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| ==Cumulative Damage Arrhenius Relationship==
| | #REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Arrhenius_Relationship]] |
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| This section presents a generalized formulation of the cumulative damage model where stress can be any function of time and the life-stress relationship is based on the Arrhenius life-stress relationship. Given a time-varying stress <math>x(t)</math> and assuming the Arrhenius relationship, the life-stress relationship is given by:
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| ::<math>L(x(t))=C{{e}^{\tfrac{b}{x(t)}}}</math>
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| In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the Arrhenius relationship:
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| ::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\tfrac{1}{x(t)}}}</math>
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| Therefore, instead of displaying and <math>b<<math>C</math>/math> as the calculated parameters, the following reparameterization is used:
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| ::<math>\begin{align}
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| {{\alpha }_{0}}= & \ln (C) \\
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| {{\alpha }_{1}}= & b
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| \end{align}</math>
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| {{cd arrhenius exponential}}
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| {{cd arrhenius weibull}}
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| {{cd arrhenius lognormal}}
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