Drilling

1
Mechanical Behavior of Materials
Objective

• Know the concepts of mechanical properties of
  materials.
• Understand the factors affecting the mechanical
  properties.
• Be aware of the basic testing procedures that
  engineers use to evaluate many of these
  properties.

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Mechanical Behavior of Materials
Outline

• Mechanical Properties of Materials
• Stress-Strain Diagram Properties
• Bend Test of Materials
• Hardness Test of Materials
• Impact Testing of Materials
• Fracture Mechanics of Materials
• Fatigue of Materials and Application
• Creep of Materials , Stress Rupture, and Stress
  Corrosion
• Evaluation of Creep Use of Creep Data

3
Behavior and Manufacturing Properties of Materials
4
Representative Strengths of Various Categories of
Materials
5
Materials Design and Selection

1. Density is mass per unit volume of a material,
   usually expressed in units of g/cm3 or lb/in.3
2. Strength-to-weight ratio is the strength of a
   material divided by its density materials with a
   high strength-to-weight ratio are strong but
   lightweight.

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Mechanical Behavior of Materials
Tension Test

• Most common test for determining such mechanical
  properties as strength, ductility, toughness,
  elastic modulus, and strain hardening.
• The test specimen made according to standard
  specifications. Most specimens are solid and
  round, some are flat-sheet.
• In this test a metal sample is pulled to failure
  at a constant rate.
• The load displacement relationship is plotted
  on a moving chart graph paper, with the signals
  coming from a load cell fixed at the top of the
  testing machine, and an extensometer (strain
  gauge) attached to the sample.
• The load displacement data obtained from the
  chart paper can be converted to engineering
  stress/strain data, and a plot of engineering
  stress vs. engineering strain can be constructed.

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Tension Testing Machine
Mechanical Behavior of Materials
Tensile Specimens
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Engineering Stress Strain Diagram For A
High-Strength Aluminum Alloy.
Mechanical Behavior of Materials
A unidirectional force is applied to a specimen
in the tensile test by means of the moveable
crosshead. The cross-head movement can be
performed using screws or a hydraulic mechanism
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Mechanical Behavior of Materials

• Mechanical property data obtained from the
  tensile test are of engineering importance for
  structural design. These are
• modulus of elasticity
• yield strength at 0.2 percent offset
• ultimate tensile strength
• percent elongation at fracture
• percent reduction in area at fracture
• - Stress (?) Force or load per unit area of
  cross-section.
• - Strain (?) Elongation change in dimension
  per unit length
• - Youngs modulus (E) The slope of the linear
  part of the stress-
• strain curve in the elastic region
• ? (stress) E x ? (strain)
• or E (stress)/(strain) psi or pa

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Mechanical Behavior of Materials

• Slope of stress strain plot (which is
  proportional to the elastic modulus) depends on
  bond strength of metal

Adapted from Fig. 6.7, Callister 7e.
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Mechanical Behavior of Materials
Comparison of the elastic behavior of steel and
aluminum. For a given stress, aluminum deforms
elastically three times as much as does steel
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Mechanical Behavior of Materials
13
Mechanical Behavior of Materials
In industry, components are formed into various
shapes by applying external forces to the
workpiece using specific tools and dies. A
typical operation is rolling of a flat sheet to
be processed into a car body. Because
deformation in these processes is carried out by
mechanical means, an understanding of the
behavior of materials in response to externally
applied forces is important. Forming
operations may be carried out at room temperature
or at higher temperatures and at a low or a high
rate of deformation. The behavior of a
manufactured part during its expected service
life is an important consideration. For example
the wing of an aircraft is subjected to static as
well as dynamic forces. If excessive, dynamic
forces can lead to cracks and can cause failure
of the component.
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Mechanical Behavior of Materials
Engineering stress-strain.
Elastic range in stress-strain.
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Mechanical Behavior of Materials
Engineering stress-strain curve, showing various
features Yield stress (Y), Ultimate tensile
strength (UTS), and Fracture. 1. Elastic and
Plastic, 2. Uniform elongation and Necking.
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Mechanical Behavior of Materials

• Alloying a metal with other metals or nonmetals
  and heat treatment can greatly affect the tensile
  strength and ductility of metals.
• During the tensile test, after necking of the
  sample occurs, the engineering stress decreases
  as the strain increases, leading to a maximum
  engineering stress in the engineering
  stress-strain curve. Thus, once necking begins
  during the tensile test, the true stress is
  higher than the engineering stress.
• Engineering stress s P/A0 and
• Engineering strain e (l-l0)/l0
• True stress sT F/Ai s (1 e) and
• True strain eT ln (li/l0) ln (1 e)

