CN116187041B - Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold - Google Patents

Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold Download PDF

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CN116187041B
CN116187041B CN202310098678.7A CN202310098678A CN116187041B CN 116187041 B CN116187041 B CN 116187041B CN 202310098678 A CN202310098678 A CN 202310098678A CN 116187041 B CN116187041 B CN 116187041B
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matrix
stress
crack
load
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CN116187041A (en
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宋迎东
刘晋辰
刘炎
孙志刚
牛序铭
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/56—Investigating resistance to wear or abrasion
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0073—Fatigue
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a load spectrum filtering method based on a continuous fiber reinforced composite material microscopic damage threshold, which comprises the following steps: calculating stress, strain, axial average stress, axial average strain and axial strain of the fiber and the matrix; calculating the crack growth increment of the matrix, the crack tip stress intensity factor when the crack of the matrix starts, the relative slip quantity ratio of the fiber and the matrix, and the increment of the cumulative failure percentage of the fiber; judging whether the crack expansion rate of the matrix is 0, the relative slippage of the fiber/matrix is less than ten percent, the stress intensity factor of the crack tip is less than the crack expansion threshold value or not under loading and unloading, and deleting the peak-valley value of the loading if the crack expansion rate of the matrix is 0; and judging whether the whole original load spectrum is loaded, if so, ending, outputting the pruned load spectrum, and if not, returning to the step two to continue loading. The invention can reduce the calculation workload and improve the calculation efficiency.

Description

Load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold
Technical Field
The invention relates to a load spectrum filtering method based on continuous fiber reinforced composite material fatigue damage, in particular to a load spectrum filtering method based on continuous fiber reinforced composite material microscopic damage threshold.
Background
The continuous fiber reinforced composite material, such as a metal matrix composite material, has the characteristics of high specific strength, specific rigidity and the like, has potential to be applied to aeroengine rotor parts, such as a compressor blade ring and the like, and the continuous SiC reinforced Ti matrix composite material structure usually bears tensile load when bearing centrifugal stress, and in practical working conditions, the tensile load is complex and random, so that the fatigue performance of the fiber reinforced composite material under the spectral load condition is necessary to be studied. In order to understand the deformation and failure mechanism of the fiber reinforced composite material in depth, it is necessary to study the micromechanics of the fiber/interface/matrix of the fiber reinforced composite material and the influencing factors thereof.
In the prior art, patent CN111291477A 'a method for deleting low-cycle fatigue and small load in an aeroengine load spectrum' discloses a method for deleting low-cycle fatigue and small load in an aeroengine load spectrum, and the method is mainly applied to metal materials on the basis of a probability density function of equivalent load amplitude. For continuous fiber reinforced composite materials, as the microscopic failure mechanism is more complex, including matrix cracking, interface debonding, fiber breakage and the like, the load spectrum filtering method for the metal material cannot be applied to the metal matrix composite material structure, but the related load spectrum filtering method for the composite material is not found in related patents and documents.
Disclosure of Invention
Aiming at the defects of the prior art, a load spectrum filtering method based on a continuous fiber reinforced composite material microscopic damage threshold is established.
In order to achieve the above object, the present invention is realized by the following technical scheme:
a load spectrum filtering method based on a continuous fiber reinforced composite material microscopic damage threshold comprises the following steps:
step 1, calculating stress, strain, axial average stress and axial average strain of fibers and a matrix based on a fiber reinforced composite constitutive model under a spectrum load, and calculating axial strain of a composite material;
step 2, calculating the crack growth increment of the matrix based on the axial average stress and strain of the matrix obtained in the step 1;
step 3, calculating a crack tip stress intensity factor when the base crack starts based on the base stress in the step 1;
step 4, calculating the relative slippage ratio of the fiber and the matrix based on the strain gauge of the fiber and the matrix obtained in the step 1;
step 5, calculating the increment of the cumulative failure percentage of the fiber based on the stress born by the fiber of the crack plane of the matrix;
step 6, judging whether the increment percentage of the fiber cumulative failure probability is 0, the matrix crack growth rate is 0, the relative slippage of the fiber/matrix is less than ten percent, the crack tip stress intensity factor is less than the crack growth threshold value under loading and unloading, and deleting the loading peak-valley value if the increment percentage is met;
and 7, judging whether the whole original load spectrum is loaded, if so, ending, outputting the pruned load spectrum, and if not, returning to the step two to continue loading.
