4.2.2         Fracture Toughness – Abrupt Fracture

In a cracked structure, as discussed in Section 2, the stress intensity factor (K) interrelates the local stresses in the region of the crack tip with crack geometry, structural geometry, and the level of load on the structure.  When the applied load level increases, the K value also increases and reaches a critical value at which time the crack growth becomes unstable, as shown in Figure 4.2.3. 

Figure 4.2.3.  The Fracture Mechanics Basis for Establishing Residual Strength

This critical level of K, which is independent of the crack length, is a material property called fracture toughness.  The fracture toughness is a measure of the material’s resistance to unstable cracking.  Several test procedures are available to evaluate the fracture toughness.  Also, various theoretical and numerical solution techniques are available, as discussed in Section 2, which can be used to estimate the (applied) stress intensity factor, K, for a given structure.

The failure criterion (Irwin’s Criterion) states that abrupt fracture occurs when the crack-tip stress-intensity factor reaches or exceeds the fracture toughness of the material.  The corresponding applied stress at failure is called the fracture strength.  The failure criterion becomes simple

where K_cr is the material’s fracture toughness.

The critical K_cr for abrupt fracture mode is denoted as K_Ic for plane strain conditions and K_c for plane stress conditions; the conditions for plane stress or plane strain are determined by experiment.  The test requirements necessary for generating K_Ic and K_c are discussed in Section 7.

The Damage Tolerant Design (Data) Handbook [Skinn, et al., 1994] contains a large quantity of fracture toughness data.  Examples of the formats associated with individual test data for 7075 aluminum alloy are shown in Figures 4.2.4 and 4.2.5 for plane strain and plane stress fracture toughness values, respectively. 

Figure 4.2.4.  Plane-Strain Fracture Toughness (K_Ic) Data for 7075 Aluminum in the Format of the Damage Tolerant Design (Data) Handbook [Skinn, et al., 1994]

Figure 4.2.5.  Plane-Stress Fracture Toughness (K_c) Data for 7075 Aluminum in the Format of the Damage Tolerant Design (Data) Handbook [Skinn, et al., 1994]

In general, a material’s toughness depends on thickness, as shown in Figure 4.2.6.  When the thickness is such that the crack tip plastic zone size is on the order of the plate thickness, the toughness reaches a maximum value, K_c(max).  With increasing thickness of the plate, the plastic zone size reduces and thus the toughness gradually decreases, from K_c(max) to K_Ic.  When the thickness is large enough that the crack tip deformation is not affected by the thickness, plane strain conditions prevail at the crack tip.  The toughness in the plane strain regime is virtually independent of thickness.  For increasing thickness, the toughness asymptotically approaches the plane strain fracture toughness, K_Ic.

Figure 4.2.6.  Fracture Toughness as a Function of Thickness