13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- indenter was much stiffer than the test material, the indenter was considered as a perfect rigid and modeled as axisymmetric analytical rigid 140.6° cone, based on the equivalent contact area to depth ratio as a perfect Berkovich indenter. A reference point was defined to manipulate the translation of the indenter. The analysis was carried out under the displacement control without friction between the contact surfaces. Fig. 3 shows the mesh used in the analysis. The length of the whole mesh square is 30 micrometer. Finer meshes near the indenter were created to be able to describe the deformation and stress gradient below the indenter with sufficiently high accuracy. The base of the square was completely constrained, and the nodes along the center line were constrained in the horizontal direction due to axi-symmetry. Figure 3. Mesh used in the finite element simulations 3.2 Elastoplastic material model Due to the negligible heat affect zone, the fusion zone was assumed isotropic and homogeneous. A one-dimensional constitutive relation for the linear elastic, power law plastic material indicated in Eq. 1 was applied to describe the stress-strain relationship, ⎩ ⎨ ⎧ > ≤ = y n K E σ σ ε σ σ ε σ , , y , (1) where parameter σy is the initial yield stress, E represents the Young’s modulus, K is the strain hardening coefficient and n is the strain hardening exponent. Young’s modulus can be evaluated based on Oliver and Pharr method [3]. Through adjusting these input material parameters, different load-displacement curves can be obtained from finite element simulation. By comparing FE load-displacement curves with the experimental one, the best match should represent the correct input of material parameters, as shown in Fig. 7. 3.3 Simulation results Fig. 4a shows the Mises stress distribution at indentation depth 1.94 µm. The stresses in the right part of the sample square are nearly zero, which means that the dimension of the sample square is enough and the boundary effect could be neglected. After unloading as shown in Fig. 4b, compression residual stresses could be found beneath the indenter tip.
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