Abstract：Brittle solids usually break into many pieces (fragmentizes) during a uniform high strain rate expansion process. This paper established a 1-D theoretical model to study the inner unloading of a 1-D brittle solid during a fragmentation process, and developed a method to calculate the average fragment size. Assuming that there exists an array of equally-spaced cracks in the 1-D solid, and the cracks open and develop simultaneously under a rapidly expanding rate. By symmetry, a unit crack body containing a crack is analyzed, with the separation behavior described by a cohesive law, and the dynamic response of the undamaged solid described by the elastodynamic equations. The problem is numerically solved using a differential scheme along the characteristic lines. Stress distributions in the crack body at different times and the average stress across the crack body are gained. The critical time at which the average stress is unloaded to zero is determined. It is found that for a prescribed strain rate, there exists an optimum crack spacing corresponding to the rapidest unloading process. Assuming that in a natural fragmentation process the brittle solid is unloaded in the fastest way, the average fragment size can be estimated. The calculation results show that this fragment size estimation agrees fairly well with the numerical results obtained previously allowing random crack nucleation. Effect of the cohesive fracture law on the average fragment size is also investigated with this “rapidest unloading property”.
2010, Vol. 31 
