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Steady state crack growth in viscoelastic solids: Full-field analysis for the strip geometry with finite damage zone
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DOI：10.1016/j.jmps.2026.106662.png)
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Abstract
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We present an exact, full-field analysis for the steady state growth of a Mode III crack in a long strip of linear viscoelastic solid. While exponential and power-law creep functions are assumed to illustrate the results, our analysis is applicable to all linear viscoelastic solids. A Dugdale-Barenblatt cohesive zone is introduced ahead of the crack tip to model material damage. Our results cover the full range of cohesive zone size: from small-scale damage (SSD), where damage is confined near the crack tip, to large-scale damage (LSD), where the cohesive zone is comparable to or even exceeds the strip height. We identify a new dimensionless damage parameter (ranging from 0 to 1) governing the transition from SSD to LSD. In the SSD regime, the fracture toughness increases with crack velocity and reaches a plateau set by the product of the low-velocity toughness and the ratio of instantaneous to long-term moduli —consistent with prior theoretical studies. In the LSD regime, the fracture toughness is still an increasing function of crack velocity, but is capped by an upper bound imposed by the damage parameter, beyond which no solution for steady state crack growth exists. Interestingly, although the damage zone size tends to increase under higher crack velocity or stronger viscoelasticity (i.e., larger ratio of instantaneous to long-term moduli), larger damage zone in turn reduces viscous dissipation under the same crack velocity and viscoelastic parameters. Our full-field solution enables direct computation of stress, strain, and viscoelastic dissipation fields. We report how these fields and the region of viscous dissipation vary with crack velocity and the damage parameter. Finally, the analysis shows that stress concentration at the crack tip, besides crack velocity, is also a necessary condition for inducing viscoelastic energy dissipation.
Keywords:
Mode III crack
viscoelastic solid
cohesive zone
steady state growth
fracture toughness
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