Chapter 2: Mechanical Properties Flashcards
Mechanical properties
Standardized interpretations of a material’s response to stress that compare their response during plastic and elastic deformation.
Stress
Measure of what a material feels from externally applied forces.
Types of Stress (3)
Tension, compression, shear
Stress Formula
σ = P/A
Strain
Deformation of a material from stress.
Strain formula
ε = ΔL/L
Shear Strain Formula
γ = b/h = tanθ = θ for small angles
Hooke’s law formulae
σ = Eε
τ = γG
Poisson’s ratio
v = - Lateral Strain / Longitudinal (axial) Strain
Anisotropic materials
Mechanical properties depend on the orientation of the material’s body, unsymmetrical crystalline structures.
Isotropic materials
Identical material properties in all directions at every given point
Poisson’s ratio range
0 - 0.5
v = 0.5
Perfectly incompressible isotropic material
Elastic deformation
Bonds stretch and shorten as stress is applied, deformations recover quickly.
Plastic deformation
Bonds are stretched and/or broken, deformations are permanent.
Metallic deformation behavior below the yield point
Elastic
Metallic deformation behavior above the yield point
Elastic and plastic
Tension testing
Constant rate of elongation applied to a dog bone specimen so that plastic deformation occurs only in the gauge section.
Young’s modulus (E)
Slope of the elastic portion of a stress-strain curve
Resilience modulus (U)
Measure of material stiffness, area under a stress-strain curve
Yield strength, proportional/elastic limit (σy)
Stress on a stress-strain curve that is the limit of elastic behavior and the beginning of plastic behavior.
Offset yield strength
When the yield point is difficult to define, stress is measured from ε = 0.002
Ultimate yield strength
Highest stress on a stress-strain curve, where a material begins to deform (have a local instability).
Reduction in area and length
Measures of ductility
Ductility
The measure of plastic strain to fracture, the quality of being flexible.
Hardness
Material’s resistance to localized plastic deformation, the ability to withstand force without scratching, penetration or indentation.
Toughness
Amount of energy a material can absorb before fracturing
Reduction in area formula
RA = (Ao - Af)/Ao
Brittle fracture
Breakage of a material via rapid crack propagation with low energy release and without significant plastic deformation. Less strain is needed.
Ductile fracture
Breaking of a material after extensive plastic deformation. Uses a lot of time and energy and needs an increased load.
True stress
Instantaneous stress
True stress formula
σT = σ(1+ε)
True strain
Instantaneous strain
True strain formula
εT = ln(Li/Lo) = ln(1+ ε)
Hardness Formula
H = F/A
Safety Factor
Ratio of a material’s strength to an expected strain.
Safety factor formula
FS = σy or uts / σdesign
Thermal expansion
Tendency of a material to change its shape, area, volume, and density in response to a change in temperature
Thermal expansion formula
ΔL = αLΔT
Thermal stress
Stress created by any change in temperature of a material.
Thermal stress formula
σt = -EαΔT
Thermal stress/strain gradient
Thermal stress/strain between 2 points
Thermal stress gradient formula
σ = -E(α1 - α2)ΔT
Thermal conductivity
The rate at which heat passes through a material
Thermal conductivity formula
q = -k(dT/dx)
Thermal conductivity mechanisms (k)
- Lattice Vibrations/photons in non-metals (kl)
- Free electrons in metals (ke)
k = kl + ke
Thermal strain gradient formula
εt = (α1 - α2)ΔT
Wiedemann-Franz law
Thermal and electrical properties are related and proportional
Thermal shock resistance
The ability of a material to withstand sudden changes in temperature
Thermal shock resistance formula
TSR = σk / Eα
Heat capacity
Amount of heat energy required to raise the temperature of a material by 1C
Heat capacity formula
C = dQ/dT, K/(mol*K)
Bond stiffness
Inflection point on a bond-energy curve, above this point, a material will melt.
Bond stiffness formula
F = αEΔr
Ohm’s law
R = V/I
Resistivity
Measure of the resisting power of a specified material to the flow of an electric current. Affected by temperature, impurities and deformation. p = RA/l
Conductivity
The degree to which a specified material conducts electricity. σ = 1/p
Bonding force formula
F = dU/dr
Work hardening
Toughening (increase of hardness) of a metal, happens during plastic deformation
