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

Wróbel, Michał; Papanastasiou, Panos; Mishuris, Gennady

doi:10.1016/j.gete.2019.100147

Cited by 17 publications

(11 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and the fluid front velocity in the form (30). The four unknowns p(r, t n+1 ), w(r, t n+1 ), a(t n+1 ), and (t n+1 ) of non the linear problem (58) have been determined by means of a staggered approach, as detailed in box 3. Therein, µ and j stand for the counter of the outer loop devoted to compute the crack radius and the counter of the inner loop devoted to compute the fluid front position, respectively.…”

Section: Space and Time Discretization Of Governing Equationsmentioning

confidence: 99%

“…A hybrid scheme is employed: the elasto-hydrodynamic problem is solved implicitly, while the crack front is explicitly updated with the velocity computed at previous iteration. To escape the limitation of propagation in pure mode I loading conditions, recent investigations on mixed mode hydraulic fracture propagation can be found in [57,58].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel hydraulic fractures growth formulation

Fantoni,

Salvadori

2020

Preprint

View full text Add to dashboard Cite

Propagation of a fluid-driven crack in an impermeable linear elastic medium under axis-symmetric conditions is investigated in the present work. The fluid exerting the pressure inside the crack is an incompressible Newtonian one and its front is allowed to lag behind the propagating fracture tip. The tip cavity is considered as filled by fluid vapors under constant pressure having a negligible value with respect to the far field confining stress. A novel algorithm is here presented, which is capable of tracking the evolution of both the fluid and the fracture fronts. Particularly, the fracture tracking is grounded on a recent viscous regularization of the quasi-static crack propagation problem as a standard dissipative system. It allows a simple and effective approximation of the fracture front velocity by imposing Griffith's criterion at every propagation step. Furthermore, for each new fracture configuration, a non linear system of integro-differential equations has to be solved. It arises from the non local elastic relationship existing between the crack opening and the fluid pressure, together with the non linear lubrication equation governing the flow of the fluid inside the fracture.

show abstract

Section: Space and Time Discretization Of Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel hydraulic fractures growth formulation

Fantoni,

Salvadori

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…If we categorize the plasticity effects into two groups: i) those that affect the rock splitting ahead of the fracture tip and as such contribute to the crack length extension and, ii) the effects of plastic deformation of the bulk of the fractured material, the question arises whether accounting only for the first group can be sufficient for modeling at least in the small yield cases. The question becomes even more vital if we recall that the plastic deformation effects in the near tip zone can substantially affect fracture development, for example the crack redirection (Wrobel et al, 2021a).…”

Section: Introductionmentioning

confidence: 99%

A simplified modelling of hydraulic fractures in elasto-plastic materials

Wrobel,

Papanastasiou,

Peck

2021

Preprint

View full text Add to dashboard Cite

In this paper the problem of a plane strain hydraulic fracture propagating in an elasto-plastic material is analyzed. A new stress redistribution model for the proximity of the fracture tip is formulated and a resulting plasticity-dependent crack propagation condition is introduced. A modified variant of the KGD problem that accounts for the plastic deformations in the near-tip zone only is proposed. It is demonstrated that this model can be a credible substitute for the full elasto-plastic hydraulic fracture problem in the case of moderate plastic deformation. The crack-tip shielding effect introduced by the plastic deformation is quantified.

show abstract

“…Naturally, it has a significant effect on the evaluation of the fracture Energy Release Rate (ERR). It was demonstrated that the differing tip asymptotics offered an alternative physical explanation for the transition in fracture growth behaviour which occurs over time (between viscosity and toughness dominated regimes), while a follow-up investigation demonstrated a possible impact on fracture redirection [Perkowska et al, 2017, Wrobel et al, 2021b and examined the dependence of these effects on fluid rheology [Wrobel et al, 2021a].…”

Section: Introductionmentioning

confidence: 99%

“…Below we give a short overview of results obtained in the study of hydraulic fracture with shear stress induced upon the crack walls by the fluid, which provides the motivation for this work. In the original paper of , alongside a later extension to the mixed-mode case in [Perkowska et al, 2017, Wrobel et al, 2021b, it was demonstrated that the asymptotics of the displacement and stress fields near the crack-tip (r → 0) are…”

Section: Introductionmentioning

confidence: 99%

Energy Release Rate, the crack closure integral and admissible singular fields in Fracture Mechanics

Piccolroaz,

Peck,

Wrobel

et al. 2021

Preprint

View full text Add to dashboard Cite

One of the assumptions of Linear Elastic Fracture Mechanics is that the crack faces are tractionfree or, at most, loaded by bounded tractions. The standard Irwin's crack closure integral, widely used for the computation of the Energy Release Rate, also relies upon this assumption. However, there are practical situations where the load acting on the crack boundaries is singular. This is the case, for instance, in hydraulic fracturing, where the fluid inside the crack exerts singular tangential tractions at its front. Another example of unbounded tractions is the case of a rigid line inclusion (anticrack) embedded into an elastic body. In such situations, the classical Irwin's crack closure integral fails to provide the correct value of the Energy Release Rate. In this paper, we address the effects occurring when square-root singular tractions act at the boundary of a line defect in an elastic solid and provide a generalisation of Irwin's crack closure integral. The latter yields the correct Energy Release Rate and allows broad applications, including, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. We present the results in the most general form, where six Stress Intensity Factors are present: three of them are classical SIFs corresponding to the modes I-II-III and computed under the assumption of homogeneous boundary conditions at the defect surfaces, while the other three SIFs are associated with singular admissible tractions (those that lead to a finite ERR value). It is demonstrated that this approach resolves an ambiguity in using the same SIF's terminology in the cases of open cracks and rigid inclusions, among other benefits.

show abstract

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

Cited by 17 publications

References 29 publications

A novel hydraulic fractures growth formulation

A novel hydraulic fractures growth formulation

A simplified modelling of hydraulic fractures in elasto-plastic materials

Energy Release Rate, the crack closure integral and admissible singular fields in Fracture Mechanics

Contact Info

Product

Resources

About