MECHANICAL
PROPERTIES
OF METALS
ACUÑA, ALI, GOZUM, REFUGIO
MECHANICAL
PROPERTIES
OF METALS I
METALS
• formed into functional shapes using a
wide variety of metal-forming
operations under both cold and hot
conditions.
• The most important example is
manufacturing automobile parts (both
body and engine).
6.1 THE PROCESSING OF METALS AND ALLOYS
6.1.1 THE CASTING OF METALS AND ALLOYS
Alloying elements can be added to the molten
metal to produce various alloy compositions. For
example, solid magnesium metal may be added to
molten aluminum and, after melting, may be
mechanically mixed with the aluminum to produce
a homogeneous melt of an aluminum-magnesium
alloy.
• Ingots are then used to manufacture semifinished products such as sheets and plates.
• products that are manufactured through wrought
alloy products are Extrusion, electrical
conductors and bus bars, welding rods, cooking
utensils, pressure vessels, sheeting and etc.
• wrought alloy products - significant
permanent/plastic deformation of the metal by hot
and cold working of large ingots
example of ingot sheets and the
other one is extrusion ingots
• Cast products are a small amount
of machining or another finishing
operation is required to produce
the final casting.
• Casting alloys produces them.
• Examples: For example, pistons
used in automobile engines are
usually made by casting molten
metal into a permanent steel mold.
Example of permanent mold casting
Example of the process of casting
6.1.2 HOT AND COLD ROLLING
OF METALS AND ALLOYS
• Hot and cold rolling are commonly used
methods for fabricating metals and alloys.
• Hot Rolling of Sheet Ingots is carried out
first since greater reductions in thickness
can be taken with each rolling pass when
the metal is hot.
• Before hot rolling, sheet and plate ingots
are preheated to a high temperature
(depending on the recrystallization
temperature of the metal).
• After removal from the preheat furnace,
the ingot sections are usually hot rolled in a
reversing break-down rolling mill.
Example of rolling mill.
• Cold Rolling of Metal Sheet After
hot rolling, which may also
include some cold rolling, the
coils of metal are usually given a
reheating treatment called
annealing to soften the metal to
remove any cold work introduced
during the hot-rolling operation.
introduced during the hot-rolling
operation.
6.1.3 EXTRUSION OF
METALS AND ALLOYS
 Direct extrusion(a)also called forwarding extrusion, is a type of
extrusion that occurs when the direction of flow of metal is the
same as that movement of the ram. Many cross sections are
manufactured by this method. The cross-section produced will be
uniform over the entire length of the metal extrusion.
 Indirect Extrusion(b) is a method in which the Ram is stationary
and the dye moves to force the Billet through the dye. To keep the
die stationary a stem is used which should be longer than the
container containing the Billet.
• Forging is another primary method
for working metals into useful
shapes. In the forging process, the
metal is hammered or pressed into
the desired shape.
• Most forging operations are carried
out with the metal in hot
conditions, although in some cases
the metal may be forged cold.
• There are two major types of
forging methods: hammer and
press forging
• In hammer forging, a drop hammer repeatedly
exerts a striking force against the surface of the
metal. In press forging, the metal is subjected to
a slowly increasing compressive force.
• Forging processes can also be classified as open-die
forging or closed-die forging. Open-die forging is
carried out between two flat dies or dies with very
simple shapes such as vees or semicircular cavities.
• Closed Die Forging is a forging process in which dies
move towards each other and cover the workpiece in
whole or in part. The heated raw material, which is
approximately the shape or size of the final forged
part, is placed in the bottom die.
• In general, the forging process is used for producing
irregular shapes that require working to improve the
structure of the metal by reducing porosity and
refining the internal structure.
Section through a wire-drawing die.
• wire-drawing process consists of pointing the rod,
threading the pointed end through a die, and
attaching the end to a drawing block. The block,
made to revolve by an electric motor, pulls the
lubricated rod through the die, reducing it in
diameter and increasing its length.
• Deep drawing process is another metal-forming process and is used for
shaping flat sheets of metal into cup-shaped articles.
Example of deep drawing of a cylindrical cup.
6.2 STRESS AND STRAIN IN
METALS
6.2.1 ELASTIC AND PLASTIC DEFORMATION
• If the metal recovers and returns to its original dimensions when the force is removed, the
metal is said to have undergone elastic or recoverable deformation.
