Plane strain cylindrical indentation of functionally graded half-plane with exponentially varying shear modulus in the presence of residual surface tension

摘要

Highlights?Inhomogeneity doesn’t modify the effect of surface parameters on contact response.?Contact response changes if contact size nears surface parameter based length scale.?Smaller indenter leads to stiffer response of inhomogeneous half-plane.?Exponentially graded half-plane will be relatively tougher during nano-indentation.Graphical abstractSmoother transition and relatively lesser tensile magnitude of the in-plane normal stressσyyalong the surfacex=0in the vicinity of contact edge is observed during cylindrical indentation of elastic half-plane with exponential graded shear modulus (k?>?0) in the presence of residual surface tension(S=/0). Hence it is speculated that chances of crack formation are lesser during sub-micron level indentation as compared to micro or macro indentation in such graded half-plane.Display OmittedAbstractA functionally graded half-plane with shear modulus varying exponentially along the direction normal to the surface and surface effects accounted through Gurtin–Murdoch model, indented by long rigid smooth cylindrical indenter is solved to understand the effect of material inhomogeneity and surface effects on indentation response. The Green’s function relating surface load to surface displacement under plane strain condition is obtained semi-analytically through the combination of Airy stress function approach and Fourier transforms and utilized to solve the contact problem. The solution is used to study the effect of inhomogeneity through grading parameter and surface effects through residual surface tension based intrinsic length scale on the contact pressure, contact size and in-plane normal stress on the surface responsible for cracks during indentation.]]>