CN110763567B - Method for measuring thickness anisotropy coefficient and yield stress of pipe in any direction - Google Patents
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Abstract
Method for measuring thickness anisotropy coefficient and yield stress of pipe in any directionThe method belongs to the field of pipe performance test. The determination method comprises the following steps: performing a bidirectional loading experiment on a pipe to obtain stress and strain experiment data of the pipe in a plurality of bidirectional stress states; preparing a pipe shearing sample, and acquiring shearing stress and strain experimental data of the pipe in a pure shearing stress state; thirdly, calculating stress values and/or plastic strain increment ratios of the pipe under different stress states in a bidirectional loading and pure shearing experiment when the same plastic work is achieved, and determining all coefficients in a yield function and a plastic potential function of the pipe; establishing an expression for measuring the yield stress of the pipe in the direction and measuring the thickness anisotropy coefficient; fifthly, giving an angle to obtain the yield stress and the thickness anisotropy coefficient of the pipe in the direction
A value; and sixthly, changing the angle to obtain the yield stress and the value of the thickness anisotropy in any direction of the pipe. The method is used for measuring the thickness anisotropy coefficient and the yield stress of the pipe in any direction.
Description
Technical Field
The invention belongs to the field of pipe performance testing, and particularly relates to a method for measuring the thickness anisotropy coefficient and yield stress of a pipe in any direction.
Background
Pipe is commonly used to form pipe-like members having various profiles. Commonly used pipes are aluminum alloy, steel, titanium alloy, magnesium alloy and the like. Pipes tend to develop anisotropic characteristics during the manufacturing process. For pipes with anisotropic characteristics, different mechanical properties are present in different directions. Generally expressed as differences in yield stress and plastic flow behavior in different directions, the anisotropy characteristics are often characterized by the coefficients of thickness anisotropy and yield stress in different directions. The anisotropic characteristic directly influences the deformation behavior of the pipe, and further influences the formulation of pipe forming process parameters. Therefore, in order to accurately characterize the anisotropy of a pipe and provide reliable data for process parameter formulation, it is necessary to accurately determine the thickness anisotropy coefficients and yield stresses in different directions of the pipe.
For the plate, a mature test method is used for measuring the thickness anisotropy coefficient and the yield stress of the plate in different directions. The thickness anisotropy coefficient of the plate can be measured by adopting the GB/T5027-2016 standard; the yield stress of the sheet material can be determined using the GB/T228.1-2010 standard. The thickness anisotropy coefficient and yield stress in any direction in the plane of the plate can be obtained by changing the sampling direction of the sample. For pipes, however, these measurement methods applied to the sheet cannot be equally applied to measuring the thickness anisotropy coefficient and yield stress of the pipe in any direction, since the geometry is different from that of the sheet. The literature (Experimental characteristics and additive synthetic parameters identification for tube hydroforming process; Temim Zribi, Ali khalflah, Hedi Bel HadjSalah; Materials & Design; 2013) spreads the tube into sheets and then measures the thickness anisotropy coefficient and yield stress of the sheets according to the method. The method has the problems that the mechanical property of the pipe is changed due to plastic deformation generated in the process of flattening the pipe, and the obtained thickness anisotropy coefficient and yield stress are inaccurate. The test result can not accurately reflect the real performance of the pipe, and is not suitable for representing the anisotropic characteristics of the pipe and formulating the process parameters. 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, the two methods have friction force between the sample and the fixture used during the test, which affects the experimental result, and the two methods only measure the yield stress and the anisotropy coefficient of the pipe in the circumferential direction. The thickness anisotropy coefficients and yield stresses in other directions of the pipe (such as directions similar to 15 °, 30 °, 45 °, 60 °, 75 ° of the plate) cannot be determined.
The lack of relevant data of the thickness anisotropy coefficient and the yield stress of the pipe in any direction becomes the bottleneck of the development of the plastic constitutive model of the pipe and the theoretical research of the plastic deformation of the pipe at present. Sufficient anisotropy parameters (thickness anisotropy coefficients and yield stress in different directions) of the pipe cannot be obtained, so that the complex plastic deformation characteristics of the pipe cannot be comprehensively and accurately described. Meanwhile, anisotropic parameters (thickness anisotropy coefficients and yield stress in different directions) with definite physical significance cannot be used for intuitively or directly evaluating the performance of the pipe so as to guide the selection of the pipe in practical engineering application.
