Solve each question via both analytical and numerical calculation methods in your answer sheets.
Note: ANSYS, ABAQUS, or any other software can be used in the analysis
QUESTIONS
1) In typical single edge and center cracked cases following material properties are used:
Young's modulus $E = 80000$ MPa
Poisson's ratio = 0.3
Applied stress $\sigma = 100$ MPa
Plate width $w = 20$ mm
Calculate $K_1$ values for different crack lengths $a = 2, 4, 6$ and $8$ mm by using;
a) analytical
b) numerical methods
In case of single edge crack
$K_1 = \sigma \sqrt{\pi a} \left[ 1.122 - 0.231 \left( \frac{a}{b} \right) + 10.550 \left( \frac{a}{b} \right)^2 - 21.710 \left( \frac{a}{b} \right)^3 + 30.382 \left( \frac{a}{b} \right)^4 \right]$
In case of center crack
$K_1 = \sigma \sqrt{\pi a} \left[ 1 - 0.5 \left( \frac{a}{b} \right) + 0.370 \left( \frac{a}{b} \right)^2 - 0.044 \left( \frac{a}{b} \right)^3 \right] / \sqrt{1 - \frac{a}{b}}$
where: 2a is the length of crack, 2b is the width of plate