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# HW10 - 14:440:407 Section 02 Fall 2010 SOLUTION OF HOMEWORK...

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14:440:407 Section 02 Fall 2010 SOLUTION OF HOMEWORK 10 FAILURE (Chapter 8) PROBLEM SOLUTIONS Principles of Fracture Mechanics 8.1 What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of 2.5 10 -4 mm (10 -5 in.) and a crack length of 2.5 10 -2 mm (10 -3 in.) when a tensile stress of 170 MPa (25,000 psi) is applied? Solution This problem asks that we compute the magnitude of the maximum stress that exists at the tip of an internal crack. Equation 8.1 is employed to solve this problem, as m = 2 0 a t 1/ 2 = (2)(170 MPa) 2.5 10 2 mm 2 2.5 10 4 mm 1/2 = 2404 MPa (354,000 psi)

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8.2 Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in.) and having a tip radius of curvature of 1.2 10 -3 mm (4.7 10 -5 in.) when a stress of 1200 MPa (174,000 psi) is applied. Solution In order to estimate the theoretical fracture strength of this material it is necessary to calculate m using Equation 8.1 given that 0 = 1200 MPa, a = 0.25 mm, and t = 1.2 10 -3 mm. Thus, m = 2 0 a t 1/ 2 = (2)(1200 MPa) 0.25 mm 1.2 10 3 mm 1/2 = 3.5 10 4 MPa = 35 GPa ( 5.1 10 6 psi )