CN110763567B - Method for measuring thickness anisotropy coefficient and yield stress of pipe in any direction - Google Patents

Method for measuring thickness anisotropy coefficient and yield stress of pipe in any direction Download PDF

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CN110763567B
CN110763567B CN201911186245.7A CN201911186245A CN110763567B CN 110763567 B CN110763567 B CN 110763567B CN 201911186245 A CN201911186245 A CN 201911186245A CN 110763567 B CN110763567 B CN 110763567B
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苑世剑
何祝斌
张坤
林艳丽
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Dalian University of Technology
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Abstract

一种管材任意方向的厚向异性系数和屈服应力测定方法，属于管材性能测试领域。测定方法：一、进行管材双向加载实验以获取管材在若干个双向应力状态下的应力、应变实验数据；二、制备管材剪切试样，获取管材纯剪切应力状态下的剪切应力、应变实验数据；三、计算达到相同塑性功时管材双向加载和纯剪切实验不同应力状态下的应力值和/或塑性应变增量比值，确定管材的屈服函数和塑性势函数中的所有系数；四、建立测定管材方向的屈服应力、测定厚向异性系数的表达式；五、给定一个角度，得到管材方向的屈服应力和厚向异性系数

Figure DDA0002292470630000011
值；六、改变角度来获得管材任意方向的屈服应力和厚向异性系数值。本发明用于管材任意方向的厚向异性系数和屈服应力测定。

Figure 201911186245

A method for measuring thickness anisotropy coefficient and yield stress of pipes in any direction belongs to the field of pipe performance testing. Determination methods: 1. Carry out bidirectional loading experiments of pipes to obtain experimental data of stress and strain of pipes under several bidirectional stress states; 2. Prepare shear samples of pipes to obtain shear stress and strain of pipes under pure shear stress states Experimental data; 3. Calculate the stress value and/or the ratio of plastic strain increments under different stress states in the bidirectional loading and pure shear experiments of the pipe when the same plastic work is achieved, and determine all the coefficients in the yield function and plastic potential function of the pipe; 4. , Establish the expression for measuring the yield stress in the direction of the pipe and the thickness anisotropy coefficient; 5. Given an angle, get the yield stress and the thickness anisotropy coefficient in the direction of the pipe

Figure DDA0002292470630000011
6. Change the angle to obtain the yield stress and thickness anisotropy coefficient values in any direction of the pipe. The invention is used for the determination of thickness anisotropy coefficient and yield stress of pipes in any direction.

Figure 201911186245

Description

一种管材任意方向的厚向异性系数和屈服应力测定方法A method for measuring thickness anisotropy coefficient and yield stress of pipes in any direction

技术领域technical field

本发明属于管材性能测试领域，具体涉及一种管材任意方向的厚向异性系数和屈服应力测定方法。The invention belongs to the field of pipe material performance testing, and particularly relates to a method for measuring thickness anisotropy coefficient and yield stress of pipe material in any direction.

背景技术Background technique

管材常用于成形具有各种外形的管类构件。常用的管材有铝合金、钢、钛合金、镁合金等。管材在制备的过程中往往会产生各向异性特征。对于具有各向异性特征的管材，在不同的方向上具有不同的机械性能。一般表现为不同方向屈服应力和塑性流动行为的差异，常用不同方向上的厚向异性系数和屈服应力来表征这种各向异性特征。这种各向异性特征直接影响管材的变形行为，进而影响管材成形工艺参数制定。因此，为了准确地描述管材的各向异性特征并为工艺参数制定提供可靠数据，需要准确地测定管材不同方向上的厚向异性系数和屈服应力。Tubes are often used to form tubular components with various shapes. Commonly used pipes are aluminum alloy, steel, titanium alloy, magnesium alloy, etc. Pipes tend to have anisotropic characteristics during the production process. For pipes with anisotropic characteristics, there are different mechanical properties in different directions. It is generally manifested as the difference in yield stress and plastic flow behavior in different directions. The anisotropy coefficient and yield stress in different directions are often used to characterize this anisotropy feature. This anisotropic feature directly affects the deformation behavior of the pipe, which in turn affects the formulation of the pipe forming process parameters. Therefore, in order to accurately describe the anisotropic characteristics of the pipe and provide reliable data for the formulation of process parameters, it is necessary to accurately determine the thickness anisotropy coefficient and yield stress of the pipe in different directions.