The invention further improves that: the calculation expression of the stress and the strain of the fiber and the matrix in the step 1 is as follows:
wherein ,εf (i, j) is the strain, ε, that the ith unit of fiber developed after the jth load step was loaded m (i, j) is the strain produced by the ith cell of the substrate after the jth load step, r f Is the fiber radius sigma f1 Stress borne by the fibre, f k,j For interfacial shear force of the kth unit at the jth load step, E f For modulus of elasticity, sigma of the fiber m1 Stress borne by the substrate, E m For modulus of elasticity of matrix, r m Radius of matrix, sigma f (i, j) is the stress, σ, assumed by the ith element of the fiber after the jth load step is loaded m (i, j) is the stress, ε, assumed by the ith element of the substrate after the jth load step is loaded p (i, j) is the plastic strain produced by the ith cell after the jth load step is loaded;
the average strain of the fiber and the matrix can be obtained after the strain of all the units is weighted and averaged;
the fiber axial average strain is:
the fiber axial average stress is:
σ f,j ＝E f ε f,j +E f (α c -α f )ΔT (3)
the axial average strain of the matrix is:
the axial average stress of the matrix is as follows:
wherein ,αc ,α m ,a f The thermal expansion coefficients of the composite material, the matrix and the fiber are respectively shown, delta T is the temperature difference, and n is the total number of units;
axial strain epsilon of composite material c,j Equal to the average strain in the fiber axial direction:
the invention further improves that: by a means ofThe crack growth increment calculation process of the matrix in the step 2 is as follows: replacing the external stress with the average stress in the matrix, wherein the crack tip stress intensity factor K of the external stress b Expressed as:
wherein ,r is the average stress of the matrix 0 To average crack length, Y b Representing the geometric correction coefficient; the crack tip stress intensity factor for fiber bridging is:
fiber bridging stress sigma p Expressed as:
wherein ,ld Represents the debonding length of the fiber/matrix interface, l rs Is the length sum of all reverse sliding areas in the whole interface debonding area, and tau is the initial interface shear stress;
composite crack tip stress intensity factor K a The method comprises the following steps:
K a ＝K b +K c (10)；
according to the Dugdale model, the effective crack length is composed of an actual crack and a virtual crack of the crack tip plastic region, and the composite material crack plastic region tip stress intensity factor is superimposed by the following three stress intensity factors:
wherein ,σms Being a matrix of composite materialYield strength, r p For the virtual crack length, the total effect after the three loads act is to make the virtual crack tip singularity disappear:
K b +K c +K p ＝0(12)
solving the virtual crack length r by the simultaneous formulas (13) and (14) p ；
In the case of spectrum loading, assuming no hysteresis occurs in loading after high load, the maximum cyclic stress is σ req,j The crack tip residual stress is:
σ res,j ＝σ req,j -σ max,j (13)
wherein ,σmax,j Peak stress in the j-th cycle;
the actual cyclic stress at the crack tip is:
wherein ,is the effective stress maximum in the j-th cycle,/->Is the effective stress minimum in the j-th cycle;
the actual cyclic stress range and stress ratio are:
according to the Forman formula, the fatigue crack growth rate is:
wherein C, M is a matrix crack propagation parameter, K c,m ΔK, the fracture toughness of the matrix th As stress intensity factor threshold value, deltaK eff Is an effective stress intensity factor;
the effective stress intensity factor is expressed as:
wherein ,ΔKb Delta K is the actual stress intensity factor increment c Increment of crack tip stress intensity factor for fiber bridging, r i For the crack length at the ith cycle,for maximum effective actual cyclic stress of the matrix, < ->For minimum effective actual stress of the matrix, delta sigma p To bridge the stress range.