• Plastic deformation or plastic is the permanent distortion that occurs when a material is
subjected to tensile, compressive, bending, or torsion stresses that exceed its yield
strength and cause it to elongate, compress, buckle, bend, or twist.
• Deformation in metals and other materials, elastic, or plastic, is produced as a result of
the action of forces or loads. These loads may be applied in the form of a tensile force,
compressive force, shear force, torsion, or bending. Such loads produce a variety of
stresses in metals, including tensile, compressive, and shear stresses
6.2.2 ENGINEERING STRESS AND
ENGINEERING STRAIN
• Engineering stress is the applied force divided by the undeformed area over
which the force is applied.
• Engineering strain is defined as the change in length divided by the original
length.
6.2.3 POISSON’S RATIO
Poisson’s ratio is the ratio of transverse contraction strain to longitudinal extension strain
in the direction of the stretching force.
We can generalize that normal stresses and strains result in changes in length and volume of
the metal while shearing stresses and strains result in changes in the shape of the metal.
6.2.4 SHEAR STRESS AND SHEAR STRAIN
When a body is subjected to two equal and opposite forces acting tangentially, across the
resisting section.
The units for shear stress are the same as for uniaxial normal tensile stress:
U.S. customary: pounds force per square inch (lbf /in.2, or psi)
SI: newtons per square meter (N/m2) or pascals (Pa)
6.3 THE TENSILE TEST AND THE
ENGINEERING STRESS-STRAIN DIAGRAM
The tensile test is used to
evaluate the strength
and stiffness of metals
and alloys among other
properties.
6.3.1 MECHANICAL
PROPERTY DATA
OBTAINED FROM
THE TENSILE TEST
AND THE
ENGINEERING
STRESS-STRAIN
DIAGRAM
The mechanical properties of metals and alloys
that are of engineering importance for structural
design and can be obtained from the engineering
tensile test are:
1. Modulus of elasticity
In the first part of the tensile test, the metal is
deformed elastically. That is, if the load on the
specimen is released, the specimen will return to its
original length.
2. Yield strength at 0.2% offset
The yield strength (YS or σy) is a very important value
for use in engineering structural design since it is the
stress at which a metal or alloy shows significant
plastic deformation.
3. Ultimate tensile strength
6.3.1 MECHANICAL
PROPERTY DATA
OBTAINED FROM
THE TENSILE TEST
AND THE
ENGINEERING
STRESS-STRAIN
DIAGRAM
The ultimate tensile strength (UTS or σu) is the maximum
strength reached in the engineering stress-strain curve.
When one wishes to know which metals are stronger, it is
generally the ultimate tensile strengths that are compared.
4. Percent elongation at fracture
The amount of elongation that a tensile specimen
undergoes during testing provides a value for the ductility
of a metal.
5. Percent reduction in area at fracture
The ductility of a metal or alloy can also be expressed in
terms of the percent reduction in area.
6.3.1 MECHANICAL
PROPERTY DATA
OBTAINED FROM
THE TENSILE TEST
AND THE
ENGINEERING
STRESS-STRAIN
DIAGRAM
6. Modulus of resilience
The modulus of resilience, Ur, is the amount of energy
absorbed by a loaded material just prior to yielding.
7. Toughness (static)
The modulus of toughness is used to describe a
combination of strength and ductility behaviors.
6.3.2 COMPARISON OF ENGINEERING STRESS-STRAIN
CURVE FOR SELECTED ALLOY
Engineering stress-strain curves for selected metals and alloys are
shown in Figure 6.23. Alloying a metal with other metals or nonmetals
and heat treatment can greatly affect the tensile strength and ductility of
metals.
6.3.3 TRUE STRESS AND TRUE STRAIN
6.3.3 TRUE STRESS AND TRUE STRAIN
6.4 HARDNESS AND HARDNESS TESTING
Hardness is a measure of the
resistance of a metal to
permanent (plastic)
deformation. The hardness of
a metal is measured by
forcing an indenter into its
surface.
For example, hardened steel, tungsten
carbide, or diamond are commonly
used materials for indenters.
