低速碰撞下复合材料叠层板的微裂纹演化及其对弹性模量的影响

Evolution of micro-cracks in a composite laminated plate and its effect on elastic moduli under low velocity impact

采用双线性特性破坏模型研究了复合材料叠层板各层内部开裂裂纹的演化;通过引入弹性模量的裂纹影响系数表示,推导出裂纹影响系数与应变及应变率之间的微分关系,并得到裂纹耗散功率与裂纹影响系数变化率之间的关系。通过计算不同初始碰撞速度下复合材料叠层板的应变、应变率响应以及裂纹影响系数的演化,得到整个冲击过程中各层内任意点附近裂纹开裂情形及其对弹性模量的影响;通过检查界面各点处的裂纹影响系数是否发生改变,预测了碰撞完成之后复合材料叠层板中各层内微裂纹的分布区域位置与大小;并将该预测结果与其他破坏准则计算结果进行了比较。计算结果表明,在碰撞过程中各层内任意点处的应力值超过其屈服强度后,该点附近的弹性模量开始发生衰减,衰减大小随铁球初始碰撞速度的增大而增大。在四边夹支的边界条件下,复合材料叠层板的裂纹分布区域同样最先出现在碰撞点及边界中点位置,区域面积随初始碰撞速度的增大不断扩大。

The evolution of micro-cracks in a composite laminated plate was studied by using a double-linear characteristic model of damage. Inducing crack-effect coefficients for elastic moduli, a set of ordinary differential equations about crack-effect coefficients were derived. Furthermore, the relations between dissipated power and crack-effect coefficients during the cracking process were also deduced. Together with the dynamic governing equations of a composite laminate, these ordinary differential equations could be solved when initial conditions were known, the crack-effect coefficients were obtained. Hence, the micro-cracks＇ expanding in every point of a lamina and its effect on elastic moduli could be obtained. Subsequently, the distribution regions of micro-crack after impact were predicted by examining whether any of crack-effect coefficients was changed at all points in the lamina. The result showed that the elastic moduli starts to decay at the point where the stress reaches its yield strength, and the decaying amplitude increases with increase in the initial impact speed of iron ball; with all boundaries clamped, the distribution regions of micro-crack appear initially both the impact point and near the center of boundaries of composite laminates; moreover, they expand with increase in the initial impact velocity.