Mechanical Properties I

questions designers ask about materials

will it bend too much?
will it bend for good?

will it break?

different kinds of material breaks

elastic: reversible (bonds stretch and go back to original state) (ex. car coil spring)

plastic: permanent (top block slips off one full atom spacing and stays) (ex. bending paper clip)

fracture: bonds break (bonds across one plane snap) (ex. glass rod snap)

engineering stress

σ = F / A₀

force F (N) ÷ original cross-sectional area A₀ (mm²).

Units: MPa = N/m

engineering strain

ε = Δl / lo

change in length Δl ÷ original length l₀ (same units, so they cancel). Dimensionless; often quoted in %.

tensile strength testing

slope of straight line: elastic

point when line changes to curve: yield strength

top of curve: peak tensile strength

curve descends: fracture

hookes law for elastic region

σ = E ε (E = modulus of elasticity, or Young's modulus, ε = engineering strain)

poisson’s ratio

ν = − εx / εz

ν relates the lateral (sideways) contraction εx to the axial (along-the-load) stretch εz

shear modulus

τ = G γ

G relates shear stress τ to shear strain γ (the angular distortion, in radians). For isotropic materials (same properties in every direction): E = 2G(1 + ν)