Considering the impact of plastic deformation and crack closure of the substrate, one loaded crack propagation increment is:
the invention further improves that: and in the step 3, the stress intensity factor of the crack tip when the crack of the matrix is initiated is as follows:
wherein ,Δσm Average stress for matrixForce d int For the interface layer thickness, Y b Representing the geometric correction coefficients.
The invention further improves that: in the step 4, the relative slippage of the fiber/matrix is used for replacing the abrasion loss of the interface, and the relative displacement of the preloaded fiber/matrix interface is the sum of the relative displacement during loading and the relative displacement during unloading, and the expression is as follows:
Δu j/2 ＝Δu f,j -Δu m,j +Δu f,j+1 -Δu m,j+1 {j＝2n,n＝1,2,3m}(21)
wherein ,Δuf,j ＝Lε f,j For displacement of fibres at the j-th load step, deltau m,j ＝Lε m,j The displacement of the matrix under the j-th load step is shown, and L is the fiber length;
the relative slippage of the fiber and the matrix is as follows:
wherein ,Δun ＝|Δu f,n -Δu m,n |。
The invention further improves that: in said step 5, assuming that the fibers are all broken at the crack plane of the matrix, the stress sigma imposed by the fibers at the crack plane of the matrix f1 The expression is:
wherein ,
wherein ,Em Modulus of elasticity of matrix, E f Is the elastic modulus of the fiber, sigma is the external stress, V f V as fiber volume fraction m The expression is as follows:
V m ＝1-V f (25)；
the global load shear model is adopted, and the load initially born by the broken fiber is assumed to be evenly distributed to all the remained complete fibers on the same section, the stress born by the crack plane matrix is unchanged, and the stress born by the rest fiber at the crack plane after the fiber is broken is as follows:
the cumulative failure probability of the fiber is:
wherein P (T) is fiber cumulative failure probability, sigma 0 For the characteristic strength of the fibre, m f A weibull modulus for fiber strength distribution;
calculating the j-th load step fiber cumulative fracture probability P of the load spectrum section j And the j+1th load step fiber cumulative fracture probability P j+1 Obtaining the fiber failure probability increment dP j ＝P j+1 -P j 。
The beneficial effects of the invention are as follows:
(1) The invention establishes a load spectrum filtering method of a load spectrum based on the continuous fiber reinforced composite material microscopic damage, and deeply analyzes a microscopic failure mechanism of the composite material comprising matrix cracking, interfacial adhesion removal and fiber breakage.
(2) The invention can delete partial small load in the load spectrum section, in theory, the calculation workload can be reduced, the calculation efficiency can be improved, the test time can be reduced in the actual process, and the test cost can be reduced;
drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph of effective stress intensity factors of a composite material in an embodiment of the invention;
FIG. 3 is a graph of different interfacial shear thresholds IW cr Small load erasureExcept for schematic diagrams.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention relates to a load spectrum filtering method based on a continuous fiber reinforced mesoscopic damage threshold, which comprises the following steps:
step 1, calculating stress, strain, axial average stress and axial average strain of a fiber and a matrix based on a constitutive model of the continuous fiber reinforced composite material under a spectrum load, and calculating axial strain of the composite material;
step 2, calculating the crack growth increment of the matrix based on the axial average stress and strain of the matrix obtained in the step 1;
step 3, calculating a crack tip stress intensity factor when the base crack starts based on the base stress in the step 1;
step 4, calculating the relative slippage ratio of the fiber and the matrix based on the strain gauge of the fiber and the matrix obtained in the step 1; step 5, calculating the increment of the cumulative failure percentage of the fiber based on the stress born by the fiber of the crack plane of the matrix;
step 6, judging whether the increment percentage of the fiber cumulative failure probability is 0, the matrix crack growth rate is 0, the relative slippage of the fiber/matrix is less than ten percent, the crack tip stress intensity factor is less than the crack growth threshold value under loading and unloading, and deleting the loading peak-valley value if the increment percentage is met;
and 7, judging whether the whole original load spectrum is loaded, if so, ending, outputting the pruned load spectrum, and if not, returning to the step two to continue loading.
