laws:cazacutn
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laws:cazacutn [2022/03/17 10:49] carlos |
laws:cazacutn [2022/10/14 15:52] (current) carlos |
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| Where: | Where: | ||
| * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress: | * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress: | ||
| - | \[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{J=1}{\Sigma}} \big(|\Sigma_{J}| - k\Sigma_{J}\big)^a \Big] ^{\frac{1}{a}}\] | + | \[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{i=1}{\Sigma}} \big(|\Sigma_{i}| - k\Sigma_{i}\big)^a \Big] ^{\frac{1}{a}}\] |
| * $\sigma_{y}$ is the current yield stress of the material: | * $\sigma_{y}$ is the current yield stress of the material: | ||
| \[\sigma_{y} = \sigma_{0} + S_{R}\big[1-exp\big(-C_{R}\bar{\epsilon}^{p}\big)\big]\] | \[\sigma_{y} = \sigma_{0} + S_{R}\big[1-exp\big(-C_{R}\bar{\epsilon}^{p}\big)\big]\] | ||
| * STF is the stress transformation function, containing all the damage-related variables: | * STF is the stress transformation function, containing all the damage-related variables: | ||
| - | \[STF=2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2} - 1\] | + | \[STF= 1 - 2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2}\] |
| + | The corrected stress ($\hat{\sigma}$) and backstress ($\hat{X}$) are respectively calculated as: | ||
| + | \[\hat{\sigma} = L_{ijmn}T_{mnkl}\sigma_{kl}\] | ||
| + | \[\hat{X}= L_{ijmn}T_{mnkl}X_{kl}\] | ||
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| + | The backstress tensor is calculated using the Armstrong-Frederick model: | ||
| + | |||
| + | \[dX = S_{x}[C_{x}d{\epsilon^p}-Xd\bar{\epsilon}^p]\] | ||
| ==== Files ==== | ==== Files ==== | ||
laws/cazacutn.1647510548.txt.gz · Last modified: 2022/03/17 10:49 by carlos
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