Homework 8 - solutions

# Homework 8 - solutions - MAT 33 – Fall 2008 Homework#8...

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Unformatted text preview: MAT 33 – Fall 2008 Homework #8 – Solutions Due: 11/17/08 1.) Α specimen of a ceramic material having an elastic modulus of 250GPa is pulled in tension with a stress of 750MPa. Will the specimen fail if its ‘most severe flaw’ is an internal crack that has a length of 0.2mm and a tip radius of curvature of 0.001mm? Why or why not? In order to determine whether or not this ceramic material will fail we must compute its theoretical fracture (or cohesive) strength; if the maximum strength at the tip of the most severe flaw is greater than this value then fracture will occur--if less than, then there will be no fracture. The theoretical fracture strength is just E /10 or 25 GPa (3.63 x 10 6 psi), in as much as E = 250 GPa (36.3 x 10 6 psi). The magnitude of the stress at the most severe flaw may be determined using σ m = 2 σ o a ρ t = (2)(750 MPa) (0.20 mm) / 2 0.001mm = 15 GPa 2.2 x 10 6 psi ( 29 Therefore, fracture will not occur since this value is less than E /10....
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Homework 8 - solutions - MAT 33 – Fall 2008 Homework#8...

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