Fracture Nucleation Research Articles

Thermo-mechanical modelling of spalling around the deposition boreholes in an underground nuclear waste repository during its thermal phase

This paper presents a three-dimensional numerical analysis of multiple fracture growth leading to the development of excavation disturbed zones and spalling around deposition boreholes in a geological disposal facility. The development of fracture patterns is simulated with the Imperial College Geomechanics Toolkit, a finite-element based simulator that can model the simultaneous nucleation, growth, and coalescence of multiple fractures in quasi-brittle rock. In these simulations, fractures develop due to the stress concentrations around the borehole wall, caused by the local in situ stresses, and due to the thermal stresses caused by the radioactive decay of the waste. Fracture patterns, and the extent of the spalled zone, are computed after the borehole drilling, heating, and cooling stages, at the Forsmark repository site in Sweden. The effect of temperature on the nucleation and growth of spalling fractures, as well as on the reactivation of pre-existing fractures, is assessed qualitatively, by comparing fracture patterns, and quantitatively, in terms of the maximum spalling depth, width, and increase in the total fractured surface area. Overall, the simulations presented herein indicate that thermal spalling will increase the depths (away from the borehole) and angular widths of the spalled zone, but is not likely to lead to major increases in fracture aperture, and concomitant increases in hydraulic transmissivity and permeability of the spalled zone, above that which has already been caused by mechanical spalling.

Intergranular fracture, grain-boundary structure, and dislocation-density interactions in FCC bicrystals

A dislocation-density based crystalline plasticity (DCP) and nonlinear finite element (FE) analysis were used to predict, and fundamentally understand how and why fracture nucleation and propagation are related to the interrelated microstructural mechanisms of dislocation-density pileups, GB structure, orientation, and total and partial dislocation density interactions within and adjacent for a random low angle grain boundary (LAGB) and a random high angle GB (HAGB). The GB orientations and structures were obtained from micropillar experiments, such that LAGBs and the HAGBs can be accurately represented and used for the modeling predictions. The normal stress, density of pileups, and dislocation-density accumulation along and within the GB were higher for the low angle GB bicrystal. These interrelated phenomena delineate how fracture for high angle GBs nucleate and propagate at lower nominal strains than the lower angle GB bicrystal case. These predictions underscore how fundamental mechanisms can be identified and used to understand how failure nucleates and propagates for different GB structures and orientations.

Numerical Modelling of the Influence of Tidal Stresses on Fracture Patterns on the Surface of Europa

AbstractJupiter’s satellite Europa is covered by an ice shell exhibiting many surface features, including linear structures called lineae, which in this work are treated as fractures. A three-dimensional finite-element simulator is used to numerically model fracture nucleation, growth, and interaction, assuming the ice is an isotropic, linear elastic medium. Tidal stresses are exerted upon the ice through the Jovian orbital relationship. These stresses are calculated using a closed-form model derived from first principles. The fractures grow in response to stress concentration around their tips, and a damage criterion models the weakening of the ice matrix. Three-dimensional non-planar multiple fracture growth is modelled as a function of geometric multi-modal stress intensity factors computed at the fracture tips. Fracturing is evaluated over multi-scale periods, from days to millions of years, thus capturing multiple tidal effects. Fracture behaviour is modelled across the Europan surface in one domain. The patterns are dense clusters of lineae about the stress maxima with diffuse fracturing in outlying regions. Fractures are also modelled in the vicinity of subsurface meltwater lenses, where fractures form parallel to the surface in contrast to the usual perpendicular orientation. The resultant fracture patterns are qualitatively compared against images from NASA’s Galileo mission. This work contributes to the understanding of Europan lineae by illustrating how they behave in a fracture mechanics framework, and suggests interesting results regarding lineae interaction with meltwater lenses. This work is also a proof of concept for this modelling approach, and will serve as the framework for future work.

How are microstructural defect interactions linked to simultaneous intergranular and transgranular fracture modes in polycrystalline systems?