对于板材来说，有成熟的测试方法测定板材不同方向的厚向异性系数和屈服应力。板材的厚向异性系数可以采用GB/T 5027-2016标准进行测定；板材的屈服应力可以采用GB/T228.1-2010标准进行测定。只要改变试样取样方向就可以获得板材平面内任意方向的厚向异性系数和屈服应力。而对于管材，由于其几何形状不同于板材，这些应用于板材的测量方法不能同样地应用于测量管材的任意方向上的厚向异性系数和屈服应力。文献(Experimental characterization and inverse constitutive parametersidentification of tubular materials for tube hydroforming process；TemimZribi,Ali Khalfallah,Hedi BelHadjSalah；Materials&Design；2013)将管材展开为板材然后按照板材测定厚向异性系数和屈服应力的方法进行测定。存在的问题是管材在展平过程中会产生塑性变形使得管材力学性能发生改变，导致获得的厚向异性系数和屈服应力不准确。测试结果不能准确反映管材的真实性能，不宜用于表征管材的各向异性特征及用于工艺参数制定。专利(CN1865906)提出了一种管材环向拉伸性能测试方法，通过直接拉伸管材环向试样获取管材的环向性能，如环向的屈服应力。专利(CN104949884A)提出了一种管材环向的厚向异性系数直接测定方法，可以获得管材环向的厚向异性系数。但是这两种方法在测试时试样和所用的卡具之间存在摩擦力，会对实验结果产生影响，且这两种方法也仅是测量了管材环向的屈服应力和厚向异性系数。管材其它方向(比如类似于板材的15°、30°、45°、60°、75°等方向)的厚向异性系数和屈服应力无法测定。For sheets, there are well-established test methods to determine the thickness anisotropy coefficient and yield stress in different directions of the sheet. The thickness anisotropy coefficient of the plate can be measured by the GB/T 5027-2016 standard; the yield stress of the plate can be measured by the GB/T228.1-2010 standard. The thickness anisotropy coefficient and yield stress of any direction in the plate plane can be obtained by changing the sampling direction of the sample. For pipes, which differ in geometry from sheets, these measurement methods applied to sheets cannot be equally applied to measure the thickness anisotropy and yield stress of pipes in any direction. In the literature (Experimental characterization and inverse constitutive parameters identification of tubular materials for tube hydroforming process; Temim Zribi, Ali Khalfallah, Hedi Bel Hadj Salah; Materials &Design; 2013), the tubes were unfolded into sheets and then measured according to the method of sheet thickness anisotropy coefficient and yield stress. The problem is that the pipe will produce plastic deformation during the flattening process, which will change the mechanical properties of the pipe, resulting in inaccurate thickness anisotropy coefficient and yield stress obtained. The test results cannot accurately reflect the real performance of the pipe, and should not be used to characterize the anisotropic characteristics of the pipe and to formulate process parameters. The patent (CN1865906) proposes a test method for the hoop tensile properties of pipes, which can obtain the hoop properties of the pipes, such as the hoop yield stress, by directly stretching the hoop samples of the pipes. The patent (CN104949884A) proposes a method for directly measuring the thickness anisotropy coefficient in the circumferential direction of the pipe, which can obtain the thickness anisotropy coefficient in the circumferential direction of the pipe. However, these two methods have frictional force between the specimen and the fixture used during the test, which will affect the experimental results, and these two methods only measure the yield stress and the thickness anisotropy coefficient in the circumferential direction of the pipe. The thickness anisotropy coefficient and yield stress of other directions of the pipe (such as 15°, 30°, 45°, 60°, 75°, etc. similar to the sheet) cannot be determined.

管材任意方向厚向异性系数和屈服应力相关数据的缺乏，已经成为目前管材塑性本构模型开发和管材塑性变形理论研究的瓶颈。无法获得充足的管材各向异性参数(不同方向上的厚向异性系数和屈服应力)，就无法全面准确描述管材的复杂塑性变形特性。同时，也无法使用具有明确物理意义的各向异性参数(不同方向上的厚向异性系数和屈服应力)对管材性能进行直观或直接评价以指导实际工程应用中管材的选用。The lack of data related to the thickness anisotropy coefficient and yield stress in any direction of the pipe has become the bottleneck in the development of the plastic constitutive model of the pipe and the theoretical research on the plastic deformation of the pipe. If sufficient pipe anisotropy parameters (thickness anisotropy coefficient and yield stress in different directions) cannot be obtained, the complex plastic deformation characteristics of pipes cannot be fully and accurately described. At the same time, it is impossible to use the anisotropic parameters with clear physical meaning (thickness anisotropy coefficient and yield stress in different directions) to directly or directly evaluate the performance of the pipe to guide the selection of the pipe in practical engineering applications.

为了准确描述管材的各向异性特征，需要建立一种能够测定管材任意方向厚向异性系数和屈服应力的方法。In order to accurately describe the anisotropic characteristics of pipes, it is necessary to establish a method that can measure the thickness anisotropy coefficient and yield stress of pipes in any direction.

发明内容SUMMARY OF THE INVENTION

本发明是为解决现有的管材实验测试方法不能或无法准确地测定管材各向异性特征参数的问题，提出一种管材任意方向的厚向异性系数和屈服应力的测定方法。The invention proposes a method for measuring the thickness anisotropy coefficient and yield stress of the pipe in any direction to solve the problem that the existing pipe experimental testing method cannot or cannot accurately measure the anisotropic characteristic parameters of the pipe.

本发明为解决上述问题采取的技术方案是：The technical scheme that the present invention takes to solve the above problems is:

一种管材任意方向的厚向异性系数和屈服应力测定方法，步骤如下：A method for measuring the thickness anisotropy coefficient and yield stress of pipes in any direction, the steps are as follows:

步骤一、将待测管材进行切割，进行管材双向加载实验，以获取管材在不同双向应力状态下的应力、应变实验数据；Step 1: Cut the pipe to be tested, and carry out the bidirectional loading experiment of the pipe to obtain the stress and strain experimental data of the pipe under different bidirectional stress states;

步骤二、将待测管材制备成管材剪切试样，剪切试样上存在剪切区域，通过管材剪切实验来实现纯剪切应力状态下的变形，获取管材纯剪切应力状态下的剪切应力、应变实验数据；Step 2: Prepare the pipe to be tested into a pipe shear sample. There is a shear area on the shear sample. The deformation under the pure shear stress state is realized through the pipe shear experiment, and the pure shear stress state of the pipe is obtained. Shear stress and strain experimental data;

步骤三、利用步骤一、二得到的实验数据，计算达到相同塑性功Wp时管材双向加载和纯剪切实验不同应力状态下的应力值和/或塑性应变增量比值，选择合适的屈服函数和塑性势函数，利用相同塑性功时管材应力值和/或塑性应变增量比值确定管材的屈服函数f和塑性势函数g中的所有系数；Step 3: Using the experimental data obtained in Steps 1 and 2, calculate the stress value and/or the plastic strain increment ratio under different stress states in the bidirectional loading of the pipe and the pure shear experiment when the same plastic work Wp is achieved, and select an appropriate yield function. and the plastic potential function, using the pipe stress value and/or the plastic strain increment ratio at the same plastic work to determine all the coefficients in the pipe's yield function f and plastic potential function g;

步骤四、利用确定后的屈服函数f建立测定管材

Figure BDA0002292470610000021
方向的屈服应力
Figure BDA0002292470610000024
的表达式，利用厚向异性系数的定义和材料体积不变原理建立测定厚向异性系数的表达式；Step 4. Use the determined yield function f to establish the measurement of the pipe
Figure BDA0002292470610000021
direction yield stress
Figure BDA0002292470610000024
The expression of thickness anisotropy coefficient is established by using the definition of thickness anisotropy coefficient and the principle of material volume invariance;

