PSI - Issue 21

Tuncay Yalçinkaya et al. / Procedia Structural Integrity 21 (2019) 52–60 Yalc¸inkaya et al. / Structural Integrity Procedia 00 (2019) 000–000

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when the initial pore fraction is smaller, the material is more ductile and it can sustain more damage. Similarly, in Fig. 9, the principal plastic strain distribution is shown and it is higher for lower initial pore fraction which is a sign of ductility as well. The e ff ect of initial pore height, h 0 , in the RVE is presented in Fig. 7b. For the low pore height, the void becomes more crack like and the speed at which traction carrying capacity drops is increased (see Fig. 2b or d). Remember the relation, d f / (1 − f ) = dh / h , to see the e ff ect of initial pore height. Smaller the height, faster the pore fraction grows. Therefore, the failure occurs at an earlier time leading to lower toughness, which is similar to the e ff ect of higher pore fraction.

(Avg: 75%) PE, Max. Principal

(Avg: 75%) PE, Max. Principal

(Avg: 75%) PE, Max. Principal

0.000 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.166 0.183 0.200

0.000 0.012 0.024 0.036 0.049 0.061 0.073 0.085 0.097 0.109 0.121 0.133 0.146

0.000 0.011 0.022 0.033 0.043 0.054 0.065 0.076 0.087 0.098 0.109 0.120 0.130

Y

Y

Y

Z

X

Z

X

Z

X

Fig. 9. Strain distributions for di ff erent initial pore fractions

4. Concluding Remarks In this paper, a physics based traction-separation model based on the growth of pores is developed and investigated numerically through a cohesive zone model applied to a CT specimen in the context of ductile fracture. The e ff ects of micromechanic parameters such as the initial pore fraction and the pore height on the macroscopic behavior of the material is studied and realistic conclusions are obtained for the change in strength and the thoughness. In the current implementation J2 plasticity is used for the bulk material, which will be replaced by a porous plasticity model developed considering the same physical mechanism (see Yalcinkaya et al. (2019)) in order to have a consistent damage initiation and related crack propagation. 5. Acknowledgements Tuncay Yalcinkaya gratefully acknowledges the support by the Scientific and Technological Research Council of Turkey (TU¨ B ˙ITAK) under the 3501 Programme (Grant No. 117M106). References Barenblatt, G.I., 1959. The formation of equilibrium cracks during brittle fracture. general ideas and hypotheses. axially-symmetric cracks. Journal of Applied Mathematics and Mechanics 23, 622–636. Cerrone, A., Wawrzynek, P., Nonn, A., Paulino, G.H., Ingra ff ea, A., 2014. Implementation and verification of the park–paulino–roesler cohesive zone model in 3d. Engineering Fracture Mechanics 120, 26–42. Cocks, A., 1989. Inelastic deformation of porous materials. Journal of the Mechanics and Physics of Solids 37, 693–715. Dugdale, D.S., 1960. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8, 100–104. Fleck, N.A., Hutchinson, J.W., 1986. Void growth in shear. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 407, 435–458. Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voidscase of axisymmetric prolate ellipsoidal cavities. Journal of the Mechanics and Physics of Solids 41, 1723–1754. Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: Part iyield criteria and flow rules for porous ductile media. Journal of engineering materials and technology 99, 2–15. Hardy, G.H., Littlewood, J.E., George, P., 1978. Inequalities. By G.H. Hardy, J.E. Littlewood, and G. Polya. Cambridge University Press. Hillerborg, A., Mode´er, M., Petersson, P.E., 1976. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and concrete research 6, 773–781.