PSI - Issue 14

Taslim D. Shikalgar et al. / Procedia Structural Integrity 14 (2019) 529–536 T.D.Shikalgar et al./ Structural Integrity Procedia 00 (2018) 000–000

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(2016) like elastic deformation, elastic-plastic transition zone, generalized plastic zone, plastic instability and fracture initiation, fracture softening and final failure are noticeable in this figure. These experimental data are then used in the finite element modeling of the specimens as described below. 3. Elastic-plastic finite element analysis of p-SPT specimen 3.1. In-house FE code, FE model, and analysis results FE model of pre-cracked small punch test is analyzed using BARC in-house finite element implicit code MADAM (MAterial DAmage Modeling) (1999). The code has the ability to solve both two and three-dimensional FE models. The geometric nonlinearity is considered by using the updated Lagrangian formulations. The direct sparse solver is used to solve a linear set of simultaneous equations. The load v/s displacement equilibrium conditions are obtained by using Modified-Riks Algorithm. The Gurson-Tvergaard-Needleman material model is also available in this code. The propagation of crack is traced along the damaged gauss points along crack-line. A gauss point is assumed to be completely damaged when its void volume becomes void volume fraction at fracture ( f f ). The elastic-plastic constitutive equation with the pressure dependent Gurson-Tvergaard yield model is integrated using the generalized mid-point algorithm formulated by Z. Zhang et al. (1995).

Fig. 4. Numerical model of p-SPT (a) General scheme (the upper die is not shown) (b) FE mesh (c) refined mesh near the crack tip

In the present work, the p-SPT specimen is analyzed using FE 3D model. Due to the symmetry of the specimen geometry and loading conditions, only one-half of the pre-cracked specimen is modeled by means of 8-noded fully integrated iso-parametric 46,965 brick elements. Mesh is refined near the crack, where minimum length of the brick element is equal to 35.7 μm along the direction of the length of the crack. The lower die, upper die and punch are modeled as rigid bodies. The multi-body dynamic concept is used to model the progress of contact between the specimen and die with associated friction between the two surfaces. The friction coefficient was taken as 0.1, as suggested by T. E. Garcia (2015) and E. Martinez-Paneda (2016). Fig. 4 shows the punching scheme, FE mesh of the specimen and the refined mesh near the crack tip of the specimen. Materials properties shown in Table 2 are used in this analysis. Fig. 5 shows the computed load v/s displacement curve along with the experimental data for the tested specimens of both the materials.

Fig. 5. Comparison of elastic plastic FEA results with experimental data for pre-cracked specimens of (a) 20MnMoNi55 and (b) T91.