Write two computer programs $($FORTRAN$,$ C$,$ C$++,$ MatLab, $...)$ using the numerical

integration techniques outlined in class to compute stress intensity factors $K_{\text{I}}$ and $K_{II}$ for

internal cracks and $2)$ edge cracks subjected to "arbitrary" loading.

For the internal crack program, test your program with uniform crack surface pressure

and uniform shear. Determine the number of integration points necessary for

convergence to $4-$figure accuracy.

Use your internal crack program to solve a welding residual stress problem. Assume

that the equation for the residual stresses in the absence of the crack is given by

${}_y(x)={}_0{e}^{-\frac{1}{2}(\frac{x}{c}{)}^2}\{1-(\frac{x}{c}{)}^2\}$

where c is the coordinate on the x $-$axis, which is perpendicular to the axial weld,

where the residual stress goes from tension to compression. Select reasonable

dimensions for the crack length $2$ a and the value of c $.$ Plot the stress intensity factor

as a function of crack length for this loading.

Using your edge crack program, test the program for uniform crack surface pressure

and uniform shear. Determine the number of integration points necessary for

convergence to $4-$figure accuracy.

Generate results using your edge crack program for the following stress state near the

surface, where $a$ is the crack length.

${}_y(x)={}_0\{2-sin(\frac{}{2}\frac{x}{a})\}$

${}_{xy}(x)={}_0\frac{e^{\frac{x}{a}}-1}{e-1}$