Browsing by Subject "Fracture mechanics"

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Applications of phase-field modeling in hydraulic fracture
(2019-12) Alotaibi, Talal Eid; Landis, Chad M.; Sharma, Mukul M; Mear, Mark E; Ravi-Chandar, Krishnaswa; Foster, John T
Understanding the mechanisms behind the nucleation and propagation of cracks is of considerable interest in engineering application and design decisions. In many applications in the oil industry, complicated fracture geometries and propagation behaviors are encountered. As a result, the development of modeling approaches that can capture the physics of non-planar crack evolution while being computationally tractable is a critical challenge. The phase-field approach to fracture has been shown to be a powerful tool for simulating very complex fracture topologies, including the turning, splitting, and merging of cracks. In contrast to fracture models that explicitly track the crack surfaces, crack propagation and the evolution thereof arise out of the solution to a partial differential equation governing the evolution of a phase-field damage parameter. As such, the crack growth emerges naturally from solving the set of coupled differential equations linking the phase-field to other field quantities that can drive the fracture process. In the present model, the physics of flow through porous media and cracks is coupled with the mechanics of fracture. Darcy-type flow is modeled in the intact porous medium, which transitions to a Stokes-type flow regime within open cracks. This phase-field model is implemented to gain insights into the propagation behavior of fluid-injected cracks. One outstanding issue with phase-field fracture models is the decomposition of the strain energy required to ensure that compressive stress states do not cause crack propagation and damage evolution. In the present study, the proper representation of the strain energy function to reflect this fracture phenomenon is examined. The strain energy is constructed in terms of principle strains in such a way that it has two parts; the tensile and the compressive. A degradation function only applies to the tensile part enforcing that the crack is driven only by that part of the strain energy. We investigated the split operator proposed by Miehe et al. [1], and then proposed a split approach based on masonry-like material behavior [2, 3]. We have found that when using Miehe’s form for the strain energy function, cracks can propagate under compressive stresses. In contrast, the approach based on a masonry-like materials constitutive model we proposed ensures that cracks do not grow under compressive stresses. To demonstrate the capabilities of phase-field modeling for fluid-driven fractures, four general types of problems are simulated: 1) interactions of fluid-driven, natural, and proppant-filled cracks, 2) crack growth through different material layers, 3) fluid-driven crack growth under the influence of in-situ far-field stresses, and 4) crack interactions with inclusions. The simulations illustrate the capabilities of the phase-field model for capturing interesting and complex crack growth phenomena. To understand how fluid-driven cracks interact with inclusions, AlTammar et al. [4] performed experiments. Three tests with tough inclusions were performed to understand the effects of orientation angle, thickness, and material properties. Additionally, one test with a weak inclusion was performed to compare the results with those of the tough inclusion cases. The experiments show a clear tendency for the fluid-driven hydraulic fracture to cross thick natural fractures filled with materials weaker and softer than the matrix and to be diverted by thick natural fractures with tougher and stiffer filling materials. To replicate these experiments numerically and to gain a mechanistic understanding, in the present study, we ran simulations using phase-field modeling. Results from both the experiments and the simulations provide clear evidence that inclusion width, angle, material properties, and distance from the injection point affect the outcome of the crack evolution. Phase-field modeling was able to capture the trends of crack deflection/crossing in all the test cases. Finally, we extended the phase-field model has been extended to three dimensions and tested it on bench-mark problems. The first bench-mark problem is a compact test for a CT specimen. In this problem, the mechanical equations are only considered. The simulation shows that the CT specimen is split into two symmetric parts. The second bench-mark problem is a fluid-driven circular crack. The simulation for this problem shows that the crack grows in a radial direction.
Characterization of transport properties in granitic rock fractures with skins
(2007-05) Garner, Terence Travis, 1975-; Sharp, John Malcolm, 1944-
Hydraulic properties of fracture skins in granitic rocks from three climatically different field sites show that fracture skins can increase permeability, compared to unaltered granite, through microfractures or weathering rinds, or decrease it through the effects of mineral nucleation or precipitation and growth of biological organisms. In comparable granitic crystalline rocks, fracture skins formed in more arid climates have a higher porosity than fracture skins formed in more humid climates. Granite fractures have been collected from three field sites Elberton, Georgia, Fredericksburg, Texas, and Eyre Peninsula, South Australia. Fracture skins in Elberton are predominantly surface coatings of dust films, clay infillings, organic growths, and infillings of iron precipitates. Town Mountain Granite skins are dominated by iron banding, weathering rinds, and surface coatings of pyrolusite. The Calca Granites from the Eyre Peninsula have similar fracture skins to the Town Mountain Granite, but skin thicknesses are greater. Modeling studies with fracture skins demonstrate that the most important hydraulic properties are skin porosity, diffusion coefficients, and retardation. Through combined laboratory analyses and field investigations, the variations in transport properties of rock matrix and fracture alteration zones are documented. Transport properties of fracture skins in granitic rocks with surface coatings enhance fracture transport and alteration zones of more porous skins attenuate transport. A new laboratory method is employed to measure diffusion coefficients using laser ablation ICP-MS. Diffusive transport is shown to be preferential to grain boundaries and zones of mineral cleavage planes. Tracer tests show channeling to be a significant factor in breakthrough results on the field scale. Channels on the field scale are imaged using high frequency GPR providing an image of preferential flow paths in a fracture.
