Template:Cd power exponential: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
 
(4 intermediate revisions by one other user not shown)
Line 1: Line 1:
===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:
 
<br>
::<math>L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}</math>
 
<br>
In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the power law relationship:
 
<br>
::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}</math>
 
<br>
Therefore, instead of displaying  <math>a</math>  and  <math>n</math>  as the calculated parameters, the following reparameterization is used:
 
<br>
::<math>\begin{align}
{{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\
{{\alpha }_{1}}=\ & -n 
\end{align}</math>
 
<br>

Latest revision as of 23:41, 15 August 2012

Redirect to:

Retrieved from "https://www.reliawiki.com/index.php?title=Template:Cd_power_exponential&oldid=32062"