Page 242 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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222 Fracture Mechanics: Fundamentals and Applications

models (Equation (5.1) and Equation (5.4)), which apply to particles with r > 1 µm, imply that σ c
is independent of particle size.
Experimental observations usually differ from both continuum and dislocation models, in that
void nucleation tends to occur more readily at large particles [10]. Recall, however, that these
models only considered nucleation by particle-matrix debonding. Voids can also be nucleated when
particles crack. Larger particles are more likely to crack in the presence of plastic strain, because
they are more likely to contain small defects that can act like Griffith cracks (see Section 5.2). In
addition, large nonmetallic inclusions, such as oxides and sulfides, are often damaged during
fabrication; some of these particles may be cracked or debonded prior to plastic deformation,
making void nucleation relatively easy. Further research is obviously needed to develop void
nucleation models that are more in line with experiments.

5.1.2 VOID GROWTH AND COALESCENCE
Once voids form, further plastic strain and hydrostatic stress cause the voids to grow and eventually
coalesce. Figure 5.3 and Figure 5.4 are scanning electron microscope (SEM) fractographs that show
dimpled fracture surfaces that are typical of microvoid coalescence. Figure 5.4 shows an inclusion
that nucleated a void.
Figure 5.5 schematically illustrates the growth and coalescence of microvoids. If the initial volume
fraction of voids is low (<10%), each void can be assumed to grow independently; upon further
growth, neighboring voids interact. Plastic strain is concentrated along a sheet of voids, and local
necking instabilities develop. The orientation of the fracture path depends on the stress state [11].
Many materials contain a bimodal or trimodal distribution of particles. For example, a precipitation-
hardened aluminum alloy may contain relatively large intermetallic particles, together with a fine
dispersion of submicron second-phase precipitates. These alloys also contain micron-size dispersoid
particles for grain refinement. Voids form much more readily in the inclusions, but the smaller
particles can contribute in certain cases. Bimodal particle distributions can lead to so-called shear
fracture surfaces, as described in the next paragraph.

FIGURE 5.3 Scanning electron microscope (SEM) fractograph which shows ductile fracture in a low carbon
steel. Photograph courtesy of Mr. Sun Yongqi.