The composite material in this example is a SiCf/Ti composite material, and the parameters are shown in the following table:
in the step 1, based on the constitutive model of the metal matrix composite under the spectrum load, the stress of the fiber and the matrix unit is as follows:
wherein ,rf Is the fiber radius, E f For modulus of elasticity of fibres, E m For modulus of elasticity of matrix, f k,j Interfacial shear force, σ, at the jth load step for the kth cell f1 Stress, sigma, assumed by the fibre m1 Stress, ε, assumed by the substrate f (i, j) is the strain, ε, that the ith unit of fiber developed after the jth load step was loaded m (i, j) is the strain, ε, that the ith cell of the substrate developed after the jth load step was loaded p (i, j) is the plastic strain, sigma, generated by the ith unit of the matrix after the jth load step is loaded f (i, j) is the stress, σ, assumed by the ith element of the fiber after the jth load step is loaded m (i, j) is the stress that the ith unit of the matrix assumes after loading at the jth load step;
the average strain of the fiber and the matrix can be obtained after the strain of all the units is weighted and averaged, and the strain of the composite material is equal to the strain of the fiber;
wherein, the fiber axial average strain is:
the fiber axial average stress is:
σ f,j ＝E f ε f,j +E f (α c -α f )ΔT(11)
the axial average strain of the matrix is:
the axial average stress of the matrix is as follows:
wherein ,αc ,α m ,a f The thermal expansion coefficients of the composite material, the matrix and the fiber are respectively, delta T is the temperature difference, and the axial strain epsilon of the composite material c,j Equal to the fiber axial strain:
in step 2, in order to simplify the evolution process of fatigue damage, it is assumed that the interfacial peeling degree of all matrix cracks and each fiber in the composite is the same; during fatigue, all matrix cracks and interfacial peeling are assumed to be of the same length and are uniformly spaced.
The expansion of the crack of the matrix of the axial tensile composite material can be regarded as the expansion of the type I central crack, as shown in figure 2, the average stress in the matrix is used for replacing the external stress, and the crack tip stress intensity factor K of the external stress b Can be expressed as:
wherein ,r is the average stress of the matrix 0 To average crack length, Y b Representing a geometric correction factor reflecting the effect of crack geometry on crack tip stress fieldFrom the stress intensity factor manual, the geometric correction factor for a center crack that is uniformly stretched is:
wherein rm Is the radius of the matrix.
As the crack length increases, which resists crack propagation due to fiber bridging, so does the fiber bridging stress. The bridging stress of the fiber is related to the interfacial debonding length, and the bridging stress sigma p Can be expressed as:
wherein ,ld Represents the debonding length of the fiber/matrix interface, l rs Is the sum of the lengths of all the reverse slip regions in the whole interface debonding region, and τ is the initial interface shear stress.
The crack tip stress intensity factor due to fiber bridging is:
fiber bridging stress sigma p Increasing with increasing crack length, fiber bridged crack tip stress intensity factor K c Decreasing with increasing crack length.
According to the superposition principle, the stress intensity factor K of the crack tip of the SiCf/Ti composite material a The method comprises the following steps:
K a ＝K b +K c (15)
crack tip stress intensity factor K of SiCf/Ti composite material a Gradually decreasing with crack growth. Considering the plastic deformation of the crack tip of the matrix, the effective crack length is composed of the actual crack and the virtual crack of the plastic zone of the crack tip according to the Dugdale model, which is processed by Dugdale to the sum of two loads, which can be processed to the sum of three loads for a composite material, one of themThe stress intensity factors of the tip of the crack plastic region of the composite material are overlapped by the following three stress intensity factors:
wherein ,σms Is the yield strength of the composite material matrix, r p For the virtual crack length, the total effect after the three loads act is to make the virtual crack tip singularity disappear:
K b +K c +K p ＝0 (17)
the virtual crack length r can be solved by the simultaneous formulas (18) and (19) p 。
In the case of spectral loading, the size of the plastic region r 'generated in this cycle is assumed to be such that no hysteresis occurs in the loading after high loading' p，j r max -r j The maximum cyclic stress required is sigma req，j The crack tip residual stress is:
σ res，j ＝σ req，j -σ max，j (20)
wherein ,σmax，j Is the peak stress in the j-th cycle.
