Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-09 GTBL042-Callister-v3 October 4, 2007 11:53

2nd Revised Pages

296 • Chapter 9 / Failure

(b)

Grain boundaries

SEM micrograph

Path of crack propagation

(a)

Figure 9.7 (a) Schematic

cross-section profile showing

crack propagation along grain

boundaries for intergranular

fracture. (b) Scanning electron

fractograph showing an

intergranular fracture surface.

50 ×. [Figure (b) reproduced with

permission fromASM Handbook,

Vol. 12,Fractography,ASM

International, Materials Park, OH,

1987.]

whereσ 0 is the magnitude of the nominal applied tensile stress,ρtis the radius of

curvature of the crack tip (Figure 9.8a), andarepresents the length of a surface crack,

or half of the length of an internal crack. For a relatively long microcrack that has a

small tip radius of curvature, the factor (a/ρt)^1 /^2 may be very large. This will yield a

value ofσmthat is many times the value ofσ 0.

Sometimes the ratioσm/σ 0 is denoted as thestress concentration factor Kt:

Kt=

σm

σ 0

= 2

(

a

ρt

) 1 / 2

(9.2)