M.Sc Thesis


M.Sc StudentTal Cohen
SubjectConstitutive Aspects of Static and Dynamic Cavitation in
Elastoplastic Solids
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Emeritus Durban David


Abstract

Spontaneous growth of an embedded cavity in a solid due to constant external or internal applied pressure is defined as cavitation. Assessment of cavitation fields is helpful in studying penetration behavior and severe stress concentration factors, which are related to fracture and fatigue, with further examples of cavitation processes in the field of biomechanics of soft tissue. Naturaly, cavitation models are based on several constitutive assumptions such as material parameters and yield criteria which may influence theoretical predictions.

In the present study we have conducted analytical and numerical investigation of static and dynamic cavitation fields in elastoplastic media with different geometries. We expose constitutive sensitivities of the phenomena while aiming at uniform treatment of cavitation and facilitating the application of plane-stress cavitation fields to penetration predictions.

We begin by investigating quasi-static plane-stress cavitation in elastic, hypereslastic and elastoplastic materials. It has been found that while uniformly, in all examined materials, cavitation due to remote tension does occur, in the case of internal pressure no asymptotic value of applied pressure exists. This finding contradicts the results of available studies in plane-strain and spherical cavitation fields, where cavitation due to internal pressure does occur. However, a new energy based definition does predict cavitation under internal and external pressure for all three geometries. Further application of the suggested specific cavitation energy concept to penetration prediction in elastoplastic media shows good agreement with experimental data. 

The dynamic process of steady-state self-similar spherical cavity expansion in elastoplastic media with arbitrary hardening characteristics is also examined. Emergence of plastic shock waves at high expansion velocities is exposed and identified with appearance of spherical singularity surfaces. All jump conditions at the shock discontinuity are accounted for and entire deformation field is analyzed. Constitutive sensitivities of field variables and effect of the plastic shock on cavitation pressure are illustrated. Simple relations for characteristic values at the shock are obtained and asymptotic analysis of the near cavity wall boundary layer is conducted, supporting the obtained numerical, solution.

Overall, we expect the contribution of this study to shed light on sensitivities of static and dynamic cavitation models to constitutive assumptions. The new energy based definition of cavitation allows unified treatment of cavitation fields for different materials and different geometries, under internal and external pressure and is useful in prediction of penetration processes. Furthermore, the exposure of shock wave behavior in dynamic cavity expansion may broaden our understanding of extreme penetration processes such as impact cratering.