CN113033010B - Crack propagation rate model for small cracks and method for performing crack propagation rate modeling on titanium alloy material - Google Patents

Crack propagation rate model for small cracks and method for performing crack propagation rate modeling on titanium alloy material Download PDF

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CN113033010B
CN113033010B CN202110354593.1A CN202110354593A CN113033010B CN 113033010 B CN113033010 B CN 113033010B CN 202110354593 A CN202110354593 A CN 202110354593A CN 113033010 B CN113033010 B CN 113033010B
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crack
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关雪飞
王新艳
王罗斌
韦利明
何晶靖
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Graduate School Of Chinese Academy Of Engineering Physics
Beihang University
General Engineering Research Institute China Academy of Engineering Physics
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Abstract

The invention provides a crack propagation rate model for small cracks, and a modeling method of the crack propagation rate model for the small cracks comprises the following steps: s1, establishing a primary small crack propagation rate model; s2, determining local yield strength sigmaym(ii) a S3, correcting the established initial small crack propagation rate model and correcting the local yield strength sigmaymAnd substituting the small crack propagation rate model into the small crack propagation rate model to obtain a corrected small crack propagation rate model. Meanwhile, the invention also utilizes the model to establish a fatigue crack propagation rate model of the titanium alloy material. The invention provides a small crack modeling method and applies the method to electric arc additive manufacturing of small cracks of titanium alloy materials, establishes a model aiming at the crack propagation rate of the small cracks, and considers dissimilar effect of microstructure and local yield strength change. Then, a multi-scale fatigue crack propagation rate model of the whole process of the microscopic small cracks, the physical small cracks and the long cracks can be established based on the model.

Description

Crack propagation rate model for small cracks and method for performing crack propagation rate modeling on titanium alloy material
Technical Field
The invention relates to the field of additive manufacturing of titanium alloy materials, in particular to a crack propagation rate model for small cracks and a method for modeling the crack propagation rate of a titanium alloy material.
Background
Additive manufacturing of metallic materials is a metal part manufacturing technique based on a layer-by-layer build-up process. It allows structural components with complex geometries to be manufactured on demand in a shorter design and manufacturing cycle time than conventional manufacturing. Wherein arc additive manufacturing can achieve near net shape directional energy deposition manufacturing with higher material deposition rates and lower process costs compared to other additive techniques using heat sources such as lasers.
In recent years, the manufacture of parts by arc additive technology can meet the manufacturing and maintenance requirements of large titanium alloy parts, and has received more and more attention as a substitute for the traditional manufacture. Fatigue damage is one of the main causes of failure of metallic materials in engineering applications. In order to fully understand the fatigue failure mechanism of the arc-added Ti-6Al-4V alloy, it is necessary to study the fatigue crack propagation behavior. Research has shown that the fatigue crack propagation behavior is different from that of traditional cast and wrought alloys due to the unique microstructure of the arc additive material. Metallographic experiments show that the grain size of the arc additive Ti-6Al-4V material can be large and highly uneven. The size of the crack in the arc additive Ti-6Al-4V material at the early expansion stage can be equivalent to the size of the crystal grain, the expansion time of the crack in a single crystal grain is relatively long, the crack belongs to small crack expansion, and the expansion mechanism of the crack is different from the expansion behavior of a long crack. Few researchers currently research the in-grain fatigue crack propagation behavior of the arc additive Ti-6Al-4V alloy, and how to more accurately model the crack propagation rate of small cracks is also the current research difficulty.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a small crack propagation rate model modeling method, which can model the small crack propagation rate of an additive material, so that the in-grain fatigue crack propagation behavior of the arc additive Ti-6Al-4V alloy can be conveniently researched.