Crack nucleation on V-notched PMMA and Polycarbonate
(2022-08-10) Eom, Kyumin; Ravi-Chandar, Krishnaswamy
This study examined the criteria for a crack nucleation on a V-notched geometry for Polymethylmethacrylate (PMMA) and Polycarbonate (PC). V-notched geometries are known to have their specific notch stress intensity factor depending on the V-notch angle and the depth of the V-notch itself. It is crucial to understand the relationship between the stress concentration effect the notch geometry imposes and crack initiation. By investigating the relationship and quantifying driving factors, a reliable conclusion can be made on the criteria for crack nucleation on V-Notch. This study carried out symmetric three-point bend tests on PMMA and PC with varying V-notch angle and depth. The V-notch angles range from 60° to 120° while the depths range from 0.1 to 0.4 of the specimen height. The asymptotic analysis from Williams (1952) combined with a full 3-D finite element analysis were used to determine the V-notch stress intensities. Later, fractography was performed on the fractured specimens to determine the initial crack location and size to estimate the fracture toughness. PMMA showed exclusively brittle fracture while PC showed moderate to significant plastic deformation dominance depending on the V-notch angle and depth. Additionally, PMMA mostly showed a half-elliptical initial crack that nucleated and propagated slowly first, and then transitioned into an unstable, fast fracture. However, PC showed signs of a complex combination of nucleation of brittle fracture as well as significant plastic deformation depending on specimen geometry. A digital camera was used to capture the initial crack nucleation and the slow-crack growth before fast-fracture. This investigation showed that the theory of linear elastic fracture mechanics is effective in predicting crack initiation in V-notched geometries if proper account is taken of the initiation and growth of a sharp crack from the notch. Finally, as a conservative estimate, it is suggested that notches be considered to be cracks of corresponding depth, providing a lower bound for the allowable load in structures.
Detection of transverse cracking in a hybrid composite laminate using acoustic emission
(2003-12) Jong, Hwai-jiang, 1962-; Schapery, Richard Allan; Ravi-Chandar, K.
Transverse cracking detection in a uniaxially-loaded symmetric cross-ply hybrid laminate containing 0◦ IM7/8552 carbon/epoxy and a very thin 90◦ S2/8552 glass/epoxy layer is studied using the acoustic emission (AE) technique. By conducting modal-based AE experiments and analysis, we investigate some parameters that can be used as the waveform signatures to identify transverse crack growth in the hybrid laminate. Wave dispersion relations of the hybrid laminate are established, and a comparison with those from a material homogenization model based on the equivalent stiffness is made. It is found that material homogenization is not accurate for predicting wave dispersion in the hybrid laminate. Wave dispersion for a homogeneous IM7/8552 unidirectional plate is also constructed. Cut-off frequencies belonging to various wave modes are discussed concerning their significance in interpreting AE signals. The wave attenuation behaviors that exist in the hybrid laminate and in the homogeneous IM7/8552 plate are compared and discussed using the finite element method (FEM). The use of singular elements dealing with the high strain gradient near the crack tip is addressed for convergence purposes. It is shown by the FEM results and demonstrated in the AE experiments that wave attenuation in the cross-ply hybrid laminate is much stronger than in the plain IM7/8552 plate. A simple calibration method for the AE sensors is discussed. Some important aspects in conducting an AE experiment, such as the sensor averaging effect and sensor frequency response range, are addressed. A new source location method based on the waveform’s first peak search and the associated primary frequency content is proposed. The accuracy of the source location method is verified by pencil-lead break experiments. The so-called symmetric energy fraction (SEF) of the AE signals in conjunction with the finite element analysis result in identification of the transverse cracking event. Lastly, a material failure kinetics-based characterization of the transverse cracking process is proposed in terms of the unloading forcing function on the transverse crack face. Finite element results based on this loading are compared to the AE signals.
Digital gradient sensing and analysis of dynamic crack stability, propagation, and branching
(2018-12) Chichester-Constable, Alexander James; Ravi-Chandar, K.
Understanding the underlying mechanisms of fracture mechanics plays a critical role in engineering design and analysis. This work investigates aspects of dynamic fracture and the transition from stable to unstable crack propagation by employing the digital gradient sensing method in conjunction with high-speed photography. Both quasi-static and dynamic loading scenarios are evaluated. Furthermore, the micromechanical fracture mechanisms are evaluated using optical microscopy and optical profilometry. Significant insights are gained regarding the relationship between loading, crack branching, and the micromechanical mechanisms that govern dynamic fracture. Differences between two models for formation of crack surface patterns, based on crack front waves and Wallner lines, are examined. Most interestingly, insights developed with respect to crack branching phenomenon, and its speed past branching have significant impact on the modeling of crack branching and dynamic fracture. Discovery of constant crack branch speed will require additional study of energy release rates associated with branching cracks
Discrete element modeling of rock fracture behavior: fracture toughness and time-dependent fracture growth
(2006) Park, Namsu; Olson, Jon E.
