Problem $1$

The plate shown in Figure $1$ with dimensions $w=100mm,a=15mm$ and thickness $=10mm$ is made from a material with $K_{IC}=70$MPa$(m{)}^{0\mathrm{.}5}.$ The load pair $P_A$ is at a position x with respect to the edge of the plate as shown.

a$)$ Determine $P_A$ when the plate fails for $x=0.$

b$)$ Determine $P_A$ when the plate fails for $x=\frac{w}{2}.$

SUGGESTION: depending on the configuration, you may have K from $M,Sg,$ or both of them.

$K=\sqrt[\phantom{2}]{a}*F,=\frac{6M}{b^{2}t}$

$F=\sqrt[\phantom{2}]{\frac{2}{}tan(\frac{}{2})}[\frac{0\mathrm{.}923+0\mathrm{.}199(1-sin(\frac{}{2}){)}^4}{cos(\frac{}{2})}]$

$K=\sqrt[\phantom{2}]{a}*F$

$F=0\mathrm{.}265(1-{)}^4+\frac{0\mathrm{.}857+0\mathrm{.}265}{(1-{)}^{\frac{3}{2}}}$

Figure $1$ Stress intensity factor solutions for the problem