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
)