The major objective of this investigation is to fundamentally understand and predict how intergranular (IG) and transgranular (TG) fracture modes nucleate and propagate in f.c.c. polycrystalline systems due to defects, such as total and partial dislocation densities and grain boundary (GB) structures and misorientations. A dislocation density crystalline plasticity (DCP) formulation based on the evolution and interaction of total and partial dislocation densities was integrated with a recently developed fracture approach to investigate the fracture nucleation and propagation of simultaneous multiple fracture events, including both IG and TG fracture events. The aggregate grains and GB orientations and morphologies are based on EBSD measurements that are representative of polycrystalline copper aggregates with a broad range of random high angle and low angle GBs. The predictions indicate that dislocation density pileups induce IG fracture due to interrelated stress, slip, and total and partial dislocation density accumulations and interactions for both high angle GBs (HAGBs) and low angle GBs (LAGBs). TG fracture nucleation and propagation occurred due to normal stress accumulations, which exceeds the fracture stress, along cleavage planes. Furthermore, it is shown how IG cracks transition from the GB plane to the cleavage planes as cracks nucleate and propagate. Accumulated plastic zones due to different slip system activities can impede and blunt crack propagation and fronts. These plastic zones form due to high Lomer and Shockley partial dislocation densities. These predictions, which are consistent with experimental observations, provide a fundamental understanding of how simultaneous failure modes initiate and propagate for physically representative microstructures.

Strain energy dependent numerical simulation of rock fracture initiation and propagation using soundless cracking demolition agents (SCDA): Effects of SCDA-filled rock joints

Soundless Cracking Demolition Agents (SCDA) are gaining traction as an innovative technique for controlled rock fracturing in applications such as underground energy, mineral extraction, and excavation. This paper presents a novel numerical approach to simulate SCDA-charged rock fracture initiation using the strain energy density of SCDA. This approach eliminates the need for prior knowledge of the peak expansive pressure developed in a rock, a common requirement in conventional SCDA modelling. An empirically derived model is presented which captures the rate of energy release in SCDA as a function of applied strain to the surrounding material. The model was implemented in the 3-dimensional Distinct Element Code by applying an exponential strain-rate decay function. The proposed fracture stimulation method accurately mimics the expansion behaviour and finite strain energy release from SCDA expansion. The method was extended to simulate SCDA expansion in rock joints. The SCDA expansion method was assessed by creating a numerical model in which a central injection well was intersected by a horizontal joint and SCDA expansion was simulated in the injection well and the joint. The simulations were verified against laboratory fracture experiments. The model was extended to evaluate the fracturing performance of SCDA under varying joint roughness and confining pressures. SCDA expansion in rock joints introduces an additional compressive stress field that inhibits fracture initiation and propagation near the joint. Increasing fracture roughness suppressed fracture growth, but led to more fracture nucleation points around the injection well and shear damage at the joint interface. The simulation method employed shows sensitivity to confining pressures and simulates the fracturing potential of SCDA in different rocks subjected to confining pressures without requiring further calibration of the SCDA expansion parameters. The proposed numerical simulation method improves the accuracy in investigating the fracturing potential of expansive agents over existing simulation methods for SCDA.

A multiscale preconditioner for crack evolution in porous microstructures: Accelerating phase‐field methods

AbstractPhase‐field methods are attractive for simulating the mechanical failure of geometrically complex porous microstructures described by 2D/3D x‐ray CT images in subsurface (e.g., CO storage) and manufacturing (e.g., Li‐ion battery) applications. They capture the nucleation, growth, and branching of fractures without prior knowledge of the propagation path or having to remesh the domain. Their drawback lies in the high computational cost for the typical domain sizes encountered in practice. We present a multiscale preconditioner that significantly accelerates the convergence of Krylov solvers in computing solutions of linear(ized) systems arising from the sequential discretization of the momentum and crack‐evolution equations in phase‐field methods. The preconditioner is an algebraic reformulation of a recent pore‐level multiscale method (PLMM) by the authors and consists of a global preconditioner and a local smoother . Together, and attenuate low‐ and high‐frequency errors simultaneously. The proposed , used in the momentum equation only, is a simplification of a recent variant proposed by the authors that is much cheaper and easier to deploy in existing solvers. The smoother , used in both the momentum and crack‐evolution equations, is built such that it is compatible with and more robust and efficient than black‐box smoothers like ILU(). We test and systematically for static‐ and evolving‐crack problems on complex 2D/3D porous microstructures, and show that they outperform existing algebraic multigrid solvers. We also probe different strategies for updating as cracks evolve and show the associated cost can be minimized if is updated adaptively and infrequently. Both and are scalable on parallel machines and can be implemented non‐intrusively in existing codes.

