CN110763566A - Method for determining circumferential thickness anisotropy coefficient of anisotropic pipe - Google Patents
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Abstract
A method for determining the circumferential direction thickness anisotropy coefficient of an anisotropic pipe belongs to the field of pipe performance testing. The method comprises the following steps: acquiring stress and strain experimental data of a pipe sample in a bidirectional stress state under different loading paths through experiments; regression is carried out on the discrete stress-strain experimental data under each loading path, and flowing stress-strain curves in two directions are represented into a continuous function form; selecting equivalent strengthening state parameters, and selecting the flow stress of an axial uniaxial stress state as equivalent stress; fourthly, stress and strain data corresponding to different stress paths under the same equivalent strengthening state parameter are calculated by utilizing the regression curve; fifthly, selecting a proper yield function f; sixthly, determining an undetermined coefficient matrix of the yield function f; and seventhly, further calculating by using a plastic flow criterion through the yield function f to obtain the circumferential anisotropy coefficient of the pipe. The method can accurately determine the circumferential direction thick anisotropy coefficients of various anisotropic pipes.
Description
Technical Field
The invention belongs to the field of pipe performance testing, and particularly relates to a method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe.
Background
The high-pressure forming in the pipe is an advanced forming method for producing hollow variable-section complex parts, and the parts manufactured by the method have excellent comprehensive mechanical properties such as high strength, large bending modulus and the like, so that the parts are increasingly widely applied in the fields of automobiles, aviation, aerospace, sports vehicles and the like. However, the pipe used for internal high pressure forming is generally formed by extrusion or rolling and then coil welding, has obvious anisotropy along the axial direction and the circumferential direction of the pipe, and is easy to have the defects of unstable wrinkling or local thinning and overlarge fracture and the like in the plastic deformation process. When a new part is developed, a mold needs to be repeatedly tested and modified, so that time and labor are wasted, and the cost is high. Therefore, before forming, accurate finite element analysis is carried out by using an accurate pipe plastic constitutive relation model so as to realize accurate prediction and accurate control on the pipe plastic deformation behavior. The axial and circumferential anisotropy coefficients of the pipe are the basis for constructing an accurate plastic constitutive relation model of the pipe, and the accurate determination of the constitutive relation model is very important.
As the pipe has closed geometric characteristics, the axial direction can also refer to a plate testing method, an arc-shaped unidirectional tensile sample is cut along the axial direction of the pipe, the end part of the sample is flattened, and the axial direction thickness anisotropy coefficient of the pipe is obtained through a unidirectional tensile test. For the circumferential direction of the pipe, the large-diameter rolled and coil-welded pipe can replace the coil-welded pipe by testing the anisotropy coefficient of the original plate approximately, but if the small-diameter coil-welded pipe and the extruded pipe are also cut and then subjected to flattening measurement, obvious plastic deformation can be generated in the flattening process, even cracking is generated in the flattening process, so that the obtained circumferential anisotropy coefficient is inaccurate, and the accurate plastic constitutive relation cannot be constructed.
Through searching and finding the determination technology of the circumferential direction thick anisotropy coefficient of the pipe, the patent with the authorization notice number of CN104949884A discloses a determination method of the circumferential direction thick anisotropy coefficient of the pipe, and the invention content is as follows: and (3) cutting out a hoop tensile sample along the hoop direction of the pipe, and obtaining the hoop thickness anisotropy coefficient of the pipe through a hoop tensile test. However, in the method, friction force exists between the sample and the fixture used during testing, so that the experimental result is inaccurate. The patent CN 109708969A-a method for determining anisotropy and tension-compression asymmetry characteristics of a metal material, the invention needs to perform conventional uniaxial tension and uniaxial compression tests on the material, determine microstructure information and texture distribution information under the conditions of uniaxial tension and uniaxial compression through EBSD, and combine with a virtual experiment based on a VPSC model, so as to obtain the anisotropy and tension-compression asymmetry characteristics of the material. The method mainly analyzes the anisotropic yield and the tension-compression asymmetric yield characteristics of the material, a method for testing the circumferential thickness anisotropy coefficient of the pipe is not provided, an EBSD (electron back scattering) experiment is required, the anisotropic yield characteristics of the material are analyzed through the microstructure information of the original material, and the method is very difficult for many scholars without the microstructure foundation of the material.
