Template:Cd power exponential: Difference between revisions

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===Cumulative Damage Power Relationship===
#REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Power_Relationship]]
 
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 power relationship. Given a time-varying stress  <math>x(t)</math>  and assuming the power law relationship,  the life-stress relationship is given by:
 
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::<math>L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}</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 power law relationship:
 
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::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}</math>
 
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Therefore, instead of displaying  <math>a</math>  and  <math>n</math>  as the calculated parameters, the following reparameterization is used:
 
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::<math>\begin{align}
{{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\
{{\alpha }_{1}}=\ & -n 
\end{align}</math>
 
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Latest revision as of 23:41, 15 August 2012

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