טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKadin Yuri
SubjectCyclic Loading of Elastic-Plastic Spherical Contacts
DepartmentDepartment of Mechanical Engineering
Supervisors Dr. Yuri Kligerman
Professor Emeritus Izhak Etsion
Full Thesis textFull thesis text - English Version


Abstract

The frictionless cyclic contact between an elastic-plastic sphere and a rigid flat is investigated theoretically in the present work. Two types of contact are considered here: non-adhesive contact in which attraction between surfaces of contacting bodies is excluded, and adhesive contact in which surface attraction exists along with surface compression. A single loading-unloading cycle was analyzed in the case of non-adhesive contact. Numerical simulations were performed for a wide range of material and geometrical properties of a deformable sphere. The results of the numerical study were presented in a dimensionless form, normalized by the critical values of interference, contact load, contact radius and contact area at the inception of plastic deformation. An elastic-plastic loading index was suggested, using energy considerations. This index may serve as a measure of the level of plasticity of the loaded sphere. The study of a single loading-unloading cycle was continued for subsequent loading-unloading cycles, showing purely elastic behavior after the completion of the first cycle. A statistical model of the single loading-unloading cycle of elastic-plastic contact of rough surfaces was developed and analyzed in the current work. The relations for mean separation and real contact area vs. the contact load during single loading-unloading cycle, and some residual topography parameters (new statistical distribution of asperity heights and the summit radii) after unloading completion were obtained. The concept of rough surface plasticity index, introduced in the classical work of Greenwood and Williamson, was revised in the current work introducing a new modified plasticity index, based on energy considerations. A numerical model for a single load-unload cycle of an elastic-plastic adhesive spherical micro-contact was developed in the current work. It was found that additional plastic deformation can occur during the unloading stage, indicating the so called ductile separation as was predicted in many previous works. It was also found that for the specific combination of physical parameters the surface of unloaded sphere can remain bonded to the flat causing material transfer from the sphere to flat. The adhesive contact model for the single loading-unloading cycle was later used for the simulation of cyclic contact. It was shown that in the case of a gold micro-sphere, which can simulate, for example, a MEMS micro-switch contact bump, plastic shakedown can take place. This finding can explain the specific failure mechanism which is frequently observed in MEMS micro-switches.