Showing papers on "Fracture (geology) published in 2010"

Application of extended Mohr–Coulomb criterion to ductile fracture

Abstract: The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids. This criterion has been extensively used in rock and soil mechanics as it correctly accounts for the effects of hydrostatic pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes are the equivalent strain to fracture $${\bar \varepsilon_f}$$ , the stress triaxiality η, and the normalized Lode angle parameter $${\bar \theta}$$ . For a proportional loading, the fracture surface is shown to be an asymmetric function of $${\bar \theta}$$ . A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality, which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie (1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic. Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.

A statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel

Abstract: Intergranular cracking associated with hydrogen embrittlement represents a particularly severe degradation mechanism in metallic structures which can lead to sudden and unexpected catastrophic fractures. As a basis for a strategy for the prognosis of such failures, here we present a comprehensive physical-based statistical micro-mechanical model of such embrittlement which we use to quantitatively predict the degradation in fracture strength of a high-strength steel with increasing hydrogen concentration, with the predictions verified by experiment. The mechanistic role of dissolved hydrogen is identified by the transition to a locally stress-controlled fracture, which is modeled as being initiated by a dislocation pile-up against a grain-boundary carbide which in turn leads to interface decohesion and intergranular fracture. Akin to cleavage fracture in steel, the “strength” of these carbides is modeled using weakest-link statistics. We associate the dominant role of hydrogen with trapping at dislocations; this trapped hydrogen reduces the stress that impedes dislocation motion and also lowers the reversible work of decohesion at the tip of dislocation pile-up at the carbide/matrix interface. Mechanistically, the model advocates the synergistic action of both the hydrogen-enhanced local plasticity and decohesion mechanisms in dictating failure.

Temperature and strain-rate dependent fracture strength of graphene

Abstract: We investigate the variation in fracture strength of graphene with temperature, strain rate, and crack length using molecular dynamics (MD) simulations, kinetic analysis of fracture with a nonlinear elastic relation, and the quantized fracture mechanics theory. Young’s modulus does not vary significantly with temperature until about 1200 K, beyond which the material becomes softer. Temperature plays a more important role in determining the fracture strength of graphene. Our studies suggest that graphene can be a strong material even, when subjected to variations in temperature, strain rate, and cracks.

A New Coal-Permeability Model: Internal Swelling Stress and Fracture–Matrix Interaction

Abstract: We have developed a new coal-permeability model for uniaxial strain and constant confining-stress conditions The model is unique in that it explicitly considers fracture–matrix interaction during coal-deformation processes and is based on a newly proposed internal swelling stress concept This concept is used to account for the impact of matrix swelling (or shrinkage) on fracture-aperture changes resulting from partial separation of matrix blocks by fractures that do not completely cut through the whole matrix The proposed permeability model is evaluated using data from three Valencia Canyon coalbed wells in the San Juan Basin, where increased permeability has been observed during CH4 gas production, as well as using published data from laboratory tests Model results are generally in good agreement with observed permeability changes The importance of fracture–matrix interaction in determining coal permeability, demonstrated in this study using relatively simple stress conditions, underscores the need for a dual-continuum (fracture and matrix) mechanical approach to rigorously capture coal-deformation processes under complex stress conditions, as well as the coupled flow and transport processes in coal seams

“Electrochemical Shock” of Intercalation Electrodes: A Fracture Mechanics Analysis

Abstract: Fracture of electrode particles due to diffusion-induced stress has been implicated as a possible mechanism for capacity fade and impedance growth in lithium-ion batteries. In brittle materials, including many lithium intercalation materials, knowledge of the stress profile is necessary but insufficient to predict fracture events. We derive a fracture mechanics failure criterion for individual electrode particles and demonstrate its utility with a model system, galvanostatic charging of Li x Mn 2 O 4 . Fracture mechanics predicts a critical C-rate above which active particles fracture; this critical C-rate decreases with increasing particle size. We produce an electrochemical shock map, a graphical tool that shows regimes of failure depending on C-rate, particle size, and the material's inherent fracture toughness K Ic . Fracture dynamics are sensitive to the gradient of diffusion-induced stresses at the crack tip; as a consequence, small initial flaws grow unstably and are therefore potentially more damaging than larger initial flaws, which grow stably.

Microseismic moment tensors: A path to understanding frac growth

Abstract: Microseismic monitoring is a valuable tool in understanding the efficacy of hydraulic fracture treatments. Determination of event locations and magnitudes leads to estimations of the geometry of the fracture zone and certain dynamics of the fracturing process. With sufficient resolution, the hypocenters may even reveal failure planes or other underlying structures controlling the distribution of events and of interest to petroleum engineers to test various hypotheses on fracture growth.

Cubic law with aperture-length correlation: implications for network scale fluid flow

Abstract: Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling.

Spall fracture: methodological aspects, mechanisms and governing factors

Abstract: The dynamic tensile strength of materials at load durations of a few microseconds or less is studied by analyzing the spall phenomena under shock pulse loading. The paper is devoted to discussing the methodology and capabilities of the technique to measure spall strength, its error sources, spall fracture of materials of different classes and the factors governing the high-rate fracture of metals and alloys under such conditions.

