Problem Statement:

A notched thin plate subjected to a load$-$time history was analyzed by an elastic finite element

analysis. A linear elastic finite element analysis indicates that the stress at the notch root is $0\mathrm{.}045$MPa

due to a unit applied load $(P=1$ Newton$).$ This plate is made of steel that has the following cyclic and

fatigue properties:

$E=210,000$MPa,$K^{\text{'}}=1300$MPa,$n^{\text{'}}=0\mathrm{.}30,{}_f^{\text{'}}=910$MPa,$b=-0\mathrm{.}15,{}_f^{\text{'}}=0\mathrm{.}31,c=-0\mathrm{.}52.$

Objective:

To estimate the fatigue life of the notched thin plate made of SAE $1005$ steel, subjectd to the

variable amplitude loading condition shown in Figure $1.$ It is assumed that the notched plate follows

normally elastic behavior.

a$.)$ Use the Molsky$-$Glinka energy density method to simulate the local hysteresis behavior;

b$.)$ Predict the fatigue life of the notched plate using the SWT mean stress correction formula;

c$.)$ Predict the fatigue life of the notched plate using the Morrow mean stress method.

Figure $1$ Notched Plate Variable Amplitude Load$-$Time History