Template:Cd relationship

Cumulative Damage Arrhenius 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 Arrhenius life-stress relationship. Given a time-varying stress $$x(t)$$  and assuming the Arrhenius relationship, the life-stress relationship is given by:


 * $$L(x(t))=C{{e}^{\tfrac{b}{x(t)}}}$$

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


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

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


 * $$\begin{align}

{{\alpha }_{0}}=\ & \ln (C) \\ {{\alpha }_{1}}=\ & b \end{align}$$