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Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science by Mark F. Horstemeyer

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3.4 UPSCALING: BRIDGING THE CRYSTAL LEVEL TO THE POLYCRYSTALLINE CONTINUUM LEVEL

There are several upscaling bridges from the crystal plasticity level to the macroscale continuum level. In particular, these include (i) plastic spin, (ii) texture, (iii) yield surfaces, (iv) isotropic hardening, and (v) kinematic hardening. Each of these quantities is prescribed in some manner at the macroscale but fall out naturally at the crystal plasticity level. As such, the volume averaged polycrystalline responses can be used as data for the macroscale modeling. The plastic spin, texture, and yield surface shape are all interdependent. Depending on how one would model the macroscale continuum equations, an emphasis might be on one or all of these parameters. The isotropic and kinematic hardening operates on the crystal level glide planes in the crystal plasticity formulation, but they can be volume averaged to give the polycrystalline averages so that the macroscale model could use the “data” from the polycrystalline averaged results.

3.4.1 Upscaling for Plasticity

3.4.1.1 Polycrystalline Plasticity Upscaling Averaging Assumptions. 

The final topic of discussion pertinent to crystal plasticity is the averaging of the crystals or grains to make a polycrystal, which then can be compared with the macroscale continuum material point. The relation between the single crystal and the associated polycrystalline continuum point can be obtained using a mean-field hypothesis or partitioning rule. One ...

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