Specifically, the invention provides a crack propagation rate model for small cracks, which comprises the following steps:
s1, establishing a primary small crack propagation rate model, wherein the model expression is as follows:
da/dN＝A(φ′mφ′cσym)n
wherein, A and n are material parameters, and are determined by fatigue experimental data, sigmaymIs local yield strength, phi'm，φ′cMonotonic crack tip opening displacement and cyclic crack tip opening displacement, respectively, taking into account the form factor; phi'm，φ′cRespectively as follows:
φ′m＝Y2φm
and
φ′c＝Y2φc
wherein Y is a crack geometry correction factor that follows the format defined in the stress intensity factor; using monotonic crack tip opening displacement phimAnd cyclic crack tip opening displacement phicCalculating a formula to obtain phi'm，φ′cExpression of (1), monotonic crack tip opening displacement phimAnd cyclic crack tip opening displacement phicThe expression of (a) is as follows:
Figure BDA0002999439130000021
and
Figure BDA0002999439130000022
wherein σmaxThe maximum stress to which the test piece is subjected; sigmaysMacroscopic yield strength; a is the crack length; r is stress ratio; e ' is the effective Young's modulus, and E ' is defined as:
Figure BDA0002999439130000023
wherein v is Poisson's ratio and E is Young's modulus;
s2, determining local yield strength sigmaymWherein the local yield strength σymThe calculation formula of (a) is as follows:
Figure BDA0002999439130000024
wherein σfIs the fatigue limit; a is the crack length; d is the average grain size; sigmaysMacroscopic yield strength; the coefficient kappa reflects the change rate of the crack propagation resistance of the small cracks in a single crystal grain, and the value of the coefficient kappa is determined by the capability of resisting dislocation slip of the microstructure of the material;
s3, correcting the established initial small crack propagation rate model and correcting the local yield strength sigmaymSubstituting the small crack propagation rate model into a small crack propagation rate model to obtain a corrected small crack propagation rate model as follows:
Figure BDA0002999439130000031
and is
Figure BDA0002999439130000032
Preferably, the local yield strength σ in step S3ymTo control the microscopic parameters of the local yield behavior, the local yield strength varies according to the size of the crack and the grain size; local yield strength at the onset of small cracks σymThe value of (A) is fatigue poleLimit, as the crack length increases, the size of the crack tip plastic zone and the number of grains in the plastic zone increase, so that the local yield strength σ increasesymFrom a lower fatigue limit σfMonotonously increasing to macroscopic yield strength value sigmays。
Preferably, the invention also provides a method for modeling the crack propagation rate of the titanium alloy material by using the crack propagation rate model for the small cracks, which comprises the following steps:
s1, carrying out in-situ fatigue experiments on the 2 arc additive Ti-6Al-4V alloy material test pieces to obtain a-N experimental data, and calculating to obtain a crack propagation rate da/dN data value;
s2, determining the Young modulus E, the average grain size D and the local yield strength sigma in the model based on the microstructure characteristics and the mechanical characteristics of the material and by combining fatigue experiment dataymThe method comprises the following steps of:
s21, carrying out tensile test on the titanium alloy material test piece, and obtaining the material with Young modulus and yield strength respectively of E-96 GPa and sigmays920MPa, in the test, because the fatigue test piece is in a plane stress state, E' is 96 GPa;
s22, inspecting a metallographic specimen of the arc additive Ti-6Al-4V alloy material by using a metallographic microscope to obtain the grain size distribution of the material, and obtaining the average grain size D of the material which is 448.75 mu m;
s23 geometric correction factor Y of crack2Comprises the following steps:
Figure BDA0002999439130000033
wherein b is the width of the fatigue test piece made of the titanium alloy material, and the width b of the test piece in the test is 2.5 mm;
s24, determining the local yield strength of the Ti-6Al-4V alloy material test piece and the fatigue limit sigma of the Ti-6Al-4V alloy material test piecef441.6MPa, coefficient κ 1.25, local yield strength σymThe expression is as follows:
Figure BDA0002999439130000041
s25, converting the a-N experimental data into phi 'based on the data obtained by the in-situ fatigue experiment in the step S1 and by utilizing the parameters determined in the steps S21 to S24'mφ′cσym-da/dN data and plotted in a log-log coordinate system, and performing least squares-based linear regression fitting on the data to obtain material parameters (lnA, n) of the fatigue crack propagation model, wherein the mean and covariance matrices of the fitted material parameters (lnA, n) are μ ═ 4.151,1.586) and
Figure BDA0002999439130000042
obtaining the optimal values of the parameters A and n;
s3, substituting the parameter values obtained in the step S2 into the small crack propagation rate model in the step S1 to obtain the final small crack propagation rate model of the arc additive titanium alloy material, wherein the small crack propagation rate model comprises the following steps:
Figure BDA0002999439130000043
and is provided with
Figure BDA0002999439130000044
And
Figure BDA0002999439130000045
among them, σ in the fatigue testmax＝476.19MPa；R＝0.1。
Preferably, step S1 is specifically: performing in-situ fatigue test on the arc additive Ti-6Al-4V alloy material, observing crack propagation behavior by using a scanning electron microscope, and applying stress ratio R to the test piece to be 0.1 and maximum force FmaxCycle of a sinusoidal waveform at a frequency of 5Hz, 1kNThe ring load is characterized in that a scanning electron microscope is used for recording the state of cracks on the test piece in different loading cycle periods, then the scanning electron microscope image is used for obtaining the length a of the cracks, and the corresponding cycle number N is combined to obtain a-N data of the test piece; then, the data values of the crack propagation rate da/dN can be calculated by using every two adjacent points on the a-N curve.