Understanding the mechanics of fracture is important in oil and gas reservoirs. Applications range from the characterization of natural fractures that enhance fluid flow to the prediction of fracturing around a wellbore that can affect its integrity and stability. Two parameters that are of particular importance in the fracturing process are fracture toughness and subcritical index. There is a fair amount of experimental data on different rock types for these parameters but it is not well-known what petrographic properties control their magnitude. Also, because of sample preparation difficulty, fracture mechanics testing of weakly cemented sandstone is very challenging. In order to better understand the micro-mechanics of fracturing of clastic rocks (sandstones of various cementation), a numerical study was performed using the Discrete Element Method (DEM). DEM was employed in order to model laboratory test behavior, vii by assessing individually the sensitivity of results to volume of cement, time-dependent cement properties, grain/cement mineralogy, temperature, and confining pressure. The micro-mechanical properties of DEM (stiffness and friction of grains and stiffness, strength, and volume of cement) were determined using macroscopic uniaxial and triaxial compression tests. The time-dependent properties of subcritical crack growth were implemented by incorporating stress corrosion of inter-particle bonds. The stress corrosion rate was quantified by the activation energy and volume of quartz. The fracture toughness and subcritical index of Berea sandstone was measured and the results were extended to weaker rock by reducing the cement volume. The DEM results generally agree with laboratory experiments. As intergranular cement volume is reduced, fracture toughness and subcritical index decrease. Based on this relationship, the fracture mechanics properties of weak rocks, which are difficult to measure in the laboratory, can be predicted. Using the DEM model constrained by laboratory results, the importance of subcritical crack growth in wellbore stability problems was investigated. Wellbore instability in shale can be an immediate result of stress redistribution and increasing formation pore pressure following the removal of the rock mass in the wellbore. Additionally, because of large clay content and the potentially high chemical reactivity with drilling fluids, shale can be susceptible to time-dependent failure. Previous studies (mostly based on continuum modeling using poroelasticity) have concentrated on predicting the onset of failure. However, the use of DEM makes it possible to evaluate the progression of failure over time by tracking the propagation of the damage zone boundary
The dynamic failure behavior of tungsten heavy alloys subjected to transverse loads
(2004) Tarcza, Kenneth Robert; Taleff, Eric M.; Bless, Stephan J.
Tungsten heavy alloys (WHA), a category of particulate composites used in defense applications as kinetic energy penetrators, have been studied for many years. Even so, their dynamic failure behavior is not fully understood and cannot be predicted by numerical models presently in use. In this experimental investigation, a comprehensive understanding of the high-rate transverse-loading fracture behavior of WHA has been developed. Dynamic fracture events spanning a range of strain rates and loading conditions were created via mechanical testing and used to determine the influence of surface condition and microstructure on damage initiation, accumulation, and sample failure under different loading conditions. Using standard scanning electron microscopy metallographic and fractographic techniques, sample surface condition is shown to be extremely influential to the manner in which WHA fails, causing a fundamental change from externally to internally nucleated failures as surface condition is improved. Surface condition is characterized using electron microscopy and surface profilometry. Fracture surface analysis is conducted using electron microscopy, and viii linear elastic fracture mechanics is used to understand the influence of surface condition, specifically initial flaw size, on sample failure behavior. Loading conditions leading to failure are deduced from numerical modeling and experimental observation. The results highlight parameters and considerations critical to the understanding of dynamic WHA fracture and the development of dynamic WHA failure models.
Experiments on dynamic fracture and friction
(2007-12) Lim, Jaeyoung, 1972-; Ravi-Chandar, K.
Dynamic fracture and friction under dynamic loading conditions are examined through direct observations in carefully controlled experiments. An electromagnetic loading device is used to generate a compressive stress wave and the full-field optical technique of dynamic photoelasticity and high-speed photography are used as diagnostic tools. In addition, a new optical method to determine both principal stresses and their orientations simultaneously is developed. In this dissertation, the results from experiments aimed at investigating fracture and frictional sliding under shear loading conditions are presented. For dynamic fracture problems, we examine shear cracks in homogeneous materials by introducing a groove in the specimen and trapping the crack to grow within it. The groove does not affect the fracture mechanisms inherent to the material, but influences the energy flux and loading symmetry. Such shear induced cracks growing at speeds in the intersonic regime are demonstrated. Furthermore, it is shown that the main mechanism of the shear crack growth is the sequential nucleation, growth and coalescence of echelon cracks. The spacing and angle relative to the groove plane of the echelon cracks are measured directly from the experimental specimen. Numerical simulation shows that the echelon cracks are well aligned perpendicular the maximum principal (tensile) stress generated in this specimen. The spacing is interpreted as an intrinsic characteristic of the failure process. These experiments also enable the determination of the dynamic failure stress at which microcracks are nucleated. For frictional sliding along an interface, a novel apparatus has been constructed for the understanding of the nature of dynamic friction and studying the slip pulse propagation under extremely high rates of loading. In experiments, dynamic slip along the frictional interface are triggered either by a compressional planar wave, or a compressional cylindrical wave. In both methods, the stress state across a frictional interface is brought to the critical state behind the wave. When slip occurs across the interface, it is forced to run along the interface at the speed of this wave. Several interesting results on frictional sliding are presented. First, the stress drop across the slip interface is characterized from isochromatic fringe patterns. Evaluation of the fringe pattern yields a description of the evolution of the shear stress both ahead and behind the slip event. The shear stress is seen to build up gradually to a maximum at the leading edge of a slip pulse and to decay rapidly over a few mm slip length. Second, slip pulses can be generated from frictional interfaces through interaction with propagating stress waves and are observed to propagate at a speed controlled by the wave that generates slip. Accumulation of fringes near the slip pulse and the orientation of the Mach lines suggestion the slip pulse propagates at a speed close to the dilatational wave speed. Finally, new optical method in which the classical methods of photoelasticity and Mach-Zehnder interferometry are used in a combined arrangement is presented. In dynamic problems the measurement is made with a high-speed photodetector at very high temporal resolution at a single point or a small array depending on the detector array and recording device; this eliminates the need for a high-speed photographic system, but more importantly provides complete, time-resolved evolution of all stress components. Examples of application of the method are demonstrated.