So far, no reliable method for determining the circumferential thickness anisotropy coefficient of the pipe exists, and the method becomes an international difficult problem.
Disclosure of Invention
The invention provides a method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe, aiming at solving the problems that the circumferential thickness anisotropy coefficient of the pipe cannot be accurately determined by the existing methods, and further the deformation performance of the anisotropic pipe cannot be comprehensively and accurately described.
The technical scheme adopted by the invention for solving the problems is as follows:
a method for determining the circumferential direction thickness anisotropy coefficient of an anisotropic pipe is shown in figure 1 and comprises the following steps:
cutting a tube blank to be tested into a tube sample, and performing an experiment of the tube in a two-way stress state to obtain stress and strain experiment data of the tube sample in the two-way stress state under different loading paths;
step two, respectively regressing the discrete stress-strain experimental data under each loading path obtained in the step one, and representing the flow stress-strain curves in two directions obtained under each loading path into a continuous function form;
selecting appropriate equivalent strengthening state parameters, and selecting the flow stress of an axial uniaxial stress state as equivalent stress;
step four, calculating stress and strain data corresponding to different stress paths under the same equivalent strengthening state parameter by using regression curves under different loading paths obtained in the step two;
step five, selecting a proper yield function f;
step six, determining an undetermined coefficient matrix of the yield function f according to the stress and strain data determined in the step four;
and step seven, further calculating to obtain the circumferential direction anisotropy coefficient of the pipe by using a plastic flow criterion through the yield function f determined in the step six.
Further, in the first step, the experiment in the pipe bidirectional stress state is to apply pressure inside the pipe and apply axial tension or pressure at the end of the pipe at the same time, so that the pipe deforms in a set linear stress path, and flow stress and flow strain experiment data in the pipe bidirectional stress state are obtained, including the axial and circumferential flow stress and axial and circumferential flow strain data of the pipe, and the experimental schematic diagram is shown in fig. 3.
The second embodiment is as follows: the experiment in the two-way stress state of the pipe in the first step is a free bulging experiment with two fixed ends of the pipe, the experimental schematic diagram is shown in fig. 4, different stress loading paths are obtained by changing the length of the bulging area of the middle pipe, and two-way stress and strain components under different stress paths are obtained. Other steps are the same as those in the first embodiment.
Further, in the second step, the regression function used for performing regression on the discrete stress-strain experimental data under each loading path is a piecewise power exponential function, a quadratic polynomial function, or a quartic polynomial function.
(1) The expression of the piecewise power exponential function is as follows:
wherein σ is a flow stress component; ε is the flow strain component; k is the number of segments into which the stress-strain curve is divided; kkIs the intensity coefficient corresponding to the k section; n iskIs the strain hardening index of the corresponding k-th segment.
(2) The quadratic polynomial regression function expression is:
X1(σmax-σ)2+X2(ε-εy)(σmax-σ)+X3(ε-εy)2-1＝0
wherein epsilonyAnd σyRespectively is a strain component and a stress component corresponding to the initial yield; epsilonmaxAnd σmaxRespectively corresponding strain component and stress component of the experimental point with the maximum stress value; epsilonAAnd σARespectively is a strain component and a stress component corresponding to an arbitrary point A between the initial yield and the maximum stress value; x1,X2,X3For three undetermined coefficients, three experimental points were used in the model to determine: experimental point at initial yield (. epsilon.)y,σy) Experimental point (epsilon) corresponding to maximum stress valuemax,σmax) And any experimental point A (epsilon) between the twoA,σA)。
(3) The expression of the fourth-order polynomial regression function is as follows:
X1(σmax-σ)4+X2(σmax-σ)3(ε-εy)+X3(σmax-σ)2(ε-εy)2+X4(σmax-σ)(ε-εy)3+X5(ε-εy)4＝1
wherein epsilonyAnd σyRespectively is a strain component and a stress component corresponding to the initial yield; epsilonmaxAnd σmaxRespectively corresponding strain component and stress component of the experimental point with the maximum stress value; epsilonA、εB、εCAnd σA、σB、σCA strain component and a stress component corresponding to any point A, B, C between the two initial yield and maximum stress values, respectively; x1,X2,X3,X4,X5For three undetermined coefficients, it was determined in this model using five experimental points: experimental point at initial yield (. epsilon.)y,σy) Experimental point (epsilon) corresponding to maximum stress valuemax,σmax) And any experimental point A (epsilon) between the twoA,σA) Experimental Point B (. epsilon.)B,σB) And experimental point C (. epsilon.)C,σC)。
Further, in the third step, the equivalent strengthening state parameter is plastic work WpFirst order increment of plastic work dWpOr second order increase of plastic work d2Wp. The same equivalent reinforcement state parameter reflects the same reinforcement state, i.e., is differentThe equivalent strengthening state parameters under the loading path are the same.
