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 The failure of engineering materials is almost always an undesirable
event for several reasons; these include human lives that are put in
jeopardy, economic losses, and the interference with the availability
of products and services.
 Even though the causes of failure and the behavior of materials may
be known, prevention of failures is difficult to guarantee
 The usual causes are improper materials selection and processing and
inadequate design of the component or its misuse.

 Simple fracture is the separation of a body into two or more pieces in
response to an imposed stress that is static (i.e., constant or slowly
changing with time) and at temperatures that are low relative to the
melting temperature of the material.
 The applied stress may be tensile, compressive, shear, or torsional
 Any fracture process involves two steps—crack formation and
propagation—in response to an imposed stress.
 The mode of fracture is highly dependent on the mechanism of crack
propagation.
 Ductile fracture is characterized by extensive plastic deformation in
the vicinity of an advancing crack.

 Ductile fracture surfaces will have their own distinctive
features on both macroscopic and microscopic levels.
 Figure 8.1 shows schematic representations for two
characteristic macroscopic fracture profiles.
 The configuration shown in Figure 8.1a is found for
extremely soft metals, such as pure gold and lead at room
temperature, and other metals, polymers, and inorganic
glasses at elevated temperatures.
 These highly ductile materials neck down to a point fracture,
showing virtually 100% reduction in area.

 Brittle fracture takes place without any appreciable deformation, and
by rapid crack propagation.
 The direction of crack motion is very nearly perpendicular to the
direction of the applied tensile stress and yields a relatively flat
fracture surface, as indicated in Figure 8.1c.
 Fracture surfaces of materials that failed in a brittle manner will have
their own distinctive patterns; any signs of gross plastic deformation
will be absent.
 For example, in some steel pieces, a series of V-shaped “chevron”
markings may form near the center of the fracture cross section that
point back toward the crack initiation site (Figure 8.5a).
 Other brittle fracture surfaces contain lines or ridges that radiate from
the origin of the crack in a fanlike pattern (Figure 8.5b).

 For most brittle crystalline materials, crack
propagation corresponds to the successive and
repeated breaking of atomic bonds along
specific crystallographic planes (Figure 8.6a);
such a process is termed cleavage.
 This type of fracture is said to be
transgranular (or transcrystalline), because
the fracture cracks pass through the grains.
Figure 8.6 (a) Schematic cross-section
profile showing crack propagation
through the interior of grains for
transgranular fracture.
(b) Scanning electron fractograph of
ductile cast iron showing a transgranular
fracture surface. Magnification unknown.

 STRESS CONCENTRATION
1. The measured fracture strengths for most brittle materials are
significantly lower than those predicted by theoretical calculations
based on atomic bonding energies.
2. This discrepancy is explained by the presence of very small,
microscopic flaws or cracks that always exist under normal conditions
at the surface and within the interior of a body of material.
3. These flaws are a detriment to the fracture strength because an
applied stress may be amplified or concentrated at the tip, the
magnitude of this amplification depending on crack orientation and
geometry.
4. This phenomenon is demonstrated in Figure 8.8, a stress profile across
a cross section containing an internal crack.

 As indicated by this profile, the magnitude of this localized stress
diminishes with distance away from the crack tip.
 At positions far removed, the stress is just the nominal stress or the
applied load divided by the specimen cross-sectional area
(perpendicular to this load).
 Due to their ability to amplify an applied stress in their locale, these
flaws are sometimes called stress raisers.
 If it is assumed that a crack is similar to an elliptical hole through a
plate, and is oriented perpendicular to the applied stress, the
maximum stress,
the radius of curvature of the crack tip
a represents the length of a surface crack

 For a relatively long microcrack that has a small tip
radius of curvature, the factormaybeverylarge

 All brittle materials contain a population of small cracks and flaws that have a
variety of sizes, geometries, and orientations.
 When the magnitude of a tensile stress at the tip of one of these flaws exceeds
the value of this critical stress, a crack forms and then propagates, which
results in fracture.

 Furthermore, using fracture mechanical principles, an
expression has been developed that relates this critical stress
for crack propogation бc and crack length (a) as
In this expression Kc is the fracture toughness, a property that is a measure
of a material’s resistance to brittle fracture when a crack is present.
Y is a dimensionless parameter or function that depends on both crack and
specimen sizes and geometries, as well as the manner of load application

 Relative to this Y parameter, for planar specimens containing cracks
that are much shorter than the specimen width, Y has a value of
approximately unity.
 For example, for a plate of infinite width having a through-thickness
crack (Figure 8.9a) Y= 1.0 , whereas for a plate of semi-infinite width
containing an edge crack of length a (Figure 8.9b), Y is approx. equal
to 1.1.
 Mathematical expressions for Y have been determined for a variety of
crack-specimen geometries; these expressions are often relatively
complex.
 For relatively thin specimens, the value of will depend on specimen
thickness.
 However, when specimen thickness is much greater than the crack
dimensions,Kc becomes independent of thickness; under these
conditions a condition of PLANE STRAIN exists.

