface unit is considered to be debonded and slide, and the debonded fiber transmits the stress to the matrix through the interface friction force; by introducing the maximum frictional shear force f of the interfacemax＝2πrfleτi,maxAnd interfacial bonding strength τultWherein, τi,maxAssuming the maximum frictional shear stress tau of the interfacei,max＝τultEstablishing the following slip criterion:
if Δ f is satisfiedi,j+fi,j＞fmaxForward slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝fmax-fi,j；
If Δ f is satisfiedi,j+fi,j＜-fmaxReverse slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝-fmax-fi,j；
The equation for the ith cell is deleted at this point because this cell has already occurredSlipping, reconstructing an equation of n-1 units, and solving delta fi,jRepeatedly judging whether the unit slips or not until no new unit slips, and then updating the interface shearing force fi,j＝Δfi,j+fi,j(not an equality relation, but an assignment) and counting the number of units generating slippage and the slippage direction; strain epsilon of matrix and fibre unitm(i,j)、εf(i, j) is:
Figure BDA0002979792480000051
wherein: f. ofk,jDenotes the interfacial shear stress of the k-th cell, fk,jSubscript k of (a) denotes a cell number, fk,jThe subscript j of (a) denotes the number of load steps;
the stress assumed by the base unit is expressed as:
Figure BDA0002979792480000052
wherein: sigmam(i, j) is the matrix stress of the i-th cell, σm(n, j) is the matrix stress of the nth cell.
Further, the fourth step specifically comprises:
the principal stress at any point of the matrix is as follows:
Figure BDA0002979792480000053
Figure BDA0002979792480000054
σ3＝0
wherein: sigma1、σ2And σ3First, second and third principal stresses, σ, respectively, at any point in the matrixmDue to the stress borne by the externally loaded substrate,
Figure BDA0002979792480000055
is the axial thermal residual stress of the matrix,
Figure BDA0002979792480000056
is the radial thermal residual stress of the matrix, which is respectively:
Figure BDA0002979792480000057
Figure BDA0002979792480000058
Figure BDA0002979792480000059
Figure BDA00029797924800000510
wherein: alpha is alphaf,αm,αcRespectively the coefficients of thermal expansion, upsilon, of the fibres, the matrix and the composite materialf,υmThe Poisson ratio of the fiber and the matrix is respectively, delta T is temperature difference, gamma is an intermediate quantity, and the purpose is to simplify a formula and have no practical significance;
according to the Von Mises yield criterion:
(σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2＝2σms
wherein: sigmamsSolving the maximum axial stress sigma which can be borne by the matrix for the yield strength of the matrixm(max) is:
Figure BDA0002979792480000061
if the substrate is an ideal elastoplastic material, when σm1≥σm(max) the matrix goes into plastic yield and the stress it is subjected to will not increase any more, the strain being that of the fibres, at which point the matrix crack plane is subjected to a stress σm1＝σm(max), stress σ the fiber assumes at the crack plane of the matrixf1Comprises the following steps:
Figure BDA0002979792480000062
further, the concrete steps of the fifth step are as follows:
if σm(i,j)≥σm(max) the matrix unit yields, the matrix plastically flows, the shear stress transmitted to the matrix by the fiber through the interface is released, and the interface shear force df to be releasedi,jComprises the following steps:
Figure BDA0002979792480000063
stress sigma borne by the base unit after the interface shear stress is releasedm(i,j)＝σm(max) the strain of the matrix elements follows the strain of the fibres, i.e.. epsilon. -%m(i,j)＝εf(i, j) and subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jSince the stress needs to be balanced, this portion of the released interfacial shear force is borne by the following interfacial unit, which has an interfacial shear force fi+1,j＝fi+1,j+dfi,jIf the interface shear stress exceeds the load limit which can be transmitted by the interface, the residual force is transmitted to a subsequent unit until the interface shear stress does not exceed the limit load; and so on until the stress of all the base body units is less than or equal to sigmam(max), at which point the strain of the fiber and matrix unit is:
Figure BDA0002979792480000064
wherein: epsilonp(i, j) is the plastic strain of the matrix;
the stresses to be borne by the fibers and the matrix elements are,
Figure BDA0002979792480000065
wherein σm(i,j)，σf(i, j) stresses to the matrix and the fibers, respectively.
