Numerical Study of the Brinnel Test of Elastoplastic Indentation

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 80; no. 8; pp. 555 - 563
• Main Authors: Guyot, N., Kosior, F., Maurice, G.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.08.2000; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Elasticity, plasticity: general mathematical aspects; Exact sciences and technology; Physics; Finite element method; Piling; Brinell test; Yield criterion; Elastoplastic material; Pressure distribution; Contact problems; Numerical method; Nonlinear problems; Indentation; Nonlinear systems
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/1521-4001(200008)80:8<555::AID-ZAMM555>3.0.CO;2-U

In this paper, we present the numerical study of the elastoplastic contact without friction between a deformable spherical punch and a deformable support, using the finite element method. We describe the elastoplastic behaviour using the Prandtl‐Reuss model (isotropic work hardening) associated with the von Mises yield criterion. The contact problem leads to a non‐linear system we solve by applying loading increments. We carry out computations in the work hardening and perfectly plastic cases. Our results are presented in the form of stresses distribution and evolution of the yield zone and deformed shape. Then we study the influence of work hardening on the pressure distribution and on the deformed shape. Moreover, we observe the “sinking‐in” and “piling‐up” phenomena in the work hardening and perfectly plastic cases. All these results are in conformity, on one hand with those published by Johnson, and Sinclair et al. and on other hand with those of Biwa et al.