For metallic materials, elastic deformation typically occurs up to strains of about $0.005$. Beyond this, plastic deformation occurs.

Caused by slip, where atomic bonds are broken by dislocation motion and new bonds are formed.

Maximum stress a material can withstand before necking and fracture.
Also known as Ultimate Tensile Strength (UTS).
Formula: $R_m = \frac{P_{max}}{A_0}$
For ductile metals, yield strength is often more critical for design than tensile strength.

Ability of a material to deform plastically before fracture.
Opposite of brittleness.
Measured by:
- Percent maximum elongation ($e_{max}$): Engineering strain at fracture, $e_f = \frac{L_f - L_0}{L_0}$.
- Reduction of area ($q$): $q = \frac{A_0 - A_f}{A_0}$.
Indicates material's ability to flow plastically and accommodate stress concentrations.

Ability of a material to absorb energy when deformed elastically and return it upon unloading.
Represented by the area under the elastic region of the stress-strain curve.
Modulus of Resilience ($U_r$): Strain energy per unit volume required to stress material from zero stress to yield stress.
- Formula: $U_r = \frac{\sigma^2}{2E} = 0.5\sigma\epsilon = 0.5\sigma\left(\frac{\sigma}{E}\right)$
- For uniaxial tension: $U_r = \frac{1}{2}\sigma_x\epsilon_x$

Material	E, psi	$s_0$, psi	$U_r$
Medium-carbon steel	$30 \times 10^6$	$45000$	$33.7$
High-carbon spring steel	$30 \times 10^6$	$140000$	$320$
Duraluminium	$10.5 \times 10^6$	$18000$	$17.0$
Copper	$16 \times 10^6$	$4000$	$5.3$
Rubber	$150$	$300$	$300$
Acrylic polymer	$0.5 \times 10^6$	$2000$	$4.0$

Energy a material can absorb before rupture (area under the entire stress-strain curve).
Resistance of a material to crack propagation.
Combines strength and ductility. A tough material has both high strength and high ductility.
Influenced by:
- Strain rate (rate of loading)
- Temperature
- Notch effect
Impact Toughness: Measured by Charpy or Izod tests, determining energy absorbed during fracture.
Notch-Toughness: Ability to absorb energy in the presence of a flaw (notch/crack).
- Flaws induce triaxial tension stress, restricting plastic deformation and promoting brittle failure.
Fracture Toughness ($K_{Ic}$): Property des