|
|
| Line 1: |
Line 1: |
| =Cumulative Damage Exponential Relationship=
| | #REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Exponential_Relationship]] |
| <br>
| |
| 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 <math>x(t)</math> and assuming the exponential relationship, the life-stress relationship is given by:
| |
| | |
| | |
| ::<math>L(x(t))=C{{e}^{bx(t)}}</math>
| |
| | |
|
| |
| 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<math>C</math>playing and <math>b</math> as the calculated parameters, the following reparameterization is used:
| |
| | |
| | |
| ::<math>\begin{align}
| |
| {{\alpha }_{0}}=\ & \ln (C) \\
| |
| {{\alpha }_{1}}=\ & b
| |
| \end{align}</math>
| |