Mathematical Model of the Specimen Shape During the Necking Stage in the Uniaxial Tensile Test
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摘要: 在分析圆棒试样单向拉伸试验颈缩阶段试样形状特征的基础上建立了描述试样形状的数学模型,即试样自由表面上任一点所在垂直于中心轴线截面的半径r关于该截面与颈缩底部最小截面间的距离z(z≥0)的分布函数为r=${r_n} + \frac{{{r_c} - {r_n}}}{{1 + {{(\frac{z}{{{z_1}}})}^{{p_1}}} + {{(\frac{z}{{{z_2}}})}^{{p_2}}}}}$,在以颈缩底部最小截面中心为原点、中心轴线为z轴的直角坐标系中,试样自由表面的曲面函数为√x2+y2=${r_n} + \frac{{{r_c} - {r_n}}}{{1 + {{(\frac{z}{{{z_1}}})}^{{p_1}}} + {{(\frac{z}{{{z_2}}})}^{{p_2}}}}}$;在该数学模型中,试样形状可以通过6个特征参数(rc、rn、z1、z2、p1、p2)来表征。一种低合金钢圆棒试样单向拉伸试验颈缩形状实测数据和3种不同的各向同性均质弹塑性材料圆棒试样单向拉伸试验数值模拟结果验证了上述数学模型的有效性。Abstract: The mathematical model of the necking shape is built based on the analysis of the shape characteristics during the necking stage in the uniaxial tensile test. It is that the radius r of the section vertical to the central axis is the function about the distance z(z≥0) from this section to the minimal section. This function is r=${r_n} + \frac{{{r_c} - {r_n}}}{{1 + {{(\frac{z}{{{z_1}}})}^{{p_1}}} + {{(\frac{z}{{{z_2}}})}^{{p_2}}}}}$. The function of the necking sample's surface is √x2+y2= ${r_n} + \frac{{{r_c} - {r_n}}}{{1 + {{(\frac{z}{{{z_1}}})}^{{p_1}}} + {{(\frac{z}{{{z_2}}})}^{{p_2}}}}}$ in the coordinate system with the origin at the center of the minimal sec[JP4]tion of the necking specimen and the central axis as the z-axis. The necking shape can be attributed with the six characteristic parameters of rc、rn、z1、z2、p1、p2 in this mathematical model. The availability of the necking shape's mathematical model is verified by the curves' fitting with the test data of the low alloy steel and the simulation data with three sets of the stress-strain relationship's parameters.
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Keywords:
- uniaxial tensile test /
- necking shape /
- mathematical model
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