SHPB实验中粘弹性试件内部应力波的传播

建立描述SHPB实验中线性粘弹性试件内部应力波传播的控制方程组.根据试件两端与入射杆及透射杆接触的应力波特征关系给出耦合边界条件.对方程组和定解条件进行Laplace变换,求得试件内部应力在变换域像函数的表达式.采用数值反变换技术进行反Laplace变换,获得试件两端的应力时程曲线.对现有的固定Talbot反变换算法进行改进:将入射波像函数分解为基本部分和延迟部分,利用固定Talbot算法对基本部分入射波作用下的波动问题求解,其他部分的解通过延迟定理得到,最终解为两部分的叠加.采用这种改进算法得到的不同入射波下粘弹性试件的内部应力解与传统的基于特征线数值模拟方法的结果吻合.在此基础上探讨了粘弹性试件的几何参数和材料本构参数对透射波波形的影响.

STRESS WAVE PROPAGATION IN A VISCOELASTIC SPECIMEN DURING SHPB TESTS

Partial differential equations (PDEs) governing one-dimensional stress wave propagating within a viscoelastic specimen in Split Hopkinson Pressure Bar (SHPB) tests are established.Coupled boundary conditions (BCs) at both ends of the specimen are derived by using the characteristic equations in the incident bar and the transmitting bar.Laplace transform of the governing equations turns the PDEs into ordinary differential equations,which can be solved analytically together with the transformed BCs.The inverse Laplace transform of the solution gives the time histories of stress at arbitrary site.A modified Fixed Talbot (FT) algorithm is proposed to realize the inverse transform numerically.Results from this algorithm agree well with those obtained from the finite difference computation.Using this technique,parametric investigations are conducted to study the influences of specimen length and material parameters on the transmitting stress waveforms.