(1) When taking out the plastic work WpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein p represents that all experimental quantities are plastic components,is the incremental component of the axial plastic strain of the pipe,
is the incremental component of hoop plastic strain of the pipe, sigmazIs the axial stress component, σ, of the pipeθIs the hoop stress component of the pipe.
(2) When the first-order increment dW of the plastic work is takenpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein σijFor any of the components of the stress,
is any incremental component of plastic strain.
(3) Second order increment d of plastic work2WpWhen the equivalent enhanced state parameter is obtained, the method passes
Stress and strain data under different loading paths under the same strengthening state are calculated. The specific calculation method is shown in fig. 5.
Further, in the fifth step, the selected yield function is uniformly expressed asWherein sigmazAnd σθIs a tubeStress components of the material in two main axis directions (axial direction and circumferential direction), A is a matrix of coefficients to be determined, and sigmaiM is the power of the yield function for equivalent stress; the yield function is Hill series yield criterion, Barlat89 yield criterion or YLd2000-2d yield criterion, and the selectable yield functions have a wide range. Further, in the sixth step, the method for determining the undetermined coefficient matrix is as follows: the experimental data in the first step comprises stress and strain components of two main shafts (axial direction and circumferential direction) of a plurality of groups of pipes, the stress and strain components are further processed into stress and strain data in the fourth step, a coefficient matrix A to be determined can be determined by utilizing the data, the plastic strain experimental data are utilized as much as possible when the coefficient matrix A is determined, and the more the plastic strain data are utilized, the more the anisotropic plastic flow characteristics of the material can be comprehensively and accurately described.
Further, in the seventh step, the plastic flow criterion calculates the axial and circumferential strain increment components for the Drucker flow criterion (see formula (1)):
wherein d εzAnd d εθRespectively the axial and circumferential plastic strain increment of the pipe; d λ is a constant.
Further according to the definition of the anisotropy coefficient of thickness and the condition that the volume of the material is not changed, the anisotropy coefficient r of the circumferential direction of the pipeθExpressed as:
wherein d εθ、dεzAnd d εtRespectively the plastic strain increment in the stretching direction, the width direction and the thickness direction corresponding to the annular unidirectional stretching test of the pipe.
The invention has the beneficial effects that:
the blank of the experiment is an original tube blank, the shape of the tube is not required to be damaged, pre-deformation is not introduced, deformation areas of the tube blank tested in all the experiments are in a free deformation state and are not in contact with a die, extra friction force is not introduced, pre-deformation caused by a traditional flattened sample and influence caused by friction between the sample and a used fixture in a hoop tensile test are avoided, and the obtained experiment result can accurately reflect the plastic deformation performance of the tube;
the yield criterion of the pipe is determined by directly utilizing experimental data obtained by the pipe in the two-way stress state in the experiment, the deformation type of the pipe in the two-way stress state is close to the deformation type of the pipe in the high-pressure forming process in the pipe, the plastic deformation characteristic of the pipe under the deformation can be more accurately described by using the yield criterion constructed by the experimental data of similar deformation types, the determined yield criterion is more reasonable and accurate, and the reasonable yield criterion ensures that the further determined annular thickness anisotropy coefficient is accurate and reliable;
and thirdly, the method does not need additional knowledge related to materials science, does not need EBSD, and is simple and easy to understand and popularize and apply.
Fourthly, the plastic constitutive relation which can accurately reflect the annular plastic flow characteristic of the pipe can be constructed by using the annular thickness anisotropy coefficient of the pipe determined by the invention, and a foundation is provided for the precise finite element analysis of the forming of the integral component with the complicated section of the pipe.
Fifthly, the method can be used for determining the circumferential direction thick direction anisotropy coefficient of various anisotropic pipes, such as aluminum alloy, titanium alloy, magnesium alloy, high-strength steel and the like, and has wide application range.
And sixthly, initial samples of the experiment related to the invention are all original tube blanks with certain lengths, and the samples are easy to process.
