Template:Cd exponential

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


 * $$L(x(t))=C{{e}^{bx(t)}}$$

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

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


 * $$\begin{align}

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