Control of Mechanical and Fracture Properties in Two-Phase Materials Reinforced by Continuous, Irregular Networks.

Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the behavior of materials with an irregular reinforcement phase offers fundamental guidelines for tailoring their performance. Here, the fracture nucleation and propagation in two phase composites, as a function of the topology of their irregular microstructures is studied. A stochastic algorithm is used to design the polymeric reinforcing network, achieving independent control of topology and geometry of the microstructure. By tuning the local connectivity of isodense tiles and their assembly into larger structures, the mechanical and fracture properties of the architected composites are tailoredat the local and global scale. Finally, combining different reinforcing networks into a spatially determined meso-scale assembly, it is demonstrated how the spatial propagation of fracture in architected composite materials can be designed and controlled a priori.

Microseismic Monitoring of the Fracture Nucleation Mechanism and Early Warning for Cavern Rock Masses

The rock mass is susceptible to instability and damage during cavern construction. The blast-induced cracking process of the rock mass contains a wealth of information about the precursors of instability, and the identification of fracture nucleation signals is a prerequisite for effective hazard warning. A laboratory mechanical test and microseismic (MS) monitoring were carried out in the Baihetan Cavern to investigate the fracture nucleation process in the rock mass. MS monitoring shows that pre-existing microcracks were closed or new cracks were generated under the action of high stress, which caused the migration of microcracks. As the crack density increases, the fracture interaction gradually increases. The study of the rock fracture nucleation mechanism helps to reveal the MS sequences during the rock fracture process, and the fore-main shock was found in the MS sequence during access tunnel excavation. This study can effectively provide guidance for the early warning of rock mass failure and the stability analysis of underground caverns under blasting excavation disturbance.

A phase‐field model for hydraulic fracture nucleation and propagation in porous media

AbstractMany geo‐engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase‐field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase‐field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy‐based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase‐field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase‐field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. The comparison of numerical results for two‐dimensional test cases with existing analytical solutions demonstrates that the proposed phase‐field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three‐dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

An enriched mixed finite element model for the simulation of microseismic and acoustic emissions in fractured porous media with multi‐phase flow and thermal coupling

AbstractA novel mixed enriched finite element model is developed for coupled non‐linear thermo‐hydro‐mechanical simulation of fractured porous media with three‐phase flow and thermal coupling. Simulation of induced acoustic emission (AE) and microseismic emission (ME) due to tensile fracturing and shear slip instability of pre‐existing fracture interfaces is carried out and the numerical results of the emitted signals are analysed. The mathematical model is based on the generalized Biot's theory for coupled interaction of solid and fluid phases. A computationally robust non‐linear solver is developed to handle the severe non‐linearities arising from fluid saturations, relative permeabilities of fluids, constitutive models of interfaces and convective thermal coupling. To model pre‐existing natural fractures and faults, discrete fracture propagation and nucleation of cracks (micro‐cracking) independently of the original mesh topology, a local Partition‐of‐Unity (PU) finite element method, namely, the Phantom Node Method (PNM) is implemented. The cohesive fracture modelling scheme is implemented to account for the non‐linear behaviour of fracturing and localization, and to rectify the non‐physical stress singularity condition at the fracture tip. Effects of different system parameters on fracturing, shear‐slip instability and the associated induced AEs and MEs are investigated through various numerical results.

How can machine learning be used for accurate representations and predictions of fracture nucleation in zirconium alloys with hydride populations?

