The crack tip region in hydraulic fracturing

1994 ◽  
Vol 447 (1929) ◽  
pp. 39-48 ◽  
Keyword(s):  
Hydraulic Fracturing ◽  
Elastic Solid ◽  
Square Root ◽  
Power Law Fluid ◽  
Fracture Width ◽  
Linear Elastic ◽  
Finite Case ◽  
Strain Fracture ◽  
Square Root Singularity ◽  
Elastic Fracture

We present analytical tip region solutions for fracture width and pressure when a power law fluid drives a plane strain fracture in an impermeable linear elastic solid. Our main result is an intermediate asymptotic solution in which the tip region stress is dominated by a singularity which is particular to the hydraulic fracturing problem. Moreover this singularity is weaker than the inverse square root singularity of linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximation for the finite case.

The Tip Region of a Fluid-Driven Fracture in an Elastic Medium

1999 ◽  
Vol 67 (1) ◽  
pp. 183-192 ◽  
Author(s):  
D. Garagash ◽  
E. Detournay
Keyword(s):  
Elastic Medium ◽  
A Priori ◽  
Fluid Flows ◽  
Universal Relation ◽  
Linear Elastic ◽  
Square Root Singularity ◽  
Elastic Fracture ◽  
Fluid Lag ◽  
Intermediate Part ◽  
Unknown Length

The focus of this paper is on constructing the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip. First, we formulate the governing equations for a semi-infinite fluid-driven fracture propagating steadily in an impermeable linear elastic medium. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. We then calculate explicitly the contribution to the opening from the loading in the lag zone, and reformulate the problem over the fluid-filled portion of the crack. The asymptotic forms of the solution near and away from the tip are then discussed. It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is actually given by the singular solution of a semi-infinite hydraulic fracture constructed on the assumption that the fluid flows to the tip of the fracture and that the solid has zero toughness. Further, the asymptotic solution for large dimensionless toughness is derived, including the explicit dependence of the solution on the toughness. The intermediate part of the solution (in the region where the solution evolves from the near tip to the far from the tip asymptote) of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness. [S0021-8936(00)02401-6]

A Theory of Fracture Based Upon an Extension of Continuum Mechanics to the Nanoscale

2005 ◽  
Vol 73 (5) ◽  
pp. 792-798 ◽  
Author(s):  
Eun-Suok Oh ◽  
Jay R. Walton ◽  
John C. Slattery
Keyword(s):  
Numerical Simulation ◽  
Long Range ◽  
Continuum Mechanics ◽  
Bulk Material ◽  
Stress Singularity ◽  
Intermolecular Forces ◽  
Square Root ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Root Stress

A theory of fracture is presented that is based upon an extension of continuum mechanics to the nanoscale through the incorporation of long-range intermolecular forces which correct bulk material descriptions near interfaces. The surface energy on crack surfaces, which is given in terms of the long-range intermolecular forces, plays an important role in an expression for the stress distribution near the crack tip. It is observed through numerical simulation that the incorporation of these long-range intermolecular forces removes the square-root stress singularity predicted by classical linear elastic fracture mechanics.

On the Use of the Theory of Critical Distances to Estimate KIc and ∆Kth from Experimental Results Generated by Testing Standard Notches

2009 ◽  
Vol 417-418 ◽  
pp. 25-28
Author(s):  
Luca Susmel ◽  
David Taylor
Keyword(s):  
Fatigue Limit ◽  
Material Properties ◽  
Reliable Method ◽  
Threshold Value ◽  
Experimental Results ◽  
Plane Strain Fracture Toughness ◽  
Linear Elastic ◽  
Experimental Strategy ◽  
Strain Fracture ◽  
Elastic Fracture

The present paper is concerned with the use of the Theory of Critical Distances (TCD), applied in the form of the Point Method (PM), to estimate the range of the threshold value of the stress intensity factor, Kth, as well as the plane strain fracture toughness, KIc. In more detail, by reanalysing a large amount of experimental data taken from the literature, it is proved that Kth can successfully be evaluated through the plain fatigue limit and another fatigue limit generated by testing samples containing a known geometrical feature, whereas KIc is suggested here as being estimated by using experimental results generated by testing samples weakened by notches of different sharpness. The validation exercise summarised in the present paper fully confirms that the TCD is not only a reliable method suitable for performing the static and fatigue assessment of real components, but also an efficient experimental strategy capable of accurately estimating the classical Linear Elastic Fracture Mechanics (LEFM) material properties.

Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution

2005 ◽  
Vol 72 (6) ◽  
pp. 916-928 ◽  
Author(s):  
Dmitry I. Garagash ◽  
Emmanuel Detournay
Keyword(s):  
Boundary Layer ◽  
Plane Strain ◽  
Boundary Layer Thickness ◽  
Elastic Solid ◽  
Matching Condition ◽  
Fluid Viscosity ◽  
Fracture Length ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Layer Solution

