有机玻璃非线性应力松弛行为表征与本构模型

On the characterization and constitutive model of PMMA nonlinear stress relaxation behavior

通过实验测定了有机玻璃(PMMA)在不同初始应变率和初始应变下的应力松弛曲线。分析了三种应变率(0. 001s^-1.0. 01s^-1和0.1s^-1)下不同初始应变(5%、7%、10%和15%)的实验结果。结果表明:初始加载应变率会影响有机玻璃高分子链段的运动速度,进而对应力松弛行为产生影响;不同初始应变对应力松弛的影响,则体现为不同变形程度对PMMA高分子链运动速度的影响。将PMMA的应力松弛视为两个阶段即应力快速松弛段和应力缓慢松弛段,基于对这两个阶段的分析,提出了一个非线性应力松弛本构模型。对实验得到的应力松弛曲线采用上面提出的本构模型进行数值拟合,吻合结果良好。此外,还对模型中参数的影响因素进行了分析讨论。结果表明该本构模型可以用于描述PMMA的非线性应力松弛行为。

In this paper, stress relaxation curve of PMMA at different initial strain rates and initial strains has been measured experimentally. Experimental results at different initial strains (5%, 7%, 10% and 15%) and three strain rates (0. 001^s-1 , 0. 01s^-1 and 0.1s^-1) were analyzed, respectively. Results show that the initial loading strain rate will affect the velocity of polymer chain motion of PMMA, and then further affect the stress relaxation. The effect of different initial strain on stress relaxation is reflected in the effect of different degree of deformation on velocity of PMMA polymer chain. Stress relaxation of PMMA may be regarded as two stages, that is, the stress fast relaxation stage and the stress slow relaxation stage. Based on the analysis of these two stages, a nonlinear stress relaxation constitutive model is proposed. Stress relaxation curve obtained from the experiment was fitted numerically by the constitutive model proposed above, and the result is in good agreement. In addition, the influence factors of parameters in the model were analyzed and discussed. It is concluded that the proposed constitutive model can be used to describe the nonlinear stress relaxation behavior of PMMA.