Preferably, the titanium alloy material is manufactured into a Ti-6Al-4V alloy ingot using an arc additive system and the Ti-6Al-4V alloy ingot is prepared on a forged Ti-6Al-4V substrate using a cold metal transition arc welding mode in step S1.
Preferably, the specific steps are as follows: firstly, planning a path by additive driving software according to the shape of an alloy block to be prepared; then, the six-axis robot drives a welding machine to move according to the planned material increase path, and the welding machine is driven by the robot to realize the process of gradually forming a metal part from a line-surface-body of a test piece to be prepared on the basis of the layer-by-layer stacking principle by adding Ti-6Al-4V wire materials; the arc current is 150A, the welding wire feeding speed is 2m/min, the welding gun advancing speed is 4m/min, the layer-to-layer vertical construction interval is 5mm, and the geometric dimension of the prepared Ti-6Al-4V alloy block is 300mm multiplied by 250mm multiplied by 20 m.
Preferably, machining the Ti-6Al-4V alloy to obtain a plurality of fatigue test pieces with the geometrical shapes of dog bones, wherein the width of the center of each test piece is 2.5mm, and a single notch with the depth of 0.085mm and the width of 0.2mm is machined in the center of each test piece, so that the approximate propagation direction of cracks on each test piece can be perpendicular to the construction direction and the deposition direction; in order to facilitate the imaging of the scanning electron microscope, the surface of the test piece is polished to enable the final thickness of the test piece to be 0.85 mm.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a crack growth rate model modeling method aiming at small cracks by considering the influence of local yield strength change on small crack growth behavior, and establishes a small crack growth rate model of an arc additive Ti-6Al-4V alloy material based on arc additive Ti-6Al-4V alloy in-situ fatigue test data. And then establishing a multi-scale fatigue crack propagation rate model of the whole process from the microscopic small cracks, the physical small cracks to the long cracks based on the model.
Drawings
FIG. 1 is a modeling method of a crack propagation rate model for small cracks according to the present invention;
FIG. 2 is a schematic flow chart of a method for modeling additive titanium alloy microcracks in accordance with the present invention;
FIG. 3 is a schematic structural diagram of a test piece for a fatigue test of a Ti-6Al-4V alloy material;
FIG. 4 is a schematic view of crack length a obtained by scanning electron microscope images at different loading cycle numbers N;
FIG. 5 is experimental data of a sample tensile test according to the present invention;
6 a-6 c are schematic diagrams of metallographic specimen observed by a metallographic microscope to obtain grain size distribution;
FIG. 7 is a histogram of grain size distribution;
FIG. 8 shows the local yield strength σ of the arc additive Ti-6Al-4V alloy material in the example of the inventionym；
FIG. 9 is a graphical representation of the results of the mean and 95% confidence ranges of the fitted material parameters (lnA, n) for the example of the present invention;
FIG. 10 is a graphical representation of experimental data and predicted results for crack growth rates in accordance with the present invention;
FIG. 11 is a graph of the sum of squares of errors under a logarithmic coordinate system fit for a comparative proposed model, a reference model without geometric correction, and a reference model with geometric correction of the present invention.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
The invention provides a crack propagation rate model for small cracks, which comprises the following steps as shown in figure 1:
s1, establishing a preliminary small crack propagation rate model, wherein the model expression is as follows:
da/dN＝A(φ′mφ′cσym)n
wherein A and n are material parameters, and fatigue test is utilizedData is determined, σymIs local yield strength, phi'm，φ′cMonotonic crack tip opening displacement and cyclic crack tip opening displacement, respectively, taking into account the form factor; phi's'm，φ′cRespectively as follows:
φ′m＝Y2φm
and
φ′c＝Y2φc
wherein Y is a crack geometry correction factor that follows the format defined in the stress intensity factor; using the monotonic crack tip opening displacement phi proposed by DugdalemAnd cyclic crack tip opening displacement phicCalculating a formula to obtain phi'm，φ′cExpression (c):
Figure BDA0002999439130000061
and
Figure BDA0002999439130000062
wherein σmaxIs the maximum stress to which the test piece is subjected; sigmaysIs the macroscopic yield strength; a is the crack length; r is the stress ratio; e ' is the effective Young's modulus, and E ' is defined as:
Figure BDA0002999439130000063
wherein ν is poisson's ratio and E is Young's modulus;
s2, determining local yield strength sigmaymWherein the local yield strength σymThe calculation formula of (a) is as follows:
Figure BDA0002999439130000071
wherein σfIs the fatigue limit; a is the crack length; d is the average grain size; sigmaysMacroscopic yield strength; the coefficient kappa reflects the change rate of the crack propagation resistance of the small cracks in a single crystal grain, and the value of the coefficient kappa is determined by the capability of resisting dislocation slip of the microstructure of the material;
s3, correcting the established initial small crack propagation rate model and correcting the local yield strength sigmaymSubstituting the small crack propagation rate model into the small crack propagation rate model to obtain a corrected small crack propagation rate model as follows:
Figure BDA0002999439130000072
and is
Figure BDA0002999439130000073
Preferably, the local yield strength σymTo control the microscopic parameters of the local yield behavior of the material, the local yield strength varies according to the size of the crack and the grain size, the local yield strength σ at the onset of a small crackymThe value of (A) is the fatigue limit, the size of the plastic zone at the tip of the crack and the number of grains in the plastic zone increase with increasing crack length, the local yield strength σ increasesymFrom a lower fatigue limit σfMonotonously increasing to macroscopic yield strength value sigmays。
In practical application, the invention also provides a method for performing crack growth rate modeling on a titanium alloy material by using the crack growth rate model for the small cracks, which comprises the following steps:
s1, carrying out in-situ fatigue experiments on the 2 arc additive Ti-6Al-4V alloy material test pieces to obtain a-N experimental data, and calculating to obtain a crack propagation rate da/dN data value;
s2, determining the Young modulus E, the average grain size D and the local yield strength sigma in the model based on the microstructure characteristics and the mechanical characteristics of the material and by combining fatigue experiment dataymThe method comprises the following steps of:
s21, carrying out tensile test on the titanium alloy material test piece, and obtaining the material with Young modulus and yield strength respectively of E-96 GPa and sigmays920MPa, the fatigue test piece in the patent is in a plane stress state, so that E' is 96 GPa;
s22, inspecting a metallographic specimen of the arc additive Ti-6Al-4V alloy material by using a metallographic microscope to obtain the grain size distribution of the material, and obtaining the average grain size D of the material which is 448.75 mu m;
s23 geometric correction factor Y of crack2Comprises the following steps:
Figure BDA0002999439130000081
wherein b is the width of the fatigue test piece made of titanium alloy material, and b is 2.5mm in the patent;
s24, determining the local yield strength of the Ti-6Al-4V alloy material test piece and the fatigue limit sigma of the Ti-6Al-4V alloy material test piecef441.6MPa, coefficient κ 1.25, local yield strength σymThe expression is as follows:
Figure BDA0002999439130000082
s25, converting the a-N experimental data into phi 'based on the data obtained by the in-situ fatigue experiment in the step S1 and by utilizing the parameters determined in the steps S21 to S24'mφ′cσym-da/dN data and plotted in a log-log coordinate system, and performing linear regression fitting based on least squares on the data to obtain material parameters (lnA, n) of the fatigue crack propagation model, wherein the mean and covariance matrices of the fitting parameters (lnA, n) are μ ═ 4.151,1.586) and
Figure BDA0002999439130000083
obtaining the optimal values of the parameters A and n;
s3, substituting the parameter values obtained in the step S2 into the small crack propagation rate model in the step S1 to obtain the final small crack propagation rate model of the arc additive titanium alloy material, wherein the small crack propagation rate model comprises the following steps:
Figure BDA0002999439130000084
and is
Figure BDA0002999439130000085
And
Figure BDA0002999439130000086
wherein, in the fatigue test, the sigmamax＝476.19MPa；R＝0.1。
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The invention also provides a small crack modeling method for the additive manufacturing of the titanium alloy material based on the model, which comprises the following steps as shown in fig. 2:
s1, carrying out in-situ fatigue test on 2 electric arc additive Ti-6Al-4V alloy materials, observing crack propagation behavior by using a scanning electron microscope, and applying stress ratio R to the test piece to be 0.1 and maximum force FmaxRecording the state of cracks on the test piece at different loading cycle periods by using a scanning electron microscope under a sine-wave cyclic load with the frequency of 5Hz at 1kN, then obtaining the length a of the cracks by using an image of the scanning electron microscope, and combining the corresponding cyclic cycle N to obtain a-N data of the test piece; then, the data value of the crack propagation rate da/dN can be calculated by using each two adjacent points on the a-N curve.