The actual cyclic stress at the crack tip is:
wherein ,is the effective stress maximum, +.>Is the effective stress minimum in the j-th cycle;
the actual cyclic stress range and stress ratio are:
according to the Forman formula, the fatigue crack growth rate is:
wherein ,ΔKth Is a crack propagation threshold value of a matrix, is a constant, K c，m ΔK, the fracture toughness of the matrix eff For an effective stress intensity factor, the effective stress intensity factor range can be expressed as:
considering the influence of plastic deformation and crack closure of the matrix, one loaded crack increment is:
the thickness of the brittle interface reaction layer in the step 3 plays a very important role in crack initiation, and when the brittle interface reaction layer generates cracks, if the cracks propagate to the inside of the matrix, the cracks are formed
ΔK tip ＞ΔK th (26)
The stress intensity factor of the crack tip when the crack of the matrix is initiated is as follows:
in the step 4, no contribution is made to the crack propagation of the matrix in the unloading process, and the stress borne by the fiber easy-break point is not increased, so that the unloading is not considered to be contributed to the crack propagation and the fiber breakage of the matrix, but the fiber/matrix interface can slide in the unloading process, so that the interface is worn, and the influence of the unloading on the interface is considered. The relative displacement of the preloaded fiber/matrix is the sum of the relative displacement during loading and the relative displacement during unloading,
Δu j/2 ＝Δu f,j -Δu m,j +Δu f,j+1 -Δu m,j+1 {j＝2n,n＝1,2,3m}(27)
wherein Δuf,j ＝Lε f,j For displacement of fibres at the j-th load step, deltau m,j ＝Lε m,j For displacement of the substrate at the j-th load step, where ε f,j and εm,j The average strains of the fibers and the matrix obtained in the first step are respectively. L is the fiber length. A load spectrum profile, a load/unload slip ratio being the ratio of the maximum slip displacement of the load spectrum:
wherein ,Δun ＝Δu f,n -Δu m,n 。
SiC fibers have a dispersion in tensile strength due to microscopic defects generated internally during the production process, for example, due to processing. Since fiber breakage occurs mostly near the plane of the matrix crack, it is believed that the fibers are broken at the plane of the matrix crack, which is the stress σ that the fibers assume f The expression is:
wherein ,
matrix volume fraction V m The method comprises the following steps:
V m ＝1-V f (31)
wherein sigma is the applied stress.
The global load shear model is adopted, and the load initially born by the broken fiber is assumed to be evenly distributed to all the remained complete fibers on the same section, the stress born by the crack plane matrix is unchanged, and the stress born by the rest fiber at the crack plane after the fiber is broken is as follows:
the cumulative failure probability of the fiber is
Wherein P (T) is fiber cumulative failure probability, sigma 0 For the characteristic strength of the fibre, m f The weibull modulus is the fiber strength distribution. Calculating the j-th step fiber cumulative fracture probability P of the load spectrum section according to the steps j And j+1 th step fiber cumulative fracture probability P j+1 Obtaining the fiber failure probability increment dP j ＝P j+1 -P j 。
Judging the crack growth rate dr of the matrix in the steps j Crack tip stress intensity factor ΔK tip Fiber cumulative failure probability increment dP j If dr, whether the relative slip ratio IW of the fiber/substrate satisfies the condition of small influence on the fatigue life of the composite material j ＝0、dP j ＝0、IW≤IW cr 、ΔK tip ≤ΔK th It is believed that these small loads do not contribute to damage to the composite material and that the load history has a small impact on the fatigue life of the composite material, which can be removed. Wherein IW cr The interface abrasion threshold value can be determined according to the test and the required precision.
