CN112257221A - Method for calculating matrix crack propagation rate of metal matrix composite under spectral loading - Google Patents

Method for calculating matrix crack propagation rate of metal matrix composite under spectral loading Download PDF

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CN112257221A
CN112257221A CN202010894497.1A CN202010894497A CN112257221A CN 112257221 A CN112257221 A CN 112257221A CN 202010894497 A CN202010894497 A CN 202010894497A CN 112257221 A CN112257221 A CN 112257221A
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crack
stress
matrix
cycle
metal matrix
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孙志刚
牛序铭
陈西辉
刘炎
宋迎东
邹鹏健
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for calculating the crack propagation rate of a matrix of a metal matrix composite under spectral loading, which comprises the following steps: calculating the stress intensity factor of the crack tip of the matrix based on the unit cell model containing the local cracks and fracture mechanics; step two: solving the size of the plastic zone of the crack tip of the matrix based on a Dugdale model; step three: calculating the effective stress intensity factor of the metal matrix composite under the spectrum loading based on the second step and a Willenborg model; step four: combining the first step with the third step, and calculating the matrix crack propagation rate of the metal matrix composite material under spectral loading based on a Forman formula; the invention provides a theoretical basis for the subsequent research of fatigue fracture of the metal matrix composite material under spectral load; the crack propagation rate of the metal matrix composite under the spectral load can be calculated, and the cyclic constitutive relation of the metal matrix composite under the spectral load can be obtained by combining the related damage theory of the metal matrix composite.

Description

Method for calculating matrix crack propagation rate of metal matrix composite under spectral loading
Technical Field
The invention relates to a method for simulating the matrix crack propagation rate of a metal matrix composite under spectral load in a normal temperature environment, in particular to a method for simulating the matrix crack propagation rate of a continuous silicon carbide fiber reinforced titanium matrix composite under the condition of pulling-spectral loading in the normal temperature environment.
Background
Continuous silicon carbide fiber reinforced Titanium Matrix Composites (hereinafter SiC)f/Ti) is mainly applied to rotor parts of aircraft engines, and has the characteristics of high specific strength, specific rigidity and the like. When the continuous SiC reinforced Ti-based composite material structure bears centrifugal stress, tensile load is generally borne, and in actual working conditions, the tensile load is complex and random, so that the research on SiC is necessaryfFatigue properties of Ti under spectral load. SiCfThe cracking of the matrix of the Ti-based composite material is one of the main damage modes in fatigue loading, so that the accurate simulation of the matrix crack propagation rate has important significance for researching the fatigue performance of the metal-based composite material.
In the prior art, a document of false-life prediction of fiber-reinforced titanium matrix composites proposes a fatigue crack propagation rate calculation method of a metal matrix composite material under a normal amplitude, but the method is suitable for the normal amplitude, and the amplitude-variable loading has the influence of a load sequence and has a great influence on the crack propagation rate. The document "YIELDING OF STEEL SHEETS CONSTITUTING SLITS" proposes a method for calculating the size of the plastic zone at the crack tip, called Dugdale model for short, which treats the crack tip stress as the sum of the applied stress and the compressive stress of the plastic crack zone, but the composite material matrix cracks are also subjected to the compressive stress generated by the fiber bridging action. The document "A crack growth recovery model using an effective stress concept" proposes a model for predicting crack propagation delay, hereinafter referred to as Willenborg model, which can consider the crack propagation rate of a metal material under load interaction, but the application of the model to a metal matrix composite material has not been found. The literature, "Numerical analysis of crack propagation in cyclic-loaded structure" proposes a modified paris formula, abbreviated as the foman formula, which considers the influence of stress ratio and material fracture toughness when calculating the crack propagation rate and is widely applied to metal materials, but the application of the formula to metal-based composite materials is not found yet.
In view of the foregoing, there is a need for a method for efficiently calculating crack propagation rate under spectral loading in metal matrix composites.
