Energy absorption and ductile failure in metal sheets under lateral indentation by a sphere

This paper is concerned with the mechanics of lateral indentation of a rigid sphere into a thin, ductile metal plate. The paper presents a study including experiments, analytical theories and finite element calculations. The focus is on the prediction plate failure and on the energy absorption up to this point. Load–displacement curves from experiments are presented for various plate geometries (circular, square, rectangular), indentor radii and locations of loading on the plate. The experiments show that the penetration to ductile fracture and the energy absorption is sensitive to both plate geometry, loading position and indentor geometry. The plate fails by localised necking followed closely by material fracture. Analytical theories are derived for the load–displacement behaviour of a plastic membrane up to failure. The point of plate failure is determined by a global stability criterion taking into account both the change of geometric and material stiffness during the indentation process. For the cases of axis-symmetric loading very good agreement between measured and theoretical load–displacement curves up to — and including — the point of initial plate failure is found. Curve fitting to the theoretical solutions produced the following expressions for the penetration and absorbed energy up to plate failure: δ f =1.41n 0.33R 0.48R b 0.52, E= πC 0t 0RR b 0.318 R b R 0.607−0.387R b/R+1.20(R b/R) 2 +0.067(n−0.2) where C 0 and n are the strength coefficient and the hardening exponent in the material power law, t 0 is the initial plate thickness, R b is the indentor radius and R is the plate radius. The tests were also modelled by the use of a commercially available finite element program. It is shown that the applied finite element method can accurately predict the response up to necking and fracture initiation for both symmetric and non-symmetric loading.