Question

A ceramic matrix composite contains internal flaws as large as 0.001 cm in length. The plane strain fracture toughness of the composite is 45 MPaÏm and the tensile strength is 550 MPa. Will the stress cause the composite to fail before the tensile strength is reached? Assume that f 5 1.

Answer 1

Since the applied stress required for failure due to crack propagation is still higher than 550 MPa, the ceramic is expected to fail due to overload and not because of the flaws

Explanation:

Plane -Strain Fracture toughness is calculated as

$k_{IC}$=$f$б$\sqrt{\pi a}$

F=geometry factor of the flaw

б=Stress applied

$k_{IC}$=Fracture toughness

a=Flaw size

Given that

Internal Flaw,a=0.001cm

Fracture Toughness $k_{IC}$=45MPa$\sqrt{m}$

Tensile Strength б=550 MPa

Geometry Factor,$f$=1

Calculation

An internal Flaw i s 0.001 cm

2a=0.001cm

a=0