Transcript MENG 286 MATERIALS SCIENCE

MECHANICAL PROPERTIES AND
TESTS
Fracture Mechanic
MENG 486
Stress
• Stress is a measure of the intensity of the
internal forces acting within a deformable
body.
• Mathematically, it is a measure of the average
force per unit area of a surface within a the
body on which internal forces act
• The SI unit for stress is Pascal (symbol Pa),
which is equivalent to one Newton (force) per
square meter (unit area).
• Three types of stresses -> Tensile;
Compressive; Shear
Mechanism of Stress (Tensile)
Tensile, Compressive and Shear Stresses
A1
Stress???
Strain
• Strain is deformation of a physical body under
the action of applied forces
• It is the geometrical measure of deformation
representing the relative displacement between
particles in the material body
• Strain is a dimensionless quantity
• Strain accounts for elongation, shortening, or
volume changes, or angular distortion
• Normal stress causes normal strain (tensile or
compressive)
• Shear strain is defined as the change in right
angle ( or angle change between two originally
orthogonal material lines)
Types of Strains
tensile load
produces
an elongation and
positive linear
strain.
compressive load
produces contraction
and a negative linear
strain.
torsional
deformation
Tensile Test and Stress-strain
relationship
Tensile Test
• Used for determining UTS, yield
strength, %age elongation, and
Young’s Modulus of Elasticity
• The ends of a test piece are fixed into
grips. The specimen is elongated by
the moving crosshead; load cell and
extensometer measure, respectively,
the magnitude of the applied load
and the elongation
Stress-Strain Relationship
For structural applications,
the yield stress is usually a
more important property
than the tensile strength,
since once the yield stress
has passed, the structure has
deformed beyond acceptable
limits.
Important Terms (Stress-Strain Rel.)
• Elastic Limit -> Maximum
amount of stress up to which
the
deformation
is
absolutely temporary
• Proportionality Limit ->
Maximum stress up to
which
the
relationship
between stress & strain is
linear.
• Hooke’s Law -> Within
elastic limit, the strain
produced in a body is
directly proportional to the
stress applied.
σ=Eε
Important Terms (Stress-Strain Rel.)
• Young’s Modulus of elasticity > the ratio of the uniaxial
stress over the uniaxial strain
in the range of stress in which
Hooke's Law holds
• Elasticity -> the tendency of a
body to return to its original
shape after it has been
stretched or compressed
• Yield Point -> the stress at
which a material begins to
deform plastically
Important Terms (Stress-Strain Rel.)
• Plasticity -> the deformation
of a material undergoing
non-reversible changes of
shape in response to applied
forces
• Ultimate Strength -> It is the
maxima of the stress-strain
curve. It is the point at which
necking will start.
• Necking -> When tensile
deformation
becomes
localized in a small region of
the material, the deformation
mode is called necking
Important Terms (Stress-Strain Rel.)
• Fracture Point -> The stress
calculated immediately before
the fracture.
• Ductility -> The amount of
strain a material can endure
before failure.
• Ductility is measured by
percentage elongation or area
reduction
Important Terms (Stress-Strain Rel.)
• A knowledge of ductility is
important for two reasons:
1. It indicates to a designer the
degree to which a structure
will deform plastically before
fracture.
2. It specifies the degree of
allowable deformation during
fabrication
Engineering stress– strain behavior for
Iron at three temperatures
Resilience
• Resilience is the capacity of a material
to absorb energy when it is deformed
elastically and then, upon unloading, to
have this energy recovered
• Modulus of Resilience (Ur) is the strain
energy per unit volume required to
stress a material from an unloaded
state up to the point of yielding.
Resilience
• Assuming a linear elastic region
• For SI units, this is joules per cubic meter (J/m3,
equivalent to Pa)
• Thus, resilient materials are those having high
yield strengths and low moduli of elasticity; such
alloys would be used in spring applications
EXAMPLE PROBLEM
• A piece of copper originally 305mm (12 in.)
long is pulled in tension with a stress of
276MPa (40,000psi). If the deformation is
entirely elastic, what will be the resultant
elongation?