Fracture and permeability analysis of the Santana Tuff, Trans-Pecos Texas
(1990-12) Fuller, Carla Matherne; Sharp, John Malcolm, 1944-
A fracture and permeability analysis was performed on the Santana Tuff because of its similarity to the Topopah Springs unit at the Yucca Mountain site. The Topopah Springs unit is the proposed horizon for the spent nuclear fuel repository. Because of the impossibility of completely characterizing the flow properties of the unit without destroying the characteristics that make it desirable as a repository, other ash flow tuffs must be studied. The Santana Tuff and the Topopah Springs tuff both are rhyolitic in composition, nonwelded to densely welded and fractured. Fractures were examined at six outcrop locations spanning a five mile area. Stereonets and rose diagrams were constructed from over 312 fracture orientations. Although the composite data showed two major orientations of nearly vertical fractures, fracture trends at individual outcrops showed a variety of preferred orientations. Over 900 surface permeability measurements were taken using a mini-permeameter. The samples were categorized by three observed types of surface weathering: fresh, weathered, or varnished. Fracture surfaces were generally classified as weathered. The average permeabilities for the samples are 55.33 millidarcies, 5.03 millidarcies, and 3.31 millidarcies, respectively. The one-way statistical analysis performed on the data indicated that the permeability of fresh tuff surfaces is significantly different than both the permeabilities of the weathered and varnished tuffs, using both a least significant difference and greatest significant difference test. However, no difference was shown to exist between the weathered and varnished tuff permeabilities. Samples of fresh, weathered, and varnished tuffs were examined by X-Ray Defraction, the Scanning Electron Microscope, and in thin section. The SEM analysis showed surface differences between the three weathering classifications. The weathered and varnished samples were similar, exhibiting a platy, lamellate texture. The fresh surfaces were irregular and jagged. In thin section, a thin rind of dark minerals (FE-oxides) is observed on the edges of the varnished samples and in microcracks. This fills surface pores and causes the reduction in permeability. Two other zones of weathering have been identified in some of the samples, which may also cause changes in permeability. Tuff permeabilities were also analyzed for directional dependence. After an ash flow tuff is deposited and cooled, it may undergo flattening of pumice fragments and glass shards. These flattened fragments can be identified in handsamples, and are indicative of the direction of flow emplacement. The analysis showed that permeability is enhanced parallel to the emplacement direction, which is generally horizontal. Cut surfaces showed a 30% decrease in permeability perpendicular to flow direction. On varnished surfaces, this trend is still evident, although decreased in magnitude. This is expected because of the clay particles which make up the desert varnish. This study indicates that the formation of low permeability weathering rinds in association with vertical fractures may inhibit infiltration at the surface. It may accelerate infiltration at depth and allow more fluid to penetrate vertically into the tuff. In the event that fluid is absorbed into the matrix, it will travel horizontally, along the enhanced permeability parallel to the emplacement direction.
Fracture-size scaling and stratigraphic controls on fracture intensity
(2002) Ortega Pérez, Orlando José; Marrett, Randall A.
Scaling techniques offer an opportunity to solve subsurface fracturesampling problems by extrapolating fracture properties from sub-millimeterscales to scales important for economic applications. Although extrapolation of fracture length and aperture distributions across observation scales is fraught with potential errors, sampling of opening-mode kinematic apertures along scanlines using new fracture-aperture measuring tools produces consistent power-law aperture distributions from the micron-scale to outcrop-scale. One-dimensional sampling avoids fracture connectivity issues inherent to traditional twodimensional length sampling methods. Sampling artifacts and mechanical layer effects can be diagnosed and accounted for, and extrapolation of power-law fracture intensities from the sub-millimeter scale up to the length scale of mechanical layers is feasible. Tests were performed in turbidite beds of the Ozona Sandstone, Texas, eolian Weber Formation sandstones, Colorado, and Lower Cretaceous carbonates of the Sierra Madre Oriental (SMO), Mexico. Outcrop studies in Weber Formation sandstones provided an opportunity to characterize well-exposed macrofracture systems as potential analogues for subsurface fractured reservoirs at Rangely Field. However, differences in stratigraphy and diagenetic history between surface and subsurface do not allow the direct extrapolation of these results to subsurface, reinforcing the idea that local data are necessary for fracture system characterization even in cases where long geologic time has passed between the time of sedimentation and the time of deformation that brought potential outcrop analogs to the surface. Another way to predict fracture properties in the subsurface is to analyze the relationships between fracture attributes and the geologic parameters of the rock volume that govern fracturing. Fracture-fill prediction using relative volumes of cement phases precipitated during and after fracture timing shows an empirical relationship with sedimentary facies in Weber Formation sandstones. Multivariate analysis of unbiased fracture intensity in SMO carbonates suggests that degree of dolomitization and position of a bed at the top of a stratigraphic cycle are the most important controls on fracture intensity in these rocks. Mud content has only a modest control on fracture intensity and bed thickness has the least control on fracture intensity, suggesting that published work concluding that fracture intensity is strongly governed by bed thickness may be biased by scale or sampling effects.
