Mode-I Fracture Toughness

K_{I} = σ π a Y fracture when K_{I} = K_{I c}

Stress-intensity factor KI for a crack of half-length a (through-crack in an infinite plate uses Y ≈ 1). Fracture when KI reaches KIc (a material property, function of T, rate, thickness). Units ksi√in or MPa√m. Critical stress falls as 1/√a.

$K_{I}$ (ksi√in): Stress intensity
$σ$: Remote tensile stress
$a$: Crack length parameter
$K_{I c}$: Fracture toughness

Step-by-step solved example

Through-crack 2a = 0.50 in (a = 0.25 in), Y = 1, KIc = 25 ksi√in. Critical σ?

Crack length a in K_I = σ√(πa). Mode I opening.

1. √(πa)
πa = 0.785; √(πa) = 0.886 in^{1/2}.
2. σc
σc = KIc / √(πa) = 25/0.886 = 28.2 ksi.
$σ_{c} = 28.2 ksi$

Answer: 28.2 ksi

10 practice questions

0/10 correct

1.KIc has units

2.Doubling crack length a multiplies critical σ by

3.Mode I is

4.A tougher alloy (larger KIc) allows

5.Plane-strain KIc (thick) compared with thin-sheet Kc is typically

6.Y is a

7.Fatigue cracks grow when

8.Glass has

9.If Y = 1.12 (edge crack) vs 1.0, critical σ

10.LEFM requires