Redirection of a crack driven by viscous fluid

Abstract

As shown by Wrobel, Mishuris, and Piccolroaz (2017), the hydraulically induced tangential traction on fracture walls changes local displacement and stress fields. This resulted in the formulation of a new hydraulic fracture (HF) propagation condition based on the critical value of the energy release rate that accounts for the hydraulically-induced shear stress. Therefore it is clear that the crack direction criteria, which depend on the tip distributions of the stress and strain fields, need to be changed. We analyse the two commonly used criteria, one based on the maximum circumferential stress (MCS) and another - on the minimum strain energy density (MSED). We show that the impact of the hydraulically induced shear stress on the direction of the crack propagation is negligible in the case of large material resistance to fracture, while for small toughness the effect is significant. Moreover, values of the redirection angles, corresponding to the so-called viscosity dominated regime (KIC???0), depend dramatically on the ratios of the stress intensity factors.publishersversionPeer reviewe

Redirection of a crack driven by viscous fluid taking into account plastic effects in the process zone

“…To complement the analysis of the MDSED criterion we show in Fig.5 the sensitivity of the crack propagation angle to the value of the Poisson's ratio. It turns out that for the toughness dominated regime one obtains the same results regardless of the value of ν (the same trend was reported in [16] for the Minimum Strain Energy Density Criterion). Some differences between the results for various ν can be observed when moving towards the viscosity dominated mode, however the influence of the Poisson's ratio on θ f is rather limited.…”

“…For the plane strain Ψ zz = ν Ψ rr + Ψ θθ . To define the critical fracture state, we use the Energy Release Rate (ERR) criterion as evaluated in [16] that accounts for the shear traction induced by the fluid on the crack surfaces:…”

“…As it was in the case of the Minimum Strain Energy Density criterion (see [16]), to preserve the physical sense of solution, the maximum should be sought for under additional condition that the circumferential stress is positive. According to [16] the expression for σ θθ has the following form:…”

“…In this study we will examine the influence of plasticity in the re-orientation of the hydraulic fracture within an analytical solution framework, considering the role of viscous shear stresses. In a recent study [16] the authors considered the effect of the shear stress induced by the fluid on the crack surfaces to determine the direction of the HF crack propagation in elastic rocks and showed that it may play an essential role in the case of the mixed mode when the total contribution of the classical Stress Intensity Factors (SIF) leads to ERR value close to its critical one. They used the two most popular criteria: the maximum circumferential stress (MCS) criterion [8] and the minimum strain energy density (MSED) criterion [19].…”

“…We start from the maximum dilatational strain energy density (MDSED) criterion introduced in [20,26] to show that, in contrast to the classic fracture mechanics, this criterion in the case of hydraulic fracture does not always allow for predicting the direction of the crack propagation due to the problems with uniqueness and stability of solution. In particular, MDSED criterion fails to produce reasonable results in the proximity of the so-called viscosity dominated regime [16]. To eliminate this drawback, we propose a concept of a modified maximum circumferential stress criterion (MMCS) that accounts for local plastic effects by implementing, similarly to MDSED, the plastic zone described by the respective yield condition (von Mises, Drucker-Prager, Tresca or Mohr-Coulomb).…”