Further, the sixth step comprises the following specific steps:
shear force when unit interfacei,j|<fmaxWhen the fiber and the matrix unit do not slide, the strain of the fiber and the matrix is equal, but during the unloading process, the unrecoverable strain generated by the matrix due to plastic deformation can cause the fiber strain to be unloaded to a certain extent, the matrix can only be pressed due to the plastic deformation, the strain is uncoordinated, at the moment, the fiber needs to release a part of stress to the matrix through the interface for strain coordination, the fiber/the matrix reversely slides, the released interface shear force is,
Figure BDA0002979792480000071
subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jBut the interface shear stress can not exceed the load limit which can be transmitted by the interface, if the interface shear stress exceeds the load limit, the interface shear stress is equal to the maximum load which can be carried by the interface shear stress, and the like is carried out until the fiber and the matrix are in strain coordination or the interface completely slides; fiber and matrix unit strains and stresses are then updated:
Figure BDA0002979792480000072
further, the specific steps of the seventh step are as follows:
solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material:
mean axial strain epsilon of the fibresf,jComprises the following steps:
Figure BDA0002979792480000073
mean axial stress σ of the fiberf,jComprises the following steps:
σf,j＝Efεf,j+Ef(αc-αf)ΔT
axial average strain epsilon of matrixm,jComprises the following steps:
Figure BDA0002979792480000074
mean axial stress σ of the matrixm,jComprises the following steps:
Figure BDA0002979792480000075
axial strain of the composite material is equal to axial strain epsilon of the fiberc,jComprises the following steps:
Figure BDA0002979792480000076
wherein: epsilonf(k,j),εm(k, j) are the fiber and matrix strains of the kth cell, respectively, k represents the cell number, j represents the number of load steps, m is the total number of cells, σm(k, j) is the matrix stress of the kth cell.
Further, the specific steps of the step eight are as follows:
and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model with the matrix crack length and the matrix plastic yield.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention provides a method capable of effectively calculating the stress-strain response of the SiC/Ti composite material under the specific damage under the spectral load, and can provide a theoretical basis for the subsequent research on the performance of the metal matrix composite material under the spectral load.
(2) The invention is mainly based on a friction slip model, considers the non-through crack of a metal matrix composite material and the plastic yield of a matrix, and provides a mesomechanics model of a unidirectional fiber reinforced metal matrix composite material, which overcomes the defect that the traditional shear hysteresis model cannot simulate the load spectrum loading and also overcomes the defect that the shear hysteresis model is used for the metal matrix composite material and does not consider the plastic deformation of the matrix.
(3) The invention provides a theoretical basis for the fatigue life research of the metal matrix composite material in the actual working condition.
Drawings
FIG. 1 is a flow chart of a method for mesomechanics calculation of stress-strain response of a composite material under spectral loading;
FIG. 2 is a metal matrix composite feature cell;
FIG. 3 is a load spectrum;
FIG. 4 is a spectral loading stress-strain curve for a maximum stress load at 1500MPa for a particular damage.
Detailed Description
The present invention will be further described with reference to the following examples.
The parameters used in this example are shown in the following table.
TABLE 3.1 SiC/Ti composite base Material parameters
Figure BDA0002979792480000081
A stress-strain response calculation method of a metal matrix composite under spectral load comprises the following steps:
the method comprises the following steps: solving the stress born by the composite material matrix and the fiber at the crack plane of the unit cell model based on the unit cell model with the matrix crack length;
specifically, the specific steps of the first step are as follows:
based on the metal-based composite material unit cell model with the crack length, solving the stress born by the matrix and the fiber at the crack plane of the metal-based composite material unit cell model;
the invention takes the characteristic volume element containing single fiber and surrounding matrix in the unidirectional silicon carbide fiber reinforced titanium-based composite material as a research object and introduces the length of matrix crack, as shown in figure 2(a), wherein rfIs the radius of the fiber, rmIs the radius of the matrix, r0L represents the average crack length, L represents the average crack spacing of the matrixdRepresents the fiber/matrix interface debond length;