The paper considers the problem of a plane-strain fluid-driven fracture propagating in an impermeable elastic solid, under condition of small (relative) solid toughness or high (relative) fracturing fluid viscosity. This condition typically applies in hydraulic fracturing treatments used to stimulate hydrocarbons-bearing rock layers, and in the transport of magma in the lithosphere. We show that for small values of a dimensionless toughness K, the solution outside of the immediate vicinity of the fracture tips is given to O(1) by the zero-toughness solution, which, if extended to the tips, is characterized by an opening varying as the (2∕3) power of the distance from the tip. This near tip behavior of the zero-toughness solution is incompatible with the Linear Elastic Fracture Mechanics (LEFM) tip asymptote characterized by an opening varying as the (1∕2) power of the distance from the tip, for any nonzero toughness. This gives rise to a LEFM boundary layer at the fracture tips where the influence of material toughness is localized. We establish the boundary layer solution and the condition of matching of the latter with the outer zero-toughness solution over a lengthscale intermediate to the boundary layer thickness and the fracture length. This matching condition, expressed as a smallness condition on K, and the corresponding structure of the overall solution ensures that the fracture propagates in the viscosity-dominated regime, i.e., that the solution away from the tip is approximately independent of toughness. The solution involving the next order correction in K to the outer zero-toughness solution yields the range of problem parameters corresponding to the viscosity-dominated regime.

Limits of Linear Elastic Fracture Mechanics

1984 ◽  
Vol 106 (2) ◽  
pp. 196-200 ◽  
Author(s):  
J. M. Bloom ◽  
J. L. Hechmer
Keyword(s):  
Fracture Mechanics ◽  
Plane Strain ◽  
Simple Procedure ◽  
Linear Elastic Fracture Mechanics ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Strain Fracture ◽  
Elastic Fracture ◽  
Flaw Location

This paper presents a simple procedure for determining the validity limits of linear elastic fracture mechanics (LEFM) calculations for low alloy steel (ferritic) structures. The procedure is limited to structures with flaws whose depths are 50 percent or less of the wall thickness of the component at the flaw location and to components which can be considered to be in a plane strain state. Typical yield and ultimate strengths are assumed to be 60 and 80 ksi (414 and 552 MPa), respectively. The procedure is based upon failure assessment curves derived for typical nuclear vessels and components. Calculations of the ratios of the linear elastic stress intensity factor to the plane strain fracture toughness and the applied load to the plastic collapse load are used in conjunction with these curves to determine the validity limits of LEFM. The procedure is limited to the consideration of primary loading. When the load calculated by LEFM deviates significantly from the load calculated assuming elastic-plastic behavior, LEFM is deemed to be invalid and an elastic-plastic calculation procedure is recommended. Example problems are given which demonstrate the applicability of LEFM analysis in one case and the inapplicability in another case. The paper is an extension of the ideas and work generated from the Electric Power Research Institute research project RP 1237-2.

Packer-Induced Stresses During Hydraulic Well Fracturing

1981 ◽  
Vol 103 (4) ◽  
pp. 336-343 ◽  
Author(s):  
W. E. Warren
Keyword(s):  
Hydraulic Fracturing ◽  
Oil And Gas ◽  
Circular Cylindrical Shell ◽  
Elastic Solid ◽  
Gas Recovery ◽  
Linear Elastic ◽  
Analytical Approximations ◽  
Induced Stresses ◽  
The Difference

Well bore stresses induced by inflatable packers during hydraulic fracturing operations are investigated. The geologic formation is modeled as an unbounded homogeneous isotropic linear elastic solid containing an infinitely long circular cavity, while the packer is modeled as a semi-infinite thin-walled circular cylindrical shell. For given packer properties, these induced stresses are shown to depend on the difference between packer pressure and fracturing pressure and can become significant. Typical numerical results are obtained and presented graphically. Analytical approximations for the maximum values of these stresses are also presented. While these effects are of no importance in the usual application of hydraulic fracturing to enhance oil and gas recovery, they are crucial in attempts to estimate in-situ stresses from hydraulic fracturing pressure data.

Fatigue Failure Analysis Using the Theory of Critical Distance

2011 ◽  
Vol 462-463 ◽  
pp. 663-667 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail
Keyword(s):  
Stress Concentration ◽  
Fatigue Failure ◽  
Notch Root ◽  
High Stress ◽  
Critical Distance ◽  
Future Research ◽  
Element Analysis ◽  
Linear Elastic ◽  
The Finite Element Analysis ◽  
Elastic Fracture

This paper explores the initial potential of theory of critical distance (TCD) which offers essential fatigue failure prediction in engineering components. The intention is to find the most appropriate TCD approach for a case of multiple stress concentration features in future research. The TCD is based on critical distance from notch root and represents the extension of linear elastic fracture mechanics (LEFM) principles. The approach is allowing possibilities for fatigue limit prediction based on localized stress concentration, which are characterized by high stress gradients. Using the finite element analysis (FEA) results and some data from literature, TCD applications is illustrated by a case study on engineering components in different geometrical notch radius. Further applications of TCD to various kinds of engineering problems are discussed.

scholarly journals Unconventional singularities and energy balance in frictional rupture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Efim A. Brener ◽  
Eran Bouchbinder
Keyword(s):  
Energy Balance ◽  
Square Root ◽  
Earthquake Physics ◽  
Macroscopic Theory ◽  
Scale Separation ◽  
Rate Dependent ◽  
Theoretical Predictions ◽  
Spatially Extended ◽  
Singularity Order ◽  
Square Root Singularity

AbstractA widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid. Here we develop a macroscopic theory that shows that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, and that even if this deviation is small, significant non-edge-localized rupture-related dissipation emerges. The physical origin of the latter, which is predicted to vanish identically in the crack analogy, is the breakdown of scale separation that leads an accumulated spatially-extended dissipation, involving macroscopic scales. The non-edge-localized rupture-related dissipation is also predicted to be position dependent. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

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