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Mechanical Behavior of Materials
Chapter 4, mechanical properties of metals
Engineering stress-strain curves for some metals
and alloys
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Mechanical Behavior of Materials
Chapter 4, mechanical properties of metals
Comparison between engineering and tue
stress-strain curve
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Mechanical Behavior of Materials
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Mechanical Behavior of Materials
Yield strength is a very important value in
engineering structural design since it is the
strength at which a metal or alloy begins to show
significant plastic deformation. Since there is
no definite point on the stress-strain curve
where elastic strain ends and plastic strain
begins, the yield strength is chosen to be that
at which a finite amount of plastic strain has
occurred. For American structural design, the
yield strength is chosen at 0.2 plastic strain.
The ultimate tensile strength (UTS) is the
maximum strength reached in the engineering
stress-strain curve. If the specimen develops a
localized reduction in cross-sectional area
(necking), the engineering stress will decrease
with further strain until fracture.
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Mechanical Behavior of Materials
Determining the 0.2 offset yield strength in
gray cast ion, and (b) upper and lower yield
point behavior in a low-carbon steel
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Resilience, Ur
Mechanical Behavior of Materials

• Ability of a material to store energy
• Energy stored best in elastic region

If we assume a linear stress-strain curve this
simplifies to
Adapted from Fig. 6.15, Callister 7e.
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Mechanical Behavior of Materials
The area under the elastic region is the elastic
strain energy (in.lb./in.3), a measure of the
amount of elastic energy that can be stored in
each cubic inch of the specimen.
For spring steel, MR 385 in.lb./in.3 or 1355
in.lb./lb. For rubber, MR 1680 385 in.lb./in.3
or 48,000 in.lb./lb.. Rubber can store much more
energy per unit volume or weight than can steel.
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Elastic Strain Recovery
Mechanical Behavior of Materials
Adapted from Fig. 6.17, Callister 7e.
25
Mechanical Behavior of Materials
The more ductile a metal is, the more the
decrease in the stress on the stress-strain curve
beyond the maximum stress. For high strength
aluminum alloy, there is only a small decrease in
stress beyond the maximum stress because this
material has relatively low ductility. The
ultimate tensile strength is not used much in
engineering design for ductile alloys since too
much plastic deformation takes place before it is
reached. However, the ultimate tensile strength
can give some indication of the presence of
defects. If the metal contains porosity or
inclusions, these defects may cause the ultimate
tensile strength of the metal to be lower than
normal.
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Mechanical Behavior of Materials
Ductility of metals is most commonly expressed
as percent elongation and percent reduction in
area. The percent elongation and percent
reduction in area at fracture is of engineering
importance not only as a measure of ductility but
also as an index of the quality of the metal.
Percent elongation is the amount of
elongation that a tensile specimen under goes
during testing provides a value for the ductility
of a metal. Percent reduction in area is
usually obtained from a tensile test using a
specimen 0.50 in (12.7 mm) in diameter.
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Mechanical Behavior of Materials
Localized deformation of a ductile material
during a tensile test produces a necked region.
The micrograph shows necked region in a fractured
sample
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Mechanical Behavior of Materials
The stress-strain behavior of brittle materials
compared with that of more ductile materials
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Mechanical Behavior of Materials
Chapter 4, mechanical properties of metals
30
Mechanical Behavior of Materials
Toughness is defined as the total area under the
stress strain curve up to fracture (in.lb./in.3).
It is a measure of the total amount of energy
that can be absorbed prior to fracture. Brittle
materials are not tough.
Note It is not possible to make this integration
unless we have some mathematical function that
describes the relationship between stress and
strain up to fracture (? Ee only describes the
relationship during elastic deformation, not
plastic deformation). Some possible mathematical
models will be described in the following
section. As an approximation, toughness can be
estimated as the area under the curve using the
combined areas of simple shapes such as
rectangles and triangles.
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Mechanical Behavior of Materials
Given the true stress strain curve ? K?n , the
toughness (the specific energy (in.lb./in3)
dissipated up to fracture) can be calculated by
integrating with respect to strain up to the
strain at fracture (?f)
Then using the true stress strain model ? K?n
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Mechanical Behavior of Materials
Example Problem
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Mechanical Behavior of Materials
Example Problem
Figure 6.10 The stress-strain curve for an
aluminum alloy from Table 6-1
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Mechanical Behavior of Materials
Example Problem
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Mechanical Behavior of Materials
Youngs Modulus of Aluminum Alloy
From the data in Example 6.1, calculate the
modulus of elasticity of the aluminum alloy. Use
the modulus to determine the length after
deformation of a bar of initial length of 50 in.
Assume that a level of stress of 30,000 psi is
applied. Example 6.3 SOLUTION
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Mechanical Behavior of Materials
Ductility of an Aluminum Alloy
The aluminum alloy in Example 6.1 has a final
length after failure of 2.195 in. and a final
diameter of 0.398 in. at the fractured surface.
Calculate the ductility of this alloy. Example
6.4 SOLUTION
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Mechanical Behavior of Materials
The effect of temperance (a) on the stress-strain
curve and (b) on the tensile properties of an
aluminum alloy
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Mechanical Behavior of Materials
True Stress and True Strain Calculation
Compare engineering stress and strain with true
stress and strain for the aluminum alloy in
Example 6.1 at (a) the maximum load and (b)
fracture. The diameter at maximum load is 0.497
in. and at fracture is 0.398 in. Example 6.5
SOLUTION
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Mechanical Behavior of Materials
SOLUTION (Continued)
40
Mechanical Behavior of Materials
Compression Many manufacturing processes such as
forging, rolling, extrusion, are performed with
the work piece subjected to compressive forces.
Compression test, in which the specimen is
subjected to compressive load, gives information
useful for these processes. When the results of
compression tests and tension tests on ductile
metals are compared, the true stress-true strain
curves for the two tests coincide. This
comparability does not hold true for brittle
materials, which are generally stronger and more
ductile in compression than in tension
41
Design or Safety Factors
Mechanical Behavior of Materials
Often N is between 1.2 and 5
. Factor of safety, N
Example Calculate a diameter, d, to ensure
that yield does not occur in the 1045 carbon
steel rod below. Use a factor of safety of
5.
d 0.067 m 6.7 cm
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Bend Test for Materials
43
Mechanical Behavior of Materials
Bend Test for Brittle Materials