assuming that the stress borne by the matrix is in linear relation with the cross-sectional area of the matrix, when the two ends of the composite material are subjected to tensile load with the size of sigma, the stress sigma borne by the intact matrix at the crack planem1In order to realize the purpose,
Figure BDA0002979792480000091
wherein: emModulus of elasticity of the matrix, EcThe elastic modulus of the composite material, σ, is the applied stress according to the mixing ratio Ec＝VfEf+VmEm，EfIs the modulus of elasticity, V, of the fiberf,VmVolume fraction, V, of the fibres and matrix, respectivelym＝1-Vf；r0To average crack length, rfIs the radius of the fiber, rmThe radius of the matrix is, and Q is the ratio of the intact matrix at the crack plane of the matrix to the whole area of the matrix;
balanced by the axial stress at the crack plane,
σπrm 2＝σf1πrf 2+σm1π(rm 2-r0 2)
wherein: pi is the circumferential ratio, sigmaf1The stress borne by the fibers in the plane of the matrix cracks,
the stress of the fibres at the crack plane is obtained as,
Figure BDA0002979792480000092
wherein: p is an intermediate quantity, the purpose of which is to simplify the formula without any substantial meaning;
Figure BDA0002979792480000093
Figure BDA0002979792480000094
step two: dividing the substrate and the fiber of the unit cell model with the cracks into n units;
specifically, the second step comprises the following specific steps:
as shown in fig. 2(b), the matrix and the fiber in the unit cell model with the matrix crack length are divided into n units, the n units are numbered as 1,2,3, …, i, … n, i sequentially and represent the ith unit, and the units are connected by springs; wherein the unit cell length L/2 is half of the distance L between two adjacent cracks, and each unit cell length
Figure BDA0002979792480000095
Compliance between substrates cfComprises the following steps:
Figure BDA0002979792480000101
compliance between fibres cmComprises the following steps:
Figure BDA0002979792480000102
step three: establishing a friction slip model containing the length of the matrix crack based on the first step and the second step;
specifically, the third step comprises the following specific steps:
slippage of the fiber with the matrix during loadingThe processing is a quasi-static balancing process, and is divided into a balancing state and an incremental state, as shown in fig. 2 (d); when an additional stress increment delta sigma is applied to the composite material, if the matrix yields at the crack plane, the matrix and the fibers bear the stress increment delta sigmam1、Δσf1Respectively, are as follows,
Δσm1＝σm(max)-σm
Figure BDA0002979792480000103
wherein: sigmam(max) is the maximum axial stress that the matrix can bear, σmIs the stress born by the matrix due to the external load;
the incremental force borne by the fibres at this point
Figure BDA0002979792480000104
Incremental force borne on the substrate
Figure BDA0002979792480000105
In equilibrium, the fiber and matrix of the ith cell satisfy the equilibrium equation of force:
Figure BDA0002979792480000106
wherein: i denotes the cell number, j denotes the number of load steps, Ff(i, j) represents the axial tension to which the fibre of the ith unit is subjected, Fm(i, j) represents the axial tension to which the matrix of the ith cell is subjected, fi,jDenotes the interfacial shear force of the i-th cell, Ff(i +1, j) is an axial tension to which the fiber representing the (i + 1) th unit is subjected, Fm(i +1, j) represents the axial tension to which the matrix of the (i + 1) th unit is subjected;
when an incremental force deltaf is applied in an incremental state, the fiber and matrix also produce a corresponding force increment, when the fiber and matrix of the ith cell satisfy the force balance equation:
ΔFf(i,j)＝Δfi,j+ΔFf(i+1,j)
ΔFm(i,j)＝-Δfi,j+ΔFm(i+1,j)
wherein: Δ Ff(i，j)，ΔFm(i, j) represents the force increment, Δ F, experienced by the fiber and the matrix of the ith cell, respectivelyf(i+1,j)，ΔFm(i +1, j) represents the force increment experienced by the fiber and matrix of the (i + 1) th cell, respectively, Δ fi,jThe increase in interfacial shear of the ith cell, wherein: Δ fi,jSubscript i of (a) denotes a cell number,. DELTA.fi,jThe subscript j of (a) denotes the number of load steps;
according to the displacement superposition principle, the displacement increment of the unit n is as follows:
Figure BDA0002979792480000111
Figure BDA0002979792480000112
wherein:
Figure BDA0002979792480000113
indicating the incremental force that the fiber is subjected to,
Figure BDA0002979792480000114
representing the incremental force borne by the matrix, Δ σ representing the incremental applied stress exerted on the composite, k representing the kth unit, Δ fk,jDenotes the increase in interfacial shear force, Δ u, of the k-th cellm(i，j)，Δuf(i, j) represents the displacement increment of the matrix and the fiber of the ith cell, respectively, Delauuf(i+1,j)，Δum(i +1, j) represents displacement increments of the fiber and matrix of the (i + 1) th cell, respectively;
since in the incremental state, the displacement produced by the unit fibers and the matrix, which are not slipped, is equal:
Δuf(i,j)＝Δum(i, j), i ∈ { units where no slip occurred }
Solving to obtain:
Figure BDA0002979792480000115