Zirconium alloys are critical material components of systems subjected to harsh environments such as high temperatures, irradiation, and corrosion. When exposed to water in high temperature environments, these alloys can thermo-mechanically degrade by forming hydrides that have a crystalline structure that is different from that of zirconium. Cracks can nucleate near these hydrides; hence, these hydrides are a direct link to fracture failure and overall large inelastic strain deformation modes. To fundamentally understand and predict these microstructural failure modes, we interrogated a finite-element database that was deterministically tailored and generated for large strain-dislocation-density crystalline plasticity and fracture modes. A database of 210 simulations was created to randomly sample from a group of microstructural fingerprints that encompass hydride volume fraction, hydride orientation, grain orientation, hydride length, and hydride spacing for a hydride that is physically representative of an aggregate of a hydride population. Machine learning approaches were then used to understand, identify, and characterize the dominant microstructural mechanisms and characteristics. We first used fat-tailed Cauchy distributions to determine the extreme events. A multilayer perceptron was used to learn the mechanistic characteristics of the material response to predefined strain levels and accurately determine the critical fracture stress response and the accumulated shear slips in critical regions. The predictions indicate that hydride volume fraction, a population-level parameter, had a significant effect on localized parameters, such as fracture stress distribution regions, and on the accumulated immobile dislocation densities both within the face centered cubic hydrides and the hexagonal cubic packed h.c.p. matrix.

Proposal of a hydrogen embrittlement index for a martensitic advanced high-strength steel

This paper proposes a definition of a Hydrogen Embrittlement Index for assessing structural components made by a martensitic advanced high-strength steel. A material model, including a damage model and a fracture criterion, was developed to reproduce the tensile behaviour until fracture nucleation under different hydrogen concentrations. The analysis of the tests with different specimen geometries demonstrated that the maximum principal strain at fracture is correlated to hydrogen concentration, and it can be used to define the embrittlement index for quantifying the hydrogen susceptibility of material in a wide range of notch severity.

Effect of a singular planar heterogeneity on tensile failure

Many rocks contain planar heterogeneities, in the form of open fractures, veins and/or stylolites, but scarce data exist on how strength and fracture pattern formation is affected by the presence of a singular planar heterogeneity in an otherwise uniform matrix. The mechanics of stylolite-bearing and/or fractured limestone is of interest to several engineering applications, from quarries to subsurface gas or geothermal reservoirs. We have performed Brazilian Disc tests on pre-fractured Indiana limestone samples and Treuchtlinger Marmor discs which contain cohesive stylolites, investigating Brazilian test Strength and the resulting fracture pattern. All experiments were filmed, and where possible analyzed with particle image velocimetry. When viewed in 2D, the planar discontinuity was set at different rotation angles compared to the principal loading direction, where perpendicular to the loading direction is defined as 0⁰. The results show that all samples are weaker than their intact counterparts. For the pre-fractured Indiana limestone, there is 10–75% angle-dependent weakening. However, in the samples with a stylolite, strength is weakened by 35–75%, independent of direction. Several new cracks appeared when fracturing a stylolite-sample, where the orientation is heavily influenced by the stylolite orientation. The fracture pattern and associated stress drops are more complex for high angles. In these samples always more than one fracture formed, whereas in pre-fractured samples usually only one new fracture formed. This suggests a potential for more permeability increase when hydrofracturing a stylolite-rich interval. Comparison with Finite Element Models indicates that this difference in fracture pattern is caused by the strength contrast between the anastomosing stylolite zone and the matrix material, leading to stress concentrations effects. This causes (micro-) fracture nucleation to occur locally, promotes fracture coalescence and fracture growth at lower overall sample-load conditions compared to intact samples.

Effect of fluid pressure on adhesive wear of spherical contact

Lubrication with fluid between two rough surfaces has been extensively studied, while the present work provides an additional principle for its effect on adhesive wear reduction associated with the fluid pressure. In this work, a finite element model for elastoplastic spherical contact with fluid pressure applied on surface is established, considering the realistic ductile failure criteria. It is found that as the fluid pressure increases, the location of fracture nucleation in the front contact region moves towards the contact surface. Two wear modes, namely the detaching and scratching modes, are identified by defining a critical dimensionless fluid pressure. Accordingly, the wear coefficient decreases as the fluid pressure increases, serving as the additional principle for wear reduction in lubrication systems.

