Spherical Indentation and Flow Property Measurement-Finite Element Simulation
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Spherical Indentation and Flow Property Measurement-Finite Element Simulation Ming Y. He, G. R. Odette and G. E. Lucas Materials Department, University of California, Santa Barbara, CA 93106-5050, U.S.A. ABSTRACT Finite element simulations of ball indentation tests were performed and analyzed using the automated ball indentation method. The accuracy and reliability of this methods were assessed.
INTRODUCTION Previous work by Au, Lucas, Sheckerd & Odette [1] and Haggag and Lucas [2] and others showed that ball indentation testing techniques can be used to evaluate flow properties. More recently Haggag et al [3] have extended and refined the general approach. This work is aimed at assessing the accuracy and reliability of this method based on finite element analysis (FEA) simulations of the ball indentation process. While there have been numerous FEA studies of elastic-plastic contact of rigid bodies on a half-space1, in most of these analyses the indentation loads were much smaller than those required by the this testing method. THE PROBLEM AND METHOD OF ANALYSIS Constitutive Equations It is assumed that the true-stress (σ) and true-strain (ε) relations used in the FEA simulations can be represented by a power law constitutive equation given below in (1). The simulations were carried out for combinations of two different values of the yield stress σ y=500 and 792 MPa and four strain hardening exponents (n = 0.0, 0.1, 0.2 and 0.3). Further, the effects of variations in flow stress at low strains were also examined by including a non strain hardening region between a plastic strain ε p = ε - ε e =0 and ε 1, taken as either 0.002 or 0.02. The constitutive behavior resembles a Luders-type strain regime often observed in tensile tests of steels, but it is not reflective of a propagating Luder’s band deformation pattern. The true stress was assumed to be constant above a strain of ε 2=1. = E for
≤
Y
E = Y for 0 ≤ p ≤ 1 = p n for 1 ≤ p ≤ 2 = B for p ≥ 2 The elastic modulus E is taken to be 200 GPa (steel).
1
(1)
Comprehensive reviews can be found in Kalker [4], Gladwell [5], Johnson [6], and Hills, Nowell and Sackfield [7]
Q7.9.1
The various input constitutive equations were compared to corresponding results based on using the simulated load (P)-penetration depth results (hp and ht are the residual depth and depth under load, respectively) in the recommended testing procedure. Finite Element Mesh In order to simulate the automated ball indentation method, the finite element analysis covered a load range of a applied (P) to yield load (PY) up to P/ PY=40000. Based on convergence studies two different meshes were used for low (P/PY < 5000) and high load ranges (P/ PY > 5000), respectively. Both consisted of 3292 four-node quadrilateral axisymmetric elements and 3275 nodes. While these two meshes have the same number of elements, the smallest element size and the element size distribution beneath the ball differed in the two cases. The radial (r) and depth (z) dimensions of the mesh were 25 R and 10 R, respectively,
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