• Magnitude of E for copper is 110GPa
Poisson’s Ratio
• Poisson’s ratio is defined as the
ratio of the lateral and axial strains
• Theoretically, Poisson’s ratio for
isotropic materials should be 1/4;
furthermore, the maximum value
for ν is 0.50
• For isotropic materials, shear and
elastic moduli are related
G=0.4E
EXAMPLE PROBLEM 6.2
• A tensile stress is to be applied along the long axis of a
cylindrical brass rod that has a diameter of 10mm.
Determine the magnitude of the load required to produce a
0.0025mm change in diameter if the deformation is entirely
elastic.
For the strain in the x direction:
EXAMPLE PROBLEM
True stress =
load/ actual area in the
necked-down region,
continues to rise to the
point of fracture, in
contrast to the
engineering stress.
σ = F/Ao ε = (li-lo/lo)
σT = F/Ai εT = ln(li/lo)
True Stress and Strain
• The decline in the stress necessary to continue
deformation past the point M, indicates that the
metal is becoming weaker.
• But material is increasing in strength.
True Stress and Strain
• True stress σT is defined as the load F divided by the
instantaneous cross-sectional area Ai over which
deformation is occurring
• True strain ЄT is defined as:
n= slope of True Stress-strain curve
True Stress and Strain
• If
no
volume
change
occurs
during
deformation—that is, if
Aili = A0l0
• Then true and engineering stress and strain are
related according to
• The equations are valid only to the onset of
necking; beyond this point true stress and strain
should be computed from actual load, crosssectional area, and gauge length measurements
EXAMPLE PROBLEM
• A cylindrical specimen of steel having an original
diameter of 12.8mm is tensile tested to fracture and
found to have an engineering fracture strength σf of
460MPa. If its cross-sectional diameter at fracture is
10.7mm, determine:
(a) The ductility in terms of percent reduction in area
(b) The true stress at fracture
Ductility is computed as
EXAMPLE PROBLEM 6.4
True stress is defined by Equation
where the area is taken as the fracture area Af
However, the load at fracture must first be
computed from the fracture strength as
And the true stress is calculated as:
Ductile Material
Uniform deformation
Deformation concentrated in neck
Neck begins to form – max. load
Fracture
Ductile Failure
Copper
Duralumin
Ductile materials exhibit significant permanent deformation after
yielding before fracture.
Brittle Materials
Exhibit very little deformation after yielding and fracture immediately
Effect of Temperature on Properties
• Generally speaking, materials are lower in
strength and higher in ductility, at elevated
temperatures
Temperature Effects
• As temperature
increases:
– Ductility and toughness
increase.
– Yield stress and the
modulus of elasticity
decrease.
• Temperature also affects
the strain-hardening
exponent of most metals,
in that n decreases as
temperature increases.
TOUGHNESS
• It is a property of material by virtue of which
it resists against fracture under impact loads.
• Toughness is the resistance to fracture of a
material when stressed
• Mathematically, it is defined as the amount of
energy per volume that a material can absorb
before rupturing
• Toughness can be determined by measuring
the area (i.e., by taking the integral)
underneath the stress-strain curve
Toughness (contd…)
• Toughness =
Where
• ε is strain
• εf is the strain upon failure
• σ is stress
The Area covered under stress
strain curve is called
toughness
Toughness (contd…)
• Toughness is measured in units of joules per
cubic meter (J/m3) in the SI system
• Toughness and Strength -> A material may be
strong and tough if it ruptures under high
forces, exhibiting high strains
• Brittle materials may be strong but with
limited strain values, so that they are not tough
• Generally, strength indicates how much force
the material can support, while toughness
indicates how much energy a material can
absorb before rupture
IMPACT TEST
Impact Fracture Testing
Fracture behavior depends on many external factors:
•Strain rate
•Temperature
•State of Stress
Impact testing is used to ascertain the fracture characteristics
of materials at a high strain rate and a triaxial stress state.