In order to accurately describe the anisotropic characteristics of the pipe, a method capable of measuring the thickness anisotropy coefficient and the yield stress of the pipe in any direction needs to be established.
Disclosure of Invention
The invention provides a method for measuring the thickness anisotropy coefficient and the yield stress of a pipe in any direction, aiming at solving the problem that the existing pipe experiment test method can not or can not accurately measure the anisotropy characteristic parameters of the pipe.
The technical scheme adopted by the invention for solving the problems is as follows:
a method for measuring the anisotropy coefficient and yield stress of a pipe in any direction comprises the following steps:
cutting a pipe to be tested, and performing a bidirectional pipe loading experiment to obtain stress and strain experiment data of the pipe in different bidirectional stress states;
preparing a pipe to be tested into a pipe shearing sample, wherein a shearing area exists on the shearing sample, and deformation of the pipe in a pure shearing stress state is realized through a pipe shearing experiment to obtain shearing stress and strain experiment data of the pipe in the pure shearing stress state;
step three, calculating to achieve the same plastic work W by using the experimental data obtained in the step one and the step twopStress values and/or plastic strain increment ratios in different stress states of a time-tube bidirectional loading and pure shearing experiment are adopted, a proper yield function and a proper plastic potential function are selected, and all coefficients in a yield function f and a plastic potential function g of the tube are determined by utilizing the stress values and/or the plastic strain increment ratios of the tube under the same plastic work;
step four, establishing a measured pipe by using the determined yield function f
Directional yield stress
The expression of (3) is established by utilizing the definition of the thickness anisotropy coefficient and the principle of constant material volume;
step five, giving an angle
Can obtain the pipe
Directional yield stress
Coefficient of anisotropy of thickness
A value;
step six, changing the angle
The yield stress of the pipe in any direction can be obtained
Coefficient of anisotropy of thickness
The value is obtained.
Further, in the step one, the bidirectional pipe loading experiment is performed on a special bidirectional pipe loading experiment device, a tensile or compressive load is applied to the end of the pipe, a pressure medium is applied to the interior of the pipe to deform the pipe under a set stress path, axial and circumferential stress and strain data of the pipe under a bidirectional pipe stress state are obtained, and different experimental data are obtained by changing the set stress path; the length of the cut pipe is 2-3 times of the outer diameter of the pipe and the length of the clamping sections at two ends.
Furthermore, in the second step, the tube shearing sample is formed by processing two notches which are centrosymmetric on the tube, the notches are provided with a V-shaped feature towards the direction of a symmetric central point, the opening angle of the V-shaped feature is 30-90 degrees, the V-shaped feature is symmetrical about the plane of the tube central line, the connecting line between the V-shaped sharp points of the two notches is parallel to the axial direction, a shearing area parallel to the axial direction is formed between the sharp points, and the length of the shearing area is 1-3 times of the tube wall thickness; the pipe shearing experiment is to apply axial tensile load to the prepared pipe shearing sample, so that the pipe shearing sample is subjected to pure shearing deformation, and shear stress and strain experimental data are obtained through measurement.
Further, in the fourth step, the pipe
Directional yield stress
The expression (c) is established as follows:
when in use
A unidirectional stretching effect exists in the direction, and the yield stress when the yield is reached is
Then
Expressed in the Z-theta coordinate system as:
substituting each stress component shown in the formula (1) into a yield criterion expression f to obtain a test resultFixed pipe
Directional yield stress
Expression (c):
angle in the formula
Defined as the angle with the axial direction of the pipe,
the axial direction is indicated and the axial direction,
representing the annular direction, f being the selected yield function, k being the coefficient matrix in the yield criterion, is determined by step three.
