PSI - Issue 14

Ritesh Dadhich et al. / Procedia Structural Integrity 14 (2019) 104–111 R. Dadhich, A.Alankar/ Structural Integrity Procedia 00 (2018) 000–000

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applied at every grid point. A similar test is also done for a hard inclusion phase instead of the void whose evolution is shown in Fig. 3(b). Fig. 4(a and b) shows the stress variation along the dashed line across the void and hard inclusion. It can be seen that the stress variation behaves in the same way as concentration evolution in the phase. It is evident from the stress variation in both the cases that there is an effect of phase evolution at the interface.

Fig. 4. Variation of stress σ 33 along the dashed line in the above figure when there is (a) void, (b) hard inclusion at center.

6. Conclusion In this paper, the time integration algorithm to integrate constitutive equations was explained for elasto viscoplastic material response. The basic FFT scheme for elastic inhomogeneous material based on literature was applied for elasto-viscoplastic materials to get the full field solution. A PFM based on conserved variable was coupled with CPFFT model by taking the effect of elastic strain energy on the evolution of concentration field of phases. The computer code developed for each model was tested and compared with the results from literature and an open source package. The results from the code and literature found to be quiet similar but the calibration of the model needs to done. The current model can also be coupled with PFM for non-conserved variables to get the effect of stress on phase growth. References Cahn, J. W., Hilliard, J. E., 1958. Free energy of a nonuniform system. I. Interfacial free energy. The Journal of chemical physics 28(2), 258-267. Lebensohn, R. A., 2001. N-site modeling of a 3D viscoplastic polycrystal using fast Fourier transform. Acta materialia 49(14), 2723–2737. Lee, E., 1969. Elastic-plastic deformation at finite strains. Journal of applied mechanics 36(1), 1–6. Maniatty, A. M., Dawson, P. R., Lee, Y. S., 1992. A time integration algorithm for elasto-viscoplastic cubic crystals applied to modelling polycrystalline deformation. International Journal for Numerical Methods in Engineering 35(8), 1565–1588. Mathur, K. K., Dawson, P. R., 1989. On modeling the development of crystallographic texture in bulk forming processes. International Journal of Plasticity 5(1), 67–94. Moulinec, H., Suquet, P., 1998. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Computer Methods in Applied Mechanics and Engineering 157(1–2), 69–94. Mura, T., 1987. Micromechanics of defects in solids. Dordrecht, Netherlands: Martinus Nijhoff. Roters, F., Eisenlohr, P., Kords, C., Tjahjanto, D. D., Diehl, M., Raabe, D., 2012. DAMASK: The Düsseldorf Advanced MAterial Simulation Kit for studying crystal plasticity using an FE based or a spectral numerical solver. Procedia IUTAM 3, 3–10. Sarma, G., Zacharia, T., 1999. Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials. Journal of the Mechanics and Physics of Solids 47(6), 1219–1238. Taylor, G. I., 1938. Plastic strain in metals. Journal of the Institute of Metals 62, 307-324. Allen, S. M., Cahn, J. W., 1979. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metallurgica 27(6), 1085–1095.