Study on concavity-convexity transition of loading curve for spherical indentation

Spherical indentation has a unique deformation pattern and shows a different deformation behavior compared with other kinds of indentations. In this paper, a special feature of the loading curve for spherical indentation was found, the loading curve transforms from concavity to convexity. The traditional Meyer's law failed to cover the transition phenomenon accurately, so a cubic-polynomial empirical model was proposed based on experiment results and theoretical analysis. Comparison results proved that this model gave a good description to the both loading curve and tangent slope curve of spherical indentation. Further study was conducted using the proposed model and finite element simulation method. Parameters including hardening index(n), elastic modulus(E) to yield stress(Y) ratio, Poisson's ratio(ν), indenter radius(R) and friction coefficient(μ) were analyzed on their influence on the shape of loading curve. It was found that n had a decisive influence to the concavity-convexity transition phenomenon. When n ≤ 0.1 the quadratic coefficient C2 will be negative and the concavity-convexity transition phenomenon will never occur. When n > 0.1, the loading curve transforms from concavity to convexity. Further studies found that two deformation patterns i.e. vertical indenting and radial expansion were the reason of the concavity-convexity transition phenomenon.