1. Bend test - Application of a force to the center
   of a bar that is supported on each end to
   determine the resistance of the material to a
   static or slowly applied load.
2. Flexural strength -The stress required to
   fracture a specimen in a bend test.
3. Flexural modulus - The modulus of elasticity
   calculated from the results of a bend test,
   giving the slope of the stress-deflection curve.

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Mechanical Behavior of Materials
Bend Test for Brittle Materials
The bend test often used for measuring the
strength of brittle materials, and (b) the
deflection d obtained by bending
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Mechanical Behavior of Materials
Bend Test for Brittle Materials
Stress-deflection curve for Mg0 obtained from a
bend test
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Mechanical Behavior of Materials
Bend Test for Brittle Materials
Bending (Flexure) The Bend test is commonly used
for brittle materials. It usually involves a
specimen that has a rectangular cross-section.
The load is applied vertically, at either one
point or two as a result, these tests are
referred to as three-point and four point bend,
respectively. The longitudinal stresses in these
specimens are tensile at their lower surfaces and
compressive at their upper surfaces.
The stress at fracture in bending is known as the
transverse rupture strength.
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Hardness of Materials
48
Mechanical Behavior of Materials
Hardness of Materials
Hardness is a measure of the materials resistance
to localized plastic deformation (e.g. dent or
scratch). In general, hardness usually implies
a resistance to deformation, and for metals the
property is a measure of their resistance to
permanent or plastic deformation. To a person
concerned with the mechanics of materials
testing, hardness is most likely to mean the
resistance to indentation.
49
Mechanical Behavior of Materials
Hardness of Materials
Steel is harder than aluminum, and aluminum is
harder than lead. Several methods have been
developed to measure the hardness of materials.
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Mechanical Behavior of Materials
Hardness of Materials
Hardness and Strength Studies have shown that
(in the same units) the hardness of a cold-worked
metal is about three times its yield stress for
annealed metals, it is about five times the
yield. A relationship has been established
between the ultimate tensile strength (UTS) and
the Brinell hardness (HB) for steels. In SI
units, UTS 3.5(HB), where UTS is in Mpa. Or
UTS 500(HB), where UTS is in psi and HB is in
kg/mm2, as measured for a load of 3000 kg.
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Mechanical Behavior of Materials
Hardness of Materials

• Hardness-Testing Procedures The following
  considerations must be taken for hardness test to
  be meaningful and reliable
• The zone of deformation under the indenter must
  be allowed to develop freely.
• Indentation should be sufficiently large to give
  a representative hardness value for the bulk
  material.
• Surface preparation is necessary, if conducting
  Rockwell test and other tests, except Brinell
  test.

