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Mechanical Testing of Materials An Introduction Strength
of materials is materials
science applied to the study of engineering materials and their mechanical
behavior in general (such as stress, deformation, strain and
stress-strain relations). Strength is considered in terms of compressive strength,
tensile
strength, and shear
strength, namely the limit states of compressive
stress, tensile
stress and shear
stress respectively. NEW: An informative PowerPoint presentation on Mechanical testing of materials may be seen here.
Definitions Stress
is the force applied over an area.
Strength
terms Compressive
strength is a limit
state of compressive
stress that leads to compressive failure in the manner of ductile failure
(infinite theoretical yield) or in the manner of brittle failure (rupture as the
result of crack propagation, or sliding along a weak plane - see shear
strength). Tensile
strength is a limit
state of tensile
stress that leads to tensile failure in the manner of ductile failure (yield
as the first stage of failure, some hardening in the second stage and break
after a possible "neck" formation) or in the manner of brittle failure
(sudden breaking in two or more pieces with a low stress state). Strain
- deformation terms Deformation
of the material is the change in geometry when stress is applied (in the form of
force loading, gravitational field, acceleration, thermal expansion, etc.).
Deformation is expressed by the displacement field of the material. Strain
or reduced deformation is a mathematical term to express the trend of the
deformation change among the material field. For uniaxial loading -
displacements of a specimen (for example a bar element) it is expressed as the
quotient of the displacement and the length of the specimen. For 3D displacement
fields it is expressed as derivatives of displacement functions in terms of a
second order tensor
(with 6 independent elements). Deflection
is a term to describe the magnitude to which a structural element bends under a
load. Stress-strain
relations Elasticity
is the ability of a material to return to its previous shape after stress is
released. In many materials, the relation between applied stress and the
resulting strain is directly proportional (up to a certain limit), and a graph
representing those two quantities is a straight line. The slope of this line is
known as Young's
Modulus, or the "Modulus of Elasticity." The Modulus of Elasticity
can be used to determine stress-strain relationships in the linear-elastic
portion of the stress-strain curve. The linear-elastic region is taken to be
between 0 and 0.2% strain, and is defined as the region of strain in which no
yielding (permanent deformation) occurs. Plasticity
or plastic deformation is the opposite of elastic deformation and is accepted as
unrecoverable strain. Plastic deformation is retained even after the relaxation
of the applied stress. Most materials in the linear-elastic category are usually
capable of plastic deformation. Brittle materials, like ceramics, do not
experience any plastic deformation and will fracture under relatively low
stress. Materials such as metals usually experience a small amount of plastic
deformation before failure while soft or ductile polymers will plastically
deform much more. Consider
the difference between a fresh carrot and chewed bubble gum. The carrot will
stretch very little before breaking, but nevertheless will still stretch. The
chewed bubble gum, on the other hand, will plastically deform enormously before
finally breaking. Design
terms Ultimate
strength is an attribute directly related to a material, rather than just
specific specimen of the material, and as such is quoted force per unit of cross
section area (N/m²). For example, the ultimate tensile strength (UTS) of AISI
1018 Steel is 440 MN/m².
In general, the SI unit of stress is the pascal,
where 1 Pa = 1 N/m². In English units, the unit of stress is given as lbf/in²
or pounds-force
per square inch. This unit is often abbreviated as psi. One thousand
psi is abbreviated ksi. Factor
of safety is a design constraint that an engineered component or structure
must achieve. FS = UTS / R,
where FS: the Factor of Safety, R: The applied stress, and UTS: the Ultimate
force (or stress). Margin
of Safety is also sometimes used to as design constraint. It is defined
MS=Factor of safety - 1 For
example to achieve a factor of safety of 4, the allowable stress in an AISI 1018
steel component can be worked out as R = UTS
/ FS = 440/4 = 110 MPa, or R =
110×106 N/m². Suggested
reading
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