METALS AND METAL ALLOYS Flashcards
Mechanical Properties
four most common materials widely used today
Metals, ceramics, polymers and composites
produces an elongation and positive linear strain
tensile load
produces contraction and a negative linear strain
compressive load
To compare specimens of different sizes, the __ is calculated per unit area
load
Engineering stress
σ = F / Ao, F is load applied perpendicular to specimen’s cross section; Ao is cross-sectional
area (perpendicular to the force) before application of the load.
Engineering strain
ε = Δl / lo (× 100 %), Δl is change in length, lo is the original length
Stress and strain are – for tensile loads, – for compressive loads
positive, negative
shear stress
Shear stress: τ = F / Ao, F is load applied parallel to the upper and lower faces each of which has an
area A0.
shear strain
Shear strain: γ = tgθ (× 100 %)
θ is strain angle
variation of pure shear, change in shape not volume
torsion
twisting or rotating force applied to a structural member, causing it to resist twisting
torsion
in torsion, The shear stress in this case is a function of applied —, shear strain is related to —.
torque T, angle of twist φ
measure of the twisting force applied to a shaft or beam. It is calculated as the product of force and the perpendicular distance from the axis of rotation.
Units: Newton-meters (Nm) or pound-feet (lb-ft).
torque
angular deformation of a shaft or beam due to the applied torque. It is measured in radians or degrees
angle of twist
— is a measure of a material’s ability to resist a pulling force before it breaks or fractures. It is expressed in units of force per unit area, such as pascals (Pa) or pounds per square inch (psi).
tensile strength
In tensile tests, if the deformation is elastic, the stress-strain relationship is called –
Hooke’s Law:
σ=Eε, E is the Young’s Modulus or modulus of elasticity and has the same units as 𝛔, N/m2 or Pa.
Deformation in which stress and strain are proportional is called –
elastic deformation
A plot of stress (ordinate) versus strain (abscissa) results in a linear relationship. The slope of this linear segment corresponds to the –
modulus of elasticity, E
stiffness, or a material’s resistance to elastic deformation
modulus of elasticity, E
greater the modulus, the – the material, or the – the elastic strain that results from the application of a given stress
stiffer, smaller
– is the deformation of a material that is reversible, meaning the material will return to its original shape and size once the stress causing the deformation is removed
elastic strain
– is nonpermanent, which means that when the applied load is released, the piece returns to its original shape
elastic deformation
There are some materials (i.e., gray cast iron, concrete, and many polymers) for which this elastic portion of the stress–strain curve is –; hence, it is not possible to determine a modulus of elasticity as described previously
not linear
nonlinear behavior, either the – or – modulus is normally used
tangent, secant
– is taken as the slope of the stress–strain curve at some specified level of stress
tangent modulus
– represents the slope of a secant drawn from the origin to some given point of the curve.
secant modulus
– is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds and corresponding slight atomic displacements.
macroscopic elastic strain
Values of the modulus of elasticity —; caused by –
ceramic and metals are the same, polymers have lower; atomic bonding
increasing temperature, the modulus of elasticity –.
decreases
— occurs when a material is subjected to a force that causes it to twist or slide relative to its neighboring layers. This type of deformation is characterized by the relative displacement of particles within the material, without any change in volume
shear elastic deformation
For shear elastic deformations, shear stress and strain are proportional to each other through the expression
τ = Gγ
where G is the shear modulus, the slope of the linear elastic region of the shear stress–
strain curve
elastic deformation is – ; meaning that the strain produced in a material is directly proportional to the applied stress at any given instant, regardless of how long the stress has been applied
time independent
in reality elastic deformation takes time (finite rate of
atomic/molecular deformation processes) - continues after initial loading, and after load release
time-dependent, anelasticity
anelasticity effect is normally small for metals but can be significant for polymers
visco-elastic behavior
– is a combination of elastic and viscous properties exhibited by certain materials. These materials exhibit both solid-like and liquid-like characteristics, depending on the rate of deformation.
Viscoelastic behavior
Materials subject to tension –
shrink laterally
Those subject to compression –
bulge
ratio of lateral and axial strains is called
Poisson’s ratio υ
Sign in the above equations shows that lateral strain is in opposite sense to longitudinal strain υ is dimensionless
T
Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed –
tensile stress
Poisson’s ratio – Theoretical value for isotropic material:
isotropic material: 0.25
➢ Maximum value: 0.50, Typical value: 0.24 - 0.30
For isotropic materials, shear and elastic moduli are related to each other and
to Poisson’s ratio according to
E = 2G (1 + υ)
E = 2G (1 + υ), G is about 0.4E; thus, if the value of one modulus is known, the other may be approximated.
- stress and strain are not proportional to each other
- the deformation is not reversible
- deformation occurs by breaking and re-arrangement of atomic bonds
Plastic deformation
