CN110849727A - Method for determining anisotropy parameters of pipe - Google Patents

Method for determining anisotropy parameters of pipe Download PDF

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CN110849727A
CN110849727A CN201911186271.XA CN201911186271A CN110849727A CN 110849727 A CN110849727 A CN 110849727A CN 201911186271 A CN201911186271 A CN 201911186271A CN 110849727 A CN110849727 A CN 110849727A
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stress
ratio
pipe
anisotropy
formula
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CN110849727B (en
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何祝斌
张坤
林艳丽
苑世剑
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Dalian University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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    • G01N1/28—Preparing specimens for investigation including physical details of (bio-)chemical methods covered elsewhere, e.g. G01N33/50, C12Q

Abstract

A method for determining anisotropy parameters of a pipe belongs to the field of pipe performance testing. The method comprises the following steps: firstly, cutting a section bar sample along the axial direction of the pipe, and carrying out a unidirectional tensile experiment to obtain the axial yield stress of the pipe; performing two-group pipe bidirectional loading experiments on the pipe to be tested, recording the stress ratio, and measuring the strain increment ratio under the corresponding loading condition, wherein the loading path is linear; thirdly, establishing a relation between the stress ratio, the strain increment ratio and the yield stress in each direction; establishing the relationship between the stress ratio, the strain increment ratio and the thickness anisotropy coefficient in each direction; and fifthly, substituting the stress ratio and the strain increment ratio in the step two into the relational expressions established by the step three and the step four respectively, and obtaining anisotropic parameters by solving an equation set: hoop yield stress, double equal tension yield stress, axial thickness anisotropy coefficient and hoop thickness anisotropy coefficient. The method avoids the plastic deformation of the pipe before testing and the influence of the pre-deformation on the anisotropic parameters, and the determined anisotropic parameters are more accurate.

Description

Method for determining anisotropy parameters of pipe
Technical Field
The invention belongs to the field of pipe performance testing, and particularly relates to a method for determining anisotropic parameters of a pipe.
Background
Pipes are often used for the shaping of tubular parts. When the pipe is produced and prepared, the grain structure and the texture form inside the material are changed frequently and have certain directionality due to the severe plastic deformation of the material, so that the pipe has the characteristic of anisotropy. The main manifestation of anisotropy is the difference in yield stress and anisotropy coefficient in each direction along the pipe. The yield behavior and the plastic deformation behavior of the pipe are directly influenced by the anisotropic characteristics of the pipe in different directions, so that the deformation behavior of the pipe in the actual deformation process is influenced. Therefore, in order to accurately describe the characteristics of the pipe and to make accurate forming process parameters, it is necessary to obtain anisotropic parameters in all directions of the pipe, such as yield stress and anisotropy coefficient in the axial direction, yield stress and anisotropy parameter in the hoop direction.
For sheet materials, the method of testing the parameters of anisotropy in various directions (yield stress and thickness anisotropy coefficient) is very mature. The yield stress of the plate in a certain direction can be measured by adopting a GB/T228.1-2010 standard, and the thickness anisotropy coefficient of the plate in a certain direction can be measured by adopting a GB/T5027-2016 standard. By changing the sampling direction of the tensile sample, the anisotropic parameters (yield stress and thickness anisotropy coefficient) of the corresponding direction of the plate can be obtained. The pipe is of a circular closed structure and is completely different from the plane structure of the plate, so that the test method which is mature and applied to the plate cannot be directly applied to the pipe. The literature (On coherent modeling of aluminum alloys for tube hydroforming applications; Mikael Jansson, Larsgunnar Nilsson, Kjell Simonson; International Journal of plastics; 2005) unfolds and flattens the tube into a flat sheet, which is tested using the test method for flat sheets to obtain the anisotropy parameters of the tube. The method has the problems that the circular closed pipe generates obvious plastic deformation when being flattened into a plane plate, so that the measured result is not the performance of the original pipe and cannot represent the real anisotropic parameters of the pipe. The yield stress and the anisotropy coefficient of the pipe in the axial direction are measured by a unidirectional tensile test method by cutting a section bar sample from the pipe in the axial direction by some researchers. The yield stress of the pipe in the axial direction can be obtained. And because the section shape of the section bar sample is circular arc, the section bar sample can be curled and deformed in the width direction in the stretching process, so that the measured strain in the width direction is inaccurate, and the measured anisotropy coefficient is inaccurate. The patent (CN1865906) proposes a method for testing the hoop tensile property of a pipe, which obtains the hoop property of the pipe, such as the hoop yield stress, by directly stretching a hoop test sample of the pipe. The patent (CN104949884A) proposes a method for directly measuring the circumferential anisotropy coefficient of a pipe, which can obtain the circumferential anisotropy coefficient of the pipe. However, in the two methods, friction force exists between the sample and the used fixture during the test, which influences the experimental result and causes inaccurate test result. When the anisotropic parameters of the tested pipe are inaccurate and cannot accurately reflect the real performance of the pipe, the method is not suitable for representing the anisotropic characteristics of the pipe and formulating the process parameters. Due to the lack of anisotropic parameters of the pipe, the mechanical property of the pipe cannot be directly evaluated, so that the complex plastic deformation characteristic of the pipe cannot be comprehensively and accurately predicted, and the development and application of the pipe forming technology are limited to a great extent.