步骤五、给定一个角度

Figure BDA0002292470610000023
便能得到管材
Figure BDA0002292470610000022
方向的屈服应力
Figure BDA0002292470610000027
和厚向异性系数
Figure BDA0002292470610000028
值；Step 5. Give an angle
Figure BDA0002292470610000023
get pipe
Figure BDA0002292470610000022
direction yield stress
Figure BDA0002292470610000027
and the thick anisotropy coefficient
Figure BDA0002292470610000028
value;

步骤六、通过改变角度

Figure BDA0002292470610000025
便能获得管材任意方向的屈服应力
Figure BDA0002292470610000026
和厚向异性系数
Figure BDA0002292470610000029
值。Step 6. By changing the angle
Figure BDA0002292470610000025
The yield stress in any direction of the pipe can be obtained
Figure BDA0002292470610000026
and the thick anisotropy coefficient
Figure BDA0002292470610000029
value.

进一步的，所述步骤一中，所述管材双向加载实验是在专用的管材双向加载实验装置上进行的，在管材端部施加拉伸或压缩载荷，在管材内部施加压力介质使管材在设定的应力路径下变形，获得管材双向应力状态下的管材轴向和环向的应力、应变数据，通过改变设定的应力路径来获得不同的实验数据；切割管材的长度为2～3倍管材外径加两端夹持段长度。Further, in the first step, the pipe bidirectional loading experiment is carried out on a dedicated pipe bidirectional loading experimental device, a tensile or compressive load is applied to the end of the pipe, and a pressure medium is applied inside the pipe to make the pipe in the setting. The axial and hoop stress and strain data of the pipe under the bidirectional stress state of the pipe can be obtained, and different experimental data can be obtained by changing the set stress path; the length of the cut pipe is 2 to 3 times the outside of the pipe. The diameter plus the length of the clamping section at both ends.

进一步的，所述步骤二中，所述的管材剪切试样是在管材上加工出两个成中心对称的缺口，缺口上朝向对称中心点的方向有呈“V”形的特征，“V”形特征的开口角度为30°～90°，“V”形特征关于管材中心线的平面对称，两个缺口“V”形尖点之间连线与轴向平行，尖点之间形成一个与轴向平行的剪切区域，剪切区域长度为1～3倍的管材壁厚；所述的管材剪切实验是对制取好的管材剪切试样施加轴向拉伸载荷，使得管材剪切试样发生纯剪切变形，并测量获得剪切应力、应变实验数据。Further, in the second step, the pipe shearing sample is machined with two center-symmetrical notches on the pipe, and the direction of the notches toward the center of symmetry has a "V"-shaped feature, "V". The opening angle of the "V"-shaped feature is 30° to 90°, the "V"-shaped feature is symmetrical about the plane of the center line of the pipe, the connecting line between the two notch "V"-shaped cusps is parallel to the axial direction, and a cusp is formed between the cusps. In the shearing area parallel to the axial direction, the length of the shearing area is 1 to 3 times the wall thickness of the pipe; the pipe shearing experiment is to apply an axial tensile load to the prepared pipe shearing sample, so that the pipe The shear specimen undergoes pure shear deformation, and the experimental data of shear stress and strain are obtained by measurement.

进一步的，所述步骤四中，管材

Figure BDA0002292470610000036
方向的屈服应力
Figure BDA0002292470610000037
的表达式是按如下方法建立的：Further, in the step 4, the pipe
Figure BDA0002292470610000036
direction yield stress
Figure BDA0002292470610000037
The expression for is constructed as follows:

当

Figure BDA0002292470610000038
方向存在一个单向拉伸作用，达到屈服时屈服应力为
Figure BDA0002292470610000039
则
Figure BDA00022924706100000310
在Z-θ坐标系中表示为：when
Figure BDA0002292470610000038
There is a unidirectional tensile effect in the direction, and the yield stress is
Figure BDA0002292470610000039
but
Figure BDA00022924706100000310
In the Z-theta coordinate system, it is expressed as:

Figure BDA0002292470610000031
Figure BDA0002292470610000031

将式(1)所示的各应力分量代入屈服准则表达式f中得到测定管材

Figure BDA00022924706100000311
方向的屈服应力
Figure BDA00022924706100000312
的表达式：Substitute the stress components shown in formula (1) into the yield criterion expression f to obtain the measured pipe
Figure BDA00022924706100000311
direction yield stress
Figure BDA00022924706100000312
expression:

Figure BDA0002292470610000032
Figure BDA0002292470610000032

式中，角度

Figure BDA00022924706100000313
定义为与管材轴向的夹角，
Figure BDA00022924706100000314
表示轴向，
Figure BDA00022924706100000315
表示环向，f为所选定的屈服函数，k为屈服准则中的系数矩阵，是由步骤三确定的。In the formula, the angle
Figure BDA00022924706100000313
Defined as the included angle with the axial direction of the pipe,
Figure BDA00022924706100000314
represents the axial direction,
Figure BDA00022924706100000315
represents the hoop direction, f is the selected yield function, and k is the coefficient matrix in the yield criterion, which is determined by step three.

