Dynamic fracture problems involving highly transient crack growth histories : an investigation of dynamic failure in homgeneous and bimaterial systems

Citation

Liu, Cheng (1994) Dynamic fracture problems involving highly transient crack growth histories : an investigation of dynamic failure in homgeneous and bimaterial systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/k32y-0450. https://resolver.caltech.edu/CaltechETD:etd-12122007-141145

Abstract

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Highly transient elastodynamic fracture processes in both homogeneous and bimaterial systems have been investigated. It is found that due to the wave character of the mechanical fields during transient and dynamic crack growth, the customarily assumptions of steady state and K[superscript d]-dominance may be violated. This may be particularly true during crack growth in laboratory size specimens where crack growth seldom reaches steady state conditions due to the persistence of the initiation transients and the influence of reflected stress waves from the specimen boundaries. By relaxing both restrictions of steady state and of K[superscript d]-dominance, and by permitting the crack-tip speed and the dynamic stress intensity factor to be arbitrary functions of time, the transient asymptotic elastodynamic field near the moving crack-tip was established in the form of higher order expansion for both homogeneous solids and bimaterial systems. In homogeneous solids, we considered cracks that propagated along arbitrary smooth paths, while in bimaterial systems, we only considered crack growth along a straight interface. The higher order coefficients of the asymptotic expansion were found to depend on the time derivative of crack-tip speed, the time derivative of the dynamic stress intensity factors, and for crack propagating along curved paths, on the instantaneous value of the local curvature of the crack path.

The issue of K[superscript d]-dominance during dynamic crack initiation and transient crack growth was further investigated by solving a particular transient initial/boundary value problem. This corresponds to a planar dilatational wave impinging on a semi-infinite crack in an unbounded elastic solid. The crack initiates under the influence of the wave, and then propagates dynamically. Through comparison of this full field solution and the equivalent K[superscript d]-dominant field or the field represented by the higher order transient terms, it is found that even for points which are relatively far away from the crack-tip, or for times very close to the crack initiation, the higher order transient representation provides a very good description of the actual stress field. The K[superscript d]-dominant field, however, is incapable of approximating the complete stress field with any accuracy (lack of K[superscript d]-dominance).

The implications of the above observations (possible lack of K[superscript d]-dominance) on the interpretability of dynamic fracture experiments are also explored. The interpretation of experimental data in past laboratory investigations of dynamic fracture events is based on the assumption of K[superscript d]-dominance. However, as we have seen theoretically this assumption may often fail in laboratory situations. As a result, experimental measurements must be analyzed by techniques that allow for the possibility of the existence of transient higher order term effects. Several types of experiments are considered as examples. Plate impact experiments involving very high rates of loading are first analyzed by both a K[...]-dominant and a high order transient approach. The results clearly show the strong effects of transients on the interpretation of the data. As a second example, the optical method of caustics is reanalyzed. A new way of extracting the instantaneous value of the dynamic stress intensity factor K[...](t), which takes transients into account, is proposed and verified theoretically. For the bimaterial system, the issues are equivalent but much more complicated analytically. Here transient effects are found to be magnified by the material property mismatch between the constituent solids. It is shown however, that the higher order transient analysis can predict accurately the fringe patterns from actual experiment performed by means of the CGS (Coherent Gradient Sensing) technique and high speed photography.

The observations of this thesis suggest that a variety of conclusions made in the literature based on interpretations of experimental data on the basis of steady state or K[superscript d]-dominance may be suspect.

Thesis Files