Strengthening and failure of iron-graphene composites: A molecular dynamics study

In order to contribute to the understanding of advanced materials with improved mechanical properties we investigate strengthening and failure processes in iron-graphene composites using molecular dynamics simulations. Graphene sheets are embedded in {110} planes of bulk iron. Tensile tests and shear tests are conducted and evaluated with regard to the orientation of the graphene sheet. It is found that two different failure mechanisms involving interfacial fracture and dislocation nucleation can occur due to tensile load. The shear tests revealed three mechanisms of dislocation-obstacle interaction. The highest strengthening was found for graphene sheet orientations which normal vectors are not orthogonal to the Burgers vector of the interacting dislocation.

Robustness of Rock Damage Regions Induced by Crack Nucleation

The stress-induced fracture of brittle rocks, as a result of macrocrack evolution, is closely related to the evolution of microcracks. The study of such damage processes provides information about the mechanical behavior of rock cracks. In this study, we conducted research with respect to macrocracks using hypothetical damage regions constituted by correlated microcracks. A Gaussian mixture model was applied to describe the spatial distribution of microcracks. The Kullback–Leibler divergence was used to characterize the geometric variation of damage regions. The results showed that the robustness of the damage region’s geometry became increasingly higher during the damage evolution and the damage region became unchanged after some time. The robustness of the damage regions could be an indicator of the nucleation of macrocracks. Moreover, a fracture nucleation indicator methodology was developed to calculate the point at which nucleation was formed. This study is considered to enhance the understanding of macrocrack nucleation and it is useful to the application of macrocrack recognition and prediction.

Intraplate records of a transform margin formation: Brittle deformation in the basement of the basins from the northeastern extremity of the Brazilian equatorial margin

The diachronous rifting of the Pangea supercontinent, with the dispersion of the continental masses, resulted in the formation of numerous rift systems, which primarily evolved into passive margins, such as the Brazilian Equatorial Margin (BEM). In the South American counterpart, basement structures serve as the primary markers for direct analysis of the nucleation and development of the BEM since much of the rift record occurs in the subsurface. The geodynamic models that explain the evolution of this margin are largely based on geophysical and numerical modeling data. In this paper, we carried out an onshore, multitool, and multiscale structural analysis of the brittle deformation overprinted on the Precambrian basement of the Potiguar and Ceará basins, which led to the proposition of four superimposed events. The D1 event (Late-Brasiliano) is mainly represented by the NE-SW (dextral) stepped fracture systems and the unfilled and quartz- or chalcedony-filled NE-SW to E-W-trending extensional joints. This event is related to NE-SW intraplate transpression, associated with the progressive exhumation of the Brasiliano-Pan African orogenic belt. The D2 event (Jurassic to early Aptian) represents the intracontinental deformation related to the initial rupture of the Pangea. The brasiliano-age ductile shear zones were reactivated (brittle) along with the development of NE-SW normal faults, NNE-SSW en échelon fractures, NE-SW joints, as well as the emplacement of the basic dykes (NE-SW and E-W) related to the Rio Ceará-Mirim magmatism. This event is associated with the NW-SE extension responsible for the origin of the Cariri-Potiguar trend basins. At the beginning of the installation of the equatorial proto-margin, a significant cataclastic process took place, marking the D3 event (post-early Aptian). This enabled the nucleation of hybrid (WNW-ESE, E-W, and NW-SE), shear fractures (WNW-ESE, NNW-SSE, E-W, NNE-SSW, and ENE-WSW), and NW-SE unfilled or filled (chalcedony, iron oxide and hydroxide, and calcite) dilatational joints, which express an E-W dextral transtensional regime related to this event. E-W and NW-SE pull-apart dilatational jogs are characteristic of this event and may be analog to the E-W Messejana and Jacaúna transtensional grabens (western part of the Potiguar Basin). The younger event (D4) is characterized by N–S normal faults and joints, and dry or filled (calcite and iron oxide/hydroxide) NNW-SSE hybrid shear fractures. A clockwise rotation of the South American plate with respect to the African plate and the paleostress field change to N–S compression and E-W extension, are responsible for the formation of D4 structures. The brittle structures developed in the crystalline basement of the Potiguar and Ceará basins represent the intracontinental record of the deformation related to the formation of the Atlantic equatorial margin under a dextral transtensional regime.

