Plane Strain Fracture Research Articles

Finite domain solution of a hydraulic fracture in a permeable rock

In this work, we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium. The algorithm utilizes a domain-based method to solve the elasticity equations and integrates a multi-scale tip asymptote, which is particular to hydraulic fractures, into this framework. This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region. The algorithm combines a 2D finite volume method (FVM) for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation. Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme. The paper concludes with an analysis of the numerical results. This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.

Thickness Effect of 2195 Al-Li Alloy Friction Stir Weld Fracture Toughness.

For damage tolerance design in engineering components, the fracture toughness value, KIC, of the material is essential. However, obtaining specimens of sufficient thickness from stir friction welded plates is challenging, and often, the experimental test values do not meet the necessary criteria, preventing the experimental fracture toughness, Kq, from being recognized as plane strain fracture toughness KIC. The fracture toughness Kq of 2195 Al-Li alloy welding seams with different thicknesses was measured on the forward and backward sides. Microstructure characterization was conducted by scanning electron microscope (SEM). The results indicated minimal significant differences in grain size between the advancing and retreating sides of the weld nugget zone. In specimens of the same thickness, fracture toughness measurements along the normal direction of the joint cross-section showed a high similarity between the advancing and retreating sides of the weld nugget zone. Utilizing the quantitative relationships between fracture toughness and sample thickness derived from both the fracture K and G criteria, it is possible to predict the fracture toughness of thick plates using thin plates. This study employs these relationships to calculate the fracture toughness KIC of 2195 aluminum-lithium alloy friction stir welds. The KIC values obtained are 41.65 MPa·m1/2 from the fracture K criterion and 43.54 MPa·m1/2 from the fracture G criterion.

Coupled peridynamic modeling of hydraulic fracturing in rocks

This paper presents a fully coupled peridynamics method for simulating hydraulic fracturing in rocks. The proposed method involves a rigorous coupling between the classical total-Lagrangian formulation and a new semi-Lagrangian formulation within the framework of peridynamics. The total-Lagrangian formulation is employed to simulate a rock subjected to fluid-driven fracturing, whereas the semi-Lagrangian formulation is used to solve the Navier–Stokes equations for fluids in a nonlocal manner. A coupling algorithm is developed between the two formulations to model fluid–solid interactions without causing unphysical penetration. The proposed method was validated through a simulation of a water column collapse problem. It was further validated using a Kristianovich–Geertsma–De Klerk (KGD) fracturing problem, where a plane strain fracture propagates owing to fluid injection. The proposed method reasonably captures the fracturing pattern, fracture propagation speed, and injection pressure better than the analytical solution. It offers a unified framework within the peridynamics theory for modeling solid, fluid, and fluid-driven fractures.

Strength and Fracture Toughness of Type 304 and 316 Austenitic Stainless Steels at 4.2 K

The tensile properties and fracture toughness of type 304L, 316L and 316LN austenitic stainless steels and their weldments at cryogenic temperatures have been summarized in the literature. Rolled plates showed a trade-off relationship between 0.2% proof stress and planestrain fracture toughness with those at 4.2 K. The 0.2% proof stress increases with increasing C+N content, and the fracture toughness depends on their austenite stability to α’-martensitic transformation at the crack tip. The formation of shear bands at low strains is directly related to fracture toughness. The stacking fault energy represents the shear-band formation as well as slip deformation manner, so alloy design with higher Ni, Mn, and Mo contents in the chemical composition range of 316LN would be desirable to improve fracture toughness due to higher stacking fault energy.

Experimental investigation on the fatigue and fracture properties of a fine pearlitic rail steel

This study reports an experimental investigation of the fatigue and fracture resistance of R350HT, a heat-treated pearlitic rail steel with refined microstructure used in rails. Monotonic tensile, rotating bending, linear elastic plane strain fracture toughness, and fatigue crack growth rate tests are presented. The results are used to outline the basic properties and are corroborated by fractographic investigation. This enables the identification of the dominant type of fracture. Regarding fatigue and fracture resistance, the investigated material shows similar properties as other pearlitic rail steels, such as R260. At room temperature, the dominating fracture is of brittle cleavage type, showing some ductile regions associated with pro-eutectoid.