Improved accelerated life testing for cathodic delamination
(2012-03) Liechti, K. M.
The overall objective of this work is to establish the feasibility of modeling the cathodic delamination problem in polymer coated submarine components with a view to developing a more accurate testing standard for Accelerated Life Testing (ALT) and to determining the effectiveness of new approaches for combating cathodic delamination in a quantitative manner ... An approach has ... been taken to characterize cathodically delaminating rubber/metal interfaces and forms the basis for the current attempt to model cathodic delamination between polyurethane and titanium. Once this model is established it will allow for an accelerated life protocol to be developed where stress and temperature will be used to accelerate crack growth in laboratory specimens while retaining the same crack growth mechanisms that are seen in service. The elements of the approach are threefold: 1. Determining the mechanical behavior of the polyurethane and titanium. The former is more challenging due to its nonlinearly elastic behavior. 2. Conducting a stress analysis of the specimen to be used in the cathodic delamination experiment in order to design it to provide the anticipated range of energy release rate values. 3. Conducting the cathodic delamination experiments and determining the crack velocity profiles for the polyurethane/titanium interface as a function of energy release rate and temperature.
Improving process stability and ductility in laser sintered polyamide
(2019-01-25) Leigh, David Keith; Bourell, David Lee; Beaman, Joseph J; Kovar, Desiderio; Mangolini, Filippo; Juenger, Maria
The desire to manufacture production parts using additive manufacturing has created an increased demand on the laser sintering technology to supply this need. A significant issue in laser sintered polymers is the variability of mechanical properties from build-to-build and the inability to determine the success or failure of the production process until the production builds are complete. Interlayer ductility of parts produced in the laser sintering process has been shown to be uncontrolled and unpredictable. This research focuses on improving interlayer ductility and establishing a baseline for modeling the time-temperature-transformation of production-grade, laser-sintered polymers. The background shows that there has been a significant amount of research to map processing parameters to mechanical properties and that industry has been focused on recording processing parameters and mechanical properties as part of the quality record. The research shows trends in mechanical performance that are not adequately explained with current analytical techniques. The experimental research characterized the thermal attributes of the laser sintering process using onboard sensors, production build data, external thermal cameras, and in-situ thermocouples to map the thermal profile of a complete laser sintering build. This information, used in conjunction with an array of over 80,000 production build tensile data points, provides the basis for a thermal model for laser sintered polymers. Current laser energy models in laser sintering are incomplete and do not consider many processing parameters available in the laser sintering process, focusing primarily on the build surface temperature and the laser energy applied to the part region. A more complete thermal model must also account for the energy exposure during the build. The thermal process model is developed to integrate the thermal history during the build and cooldown cycle as a metric of success. It will be shown that improved and more predictable ductility performance is achievable, and that a thermal process model can be used to characterize the energy input required over time to achieve optimal results. Ultimately, increased reliability in laser sintered polymer parts will increase their usage in commercial applications.
Investigation of pulse fracturing via peridynamics modeling and simulation
(2017-01-10) Uppati, Sai Pranav; Foster, John T., Ph. D.
Pulse fracturing is an alternative stimulation technology to enhance production from oil and gas wells, especially ones in fractured hydrocarbon reservoirs. This stimulation generates multiple radial fractures that initiate at the wellbore wall, via the application of pressure pulses at rates on the order of 10 MPa ms⁻¹ or more. These radial fractures act as conductive pathways for hydrocarbon flow into the bottom of the wellbore. Pulse fracturing has been tested via experiments and oil field implementations quite extensively in the 1970s and 1980s. The fracture mechanics of pulse stimulation, however, is not well understood. Computational efforts at modeling pulse fractures are relatively sparse in literature. Due to a recent renewal of interest in this form of stimulation, this computational study aims to develop a tool to simulate pulse fracturing. At the high loading rates experienced by rock during pulse stimulation, dynamic fracturing is expected to occur leading to the generation of a complex radial fracture network. A state-of-the-art continuum mechanics code called Peridigm is well equipped to handle dynamic fracture modeling. Peridigm's capabilities are explored to ascertain whether it can capture pulse fracture behavior accurately. Using concrete as the computational medium, the relevant modeling considerations are analyzed to determine the best approaches for modeling pulse fracturing in Peridigm. This tailored approach is then used for benchmarking Peridigm against published pulse fracturing experiments on sandstone core samples.
Mixed-mode fracture experiments on quartz/epoxy and sapphire/epoxy interfaces
(2003-12) Mello Junior, Alberto Walter da Silva; Liechti, K. M.
