Microstructural Modeling of Failure Modes in Martensitic Steel Alloys
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Microstructural Modeling of Failure Modes in Martensitic Steel Alloys P. SHANTHRAJ 1, T. M. HATEM 1, M.A. ZIKRY 1 1
Dept. of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910
ABSTRACT A unified physically-based representation of the microstructure in martensitic steels is developed to investigate its effects on the initiation and evolution of failure modes at different physical scales that occur due to a myriad of factors, such as texture, grain size and shape, grain heterogeneous microstructures, and grain boundary (GB) misorientations and distributions. The microstructural formulation is based on a dislocation-density based multiple-slip crystal plasticity model that accounts for variant distributions, orientations, and morphologies. This formulation is coupled to specialized finite-element methods to predict the scale-dependent heterogeneous microstructure, and failure phenomena such as shearstrain localization, and void coalescence. INTRODUCTION Lath martensitic steels have myriad military and civilian applications due to their high strength and toughness. These properties are a result of its unique microstructure that has distinct orientations, distributions, and morphologies pertaining to martensitic transformations. Due to the fine microstructure of lath martensite, it has been difficult to fully predict failure evolution for different loading conditions. In recent years, Morito and his colleagues [1-2] have conducted experiments to classify martensitic structures in categories of blocks (variants with low angle mismatch) and packets (collection of blocks with the same habit plane) microstructures, and to characterize their orientation relations, size and distributions. Most computational investigations of failure utilize phenomenological plasticity models [3-4]. However, these approaches do not account for critical microstructural characteristics, such as orientation relations (ORs), morphologies, and parent austenite orientations. To address these limitations and obtain greater predictive capabilities, we have extended the dislocation-density based crystalline model proposed by Zikry and Kao [5] and coupled this to a specialized microstructurally-based finite element analysis that explicitly accounts for the lath microstructure [6-7]. The formulation is used to investigate how dislocation-density interactions affect shear-strain localization in high strength martensitic steels. CONSTITUTIVE FORMULATION The constitutive formulations for multiple-slip crystal plasticity coupled to evolution equations for the dislocation-densities are presented here. For details see Zikry and Kao [5]. Multiple-Slip Crystal Plasticity Formulation
It is assumed that the velocity gradient is decomposed into a symmetric deformation rate tensor Dij and an anti-symmetric spin tensor Wij. Dij and Wij are then additively decomposed into elastic and inelastic components as
Dij = Dij* + Dijp ,
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W ij = W ij* + W ijp .
(1a-b)
The inelastic parts are defined in terms of the crystallo
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