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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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9.6 BRIDGE 9: CP TO MACROSCALE CONTINUUM SIMULATION CONNECTION

Once the four different single-crystal hardening parameters were validated, then one only needs to add many crystals together with different initial orientations to get the polycrystalline bulk response. Figures 9.14 and 9.15 illustrate the different length scales and downscaling requirements that are needed for this bridge. Figure 9.16 shows the polycrystalline stress–strain behavior of the four different sets of constants for the hardening rules assuming a Taylor averaging. These four different polycrystalline results were also volume averaged together, so this answer along with the four different polycrystals and experimental data of pure aluminum data garnered from Alcoa is shown in Figure 9.16. Clearly, the results are amazingly close. At this point, one can argue that a stress–strain behavior can be realized without conducting an experiment. Certainly, the experiments were used for the single-crystal and polycrystalline validations, but the multiscale modeling case study here did not use the experimental results to change anything in the simulations.

Figure 9.14 Schematic of Bridge 9 between the mesoscale crystal plasticity simulations and associated downscaling requirements and upscaling results to/from the macroscale continuum internal state variable theory.

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Figure 9.15 Schematic showing the bridges for downscaling ...

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