Pile-up of dislocations in DP steels
Citation for published version (APA):Scardia, L., Peerlings, R. H. J., Geers, M. G. D., & Peletier, M. A. (2010). Pile-up of dislocations in DP steels. Poster session presented at Mate Poster Award 2010 : 15th Annual Poster Contest.
Document status and date: Published: 01/01/2010 Document Version:
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Mechanics of Materials
Introduction and aim of the project
Dual Phase (DP) steels consist of a ferritic matrix con-taining a hard martensitic second phase in the form of islands. The aim of the project is to understand the inter-play between the microstructure of DP steels and their mechanical properties, in particular the effect of grain size on strain hardening.
Figure 1: Microstructures of DP steels (From K.-T. Park et al., Scripta Materialia 51 (2004), 909-913).
GOAL:To develop a physically based macroscopic model of DP steel, starting from a purely atomistic one, in a rig-orous way.
Approach
This problem has a multi-scale nature and the focus of my research will be the micro-meso upscaling, i.e., the derivation of a model for the dislocation density starting from a purely discrete model of the pile-up of disloca-tions at a grain boundary.
Micro-Model: An Idealised Pile-Up
We model the dislocation pile-up in the ferrite grains ad-jacent to martensite as follows (see [1]):
We use as a key parameter the ratioα := xh and we analyse the casesα 1 (close to the obstacle), α 1 (critical case) andα 1 (remote region) separately.
First Step: Heuristics
Results
Preliminary computations for the caseα 1 suggest that the density of dislocations is linear inx, in agree-ment with the numerical results in [2]:
We also have results for the transition region, where we derived an ODE for the dislocation density.
Future Plans
Provide a characterization of the dislocation density over the whole pile-up region. Next, consider the case of mul-tiple slip systems and the more ambitious case of moving dislocations.
References
[1] A. Roy, R.H.J. Peerlings, M.G.D. Geers and Y. Kasyanyuk (2008). Mat. Sci. Eng. A-Struct. 486,
653–661.
[2] T.W.J. de Geus, R.H.J. Peerlings and C.B. Hirschberger. In preparation.