Mechanical Characterization of Functionally Graded Materials with a Yield Strength Gradient
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Mechanical Characterization of Functionally Graded Materials with a Yield Strength Gradient A. Nayebi, G. Mauvoisin, O. Bartier and R. El Abdi University of Rennes Applied Mechanics Research Laboratory I.U.T. de Rennes. 3, rue du Clos Courtel - B.P. 90422 35704 Rennes Cedex 7,
France
ABSTRACT An elasto-plastic spherical indentation study on materials with a yield strength gradient, like steels which have undergone thermal hardening such as nitriding, is carried out using both experimental and finite element methods. A theory based on the evolution of hardness, is proposed to determine the yield stress and hardness profiles for materials with a decreasing yield stress with depth. Results for carbo-nitriding steels obtained by the standard Vickers micro hardness technique are compared with those obtained by the proposed method. INTRODUCTION Superficial heat treatment processing is capable of producing graduation in composition whereby the mechanical properties can be changed as a function of location. The indentation of materials at the nano-, micro- and macro-length scale enables estimation of local properties such as Young’s modulus, yield stress and hardening exponent. Advances in indentation testing methods and in numerical modelling of stress-strain fields beneath the indenter, offer possibilities for determining experimentally spatial variation in local mechanical properties. The aim of our study is to describe the evolution of pressure and the plastic radius according to a dimensionless parameter and to determine the yield stress and the hardness profiles of graded steels (with a yield strength gradient (figure 1)) using finite element simulations and spherical indentation tests.
900
Vickers hardness HV0.2 Kg
800 700 Vickers micro-indentation test
600 Proposed method (Linear approximation)
500 400
e2
e1
300 0
100
Indentation depth (µm) 200
300
400
Figure 1. Vickers micro-indentation profiles for the 40CrMnMo8 steel. P1.7.1
FINITE ELEMENT MODELING Simulation of the indentation of a graded thin layer-half space substrate was performed using the large strain elasto-plastic feature of the CASTEM 2000 finite element code (Millard [1]). The spherical indenter with a radius of 1.8575 mm and a high elastic modulus was used. An axisymmetric mesh was constructed. Four-noded, axisymmetric elements with varying element sizes were used. The mesh has at least 7380 elements and 7579 nodes. The outer boundary was modeled with stress free conditions on the right side and vertically constrained on the lower side. Thermal treatment modifies the yield stress σy but modifies the strain hardening exponent n very little, and leaves the other mechanical characteristics such as Young’s modulus unaffected [2]. Thereafter, and for all steels studied, the strain hardening exponent n, Young’s modulus E and the Poisson’s ration ν, will be the same for the hardened layer and the substrate. Strain hardening was represented by the following relationship [3]: σ = Kε
n
(1-n) n
where K=σy
E
(1)
where K is the strength coeff
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