for the solved i-th unit interfacial shear force increment delta fi,jBased on the maximum shear stress criterion, once the shear stress of the unit is greater than the shear strength of the interface, the interface unit is considered to be debonded and slide, and the debonded fiber transmits the stress to the matrix through the interface friction force; by introducing the maximum frictional shear force f of the interfacemax＝2πrfleτi,maxAnd interfacial bonding strength τultWherein, τi,maxAssuming the maximum frictional shear stress tau of the interfacei,max＝τultEstablishing the following slip criterion:
if Δ f is satisfiedi,j+fi,j＞fmaxForward slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝fmax-fi,j；
If Δ f is satisfiedi,j+fi,j＜-fmaxReverse slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝-fmax-fi,j；
At this point the equation for the ith cell is deleted, because this cell has slipped, the equations for n-1 cells are reconstructed, and Δ f is solvedi,jRepeatedly judging whether the unit slips or not until no new unit slips, and then updating the interface shearing force fi,j＝Δfi,j+fi,j(not an equality relation, but an assignment) and counting the number of units generating slippage and the slippage direction; strain epsilon of matrix and fibre unitm(i,j)、εf(i, j) is:
Figure BDA0002979792480000121
wherein: f. ofk,jDenotes the interfacial shear stress of the k-th cell, fk,jSubscript k of (a) denotes a cell number, fk,jThe subscript j of (a) denotes the number of load steps;
the stress assumed by the base unit is expressed as:
Figure BDA0002979792480000122
wherein: sigmam(i, j) is the matrix stress of the i-th cell, σm(n, j) is the matrix stress of the nth cell.
Step four: determining the yield condition of the SiC/Ti composite material matrix, judging whether the matrix enters plastic yield, and solving the stress born by the composite material matrix and the fibers at the crack plane after the single cell model with the cracks enters the plastic yield;
specifically, the specific steps of the fourth step are as follows:
the principal stress at any point of the matrix is as follows:
Figure BDA0002979792480000123
Figure BDA0002979792480000124
σ3＝0
wherein: sigma1、σ2And σ3First, second and third principal stresses, σ, respectively, at any point in the matrixmDue to the stress borne by the externally loaded substrate,
Figure BDA0002979792480000125
is the axial thermal residual stress of the matrix,
Figure BDA0002979792480000126
is the radial thermal residual stress of the matrix, which is respectively:
Figure BDA0002979792480000131
Figure BDA0002979792480000132
Figure BDA0002979792480000133
Figure BDA0002979792480000134
wherein: alpha is alphaf,αm,αcRespectively the coefficients of thermal expansion, upsilon, of the fibres, the matrix and the composite materialf,υmThe Poisson ratio of the fiber and the matrix is respectively, delta T is temperature difference, gamma is an intermediate quantity, and the purpose is to simplify a formula and have no practical significance;
according to the Von Mises yield criterion:
(σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2＝2σms
wherein: sigmamsSolving the maximum axial stress sigma which can be borne by the matrix for the yield strength of the matrixm(max) is:
Figure BDA0002979792480000135
if the substrate is an ideal elastoplastic material, when σm1≥σm(max) the matrix goes into plastic yield and the stress it is subjected to will not increase any more, the strain being that of the fibres, at which point the matrix crack plane is subjected to a stress σm1＝σm(max), stress σ the fiber assumes at the crack plane of the matrixf1Comprises the following steps:
Figure BDA0002979792480000136
step five: based on the third step, the fourth step is to solve the interface shear stress and the fiber and matrix stress strain when the matrix non-boundary unit yields;
specifically, the concrete steps of the fifth step are as follows:
if σm(i,j)≥σm(max) the matrix unit yields, the matrix plastically flows, the shear stress transmitted to the matrix by the fiber through the interface is released, and the interface shear force df to be releasedi,jComprises the following steps:
Figure BDA0002979792480000137
stress sigma borne by the base unit after the interface shear stress is releasedm(i,j)＝σm(max) the strain of the matrix elements follows the strain of the fibres, i.e.. epsilon. -%m(i,j)＝εf(i, j) and subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jSince the stress needs to be balanced, this portion of the released interfacial shear force is borne by the following interfacial unit, which has an interfacial shear force fi+1,j＝fi+1,j+dfi,jIf the interface shear stress exceeds the load limit which can be transmitted by the interface, the residual force is transmitted to a subsequent unit until the interface shear stress does not exceed the limit load; and so on until the stress of all the base body units is less than or equal to sigmam(max), at which point the strain of the fiber and matrix unit is:
Figure BDA0002979792480000138
wherein: epsilonp(i, j) is the plastic strain of the matrix;
the stresses to be borne by the fibers and the matrix elements are,
Figure BDA0002979792480000141
wherein σm(i,j)，σf(i, j) stresses to the matrix and the fibers, respectively.