Drawings
FIG. 1 is a schematic diagram of a method for determining the circumferential direction anisotropy coefficient of an anisotropic pipe material according to the present invention;
FIG. 2 is a schematic view of the principal coordinate axes of the pipe of the present invention;
FIG. 3 is a schematic diagram of the experimental principle of controllable bidirectional loading of the pipe according to the present invention;
FIG. 4 is a schematic diagram of the experimental principle of free bulging at two ends of the pipe according to the present invention;
FIG. 5 is an explanatory diagram of experimental data calculation under the condition of calculating the same equivalent strengthening state parameter under different stress states; wherein (a) represents a schematic diagram for calculating plastic work in a uniaxial tensile stress state, and (b) represents a schematic diagram for calculating plastic work in a biaxial stress state;
FIG. 6 is an explanatory diagram of experimental data calculation under the condition of calculating the same equivalent strengthening state parameter under different stress states; wherein, (a) shows a schematic diagram for calculating the first-order increment of plastic work in a uniaxial tensile stress state, and (b) shows a schematic diagram for calculating the first-order increment of plastic work in a biaxial stress state;
FIG. 7 is an explanatory diagram of experimental data calculation under the condition of calculating the same equivalent strengthening state parameter under different stress states; wherein, (a) shows a schematic diagram for calculating the second-order increment of plastic work in a uniaxial tensile stress state, and (b) shows a schematic diagram for calculating the second-order increment of plastic work in a biaxial stress state;
FIG. 8 is a graph of regression results of discrete stress-strain experimental data under two loading paths; the method comprises the following steps of (a) representing a regression result of axial unidirectional tensile stress-strain experimental data, and (b) representing a regression result of two-direction stress-strain component experimental data of a tubular product bidirectional controllable loading experiment when the stress ratio of a shaft collar is 1: 4;
in the figure, 1 is the initial tube blank.
Detailed Description
The technical solution of the present invention will be further described with reference to specific examples.
The implementation of the present invention will be described with reference to FIGS. 1 to 3 and 7, taking an IF cold-rolled coil-welded steel tube with an outer diameter of 46mm and a wall thickness of 0.7mm as an example:
cutting a pipe to be tested into pipes with the length of 200mm, performing 2 groups of controllable bidirectional loading experiments on the pipes under different stress ratios, and acquiring experimental data of stress and strain of the pipes under a bidirectional stress state as shown in figure 3;
the pipe bidirectional loading experiment is carried out on a special pipe bidirectional loading experiment testing device (refer to a patent CN105300802B), tensile or compressive load is applied to the end part of a pipe, pressure medium is applied to the inside of the pipe to enable the pipe to deform under a set stress path, experimental data (axial and circumferential stress and strain data of the pipe) under the bidirectional stress state of the pipe are obtained, and a plurality of groups of experimental data are obtained by changing the set stress path;
step two, respectively regressing the discrete stress-strain experimental data under the two loading paths obtained in the step one by utilizing a quartic polynomial regression function, expressing the flow stress-strain curves in two directions obtained under each loading path into a continuous function form, and showing the regression result as shown in figure 8;
step three, taking second-order increment d of plastic work2WpSelecting the flow stress of an axial uniaxial stress state as equivalent stress for equivalent strengthening state parameters;
step four, taking the equivalent stress sigmaz＝σi244.22 order d2WpThe stress and strain components for each loading path were calculated as 0.05, and the results are shown in table 1.
TABLE 1 stress data points for the same plastic work
Step five, selecting a Hill48 yield criterion for the yield function f, considering the coincidence of the stress main axis and the anisotropy main axis direction of the pipe, and the expression is
Step six, the yield function containing 2 undetermined parameters a can be seen from the formula (3)1,a2It can be determined from 2 sets of stress and strain data obtained in step four, and the determined coefficients are shown in table 2.
TABLE 2 coefficients of Hill48 yield function
And step seven, the coefficient of the yield criterion obtained in the step six is shown in the table 2, and the thickness anisotropy coefficient of the annular pipe can be further calculated and obtained to be 2.02 according to the formula (2).
The present invention is not limited to the above embodiments, and any person skilled in the art can make many modifications and equivalent variations by using the above-described structures and technical contents without departing from the scope of the present invention.
