Page 239 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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5 Fracture Mechanisms in Metals

Figure 5.1 schematically illustrates three of the most common fracture mechanisms in metals and
alloys. (A fourth mechanism, fatigue, is discussed in Chapter 10.) Ductile materials (Figure 5.1(a))
usually fail as the result of nucleation, growth, and the coalescence of microscopic voids that initiate
at inclusions and second-phase particles. Cleavage fracture (Figure 5.1(b)) involves separation along
specific crystallographic planes. Note that the fracture path is transgranular. Although cleavage is
often called brittle fracture, it can be preceded by large-scale plasticity and ductile crack growth.
Intergranular fracture (Figure 5.1(c)), as its name implies, occurs when the grain boundaries are
the preferred fracture path in the material.
5.1 DUCTILE FRACTURE

Figure 5.2 schematically illustrates the uniaxial tensile behavior in a ductile metal. The material
eventually reaches an instability point, where strain hardening cannot keep pace with the loss in
the cross-sectional area, and a necked region forms beyond the maximum load. In very high purity
materials, the tensile specimen may neck down to a sharp point, resulting in extremely large local
plastic strains and nearly 100% reduction in area. Materials that contain impurities, however, fail
at much lower strains. Microvoids nucleate at inclusions and second-phase particles; the voids grow
together to form a macroscopic flaw, which leads to fracture.
The commonly observed stages in ductile fracture [1–5] are as follows:

1. Formation of a free surface at an inclusion or second-phase particle by either interface
decohesion or particle cracking.
2. Growth of the void around the particle, by means of plastic strain and hydrostatic stress.
3. Coalescence of the growing void with adjacent voids.

In materials where the second-phase particles and inclusions are well-bonded to the matrix, void
nucleation is often the critical step; fracture occurs soon after the voids form. When void nucleation
occurs with little difficulty, the fracture properties are controlled by the growth and coalescence of
voids; the growing voids reach a critical size, relative to their spacing, and a local plastic instability
develops between voids, resulting in failure.

5.1.1 VOID NUCLEATION

A void forms around a second-phase particle or inclusion when sufficient stress is applied to break
the interfacial bonds between the particle and the matrix. A number of models for estimating void
nucleation stress have been published, some of which are based on continuum theory [6, 7] while
others incorporate dislocation-particle interactions [8, 9]. The latter models are required for particles
<1 µm in diameter.
The most widely used continuum model for void nucleation is due to Argon et al. [6]. They
argued that the interfacial stress at a cylindrical particle is approximately equal to the sum of the
mean (hydrostatic) stress and the effective (von Mises) stress. The decohesion stress is defined as
a critical combination of these two stresses:
σ c σ = e σ + m (5.1)

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