Step six: carrying out strain coordination judgment on the matrix and the fiber;
specifically, the step six specifically comprises the following steps:
shear force when unit interfacei,j|<fmaxWhen the fiber and the matrix unit do not slide, the strain of the fiber and the matrix is equal, but during the unloading process, the unrecoverable strain generated by the matrix due to plastic deformation can cause the fiber strain to be unloaded to a certain extent, the matrix can only be pressed due to the plastic deformation, the strain is uncoordinated, at the moment, the fiber needs to release a part of stress to the matrix through the interface for strain coordination, the fiber/the matrix reversely slides, the released interface shear force is,
Figure BDA0002979792480000142
subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jBut the interface shear stress can not exceed the load limit which can be transmitted by the interface, if the interface shear stress exceeds the load limit, the interface shear stress is equal to the maximum load which can be carried by the interface shear stress, and the like is carried out until the fiber and the matrix are in strain coordination or the interface completely slides; fiber and matrix unit strains and stresses are then updated:
Figure BDA0002979792480000143
step seven: solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material;
specifically, the specific steps of the seventh step are as follows:
solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material:
mean axial strain epsilon of the fibresf,jComprises the following steps:
Figure BDA0002979792480000144
mean axial stress σ of the fiberf,jComprises the following steps:
σf,j＝Efεf,j+Ef(αc-αf)ΔT
axial average strain epsilon of matrixm,jComprises the following steps:
Figure BDA0002979792480000145
mean axial stress σ of the matrixm,jComprises the following steps:
Figure BDA0002979792480000151
axial strain of the composite material is equal to axial strain epsilon of the fiberc,jComprises the following steps:
Figure BDA0002979792480000152
wherein: epsilonf(k,j),εm(k, j) are the fiber and matrix strains of the kth cell, respectively, k represents the cell number, j represents the number of load steps, m is the total number of cells, σm(k, j) is the matrix stress of the kth cell.
Step eight: and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model containing the crack length of the matrix and the plastic yield of the matrix in the step.
The concrete steps of the step eight are as follows:
specifically, the stress-strain response of the metal matrix composite under spectral load is calculated based on a friction slip model with matrix crack length and matrix plastic yield, and a flow chart of a mesomechanics calculation method is shown in fig. 1. The method of the invention simulates the stress-strain response of the SiC/Ti composite material with specific damage under spectral load. The profile of the applied load spectrum is shown in FIG. 3, and the results of the stress-strain curve are shown in FIG. 4.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (9)

1. A stress-strain response calculation method of a metal matrix composite under spectral load is characterized by comprising the following steps:
the method comprises the following steps: solving the stress born by the composite material matrix and the fiber at the crack plane of the unit cell model based on the unit cell model with the matrix crack length;
step two: dividing the substrate and the fiber of the unit cell model with the cracks into n units;
step three: establishing a friction slip model containing the length of the matrix crack based on the first step and the second step;
step four: determining the yield condition of the SiC/Ti composite material matrix, judging whether the matrix enters plastic yield, and solving the stress born by the composite material matrix and the fibers at the crack plane after the single cell model with the cracks enters the plastic yield;
step five: based on the third step, the fourth step is to solve the interface shear stress and the fiber and matrix stress strain when the matrix non-boundary unit yields;
step six: carrying out strain coordination judgment on the matrix and the fiber;
step seven: solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material;
step eight: and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model containing the crack length of the matrix and the plastic yield of the matrix in the step.