In an impact test, a notched specimen is fractured by an impact
blow, and the energy absorbed during the fracture is measured.
There are two types of tests – Charpy impact test and Izod
impact test.
Impact Test: The Charpy Test
The ability of a material to
withstand an impact blow is
referred to as notch toughness.
The energy absorbed is the
difference in height between
initial and final position of the
hammer. The material fractures
at the notch and the structure of
the cracked surface will help
indicate whether it was a brittle
or ductile fracture.
Impact Test (Charpy) Data for some of the Alloys
In effect, the Charpy test takes the tensile test to completion very
rapidly. The impact energy from the Charpy test correlates with
the area under the total stress-strain curve (toughness)
Impact Test: The Izod Test
Generally used for polymers. Izod test is different from the
Charpy test in terms of the configuration of the notched test
specimen
Impact Test (Izod) Data for various polymers
Impact Tests: Test conditions
• The impact data are sensitive to test conditions. Increasingly
sharp notches can give lower impact-energy values due to the
stress concentration effect at the notch tip
• The FCC alloys→ generally ductile fracture mode
• The HCP alloys→ generally brittle fracture mode
• Temperature is important
• The BCC alloys→ brittle modes at relatively low temperatures
and ductile mode at relatively high temperature
Transition Temperatures
• As temperature decreases a ductile material can
become brittle - ductile-to-brittle transition
– The transition temperature is the temp at which
a material changes from ductile-to-brittle
behavior
• Alloying usually increases the ductile-to-brittle
transition temperature. FCC metals remain ductile
down to very low temperatures. For ceramics, this
type of transition occurs at much higher
temperatures than for metals.
Ductile to Brittle Transition
The results of impact tests are absorbed energy, usually as a function of temperature. The
ABSORBED ENERGY vs. TEMPERATURE curves for many materials will show a
sharp decrease when the temperature is lowered to some point. This point is called the
ductile to brittle transition temperature (relatively narrow temperature range) .
A typical ductile to brittle transition as a function of temperature. The properties of BCC
carbon steel and FCC stainless steel, where the FCC crystal structure typically leads to
higher absorbed energies and no transition temperature.
Transition Temperatures
(summary)
• BCC metals have transition temperatures
• FCC metals do not
• Can use FCC metals at low temperatures (eg
Austenitic Stainless Steel)
Hardness
• Hardness is the property of material by virtue
of which it resists against surface indentation
and scratches.
• Macroscopic hardness is generally
characterized by strong intermolecular bonds
• Hardness is dependent upon strength and
ductility
• Common examples of hard matter are
diamond, ceramics, concrete, certain metals,
and superhard materials (PcBN, PcD, etc)
Hardness Tests (BRINELL HARDNESS
TEST)
• Used for testing metals and nonmetals of low to
medium hardness
• The Brinell scale characterizes the indentation
hardness of materials through the scale of
penetration of an indenter, loaded on a material
test-piece
• A hardened steel (or cemented carbide) ball of
10mm diameter is pressed into the surface of a
specimen using load of 500, 1500, or 3000 kg.
BRINELL HARDNESS TEST
P
where:
P = applied force (kgf)
D = diameter of indenter (mm)
d = diameter of indentation (mm)
• The resulting BHN has
units of kg/mm2, but the
units are usually omitted
in expressing the
numbers
Rockwell Hardness Test
• A cone shaped indenter or
small diameter ball (D = 1.6 or
3.2mm) is pressed into a
specimen using a minor load
of 10kg
• Then, a major load of 150kg
(at max) is applied
• The additional penetration
distance d is converted to a
Rockwell hardness reading by
the testing machine. This is an
advantage as we don’t need to
make calculations.
Rockwell Hardness Test
• The differences in load and indenter geometry
provide various Rockwell scales for different
materials. The most common scales are listed in
table below:
Diamond
Steel
Diamond
Vickers Hardness Test
• Uses a pyramid shaped indenter made of diamond.
• It is based on the principle that impressions made by this
indenter are geometrically similar regardless of load.
