Page 316 - Materials Science and Engineering An Introduction

288 • Chapter 8 / Failure

Principles of Fracture • The significant discrepancy between actual and theoretical fracture strengths of brittle
Mechanics materials is explained by the existence of small flaws that are capable of amplifying an
applied tensile stress in their vicinity, leading ultimately to crack formation. Fracture
ensues when the theoretical cohesive strength is exceeded at the tip of one of these flaws.
• The maximum stress that may exist at the tip of a crack (oriented as in Figure 8.8a)
is dependent on crack length and tip radius, as well as on the applied tensile stress
according to Equation 8.1.
• Sharp corners may also act as points of stress concentration and should be avoided
when designing structures that are subjected to stresses.
• There are three crack displacement modes (Figure 8.10): opening (tensile), sliding,
and tearing.
• A condition of plane strain is found when specimen thickness is much greater than
crack length—that is, there is no strain component perpendicular to the specimen faces.
• The fracture toughness of a material is indicative of its resistance to brittle fracture
when a crack is present. For the plane strain situation (and mode I loading), it is
dependent on applied stress, crack length, and the dimensionless scale parameter Y
as represented in Equation 8.5.
• K Ic is the parameter normally cited for design purposes; its value is relatively large for
ductile materials (and small for brittle ones) and is a function of microstructure, strain
rate, and temperature.
• With regard to designing against the possibility of fracture, consideration must be given
to material (its fracture toughness), the stress level, and the flaw size detection limit.
Fracture Toughness • Three factors that may cause a metal to experience a ductile-to-brittle transition are
Testing exposure to stresses at relatively low temperatures, high strain rates, and the presence
of a sharp notch.
• Qualitatively, the fracture behavior of materials may be determined using the Charpy
and the Izod impact testing techniques (Figure 8.12).
• On the basis of the temperature dependence of measured impact energy (or the
appearance of the fracture surface), it is possible to ascertain whether a material
experiences a ductile-to-brittle transition and, if it does, the temperature range over
which such a transition occurs.
• Low-strength steel alloys typify this ductile-to-brittle behavior and, for structural
applications, should be used at temperatures in excess of the transition range.
Furthermore, low-strength FCC metals, most HCP metals, and high-strength materials
do not experience this ductile-to-brittle transition.
• For low-strength steel alloys, the ductile-to-brittle transition temperature may be
lowered by decreasing grain size and lowering the carbon content.
Fatigue • Fatigue is a common type of catastrophic failure in which the applied stress level fluc-
tuates with time; it occurs when the maximum stress level may be considerably lower
than the static tensile or yield strength.
Cyclic Stresses • Fluctuating stresses are categorized into three general stress-versus-time cycle modes:
reversed, repeated, and random (Figure 8.17). Reversed and repeated modes are
characterized in terms of mean stress, range of stress, and stress amplitude.

The S–N Curve • Test data are plotted as stress (normally, stress amplitude) versus the logarithm of the
number of cycles to failure.
• For many metals and alloys, stress decreases continuously with increasing number of
cycles at failure; fatigue strength and fatigue life are parameters used to characterize
the fatigue behavior of these materials (Figure 8.19b).