Page 245 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C005.fm Page 225 Monday, May 23, 2005 5:47 PM

Fracture Mechanisms in Metals 225

FIGURE 5.6 Formation of the cup and cone fracture surface in uniaxial tension: (a) void growth in a triaxial
stress state, (b) crack and deformation band formation, (c) nucleation at smaller particles along the deformation
bands, and (d) cup and cone fracture.

of change of radius in each principal direction has the form:

 2 
R ˙ i  ( + 1 G = ) ˙ + ε i ˙ ˙ D j ε j  R ε o (i, j = 1, 2, 3) (5.8)
 3 
where D and G are constants that depend on stress state and strain hardening, and R is the radius
o
of the initial spherical void. The standard notation, where repeated indices imply summation, is
followed here. Invoking the incompressibility condition ( ˙ ε 1 ˙ ε + 2 ˙ ε + 3 = ) 0 reduces the number of
˙ ε
independent principal strain rates to two. Rice and Tracey chose to express ˙ ε 2 and in terms of
3
˙ ε
1 and a second parameter:
− φ 2
˙ ε = ˙ ε (5.9a)
2 3+ φ 1
φ 3−
˙ ε = ˙ ε (5.9b)
3 3 + φ 1