2. The method for calculating the stress-strain response of a metal matrix composite under spectral load according to claim 1,
the specific steps of the first step are as follows:
based on the metal-based composite material unit cell model with the crack length, solving the stress born by the matrix and the fiber at the crack plane of the metal-based composite material unit cell model;
assuming that the stress borne by the matrix is in linear relation with the cross-sectional area of the matrix, when the two ends of the composite material are subjected to tensile load with the size of sigma, the stress sigma borne by the intact matrix at the crack planem1In order to realize the purpose,
Figure FDA0002979792470000014
wherein: emModulus of elasticity of the matrix, EcThe elastic modulus of the composite material, σ, is the applied stress according to the mixing ratio Ec＝VfEf+VmEm，EfIs the modulus of elasticity, V, of the fiberf,VmVolume fraction, V, of the fibres and matrix, respectivelym＝1-Vf；r0To average crack length, rfIs the radius of the fiber, rmThe radius of the matrix is, and Q is the ratio of the intact matrix at the crack plane of the matrix to the whole area of the matrix;
balanced by the axial stress at the crack plane,
σπrm 2＝σf1πrf 2+σm1π(rm 2-r0 2)
wherein: pi is the circumferential ratio, sigmaf1The stress borne by the fibers in the plane of the matrix cracks,
the stress of the fibres at the crack plane is obtained as,
Figure FDA0002979792470000011
wherein: p is an intermediate quantity;
Figure FDA0002979792470000012
Figure FDA0002979792470000013
3. the method for calculating the stress-strain response of a metal matrix composite under spectral load according to claim 2,
the second step comprises the following specific steps:
dividing a matrix and fibers in a unit cell model with the matrix crack length into n units, sequentially numbering the n units as 1,2,3, …, i, … n, wherein i represents the ith unit, and connecting the units by springs; wherein the unit cell length L/2 is half of the distance L between two adjacent cracks, and each unit cell length
Figure FDA0002979792470000021
Compliance between substrates cfComprises the following steps:
Figure FDA0002979792470000022
compliance between fibres cmComprises the following steps:
Figure FDA0002979792470000023
4. the method for calculating the stress-strain response of the metal matrix composite under the spectral load according to claim 3, wherein the third step comprises the following specific steps:
the slippage treatment of the fiber and the matrix in the loading process is a quasi-static balance process, and the process is divided into a balance state and an increment state; when an increase delta sigma of applied stress is applied to the composite material, the matrix and the matrix yield if the matrix yields at the crack planeIncrement of fiber bearing stress delta sigmam1、Δσf1Respectively, are as follows,
Δσm1＝σm(max)-σm
Figure FDA0002979792470000024
wherein: sigmam(max) is the maximum axial stress that the matrix can bear, σmIs the stress born by the matrix due to the external load;
the incremental force borne by the fibres at this point
Figure FDA0002979792470000025
Incremental force borne on the substrate
Figure FDA0002979792470000026
In equilibrium, the fiber and matrix of the ith cell satisfy the equilibrium equation of force:
Figure FDA0002979792470000027
wherein: i denotes the cell number, j denotes the number of load steps, Ff(i, j) represents the axial tension to which the fibre of the ith unit is subjected, Fm(i, j) represents the axial tension to which the matrix of the ith cell is subjected, fi，jDenotes the interfacial shear force of the i-th cell, Ff(i +1, j) is an axial tension to which the fiber representing the (i + 1) th unit is subjected, Fm(i +1, j) represents the axial tension to which the matrix of the (i + 1) th unit is subjected;
when an incremental force deltaf is applied in an incremental state, the fiber and matrix also produce a corresponding force increment, when the fiber and matrix of the ith cell satisfy the force balance equation:
ΔFf(i,j)＝Δfi,j+ΔFf(i+1,j)
ΔFm(i,j)＝-Δfi,j+ΔFm(i+1,j)
wherein: Δ Ff(i,j)，ΔFm(i, j) represents the force increment, Δ F, experienced by the fiber and the matrix of the ith cell, respectivelyf(i+1,j)，ΔFm(i +1, j) represents the force increment experienced by the fiber and matrix of the (i + 1) th cell, respectively, Δ fi,jThe increase in interfacial shear of the ith cell, wherein: Δ fi,jSubscript i of (a) denotes a cell number,. DELTA.fi,jThe subscript j of (a) denotes the number of load steps;
according to the displacement superposition principle, the displacement increment of the unit n is as follows:
Figure FDA0002979792470000031
Figure FDA0002979792470000032
wherein:
Figure FDA0002979792470000033
indicating the incremental force that the fiber is subjected to,
Figure FDA0002979792470000034
representing the incremental force borne by the matrix, Δ σ representing the incremental applied stress exerted on the composite, k representing the kth unit, Δ fk,jDenotes the increase in interfacial shear force, Δ u, of the k-th cellm(i,j)，Δuf(i, j) represents the displacement increment of the matrix and the fiber of the ith cell, respectively, Delauuf(i+1,j)，Δum(i +1, j) represents displacement increments of the fiber and matrix of the (i + 1) th cell, respectively;