Disclosure of Invention
The invention provides a method for calculating the crack propagation rate of a matrix of a metal matrix composite under spectral loading, which aims to solve the problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating the crack propagation rate of a matrix of a metal matrix composite under spectral loading comprises the following steps:
the method comprises the following steps: calculating the stress intensity factor of the crack tip of the matrix based on the unit cell model containing the local cracks and fracture mechanics;
step two: solving the size of the plastic zone of the crack tip of the matrix based on a Dugdale model;
step three: calculating the effective stress intensity factor of the metal matrix composite under the spectrum loading based on the second step and a Willenborg model;
step four: and combining the first step with the third step, and calculating the matrix crack propagation rate of the metal matrix composite material under the spectral loading based on a Forman formula.
Further, the specific steps of the first step are as follows:
the expansion of the crack of the axially stretched metal matrix composite can be regarded as the expansion of an I-type central crack, and the force acting on the matrix when the metal matrix composite is stretched in a single axis is divided into two parts, wherein: one part is the stress born by the matrix, the other part is the compressive stress generated by the fiber bridging to the crack, and the compressive stress generated by the fiber bridging to the crack acts on the crack with the radius rfAccording to the principle of superposition, the stress intensity factor of the crack tip of the matrixThe tip stress intensity factors from these two forces add up,
stress intensity factor K of stress borne by matrix acting on crack tipbComprises the following steps:
Figure BDA0002658008860000021
the compressive stress generated by the fiber bridging on the crack acts on the stress intensity factor K generated at the crack tipcComprises the following steps:
Figure BDA0002658008860000022
wherein:
Figure BDA0002658008860000023
the strength factor K of the crack tip of the metal matrix composite material matrixcomComprises the following steps:
Kcom＝Kb+Kc (4)
wherein, YbThe geometric correction factor, related to the shape and geometric dimensions of the crack, can be found in the handbook of stress intensity factors, σmAverage stress borne by the matrix of the metal matrix composite material, pi is the circumferential ratio, r0Radius of central crack, rfIs the radius, σ, of the metal matrix composite fiberpThe stress acting on the matrix cracks for bridging of the fibres,. tau.shear stress at the interface,. ldThe interfacial debonding length.
Further, the second step comprises the following specific steps:
considering the plastic deformation of the crack tip of the matrix, based on a Dugdale model, the effective crack length is formed by an actual crack and a virtual crack in the plastic zone of the crack tip, and for the metal matrix composite material, the stress of the crack tip is processed into the sum of three loads, namely an external load on the matrix, a compressive stress on the crack fiber section due to fiber bridging, and a compressive stress in which the crack range of the plastic zone is vertical to the crack;
considering the plastic zone crack, the stress intensity factor of the metal matrix composite material is divided into three types of load superposition,
Figure BDA0002658008860000031
wherein: sigmasIs the yield strength, r, of the composite matrixpTo a virtual crack length, KpThe overall effect of the three types of stress after the action of load is that the singularity of the crack tip disappears, namely:
Kb+Kc+Kp＝0 (6)
solving the virtual crack length r by simultaneous formula (5) and formula (6)p。
Further, the third step comprises the following specific steps:
based on the Willenborg model, in the case of spectral loading, if the jth cycle is a high-load cycle, the peak stress at that cycle is σmax,jThe valley stress is σmin,jThe fiber bridging stress is σp,jThe radius length of the central crack of the substrate is r in the jth cyclejThe plastic region size of the crack tip at the jth cycle is rp,jRespectively using σmax,j,σp,j,rj,rp,jInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,jAt this time, the effective crack size reff,j＝rj+rp,jMaximum effective crack size rmax＝reff,jAfter the high load, the peak stress is σ at the cycle when the ith cycle is subsequently loadedmax,iThe valley stress is σmin,iThe fiber bridging stress is σp,iThe radius length of the central crack of the substrate is r in the ith cycleiThe plastic zone size of the crack tip at the ith cycle is rp,iRespectively using σmax,i,σp,i,ri,rp,iInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,iWhen r isi+rpi,＜rmaxWhen the crack propagates in the high-load plastic region, high-load hysteresis occurs, and if the high-load hysteresis disappears, r needs to be satisfiedi+rp,i＝rmaxThen, within this cycle, the matrix crack tip plastic zone size r'p,i＝rmax-riR 'is'p.i,riInstead of r in the formula (5)p,r0The maximum cyclic stress sigma required by the matrix is solved by combining the formula (6)m,req,iThen residual stress σ of crack tip of matrixres,iComprises the following steps:
σres,i＝σm,req,i-σmax,i (7)
effective cyclic stress peak-to-valley at ith cyclic crack tip
Figure BDA0002658008860000032
Respectively, are as follows,
Figure BDA0002658008860000041
the ith cycle effective stress range
Figure BDA0002658008860000042
And effective stress ratio Reff,iIn order to realize the purpose,
Figure BDA0002658008860000043
Figure BDA0002658008860000044
wherein: sigmamax,i,σmin,iRespectively, the ith peak and the valley in the load course.