In order to accurately obtain the anisotropic parameters of the pipe and accurately describe the anisotropic characteristics of the pipe, an accurate determination method of the anisotropic parameters of the pipe needs to be established.
Disclosure of Invention
The invention provides a method for determining anisotropic parameters of a pipe, aiming at solving the problem that the conventional experimental test method cannot or cannot accurately determine the anisotropic characteristic parameters of the pipe.
The technical scheme adopted by the invention for solving the problems is as follows:
a method for determining the anisotropy parameters of a pipe comprises the following steps:
step one, cutting a section bar sample along the axial direction of the pipe, and carrying out a unidirectional tensile experiment to obtain the axial yield stress sigma of the pipez；
Step two, cutting the pipe to be tested into pipe samples, carrying out two-group pipe bidirectional loading experiments, recording stress ratio α, wherein the loading path is linear1、α2Measuring the incremental strain ratio β under corresponding loading conditions1、β2；
Step three, establishing the relationship between the stress ratio, the strain increment ratio and the yield stress in each direction:
Figure BDA0002292472840000021
wherein σbStress ratio α ═ σ for two-way equal tensile yield stressθ/σz，σθ、σzRespectively hoop stress and axial stress, and strain increment ratio β ═ d epsilonθ/dεz，dεθ、dεzRespectively, the hoop and axial strain increment components;
establishing the relationship between the stress ratio, the strain increment ratio and the anisotropy coefficient of the thickness direction in each direction:
Figure BDA0002292472840000022
or
Figure BDA0002292472840000023
Wherein r isz,rθThe yield stress of the tube in the axial direction and the annular direction is respectively, M is a material index, 8 is taken as a face-centered cubic material, and 6 is taken as a body-centered cubic material.
Step five, utilizing α in step two1、α2And β1、β2Respectively substituting the parameters into a formula (1), a formula (2) or a formula (3) to obtain a formula system, and solving the formula system to obtain anisotropic parameters: hoop yield stress sigmaθDouble equal tensile yield stress sigmabAxial thickness anisotropy coefficient rzAnnular thickness anisotropy coefficient rθ。
Further, in the second step, the bidirectional pipe loading experiment is carried out on a special bidirectional pipe loading experiment device, a tensile or compressive load is applied to the end part of the bidirectional pipe loading experiment sample, a pressure medium is applied to the interior of the sample, so that an analysis point on the sample deforms under a set stress path, and a strain increment ratio β of the analysis point on the sample under a stress ratio α is obtained, wherein the analysis point is a middle point of the outer surface of the sample in the length direction of the pipe.
Further, the relationship among the stress ratio, the strain increment ratio and the yield stress in each direction in the third step is established as follows:
for the plane stress state, the Hill48 yield criterion is expressed as:
Figure BDA0002292472840000031
in the formula, σz,σθSingle tensile yield stress, sigma, in axial and circumferential directions, respectively, of the pipeijFor any stress component, σ1Stress component, σ, in the direction of coordinate axis 12Stress component, σ, in the direction of coordinate axis 20The corresponding flow stress component is single-pulled in one direction along the axial direction.
According to Drucker's associated flow criteria:
Figure BDA0002292472840000032
in the formula, d ε1Increment of strain component in the direction of coordinate axis 1, d epsilon2D λ is a proportionality constant, which is an increase of the strain component in the direction of the coordinate axis 2.
Thus, the relationship of the stress ratio, the strain increment ratio and the yield stress in each direction is obtained as follows:
Figure BDA0002292472840000033
further, in the fourth step, the formula (2) is established as follows:
for the plane stress state, the Hill48 yield criterion is expressed as:
Figure BDA0002292472840000034
in the formula, rz,rθThe axial and circumferential anisotropy coefficients of the pipe are respectively.