• The Vickers test is often easier to use than other hardness
tests since the required calculations are independent of the
size of the indenter, and the indenter can be used for all
materials irrespective of hardness
• Indenter= diamond
• Accordingly, loads of various sizes are applied, depending
on the hardness of the material to be measured
Vickers Hardness Test
Where:
F = applied load (kg)
D = Diagonal of the impression
made the indenter (mm)
The hardness number is
determined by the load over
the surface area of the
indentation and not the area
normal to the force
Vickers Hardness Test
Vickers Hardness Test
Knoop Hardness Test
• It is a microhardness test - a test for mechanical
hardness used particularly for very brittle materials
or thin sheets
• A pyramidal diamond point is pressed into the
polished surface of the test material with a known
force, for a specified dwell time, and the resulting
indentation is measured using a microscope
• Length-to-width ratio of the pyramid is 7:1
Knoop Hardness Test (contd…)
• The indenter shape facilitates reading the
impressions at lighter loads
• HK = Knoop hardness value;
• F = load (kg);
• D = long diagonal of the impression (mm)
Hardness of Metals and Ceramics
Hardness of Polymers
Conversion of Hardness on Scales
Hot Hardness
• A property used to characterize strength and
hardness at elevated temperatures is Hot
Hardness
• It is the ability of a material to retain its
hardness at elevated temperatures
Numerical Problems
•
•
•
•
Problems 6.3 to 6.9;
6.14 to 6.23;
6.25 to 6.33;
6.46 to 6.48
Self Study
COMPRESSION
•
•
•
•
•
Compression test is where specimen is subjected to a
compressive load
Carried out by compressing a solid cylindrical specimen
between two well-lubricated flat dies
Slender specimens can buckle during this test
Cross-sectional area of the specimen will change along its
height and obtaining the stress–strain curves in compression
is difficult
When results of compression and tension tests on ductile
metals are compared, true stress–true strain curves coincide
COMPRESSION
•
•
•
Behavior is not true for brittle materials as they are stronger
and more ductile in compression than in tension
When a metal is subjected to tension into the plastic range,
the yield stress in compression is lower than that in tension
Phenomenon known as Bauschinger effect
COMPRESSION
Disk Test
• Disk test is where a disk is subjected to compression
between two hardened flat plates
• Tensile stresses develop perpendicular to the vertical
centerline along the disk
• Fracture begins and the disk splits in half vertically
• Tensile stress in the disk is
P = load at fracture
d = diameter of the disk
t = thickness
TORSION
TORSION
•
•
•
•
A workpiece may be subjected to shear strains
Torsion test can be used to determine properties of materials
in shear
Performed on a thin tubular specimen
The shear stress can be calculated from the formula
T = torque
r = average radius of the tube
t = thickness of the tube at its narrow section
TORSION
•
Shear strain can be calculated from
l = length of tube subjected to torsion
Φ = angle of twist in radians
•
•
Ratio of shear stress to the shear strain in the elastic range is
called shear modulus, or modulus of rigidity, G
G is a quantity related to the modulus of elasticity E
BENDING
Bending
• Preparing specimens from brittle materials, such
as ceramics and carbides, is difficult because of
problems in shaping and machining them to
certain dimensions.
• The most common test for brittle materials is the
bend or flexure test.
Bend / Flexure Test
• Rectangular specimen
supported at its ends.
• Load is applied vertically at
1 or 2 pts.
• The stress at fracture in
bending is known as the
modulus of rupture,
flexural strength, or
transverse rupture
strength.
Section 6.6
The Bend Test for Brittle Materials
 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.
 Flexural strength or modulus of rupture -The stress required to fracture a
specimen in a bend test.
 Flexural modulus - The modulus of elasticity calculated from the results
of a bend test, giving the slope of the stress-deflection curve.
The stress-strain behavior of brittle materials compared with that of more
ductile materials
(a) The bend test often used for measuring the strength of brittle materials,
and (b) the deflection δ obtained by bending