Further, the fourth step specifically comprises:
the effective stress range obtained in the third step
Figure BDA0002658008860000045
riReplaces sigma in formula (1) in the step onem,r0Calculating to obtain the difference value delta K of the stress intensity factor of the crack tip under the stress action born by the ith cycle peak-valley matrixb,iBy Δ σp,i,riSubstitution of σ in equation (2)p,r0Calculating to obtain the difference value delta K of the crack strength factor under the fiber bridging action under the ith cycle peak value and the valley valuec,iThen, at the i-th cycle, the effective stress intensity factor delta K of the crack tip of the metal matrix composite material matrixeff,iAs indicated by the general representation of the,
Figure BDA0002658008860000046
wherein, the superscript delta represents the difference of the corresponding calculation parameters of the ith cycle peak value and the valley value, and delta sigmap,iFor the fibre bridging stress sigma at the ith cycle peakp,max,iAnd fiber bridging stress σ at the ith cycle valleyp,min,iDifference of (a) Δ σp,iExpressed as Δ σp,i＝σp,max,i-σp,min,i；
Based on the Forman formula, considering the crack closing effect, the crack propagation rate dr/dN of the metal matrix composite material matrix is,
Figure BDA0002658008860000047
wherein: r is the crack radius length of the matrix, N represents the number of cycles,
Figure BDA0002658008860000048
showing the increase in the radius and length of the crack in the substrate, i.e., the crack propagation rate of the substrate, Δ K, for one cyclethExpressing crack growth threshold values, C and m being fatigue crack growth materialsParameter, ReffThe fracture toughness is expressed by the effective stress ratio, and the length of the crack is the critical size when the crack penetrates through the metal matrix composite material
Figure BDA0002658008860000049
Wherein: sigmam0Is the stress borne by the matrix when the composite material is not damaged, rmIs the radius of the substrate;
r obtained by the formula (10)eff,iInstead of R in the formula (12)effThen, the Δ K obtained by the formula (11)eff,iInstead of Δ K in equation (12)effNamely, the crack propagation rate under the ith cycle is obtained
Figure BDA0002658008860000051
The (i + 1) th cycle matrix crack radius length
Figure BDA0002658008860000052
And the like, and obtaining the radius length of the matrix crack and the crack propagation rate under each loading cycle. Compared with the prior art, the invention has the following beneficial effects:
(1) the invention provides a calculation method capable of effectively calculating the matrix crack propagation rate of a metal matrix composite under spectral load, which can provide a theoretical basis for the subsequent research on fatigue fracture of the metal matrix composite under the spectral load.
(2) The method can calculate the crack propagation rate of the metal matrix composite under the spectral load, and can obtain the cyclic constitutive relation of the metal matrix composite under the spectral load by combining the related damage theory of the metal matrix composite.
(3) The invention lays a theoretical foundation for the fatigue life research of the metal matrix composite material in actual working conditions.