According to Drucker's associated flow criteria:
Figure BDA0002292472840000041
therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure BDA0002292472840000042
further, in the fourth step, the formula (3) is established as follows:
for the in-plane stress state, the Balart89 anisotropic yield criterion is expressed as:
Figure BDA0002292472840000043
derived from Drucker's associated flow criteria
Figure BDA0002292472840000044
Therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure BDA0002292472840000045
further, in the second step, a plurality of groups of pipe bidirectional loading experiments are carried out to obtain a plurality of groups of experimental data (stress ratio α)1、α2、α3……αnApplication of herba Lycopodii inDelta ratio β1、β2、β3……βn) Step five, taking the established relational expressions of the stress ratio, the strain increment ratio and the yield stress in each direction and the established relational expressions of the stress ratio, the strain increment ratio and the thickness anisotropy coefficient in each direction as objective functions, and utilizing a plurality of groups of experimental data (stress ratio α)1、α2、α3……αnAnd strain delta ratio β1、β2、β3……βn) Fitting to obtain anisotropic parameters: hoop yield stress sigmaθDouble equal tensile yield stress sigmabAxial thickness anisotropy coefficient rzAnnular thickness anisotropy coefficient rθ。
The invention has the advantages of
The method provided by the invention can solve the problem that the conventional test method cannot accurately obtain the axial and circumferential anisotropy coefficients, the circumferential yield stress and the double equal-tensile yield stress of the pipe;
secondly, when the method provided by the invention is used for carrying out experimental test on the pipe, the clamp does not contact with the pipe test position, so that the influence of friction action is avoided, and the determined anisotropic parameters are more accurate;
the method provided by the invention avoids plastic deformation of the pipe before testing, thereby avoiding the influence of pre-deformation on the anisotropic parameters, and ensuring more accurate anisotropic parameters.
Drawings
FIG. 1 is a schematic process diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of the experimental principle of bidirectional loading of the pipe according to the present invention.
In the figure, 1 is a sample, and 1-1 is an analysis point on the sample.
Detailed Description
The technical solution of the present invention will be further described with reference to specific examples.
The implementation process of the invention is described by taking a 6061F state aluminum alloy extruded pipe with the outer diameter of 40mm and the wall thickness of 1.2mm as an example and combining the figure 1:
step one, alongCutting a section bar sample in the axial direction of the pipe, and performing a uniaxial tension experiment to obtain the axial yield stress sigma of the pipez＝94.1MPa；
Step two, cutting the pipe to be measured into a proper length of 270mm, performing 2 groups of pipe bidirectional loading experiments, wherein the loading path is linear and is recorded as α -0.25 and 1.0, and the measured strain increment ratio β -0.1662 and 0.4356;
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 three, establishing the relation between the stress ratio, the strain increment ratio and the yield stress in each direction
Figure BDA0002292472840000051
Wherein σbIs a bi-directional equal tensile yield stress.
Step four, establishing the relation between the stress ratio, the strain increment ratio and the thickness anisotropy coefficient in each direction
Figure BDA0002292472840000052
Step five, respectively substituting the stress ratio α and the strain increment ratio β in the step one into the relational expression of the stress ratio, the strain increment ratio and the yield stress in each direction established in the step three and the relational expression of the stress ratio, the strain increment ratio and the thickness anisotropy coefficient in each direction established in the step four to obtain an equation set, and obtaining the anisotropic parameter sigma through solving the equationsθ＝119.1MPa、σb＝96.3MPa、rz＝0.44、rθ＝1.01。
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method for determining the anisotropy parameters of a pipe is characterized by comprising the following steps:
step one, cutting a section bar sample along the axial direction of the pipe, and carrying out a unidirectional tensile experiment to obtain the axial yield stress sigma of the pipez；
Step two, cutting the pipe to be tested into pipe samples, carrying out two-group pipe bidirectional loading experiments, recording stress ratio α, wherein the loading path is linear1、α2Measuring the incremental strain ratio β under corresponding loading conditions1、β2；
Step three, establishing the relationship between the stress ratio, the strain increment ratio and the yield stress in each direction:
wherein σbStress ratio α ═ σ for two-way equal tensile yield stressθ/σz，σθ、σzRespectively hoop stress and axial stress, and strain increment ratio β ═ d epsilonθ/dεz，dεθ、dεzRespectively, the hoop and axial strain increment components;
establishing the relationship between the stress ratio, the strain increment ratio and the anisotropy coefficient of the thickness direction in each direction:
Figure FDA0002292472830000012
or
Figure FDA0002292472830000013
Wherein r isz,rθRespectively axial and circumferential yield stress of the pipe, wherein M is a material index, 8 is taken as a face-centered cubic material, and 6 is taken as a body-centered cubic material;
step five, utilizing α in step two1、α2And β1、β2Respectively substituting the parameters into a formula (1), a formula (2) or a formula (3) to obtain a formula system, and solving the formula system to obtain anisotropic parameters: hoop yield stress sigmaθDouble equal tensile yield stress sigmabAxial thickness anisotropy coefficient rzAnnular thickness anisotropy coefficient rθ。
2. The method for determining the anisotropy parameters of the tubular product as claimed in claim 1, wherein, in the second step, the bi-directional loading experiment of the tubular product is carried out on a special bi-directional loading experiment device of the tubular product, a tensile or compressive load is applied to the end of the bi-directional loading experiment sample of the tubular product, a pressure medium is applied inside the sample to deform an analysis point on the sample under a set stress path, and a strain increment ratio β of the analysis point on the sample under a stress ratio α is obtained, wherein the analysis point is a middle point of the outer surface of the sample in the length direction of the tubular product.
