Experimental evaluation of a polycrystal deformation modeling scheme using neutron diffraction measurements
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I.
INTRODUCTION
THE numerical simulations are based on an implementation[1] of a modeling scheme introduced by Hutchinson.[2] It is a rate-independent incremental self-consistent elasticplastic model based on crystallographic slip in the grains. The model regards the polycrystal as an agglomerate of spherical single crystals, or grains, where the elastic and plastic interaction between the grains is taken into account by means of a self-consistent scheme. For further description of the model, refer to Reference 3. Polycrystal models are typically evaluated by their capability to simulate texture development. For large deformations and strong textures, model predictions are readily compared to textures determined experimentally, i.e., by neutron diffraction, as shown in Reference 4. In the case of small deformations, however, the texture development is minimal and cannot serve as a means of evaluating the model predictions. However, the model can be evaluated on a much more specific micromechanical level using the novel technique of lattice strain characterization by neutron diffraction, as detailed in Reference 5. Neutron diffraction provides the possibility for an in situ determination of the elastic lattice strain in selected grain subsets within the polycrystal as a function of the applied load. Such results can be directly compared to model predictions of volume-average elastic lattice strains in selected grain subsets resembling the family of grains participating in the particular diffraction measurements.
II.
THE POLYCRYSTAL MODEL
The initial critical resolved shear stress (t0) is identical on all the slip systems, and the rate of the critical resolved shear stress (tz ) is determined by the hardening law. As described in Reference 3, the hardening law can be expressed as a relationship between the accumulated slip in the grains (g acc) and the instantaneous hardening coefficient (hg). The rate of the critical resolved shear stress is determined as
BJØRN CLAUSEN, Postdoc, formerly with the Materials Research Department, Risø National Laboratory, is with the Lujan Center, Los Alamos National Laboratory, Los Alamos, NM 87545. TORBEN LORENTZEN, Senior Scientist, is with the Materials Research Department, Risø National Laboratory, 4000 Roskilde, Denmark. Manuscript submitted April 2, 1997.
METALLURGICAL AND MATERIALS TRANSACTIONS A
tz i 5
Σh gz ij
j
j
where hij 5 hg (q 1 (1 2 q)d ij )
[1]
In the present implementation of this model, two different relations between hg and the accumulated slip in the grain are used: a linear function and an exponentially decreasing function. In the linear function, hg is given by a constant, h, times g acc. In the exponentially decreasing function, hg is described by the final hardening coefficient (hfinal), the ratio between the initial and the final hardening coefficient (hratio), and a parameter that determines the strength of the exponential part (hexp): hg 5 hfinal (1 1 (hratio 2 1) e(2hexpg acc))
[2]
Selecting t0 and the hardening law, and, thus, the hardening
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