 By plane strain we mean that when a load operates on a
crack in the manner represented in Figure 8.9a, there is no
strain component perpendicular to the front and back faces.
 The Kc value for this thick specimen situation is known as the
PLANE STRAIN Fracture toughness KIC

 Prior to the advent of fracture mechanics as a scientific discipline,
impact testing techniques were established so as to ascertain the
fracture characteristics of materials.
 It was realized that the results of laboratory tensile tests could not be
extrapolated to predict fracture behavior;
 For example, under some circumstances normally ductile metals
fracture abruptly and with very little plastic deformation.
 Impact test conditions were chosen to represent those most severe
relative to the potential for fracture—namely, (1) deformation at a
relatively low temperature, (2) a high strain rate (i.e., rate of
deformation), and (3) a triaxial stress state (which may be introduced
by the presence of a notch).

 Two Standardized test
1. Charpy
2. Izod Impact test

 For both Charpy and Izod, the specimen is in the shape of a bar of square cross
section, into which a V-notch is machined (Figure 8.12a).
 The apparatus for making V-notch impact tests is illustrated schematically in
Figure 8.12b.
 The load is applied as an impact blow from a weighted pendulum hammer that
is released from a cocked position at a fixed height h.
 The specimen is positioned at the base as shown.
 Upon release, a knife edge mounted on the pendulum strikes and fractures the
specimen at the notch, which acts as a point of stress concentration for this
high-velocity impact blow.
 The pendulum continues its swing, rising to a maximum height which is lower
than h. The energy absorption, computed from the difference between h and
h’ is a measure of the impact energy.

 One of the primary functions of Charpy and Izod tests is to determine
whether or not a material experiences a ductile to brittle transition with
decreasing temperature and, if so, the range of temperatures over which it
occurs.
 The ductile-to-brittle transition is related to the temperature dependence
of the measured impact energy absorption.
 This transition is represented for a steel by curve A in figure shown
 At higher temperatures the CVN energy is relatively large, in correlation
with a ductile mode of fracture.
 As the temperature is lowered, the impact energy drops suddenly over a
relatively narrow temperature range, below which the energy has a
constant but small value; that is, the mode of fracture is brittle.

 Fatigue is a form of failure that occurs in structures subjected to
dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine
components).
 Under these circumstances it is possible for failure to occur at a stress
level considerably lower than the tensile or yield strength for a static
load.
 The term “fatigue” is used because this type of failure normally occurs
after a lengthy period of repeated stress or strain cycling.
 Fatigue is important inasmuch as it is the single largest cause of failure
in metals, estimated to comprise approximately 90% of all metallic
failures; polymers and ceramics (except for glasses) are also
susceptible to this type of failure.

 Furthermore, fatigue is catastrophic and insidious, occurring very suddenly and
without warning.
 Fatigue failure is brittle like in nature even in normally ductile metals, in that
there is very little, if any, gross plastic deformation associated with failure.
 The process occurs by the initiation and propagation of cracks, and ordinarily
the fracture surface is perpendicular to the direction of an applied tensile
stress.

 The applied stress may be axial (tension-compression), flexural
(bending), or torsional (twisting) in nature.
 In general, three different fluctuating stress–time modes are possible.
 One is represented schematically by a regular and sinusoidal time
dependence in Figure 8.17a, wherein the amplitude is symmetrical
about a mean zero stress level,

 As with other mechanical characteristics, the fatigue properties of
materials can be determined from laboratory simulation tests.
 A test apparatus should be designed to duplicate as nearly as possible
the service stress conditions (stress level, time frequency, stress
pattern, etc.).
 A schematic diagram of a rotating-bending test apparatus, commonly
used for fatigue testing, is shown in Figure 8.18; the compression and
tensile stresses are imposed on the specimen as it is simultaneously
bent and rotated.
 Tests are also frequently conducted using an alternating uniaxial
tension-compression stress cycle.

 A series of tests are commenced by subjecting a specimen to the stress cycling
at a relatively large maximum stress amplitude (бmax), usually on the order of
two thirds of the static tensile strength; the number of cycles to failure is
counted.
 This procedure is repeated on other specimens at progressively decreasing
maximum stress amplitudes
 Data are plotted as stress S versus the logarithm of the number N of cycles to
failure for each of the specimens.