3. The method for determining the anisotropy parameter of the tubular product as claimed in claim 1 or 2, wherein the relationship between the stress ratio, the strain increment ratio and the yield stress in each direction in the three steps is established as follows:
for the plane stress state, the Hill48 yield criterion is expressed as:
Figure FDA0002292472830000021
in the formula, σz,σθSingle tensile yield stress, sigma, in axial and circumferential directions, respectively, of the pipeijFor any stress component, σ1Stress component, σ, in the direction of coordinate axis 12In the direction of coordinate axis 2Component of force, σ0The flow stress component corresponding to axial one-way single pulling;
according to Drucker's associated flow criteria:
Figure FDA0002292472830000022
in the formula, d ε1Increment of strain component in the direction of coordinate axis 1, d epsilon2The increment of the strain component in the direction of the coordinate axis 2 is shown, and d lambda is a proportionality constant;
thus, the relationship of the stress ratio, the strain increment ratio and the yield stress in each direction is obtained as follows:
4. the method for determining the anisotropy parameter of a tube according to claim 1 or 2, wherein in the fourth step, the formula (2) is established as follows:
for the plane stress state, the Hill48 yield criterion is expressed as:
Figure FDA0002292472830000024
in the formula, rz,rθThe axial and circumferential anisotropy coefficients of the pipe are respectively set;
according to Drucker's associated flow criteria:
Figure FDA0002292472830000031
therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure FDA0002292472830000032
5. the method for determining the anisotropy parameter of the tube according to claim 3, wherein in the fourth step, the formula (2) is established as follows:
for the plane stress state, the Hill48 yield criterion is expressed as:
in the formula, rz,rθThe axial and circumferential anisotropy coefficients of the pipe are respectively set;
according to Drucker's associated flow criteria:
Figure FDA0002292472830000034
therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure FDA0002292472830000035
6. the method for determining the anisotropy parameter of a tube according to claim 1, 2 or 5, wherein in the fourth step, formula (3) is established as follows:
for the in-plane stress state, the Balart89 anisotropic yield criterion is expressed as:
Figure FDA0002292472830000036
derived from Drucker's associated flow criteria
Figure FDA0002292472830000041
Therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure FDA0002292472830000042
7. the method for determining the anisotropy parameter of the tube according to claim 3, wherein in the fourth step, the formula (3) is established as follows:
for the in-plane stress state, the Balart89 anisotropic yield criterion is expressed as:
Figure FDA0002292472830000043
derived from Drucker's associated flow criteria
Therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure FDA0002292472830000045
8. the method for determining the anisotropy parameter of the tube according to claim 4, wherein in the fourth step, the formula (3) is established as follows:
for the in-plane stress state, the Balart89 anisotropic yield criterion is expressed as:
Figure FDA0002292472830000046
derived from Drucker's associated flow criteria
Figure FDA0002292472830000047
Therefore, the relation between the stress ratio and the strain increment ratio and the thickness anisotropy coefficient in each direction is obtained as follows:
Figure FDA0002292472830000051
9. a method of determining parameters of anisotropy for tubes as claimed in claims 1, 2, 5, 7 or 8, characterized in that M is 8 for face-centered cubic materials and 6 for body-centered cubic materials.
10. The method of claim 6, wherein M is 8 for face centered cubic material and 6 for body centered cubic material.
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