In the step S1, the titanium alloy material is used for manufacturing a Ti-6Al-4V alloy block by using an electric arc additive system, and the Ti-6Al-4V alloy block is prepared on a forged Ti-6Al-4V substrate by adopting a cold metal transition arc welding mode; firstly, planning a path according to the shape of an alloy block to be prepared by additive driving software, then driving a welding machine to move by a six-axis robot according to the planned additive path, and realizing the process of gradually forming a metal part from a line-surface-body of a test piece to be prepared by the welding machine under the driving of the robot on the basis of the layer-by-layer stacking principle by adding Ti-6Al-4V wires; the arc current is 150A, the welding wire feeding speed is 2m/min, the welding gun advancing speed is 4m/min, the layer-to-layer vertical construction interval is 5mm, and the geometric dimension of the prepared Ti-6Al-4V alloy block is 300mm multiplied by 250mm multiplied by 20 m.
During the test, a plurality of fatigue test pieces 100 with the geometrical shapes of dog bones are machined on the Ti-6Al-4V alloy, as shown in figure 3, the center width of the test piece is 2.5mm, a single notch 101 with the depth of 0.085mm and the width of 0.2mm is arranged at the center of the test piece, and the approximate propagation direction of cracks on the test piece can be perpendicular to the construction direction and the deposition direction; in order to facilitate the imaging of the scanning electron microscope, the surface of the test piece is polished to enable the final thickness of the test piece to be 0.85 mm.
From the microstructure of a sample taken from the top deposited layer (X-Y cross section) of the arc additive material, the material consists of a number of beta columnar grains with an alpha + beta structure. The alpha phase nucleates at the beta grain boundary and forms a grain boundary alpha (alpha)GB) The structure of (1). The alpha layer continues to grow to form from alphaGBTo alpha bundling inside the beta grains. Bundling is a layered microstructure consisting of parallel alpha layers separated by beta matrices. Inside the grains, α nucleates in a basket-like morphology within the β grains at a higher cooling rate.
Fig. 4 shows a schematic representation of the crack length a obtained with scanning electron microscope images at different number of loading cycles N. If the crack is branched during the fatigue test, the length of the main crack is used as the crack length.
