Template:Cd power exponential

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 $$x(t)$$  and assuming the power law relationship,  the life-stress relationship is given by:


 * $$L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}$$

In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the power law relationship:


 * $$L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}$$

Therefore, instead of displaying $$a$$  and  $$n$$  as the calculated parameters, the following reparameterization is used:


 * $$\begin{align}

{{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\ {{\alpha }_{1}}=\ & -n \end{align}$$