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ABSTRACT Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase‐field fracture model to study this fracture process. While phase‐field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non‐singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a recently developed phase‐field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase‐field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations.
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Cohesive Zone Interpretations of Phase-Field Fracture Models
Abstract Unlike micromechanics failure models that have a well-defined crack path, phase-field fracture models are capable of predicting the crack path in arbitrary geometries and dimensions by utilizing a diffuse representation of cracks. However, such models rely on the calibration of a fracture energy (Gc) and a regularization length-scale (lc) parameter, which do not have a strong micromechanical basis. Here, we construct the equivalent crack-tip cohesive zone laws representing a phase-field fracture model, to elucidate the effects of Gc and lc on the fracture resistance and crack growth mechanics under mode I K-field loading. Our results show that the cohesive zone law scales with increasing Gc while maintaining the same functional form. In contrast, increasing lc broadens the process zone and results in a flattened traction-separation profile with a decreased but sustained peak cohesive traction over longer separation distances. While Gc quantitatively captures the fracture initiation toughness, increasing Gc coupled with decreasing lc contributes to a rising fracture resistance curve and a higher steady-state toughness—both these effects cumulate in an evolving cohesive zone law with crack progression. We discuss the relationship between these phase-field parameters and process zone characteristics in the material.
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- Award ID(s):
- 2009684
- PAR ID:
- 10533002
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 89
- Issue:
- 12
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4055660