Modeling competing fracture for dry transfer of thin films to a flexible substrate
(2018-08-03) Jain, Shruti, Ph. D.; Bonnecaze, R. T. (Roger T.); Liechti, K. M.; Li, Wei; Willson, Carlton G; Hwang, Gyeong S
Dry transfer printing is where a thin film is transferred from a host substrate to a target substrate by taking advantage of the difference in adhesion between the thin layer and the substrates. This technique can lead to high throughput industrial-scale manufacturing of flexible devices using thin films and 2D materials. A major roadblock for applying the method is an inadequate understanding of how transfer printing depends on the material properties of the substrates and the thin film and their interfacial interactions, which limits the reliability of dry transfer methods. This dissertation provides this knowledge through computational analysis with cohesive zone models. Two approaches are used: 2D finite element simulations and 1D finite difference beam theory models. Both mode I and mixed-mode fractures are simulated. Scaling equations are developed to quantify load, crack length, end rotation, damage zone length and mode-mix as a function of material and interface properties. Competing fracture during the transfer of a 2D material like graphene is simulated with finite element models in ABAQUS®. Two damage initiation criteria are used with cohesive zone models. Interface strength is observed to be the primary factor affecting crack path selection for both damage criteria. Weaker interfaces break first, independent of the fracture energy. However, convergence issues with ABAQUS® are identified. So, fast, robust beam theory models are developed to understand the parametric dependence of crack growth on material and interface properties and captured in a fracture map. In addition to 2D materials, transfer printing of thin films is also studied. Parameters such as interface defects, thin film thickness and interface properties are varied to understand crack growth in thin film transfer. Interface defects modeled as initial crack lengths are observed to be the most significant factor in determining the success of the transfer process. When interface cracks are of equal lengths, fracture energy determines the crack path selection for stiff thin films and thicker films whereas for soft thin films, interface strength determines which interface breaks. A strong correlation between steady state crack tip mode-mix and crack path selection is observed despite using a mode-independent fracture energy.
Natural fractures in mudrocks and top seal integrity : insights from diagenesis, rock mechanics, and modeling applied to CO₂ sequestration and hydrocarbon exploration
(2018-08) Major, Jonathan R., 1984-; Eichhubl, Peter; Barnes, Jaime D; Gale, Julia F; Behr, Whitney; Hesse, Marc A
The viability of carbon sequestration for climate change mitigation depends on both the short and long-term security of injected CO₂, which may be impacted by the coupled chemical and mechanical properties of reservoir and seal rocks. Analogs such as the Crystal Geyser/Little Grand Wash fault field site near Green River, Utah allow investigation on longer time scales than laboratory or numerical experiments and was studied to assess the potential for leakage via fracturing or capillary failure of reservoir and seal rocks altered by natural, long-term CO₂-water-rock interactions. Fracture mechanics testing using the double torsion method was first performed on a suite of naturally altered and unaltered rocks exposed at Crystal Geyser. CO₂-related alteration measurably changed fracture toughness (K [subscript IC]) and subcritical index (SCI). A schematic model based on measured K [subscript IC] and SCI values and their predicted influence on fracture pattern development, and their chemical and spatial context relative to the main fault, was developed that qualitatively matches three distinct fracture network patterns observed. Fracture toughness and subcritical index (SCI) are also sensitive to chemical environment and temperature, for example, decreasing by up to 60% and 90%, respectively, in five different sandstone samples immersed in water versus ambient conditions. Sensitivity is controlled by rock composition, grains, cements, and fabric. Aztec Sandstone, a silica-cemented subarkose is relatively insensitive to pH and salinity compared to other sandstones such as the chlorite-cemented Tuscaloosa Sandstone, a CO₂ sequestration reservoir. In general, inert grains and cements such as quartz were less sensitive to the changing chemistry than carbonates and clays. The potential for capillary failure or enhancement of top seals over long (> 10³ years) scales was also studied by mercury intrusion capillary pressure (MICP) analyses on altered shale samples from Crystal Geyser Relatively low capillary seal capacity was measured < 5 m from the fault where CO₂-alteration is most intense but then increases by over an order of magnitude before gradually declining to background levels > 100 m from the fault. Systematic variations in the petrophysical properties are largely explained by changes in pore networks due to matrix replacement with calcite observed by SEM imaging.