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Mechanical Behavior of Materials
Hardness of Materials
53

• Temperature Effects Increasing the temperature
  generally has the following effects on
  stress-strain curves
• It raises ductility and toughness
• It lowers the yield stress and the modulus of
  elasticity
• It lowers the strain-hardening exponent of most
  metals

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Mechanical Behavior of Materials
55
Rate-of-Deformation (Strain Rate) Effects
Deformation (strain) rate is defined as the speed
at which a tension test is being carried out, in
units of, say, mm/s.
The strain rate is a function of the specimen
length. A short specimen elongates
proportionately more during the same time period
than does a long specimen.
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Mechanical Behavior of Materials
When a ductile material is pulled in a tensile
test, necking begins and voids form starting
near the center of the bar by nucleation at
grain boundaries or inclusions. As deformation
continues a 45 shear lip may form, producing a
final cup and cone fracture
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Impact Testing of Materials
58
Mechanical Behavior of Materials

• Impact test - Measures the ability of a material
  to absorb the sudden application of a load
  without breaking.
• Impact energy - The energy required to fracture a
  standard specimen when the load is applied
  suddenly.
• Impact toughness - Energy absorbed by a material,
  usually notched, during fracture, under the
  conditions of impact test.
• Fracture toughness - The resistance of a material
  to failure in the presence of a flaw.

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Mechanical Behavior of Materials
The impact test (a) The Charpy and Izod tests,
and (b) dimensions of typical specimens
60
Mechanical Behavior of Materials

• Ductile to brittle transition temperature (DBTT)
  - The temperature below which a material behaves
  in a brittle manner in an impact test.
• Notch sensitivity - Measures the effect of a
  notch, scratch, or other imperfection on a
  materials properties, such as toughness or
  fatigue life.

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Mechanical Behavior of Materials
Results from a series of Izod impact tests for a
super-tough nylon thermoplastic polymer
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Mechanical Behavior of Materials
The Charpy V-notch properties for a BCC carbon
steel and a FCC stainless steel.
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Mechanical Behavior of Materials
The area contained within the true stress-true
strain curve is related to the tensile toughness.
Although material B has a lower yield strength,
it absorbs a greater energy than material A.
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Schematic drawing of fracture toughness specimens
with (a) edge and (b) internal flaws
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Mechanical Behavior of Materials
The fracture toughness Kc of a 3000,000psi yield
strength steel decreases with increasing
thickness, eventually leveling off at the plane
strain fracture toughness Klc
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Fatigue of Materials
67
Type of Fatigue Stresses
Typical fatigue stress cycles. (a) Reversed
stress (b) repeated stress (c) irregular or
random stress cycle

• Reversed cycle of stress i.e. the maximum and
  minimum stresses are equal.
• A repeated stress cycle i.e. smax (Rmax) and
  smin (Rmin) are not equal.
• A complicated stress cycle which might be
  encountered in a part such as an aircraft wing
  which is subjected to periodic unpredictable
  overloads due to gusts.

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Mechanical Behavior of Materials

• The basic method of presenting engineering
  fatigue data is by means of the S-N curve, a plot
  of stress S against the number of cycles to
  failure N. The value of stress that is plotted
  can be sa, smax, or smin.
• The most commonly used parameter is the stress
  ratio is R (S min/S max). If the stresses are
  fully reversed, then R -1. If the stresses are
  partially reversed, R a negative number less
  than 1. If the stress is cycled between a maximum
  stress and no load, R zero. If the stress is
  cycled between two tensile stresses, R a
  positive number less than 1.
• The S-N curve is determined for a specified value
  of sm , R (R smin/smax).
• The usual procedure for determining an S-N curve
  is to test the first specimen at a high stress
  where failure is expected in a fairly short
  number of cycles, e.g., at about two-thirds the
  static tensile strength of the material.
• The test stress is decreased for each succeeding
  specimen until one or two specimens do not fail
  in the specified numbers of cycles.

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Mechanical Behavior of Materials
The S-N fatigue curve for an acetal polymer
70
Examples of stress cycles. (a) Equal stress in
tension and compression, (b) greater tensile
stress than compressive stress, and (c) all of
the stress is tensile
71
Mechanical Behavior of Materials

• A fatigue failure is particularly insidious
  because it occurs without any obvious warning.
• Thermal fatigue. Thermal cycling cause expansion
  and contraction, hence thermal stress, if
  component is restrained.
• Corrosion fatigue. Chemical reactions induce
  pits which act as stress raisers. Corrosion also
  enhances crack propagation
• Fatigue tests are usually made with smooth,
  polished specimens under completely reversed
  stress conditions.
• Fatigue properties are frequently correlated
  with tensile properties. In general, the fatigue
  limit of cast and wrought steels is approximately
  50 percent of the ultimate tensile strength. The
  ratio of the fatigue limit (or the fatigue
  strength at 106 cycles) to the tensile strength
  is called the fatigue ratio.

