Extension of Fracture Mechanics Principles to Viscoelastic Continuum Media

The fracturing of materials is well known on the basis of the theory of fracture mechanics. An important concept in fracture mechanics theory is that crack propagation is governed by the fundamental material properties of energy dissipation and energy threshold. However, to apply the fracture mechanics approach and measure these properties, a notch needs to be introduced into a continuum body. This requires additional effort to make the notch, which is often sensitive to the formation of materials surrounding the area near the crack tip. These effects become more complex for a material that exhibits time, rate, and temperature dependency. To overcome these complexities and problems regarding fracture testing, this study used the analogy between the material’s behaviors with and without a notch. A transfer of the fracture mechanics principle to continuum viscoelastic media was the key to the model developed in this study. For this purpose, the energy release rate ($G$) which is theoretically derived from a viscoelastic cracked body, was transferred to a continuum body by employing the same energy principles but used in continuum damage mechanics. From the evaluation of the model for various mixtures at multiple temperatures, predictions made were in agreement with the expected results from the well-known fatigue model. Consequently, it is expected that the developed model will bridge the gap between viscoelastic fracture and continuum damage mechanics, and provide better cracking performance predictions of asphalt mixtures.