动态碎裂过程中的最快速卸载现象

The rapidest unloading in dynamic fragmentation events

固体在高应变率加载作用下常常断裂成多个碎片.Grady针对韧性碎裂和脆性碎裂提出了一个同样形式的碎片尺度预测公式,对韧性碎裂结果预测较好,而对脆性碎裂结果的预测相对较差.是否存在一种物理机制可以同时阐述韧性碎裂和脆性碎裂过程呢?本文借鉴Grady解决绝热剪切问题时提出的最小集中化时间的思想,认为固体的动态碎裂过程中存在着最快速卸载现象.对韧性碎裂过程和脆性碎裂过程从理论和数值计算上进行分析,发现最快速卸载理论得到的平均碎片尺度和目前文献报道结果均吻合较好.

Solids usually break （fragmentize） into many pieces under high rate loading. Grady and co-worker have proposed one-dimensional theoretical models to estimate the average size of the fragments created in a ductile or a brittle fragmentation process. Numerical simulations have shown that the formulae, albeit identical in appearance, work well for the ductile fragmentation event, but poorly for the brittle case. In this paper we seek the physical mechanism that describes both the ductile and the brittle fragmentation processes. In analyzing the formation of multiple adiabatic shear bands, Grady and co-worker have proposed a conjecture that the bands automatically arrange their spacing so that the stress within the material is unloaded at the shortest time. In this paper, we apply Grady＇s ＂rapidest unloading＂ principle to three types of solid fragmentations： the multiple adiabatic shear localizations, the ductile tensile fragmentation, and the brittle tensile fragmentation. We analyzed the simultaneous formation and growth of an array of equally-spaced defects, and the unloading wave propagations in the defect-free region. The average stress across the region was determined, from which the critical fracture time, defined as the time when the average stress drops to zero, is evaluated. It appears that for a prescribed strainrate, there always exists an optimum defect spacing corresponding to the rapidest unloading process. Assuming that in a natural fragmentation process the solids is unloaded in the fastest way, this optimum spacing provides an estimate for the average fragment size. For the three types of fragmentation events, the fragment size evaluated by using ＂the rapidest unloading＂ principle compares fairly well with the other reasonable fragment size models.