טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTylis Arie
SubjectRigid Spherical Projectile Penetration into Semi Infinite
Target
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Emeritus Jehuda Tirosh
Dr. Amnon Shirizly
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The mechanics of plastic indentation by spherical impression is a widely considered subject in engineering and material sciences. It involves the measurement of the size of the residual plastic impression on the specimen face for a given indenting load (via a rigid ball), from which the material hardness is assessed, as suggested long time ago by Brinell (Brinell hardness test). Bounding analysis of such slow process is suggested with the inclusion of frictional effects. In addition, the present work analyses dynamic ballistic penetration of rigid spherical projectile into semi infinite targets which are brittle or ductile like materials. The target reacts ideally as perfect plastic solid, meaning that the elastic strains are neglected and the plastic flow is fully developed from the beginning of the penetration process. Physical equations which describe the indenting load in slow process were developed in part A of the work. These equations were widened in part B in order to calculate the residual penetration depth of rigid projectiles impacting the target in a relatively high speed (up to 1 km/sec). The difference between the two solutions is that the quasi-static solution deals with the evolution of the non-steady indentation whereas the dynamic solution includes the inertia terms in a self-similar fashion throughout. The influence of the frictional shear along the projectile/target interface is included in the solution. As the ball indents deeper into the solid, the analysis indicates that the friction effect starts to show significance due to wider contact area. The work incorporated analysis for estimating the evolving plastic zone size near the projectile head. In slow indentation process it is based on minimum dissipation rate and backed with self-made laboratory tests. In the dynamic penetration process the evolution of the plastic zone is chosen such that their locus provides the highest residual penetration depth. Agreements with independent FEM solution and field data accompany successfully the suggested solution. From the visual indentation experiment it is apparent that there is no significant deviation in the indenting loads between various geometries of indenter's nose. It is due to the fact that the flow stream lines do not always follow the geometries of the indenters’ faces. The ‘decision’ where to flow is provided by the minimum energy consideration, which depends somewhat on the tool/material frictional conditions. This information, in contrast to the well known Cavity Expansion Model (CEM), is accessible in the suggested bounding approach.