Template:Cd relationship: Difference between revisions

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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}
{{\alpha }_{0}}= & \ln (C) \\
{{\alpha }_{1}}= & b 
\end{align}</math>
 
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{{cd arrhenius exponential}}
 
{{cd arrhenius weibull}}
 
{{cd arrhenius lognormal}}

Latest revision as of 00:20, 16 August 2012

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