Micro-macro Analysis of the Notch Tip Radius and Loading Rate Dependences of the Dynamic Crack Initiation Toughness during a High Transient Dynamic crack Growth Experiment

摘要

The risks due to crack propagation under dynamic loading are still difficult to estimate. Unlike quasi-static cases, where the loading and crack position can be easily established, in dynamic impact cases, loading conditions, propagation parameter variations and exact crack positions are difficult to control. The determination of relevant constitutive crack propagation laws from dynamic crack propagation experiments is thus a challenging operation. Consequently, the first step for assessing dynamic crack propagation laws is the development of numerical simulation tools. Some numerical tools are now able to represent dynamic crack growth but these numerical results have to be compared with experimental results to ensure that the numerical laws introduced are physically consistent. In a previous work [1], crack tip position histories have been determined by standard optical tools. The test rig was a split Hopkinson pressure bar (SHPB) and the specimen geometry was chosen in order to provide direct conversion between impacting compressive waves and tensile waves in the vicinity of a machined notch. Since the material used (PMMA) was transparent, the crack tip position history was obtained by using standard optical tools (four cameras providing one picture per camera) and by carrying out the same tests, repetitively and reproducibly. Three different phases were observed: two propagation phases were separated by a crack arrest phase. Using an eXtended Finite Element Method (X-FEM), numerical simulations were performed and both the crack path and the crack position histories fitted the experimental results. Failure in glassy polymers has been extensively investigated for PMMA, which is well documented [2, 3, 4]. The toughness under mode I loading increases with loading rate and its value is also notch sensitive. Therefore, the criterion adopted in the foregoing X-FEM analysis with a set of parameters for the onset of crack advance, its dynamic propagation, arrest and conditions for re-propagation appears to approximate the rate-dependent process underlying failure. However this kind of comparison allowed the validation of a dynamic crack growth criterion but only in a unique case of loading. The previous process leads to a large experiments number for obtaining different crack tip position histories corresponding to different loading rate and the loading rate influence on the transient propagation phases as arrest and restart cannot be represented accurately if several experiments are needed to obtain a crack tip position history.