Comparison of discrete dislocation and continuum plasticity predictions for a composite material

Abstract

Comparison of discrete dislocation and continuum plasticity predictions for a composite material Cleveringa, H.H.M.; van der Giessen, E.; Needleman, A. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 11-04-2019Acfcr maf~r. Vol. 45, No. 8, pp. 3163.-3179, 1997 G (Received 8 October 1996; accepted 18 December 1996) Abstract-A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is analyzed using both discrete dislocation plasticity and conventional continuum slip crystal plasticity. In the discrete dislocation formulation, the dislocations are modeled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complimentary solution that enforces the boundary conditions, which is non-singular and obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. Results are presented for materials with a single slip system. A reinforcement size effect is exhibited by the discrete dislocation-based analysis whereas the continuum slip results are size independent. The discrete dislocation results have higher average reinforcement stress levels than do the corresponding continuum slip calculations. Averaging of stress fields over windows of increasing size is used to gain insight into the transition from discrete dislocation-controlled to continuum behavior. IQ 1997 Acta Metallurgica Inc.1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rrghts reserved Printed in Great Britain PII: S1359-6454(97)00011-6 1359

Comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations

“…The results to be presented are close to those obtained by Cleveringa et al (1997Cleveringa et al ( , 1998Cleveringa et al ( , 1999a but di er in the fact that here we do not assume an initial distribution of dislocation obstacles inside the matrix. There are no dislocations present initially, and dislocation sources are assumed to be distributed randomly in the matrix with a uniform density of n = 61:2L −2 for morphology (i) and n = 55:4L −2 for morphology (iii).…”

“…The resulting theory contains a length scale through a set of coupled transport equations for two dislocation density ÿelds: one is the total dislocation density and the other is a net-Burgers vector density. After a summary of the theory for single slip, we proceed to numerical implementation of the theory and to a comparison with direct simulations of discrete dislocation plasticity in a model composite material based on the work of Cleveringa et al (1997Cleveringa et al ( , 1998Cleveringa et al ( , 1999a. Similar comparisons have been carried out by Bassani et al (2001) and Bittencourt et al (2003) with the nonlocal theories of Acharya and Bassani (2000) and Gurtin (2002), respectively.…”

“…Groma (1997) and Groma and Balogh (1999). Let us ÿrst look at the nucleation and annihilation mechanism incorporated in the discrete dislocation simulations of Cleveringa et al (1997Cleveringa et al ( , 1998Cleveringa et al ( , 1999a which will serve as "numerical experiments" for veriÿcation in a subsequent section. In these simulations, based on the discrete dislocation plasticity description proposed by Van der Giessen and Needleman (1995), new dislocations are generated by mimicking the Frank-Read mechanism.…”

“…In two dimensions, a Frank-Read source is emulated by a point source on the slip plane which generates a dislocation dipole when the magnitude of the resolved shear stress at the source exceeds the source strength nuc during a period of time t nuc . Annihilation of two dislocations on the same slip plane with opposite Burgers vectors occurs when they are within a material-dependent, critical annihilation distance L e , which is taken to be L e = 6b (Cleveringa et al, 1997(Cleveringa et al, , 1998(Cleveringa et al, , 1999a). As we are here aiming at a comparison with the discrete dislocation results in these references, we choose a form of the source term in (7) that mimics the above-mentioned nucleation and annihilation rules:…”

“…1. This is the same problem as analyzed using discrete dislocation dynamics by Cleveringa et al (1997Cleveringa et al ( , 1998Cleveringa et al ( , 1999a, and is used to check the quality of the present nonlocal theory in reproducing the size-dependent results. Two reinforcement morphologies are analyzed which have the same area fraction of 20% but di erent geometric arrangements of the reinforcing phase.…”