The formula (2) is a compound containing a unique unknown number
By solving the equation
Directional yield stress
Further, in the fourth step, the pipe
Coefficient of thickness anisotropy of direction
The expression (c) is established as follows:
according to the definition of the thickness anisotropy coefficient and the principle of unchanged material volume,
coefficient of anisotropy in thickness direction
Comprises the following steps:
wherein,
is composed of
Increase in directional plastic strain, d epsilontIs the increase in plastic strain in the thickness direction.
As represented by the incremental components of each plastic strain,
then
Coefficient of thickness anisotropy of direction
The expression of (a) is:
wherein d εzz、dεθθAnd d εzθRespectively is a pipe in
The axial and circumferential strain increment and the shear strain increment of the pipe in the state of the directional uniaxial tensile stress are determined by a plastic potential function g:
further, in the third step, the plastic potential function g can adopt an expression of a yield function f, that is, g ═ f.
Further, in the third step, the yield function f is a Hill48 yield function, a Barlat89 yield function or a YLd2000-2d yield function.
Furthermore, the tested pipe material can be round pipe materials made of various materials such as aluminum alloy, magnesium alloy, titanium alloy, steel and the like.
Further, the tested pipe objects can be pipes prepared by an extrusion process, pipes prepared by a spinning process and pipes prepared by rolling plates.
The invention has the beneficial effects that:
the method provided by the invention can solve the problem that the conventional test method cannot obtain the thickness anisotropy coefficient and the yield stress of the pipe in any direction;
secondly, the anisotropic parameters of the pipe determined by the method provided by the invention can be used for accurately and comprehensively describing the plastic deformation characteristics of the anisotropic pipe;
the anisotropic parameters of the pipe determined by the method provided by the invention can provide important data for constitutive model development, theoretical research, process parameter formulation and pipe application of the pipe;
the method for measuring the thickness anisotropy coefficient and the yield stress of the pipe in any direction can provide an effective means for evaluating the performance of the pipe.
Drawings
FIG. 1 is a schematic diagram of the measuring process of the method for measuring the anisotropy coefficient and yield stress of the pipe in any direction.
FIG. 2 is a schematic diagram of the experimental principle of bidirectional loading of the pipe according to the present invention.
FIG. 3 is a schematic diagram of the pipe shearing experiment principle according to the present invention.
FIG. 4 shows the present invention defining arbitrary direction of pipe
Schematic representation of (a).
FIG. 5 shows the sample after the two-way loading experiment of the pipe according to the example.
FIG. 6 is a schematic view of a pipe shear specimen according to the example.
FIG. 7 is a schematic diagram of a pipe shearing experiment and an effect diagram according to an embodiment; wherein, (a) is an experimental schematic diagram, and (b) is an effect diagram.
FIG. 8 shows the results of the yield stress in any direction of the pipe measured in the examples.
FIG. 9 shows the results of the anisotropy coefficients of the pipes measured in the examples in any direction.
In the figure, 1 is a pipe bidirectional loading experiment sample, and 2 is a pipe shearing experiment 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 6061O-state aluminum alloy extruded pipe with the outer diameter of 60mm and the wall thickness of 1.8mm as an example and combining figures 1-9:
firstly, cutting a pipe to be tested into a proper length (the length is 270mm), and performing 9 groups of pipe bidirectional loading experiments, as shown in fig. 5, to obtain stress and strain experimental data of the pipe in the 9 bidirectional stress states;
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;
preparing a pipe to be tested into a pipe shearing sample, wherein a shearing area exists on the shearing sample, the deformation of the pipe in a pure shearing stress state can be realized in the area, and the shearing stress strain experimental data of the pipe in the pure shearing stress state are obtained;
the pipe shearing test sample is shown in fig. 6, and the pipe shearing test is that tensile load is applied to the prepared shearing test sample to enable the test sample to generate pure shearing deformation and measure shearing stress and strain, and is shown in fig. 7;
step three, calculating to achieve the same plastic work WpStress data points of the pipe under different stress states in a bidirectional loading and pure shearing experiment are shown in table 1, a yield function f is selected from YLd2000-2d, and plasticity potential functions g and f are the same; the yield function is:
the YLD2000-2d yield function is defined as follows:
f＝φ＝φ′+φ″-2σi k＝0 (6)
equivalent stress of σi＝(φ/2)1/kIn the formula, phi 'and phi' are expressed as formula (7):
x 'in formula (7)'1、X′2And X ″)1、X″2Eigenvalues of the stress tensors X' and X ", respectively, the solving expression of the eigenvalues is:
the stress tensors X' and X "are obtained by linear transformation, as shown in equation (9):
in the formula: σ is the Cauchy stress tensor, and L' are linear transformation matrices.
