基于有限差分法薄板激光冲击响应的数值模拟

在激光冲击载荷作用下, 薄板变形速度快, 诱导产生的应力波的传播过程较为复杂. 传统的测量工具难以对薄板变形过程中的动态响应进行有效的测量. 本文采用理论与实验相结合的方法, 构建了薄板在激光冲击下二维轴对称平面模型, 建立其拉格朗日运动方程, 利用有限差分法求其显式解, 分析薄板在激光冲击载荷作用下薄板的变形过程和应力波的传播过程, 并研究不同工艺参数对薄板动态响应特性的影响. 结果表明, 薄板变形初期的速度为振荡式增加, 在快速的拉胀式变形过程中会出现明显的回弹现象, 在光斑边界处产生向内和向外传播的应力波, 载荷的压力-空间分布以及边界约束条件也对薄板的动态响应结果有显著的影响. 激光冲击实验得到的结果与数值结果和预测结果基本吻合. 研究方法与所得结论可为薄板激光冲击成形过程中的参数优化提供参考. 

NUMERICAL SIMULATION ON RESPONSE OF SHEET METAL SUBJECTED TO LASER SHOCK WITH FINITE DIFFERENCE METHOD1)

With the action of laser pulse, the deformation velocity of sheet metal is fast, and the propagation of stress wave induced by laser shock wave in material is complex. It is difficult to effectively measure the dynamic responses of sheet metal with traditional measuring tools during the forming process. To solve this problem, theoretical analyses and experiments are used in this paper, a two-dimensional axial symmetric numerical model of sheet metal subjected to laser shock is constructed, the Lagrangian equation of motion is established to obtain its explicit solution with finite difference method, the displacement responses and the propagation of stress wave in the forming process of sheet metal with laser shock are studied, and the effects of different technological parameters on dynamic response characteristics of sheet metal are discussed. The results show that the velocity of sheet metal increases in an oscillatory manner in the initial stage of forming process, an obvious phenomenon of bounce can be observed during the rapid tensile deformation, and the stress wave formed at the edge of laser spot propagates inwards and outwards respectively along the redial. In addition, the dynamic response characteristics of sheet metal very rely on the spatial distribution of pressure pulse and the boundary conditions have considerable effects on final forming results of sheet metal. The results of laser shock experiment are consistent well with the numerical results and the theoretical prediction value. The method and the conclusions in this paper can be utilized to provide a reference for the parameters optimization in the process of laser shock forming.