GTBL042-09 GTBL042-Callister-v3 October 4, 2007 11:53
2nd Revised PagesQuestions and Problems • 335Hertzberg, R. W.,Deformation and Fracture Me-
chanics of Engineering Materials, 4th edition,
Wiley, New York, 1996.
Stevens, R. I., A. Fatemi, R. R. Stevens, and H. O.
Fuchs,Metal Fatigue in Engineering, 2nd edi-
tion, Wiley, New York, 2000.
Tetelman, A. S. and A. J. McEvily,Fracture of Struc-
tural Materials, Wiley, New York, 1967. Re-
printed by Books on Demand, Ann Arbor, MI.Wachtman, J. B.,Mechanical Properties of Ceram-
ics, Wiley, New York, 1996.
Ward, I. M. and J. Sweeney,An Introduction to
the Mechanical Properties of Solid Polymers,
2nd edition, John Wiley & Sons, Hoboken, NJ,
2004.
Wulpi, D. J., Understanding How Components
Fail, 2nd edition, ASM International, Materi-
als Park, OH, 1999.QUESTIONS AND PROBLEMS
Additional problems and questions for this chapter may be found on both Student and
Instructor Companion Sites atwww.wiley.com/college/callister.Principles of Fracture Mechanics
9.1What is the magnitude of the maximum stress
that exists at the tip of an internal crack having
a radius of curvature of 1.9× 10 −^4 mm (7.5×
10 −^6 in.) and a crack length of 3.8× 10 −^2 mm
(1.5× 10 −^3 in.) when a tensile stress of 140
MPa (20,000 psi) is applied?
9.2A specimen of a ceramic material having an
elastic modulus of 250 GPa (36.3× 106 psi)
is pulled in tension with a stress of 750 MPa
(109,000 psi). Will the specimen fail if its “most
severe flaw” is an internal crack that has a
length of 0.20 mm (7.87× 10 −^3 in.) and a tip
radius of curvature of 0.001 mm (3.94× 10 −^5
in.)? Why or why not?
9.3An MgO component must not fail when a ten-
sile stress of 13.5 MPa (1960 psi) is applied. De-
termine the maximum allowable surface crack
length if the surface energy of MgO is 1.0 J/m^2.
Data found in Table 7.1 may prove helpful.
9.4Some aircraft component is fabricated from
an aluminum alloy that has a plane strain frac-
ture toughness of 40 MPa√
m (36.4 ksi√
in.).
It has been determined that fracture results
at a stress of 300 MPa (43,500 psi) when the
maximum (or critical) internal crack length is
4.0 mm (0.16 in.). For this same component
and alloy, will fracture occur at a stress level
of 260 MPa (38,000 psi) when the maximum in-
ternal crack length is 6.0 mm (0.24 in.)? Why
or why not?
9.5A large plate is fabricated from a steel alloy
that has a plane strain fracture toughness of
82.4 MPa√
m (75.0 ksi√
in.). If, during serviceuse, the plate is exposed to a tensile stress of
345 MPa (50,000 psi), determine the minimum
length of a surface crack that will lead to frac-
ture. Assume a value of 1.0 forY.
9.6A structural component in the form of a wide
plate is to be fabricated from a steel alloy that
has a plane strain fracture toughness of 98.9
MPa√
m (90 ksi√
in.) and a yield strength of
860 MPa (125,000 psi). The flaw size resolu-
tion limit of the flaw detection apparatus is 3.0
mm (0.12 in.). If the design stress is one-half of
the yield strength and the value ofYis 1.0, de-
termine whether or not a critical flaw for this
plate is subject to detection.
Fracture of Ceramics
Fracture of Polymers
9.7Briefly explain(a)why there may be signifi-
cant scatter in the fracture strength for some
given ceramic material, and(b)why fracture
strength increases with decreasing specimen
size.
9.8The tensile strength of brittle materials may
be determined using a variation of Equation
9.1. Compute the critical crack tip radius for
a glass specimen that experiences tensile frac-
ture at an applied stress of 70 MPa (10,000
psi). Assume a critical surface crack length of
10 −^2 mm and a theoretical fracture strength of
E/10, whereEis the modulus of elasticity.
Impact Fracture Testing
9.9Following is tabulated data that were gathered
from a series of Charpy impact tests on a tem-
pered 4340 steel alloy.