While the foregoing is directed to embodiments of the present invention, other and further details of the invention may be had by the present invention, it should be understood that the foregoing description is merely illustrative of the present invention and that no limitations are intended to the scope of the invention, except insofar as modifications, equivalents, improvements or modifications are within the spirit and principles of the invention.

Claims (4)

1. A load spectrum filtering method based on a continuous fiber reinforced composite material microscopic damage threshold is characterized by comprising the following steps of: the method comprises the following steps:
step 1, calculating stress, strain, axial average stress and axial average strain of a fiber and a matrix based on a constitutive model of the continuous fiber reinforced composite material under a spectrum load, and calculating axial strain of the composite material;
step 2, calculating the crack growth increment of the matrix based on the axial average stress and strain of the matrix obtained in the step 1;
step 3, calculating a crack tip stress intensity factor when the base crack starts based on the base stress in the step 1;
step 4, calculating the relative slippage ratio of the fiber and the matrix based on the strain gauge of the fiber and the matrix obtained in the step 1;
step 5, calculating the increment of the cumulative failure percentage of the fiber based on the stress born by the fiber of the crack plane of the matrix;
step 6, judging whether the increment percentage of the fiber cumulative failure probability is 0, the matrix crack growth rate is 0, the relative slippage of the fiber/matrix is less than ten percent, the crack tip stress intensity factor is less than the crack growth threshold value under loading and unloading, and deleting the loading peak-valley value if the increment percentage is met;
step 7, judging whether the whole original load spectrum is loaded, if so, ending, outputting the pruned load spectrum, and if not, returning to the step two to continue loading;
the calculation expression of the stress and the strain of the fiber and the matrix in the step 1 is as follows:
wherein ,εf (i, j) is the strain, ε, that the ith unit of fiber developed after the jth load step was loaded m (i, j) is the strain produced by the ith cell of the substrate after the jth load step, r f Is the fiber radius sigma f (i, j) is the stress, σ, assumed by the ith element of the fiber after the jth load step is loaded m (i, j) is the stress borne by the ith unit of the matrix after the jth load step is loaded, f k,j For interfacial shear force of the kth unit at the jth load step, E f For modulus of elasticity, sigma of the fiber m1 Stress borne by the substrate, E m For modulus of elasticity of matrix, r m Radius of the matrix, epsilon p (i, j) is the plastic strain produced by the ith cell after the jth load step is loaded;
the average strain of the fiber and the matrix can be obtained after the strain of all the units is weighted and averaged;
the fiber axial average strain is:
the fiber axial average stress is:
σ f,j ＝E f ε f,j +E f (α c -α f )ΔT (3)
the axial average strain of the matrix is:
the axial average stress of the matrix is as follows:
wherein ,αc ,α m ,a f The thermal expansion coefficients of the composite material, the matrix and the fiber are respectively shown, delta T is the temperature difference, and n is the total number of units;
axial strain epsilon of composite material c,j Equal to the average strain in the fiber axial direction:
in the step 4, the relative slippage of the fiber/matrix is used for replacing the abrasion loss of the interface, and the relative displacement of the preloaded fiber/matrix interface is the sum of the relative displacement during loading and the relative displacement during unloading, and the expression is as follows:
Δu j/2 ＝|Δu f,j -Δu m,j |+|Δu f,j+1 -Δu m,j+1 |{j＝2n,n＝1,2,3…m} (21)
wherein ,Δuf,j ＝Lε f,j For displacement of fibres at the j-th load step, deltau m,j ＝Lε m,j The displacement of the matrix under the j-th load step is shown, and L is the fiber length;
the relative slippage of the fiber and the matrix is as follows:
wherein ,Δun ＝|Δu f,n -Δu m,n |。