S2, establishing a small crack propagation rate model, which comprises the following steps:
s21, establishing a preliminary small crack propagation rate model, wherein the model expression is as follows:
da/dN＝A(φ′mφ′c σym)n
wherein A and n are material parameters, and are determined by fatigue experimental data, sigmaymIs local yield strength, phi'm，φ′cMonotonic and cyclic crack tip opening displacements that take into account the shape factor, respectively; phi'm，φ′cRespectively as follows:
φ′m＝Y2φm
and
φ′c＝Y2φc
wherein Y is a crack geometry correction factor that follows the format defined in the stress intensity factor; using the monotonic crack tip opening displacement phi proposed by DugdalemAnd cyclic crack tip opening displacement phicCalculating a formula to obtain phi'm，φ′cExpression (c):
Figure BDA0002999439130000101
and
Figure BDA0002999439130000102
wherein σmaxIs the maximum stress to which the test piece is subjected; sigmaysIs the macroscopic yield strength; a is the crack length; r is the stress ratio; e ' is the effective Young's modulus, and E ' is defined as:
Figure BDA0002999439130000103
wherein v is the Poisson's ratio and E is the Young's modulus;
s22, determining local yield strength sigmaymWherein the local yield strength σymThe calculation formula of (a) is as follows:
Figure BDA0002999439130000104
wherein σfIs the fatigue limit; a is the crack length; d is the average grain size; sigmaysMacroscopic yield strength; the coefficient kappa reflects the change rate of the crack propagation resistance of the small cracks in a single crystal grain, and the value of the coefficient kappa is determined by the capability of resisting dislocation slip of the microstructure of the material;
s23, correcting the established initial small crack propagation rate model and correcting the local yield strength sigmaymSubstituting the small crack propagation rate model into a small crack propagation rate model to obtain a corrected small crack propagation rate model as follows:
Figure BDA0002999439130000105
and is
Figure BDA0002999439130000111
S3, determining the Young modulus E, the average grain size D and the local yield strength sigma in the model based on the microstructure characteristics and the mechanical characteristics of the material and by combining fatigue experiment dataymThe method comprises the following steps of:
tensile tests were carried out using test pieces to obtain macroscopic mechanical properties according to ASTM E8/E8M. The experimental data of the samples are shown in fig. 5. The Young's modulus and yield strength of the material are respectively E-96 GPa and sigmaysThe fatigue test piece in the patent is in a plane stress state at 920MPa, so that E' is 96 GPa.
Local yield strength σymThe formula of (1) requires the grain size of the arc additive Ti-6Al-4V material. And carrying out metallographic microscope observation on a metallographic specimen to obtain the distribution of the grain size. The overall image of the sample is shown in fig. 6a, where the area outlined by the red box in fig. 6a is enlarged to illustrate the grain sizing procedure, as shown in fig. 6 b. Fig. 6c shows identified grains marked with numbers and boundaries outlined by contours. The diameter of each grain of the material is defined as the diameter of its equivalent circle. By measuring the respective areas of the test piece, the distribution of the crystal grain sizes can be estimated. The grain diameter of the material is in the range of 82.80-937.23 mu mWithin, and the average grain size was 448.75 μm. The histogram of the grain size distribution is shown in fig. 7.
In this patent, the fatigue limit of the arc additive Ti-6Al-4V material studied here was determined to be σ, with reference to the mechanical properties of the additive Ti-6Al-4V material with a similar microstructuref441.6 MPa. The coefficient κ is 1.25, which means that σ is the length of crack propagation when the grain size D is reachedymIncrease to sigmaf1.25 times that required to cause dislocation of the α + β bundles, 1.25 times greater than the driving force for cracking of the α crystals.
Using the above parameters, the local yield strength σ of the material is calculatedymAs shown in fig. 8. The transition point of the crack length from the microscopic small cracks to the physical small and long crack stages is about 4 to 5 times the grain diameter D of the material under study.
In the present example, the geometric correction factor Y for the crack to be investigated2Is composed of
Figure BDA0002999439130000112
Where b is 2.5mm, the width of the test piece in the patent.
According to the data obtained by the in-situ fatigue experiment in the step S1, the a-N experiment data are converted into phi 'by using the parameters determined in the above steps'mφ′cσym-da/dN data and plotted in a log-log coordinate system, and performing linear regression fitting based on least squares on the data to obtain material parameters (lnA, n) of the fatigue crack propagation model, wherein the mean and covariance matrices of the fitting parameters (lnA, n) are μ ═ 4.151,1.586) and
Figure BDA0002999439130000121
the results of the mean fit and 95% confidence range are shown in solid and dashed lines, respectively, in fig. 9.
The ratio of load to stress R set by experiment is 0.1, and the maximum stress sigma of the test piece in the patent ismax＝476.19MPa
And S4, substituting all the parameter values obtained by calculation in the step S3 and the optimal values of the parameters A and n into the small crack propagation rate model in the step S2 to obtain a final small crack propagation rate model.