式(2)是个含有唯一未知数

Figure BDA00022924706100000316
的方程，通过解方程得到
Figure BDA00022924706100000318
方向的屈服应力
Figure BDA00022924706100000317
Equation (2) is an equation with a unique unknown
Figure BDA00022924706100000316
, which is obtained by solving the equation
Figure BDA00022924706100000318
direction yield stress
Figure BDA00022924706100000317

进一步的，所述步骤四中，管材

Figure BDA00022924706100000319
方向的厚向异性系数
Figure BDA00022924706100000320
的表达式是按如下方法建立的：Further, in the step 4, the pipe
Figure BDA00022924706100000319
Orientation Pachytropy Coefficient
Figure BDA00022924706100000320
The expression for is constructed as follows:

根据厚向异性系数的定义和材料体积不变原理，

Figure BDA00022924706100000321
方向厚向异性系数
Figure BDA00022924706100000322
为：According to the definition of thick anisotropy coefficient and the principle of material volume invariance,
Figure BDA00022924706100000321
Orientation Pachytropy Coefficient
Figure BDA00022924706100000322
for:

Figure BDA0002292470610000033
Figure BDA0002292470610000033

其中，

Figure BDA00022924706100000323
为
Figure BDA00022924706100000324
方向塑性应变增量，dεt为厚度方向塑性应变增量。
Figure BDA00022924706100000325
由各塑性应变增量分量表示，
Figure BDA0002292470610000034
in,
Figure BDA00022924706100000323
for
Figure BDA00022924706100000324
direction plastic strain increment, dε t is the thickness direction plastic strain increment.
Figure BDA00022924706100000325
Represented by each plastic strain increment component,
Figure BDA0002292470610000034

则

Figure BDA00022924706100000326
方向的厚向异性系数
Figure BDA00022924706100000327
的表达式为：but
Figure BDA00022924706100000326
Orientation Pachytropy Coefficient
Figure BDA00022924706100000327
The expression is:

Figure BDA0002292470610000035
Figure BDA0002292470610000035

其中，dεzz、dεθθ和dεzθ分别为管材处于

Figure BDA00022924706100000328
方向单向拉伸应力状态时管材轴向、环向的应变增量和剪切应变增量，由塑性势函数g确定：Among them, dε zz , dε θθ and dε zθ are respectively
Figure BDA00022924706100000328
The axial and circumferential strain increments and shear strain increments of the pipe in the uniaxial tensile stress state are determined by the plastic potential function g:

Figure BDA0002292470610000041
Figure BDA0002292470610000041

进一步的，所述步骤三中，塑性势函数g能够采用屈服函数f的表达式，即g＝f。Further, in the third step, the plastic potential function g can adopt the expression of the yield function f, that is, g=f.

进一步的，所述步骤三中，屈服函数f为Hill48屈服函数、Barlat89屈服函数或Yld2000-2d屈服函数。Further, in the third step, the yield function f is the Hill48 yield function, the Barlat89 yield function or the Yld2000-2d yield function.

进一步的，所测试的管材对象可以是铝合金、镁合金、钛合金、钢等各种材质的圆管类材料。Further, the pipe material to be tested may be a round pipe material of various materials such as aluminum alloy, magnesium alloy, titanium alloy, and steel.

进一步的，所测试的管材对象可以是挤压工艺制备的管材、旋压工艺制备的管材，板材卷制成的管材。Further, the tested pipe objects may be pipes prepared by extrusion process, pipes prepared by spinning process, and pipes prepared by sheet coils.

本发明的有益效果：Beneficial effects of the present invention:

一、本发明提出的方法可以解决现有测试方法无法获得管材任意方向的厚向异性系数和屈服应力的问题；1. The method proposed by the present invention can solve the problem that the existing test method cannot obtain the thickness anisotropy coefficient and yield stress of the pipe in any direction;

二、本发明提出的方法确定的管材各向异性参数可以用于准确、全面地描述各向异性管材的塑性变形特征；2. The anisotropic parameters of the pipe determined by the method proposed in the present invention can be used to accurately and comprehensively describe the plastic deformation characteristics of the anisotropic pipe;

三、本发明提出的方法确定的管材各向异性参数可以为管材的本构模型开发、理论研究、工艺参数制定和管材应用提供重要的数据；3. The anisotropic parameters of the pipe determined by the method proposed in the present invention can provide important data for the development of the constitutive model of the pipe, the theoretical research, the formulation of process parameters and the application of the pipe;

四、本发明提出的测定管材任意方向的厚向异性系数和屈服应力的方法可以为管材性能评价提供一种有效的手段。4. The method for measuring the thickness anisotropy coefficient and the yield stress of the pipe in any direction proposed by the present invention can provide an effective means for the performance evaluation of the pipe.

附图说明Description of drawings

图1为本发明提出的一种管材任意方向的厚向异性系数和屈服应力测定方法测定过程示意图。FIG. 1 is a schematic diagram of the measuring process of a method for measuring the thickness anisotropy coefficient and yield stress of a pipe material in any direction proposed by the present invention.

图2为本发明所述的管材双向加载实验原理示意图。FIG. 2 is a schematic diagram of the experimental principle of bidirectional loading of pipes according to the present invention.

图3为本发明所述的管材剪切实验原理示意图。FIG. 3 is a schematic diagram of the principle of the pipe shearing experiment according to the present invention.

图4为本发明定义管材任意方向

Figure BDA0002292470610000042
的示意图。Figure 4 defines any direction of the pipe for the present invention
Figure BDA0002292470610000042
schematic diagram.

图5为实施例所述的管材双向加载实验后的试样。Fig. 5 is the sample after the bidirectional loading experiment of the pipe described in the embodiment.

图6为实施例所述的管材剪切试样示意图。FIG. 6 is a schematic diagram of the pipe shearing sample described in the embodiment.

图7为实施例所述的管材剪切实验示意图及效果图；其中，(a)为实验示意图，(b)为效果图。7 is a schematic diagram and an effect diagram of the pipe shearing experiment according to the embodiment; wherein, (a) is a schematic diagram of the experiment, and (b) is an effect diagram.

图8为实施例测定的管材任意方向的屈服应力结果。Figure 8 shows the results of the yield stress in any direction of the pipe measured in the embodiment.

图9为实施例测定的管材任意方向的厚向异性系数结果。Figure 9 shows the results of the thickness anisotropy coefficient of the pipe in any direction measured in the Example.

图中，1为管材双向加载实验试样，2为管材剪切实验试样。In the figure, 1 is the pipe bidirectional loading experimental sample, and 2 is the pipe shearing experimental sample.

具体实施方式Detailed ways

下面将结合具体实施例对本发明的技术方案进行进一步的说明。The technical solutions of the present invention will be further described below with reference to specific embodiments.

