View source for ICME GRP2 HW3&4

[[ICME8990 Student Contributions(Fall 2012) | < Student Contributions]]

==Abstract==
Hardening parameters from dislocation dynamics are passed upwards to crystal plasticity. At the crystal plasticity scale, various textures, number of grains, and stress states were investigated in ABAQUS/Standard. The stress–strain curves from the crystal plasticity scale was passed to the macroscale ([[Material_Models#MSU_ISV_Plasticity-Damage_Model|Internal State Variable Plasticity–Damage Modeling]]). Uncertainty was also considered.

==Introduction==
This page summaries a project which spans two length scales and crosses two bridges within the Integrated Computational Materials Engineering (ICME) paradigm. The two scales are the crystal plasticity scale and the macroscale. The bridges crossed are (1) the bridge between dislocation dynamics and crystal plasticity and (2) the bridge between crystal plasticity and the macroscale modeling scale.

==Discussion==

[[Image:Team2_polefig.png|thumb|right|491px|Deformed textures orientation distribution function of the 400 grain simulations for (a) compression, (b) tension, and (c) simple shear.]]

[[Image:Team2_ss_cp.png|thumb|right|809px|True von Mises stress-strain relationship in for 400 grains in (a) compression, (b) simple shear, and (c) tension]]

[[Image:Team2_ss_dmg.png|thumb|right|409px|Stress-strain calibration results for the macroscale internal state variable (ISV) model with the crystal plasticity data. Note that only every fifth marker of the crystal plasticity data is shown for the sake of brevity.]]

Hardening parameters were taken from Groh<ref>S. Groh, E.B. Marin, M.F. Horstemeyer, and H.M. Zbib. Multiscale modeling of the plasticity
in an aluminum single crystal. ''International Journal of Plasticity'', 25(8):1456-1473, 2009.</ref>as shown below.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Case'''
| align="center" style="background:#f0f0f0;"|'''κ<sub>s</sub>'''
| align="center" style="background:#f0f0f0;"|'''κ<sub>0</sub>'''
| align="center" style="background:#f0f0f0;"|'''h<sub>0</sub>'''
|-
| 1||47.75||3.36||29.56
|-
| 2||49.10||3.39||25.83
|-
| 3||48.84||3.38||27.06
|-
| 4||46.75||3.29||34.98
|}

These cases used for three one element ABAQUS/Standard simulation (for three stress state: tension, compression, simple shear). Also, for the one element, 1 grain, 20 grains, and 400 grains were analyzed. The stress-strain results and deformed pole figures to the right.

The stress strain curves were then imported into [[https://icme.hpc.msstate.edu/mediawiki/index.php/DMGfit_55p_v1p1 DMG Fit]] thus calibrating constants. Using ABAQUS/Standard, a one element tension simulation was run using the [[Material_Models#MSU_ISV_Plasticity-Damage_Model|MSU Internal State Variable Plasticity–Damage Model]] to verify the paratermeter found in DMGFit. The comparison if shown to the right.

The parameters determined in DMGFit are shown below. Any parameter not listed is assumed zero.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Parameter'''
| align="center" style="background:#f0f0f0;"|'''Average'''
| align="center" style="background:#f0f0f0;"|'''Lower Bound'''
| align="center" style="background:#f0f0f0;"|'''Upper Bound'''
|-
| Young's Modulus||68970||68970||68970
|-
| Poisson's Ratio||0.33||0.33||0.33
|-
| ''C''<sub>3</sub>||6||6||6
|-
| ''C''<sub>5</sub>||1||1||1
|-
| ''C''<sub>7</sub>||0.016||0.014||0.019
|-
| ''C''<sub>9</sub>||191.415||180||225
|-
| ''C''<sub>13</sub>||6||10||8
|-
| ''C''<sub>15</sub>||400||300||475
|-
| 
|}

==References==

<References />