since in the incremental state, the displacement produced by the unit fibers and the matrix, which are not slipped, is equal:
Δuf(i,j)＝Δum(i, j), i ∈ { units where no slip occurred }
Solving to obtain:
Figure FDA0002979792470000035
for the solved i-th unit interfacial shear force increment delta fi,jBased on the maximum shear stress criterion, once the shear stress of the unit is greater than the shear strength of the interface, the interface unit is considered to be debonded and slide, and the debonded fiber transmits the stress to the matrix through the interface friction force; by introducing the maximum frictional shear force f of the interfacemax＝2πrfleτi,maxAnd interfacial bonding strength τultWherein, τi,maxAssuming the maximum frictional shear stress tau of the interfacei,max＝τultEstablishing the following slip criterion:
if Δ f is satisfiedi,j+fi,j＞fmaxForward slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝fmax-fi,j；
If Δ f is satisfiedi,j+fi,j＜-fmaxReverse slip will occur, increasing the interfacial shear of the unit by Δ fi,j＝-fmax-fi,j；
At this point the equation for the ith cell is deleted, because this cell has slipped, the equations for n-1 cells are reconstructed, and Δ f is solvedi,jRepeatedly judging whether the unit slips or not until no new unit slips, and then updating the interface shearing force fi,j＝Δfi,j+fi,jCounting the number of units with slippage and the slippage direction; strain epsilon of matrix and fibre unitm(i,j)、εf(i, j) is:
Figure FDA0002979792470000041
wherein: f. ofk,jDenotes the interfacial shear stress of the k-th cell, fk,jSubscript k of (a) denotes a cell number, fk,jThe subscript j of (a) denotes the number of load steps;
the stress assumed by the base unit is expressed as:
Figure FDA0002979792470000042
wherein: sigmam(i, j) is the matrix stress of the i-th cell, σm(n, j) is the matrix stress of the nth cell.
5. The method for calculating the stress-strain response of the metal matrix composite under the spectral load according to claim 4, wherein the step four comprises the following specific steps:
the principal stress at any point of the matrix is as follows:
Figure FDA0002979792470000043
Figure FDA0002979792470000044
σ3＝0
wherein: sigma1、σ2And σ3First, second and third principal stresses, σ, respectively, at any point in the matrixmDue to the stress borne by the externally loaded substrate,
Figure FDA0002979792470000051
is the axial thermal residual stress of the matrix,
Figure FDA0002979792470000052
is the radial thermal residual stress of the matrix, which is respectively:
Figure FDA0002979792470000053
Figure FDA0002979792470000054
Figure FDA0002979792470000055
Figure FDA0002979792470000056
wherein: alpha is alphaf,αm,αcRespectively the coefficients of thermal expansion, upsilon, of the fibres, the matrix and the composite materialf,υmThe Poisson's ratio of the fiber and the matrix is respectively, delta T is the temperature difference, and gamma is an intermediate quantity;
according to the Von Mises yield criterion:
(σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2＝2σms
wherein: sigmamsSolving the maximum axial stress sigma which can be borne by the matrix for the yield strength of the matrixm(max) is:
Figure FDA0002979792470000057
if the substrate is an ideal elastoplastic material, when σm1≥σm(max) the matrix goes into plastic yield and the stress it is subjected to will not increase any more, the strain being that of the fibres, at which point the matrix crack plane is subjected to a stress σm1＝σm(max), stress σ the fiber assumes at the crack plane of the matrixf1Comprises the following steps:
Figure FDA0002979792470000058
6. the method of calculating the stress-strain response of a metal matrix composite under spectral load according to claim 5,
the concrete steps of the fifth step are as follows:
if σm(i,j)≥σm(max) the matrix unit yields, the matrix plastically flows, the shear stress transmitted to the matrix by the fiber through the interface is released, and the interface shear force df to be releasedi,jComprises the following steps:
Figure FDA0002979792470000059
stress sigma borne by the base unit after the interface shear stress is releasedm(i,j)＝σm(max) the strain of the matrix elements follows the strain of the fibres, i.e.. epsilon. -%m(i,j)＝εf(i, j) and subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jSince the stress needs to be balanced, this portion of the released interfacial shear force is borne by the following interfacial unit, which has an interfacial shear force fi+1,j＝fi+1,j+dfi,jIf the interface shear stress exceeds the load limit which can be transmitted by the interface, the residual force is transmitted to a subsequent unit until the interface shear stress does not exceed the limit load; and so on until the stress of all the base body units is less than or equal to sigmam(max), at which point the strain of the fiber and matrix unit is:
Figure FDA00029797924700000510
wherein: epsilonp(i, j) is the plastic strain of the matrix;
the stresses to be borne by the fibers and the matrix elements are,
Figure FDA0002979792470000061
wherein σm(i,j)，σf(i, j) stresses to the matrix and the fibers, respectively.
