A beam speciment with a rectangular shape ( 10mm thick 20mm deep) has bending mo

Question

A beam speciment with a rectangular shape ( 10mm thick 20mm deep) has bending moment M applied. With given fracture toughness and safety factor what is the largest crack length that can be allowed?

A beam specimen has a rectangular beam shape as follows, Thickness(t) = 10 mm Height(b) = 20mm deep The bending moment M is being applied. The fracture toughness is 3 MPa*m1/2. We want to make sure that there is a safety factor of 2. What is the largest crack length a that can be allowed if M = 10N*m?

Explanation / Answer

sigma =M*y/I ,

I = 1/12 * b*h^3 = 6.6*10^-6

sigma = 15000 pa

K =sigma root( pi*a)

3 = 15000 root( pi*a)

pi*a = 0.04

a= 0.0127 = 12.7 mm

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