6.5 PLASTIC DEFORMATION OF METAL
SINGLE CRYSTALS
• Slipbands and Slip Lines on the Surface of Metal Crystals
• Plastic Deformation in Metal Crystals by the Slip
Mechanism
• Slip Systems
• Critical Resolved Shear Stress for Metal Single Crystals
• Schmid’s Law
• Twinning
6.6 PLASTIC DEFORMATION OF
POLYCRYSTALLINE METALS
• Effect of Grain Boundaries on the Strength of
Metals
• Effect of Plastic Deformation on Grain Shape
and Dislocation Arrangements
• Effect of Cold Plastic Deformation on
Increasing the Strength of Metals
6.7 SOLID-SOLUTION STRENGTHENING
OF METALS
• Two important factors in solid-solution strengthening are:
1. Relative-size factor. Differences in the atomic size of solute and
solvent atoms affect the amount of solid-solution strengthening
because of the crystal lattice distortions produced. Lattice distortions
make dislocation movement more difficult and hence strengthen the
metallic solid solution.
2. Short-range order. Solid solutions are rarely random in atomic mixing,
and short-range order or clustering of like atoms takes place. As a result,
dislocation movement is impeded by different bonding structures.
6.8 RECOVERY AND RECRYSTALLIZATION
OF PLASTICALLY DEFORMED METALS
• Structure of a Heavily Cold-Worked Metal before Reheating
• Recovery
• Recrystallization
6.9 SUPERPLASTICITY IN METALS
• To achieve superplasticity, the material and the loading process must
meet certain conditions:
1. The material must possess a very fine grain size (5–10 µm) and be
high-strain-rate sensitive.
2. A high loading temperature greater than 50% of the melt temperature
of the metal is required.
3. A low and controlled strain rate in the range of 0.01 to 0.0001 s^−1 is
required.
6.10 NANOCRYSTALLINE METALS
• Nanocrystalline (nc) materials are defined as the ones with an
average grain size of less than 100 nm.
MECHANICAL
PROPERTIES OF
METALS II
7.1 FRACTURE OF METALS
One of the important and practical aspects of materials selection in the design,
development, and production of new components is the possibility of failure of the
component under normal operation. Failure may be defined as the inability of a
material or a component to (1) perform the intended function, (2) meet
performance criteria although it may still be operational, or (3) perform safely and
reliably even after deterioration. Yielding, wear, buckling (elastic instability),
corrosion, and fracture are examples of situations in which a component has failed
Fracture is the process of the creation of new surfaces in a component, which
eventually leads to separation of the component, under stress, into two or more
parts.
In general, metal fractures can be classified as ductile or brittle but a fracture
can also be a mixture of the two
7.1.1 DUCTILE FRACTURE
Ductile fracture of a metal occurs after extensive plastic deformation and is
characterized by slow crack propagation.
Three distinct stages of ductile fracture can be recognized:
• the specimen forms a neck and cavities form within the necked
region
• the cavities in the neck coalesce into a crack in the center of the
specimen and propagate toward the surface of the specimen in a
direction perpendicular to the applied stress
• when the crack nears the surface, the direction of the crack
changes to 45° to the tensile axis and a cup-and-cone fracture
results
In practice, ductile fractures are less frequent than brittle fractures, and the main
cause for their occurrence is overloading of the component. Overloading could
occur as a result of :
• improper design, including the selection of materials (underdesigning)
• improper fabrication
• abuse (component is used at load levels above that allowed by the
designer)
7.1.2 BRITTLE FRACTURE
Brittle fracture, in contrast, usually proceeds along characteristic crystallographic
planes called cleavage planes and has rapid crack propagation. Owing to their
rapidity, brittle fractures generally lead to sudden, unexpected, catastrophic
failures, while the plastic deformation accompanying ductile fracture may be
detectable before fracture occurs.
Most brittle fractures in polycrystalline metals are transgranular, that is, the
cracks propagate across the matrix of the grains. However, brittle fracture
can occur in an intergranular manner if the grain boundaries contain a
brittle film or if the grain boundary region has been embrittled by the
segregation of detrimental elements. Brittle fracture in metals is believed to
take place in three stages:
1. Plastic deformation concentrates dislocations along slip planes at
obstacles.
2. Shear stresses build up in places where dislocations are blocked, and as
a result microcracks are nucleated.
3. Further stress propagates the microcracks, and stored elastic strain
energy may also contribute to the propagation of the cracks
When brittle fracture occurs, it consistently initiates at the defect location
(stress risers) regardless of the cause for the formation of the defect. Certain
defects, low operating temperatures, or high loading rates may also cause
the brittle fracture of some moderately ductile materials. The transition from
ductile to brittle behavior is called a ductile-to-brittle transition (DBT).
