Investigation On The Deformation, Fracture And Fragmentation Of Brittle Solids Under Initial Expanding Impulses

Fragmentation is an important material failure mode in high-velocity impacts. The study on dynamic fragmentation is of great significance both in the academic research and the engineering applications. This paper established a 1-D theoretical model to study the deformation-fracture process of brittle solids having an initial expanding impulse. Then fragmentation phenomena of materials under high strain rates are investigated in detail. Finally, assuming that in a natural fragmentation process the brittle solid is unloaded in the fastest way, the average fragment size are estimated. This thesis is divided into three parts:1 The deformation and fracture processes of brittle solids under initial expanding Momentum is studied.Using the elastodynamic equations for the undamaged solid and a cohesive law for the separation behavior of the material, and considering three different boundary conditions, three initial-boundary problems (IBVP) were established perfectly. The problems were solved with two approaches: using Laplace transform technique and using a differential scheme along the characteristic lines. The solutions of the IBVPs gave rise to the exact expressions for the cohesive stress of the crack. The numerical solution agrees with the theoretical solution, proving validity and reliability of both two methods. By the analysis, it is concluded that fracture of solids most easily occurs during the high strain rate expansion process.2 The fragmentation of brittle solids during a uniform high strain rate expansion process is investigated.Based on the above results, more important study is started to learn the fragmentation process of brittle solids during under a uniform high strain rate expansion process. a one-dimensional (1-D) theoretical model is established to investigate the inner unloading of a brittle solid bar during the fragmentation process. The developed method can be used to calculate the average fragment size, assuming that there exists an array of equally-spaced cracks in the 1-D solid bar, and that the cracks open and develop simultaneously during the rapid expansion process. More extensive cohesive law were exployed to describe the crack dynamic expanding process. 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.3. The"rapidest unloading property"on dynamic fragmentation process.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".