The cauchy stress tensor σ is:
l 'and L' are respectively represented as:
the coefficients of the yield function Yld2000-2d obtained by solving the experimental data shown in table 1 by the least square method are shown in table 2.
TABLE 1 stress data points for the same plastic work
TABLE 2 coefficients of yield function of YLd2000-2d
Step four, establishing a measured pipe by using the determined yield function f
Directional yield stress
Expression (2)
Solving the equation can yield
Directional yield stress
The expression of (1);
the expression for determining the thickness anisotropy coefficient is as follows:
wherein,
the solution method is shown in appendix A.
Step five, giving any angle
A pipe material can be obtained according to the formulae (13) and (14)
Directional yield stress
Coefficient of anisotropy of thickness
A value;
step six, repeating the step five, changing the angle
Can obtain the yield stress of the pipe in any direction
Coefficient of anisotropy of thickness
As shown in fig. 8 and 9, since the object of the test of this example is an extruded pipe, the performance thereof has orthogonality, and therefore, only the results in the angle range of 1/4 are given.
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.
Appendix A:
the gradient of the yield function phi derives the incremental component of plastic strain, which is expressed as follows:
derivative of A1.1 phi
Order to
Δ′＝(X′11-X′22)2+4(X′12)2 (A1.2)
A1.1.1 Case 1
If Δ '≠ 0 or X'1≠X′2(X′11≠X′22or X′12≠0)
In the formula: alpha and beta are angle marks and take the values of z and theta.
And is
A1.1.2 Case 2
If delta 'is 0 or X'1＝X′2(or X'11＝X′22And X'12＝0)
Derivative of A1.2 φ
Order to
Δ″＝(X″11-X″22)2+4(X″12)2 (A1.8)
A1.2.1 Case 1
If Δ "≠ 0 or X ″)1≠X″2(X″11≠X″22or X″12≠0)
In the formula: alpha and beta are angle marks and take the values of z and theta.
A1.2.2Case 2
If Δ ″ ═ 0 or X ″)1＝X″2(X″11＝X″22And X ″)12＝0)
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 (5)
1. A method for measuring the anisotropy coefficient and the yield stress of a pipe in any direction is characterized by comprising the following steps:
cutting a pipe to be tested, and performing a bidirectional pipe loading experiment to obtain stress and strain experiment data of the pipe in different bidirectional stress states;
preparing a pipe to be tested into a pipe shearing sample, wherein a shearing area exists on the shearing sample, and deformation of the pipe in a pure shearing stress state is realized through a pipe shearing experiment to obtain shearing stress and strain experiment data of the pipe in the pure shearing stress state;
step three, calculating to achieve the same plastic work W by using the experimental data obtained in the step one and the step twopStress values and/or plastic strain increment ratios in different stress states of a time-tube bidirectional loading and pure shearing experiment are adopted, a proper yield function and a proper plastic potential function are selected, and all coefficients in a yield function f and a plastic potential function g of the tube are determined by utilizing the stress values and/or the plastic strain increment ratios of the tube under the same plastic work;
step four, establishing a measured pipe by using the determined yield function f
Directional yield stress
The expression of (3) is established by utilizing the definition of the thickness anisotropy coefficient and the principle of constant material volume;
pipe material
Directional yield stress
The expression (c) is established as follows:
when in use
A unidirectional stretching effect exists in the direction, and the yield stress when the yield is reached is
Then
Expressed in the Z-theta coordinate system as:
substituting each stress component shown in the formula (1) into a yield criterion expression f to obtain a measured pipe
Directional yield stress
Expression (c):
angle in the formula
Defined as the angle with the axial direction of the pipe,
the axial direction is indicated and the axial direction,
representing the annular direction, wherein f is the selected yield function, k is a coefficient matrix in the yield criterion, and the coefficient matrix is determined in the third step;
the formula (2) is a compound containing a unique unknown number
By solving the equation
Directional yield stress
Pipe material
Coefficient of thickness anisotropy of direction
The expression (c) is established as follows:
according to the definition of the thickness anisotropy coefficient and the principle of unchanged material volume,
coefficient of anisotropy in thickness direction
Comprises the following steps:
wherein,
is composed of
Increase in directional plastic strain, d epsilontIs the thickness direction plastic strain increment;
as represented by the incremental components of each plastic strain,
then
Coefficient of thickness anisotropy of direction
The expression of (a) is:
wherein d εzz、dεθθAnd d εzθRespectively is a pipe in
The axial and circumferential strain increment and the shear strain increment of the pipe in the state of the directional uniaxial tensile stress are determined by a plastic potential function g:
step five, giving an angle
Can obtain the pipe
Directional yield stress
Coefficient of anisotropy of thickness
A value;
step six, changing the angle
The yield stress of the pipe in any direction can be obtained
Coefficient of anisotropy of thickness
The value is obtained.