Claims (10)
1. A method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe is characterized by comprising the following steps:
cutting a tube blank to be tested into a tube sample, and performing an experiment of the tube in a two-way stress state to obtain stress and strain experiment data of the tube sample in the two-way stress state under different loading paths;
step two, respectively regressing the discrete stress-strain experimental data under each loading path obtained in the step one, and representing the flow stress-strain curves in two directions obtained under each loading path into a continuous function form;
selecting appropriate equivalent strengthening state parameters, and selecting the flow stress of an axial uniaxial stress state as equivalent stress;
step four, calculating stress and strain data corresponding to different stress paths under the same equivalent strengthening state parameter by using regression curves under different loading paths obtained in the step two;
step five, selecting a proper yield function f;
step six, determining an undetermined coefficient matrix of the yield function f according to the stress and strain data determined in the step four;
and step seven, further calculating to obtain the circumferential direction anisotropy coefficient of the pipe by using a plastic flow criterion through the yield function f determined in the step six.
2. The method for determining the circumferential thickness anisotropy coefficient of an anisotropic tubular product according to claim 1, wherein in the step one, the experiment in the bidirectional stress state of the tubular product is to apply pressure inside the tubular product and simultaneously apply axial tension or pressure on the end part of the tubular product, so that the tubular product deforms under the set linear stress path, and flow stress and flow strain experiment data in the bidirectional stress state of the tubular product are obtained, wherein the flow stress and flow strain experiment data in the axial direction and the circumferential direction of the tubular product comprise the flow stress and the flow strain data in the axial direction and the circumferential direction of the tubular product.
3. The method for determining the circumferential thickness anisotropy coefficient of the anisotropic tubular product according to claim 1 or 2, wherein in the second step, the regression function used for performing regression on the discrete stress-strain experimental data under each loading path is a piecewise power exponential function, a quadratic polynomial function or a quartic polynomial function;
(1) the expression of the piecewise power exponential function is as follows:
wherein σ is a flow stress component; ε is the flow strain component; k is the number of segments into which the stress-strain curve is divided; kkIs the intensity coefficient corresponding to the k section; n iskIs the strain hardening index of the corresponding k section;
(2) the quadratic polynomial regression function expression is:
X1(σmax-σ)2+X2(ε-εy)(σmax-σ)+X3(ε-εy)2-1＝0
wherein epsilonyAnd σyRespectively is a strain component and a stress component corresponding to the initial yield; epsilonmaxAnd σmaxRespectively corresponding strain component and stress component of the experimental point with the maximum stress value; epsilonAAnd σARespectively is a strain component and a stress component corresponding to an arbitrary point A between the initial yield and the maximum stress value; x1,X2,X3For three undetermined coefficients, three experimental points were used in the model to determine: experimental point at initial yield (. epsilon.)y,σy) Experimental point (epsilon) corresponding to maximum stress valuemax,σmax) And any experimental point A (epsilon) between the twoA,σA)；
(3) The expression of the fourth-order polynomial regression function is as follows:
X1(σmax-σ)4+X2(σmax-σ)3(ε-εy)+X3(σmax-σ)2(ε-εy)2+X4(σmax-σ)(ε-εy)3+X5(ε-εy)4＝1
wherein epsilonyAnd σyRespectively is a strain component and a stress component corresponding to the initial yield; epsilonmaxAnd σmaxRespectively corresponding strain component and stress component of the experimental point with the maximum stress value; epsilonA、εB、εCAnd σA、σB、σCA strain component and a stress component corresponding to any point A, B, C between the two initial yield and maximum stress values, respectively; x1,X2,X3,X4,X5For three undetermined coefficients, it was determined in this model using five experimental points: experimental point at initial yield (. epsilon.)y,σy) Experimental point (epsilon) corresponding to maximum stress valuemax,σmax) And any experimental point A (epsilon) between the twoA,σA) Experimental Point B (. epsilon.)B,σB) And experimental point C (. epsilon.)C,σC)。
4. The method for determining the circumferential thickness anisotropy coefficient of the anisotropic pipe according to claim 1 or 2, wherein in the third step, the equivalent strengthening state parameter is plastic work WpFirst order increment of plastic work dWpOr second order increase of plastic work d2Wp；
(1) When taking out the plastic work WpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein p represents that all experimental quantities are plastic components,
is the incremental component of the axial plastic strain of the pipe,
is the incremental component of hoop plastic strain of the pipe, sigmazIs the axial stress component, σ, of the pipeθFor dividing the hoop stress of a pipeAn amount;
(2) when the first-order increment dW of the plastic work is takenpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein σijFor any of the components of the stress,
is any plastic strain increment component;
(3) second order increment d of plastic work2WpWhen the equivalent enhanced state parameter is obtained, the method passesStress and strain data under different loading paths under the same strengthening state are calculated.
