Spherical indentation of elastic-plastic solids
نویسندگان
چکیده
The finite-element method is used to perform an accurate numerical study of the normal indentation of an elastic-plastic half-space by a rigid sphere. The effects of elasticity and strain-hardening rate of the half-space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R) and the yield strain of the half-space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic-plastic deformation; (iii) plastic similarity regime; (iv) finite-deformation elastic contact; and (v) finite-deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain-hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain-hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2× 10−4 and a/R < 0.16. Friction between the indenter and the substrate strongly affects the strain field beneath the indenter, and has a significant effect on the contact size as a function of indent depth. The effect of pre-stress within the half-space is also explored; it is found that the indentation response is hardly affected, except for the case of the elastic-plastic indentation regime.
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