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188 Fracture Mechanics: Fundamentals and Applications

FIGURE 4.14 Comparison of dynamic measurements of stress intensity with static calculations for a wedge
loaded DCB Araldite B specimen. Taken from Kalthoff, J.F., Beinart, J., and Winkler, S., “Measurement of
Dynamic Stress Intensity Factors for Fast Running and Arresting Cracks in Double-Cantilever Beam Speci-
mens.” ASTM STP 627, American Society for Testing and Materials, Philadelphia, PA, 1977, pp. 161–176.

4.1.3 DYNAMIC CONTOUR INTEGRALS
The original formulation of the J contour integral is equivalent to the nonlinear elastic energy release
rate for quasistatic deformation. By invoking a more general definition of energy release rate, it is
possible to incorporate dynamic effects and time-dependent material behavior into the J integral.
The energy release rate is usually defined as the energy released from the body per unit crack
advance. A more precise definition [11] involves the work input into the crack tip. Consider a
vanishingly small contour Γ around the tip of a crack in a two-dimensional solid (Figure 4.15).
The energy release rate is equal to the energy flux into the crack tip, divided by the crack speed:

J = F (4.25)
V

FIGURE 4.15 Energy flux into a small contour at
the tip of a propagating crack.