Mechanical APDL Structural Analysis Guide

• Mode III – Tearing or out-of-plane mode

Fracture is generally characterized by a combination of fracture modes.

Figure 11.1: Schematic of the Fracture Modes

Opening mode

(K )

Shearing mode

(K )

Tearing mode

(K )

I II III

11.1.2. Fracture Mechanics Parameter Calculation

Typical fracture mechanics parameters describe either the energy-release rat e or the amplitude of the
stress and deformation fields ahead of the crack tip.

The following parameters are widely used in fracture mechanics analysis:

11.1.2.1. J-Integral

11.1.2.2. Energy-Release Rate

11.1.2.3. Stress-Intensity Factor

11.1.2.4. T-Stress

11.1.2.5. Material Force

11.1.2.1. J-Integral

J-Integral is one of the most widely accepted fracture mechanics parameters for linear plastic and
nonlinear elastic-plastic materials. The J-Integral is defined as follows [ 2 ]:

li ij

j

l

= o + − i

∂

∂













−>

∫

Γ Γ

Γ

0

δ σ

where W is the strain energy density, T is the kinematic energy density, σ represents the stresses, u is
the displacement vector, and Γ is the contour over which the integration is carried out.

For a crack in a linear elastic material, the J-Integral represents the energy-release rate. Also, the amp-
litudes of the crack-tip stress and deformation fields are characterized by the J-Integral for a crack in a
nonlinear elastic material.

For more information, see J-Integral Calculation (p. 351) and J-Integral as a Stress-Intensity Factor (p. 340).

11.1.2.1.1. J-Integral as a Stress-Intensity Factor

Hutchinson [ 3 ] and Rice and Rosengren [ 4 ] independently showed that the J-Integral characterizes the
crack-tip field in a nonlinear elastic material. They each assumed a power law relationship between

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Fracture Mechanics