General Theory of
Stress and Strain
in Materials
Stress
Normal Stress
Compressive Stress
τ = F / Ao
F = compressive force
Ao = original area (before loading)
Tensile Stress
σ = Ft / Ao
Fs = tensile force
Ao = original area (before loading)
Shear Stress
τ = Fs / Ao
Fs = shear force
Ao = original area (before loading)
unit, Pa or psi
unit, unitless
Strain
Lateral Strain
εL = -δL / wo
Longitudinal Strain
ε = δ / Lo
Volumetric Strain
(ΔV/Vo)
Shear Strain
sideways force exerted on a medium
Stress-Strain Curve
Elastic State
Proportional Limit
σ = E ε
Yonge's Modulus
or
Modulus of Elasticity
symbol, E
unit, gPa
rise/run
E = Stress/Strain
measures how aeasily a material streches or deforms
Elastic Yield Point
Yield Strength
unit, Pa, psi
Plastic State
Lower Yield Point
Ultimate Yield Point
Ultimate Yield Strength
unit, Pa, psi
Ultimate Stress
unit, Pa, psi
Fracture Point
Breaking Stress
unit, Pa, psi
Reversible Deformation
Permanent Deformation
Poisson's Ratio
ν = εL / ε
Lateral Strain / Longitudinal Strain
Mechanical Properties
Ductilty
%EL = [(Lf – Lo) / Lo] x 100
%RA = [(Ao – Af) / Ao] x 100
ability of a material to sustain a large permanent deformation
Toughness
the strength with which the material opposes rupture
Resilience
the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading.
Elastic Shear Modulus
symbol, G
τ = Gγ
Shear stress/shear strain
G = E / 2(1+v)
measure of the ability of a material to resist transverse deformations
Elastic Bulk Modulus
measure of the ability of a substance to withstand changes in volume when under compression on all sides
symbol, K
P = -K(ΔV/Vo)
K = E / 3(1-2v)