To verify the validity of the proposed model, the proposed model of this patent is compared with existing reference models and geometry-modified reference models. The experimental data and the predicted results of the crack propagation rate da/dN as a function of the crack length a are shown in fig. 10. The three models have different prediction results under the same crack length. Especially when a >0.6mm, the proposed model predicts higher crack propagation rates than the other two. The Sum of Squared Errors (SSE) under a logarithmic coordinate system fit comparing the small crack model proposed in this patent, the reference model without geometric correction and the reference model with geometric correction is shown in fig. 11, with a smaller SSE value indicating better fit performance. In this case, the model proposed by the present invention is superior to the other two models in terms of SSE, and the fitting performance of the model is improved by 11% compared to the reference model. In fig. 10 and 11, a model a is a model proposed in the present patent, a model B is a reference model existing in the prior art, and a model C is a reference model subjected to geometric correction.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims (7)

1. A crack propagation rate model for small cracks, characterized by: which comprises the following steps:
s1, establishing a primary small crack propagation rate model, wherein the model expression is as follows:
da/dN＝A(φ′mφ′cσym)n
wherein da/dN is the crack propagation rate, A and n are material parameters, A and n can be determined by using fatigue experiment data, and sigma isymTo give local flexionStrength of the garment, phi'm，φ′cMonotonic crack tip opening displacement and cyclic crack tip opening displacement, respectively, taking into account the form factor; phi'm，φ′cThe expressions of (a) are respectively as follows:
φ′m＝Y2φm
and
φ′c＝Y2φc
wherein, Y2Is a crack geometry correction factor that follows the format defined in the stress intensity factor; using a single crack tip opening displacement phimAnd cyclic crack tip opening displacement phicCalculating a formula to obtain phi'm，φ′cExpression of (1), monotonic crack tip opening displacement phimAnd cyclic crack tip opening displacement phicThe expression of (a) is as follows:
Figure FDA0003645412920000011
and
Figure FDA0003645412920000012
wherein σmaxThe maximum stress to which the test piece is subjected; sigmaysMacroscopic yield strength; a is the crack length; r is stress ratio; e ' is the effective Young's modulus, and E ' is defined as:
Figure FDA0003645412920000013
wherein v is the Poisson's ratio and E is the Young's modulus;
s2, determining local yield strength sigmaymWherein the local yield strength σymThe calculation formula of (a) is as follows:
Figure FDA0003645412920000014
wherein σfIs the fatigue limit; a is the crack length; d is the average grain size; sigmaysMacroscopic yield strength; the coefficient kappa reflects the change rate of the crack propagation resistance of the small cracks in a single crystal grain, and the value of the coefficient kappa is determined by the dislocation slip resistance of the microstructure of the material;
s3, correcting the established initial small crack propagation rate model and correcting the local yield strength sigmaymSubstituting the small crack propagation rate model into the small crack propagation rate model to obtain a corrected small crack propagation rate model as follows:
Figure FDA0003645412920000021
and is
Figure FDA0003645412920000022
2. The crack propagation rate model for small cracks as claimed in claim 1, wherein: local yield strength σ in step S2ymThe local yield strength varies according to the size of the crack and the size of the crystal grain in order to characterize the microscopic parameters of the local yield behavior of the material; local yield strength at the onset of small cracks σymThe value of (b) is the fatigue limit, the size of the plastic zone at the tip of the crack and the number of grains in the plastic zone increase with increasing crack length, the local yield strength of the plastic zone increases, and the local yield strength σ increasesymFrom fatigue limit value σfMonotonously increasing to macroscopic yield strength value sigmays。
3. A method of crack growth rate modeling of a titanium alloy material using the crack growth rate model for small cracks of claim 1, characterized by: which comprises the following steps:
s1, carrying out an in-situ fatigue test on the arc additive Ti-6Al-4V alloy material test piece to obtain a-N experimental data, and calculating to obtain a data value of the crack propagation rate da/dN;
s2, determining the Young modulus E, the average grain size D and the local yield strength sigma in the crack propagation rate model based on the microstructure characteristics and the mechanical characteristics of the material and in combination with fatigue experiment dataymCrack geometry correction factor Y2And the values of the parameters A and n, the specific steps are as follows:
