Modulus of Resilience and Toughness

U_{r} = \frac{F _{y}^{2}}{2 E} U_{t} = \int_{0}^{ε_{f}} σ d ε

Resilience Ur is elastic energy density (triangle under σ–ε to yield). Toughness is the whole area to fracture (ability to absorb energy before breaking). Charpy V-notch is an impact toughness test (ft·lbf) sensitive to temperature (DBTT for steels).

$U_{r}$ (psi): Modulus of resilience
$U_{t}$ (psi): Modulus of toughness

Step-by-step solved example

Fy = 36 ksi, E = 29 000 ksi. Ur?

Resilience is the elastic area; toughness is the whole area to fracture.

1. Triangle
Ur = Fy²/(2E) = 1296/(2×29000) = 0.0223 ksi = 22.3 psi.
$U_{r} = 22.3 psi$

Answer: 22.3 psi

10 practice questions

0/10 correct

1.Resilience uses the area

2.Toughness uses the area

3.A ceramic typically has

4.Charpy energy drops sharply at

5.Mild steel is tougher than glass mainly because of

6.Ur has units of

7.Raising Fy with E fixed

8.A BCC steel at very low T tends to fail

9.Area under a σ–ε curve to ε = 0.002 if still elastic is

10.Impact toughness is NOT the same number as