Numerical studies of complex materials
(2020-05-05) Zheng, Wei-Jin; Marder, Michael P., 1960-; Florin, Ernst-Ludwig; Morrison, Philip J; Niu, Qian; Torres-Verdin, Carlos
This dissertation presents two inter-related studies. Chapter 2 focuses on a study of three-dimensional numerical simulations of hydraulic fractures. Hydraulic fracturing is widely used to extract shale gas from shale formations. Pressurized water is injected into horizontal wells in shale formations to create fracture networks. If a network contains many fractures, the shale gas is easier to transport to the surface via this network. To date, the shapes of hydraulic fracture networks in shale formations are still not precisely known. This research is to numerically investigate three-dimensional hydraulic fractures with molecular dynamics simulations, which integrates the physics of linear elasticity and fracture mechanics as well as the discrete channel and fluid variables to dynamically see the propagation of hydraulic fractures. This approach allows an arbitrary number of cracks and arbitrary crack paths, and I have further developed a simulator to simulate the complex networks of hydraulic fractures in response to various states of stress in the shale formation. I have also proposed an extra term to implement the Poisson effect, which connecting deformations in perpendicular directions, for a future study for more complicated three-dimensional fracture networks such as echelon cracks. Chapter 3 presents the research on static cracks in a natural rubber sheet, seeking a strain energy functional that can accurately describe it. The type of static crack is due to the strain-induced crystallization of natural rubber and has two unusual features: pointy crack tips and a sharp boundary between the two regions with distinct deformations. When a latex rubber sheet is stretched beyond a critical stretch ratio, a slit that is cut in the middle will not cause this sheet to break apart but forms a static crack due to the crystallization of rubber. The pointy crack tips cannot be explained by the existing theories in fracture mechanics, and the sharp change of deformation is also puzzling. I have built molecular dynamics simulations to verify proposed strain energy functionals and see whether the particular crack shape in rubber can be implemented. I have got simulation results with the two features based on a strain energy functional curve with its two energy minima corresponding to the two phases. In hyperelasticity, the strain energy functional that describes the strain-induced crystallization in an isotropic material has not been mathematically formulated. The discovery shows an insight into a new form of the strain energy functional for phase separation with spatial complexity in nonlinear elasticity.
Numerical studies of complex materials
(2020-05-05) Zheng, Wei-Jin; Marder, Michael P., 1960-; Florin, Ernst-Ludwig; Morrison, Philip J; Niu, Qian; Torres-Verdin, Carlos
This dissertation presents two inter-related studies. Chapter 2 focuses on a study of three-dimensional numerical simulations of hydraulic fractures. Hydraulic fracturing is widely used to extract shale gas from shale formations. Pressurized water is injected into horizontal wells in shale formations to create fracture networks. If a network contains many fractures, the shale gas is easier to transport to the surface via this network. To date, the shapes of hydraulic fracture networks in shale formations are still not precisely known. This research is to numerically investigate three-dimensional hydraulic fractures with molecular dynamics simulations, which integrates the physics of linear elasticity and fracture mechanics as well as the discrete channel and fluid variables to dynamically see the propagation of hydraulic fractures. This approach allows an arbitrary number of cracks and arbitrary crack paths, and I have further developed a simulator to simulate the complex networks of hydraulic fractures in response to various states of stress in the shale formation. I have also proposed an extra term to implement the Poisson effect, which connecting deformations in perpendicular directions, for a future study for more complicated three-dimensional fracture networks such as echelon cracks. Chapter 3 presents the research on static cracks in a natural rubber sheet, seeking a strain energy functional that can accurately describe it. The type of static crack is due to the strain-induced crystallization of natural rubber and has two unusual features: pointy crack tips and a sharp boundary between the two regions with distinct deformations. When a latex rubber sheet is stretched beyond a critical stretch ratio, a slit that is cut in the middle will not cause this sheet to break apart but forms a static crack due to the crystallization of rubber. The pointy crack tips cannot be explained by the existing theories in fracture mechanics, and the sharp change of deformation is also puzzling. I have built molecular dynamics simulations to verify proposed strain energy functionals and see whether the particular crack shape in rubber can be implemented. I have got simulation results with the two features based on a strain energy functional curve with its two energy minima corresponding to the two phases. In hyperelasticity, the strain energy functional that describes the strain-induced crystallization in an isotropic material has not been mathematically formulated. The discovery shows an insight into a new form of the strain energy functional for phase separation with spatial complexity in nonlinear elasticity.
Phase-field modeling of fracture for multiphysics problems
(2016-12) Wilson, Zachary Adam; Landis, Chad M.; Hughes, Thomas J.R.; Mear, Mark E.; Ravi-Chandar, Krishnaswa; Foster, John T.
Several recent works have demonstrated that phase-field methods for modeling fracture are capable of yielding complex crack evolution patterns in materials. This includes the nucleation, turning, branching, and merging of cracks subject to a variety of quasi-static and dynamic loadings. What follows will demonstrate how phase-field methods for fracture can be applied to problems involving materials subject to electromechanical coupling and the problem of hydraulic fracture. Brittle fracture is a major concern in piezoelectric ceramics. Fracture propagation in these materials is heavily influenced by the mechanical and electrical fields within the material as well as the boundary conditions on the crack surfaces. These conditions can lead to complex multi-modal crack growth. We develop a continuum thermodynamics framework for a damaging medium with electromechanical coupling subject to four different crack-face boundary conditions. A theory is presented to reproduce impermeable, permeable, conducting, and energetically consistent crack-face boundary conditions, the latter of which requires a finite deformation formulation. A primary application of hydraulic fracturing involves the injection of fluid into a perforated wellbore with the intention of fracturing the surrounding reservoir and stimulating its overall production. This process involves the coupling of fluid flow with material failure, which must account for the interactions of several cracks, both natural and man-made. Many of the questions on the effects these interactions have on the performance of the frac treatments are unanswered. We develop a continuum thermodynamics framework for fluid flow through a damaging porous medium in order to represent some of the processes and interactions that occur during hydraulic fracturing. The model will be capable of simulating both Stokes flow through cracks and Darcy flow through the porous medium. The flow is coupled to the deformation of the bulk solid medium and the evolution of cracks within the material. We utilize a finite deformation framework in order to capture the opening of the fractures, which can have substantial effects on fluid pressure response. For both models, a fully coupled non-linear finite element formulation is constructed. Several benchmark solutions are investigated to validate the expected behavior and accuracy of the method. In addition, a number of interesting problems are investigated in order to demonstrate the ability of the method to respond to various complexities like material anisotropy and the interaction of multiple cracks.
