Elastoplastic load–depth hysteresis in pyramidal indentation

Extensive indentation tests were conducted for nineteen different engineering materials ranging from brittle to ductile materials, and including hard ceramics, ductile metals, and a soft organic polymer. Three tetrahedral pyramid indenters with specific face angles β [shallow pyramid (β = 10°), Vickers (β = 22°), and sharp pyramid (β = 40°) indenters] were used. All the materials tested were subjected to the quadratic load P and penetration depth h relationship P = k₁h² on loading, and most of the tested materials to the quadratic unloading relationship of P = k₂(h − h_r)² with the residual depth h_r after a complete unload. To determine the contact area at peak indentation load, a specially designed depth-sensing instrument was constructed, on which the contact behavior during loading/unloading was examined by through thickness observation of transparent specimens. All the characteristic indentation parameters were investigated on the basis of simple elastoplastic model, and correlated well with the nondimensional strain E′ tan β/H, in which the elastic modulus E′ was a measure for elasticity, true hardness H was a measure for plasticity, and the inclined face angle β characterized the indenter. The ratio of the conventional Meyer hardness H_M to the true hardness H of the materials tested ranged from 0.2 to 0.9 as a function of E′ tan β/H. The cavity model suggested that true hardness H is expressed by the yield stress Y through a constraint factor C as H = C · Y with C ≈ 5.