以外径60mm，壁厚1.8mm的6061O态铝合金挤压管材为例，结合图1～9说明本发明的实施过程：Taking the 6061O state aluminum alloy extruded pipe with an outer diameter of 60mm and a wall thickness of 1.8mm as an example, the implementation process of the present invention will be described with reference to Figures 1 to 9:

步骤一、将待测管材切割成合适的长度(长度为270mm)，进行9组管材双向加载实验，如图5所示，以获取管材在这9个双向应力状态下的应力、应变实验数据；Step 1: Cut the pipe to be tested into a suitable length (the length is 270mm), and carry out 9 sets of bidirectional loading experiments on the pipe, as shown in Figure 5, to obtain the stress and strain experimental data of the pipe under these 9 bidirectional stress states;

所述管材双向加载实验是在专用的管材双向加载实验测试装置上进行的(参考专利CN105300802B)，在管材端部施加拉伸或压缩载荷，在管材内部施加压力介质使管材在设定的应力路径下变形，获得管材的双向应力状态下的实验数据(管材轴向和环向的应力、应变数据)，通过改变设定的应力路径获得多组实验数据；The pipe bidirectional loading experiment is carried out on a special pipe bidirectional loading experimental test device (refer to patent CN105300802B), applying tensile or compressive load at the end of the pipe, and applying pressure medium inside the pipe to make the pipe in the set stress path. Under the deformation, the experimental data under the bidirectional stress state of the pipe (the stress and strain data in the axial and hoop directions of the pipe) are obtained, and multiple sets of experimental data are obtained by changing the set stress path;

步骤二、将待测管材制备成管材剪切试样，剪切试样上存在剪切区域，该区域内可以实现管材在纯剪切应力状态下变形，获取管材纯剪切应力状态下的剪切应力应变实验数据；Step 2: Prepare the pipe to be tested into a pipe shear sample. There is a shear area on the shear sample. In this area, the pipe can be deformed in a state of pure shear stress, and the shear of the pipe in a state of pure shear stress can be obtained. Shear stress strain experimental data;

所述的管材剪切试样如图6所示，所述的管材剪切实验是在制取好的剪切试样施加拉伸载荷使得试样发生纯剪切变形并测量剪切应力、应变，如图7所示；The pipe shear sample is shown in Figure 6. The pipe shear experiment is to apply a tensile load to the prepared shear sample to make the sample undergo pure shear deformation and measure the shear stress and strain. , as shown in Figure 7;

步骤三、计算达到相同塑性功Wp时管材双向加载和纯剪切实验的不同应力状态下的应力数据点，如表1所示，屈服函数f选择的是Yld2000-2d，塑性势函数g与f相同；屈服函数为：Step 3: Calculate the stress data points under different stress states of the pipe bidirectional loading and pure shear experiments when the same plastic work W p is achieved. As shown in Table 1, the yield function f is Yld2000-2d, and the plastic potential function g is equal to f is the same; the yield function is:

Yld2000-2d屈服函数定义如下：The Yld2000-2d yield function is defined as follows:

f＝φ＝φ′+φ″-2σi k＝0 (6)f=φ=φ′+φ″-2σ i k =0 (6)

等效应力为σi＝(φ/2)1/k，式中φ′、φ″的表达式如式(7)所示：The equivalent stress is σ i =(φ/2) 1/k , where the expressions of φ′ and φ″ are shown in equation (7):

Figure BDA0002292470610000051
Figure BDA0002292470610000051

式(7)中X′1、X′2和X″1、X″2分别为应力张量X′和X″的特征值，特征值的求解表达式为：In formula (7), X′ 1 , X′ 2 and X″ 1 , X″ 2 are the eigenvalues of the stress tensors X′ and X″ respectively, and the solution expressions of the eigenvalues are:

Figure BDA0002292470610000061
Figure BDA0002292470610000061

应力张量X′和X″是通过线性转换得到的，如式(9)所示：The stress tensors X′ and X″ are obtained by linear transformation, as shown in equation (9):

Figure BDA0002292470610000062
Figure BDA0002292470610000062

式中：σ为柯西应力张量，L′和L″为线性转换矩阵。where σ is the Cauchy stress tensor, and L′ and L″ are linear transformation matrices.

柯西应力张量σ为：The Cauchy stress tensor σ is:

Figure BDA0002292470610000063
Figure BDA0002292470610000063

L′和L″分别表示为：L' and L" are respectively expressed as:

Figure BDA0002292470610000064
Figure BDA0002292470610000064

Figure BDA0002292470610000065
Figure BDA0002292470610000065

通过表1所示的实验数据利用最小二乘法求解得到屈服函数Yld2000-2d的系数为表2所示。The coefficients of the yield function Yld2000-2d are obtained by solving the experimental data shown in Table 1 and using the least squares method as shown in Table 2.

表1、相同塑性功时的应力数据点Table 1. Stress data points at the same plastic work

Figure BDA0002292470610000066
Figure BDA0002292470610000066

表2、Yld2000-2d屈服函数的系数Table 2. Coefficients of Yld2000-2d Yield Function

Figure BDA0002292470610000067
Figure BDA0002292470610000067

步骤四、利用确定后的屈服函数f建立测定管材

Figure BDA0002292470610000075
方向的屈服应力
Figure BDA0002292470610000076
的表达式Step 4. Use the determined yield function f to establish the measurement of the pipe
Figure BDA0002292470610000075
direction yield stress
Figure BDA0002292470610000076
expression of

Figure BDA0002292470610000071
Figure BDA0002292470610000071

解方程可以得到

Figure BDA0002292470610000077
方向的屈服应力
Figure BDA0002292470610000078
的表达式；Solving the equation can get
Figure BDA0002292470610000077
direction yield stress
Figure BDA0002292470610000078
expression;

测定厚向异性系数的表达式为：The expression for determining the thickness anisotropy coefficient is:

Figure BDA0002292470610000072
Figure BDA0002292470610000072

其中，in,

Figure BDA0002292470610000073
Figure BDA0002292470610000073

求解方法见附录A。See Appendix A for the solution method.