A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

Abstract: Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice medium with small fracture toughness, we derive an approximate expression for the crack-tip speed, opening displacement and pressure profile. We accomplish this by first showing that a Manning-Strickler channel model for resistance to turbulent flow leads to a mathematical structure somewhat similar to that for resistance to laminar flow of a power law viscous fluid. We then adapt the plane-strain asymptotic crack solution of Desroches et al. (1994) and the power law self-similar solution of Adachi and Detournay (2002) for that case to calculate the desired quantities. The speed of crack growth is shown to scale as the overpressure (in excess of ice overburden) to the power 7/6, inversely as ice elastic modulus to the power 2/3, and as the ratio of crack length to wall roughness scale to the power 1/6. We tentatively apply our model by choosing parameter values thought appropriate for a basal crack driven by the rapid drainage of a surface meltwater lake near the margin of the Greenland Ice Sheet. Making various approximations perhaps relevant to this setting, we estimate fluid inflow rate to the basal fracture and vertical and horizontal surface displacements and find order-of-magnitude agreement with observations by Das et al. (2008) associated with lake drainage. Finally, we discuss how these preliminary estimates could be improved.

Fracture toughness of polycrystalline tungsten alloys

Abstract: Tungsten and tungsten alloys show the typical change in fracture behavior from brittle at low temperatures to ductile at high temperatures. In order to improve the understanding of the effect of microstructure the fracture toughness of pure tungsten, potassium doped tungsten, tungsten with 1 wt.% La 2 O 3 and tungsten rhenium alloys were investigated by means of 3-point bending, double cantilever beam and compact tension specimens. All these materials show the expected increase in fracture toughness with increasing temperature. The experiments demonstrate that grain size, texture, chemical composition, grain boundary segregation and dislocation density seem to have a large effect on fracture toughness below the DBTT. These influences can be seen in the fracture behavior and morphology, where two kinds of fracture occur: on the one hand transgranular and on the other hand intergranular fracture. Therefore, techniques like electron backscatter diffraction (EBSD), Auger electron spectroscopy (AES) and X-ray line profile analysis were used to improve the understanding of the parameters influencing fracture toughness.

A Study on the Effect of the Stress State on Ductile Fracture

Abstract: The main purpose of this paper is to demonstrate that besides the stress triaxiality parameter, the Lode angle, which can be related to the third invariant of the deviatoric stress tensor, also has an important effect on ductile fracture. This is achieved by conducting a series of micromechanics analyses of void-containing unit cells and experimental-numerical studies of carefully designed specimens experiencing a wide range of stress states. As a result, a fracture criterion is expressed in terms of the equivalent failure strain as a function of the stress triaxiality and the Lode angle (or the third invariant of the stress deviator) and this function is calibrated for a DH36 steel plate.

Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model

Abstract: Advanced High Strength Steels (AHSS) are increasingly used in automotive industry due to their superior strength and substantial weight advantage. However, their compromised ductility gives rise to numerous manufacturing issues. One of them is the so-called ‘shear fracture’ often observed on tight radii during stamping processes. Since traditional approaches, such as the Forming Limit Diagram (FLD), are unable to predict this type of fractures, great efforts have been made to develop failure criteria that could predict shear fractures. In this paper, a recently developed Modified Mohr–Coulomb (MMC) ductile fracture criterion ( Bai and Wierzbicki, 2010 ) is adopted to analyze the failure behavior of a Dual Phase (DP) steel sheet during stretch-bending operations. The plasticity and ductile fracture of the present sheet are fully characterized by a Hill’48 orthotropic model and a MMC fracture model, respectively. Finite element models with three different element types (3D, shell and plane strain) were built for a Stretch Forming Simulator (SFS) test ( Shih and Shi, 2008 ), numerical simulations with four different R / t values (die radius normalized by sheet thickness) were performed. It has been shown that the 3D and shell element simulations can predict failure location/mode, the upper die load–displacement responses as well as wall stress and wrap angle at the onset of fracture for all R / t values with good accuracy. Furthermore, a series of parametric studies were conducted on the 3D element model, and the effect of tension level (clamping distance), tooling friction, mesh size and fracture locus on failure modes and load–displacement responses were investigated.

Evidence for a Long-Term Strength Threshold in Crystalline Rock

Abstract: The mechanical response of brittle rock to long-duration compression loading is of particular concern in underground disposal of nuclear waste, where radionuclides must be isolated from the biosphere for periods of the order of a million years. Does the strength decrease without limit over such time, or is there, for some rock types, a lower “threshold” strength below which the rock will cease to deform? This paper examines the possibility of such a threshold in silicate crystalline rocks from several perspectives, including: (1) interpretation of the results of short-term creep tests on rock; (2) numerical analysis of the effect of decrease in fracture toughness due to stress corrosion on the strength of a crystalline rock; and (3) evidence from plate tectonics, and observations of in situ rock stress in granite quarries. The study concludes that there isclear evidence of threshold strength. The threshold is of the order of 40% of the unconfined compressive strength or higher for laboratory specimens under unconfined compressive loading, and increases rapidly in absolute value with confinement. Field evidence also leads to the conclusion that the long-term strength of crystalline rock in situ is of comparable magnitude to the laboratory value.