s21, carrying out tensile test on the titanium alloy material test piece, and obtaining the Young modulus and the macroscopic yield strength of the material as E-96 GPa and sigmays＝920MPa；
S22, inspecting the arc additive Ti-6Al-4V alloy material test piece by using a metallographic microscope to obtain the grain size distribution of the material, and obtaining the average grain size D of the material to be 448.75 mu m;
s23 geometric correction factor Y of crack2Comprises the following steps:
Figure FDA0003645412920000023
wherein b is the width of a fatigue test piece made of the titanium alloy material, and in the fatigue test, b is 2.5 mm;
s24, determining the local yield strength of the Ti-6Al-4V alloy material test piece and the fatigue limit sigma of the Ti-6Al-4V alloy material test piecef441.6MPa, coefficient κ 1.25, local yield strength σymThe expression of (a) is:
Figure FDA0003645412920000031
s25, converting the a-N experimental data into phi 'based on the data obtained by the in-situ fatigue experiment in the step S1 and by utilizing the parameters determined in the steps S21 to S24'mφ′cσymDrawing da/dN data in a log-log coordinate system, and performing least square method-based linear regression fitting on the data to obtain fatigue crack propagationThe material parameters (lnA, n) of the model, the mean and covariance matrices of the fitted material parameters (lnA, n) were μ ═ 4.151,1.586) and
Figure FDA0003645412920000032
obtaining the optimal values of the parameters A and n;
s3, substituting the parameter values obtained in the step S2 into the small crack propagation rate model in the step S1 to obtain the final small crack propagation rate model of the arc additive titanium alloy material, wherein the small crack propagation rate model comprises the following steps:
Figure FDA0003645412920000033
and is
Figure FDA0003645412920000034
And
Figure FDA0003645412920000035
wherein σmaxThe maximum stress to which the test piece is subjected; r is the stress ratio.
4. The method of modeling crack propagation rate for a titanium alloy material of claim 3, wherein: step S1 specifically includes: performing in-situ fatigue test on the arc additive Ti-6Al-4V alloy material, observing crack propagation behavior by using a scanning electron microscope, and applying stress ratio R to the test piece to be 0.1 and maximum force FmaxRecording the state of cracks on the test piece in different loading cycle periods by using a scanning electron microscope under a sinusoidal cyclic load with the frequency of 5Hz of 1kN, then obtaining the length a of the cracks by using an image of the scanning electron microscope, and obtaining a-N data of the test piece by combining with the corresponding cycle number N; then, the data value of the crack propagation rate da/dN can be calculated by using every two adjacent points on the a-N curve.
5. The method of modeling crack propagation rate for a titanium alloy material of claim 4, wherein: in step S1, the titanium alloy material is a Ti-6Al-4V alloy block manufactured by an electric arc additive system, and the Ti-6Al-4V alloy block is prepared on a forged Ti-6Al-4V substrate by adopting a cold metal transition arc welding mode.
6. The method of modeling crack propagation rate for a titanium alloy material of claim 5, wherein: the specific steps for preparing the Ti-6Al-4V alloy block are as follows:
firstly, planning a path by additive driving software according to the shape of an alloy block to be prepared;
secondly, the six-axis robot drives a welding machine to move according to the planned material increase path, and the welding machine is driven by the robot to realize the process of gradually forming a metal part from a line-surface-body of a test piece to be prepared on the basis of the layer-by-layer stacking principle by adding Ti-6Al-4V wire materials, wherein the arc current is 150A, the welding wire feeding speed is 2m/min, the welding gun advancing speed is 4m/min, the layer-to-layer vertical construction interval is 5mm, and the geometric dimension of the prepared Ti-6Al-4V alloy block is 300mm multiplied by 250mm multiplied by 20 m.
7. The method of modeling crack propagation rate for a titanium alloy material of claim 6, wherein: machining the Ti-6Al-4V alloy to obtain a plurality of fatigue test pieces with the geometrical shapes of dog bones, wherein the width of the center of each test piece is 2.5mm, and a single notch with the depth of 0.085mm and the width of 0.2mm is formed in the center of each test piece, so that the propagation direction of cracks on each test piece can be perpendicular to the construction direction and the deposition direction; in order to facilitate the imaging of the scanning electron microscope, the surface of the test piece is polished to enable the final thickness of the test piece to be 0.85 mm.
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