步骤五、给定任意一个角度

Figure BDA0002292470610000079
根据式(13)和式(14)可以得到管材
Figure BDA00022924706100000710
方向的屈服应力
Figure BDA00022924706100000711
和厚向异性系数
Figure BDA00022924706100000712
值；Step 5. Given any angle
Figure BDA0002292470610000079
According to formula (13) and formula (14), the pipe can be obtained
Figure BDA00022924706100000710
direction yield stress
Figure BDA00022924706100000711
and the thick anisotropy coefficient
Figure BDA00022924706100000712
value;

步骤六、重复步骤五，改变角度

Figure BDA00022924706100000713
可以获得管材任意方向的屈服应力
Figure BDA00022924706100000714
和厚向异性系数
Figure BDA00022924706100000715
值，如图8和图9所示，由于本实施例测试的对象是挤压管材，其性能具有正交性，因此仅给出1/4角度范围内的结果。Step 6, repeat step 5, change the angle
Figure BDA00022924706100000713
The yield stress in any direction of the pipe can be obtained
Figure BDA00022924706100000714
and the thick anisotropy coefficient
Figure BDA00022924706100000715
As shown in Figure 8 and Figure 9, since the object tested in this example is an extruded pipe, its properties are orthogonal, so only the results in the range of 1/4 angle are given.

本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

附录A：Appendix A:

屈服函数φ的梯度导出塑性应变增量分量，其表示如下：The gradient of the yield function φ derives the plastic strain incremental component, which is expressed as:

Figure BDA0002292470610000074
Figure BDA0002292470610000074

A1.1φ′的导数Derivative of A1.1φ′

令make

Δ′＝(X′11-X′22)2+4(X′12)2 (A1.2)Δ′=(X′ 11 -X′ 22 ) 2 +4(X′ 12 ) 2 (A1.2)

A1.1.1 Case 1A1.1.1 Case 1

若Δ′≠0或X′1≠X′2(X′11≠X′22or X′12≠0)If Δ′≠0 or X′ 1 ≠X′ 2 (X′ 11 ≠X′ 22 or X′ 12 ≠0)

Figure BDA0002292470610000081
Figure BDA0002292470610000081

式中：α,β为角标，取值为z,θ。In the formula: α, β are the angle scales, and the values are z, θ.

Figure BDA0002292470610000082
Figure BDA0002292470610000082

并且and

Figure BDA0002292470610000083
Figure BDA0002292470610000083

Figure BDA0002292470610000084
Figure BDA0002292470610000084

A1.1.2 Case 2A1.1.2 Case 2

若Δ′＝0或X′1＝X′2(或X′11＝X′22且X′12＝0)If Δ'=0 or X' 1 =X' 2 (or X' 11 =X' 22 and X' 12 =0)

Figure BDA0002292470610000085
Figure BDA0002292470610000085

A1.2φ″的导数Derivative of A1.2φ″

令make

Δ″＝(X″11-X″22)2+4(X″12)2 (A1.8)Δ″=(X″ 11 -X″ 22 ) 2 +4(X″ 12 ) 2 (A1.8)

A1.2.1 Case 1A1.2.1 Case 1

若Δ″≠0或X″1≠X″2(X″11≠X″22or X″12≠0)If Δ″≠0 or X″ 1 ≠X″ 2 (X″ 11 ≠X″ 22 or X″ 12 ≠0)

Figure BDA0002292470610000091
Figure BDA0002292470610000091

式中：α,β为角标，取值为z,θ。In the formula: α, β are the angle scales, and the values are z, θ.

Figure BDA0002292470610000092
Figure BDA0002292470610000092

Figure BDA0002292470610000093
Figure BDA0002292470610000093

Figure BDA0002292470610000094
Figure BDA0002292470610000094

A1.2.2Case 2A1.2.2Case 2

若Δ″＝0或X″1＝X″2(X″11＝X″22且X″12＝0)If Δ″=0 or X″ 1 =X″ 2 (X″ 11 =X″ 22 and X″ 12 =0)

Figure BDA0002292470610000095
Figure BDA0002292470610000095

本发明已以较佳实施案例揭示如上，然而并非用以限定本发明，任何熟悉本专业的技术人员，在不脱离本发明技术方案范围内，当可以利用上述揭示的结构及技术内容做出些许的更动或修饰为等同变化的等效实施案例，但是凡是未脱离本发明技术方案的内容，依据本发明的技术实质对以上实施案例所做的任何简单修改、等同变化与修饰，均仍属本发明技术方案范围。The present invention has been disclosed above with preferred embodiments, but it is not intended to limit the present invention. Any person skilled in the art, without departing from the scope of the technical solution of the present invention, can make use of the structure and technical content disclosed above to make some The modification or modification is equivalent to the equivalent implementation case of the equivalent change, but any simple modification, equivalent change and modification made to the above implementation case according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall still belong to The scope of the technical solution of the present invention.

Claims (5)

