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金属学报  2015, Vol. 51 Issue (11): 1356-1364    DOI: 10.11900/0412.1961.2015.00176
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一种基于黏弹性理论预测DP600钢板滞后回弹的新模型*
孙帅,鄂大辛()
A NOVEL MODEL BASED ON VISCOELASTIC THEO- RY TO PREDICT THE TIME-DEPENDENT SPRINGBACK FOR DP600 STEEL SHEET
Shuai SUN,Daxin E()
School of Materials, Beijing Institute of Technology, Beijing 100081
引用本文:

孙帅,鄂大辛. 一种基于黏弹性理论预测DP600钢板滞后回弹的新模型*[J]. 金属学报, 2015, 51(11): 1356-1364.
Shuai SUN, Daxin E. A NOVEL MODEL BASED ON VISCOELASTIC THEO- RY TO PREDICT THE TIME-DEPENDENT SPRINGBACK FOR DP600 STEEL SHEET[J]. Acta Metall Sin, 2015, 51(11): 1356-1364.

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摘要: 

通过加载不同预应变和保压时间获得了DP600钢板的室温滞后回弹响应. 基于黏弹性理论, 采用309 MPa恒应力室温蠕变实验, 获得了预测滞后回弹过程的蠕变柔量函数. 基于DP600钢板室温弹性和塑性加载响应, 修正了线黏弹性本构方程的积分下限, 将柔量函数与修正的应力率函数进行卷积, 获得了影响滞后回弹过程的加载历史效应. 再将加载历史应变波形与卸载脉冲叠加, 获得不同预变形量的滞后回弹应变预测值. 结果表明, 滞后回弹初期应变率较高, 之后应变率逐渐降低; 随着预应变的增加, 滞后回弹应变的绝对值逐渐递增, 并且滞后回弹占总回弹比例逐渐增加; 滞后回弹预测方向与瞬时回弹方向相同, 与加载方向相反; 相同时间段内, 蠕变回弹应变比滞后回弹应变明显降低, 与滞后回弹实验相比, 蠕变恒应力与蠕变回弹应变的比值随预应变的变化规律呈现出良好的线性关系; 基于黏弹性理论的修正模型所得到的预测值接近实验测量值, 并能够较好地反映实验变化规律.

关键词 DP600钢板滞后回弹蠕变回弹Kelvin模型    
Abstract

DP600 steel sheet with high strength has drawn much attention in the automotive industry, but the shape change following forming and unloading has not been known widely. The time-dependent springback of DP600 steel sheet was investigated under different pre-strains by uniaxial tension. According to the viscous behaviors under the elastic and plastic loading tests, the lower limit of integration in the constitutive equation of linear viscoelasticity was modified and the creep compliance was gained from the creep curve at a constant stress level of 309 MPa at room temperature. The predicted curve was acquired by using the superposition of the unloading impulse and the historical loading curve. The results reveal that the strain rates with high initial values gradually decreased following unloading at room temperature. As the pre-strain went up, both the absolute anelastic strain of time-dependent springback and the anelastic proportion of the total springback increased. Meanwhile, the direction of the time-dependent springback was same as that of the initial springback and opposite to the loading direction. In the same springback period, the ratio of the unloading stress to the creep springback strain tended to vary more linearly with the pre-strain than those obtained from immediate unloading. The simulated results using the revised model are in good agreement with the experimental data.

Key wordsDP600 steel sheet    time-dependent springback    creep springback    Kelvin model
    
基金资助:* 国家自然科学基金资助项目51175044
图1  DP600钢板单向拉伸应力-应变曲线
图2  滞后回弹瞬时模量Eu-预应变ei曲线
Specimen si / MPa Δeis Eu / GPa Δer Ei / GPa etol p / %
EI-0.06 116 -0.00060 193.3 - - -0.00060 -
PI-0.2 309 -0.00164 188.4 -0.00006 5150 -0.00170 3.53
PI-5 593 -0.00434 136.6 -0.00020 2965 -0.00454 4.41
PI-8 653 -0.00496 131.7 -0.00028 2340 -0.00524 5.32
PI-10 678 -0.00516 131.4 -0.00030 2260 -0.00546 5.49
PI-15 729 -0.00578 126.1 -0.00042 1735 -0.00620 6.77
表1  试样经直接卸载后的瞬时回弹与滞后回弹
图3  滞后回弹占比p与ei关系曲线
图4  滞后回弹应变Δer与时间的关系曲线
图5  DP600钢板在较低和较高恒应力下保压4 h的蠕变曲线
图6  DP600钢板蠕变保压4 h的蠕变回弹应变和蠕变回弹降幅占比k
图7  DP600钢板柔量函数拟合及局部放大图
Specimen sic / MPa Δeisc Euc / GPa Δerc Eic / GPa etol v / %
PC-0.2 309 -0.00178 167.4 -0.00006 5150 -0.00184 3.26
PC-0.3 362 -0.00216 166.6 -0.00008 4525 -0.00224 3.57
PC-0.33 371 -0.00224 165.1 -0.00008 4637 -0.00232 3.44
PC-0.4 384 -0.00232 163.7 -0.00008 4800 -0.00240 3.33
PC-5 593 -0.00446 132.9 -0.00014 4235 -0.00460 3.04
PC-10 678 -0.00544 124.6 -0.00016 4237 -0.00529 2.83
PC-15 729 -0.00618 117.9 -0.00018 4050 -0.00636 2.83
表2  蠕变保压4 h后的蠕变瞬时回弹与蠕变回弹
图8  应力率-时间曲线和应力-时间曲线
图9  不同预变形量的卷积拟合曲线及局部放大图
图10  弹性后效应变曲线和滞后回弹应变预测曲线
图11  滞后回弹实测应变与预测应变随预应变εi的变化规律
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