1. Reference problem#
The damage \(D(t)\) is calculated from the data of the stress tensor \(\sigma (t)\) and the cumulative plastic deformation \(p(t)\).
\(\dot{D}=\frac{1}{{(1-D)}^{2}}\left[\frac{1}{\mathrm{3ES}}(1+\nu ){\sigma }_{\mathrm{eq}}^{2}+\frac{3}{\mathrm{2ES}}(1-2\nu ){\sigma }_{H}^{2}\right]\dot{p}\) |
if \(p>{p}_{d}\) |
\(D=0\) |
otherwise |
\({\sigma }_{\mathrm{eq}}\) is the equivalent von Mises stress
\({\sigma }_{H}\) is the hydrostatic stress
\({p}_{d}\) represents the damage threshold
\(S\) is a material characteristic (\(\mathrm{MPa}\))
The total damage \(D=\underset{i=1}{\overset{N}{\Sigma }}D({t}_{i})\) is also calculated.
1.1. Material properties#
\(\mathrm{Temp}(°C)\) |
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|
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2.E+5 |
12/07/09 |
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2.E+5 |
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2.E+5 |
\({p}_{d}=0.02\)
1.2. Boundary conditions and loading#
Loading history:
\(t\) |
43.11 |
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\({\sigma }_{\mathrm{xx}}(t)\) |
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\({\sigma }_{\mathrm{yy}}(t)\) |
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\({\sigma }_{\mathrm{zz}}(t)\) |
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\({\sigma }_{\mathrm{xy}}(t)\) |
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\({\sigma }_{\mathrm{xz}}(t)\) |
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\({\sigma }_{\mathrm{yz}}(t)\) |
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\(\mathrm{Temp}\) |
\(t\) |
|
43.11 |
0.019996 |
0.046384 |
|
0.46384 |
|
4.6384 |
|
9.2768 |
|
9.74064 |
|
10.20448 |
|
10.297248 |
|
10.390016 |