1.一种管材任意方向的厚向异性系数和屈服应力测定方法，其特征在于，步骤如下：1. a thickness anisotropy coefficient and yield stress measuring method in any direction of pipe material, it is characterized in that, step is as follows: 步骤一、将待测管材进行切割，进行管材双向加载实验，以获取管材在不同双向应力状态下的应力、应变实验数据；Step 1: Cut the pipe to be tested, and carry out the bidirectional loading experiment of the pipe to obtain the stress and strain experimental data of the pipe under different bidirectional stress states; 步骤二、将待测管材制备成管材剪切试样，剪切试样上存在剪切区域，通过管材剪切实验来实现纯剪切应力状态下的变形，获取管材纯剪切应力状态下的剪切应力、应变实验数据；Step 2: Prepare the pipe to be tested into a pipe shear sample. There is a shear area on the shear sample. The deformation under the pure shear stress state is realized through the pipe shear experiment, and the pure shear stress state of the pipe is obtained. Shear stress and strain experimental data; 步骤三、利用步骤一、二得到的实验数据，计算达到相同塑性功Wp时管材双向加载和纯剪切实验不同应力状态下的应力值和/或塑性应变增量比值，选择合适的屈服函数和塑性势函数，利用相同塑性功时管材应力值和/或塑性应变增量比值确定管材的屈服函数f和塑性势函数g中的所有系数；Step 3: Using the experimental data obtained in Steps 1 and 2, calculate the stress value and/or the plastic strain increment ratio under different stress states in the bidirectional loading of the pipe and the pure shear experiment when the same plastic work Wp is achieved, and select an appropriate yield function. and the plastic potential function, using the pipe stress value and/or the plastic strain increment ratio at the same plastic work to determine all the coefficients in the pipe's yield function f and plastic potential function g; 步骤四、利用确定后的屈服函数f建立测定管材
Figure FDA0002955539020000011
方向的屈服应力
Figure FDA0002955539020000012
的表达式，利用厚向异性系数的定义和材料体积不变原理建立测定厚向异性系数的表达式；Step 4. Use the determined yield function f to establish the measurement of the pipe
Figure FDA0002955539020000011
direction yield stress
Figure FDA0002955539020000012
The expression of thickness anisotropy coefficient is established by using the definition of thickness anisotropy coefficient and the principle of material volume invariance; 管材
Figure FDA0002955539020000013
方向的屈服应力
Figure FDA0002955539020000014
的表达式是按如下方法建立的：pipe
Figure FDA0002955539020000013
direction yield stress
Figure FDA0002955539020000014
The expression for is constructed as follows: 当
Figure FDA0002955539020000015
方向存在一个单向拉伸作用，达到屈服时屈服应力为
Figure FDA0002955539020000016
则
Figure FDA0002955539020000017
在Z-θ坐标系中表示为：when
Figure FDA0002955539020000015
There is a unidirectional tensile effect in the direction, and the yield stress is
Figure FDA0002955539020000016
but
Figure FDA0002955539020000017
In the Z-theta coordinate system, it is expressed as:
Figure FDA0002955539020000018
Figure FDA0002955539020000018
 将式(1)所示的各应力分量代入屈服准则表达式f中得到测定管材
Figure FDA0002955539020000019
方向的屈服应力
Figure FDA00029555390200000110
的表达式：Substitute the stress components shown in formula (1) into the yield criterion expression f to obtain the measured pipe
Figure FDA0002955539020000019
direction yield stress
Figure FDA00029555390200000110
expression:
Figure FDA00029555390200000111
Figure FDA00029555390200000111
 式中，角度
Figure FDA00029555390200000112
定义为与管材轴向的夹角，
Figure FDA00029555390200000113
表示轴向，
Figure FDA00029555390200000114
表示环向，f为所选定的屈服函数，k为屈服准则中的系数矩阵，是由步骤三确定的；In the formula, the angle
Figure FDA00029555390200000112
Defined as the included angle with the axial direction of the pipe,
Figure FDA00029555390200000113
represents the axial direction,
Figure FDA00029555390200000114
represents the circumferential direction, f is the selected yield function, and k is the coefficient matrix in the yield criterion, which is determined by step 3; 式(2)是个含有唯一未知数
Figure FDA00029555390200000115
的方程，通过解方程得到
Figure FDA00029555390200000116
方向的屈服应力
Figure FDA00029555390200000117
Equation (2) is an equation with a unique unknown
Figure FDA00029555390200000115
, which is obtained by solving the equation
Figure FDA00029555390200000116
direction yield stress
Figure FDA00029555390200000117
 管材
Figure FDA00029555390200000118
方向的厚向异性系数
Figure FDA00029555390200000119
的表达式是按如下方法建立的：pipe
Figure FDA00029555390200000118
Orientation Pachytropy Coefficient
Figure FDA00029555390200000119
The expression for is constructed as follows: 根据厚向异性系数的定义和材料体积不变原理，
Figure FDA00029555390200000120
方向厚向异性系数
Figure FDA00029555390200000121
为：According to the definition of thick anisotropy coefficient and the principle of material volume invariance,
Figure FDA00029555390200000120
Orientation Pachytropy Coefficient
Figure FDA00029555390200000121
for:
Figure FDA00029555390200000122
Figure FDA00029555390200000122
 其中，
Figure FDA0002955539020000021
为
Figure FDA0002955539020000022
方向塑性应变增量，dεt为厚度方向塑性应变增量；
Figure FDA0002955539020000023
由各塑性应变增量分量表示，
Figure FDA0002955539020000024
in,
Figure FDA0002955539020000021
for
Figure FDA0002955539020000022
plastic strain increment in the direction, dε t is the plastic strain increment in the thickness direction;
Figure FDA0002955539020000023
Represented by each plastic strain increment component,
Figure FDA0002955539020000024
 则
Figure FDA0002955539020000025
方向的厚向异性系数
Figure FDA0002955539020000026
的表达式为：but
Figure FDA0002955539020000025
Orientation Pachytropy Coefficient
Figure FDA0002955539020000026
The expression is:
Figure FDA0002955539020000027
Figure FDA0002955539020000027
 其中，dεzz、dεθθ和dεzθ分别为管材处于
Figure FDA0002955539020000028
方向单向拉伸应力状态时管材轴向、环向的应变增量和剪切应变增量，由塑性势函数g确定：Among them, dε zz , dε θθ and dε zθ are respectively
Figure FDA0002955539020000028
The axial and circumferential strain increments and shear strain increments of the pipe in the uniaxial tensile stress state are determined by the plastic potential function g:
Figure FDA0002955539020000029
Figure FDA0002955539020000029
 步骤五、给定一个角度