2. The load spectrum filtering method based on the continuous fiber reinforced composite material microscopic damage threshold according to claim 1, wherein the method comprises the following steps: the crack growth increment calculation process of the matrix in the step 2 is as follows: the axial average stress in the matrix is used for replacing the external stress, and the crack tip stress intensity factor K of the external stress b Expressed as:
wherein ,r is the average stress of the matrix 0 To average crack length, Y b Representing the geometric correction coefficient;
the crack tip stress intensity factor for fiber bridging is:
fiber bridging stress sigma p Expressed as:
wherein ,ld Represents the debonding length of the fiber/matrix interface, l rs Is the length sum of all reverse sliding areas in the whole interface debonding area, and tau is the initial interface shear stress;
composite crack tip stress intensity factor K a The method comprises the following steps:
K a ＝K b +K c (10)；
according to the Dugdale model, the effective crack length is composed of an actual crack and a virtual crack of the crack tip plastic region, and the composite material crack plastic region tip stress intensity factor is superimposed by the following three stress intensity factors:
wherein ,σms Is the yield strength of the composite material matrix, r p For the virtual crack length, the total effect after the three loads act is to make the virtual crack tip singularity disappear:
K b +K c +K p ＝0 (12)
solving the virtual crack length r by the simultaneous formulas (13) and (14) p ；
In the case of spectral loading, assuming no hysteresis occurs in loading after high load, the maximum cyclic stress required is σ req,j The crack tip residual stress is:
σ res,j ＝σ req,j -σ max,j (13)
wherein ,σmax,j Peak stress in the j-th cycle;
the actual cyclic stress at the crack tip is:
wherein ,is the effective stress maximum in the j-th cycle,/->Is the effective stress minimum in the j-th cycle;
the actual cyclic stress range and stress ratio are:
according to the Forman formula, the fatigue crack growth rate is:
wherein C, M is a matrix crack propagation parameter, K c,m ΔK, the fracture toughness of the matrix th As stress intensity factor threshold value, deltaK eff Is an effective stress intensity factor;
the effective stress intensity factor is expressed as:
ΔK b delta K is the actual stress intensity factor increment c Increment of crack tip stress intensity factor for fiber bridging, r i For the crack length of the i-th step,for maximum effective actual cyclic stress of the matrix, < ->For minimum effective actual stress of the matrix, delta sigma p To bridge the stress range;
considering the impact of plastic deformation and crack closure of the substrate, one loaded crack propagation increment is:
3. the load spectrum filtering method based on the continuous fiber reinforced composite material microscopic damage threshold according to claim 1, wherein the method comprises the following steps: and in the step 3, the stress intensity factor of the crack tip when the crack of the matrix is initiated is as follows:
wherein ,Δσm D is the average stress of the matrix int For the interface layer thickness, Y b Representing the geometric correction coefficients.
4. The load spectrum filtering method based on the continuous fiber reinforced composite material microscopic damage threshold according to claim 1, wherein the method comprises the following steps: in said step 5, assuming that the fibers are all broken at the crack plane of the matrix, the stress sigma imposed by the fibers at the crack plane of the matrix f1 The expression is:
wherein ,
wherein ,Em Modulus of elasticity of matrix, E f Is the elastic modulus of the fiber, sigma is the external stress, V f V as fiber volume fraction m The expression is as follows:
V m ＝1-V f (25)；
the global load shear model is adopted, and the load initially born by the broken fiber is assumed to be evenly distributed to all the remained complete fibers on the same section, the stress born by the crack plane matrix is unchanged, and the stress born by the rest fiber at the crack plane after the fiber is broken is as follows:
the cumulative failure probability of the fiber is:
wherein P (T) is fiber cumulative failure probability, sigma 0 For the characteristic strength of the fibre, m f A weibull modulus for fiber strength distribution;
calculating the j-th load step fiber cumulative fracture probability P of the load spectrum section j And the j+1th load step fiber cumulative fracture probability P j+1 Obtaining the fiber failure probability increment dP j ＝P j+1 -P j 。
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