7. The method of calculating the stress-strain response of a metal matrix composite under spectral load according to claim 6,
the sixth step comprises the following specific steps:
shear force when unit interfacei,j|<fmaxWhen the fiber and the matrix unit do not slide, the strain of the fiber and the matrix is equal, but during the unloading process, the unrecoverable strain generated by the matrix due to plastic deformation can cause the fiber strain to be unloaded to a certain extent, the matrix can only be pressed due to the plastic deformation, the strain is uncoordinated, at the moment, the fiber needs to release a part of stress to the matrix through the interface for strain coordination, the fiber/the matrix reversely slides, the released interface shear force is,
Figure FDA0002979792470000062
subsequently updating the interfacial shear force f of the celli,j＝fi,j-dfi,jBut the interface shear stress can not exceed the load limit which can be transmitted by the interface, if the interface shear stress exceeds the load limit, the interface shear stress is equal to the maximum load which can be carried by the interface shear stress, and the like is carried out until the fiber and the matrix are in strain coordination or the interface completely slides; fiber and matrix unit strains and stresses are then updated:
Figure FDA0002979792470000063
8. the method of calculating the stress-strain response of a metal matrix composite under spectral loading according to claim 7,
the concrete steps of the seventh step are as follows:
solving the average stress strain of the characteristic units, the matrix and the fibers of the composite material:
mean axial strain epsilon of the fibresf,jComprises the following steps:
Figure FDA0002979792470000064
mean axial stress σ of the fiberf,jComprises the following steps:
σf,j＝Efεf,j+Ef(αc-αf)ΔT
axial average strain epsilon of matrixm,jComprises the following steps:
Figure FDA0002979792470000065
mean axial stress σ of the matrixm,jComprises the following steps:
Figure FDA0002979792470000071
axial strain of the composite material is equal to axial strain epsilon of the fiberc,jComprises the following steps:
Figure FDA0002979792470000072
wherein: epsilonf(k,j),εm(k, j) are the fiber and matrix strains of the kth cell, respectively, k represents the cell number, j represents the number of load steps, m is the total number of cells, σm(k, j) is the matrix stress of the kth cell.
9. The method of calculating the stress-strain response of a metal matrix composite under spectral loading according to claim 8,
the concrete steps of the step eight are as follows:
and calculating the stress-strain response of the metal matrix composite material under the spectral load based on the friction slip model with the matrix crack length and the matrix plastic yield.
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Publication number Priority date Publication date Assignee Title
CN115310311A (en) * 2022-07-01 2022-11-08 南京航空航天大学 Method for calculating fatigue life of metal material under spectral load
CN116187041A (en) * 2023-02-10 2023-05-30 南京航空航天大学 Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111241686A (en) * 2020-01-15 2020-06-05 南京航空航天大学 Method for predicting stress-strain curve of ceramic matrix composite in high-temperature oxidation environment during random loading and unloading
CN111400922A (en) * 2020-03-23 2020-07-10 南京航空航天大学 Method for calculating stress-strain behavior of unidirectional ceramic matrix composite material by adding and removing random strain

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111241686A (en) * 2020-01-15 2020-06-05 南京航空航天大学 Method for predicting stress-strain curve of ceramic matrix composite in high-temperature oxidation environment during random loading and unloading
CN111400922A (en) * 2020-03-23 2020-07-10 南京航空航天大学 Method for calculating stress-strain behavior of unidirectional ceramic matrix composite material by adding and removing random strain

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115310311A (en) * 2022-07-01 2022-11-08 南京航空航天大学 Method for calculating fatigue life of metal material under spectral load
CN116187041A (en) * 2023-02-10 2023-05-30 南京航空航天大学 Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold
CN116187041B (en) * 2023-02-10 2023-10-20 南京航空航天大学 Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold

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