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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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4.6 UPSCALING FOR PLASTICITY

4.6.1 Upscaling for the Macroscopic Plastic Strain

In metals, the deformation is the result of crystallographic glide on different slip systems. The area swept by a gliding dislocation represents the area of the newly slipped region due to this motion. In the framework of DD, the increment of the plastic strain can be explicitly calculated from the area swept by the dislocation segment from this relation [28],

c04e014 (4.14)

where Ns is the total number of dislocation segments, ls is the segment length, υs is the segment glide velocity, bs is the segment Burgers vector, ns is the normal to the slip plane of the segment, and V is the volume of the RVE.

4.6.2 Upscaling: Bridging the Dislocation Level to the Macroscale Continuum Level Stresses and Strains

The macroscopically observed plasticity has its origin in the complex physics occurring at the microscale. A multiscale model for plasticity would implement a continuum level framework that avoids phenomenology by explicitly incorporating the physics of plasticity at the microscale through the DD analysis. The link between the two length scale models can be developed as a concurrent or hierarchical method as a two-way bridge: the DD calculations pass the plastic strain and the internal stress field due to dislocations at each material point (after proper homogenization), while the continuum model allows the consideration ...

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