Figure FDA00029555390200000210
便能得到管材
Figure FDA00029555390200000211
方向的屈服应力
Figure FDA00029555390200000212
和厚向异性系数
Figure FDA00029555390200000213
值；Step 5. Give an angle
Figure FDA00029555390200000210
get pipe
Figure FDA00029555390200000211
direction yield stress
Figure FDA00029555390200000212
and the thick anisotropy coefficient
Figure FDA00029555390200000213
value; 步骤六、通过改变角度
Figure FDA00029555390200000214
便能获得管材任意方向的屈服应力
Figure FDA00029555390200000215
和厚向异性系数
Figure FDA00029555390200000216
值。Step 6. By changing the angle
Figure FDA00029555390200000214
The yield stress in any direction of the pipe can be obtained
Figure FDA00029555390200000215
and the thick anisotropy coefficient
Figure FDA00029555390200000216
value. 2.根据权利要求1所述的一种管材任意方向的厚向异性系数和屈服应力测定方法，其特征在于，所述步骤一中，所述管材双向加载实验是在专用的管材双向加载实验装置上进行的，在管材端部施加拉伸或压缩载荷，在管材内部施加压力介质使管材在设定的应力路径下变形，获得管材双向应力状态下的管材轴向和环向的应力、应变数据，通过改变设定的应力路径来获得不同的实验数据；切割的长度为为2～3倍管材外径加两端夹持段长度。2. The method for measuring thickness anisotropy coefficient and yield stress in any direction of a pipe material according to claim 1, wherein in the step 1, the pipe material bidirectional loading experiment is performed in a dedicated pipe material bidirectional loading experimental device Applying a tensile or compressive load at the end of the pipe, applying a pressure medium inside the pipe to deform the pipe under the set stress path, and obtaining the axial and circumferential stress and strain data of the pipe under the bidirectional stress state of the pipe , different experimental data can be obtained by changing the set stress path; the cutting length is 2 to 3 times the outer diameter of the pipe plus the length of the clamping sections at both ends. 3.根据权利要求1或2所述的一种管材任意方向的厚向异性系数和屈服应力测定方法，其特征在于，所述步骤二中，所述的管材剪切试样是在管材上加工出两个成中心对称的缺口，缺口上朝向对称中心点的方向有呈“V”形的特征，“V”形特征的开口角度为30°～90°，“V”形特征关于管材中心线的平面对称，两个缺口“V”形尖点之间连线与轴向平行，尖点之间形成一个与轴向平行的剪切区域，剪切区域长度为1～3倍的管材壁厚；3. The method for measuring the thickness anisotropy coefficient and yield stress of a pipe material in any direction according to claim 1 or 2, wherein in the step 2, the pipe material shear sample is processed on the pipe material Two centrally symmetric gaps are formed, and the direction of the gap toward the symmetrical center point has a "V"-shaped feature. The opening angle of the "V"-shaped feature is 30° to 90°, and the "V"-shaped feature is about the center line of the pipe. The plane is symmetrical, the connecting line between the two notch "V"-shaped cusps is parallel to the axial direction, and a shearing area parallel to the axial direction is formed between the cusps, and the length of the shearing area is 1 to 3 times the wall thickness of the pipe. ; 所述的管材剪切实验是对制取好的管材剪切试样施加轴向拉伸载荷，使得管材剪切试样发生纯剪切变形，并测量获得剪切应力、应变实验数据。In the pipe shearing experiment, an axial tensile load is applied to the prepared pipe shearing sample, so that the pipe shearing sample undergoes pure shear deformation, and experimental data of shear stress and strain are obtained by measurement. 4.根据权利要求1或2所述的一种管材任意方向的厚向异性系数和屈服应力测定方法，其特征在于，所述步骤四中，管材
Figure FDA00029555390200000217
方向的屈服应力
Figure FDA00029555390200000218
的表达式是按如下方法建立的：4. The method for measuring the thickness anisotropy coefficient and yield stress of a pipe material in any direction according to claim 1 or 2, wherein in the step 4, the pipe material
Figure FDA00029555390200000217
direction yield stress
Figure FDA00029555390200000218
The expression for is constructed as follows: 当
Figure FDA0002955539020000031
方向存在一个单向拉伸作用，达到屈服时屈服应力为
Figure FDA0002955539020000032
则
Figure FDA0002955539020000033
在Z-θ坐标系中表示为：when
Figure FDA0002955539020000031
There is a unidirectional tensile effect in the direction, and the yield stress is
Figure FDA0002955539020000032
but
Figure FDA0002955539020000033
In the Z-theta coordinate system, it is expressed as:
Figure FDA0002955539020000034
Figure FDA0002955539020000034
 将式(1)所示的各应力分量代入屈服准则表达式f中得到测定管材
Figure FDA0002955539020000035
方向的屈服应力
Figure FDA0002955539020000036
的表达式：Substitute the stress components shown in formula (1) into the yield criterion expression f to obtain the measured pipe
Figure FDA0002955539020000035
direction yield stress
Figure FDA0002955539020000036
expression:
Figure FDA0002955539020000037
Figure FDA0002955539020000037
 式中，角度
Figure FDA0002955539020000038
定义为与管材轴向的夹角，
Figure FDA0002955539020000039
表示轴向，
Figure FDA00029555390200000310
表示环向，f为所选定的屈服函数，k为屈服准则中的系数矩阵，是由步骤三确定的；In the formula, the angle
Figure FDA0002955539020000038
Defined as the included angle with the axial direction of the pipe,
Figure FDA0002955539020000039
represents the axial direction,
Figure FDA00029555390200000310
represents the circumferential direction, f is the selected yield function, and k is the coefficient matrix in the yield criterion, which is determined by step 3; 式(2)是个含有唯一未知数
Figure FDA00029555390200000311
的方程，通过解方程得到
Figure FDA00029555390200000312
方向的屈服应力
Figure FDA00029555390200000313
Equation (2) is an equation with a unique unknown
Figure FDA00029555390200000311
, which is obtained by solving the equation
Figure FDA00029555390200000312
direction yield stress
Figure FDA00029555390200000313
 5.根据权利要求1或2所述的一种管材任意方向的厚向异性系数和屈服应力测定方法，其特征在于，所述步骤三中，塑性势函数g能够采用屈服函数f的表达式，即g＝f；屈服函数f为Hill48屈服函数、Barlat89屈服函数或Yld2000-2d屈服函数。5. The method for measuring the thickness anisotropy coefficient and yield stress of a pipe material in any direction according to claim 1 or 2, wherein in the step 3, the plastic potential function g can adopt the expression of the yield function f, That is, g=f; the yield function f is Hill48 yield function, Barlat89 yield function or Yld2000-2d yield function.
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