 Two distinct types of S–N behavior are observed, which are
represented schematically in Figure 8.19.
 As these plots indicate, the higher the magnitude of the stress, the
smaller the number of cycles the material is capable of sustaining
before failure.
 For some ferrous (iron base) and titanium alloys, the S–N curve (Figure
8.19a) becomes horizontal at higher N values; or there is a limiting
stress level, called the fatigue limit (also sometimes the endurance
limit), below which fatigue failure will not occur.

 Most nonferrous alloys (e.g., aluminum, copper, magnesium) do not
have a fatigue limit, in that the S–N curve continues its downward
trend at increasingly greater N values (Figure 8.19b).
 Thus, fatigue will ultimately occur regardless of the magnitude of
the stress.
 For these materials, the fatigue response is specified as fatigue
strength, which is defined as the stress level at which failure will
occur for some specified number of cycles (e.g., cycles).
 Another important parameter that characterizes a material’s fatigue
behavior is fatigue life Nf
 It is the number of cycles to cause failure at a specified stress level, as
taken from the S–N plot (Figure 8.19b).

(a) a material that displays a fatigue limit

(b) a material that does not display a fatigue limit.

 The process of fatigue failure is characterized by three distinct steps:
(1) crack initiation, wherein a small crack forms at some point of high
stress concentration;
 (2) crack propagation, during which this crack advances incrementally
with each stress cycle; and
 (3) final failure, which occurs very rapidly once the advancing crack
has reached a critical size.
 Cracks associated with fatigue failure almost always initiate (or
nucleate) on the surface of a component at some point of stress
concentration.
 Crack nucleation sites include surface scratches, sharp fillets,
keyways, threads, dents, and the like.

 In addition, cyclic loading can produce microscopic surface
discontinuities resulting from dislocation slip steps that may also act
as stress raisers, and therefore as crack initiation sites.
 The region of a fracture surface that formed during the crack
propagation step may be characterized by two types of markings
termed beachmarks and striations.
 Beachmarks (sometimes also called “clamshell marks”) are of
macroscopic dimensions (Figure 8.21), and may be observed with the
unaided eye
 Fatigue striations are microscopic in size and subject to observation
with the electron microscope (either TEM or SEM)

 Mean stress level,
 Geometrical design,
 Surface effects,
 Metallurgical variables, as well as the environment

 Thermal fatigue is normally induced at elevated temperatures by
fluctuating thermal stresses; mechanical stresses from an external
source need not be present.
 The origin of these thermal stresses is the restraint to the dimensional
expansion and/or contraction that would normally occur in a structural
member with variations in temperature.
 The magnitude of a thermal stress developed by a temperature change
is dependent on the coefficient of thermal expansion and the modulus
of elasticity E according to
Failure that occurs by the simultaneous action of a cyclic stress and chemical attack is
termed corrosion fatigue.

 Materials are often placed in service at elevated temperatures and
exposed to static mechanical stresses (e.g., turbine rotors in jet
engines and steam generators that experience centrifugal stresses, and
high-pressure steam lines). Deformation under such circumstances is
termed creep.
 It is observed in all materials types; for metals it becomes important
only for temperatures greater than about 0.4Tm
 Where Tm – Absolute Melting Temperature

 A typical creep test consists of subjecting a specimen to a constant
load or stress while maintaining the temperature constant;
deformation or strain is measured and plotted as a function of elapsed
time.
 Most tests are the constant load type, which yield information of an
engineering nature; constant stress tests are employed toprovide a
better understanding of the mechanisms of creep.
 Figure 8.28 is a schematic representation of the typical constant load
creep behavior of metals.
 Upon application of the load there is an instantaneous deformation, as
indicated in the figure, which is mostly elastic.

 The resulting creep curve consists of three regions,
each of which has its own distinctive strain–time
feature.
 Primary or transient creep occurs first, typified by a
continuously decreasing creep rate

 For metallic materials most creep tests are conducted in uniaxial
tension using a specimen having the same geometry as for tensile tests
(Figure 6.2).
 On the other hand, uniaxial compression tests are more appropriate
for brittle materials; these provide a better measure of the intrinsic
creep properties inasmuch as there is no stress amplification and crack
propagation, as with tensile loads.
 Compressive test specimens are usually right cylinders or
parallelepipeds having length-to-diameter ratios ranging from about 2
to 4.
 For most materials creep properties are virtually independent of
loading direction.

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