7.1.3 TOUGHNESS AND IMPACT TESTING
Dynamic or impact toughness is a measure of the amount of energy a
material can absorb before fracturing under dynamic loading conditions.
One of the simplest methods of measuring toughness is to use an impact
testing apparatus.
7.1.4 DUCTILE-TO-BRITTLE TRANSITION TEMPERATURE
As mentioned above, under certain conditions a marked change in the
fracture resistance of some metals is observed in service, that is, ductile-tobrittle transition. Low temperatures, high-stress states, and fast loading rates
may all cause a ductile material to behave in a brittle manner; however,
customarily the temperature is selected as the variable that represents this
transition while the load rate and stress rate are held constant. The impacttesting apparatus discussed in Section 7.1.3 may be used to determine the
temperature range for the transition from ductile to brittle behavior of materials
Factors that influence the DBT temperature are alloy composition, heat
treatment, and processing. For instance, the carbon content of annealed
steels affects this transition temperature range. Low-carbon annealed steels
have a lower temperature transition range and a narrower one than highcarbon steels. Also, as the carbon content of the annealed steels is increased,
the steels become more brittle, and less energy is absorbed on impact during
fracture.
7.1.5 FRACTURE TOUGHNESS
The fracture of a metal (material) starts at a place where the stress
concentration is the highest, which may be at the tip of a sharp crack
We use the stress-intensity factor KI to express the combination of the effects
of the stress at the crack tip and the crack length. The subscript I
(pronounced “one”) indicates mode I testing in which a tensile stress causes
the crack to open. By experiment, for the case of uniaxial tension on a metal
plate containing an edge or internal crack (mode I testing), we find that
The critical value of the stress-intensity factor that causes failure of the plate is
called the fracture toughness KIC, (pronounced “kay-one-see”) of the material.
In terms of the fracture stress σf and the crack length a for an edge crack (or
one-half of the internal crack length)
7.2 FATIGUE OF METALS
In many types of service applications, metal parts subjected to repetitive or
cyclic stresses will fail due to fatigue loading at a much lower stress than that
which the part can withstand under the application of a single static stress.
These failures that occur under repeated or cyclic stressing are called fatigue
failures
Many types of tests are used to determine the fatigue life of a material. The
most commonly used small-scale fatigue test is the rotating-beam test in
which a specimen is subjected to alternating compression and tension
stresses of equal magnitude while being rotated.
Figure 7.18 shows typical SN curves for a high-carbon steel and a high-strength aluminum
alloy. For the aluminum alloy, the stress to cause failure decreases as the number of cycles is
increased. For the carbon steel, there is first a decrease in fatigue strength as the number of
cycles is increased, and then there is leveling off in the curve, the “knee,” with no decrease in
fatigue strength as the number of cycles is increased, indicating infinite life. The stress
associated with the “knee” of the SN plot is called the fatigue or endurance limit.
7.2.1 CYCLIC STRESSES
Fluctuating stress cycles are characterized by a number of parameters. Some of
the most important ones are:
• Mean stress σm is the algebraic mean (average) of the maximum and
minimum stresses in the fatigue cycle.
• Range of stress σr is the difference between σmax and σmin.
• Stress amplitude σa is one-half the stress cycle.
• Stress ratio R is the ratio of minimum and maximum stresses.
7.2.2 BASIC STRUCTURAL CHANGES THAT OCCUR
IN A DUCTILE METAL IN THE FATIGUE PROCESS
When a specimen of a ductile homogeneous metal is
subjected to cyclic stresses, the following basic structural
changes occur during the fatigue process:
•
•
•
•
Crack initiation
Slipband crack growth
Crack growth on planes of high tensile stress
Ultimate ductile failure
7.2.3 SOME MAJOR FACTORS THAT AFFECT THE FATIGUE
STRENGTH OF A METAL
The fatigue strength of a metal or alloy is affected by factors other than the
chemical composition of the metal itself. Some of the most important of these are:
•
•
•
•
Stress concentration
Surface roughness
Surface condition
Environment
7.3 FATIGUE CRACK PROPAGATION RATE
Preexisting flaws or cracks within a material component reduce or may
eliminate the crack initiation part of the fatigue life of a component. Thus,
the fatigue life of a component with preexisting flaws may be
considerably shorter than the life of one without flaws. In this section, we
will utilize fracture mechanics methodology to develop a relationship to
predict fatigue life in a material with preexisting flaws and under stressstate conditions due to cyclic fatigue action
7.3.1 CORRELATION OF FATIGUE CRACK
PROPAGATION WITH STRESS AND CRACK LENGTH
7.4 CREEP AND STRESS RUPTURE OF METALS
7.4.1 CREEP OF METALS
• This time-dependent strain is called creep
• The creep of metals and alloys is very important
for some types of engineering designs,
particularly those operating at elevated
temperatures.
