MATERIALS
ENGINEERING
CHAPTER 7
MECHANICAL
PROPERTIES
FUNDAMENTAL CONCEPTS
• Many materials, when in service, are subjected to
forces or loads; examples include the aluminum
alloy from which an airplane wing is constructed
and the steel in an automobile axle.
• In such situations it is necessary to know the
characteristics of the material and to design the
member from which it is made such that any
resulting deformation will not be excessive and
fracture will not occur.
FUNDAMENTAL CONCEPTS
• The mechanical behavior of a material reflects the
relationship between its response or deformation to
an applied load or force. Important mechanical
properties are strength, hardness, ductility, and
stiffness.
FUNDAMENTAL CONCEPTS
CONCEPTS OF STRESS AND STRAIN
• If a load is static or changes relatively slowly with
time and is applied uniformly over a cross section or
surface of a member, the mechanical behavior may
be ascertained by a simple stress–strain test.
• There are three principal ways in which a load may
be applied: namely, tension, compression, and
shear.
• In engineering practice many loads are torsional
rather than pure shear.
STRESS AND STRAIN
STRESS AND STRAIN
TENSION TESTS
• One of the most common mechanical stress–
strain tests is performed in tension. As will be
seen, the tension test can be used to ascertain
several mechanical properties of materials that
are important in design.
• A specimen is deformed, usually to fracture, with a
gradually increasing tensile load that is applied
uniaxially along the long axis of a specimen.
STRESS AND STRAIN
STRESS AND STRAIN
• The output of such a tensile test is recorded on a
strip chart (or by a computer) as load or force
versus elongation.
• To minimize these geometrical factors, load and
elongation are normalized to the respective
parameters of engineering stress and
engineering strain.
STRESS AND STRAIN
Stress (α) is defined by the relationship
Where:
α – Stress (Pa or psi)
F – Force (N or lb)
Ao – Cross sectional area (m2 of in2)
STRESS AND STRAIN
STRESS AND STRAIN
Engineering strain (ϵ) is defined according to
Where:
ϵ - strain
li – lo - change in length
lo - original length
STRESS AND STRAIN
COMPRESSION TESTS
• A compression test is conducted in a manner
similar to the tensile test, except that the force is
compressive and the specimen contracts along
the direction of the stress.
• By convention, a compressive force is taken to
be negative, which yields a negative stress.
STRESS AND STRAIN
STRESS AND STRAIN
SHEAR AND TORSIONAL STRESS
• For tests performed using a pure shear force as
shown in Figure, the shear stress is computed
according to
STRESS AND STRAIN
Where:
F is the load or force imposed parallel to the upper
and lower faces, each of which has an area of A0.
STRESS AND STRAIN
STRESS AND STRAIN BEHAVIOR
STRESS AND STRAIN DIAGRAM
• The degree to which a structure deforms or strains
depends on the magnitude of an imposed stress.
• For most metals that are stressed in tension and
at relative low levels, stress and strain are
proportional to each other through the relationship
HOOKE’S
LAW
STRESS AND STRAIN
STRESS AND STRAIN BEHAVIOR
Where:
E – Modulus of Elasticity (Gpa or psi)
STRESS AND STRAIN BEHAVIOR
• Deformation in which stress and strain are
proportional is called elastic deformation.
• The greater the modulus, the stiffer the material,
or the smaller the elastic strain that results from
the application of a given stress.
• Elastic deformation is nonpermanent, which
means that when the applied load is released, the
piece returns to its original shape.
STRESS AND STRAIN
PROBLEM
1. A piece of copper originally 305 mm (12 in.) long
is pulled in tension with a stress of 276 MPa
(40,000 psi). If the deformation is entirely elastic,
what will be the resultant elongation?
Ans: 0.77 mm
DUCTILITY
• Another important mechanical property. It is a
measure of the degree of plastic deformation
that has been sustained at fracture.
• A material that experiences very little or no
plastic deformation upon fracture is termed
brittle.
• Ductility for several common metals (and also for
a number of polymers and ceramics). These
properties are sensitive to any prior deformation,
the presence of impurities, and/or any heat
treatment to which the metal has been subjected.
RESILIENCE
• Is the capacity of a material to absorb energy
when it is deformed elastically and then, upon
unloading, to have this energy recovered.
• The associated property is the modulus of
resilience, Ur , which is the strain energy per
unit volume required to stress a material from
an unloaded state up to the point of yielding.
TOUGHNESS
• Is a mechanical term that is used in several
contexts; loosely speaking, it is a measure of
the ability of a material to absorb energy up to
fracture.
• Specimen geometry as well as the manner of
load application are important in toughness
determinations.
• Furthermore, fracture toughness is a property
indicative of a material’s resistance to fracture
when a crack is present.
REFERENCES
Materials Science and Engineering: An
Introduction, William D. Callister
John Wiley & Sons, 2010.
