A ceramic component with Young’s modulus of 300 GPa and a KIc of 4 MPa.m1/2 is to survive a water quench from 500°C to room temperature of 25°C. If the largest flaw in that material is on the order of 2 μm, what is the maximum value of thermal expansion coefficient (α) for this ceramic required to survive the quench? Assume that there are 20 flaws of 2 μm size. Poisson ratio of the ceramic material is 0.25.

NEED AN ANSWER ASAPAn aircraft component is to be fabricated from an aluminum alloy that has a plane strain fracture toughness of 45 MPa m and a yield strength of 500 MPa.  It has been determined that fracture results at a stress of 250 MPa when the maximum internal crack length is 9 mm.  For this same component and alloy, determine critical internal crack length that will result to fracture if the design stress is three-fourth of the yield strength.  If the available flaw detection apparatus has a resolution limit of 3 mm, will the crack in (1) be detected? Why or why not? Show complete solution

Material Science - please help