Drawings
FIG. 1 is a flow chart of the steps of the present invention;
FIG. 2 is a schematic view of crack propagation, wherein: (a) the principle of superposition of stress intensity factors, (b) the crack bearing load of a matrix, (c) a Willenborg model schematic diagram, and (d) a composite matrix plastic region size schematic diagram;
FIG. 3 is a graph of high-low loading and low-high loading fatigue crack propagation rates;
FIG. 4 is a graph of crack propagation rate.
Detailed Description
The present invention will be further described with reference to the following examples.
Example 1
The parameters in this example 1 are shown in the following table:
Figure BDA0002658008860000053
Figure BDA0002658008860000061
a method for calculating the crack propagation rate of a matrix of a metal matrix composite under spectral loading comprises the following steps:
the method comprises the following steps: calculating the stress intensity factor of the crack tip of the matrix based on the unit cell model containing the local cracks and fracture mechanics;
specifically, the specific steps of the first step are as follows:
the expansion of the crack of the axially stretched metal matrix composite can be regarded as the expansion of an I-type central crack, and the force acting on the matrix when the metal matrix composite is stretched in a single axis is divided into two parts, wherein: one part is the stress born by the matrix, the other part is the compressive stress generated by the fiber bridging to the crack, and the compressive stress generated by the fiber bridging to the crack acts on the crack with the radius rfAs shown in fig. 2(a) and (c), according to the superposition principle, the stress intensity factor of the tip of the crack of the matrix is superposed by the stress intensity factors of the two forces,
stress intensity factor K of stress borne by matrix acting on crack tipbComprises the following steps:
Figure BDA0002658008860000062
the compressive stress generated by the fiber bridging on the crack acts on the stress intensity factor K generated at the crack tipcComprises the following steps:
Figure BDA0002658008860000063
wherein:
Figure BDA0002658008860000064
the strength factor K of the crack tip of the metal matrix composite material matrixcomComprises the following steps:
Kcom＝Kb+Kc (4)
wherein, YbThe geometric correction factor, related to the shape and geometric dimensions of the crack, can be found in the handbook of stress intensity factors, σmAverage stress borne by the matrix of the metal matrix composite material, pi is the circumferential ratio, r0Radius of central crack, rfIs the radius, σ, of the metal matrix composite fiberpThe stress acting on the matrix cracks for bridging of the fibres,. tau.shear stress at the interface,. ldThe interfacial debonding length.
Step two: solving the size of the plastic zone of the crack tip of the matrix based on a Dugdale model;
specifically, the second step comprises the following specific steps:
considering the plastic deformation of the crack tip of the matrix, based on the Dugdale model, the effective crack length is composed of the virtual crack of the plastic zone of the actual crack and the crack tip, and for the metal matrix composite material, the stress of the crack tip is processed into the sum of three loads, as shown in fig. 2(d), one is the external load on the matrix, one is the compressive stress on the fiber section of the crack due to the fiber bridging, and the other is the compressive stress of the crack range of the plastic zone vertical to the crack;
considering the plastic zone crack, the stress intensity factor of the metal matrix composite material is divided into three types of load superposition,
Figure BDA0002658008860000071
wherein: sigmasIs the yield strength, r, of the composite matrixpTo a virtual crack length, KpThe overall effect of the three types of stress after the action of load is that the singularity of the crack tip disappears, namely:
Kb+Kc+Kp＝0 (6)
solving the virtual crack length r by simultaneous formula (5) and formula (6)p。
Step three: calculating the effective stress intensity factor of the metal matrix composite under the spectrum loading based on the second step and a Willenborg model;
specifically, the third step comprises the following specific steps:
based on the Willenborg model, as shown in FIG. 2(c), in the case of spectral loading, if the jth cycle is a high-load cycle, the peak stress at that cycle is σmax,jThe valley stress is σmin,jThe fiber bridging stress is σp,jThe radius length of the central crack of the substrate is r in the jth cyclejThe plastic region size of the crack tip at the jth cycle is rp,jRespectively using σmax,j,σp,j,rj,rp,jInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,jAt this time, the effective crack size reff,j＝rj+rp,jMaximum effective crack size rmax＝reff,jAfter the high load, the peak stress is σ at the cycle when the ith cycle is subsequently loadedmax,iThe valley stress is σmin,iThe fiber bridging stress is σp,iThe radius length of the central crack of the substrate is r in the ith cycleiThe plastic zone size of the crack tip at the ith cycle is rp,iRespectively using σmax,i,σp,i,ri,rp,iInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,iWhen r isi+rpi,＜rmaxWhen the crack propagates in the high-load plastic region, high-load hysteresis occurs, and if the high-load hysteresis disappears, r needs to be satisfiedi+rp,i＝rmaxThen, within this cycle, the matrix crack tip plastic zone size r'p,i＝rmax-riR 'is'p.i,riInstead of r in the formula (5)p,r0The maximum cyclic stress sigma required by the matrix is solved by combining the formula (6)m,req,iThen residual stress σ of crack tip of matrixres,iComprises the following steps:
σres,i＝σm,req,i-σmax,i (7)
effective cyclic stress peak-to-valley at ith cyclic crack tip
Figure BDA0002658008860000081
Respectively, are as follows,
Figure BDA0002658008860000082
the ith cycle effective stress range
Figure BDA0002658008860000083
And effective stress ratio Reff,iIn order to realize the purpose,
Figure BDA0002658008860000084
Figure BDA0002658008860000085
wherein: sigmamax,i,σmin,iRespectively, the ith peak and the valley in the load course.
Step four: combining the first step with the third step, and calculating the matrix crack propagation rate of the metal matrix composite material under spectral loading based on a Forman formula;
specifically, the fourth step comprises the following specific steps:
the effective stress range obtained in the third step
Figure BDA0002658008860000086
riReplaces sigma in formula (1) in the step onem,r0Calculating to obtain the difference value delta K of the stress intensity factor of the crack tip under the stress action born by the ith cycle peak-valley matrixb,iBy Δ σp,i,riSubstitution of σ in equation (2)p,r0Calculating to obtain the difference value delta K of the crack strength factor under the fiber bridging action under the ith cycle peak value and the valley valuec,iThen, at the i-th cycle, the effective stress intensity factor delta K of the crack tip of the metal matrix composite material matrixeff,iAs indicated by the general representation of the,
Figure BDA0002658008860000087
wherein, the superscript delta represents the difference of the corresponding calculation parameters of the ith cycle peak value and the valley value, and delta sigmap,iFor the fibre bridging stress sigma at the ith cycle peakp,max,iAnd fiber bridging stress σ at the ith cycle valleyp,min,iDifference of (a) Δ σp,iExpressed as Δ σp,i＝σp,max,i-σp,min,i；
Based on the Forman formula, considering the crack closing effect, the crack propagation rate dr/dN of the metal matrix composite material matrix is,
Figure BDA0002658008860000091
wherein: r is the crack radius length of the matrix, N represents the number of cycles,
Figure BDA0002658008860000092
showing the increase of the radius and length of the crack of the matrix under one cycleI.e. the crack propagation rate of the matrix, Δ KthRepresenting a crack propagation threshold value, C and m being fatigue crack propagation material parameters, ReffThe fracture toughness is expressed by the effective stress ratio, and the length of the crack is the critical size when the crack penetrates through the metal matrix composite material
Figure BDA0002658008860000093
Wherein: sigmam0Is the stress borne by the matrix when the composite material is not damaged, rmIs the radius of the substrate;
r obtained by the formula (10)eff,iInstead of R in the formula (12)effThen, the Δ K obtained by the formula (11)eff,iInstead of Δ K in equation (12)effNamely, the crack propagation rate under the ith cycle is obtained
Figure BDA0002658008860000094
The (i + 1) th cycle matrix crack radius length
Figure BDA0002658008860000095
And the like, and obtaining the radius length of the matrix crack and the crack propagation rate under each loading cycle. FIG. 4 shows the crack propagation rate of the matrix under one load spectrum.