Detection of prefracture zones in structural materials by magnetic and optical methods

The study of the applicability of magnetic and optical methods to the detection of prefracture zones under fatigue degradation of structural materials is exemplified by the 09G2S steel. The regularities of changes in the signal of an attached fluxgate gradiometer with the increasing number of loading cycles have been revealed; namely, significant changes in the gradiometer readings on individual specimen surface areas prove to result from the formation of fracture zones. The change in the value of the coefficient of correlation among the speckle images is studied at different stages of cyclic testing. Speckle image heterogeneity is shown to appear due to fracture nucleation. Thus, the applicability of magnetic and speckle-interferometric methods to detecting prefracture zones in objects under cyclic loading is substantiated.

Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness

It is now a well-established fact that even simple topology variations can drastically change the fracture response of structures. With the objective of gaining quantitative insight into this phenomenon, this paper puts forth a density-based topology optimization framework for the fracture response of structures subjected to quasistatic mechanical loads. One of the two key features of the proposed framework is that it makes use of a complete phase-field fracture theory that has been recently shown capable of accurately describing the nucleation and propagation of brittle fracture in a wide range of nominally elastic materials under a wide range of loading conditions. The other key feature is that the framework is based on a multi-objective function that allows optimizing in a weighted manner: (i) the initial stiffness of the structure, (ii) the first instance at which fracture nucleates, and (iii) the energy dissipated by fracture propagation once fracture nucleation has occurred. The focus is on the basic case of structures made of a single homogeneous material featuring an isotropic linear elastic behavior alongside an isotropic strength surface and toughness. Novel interpolation rules are proposed for each of these three types of material properties. As a first effort to gain quantitative insight, the framework is deployed to optimize the fracture response of 2D structures wherein the fracture is bound to nucleate in three different types of regions: within the bulk, from geometric singularities (pre-existing cracks and sharp corners), and from smooth parts of the boundary. The obtained optimized structures are shown to exhibit significantly enhanced fracture behaviors compared to those of structures that are optimized according to conventional stiffness maximization. Furthermore, the results serve to reveal a variety of strengthening and toughening mechanisms. These include the promotion of highly porous structures, the formation of tension-compression asymmetric regions, and the removal of cracks and sharp corners. The particular mechanism that is preferred by a given structure, not surprisingly, correlates directly to the elastic, strength, and toughness properties of the material that is made of.

Inhibition of Heterogeneous Nucleation in Water by Hydrogel Coating.

Heterogeneous nucleation plays a critical role in the phase transition of water, which can cause damage in various systems. Here, we report that heterogeneous nucleation can be inhibited by utilizing hydrogel coatings to isolate solid surfaces and water. Hydrogels, which contain over 90% water when fully swelled, exhibit a high degree of similarity to water. Due to this similarity, there is a great energy barrier for heterogeneous nucleation along the water-hydrogel interface. Additionally, hydrogel coatings, which possess polymer networks, exhibit higher fracture energy and more robust adhesion to solid surfaces compared to water. This high fracture and adhesion energy acts as a deterrent for fracture nucleation within the hydrogel or along the hydrogel-solid interface. With a hydrogel layer approximately 100 μm thick, the boiling temperature of water under atmospheric pressure can be raised from 100 to 108 °C. Notably, hydrogel coatings also result in remarkable reductions in cavitation pressure on multiple solid surfaces. We have demonstrated the efficacy of hydrogel coatings in preventing damages resulting from acceleration-induced cavitation. Hydrogel coatings have the potential to alter the energy landscape of heterogeneous nucleation on the water-solid interface, making them an exciting avenue for innovation in heat transfer and fluidic systems.