Plane strain wedge indentation revisited

Abstract

For a plane strain wedge indentation problem, detailed comparisons between slip-line field theory (SLFT) solutions, experimental observations and finite-element analysis results are carried out. Several past remaining questions on this problem are explored. The finite-element computations appear to account for the nature of a modified slip-line field solution (Petryk H. 1980 Journal de Mécanique Appliquée 4 , 255–282) that assumes the existence of an additional fan-shaped slip-line field just above the boundary between yielding and unyielding regions. For obtuse-angled wedges, finite-element computations show that the indentation load could be smaller for a rough wedge than for a smooth wedge. The question that was raised in the literature with respect to the reversed order of required loads for smooth and rough wedges is not necessarily a paradox. It is revealed that with increasing friction coefficient, a distinct deformation mode resembling the dead metal cap solution in the SLFT is established immediately after passing the critical friction coefficient value at which the contact mode theoretically changes from frictional sliding to perfect sticking. The profiles of the bulged-out lip material remain straight in all the finite-element computations for non-hardening materials. Nonlinearity of the lip profiles frequently observed in experiments appears in the presence of strain hardening or strain-rate sensitivity.

Characteristic material behaviors in conical indentation with friction

“…This behavior is fundamentally similar to the “dead metal cap” solution for the plane strain wedge indentation given by the slip‐line field theory [2, 8, 9, 21], whose validity has been confirmed by finite element simulations in ref. [5]. In the sliding cases with μ = 0 and μ = 0.1, instantaneous plastic loading occurs below the whole contact surface (Figure 5b left and middle).…”

“…The profiles of the bulged‐out lip portion are strongly nonlinear even for a nonhardening material under axisymmetric conditions. In plane strain wedge indentation, the bulged‐out lip profile is completely straight for nonhardening materials [5].…”

“…Under $$E/{\sigma _0}$$ = 400 with μ = 0, values of $$s/h$$ are 0.41, 0.16, and 0.03 for θ = 60°, 70°, and 80°, respectively. The corresponding $$s/h$$ values for plane strain wedge indentation were 0.47, 0.27, and 0.08 [5] for the same material. The new surface ratio $$s/h$$ is smaller in axisymmetric conical indentation than in plane strain wedge indentation for the same material.…”

“…The indentation depth c in finite element calculations is obtained by subtracting b 0 (Figure 1b) from the vertical rigid indenter displacement (downwards positive). The same finite element model with the reversed‐round portion was used for the plane strain wedge indentation problem and gave precise results consistent with experimental results [5]. As shown in Figure 1a, a rectangular fine mesh region of $$( {{R_0}/20} ) \times ( {{L_0}/40} )$$ is considered to be the indentation area with a uniform 80× 40 rectangular element mesh.…”

“…Recently, in ref. [5], the efficiency of the slip‐line field theory in the analysis of the wedge indentation has been revisited by comparing its results with finite element analysis results and experimental observations. Several past remaining questions on this problem were resolved as follows.…”