• A typical creep curve for a metal.
•
•
•
•
•
•
7.4.2 THE CREEP TEST
The effects of temperatures and stress on the creep
rate are determined by the creep test.
Determine the steady-state creep rate for the copper alloy
whose creep curve is shown in the previous slide.
Solution
The steady-state creep rate for this alloy for the creep curve
shown in the previous slide is obtained by taking the slope of
the linear part of the curve as indicated in the figure. Thus,
Creep rate = Δϵ = 0.0029 − 0.0019 = 0.001 in./in. = 1.2 × 10−6
in./in./h ◂ Δt 1000 h − 200 h
800 h
7.4.3 CREEP-RUPTURE TEST
•
7.5 GRAPHICAL REPRESENTATION OF CREEP- AND
STRESS-RUPTURE TIME-TEMPERATURE DATA USING THE
LARSEN-MILLER PARAMETER
Using the L.M. parameter plot of Figure 7.31 at a stress of 207 MPa (30 ksi), determine the time to
stress rupture at 980°C for directionally solidified alloy CM 247 (uppermost graph).
Solution
From Figure 7.31 at a stress of 207 MPa, the value of the L.M. parameter is 27.8 × 103 K · h.
Thus,
P = T(K) (20 + log tr)
T = 980°C + 273 = 1253 K
27.8 × 103 = 1253 (20 + log tr)
log tr = 22.19 − 20 = 2.19
tr = 155 h ◂
LARSEN-MILLER STRESS-RUPTURE
STRENGTH OF DIRECTIONALLY
SOLIDIFIED (DS) CM 247 LC ALLOY
VERSUS DS AND EQUIAXED MAR-M
247 ALLOY.
MFB: MACHINED FROM THE BLADE;
GFQ: GAS FAN-QUENCHED;
AC: AIR-COOLED
LARSEN-MILLER DIAGRAM FOR 0.2% STRAIN, COMPARING
ROC AND IM TI-829 AND ROC TI-25-10-3-1 TO SEVERAL
COMMERCIALLY IMPORTANT ALPHA AND BETA ALLOYS.
ROC: RAPID OMNIDIRECTIONAL COMPACTION.
Calculate the time to cause 0.2% creep strain in gamma
titanium aluminide (TiAl) at a stress of 40 ksi and 1200°F
using Figure 7.32.
Solution
For these conditions, from Figure 7.32, P = 38,000. Thus,
P = 38,000 = (1200 + 460) (log t0.2% + 20)
22.89 = 20 + log t
log t = 2.89
t = 776 h ◂
7.6 A CASE STUDY IN FAILURE OF METALLIC
COMPONENTS
Owing to among other things, material defects, poor
design, and misuse, metal components occasionally
fail by fracture fatigue and creep.
Premature failure of a fan shaft (dimensions in inches).
7.7 RECENT ADVANCES AND FUTURE DIRECTIONS IN
IMPROVING THE MECHANICAL PERFORMANCE OF METALS
7.7.1 IMPROVING DUCTILITY AND STRENGTH SIMULTANEOUSLY
• Pure copper in its annealed and coarse-grained
state shows tensile ductility as large as 70% but very
low yield strength.
• The nanocrystalline form of pure copper with grain
size less than 30 nm has significantly higher yield
strength but with tensile ductility of less than 5%.
7.7.2 FATIGUE BEHAVIOR IN NANOCRYSTALLINE METALS
• Primary fatigue experiments on nanocrystalline (4 to 20 nm),
ultrafine (300 nm), and microcrystalline pure nickel at a load
ratio R of zero (zero-tension-zero) and a cycle frequency of 1
Hz has shown a significant effect on its SN fatigue response.
• The nanocrystalline nickel shows a slightly higher increase
than the ultrafine nickel.
• However, fatigue crack growth experiments using edgenotched specimens of nickel with the same grain size as
above show a different picture
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