5. The method for determining the circumferential direction thickness anisotropy coefficient of the anisotropic pipe according to claim 3, wherein in the third step, the equivalent strengthening state parameter is plastic work WpFirst order increment of plastic work dWpOr second order increase of plastic work d2Wp；
(1) When taking out the plastic work WpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein p represents that all experimental quantities are plastic components,is the incremental component of the axial plastic strain of the pipe,
is the incremental component of hoop plastic strain of the pipe, sigmazIs the axial stress component, σ, of the pipeθIs the pipe circumferential stress component;
(2) when the first-order increment dW of the plastic work is takenpWhen the equivalent enhanced state parameter is obtained, the method passes
Calculating stress and strain data under different loading paths under the same strengthening state; wherein σijFor any of the components of the stress,
is any plastic strain increment component;
(3) second order increment d of plastic work2WpWhen the equivalent enhanced state parameter is obtained, the method passes
Stress and strain data under different loading paths under the same strengthening state are calculated.
6. The method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe according to claim 1, 2 or 5, wherein in the fifth step, the selected yield function is uniformly expressed asWherein sigmazAnd σθIs the axial and circumferential stress components of the two main shaft directions of the pipe, A is a matrix of coefficients to be determined, sigmaiM is the power of the yield function for equivalent stress; the yield function is the Hill series yield criterion, the Barlat89 yield criterion, or the YLd2000-2d yield criterion.
7. The method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe according to claim 3, wherein in the fifth step, the selected yield function is uniformly expressed as
Wherein sigmazAnd σθIs the axial and circumferential stress components of the two main shaft directions of the pipe, A is a matrix of coefficients to be determined, sigmaiM is the power of the yield function for equivalent stress; the yield function is the Hill series yield criterion, the Barlat89 yield criterion, or the YLd2000-2d yield criterion.
8. The method for determining the circumferential thickness anisotropy coefficient of an anisotropic pipe according to claim 4, wherein in the fifth step, the selected yield function is uniformly expressed as
Wherein sigmazAnd σθIs the axial and circumferential stress components of the two main shaft directions of the pipe, A is a matrix of coefficients to be determined, sigmaiM is the power of the yield function for equivalent stress; the yield function is the Hill series yield criterion, the Barlat89 yield criterion, or the YLd2000-2d yield criterion.
9. The method for determining the circumferential thickness anisotropy coefficient of an anisotropic tubular product according to claim 1, 2, 5, 7 or 8, wherein in the seventh step, the plastic flow criterion is used for calculating the axial and circumferential strain increment components for Drucker flow criterion:
wherein d εzAnd d εθRespectively the axial and circumferential plastic strain increment of the pipe; d λ is a constant;
further according to the definition of the anisotropy coefficient of thickness and the condition that the volume of the material is not changed, the anisotropy coefficient r of the circumferential direction of the pipeθExpressed as:
wherein d εθ、dεzAnd d εtRespectively the plastic strain increment in the stretching direction, the width direction and the thickness direction corresponding to the annular unidirectional stretching test of the pipe.
10. The method for determining the circumferential thickness anisotropy coefficient of the anisotropic tube according to claim 6, wherein in the seventh step, the plastic flow criterion is used for calculating the axial and circumferential strain increment components for Drucker flow criterion:
wherein d εzAnd d εθRespectively the axial and circumferential plastic strain increment of the pipe; d λ is a constant;
further according to the definition of the anisotropy coefficient of thickness and the condition that the volume of the material is not changed, the anisotropy coefficient r of the circumferential direction of the pipeθExpressed as:
wherein d εθ、dεzAnd d εtRespectively the plastic strain increment in the stretching direction, the width direction and the thickness direction corresponding to the annular unidirectional stretching test of the pipe.
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| CN111842547A (en) * | 2020-07-17 | 2020-10-30 | 太原科技大学 | Novel method for straightening metal plate with tension-compression asymmetry |
| CN112100820A (en) * | 2020-08-25 | 2020-12-18 | 华南理工大学 | Excel-based anisotropic yield function parameter calibration method |
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