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 (5)

1. A method for calculating the crack propagation rate of a matrix of a metal matrix composite under spectral loading is characterized by comprising the following steps:
the method comprises the following steps: calculating the stress intensity factor of the crack tip of the matrix based on the unit cell model containing the local cracks and fracture mechanics;
step two: solving the size of the plastic zone of the crack tip of the matrix based on a Dugdale model;
step three: calculating the effective stress intensity factor of the metal matrix composite under the spectrum loading based on the second step and a Willenborg model;
step four: and combining the first step with the third step, and calculating the matrix crack propagation rate of the metal matrix composite material under the spectral loading based on a Forman formula.
2. The method for calculating the crack propagation rate of the matrix of the metal matrix composite material under the spectral loading according to claim 1, wherein the specific step of the first step is as follows:
the expansion of the crack of the axially stretched metal matrix composite can be regarded as the expansion of an I-type central crack, and the force acting on the matrix when the metal matrix composite is stretched in a single axis is divided into two parts, wherein: one part is the stress born by the matrix, the other part is the compressive stress generated by the fiber bridging to the crack, and the compressive stress generated by the fiber bridging to the crack acts on the crack with the radius rfAccording to the superposition principle, the stress intensity factors of the tips of the cracks of the matrix are superposed by the stress intensity factors of the tips of the two forces,
stress intensity factor K of stress borne by matrix acting on crack tipbComprises the following steps:
Figure FDA0002658008850000011
the compressive stress generated by the fiber bridging on the crack acts on the stress intensity factor K generated at the crack tipcComprises the following steps:
Figure FDA0002658008850000012
wherein:
Figure FDA0002658008850000013
the strength factor K of the crack tip of the metal matrix composite material matrixcomComprises the following steps:
Kcom＝Kb+Kc (4)
wherein, YbAs geometric correction factor, σmAverage stress borne by the matrix of the metal matrix composite material, pi is the circumferential ratio, r0Radius of central crack, rfIs the radius, σ, of the metal matrix composite fiberpThe stress acting on the matrix cracks for bridging of the fibres,. tau.shear stress at the interface,. ldThe interfacial debonding length.
3. The method for calculating the crack propagation rate of the matrix of the metal matrix composite material under the spectral loading according to claim 2, wherein the specific steps of the second step are as follows:
considering the plastic deformation of the crack tip of the matrix, based on a Dugdale model, the effective crack length is formed by an actual crack and a virtual crack in the plastic zone of the crack tip, and for the metal matrix composite material, the stress of the crack tip is processed into the sum of three loads, namely an external load on the matrix, a compressive stress on the crack fiber section due to fiber bridging, and a compressive stress in which the crack range of the plastic zone is vertical to the crack;
considering the plastic zone crack, the stress intensity factor of the metal matrix composite material is divided into three types of load superposition,
Figure FDA0002658008850000021
wherein: sigmasIs the yield strength, r, of the composite matrixpTo a virtual crack length, KpThe overall effect of the three types of stress after the action of load is that the singularity of the crack tip disappears, namely:
Kb+Kc+Kp＝0 (6)
solving the virtual crack length r by simultaneous formula (5) and formula (6)p。
4. The method for calculating the crack propagation rate of the matrix of the metal matrix composite material under the spectral loading according to claim 3, wherein the concrete steps of the third step are as follows:
based on the Willenborg model, in the case of spectral loading, if the jth cycle is a high-load cycle, the peak stress at that cycle is σmax,jThe valley stress is σmin,jThe fiber bridging stress is σp,jThe radius length of the central crack of the substrate is r in the jth cyclejThe plastic region size of the crack tip at the jth cycle is rp,jRespectively using σmax,j,σp,j,rj,rp,jInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,jAt this time, the effective crack size reff,j＝rj+rp,jMaximum effective crack size rmax＝reff,jAfter the high load, the peak stress is σ at the cycle when the ith cycle is subsequently loadedmax,iThe valley stress is σmin,iThe fiber bridging stress is σp,iThe radius length of the central crack of the substrate is r in the ith cycleiThe plastic zone size of the crack tip at the ith cycle is rp,iRespectively using σmax,i,σp,i,ri,rp,iInstead of σ in the formula (5) of step twom,σp,r0,rpThen, the r is solved according to the formula (6)p,iWhen r isi+rp,i＜rmaxWhen the crack propagates in the high-load plastic region, high-load hysteresis occurs, and if the high-load hysteresis disappears, r needs to be satisfiedi+rp,i＝rmaxThe plastic region size r of the crack tip of the substrate in this cyclep',i＝rmax-riR is top'.i,riInstead of r in the formula (5)p,r0The maximum cyclic stress sigma required by the matrix is solved by combining the formula (6)m,req,iThen residual stress σ of crack tip of matrixres,iComprises the following steps:
σres,i＝σm,req,i-σmax,i (7)
effective cyclic stress peak-to-valley at ith cyclic crack tip
Figure FDA0002658008850000031
Respectively, are as follows,
Figure FDA0002658008850000032
the ith cycle effective stress range
Figure FDA0002658008850000033
And effective stress ratio Reff,iIn order to realize the purpose,
Figure FDA0002658008850000034
Figure FDA0002658008850000035
wherein: sigmamax,i,σmin,iRespectively, the ith peak and the valley in the load course.
5. The method for calculating the crack propagation rate of the matrix of the metal matrix composite material under the spectral loading according to claim 4, wherein the fourth step comprises the following specific steps:
the effective stress range obtained in the third step
Figure FDA0002658008850000036
riReplaces sigma in formula (1) in the step onem,r0Calculating to obtain the difference value delta K of the stress intensity factor of the crack tip under the stress action born by the ith cycle peak-valley matrixb,iBy Δ σp,i,riReplacement ofσ in equation (2)p,r0Calculating to obtain the difference value delta K of the crack strength factor under the fiber bridging action under the ith cycle peak value and the valley valuec,iThen, at the i-th cycle, the effective stress intensity factor delta K of the crack tip of the metal matrix composite material matrixeff,iAs indicated by the general representation of the,
Figure FDA0002658008850000037
wherein, the superscript delta represents the difference of the corresponding calculation parameters of the ith cycle peak value and the valley value, and delta sigmap,iFor the fibre bridging stress sigma at the ith cycle peakp,max,iAnd fiber bridging stress σ at the ith cycle valleyp,min,iDifference of (a) Δ σp,iExpressed as Δ σp,i＝σp,max,i-σp,min,i；
Based on the Forman formula, considering the crack closing effect, the crack propagation rate dr/dN of the metal matrix composite material matrix is,
Figure FDA0002658008850000041
wherein: r is the crack radius length of the matrix, N represents the number of cycles,
Figure FDA0002658008850000042
showing the increase in the radius and length of the crack in the substrate, i.e., the crack propagation rate of the substrate, Δ K, for one cyclethRepresenting a crack propagation threshold value, C and m being fatigue crack propagation material parameters, ReffThe fracture toughness is expressed by the effective stress ratio, and the length of the crack is the critical size when the crack penetrates through the metal matrix composite material
Figure FDA0002658008850000043
Wherein: sigmam0Is the stress borne by the matrix when the composite material is not damaged, rmIs the radius of the substrate;
r obtained by the formula (10)eff,iInstead of R in the formula (12)effThen, the Δ K obtained by the formula (11)eff,iInstead of Δ K in equation (12)effNamely, the crack propagation rate under the ith cycle is obtained
Figure FDA0002658008850000044
The (i + 1) th cycle matrix crack radius length
Figure FDA0002658008850000045
And the like, and obtaining the radius length of the matrix crack and the crack propagation rate under each loading cycle.
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