Phenomenological constitutive modeling and numerical analysis of fracture toughness for shape memory alloys
(2022-05-02) Alsawalhi, Mohammed Yousuf; Landis, Chad M.; Foster, John T; Ravi-Chandar, Krishnaswamy Ravi; Mear, Mark E; Kyriakides, Stelios
Nickel titanium (NiTi) alloys possess unique characteristics that provide them the ability to recover large mechanical strains up to 8%. Pseudoelasticity and the shape memory effect are phenomena associated with SMA behavior. Shape recovery is driven by thermomechanical loading/unloading during the martensitic phase transformation. NiTi behavior also exhibits the property of asymmetry in transformation stress and transformation strain between the tension and compression responses as a result of forward and reverse phase transformations, as well as the reorientation and detwinning of the martensite phase. Furthermore, the process of heat generation during phase transformation near a crack tip effects the local temperature variations and thus the fracture toughness of the material. A new thermomechanical constitutive modeling approach for shape memory alloys (SMAs) that undergo a martensite to austenite phase transformation is presented. The novelty of this new formulation is that a single transformation surface is implemented in order to capture the main aspects of SMAs including forward transformation, reverse transformation, and martensite reorientation. Specific forms for the transformation surface and the transformation potential are devised and results for the behaviors captured by the model are provided for a range of thermomechanical loadings. The validity of the model is assessed with experimental studies of complex thermomechanical proportional and non proportional load paths at different temperatures using numerical simulations. The phenomenological constitutive model is implemented in finite element calculations and applied to the pseudoelastic and shape memory effects of a beam in pure bending. Fracture analysis is implemented within finite element computations to model the toughening due to the austenite to martensite phase transformation and martensite reorientation during steady mode I crack growth. Several dimensionless parameters relating the thermomechanical parameters of the constitutive model, the crack growth velocity, and the prevailing sample temperature are identified and applied to study the thermomechanical crack tip fields and the toughening enhancement due to the forward and reverse phase transformations in the vicinity of the crack tip. The first part of this dissertation involves validation of the model by comparisons of numerical simulations with experimental data and by developing consistent tangent moduli and applying the model to simple structural analysis of pure beam bending. First, uniaxial tensile and compressive stress-strain responses are simulated at four different temperatures: below the martensite finish temperature, between the martensite start and austenite start temperatures, between the austenite start and austenite finish temperatures, and above the austenite finish temperature. The numerical model reproduces the major aspects of the experimental measurements including the stress and strain levels. The transformation stress and transformation strain asymmetry between the tensile and compressive responses is also implemented in the model. The second problem investigates the performance of the model for a NiTi tube under a square axial-shear strain load path. The asymmetric model outperforms the symmetric model by reproducing the main features observed in the experiments. However, there is a notable difference in the magnitudes of stresses, mainly the shear stress, due to the anisotropy of the SMA material which is not accounted for in this model. The third problem examines the behavior of the constitutive model for tension-torsion of SMA wires for temperatures at the martensite and austenite phases. Again, the asymmetric model performs better than the symmetric model in terms of fitting the model response to the experimental measurements. The exclusion of anisotropy from the constitutive model has noticeable impact on the axial strain behavior at high temperatures. Lastly, the final problem investigates the pseudoelastic and shape memory behaviors of a beam under pure bending. The analysis in each case captures the moment-curvature and the temperature-curvature responses, as well as the axial stress distribution through the cross-section of the beam. The asymmetric model produced asymmetry in the axial stress distribution that fits the behavior of real SMAs. The second part of this dissertation involves fracture computations to analyze the toughening due to the stress-induced martensitic transformation and martensite reorientation during steady mode I crack growth. First, analyses are performed on the sizes and shapes of the various transformed zones near the crack tip for a range of temperatures analyzed. Secondly, the uniaxial stress-strain response is impacted by the thermomechanical parameters in the constitutive model which results in a relatively strong dependence of the transformation toughening on the material parameters. Next, numerical simulations are used to illustrate the effects of crack growth speed and heat capacity on the toughening. Finally, different sample temperatures show the strong impact on the toughness enhancement due to phase transformation. The last part of this dissertation discusses different approaches for material modeling, including different formulations associated with the transformation potentials and the associated integration routines. The first approach introduces a new internal variable that is a function of the other two in an attempt to control the pure shear stress-strain response as being a mixture between the tensile and compressive responses. The second approach introduces two stress invariants that are a linear or non-linear combination of the strain invariant. Here the objective is to control how fast the strain invariant goes towards uniaxial tension in a pure shear loading in order to allow the pure shear response to be a controlled mixture between the tensile and compressive responses as opposed to having similar behavior to the tensile response. The last approach for the integration algorithm utilizes a classical elastic prediction-transformation correction return mapping. This method simplifies the number of unknowns solved in the integration routine to just one. Therefore, a 1-D Newton-Raphson (NR) scheme is used which allows for more robust numerical calculations.