1. Reference problem#
The damage, \(D(t)\), is calculated from the stress tensor data, \(\sigma (t)\), and the cumulative plastic deformation, \(p(t)\).
\(\dot{D}=\frac{1}{{(1-D)}^{\mathrm{2s}}}{\left[\frac{1}{\mathrm{3ES}}(1+\nu ){\sigma }_{\mathrm{eq}}^{2}+\frac{3}{\mathrm{2ES}}(1-2\nu ){\sigma }_{H}^{2}\right]}^{s}\dot{p}\) |
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 (\(\mathrm{MPa}\))
\(s\) is a material characteristic
1.1. Material properties#
\(\mathrm{Temp}(°C)\) |
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2.E+5 |
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2.E+5 |
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2.E+5 |
\({p}_{d}=0.02\)
1.1.1. Modeling A#
In this modeling, we check the Lemaître-Sermage damage calculation with respect to the reference solution given in [V9.01.109]. The values of the exponent \(s\) and \(S\) in the expression of generalized Lemaître damage apply to:
\(s=1.0\) and \(S=7.0\)
1.1.2. B modeling#
In this second modeling, the Lemaître-Sermage damage calculation is verified with respect to an analytical solution obtained by applying the algorithms presented in the reference document [R7.04.01]. The values of the exponent \(s\) and \(S\) in the expression of generalized Lemaître damage apply to:
\(s=1.003\) and \(S=7.0\)
1.2. 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 |
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0.46384 |
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4.6384 |
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9.2768 |
|
9.74064 |
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10.20448 |
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10.297248 |
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10.390016 |