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Mechanical Behavior of Materials
Fatigue limit (endurance limit) occurs for some
materials (some Fe and Ti alloys). In this case,
the S-N curve becomes horizontal at large N. The
fatigue limit is maximum stress amplitude below
which the material never fails, no matter how
large the number of cycle is.
The highest stress at which a (non-failure) is
obtained is taken as the fatigue limit. For
materials without a fatigue limit the test is
usually terminated for practical considerations
at a low stress where the life is about 108 or
5x108 cycles. The S-N curve is usually determined
with about 8 to 12 specimens.
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Mechanical Behavior of Materials
The S-N curves for a tool steel and an aluminum
alloy
74
Mechanical Behavior of Materials
Crack initiation at the sites of stress
concentration (microcracks, scratches, indents,
interior corners, dislocation slip steps,
etc.). Stage I initial slow propagation along
crystal planes with high resolved shear stress.
Involves just a few grains, and has flat fracture
surface. Stage II faster propagation
perpendicular to the applied stress. Crack grows
by repetitive blunting and sharpening process at
crack tip. Crack eventually reaches critical
dimension and propagates very rapidly.
Schematic representation of a fatigue fracture
surface in a steel shaft.
75
Mechanical Behavior of Materials
Variable affecting Fatigue

• Magnitude of stress (mean, amplitude...)
• Quality of the surface (scratches, sharp
  transitions and edges).
• Large enough variation or fluctuation in the
  applied stress, and Sufficiently large number of
  cycles of the applied stress.
• Other variables include stress concentration,
  corrosion, temperature, overload, metallurgical
  structure, residual stresses, and combined
  stresses, which tend to alter the conditions for
  fatigue.

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Mechanical Behavior of Materials
Preventing Fatigue Failure
Introducing compressive stresses into thin
surface layer by shot peening- firing small
shot into surface to be treated. Case
hardening- create C- or N-rich outer layer. Makes
harder outer and also introduces compressive
stresses Use materials with low thermal
expansion coefficients Decrease corrosiveness
of medium, if possible Add protective surface
coating Add residual compressive
stresses Prevent the development of surface
discontinuities during processing.  Reduce or
eliminate tensile residual stresses caused by
manufacturing.
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Creep of Materials
78
Mechanical Behavior of Materials
Creep Behavior
Creep is a time-dependent and permanent
deformation of materials when subjected to a
constant load at a high temperature (gt0.4Tm).
Examples turbine blades, stream generators.
Stages of Creep
Creep Testing
79
Mechanical Behavior of Materials
Creep Behavior
The effect of temperature or applied stress on
the creep curve
80
Mechanical Behavior of Materials
Secondary/steady-state creep is of longest
duration and is the most important parameter of
the creep behavior in long-life applications
??e/?t

• Stages of Creep
• Primary/transient creep.
• Secondary/steady-state creep.
• Tertiary creep.

A typical creep curve
81
Mechanical Behavior of Materials
Creep With increasing stress or temperature, the
instantaneous strain increases, the steady-state
creep rate increases and the time to rupture
decreases. The stress/temperature dependence of
the steady-state creep rate can be described
by ?ss K sn exp (-Qc/RT) where Qc is the
activation energy for creep, K and n are material
constants.

• Different mechanisms are responsible for creep in
  different materials
• The mechanisms include
• Stress-assisted vacancy diffusion
• Grain boundary diffusion
• Grain boundary sliding
• Dislocation motion

82
Mechanical Behavior of Materials

• Creep test - Measures the resistance of a
  material to deformation and failure when
  subjected to a static load below the yield
  strength at an elevated temperature.
• Climb - Movement of a dislocation perpendicular
  to its slip plane by the diffusion of atoms to or
  from the dislocation line.
• Creep rate - The rate at which a material deforms
  when a stress is applied at a high temperature.
• Rupture time - The time required for a specimen
  to fail by creep at a particular temperature and
  stress.

83
Mechanical Behavior of Materials

1. Stress-rupture curve - A method of reporting the
   results of a series of creep tests by plotting
   the applied stress versus the rupture time.
2. Larson-Miller parameter - A parameter used to
   relate the stress, temperature, and rupture time
   in creep.
3. Stress-corrosion- A phenomenon in which materials
   react with corrosive chemicals in the environment
   leading to the formation of cracks and lowering
   of strength.

84
Mechanical Behavior of Materials
Creep Behavior
Results from a series of creep tests. (a)
Stress-rupture curves for an iron-chromium-nickel
alloy and (b) the Larson-Miller parameter for
ductile cast iron