2. The method for measuring the anisotropy coefficient and the yield stress of the pipe in any direction according to claim 1, wherein in the step one, the bidirectional pipe loading experiment is performed on a special bidirectional pipe loading experiment device, a tensile or compressive load is applied to the end part of the pipe, a pressure medium is applied to the inside of the pipe to deform the pipe under a set stress path, so that axial and circumferential stress and strain data of the pipe in a bidirectional pipe stress state are obtained, and different experimental data are obtained by changing the set stress path; the cutting length is 2-3 times of the outer diameter of the pipe plus the length of the clamping sections at the two ends.
3. The method for measuring the anisotropy coefficient and the yield stress of the pipe in any direction according to claim 1 or 2, wherein in the second step, the pipe shearing sample is obtained by processing two notches which are centrosymmetric on the pipe, the notches are provided with V-shaped features towards the direction of a symmetric central point, the opening angle of the V-shaped features is 30-90 degrees, the V-shaped features are symmetric about the plane of the central line of the pipe, the connecting line between the V-shaped points of the two notches is parallel to the axial direction, a shearing area which is parallel to the axial direction is formed between the points, and the length of the shearing area is 1-3 times of the wall thickness of the pipe;
the pipe shearing experiment is to apply axial tensile load to the prepared pipe shearing sample, so that the pipe shearing sample is subjected to pure shearing deformation, and shear stress and strain experimental data are obtained through measurement.
4. The method for measuring the thickness anisotropy coefficient and the yield stress of the pipe in any direction according to claim 1 or 2, wherein in the fourth step, the pipe is
Directional yield stress
The expression (c) is established as follows:
when in use
A unidirectional stretching effect exists in the direction, and the yield stress when the yield is reached is
Then
In Z-theta coordinatesThe system is expressed as:
substituting each stress component shown in the formula (1) into a yield criterion expression f to obtain a measured pipe
Directional yield stress
Expression (c):
angle in the formula
Defined as the angle with the axial direction of the pipe,
the axial direction is indicated and the axial direction,
representing the annular direction, wherein f is the selected yield function, k is a coefficient matrix in the yield criterion, and the coefficient matrix is determined in the third step;
the formula (2) is a compound containing a unique unknown number
By solving the equation
Directional yield stress
5. The method for determining the anisotropy coefficient of thickness and the yield stress of the pipe in any direction according to claim 1 or 2, wherein in the third step, the plasticity potential function g can adopt an expression of a yield function f, namely g ═ f; the yield function f is Hill48 yield function, Barlat89 yield function or YLd2000-2d yield function.
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| CN112432849B (en) * | 2020-10-13 | 2021-09-07 | 北京交通大学 | Method for predicting shear strength of wood based on compressive strength of wood |
| CN112540012B (en) * | 2020-12-04 | 2023-11-14 | 哈尔滨工业大学 | Annular pure shear loading method and device for pipe |
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