This section gives a general discussion of fracture. Fracture is the separation or fragmentation of a solid body into two or more parts under the action of force/ stress. The process of fracture consists of two components: crack initiation and crack propagation. Fractures can be classified into two broad categories: ductile and brittle. A ductile fracture is characterized by appreciable plastic deformation with stable crack growth. A brittle fracture is characterized by a rapid rate of crack propa­gation (unstable) with no gross deformation. Stable crack growth implies that once the load is taken off, the crack does not propagate further. Figure 5.13 shows various fracture types observed in metals/alloys subjected to uniaxial tension.

Fractures are classified with respect to different factors, such as strain to fracture, crystallographic mode of fracture, and the appearance of fracture. A shear fracture occurs as the result of extensive slip on the active slip plane. This type of fracture is

promoted by shear stresses. The cleavage mode of fracture is promoted by tensile stresses acting normal to a crystallographic cleavage plane. In many cases, the frac­ture surfaces are a mixture of fibrous and granular fracture, and it is customary to report the percentage of the surface area. Fractures in polycrystalline samples are transgranular (the crack propagates through the grains) or intergranular (the crack propagates along the grain boundaries).

5.1.3.1 Theoretical Cohesive Strength

Engineering materials typically exhibit fracture stresses that are 10-100 times lower than the theoretical value. This observation leads to the conclusion that flaws or cracks are responsible for the lower-than-ideal fracture strength. Due to Inglis [4], an approach assumes that the theoretical cohesive stress can be reached locally at the tip of a crack, while the average stress is at much lower value. Then, the nominal fracture stress is given by the expression (for the sharpest possible crack):

. <5-28>

where E is the elastic modulus, cs is the surface energy, and c is the crack length.

Microcracks act as precursors for crack propagation in brittle fracture. The pro­cess of cleavage fracture involves three steps: (a) plastic deformation to create dislo­cation pileups, (b) crack initiation, and (c) crack propagation. The initiation of microcracks can be affected by the presence of second-phase particles. Cleavage cracks can also be initiated at mechanical twins.

The ductile fracture starts with the initiation of voids, most commonly at second — phase particles. The particle geometry, size, and bonding play an important role. Dimpled rupture surface (ductile fracture) consists of cup-like depressions that may be equiaxial, parabolic, or elliptical, depending on the precise stress state. Microvoids are generally nucleated at second-phase particles, and the voids grow and eventually the ligaments between the microvoids fracture.

Griffith [5], established the following criterion for crack propagation: “A crack will propagate when the decrease in elastic strain energy is at least equal to the energy required to create new crack surface.” The stress required to propagate a crack in a brittle material is a function of crack length (as shown in Figure 5.14) and is given by

Figure 5.14 The crack configuration used in Griffith’s equation.

Sohncke suggested that fracture occurs when the resolved normal stress (ac) reaches a critical value (Figure 5.15). The critical normal stress for brittle fracture is

ac — P cos ф/(A/cos ф) — (P/A) cos2 ф. (5.31)