Method for measuring large-stress range stress strain in uniaxial tensile test of metal round bar sample

[0034] Example one

[0035] (1) The present invention takes a low-carbon steel round bar sample as an example, using figure 1 The round bar sample shown is subjected to a uniaxial tensile test. The initial cross-sectional diameter of the round bar sample is 10mm, and the gauge length is 50mm. Such as figure 2 As shown, an extensometer is used to measure and record the load F from the point of maximum load (necking point) to the point before breaking. i And instantaneous gauge length l i , Formed as image 3 The load-displacement curve shown, using optical measurement method to record the minimum section radius a of the necking at each time i. Among them, i=0~N, 0 and N correspond to the point of maximum load (necking point) and breaking point respectively;

[0036] (2) The metal round rod specimen always spreads and deforms at the minimum necking point after necking instability, and does not participate in the deformation outside the minimum necking point. Such as Figure 4 As shown, the minimum necking section corresponding to time i is simplified as the radius a i The uniform cylinder and the uniform cylinder at all previous moments constitute a ladder model of the stretching and necking expansion of the round bar specimen. Based on the law of volume invariance, the uniform cylinder radius a i And instantaneous gauge length l i And the uniform cylinder radius a at the previous moment i-1 And instantaneous gauge length l i-1 Substitute into the following formula,

[0037] φ i l i-1 πa i-1 2 =(φ i l i-1 +l i -l i-1 )πa i 2 (1)

[0038] Can calculate the percentage of the cylinder at the moment in the previous moment φ i , Where 0 i <1;

[0039] (3) Set the step corner point P of each cylinder boundary at time i j Coordinates (x j ,y j ), where j=0~i-1, the boundary of the sample gauge length at the beginning of the necking i=0 (ie the corner of the cylinder boundary) is taken as the origin of the coordinate, namely P 0 The coordinates are (0,0), x i =y i =0, take the length of the sample as the x-axis and the radial direction of the cylindrical section as the y-axis, then P when j=1~i-1 j Coordinates (x j ,y j )Calculated as follows,

[0040]

[0041] Let P i Is the midpoint of the cylinder generatrix of the smallest section of necking at time i, and its coordinates are expressed as

[0042]

[0043] Through the step corner point P of each cylinder boundary at time i i (j=1~i) perform interpolation, establish an expression of the interpolation function f(x) that approximates the necking profile curve corresponding to i at this moment, and ensure that the interpolation function f(x) is in P 1 And P i The first derivative of a point is zero, that is, f'(x 1 )=f'(x i )=0. Use the curvature formula to calculate the interpolation curve in P i The radius of curvature at the point R i , which is

[0044]

[0045] (4) According to the Bridgman method, the load F at time i i , The minimum section radius at the necking a i And the radius of curvature R i , Substituted into formulas (1) and (2),

[0046]

[0047]

[0048] Calculate the true strain ε corresponding to time i i And true stress σ i.

[0049] (5) Repeat the steps (2) to (4) above to calculate the true strain ε at i=0 to N respectively i And true stress σ i , So as to obtain Figure 5 Shown is the stress-strain curve of the metal round bar specimen from tensile instability to the end of fracture.

[0050] Example two

[0051] The finite element analysis software ABAQUS was used to simulate the uniaxial tensile process of the round bar specimen. According to the size and conditions of the uniaxial round bar specimen in Example 1, a finite element model of the uniaxial tensile test process was established, and input presets The stress-strain curve is used as the material model. The simulation analysis and the experiment of Example 1 adopt the same constraints and loading conditions, one end is fixed axially, and one end is loaded with the same speed load as the axial direction of the specimen to simulate the tensile process of the specimen. According to the method of obtaining data from the tensile test, take the difference between the two cross-sectional displacements of the gauge length section of the simulation result as the displacement value, and use the resultant force of the interface of the gauge length section obtained by the simulation to draw the relationship curve between displacement and force. Load F at all times after obtaining the maximum load point (necking point) until the break i And instantaneous gauge length l i , The minimum section radius a at the necking point at each time can be calculated from the node displacement on the minimum section at the necking i , Where i=0~N, 0 and N correspond to the maximum load point (necking point) and breaking point time respectively. Load F at each time after the maximum load point is obtained based on the finite element simulation results i , Instantaneous gauge length l i And minimum section radius at necking a i Calculate the stress-strain curve according to the steps (2), (3), (4), (5) in the first embodiment, and compare it with the stress-strain curve measured by the finite element input in the first embodiment, such as Image 6 As shown, it can be seen that the two curves are almost overlapped, indicating that the stress-strain curve in the large strain range obtained by the technical solution of the present invention has high accuracy, thus proving the accuracy and effectiveness of the technical solution of the present invention.

[0052] In the first and second steps (3), the interpolation method used to establish the expression of the interpolation function f(x) that approximates the necking profile curve corresponding to this moment i is cubic spline interpolation. In this embodiment, the current Some programs or codes written in accordance with this method.