Dynamic behavior of a material is essential in applications such as collision, explosion, ballistic impact, high-speed machining, and metal forming. As impact loadings, as well as accidental or malicious explosions, may impose high loading rates to engineering structures, estimating the dynamic response of a material accurately is crucial. Therefore, an analytical strain rate-dependent criterion on ductile fracture initiation is developed at the continuum scale by further developing the energy balance concept. The criterion is based on continuum modeling of energy release rates, and the critical state is reached when the rate of energy change of fractured and unfractured states becomes equal. The formulation introduces a material length scale and a material property that is a function of strain rate and temperature. The developed ductile fracture criterion is implemented into two example applications, an aluminum alloy and a titanium alloy, whose experimental data are obtained from the open literature. Fracture loci of these alloys at various strain rates and the critical energy release rates as a function of strain rate are determined. The results of the example applications agree well with the experimental results reported in the literature.

在诸如碰撞，爆炸，弹道冲击，高速加工和金属成型等应用中，材料的动态行为至关重要。由于冲击载荷以及意外或恶意爆炸可能会给工程结构带来很高的载荷率，因此准确估算材料的动态响应至关重要。因此，通过进一步发展能量平衡概念，在连续尺度上发展了与韧性断裂起始有关的分析应变率相关准则。该标准基于能量释放速率的连续模型，当断裂状态和未断裂状态的能量变化率相等时，达到临界状态。该配方引入了材料长度尺度和作为应变率和温度的函数的材料特性。制定的延性断裂准则被应用到两个示例应用中，即铝合金和钛合金，其实验数据可从公开文献中获得。确定了这些合金在各种应变速率下的断裂轨迹以及临界能量释放速率与应变速率的关系。示例应用程序的结果与文献中报道的实验结果非常吻合。