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

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2nd Revised Pages

9.5 Principles of Fracture Mechanics • 299

2 a a

(a) (b)

Figure 9.9 Schematic

representations of (a)an

interior crack in a plate of

infinite width, and (b)an

edge crack in a plate of

semi-infinite width.

plane strain fracture and back faces. TheKcvalue for this thick-specimen situation is known as theplane

toughness strain fracture toughnessKIc; furthermore, it is also defined by

KIc=Yσ

√

πa (9.5)

Plane strain fracture

toughness for mode I

crack surface

displacement K

Icis the fracture toughness cited for most situations. TheI(i.e., Roman numeral

“one”) subscript forKIcdenotes that the plane strain fracture toughness is for mode

I crack displacement, as illustrated in Figure 9.10a.^3

Brittle materials, for which appreciable plastic deformation is not possible in

front of an advancing crack, have lowKIcvalues and are vulnerable to catastrophic

failure. On the other hand,KIcvalues are relatively large for ductile materials. Frac-

ture mechanics is especially useful in predicting catastrophic failure in materials

having intermediate ductilities. Plane strain fracture toughness values for a number

of different materials are presented in Table 9.1 (and Figure 1.6); a more extensive

list ofKIcvalues is contained in Table B.5, Appendix B.

The plane strain fracture toughnessKIcis a fundamental material property that

depends on many factors, the most influential of which are temperature, strain rate,

and microstructure. The magnitude ofKIcdiminishes with increasing strain rate and

decreasing temperature. Furthermore, an enhancement in yield strength wrought by

solid solution or dispersion additions or by strain hardening generally produces a

corresponding decrease inKIc.KIcnormally increases with reduction in grain size

as composition and other microstructural variables are maintained constant. Yield

strengths are included for some of the materials listed in Table 9.1.

Several different testing techniques are used to measureKIc.^4 Virtually any spec-

imen size and shape consistent with mode I crack displacement may be utilized, and

accurate values will be realized provided that theYscale parameter in Equation 9.5

has been properly determined.

(^3) Two other crack displacement modes denoted by II and III and as illustrated in Figures
9.10band 9.10care also possible; however, mode I is most commonly encountered.
(^4) See for example ASTM Standard E 399, “Standard Test Method for Plane Strain Fracture
Toughness of Metallic Materials.”