An approach to coupling the gas flow dynamics and thermodynamics of hydrogen solubility in L485ME steel grade for estimation of fracture toughness

The paper presents the problem of coupling the gas flow dynamics in pipelines with the thermodynamics of hydrogen solubility in steel for the estimation of the fracture toughness. In particular, the influence of hydrogen blended natural gas transmission on hydrogen solubility and, consequently, on fracture toughness is investigated with a focus on the L485ME low-alloy steel grade. Hydraulic simulations are conducted to obtain the pressure and temperature conditions in the pipeline. The hydrogen content is calculated from Sievert’s law and, as a consequence, the fracture toughness of the base metal and heat-affected zone is estimated. Experimental data is used to define hydrogen-assisted crack size propagation in steel as well as to a plane strain fracture toughness. The simulations are conducted for a real natural gas transmission system and compared against the threshold stress intensity factor. The results showed that the computed fracture toughness for the heat-affected zone significantly decreases for all natural gas and hydrogen blends. The applied methodology allows for identification of the hydrogen-induced embrittlement susceptibility of pipelines constructed from thermomechanically rolled tubes worldwide most commonly used for gas transmission networks in the last few decades.

Fatigue crack growth properties of PMMA material used in underwater transparent structures

ABSTRACT Polymethyl methacrylate (PMMA) is an ideal material used in underwater transparent structures such as submersible windows and the fully-transparent pressure chamber of the sightseeing submersibles. The failure of PMMA structures usually come from small crack-like defects. In this paper, the fatigue crack growth experiments were carried out on PMMA materials with different thicknesses (B = 3, 6, 12 mm) and stress ratios (R = 0.1, 0.3) as well as plane strain fracture toughness test for unstable crack propagation conditions. Thickness effect and dwell time effect are experimentally investigated in addition to load ratio effect. The applicability of an improved crack growth rate model on PMMA material is validated by test results. The application of this model for prediction of crack growth rates can greatly save experimental time under different working conditions and can be applied in fatigue assessment of full-transparent structures under random loading.

Fracture parameters of woven jute fibre reinforced axial flow fan blade material: an experimental investigation and FEA analysis

Airflow required for the heat and mass transfer in industrial applications is often provided by axial flow fans. Glass fibre reinforced polymers (GFRP) are most often used to make these fan blades. The usage of glass fibres in composite materials is growing. By 2025, the global market for glass fibres will be worth 16.5 billion pounds. However, non-biodegradable composite reinforcement has major ecological and human health concerns, especially when reaching the end of its operational lifespan. Until now, industries have shown a strong inclination to use GFRP without adequately contemplating the potential consequences associated with their disposal. The economic viability of glass fibre recycling is questionable. However, natural fibres like jute and fibres extracted from vegetable plants are of much popular among academics and researchers due to their sustainability and ease of use. So, they’re suitable for making polymer composites. The amount of natural fibres that may be added to GFRP composites without materially altering their mechanical characteristics is a crucial factor in improving their decreased embodied emissions and biodegradability after service life. In this work the material represents an 18-ft axial flow fan blade material made of GFRP. This study used the term denotes the specific material utilised in the fabrication of 18-feet axial flow fan blades for industrial purposes. By substituting one layer of with woven jute and changing its position in it, the materials through are produced. All the materials are tested for fracture parameters like plane strain fracture toughness and Critical strain energy release rate as per ASTM D-5045. The results were validated by using finite element models implemented in a commercially available software ANSYS R19.2. The optimal layup sequence for fan blade material with single-layer woven jute reinforcement was found, which preserves fracture properties, also improves biodegradability after service life.

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

High-strength and high-toughness austenitic stainless steels based on type 316LN at 4.2 K

High-strength and high-toughness prototype steel forgings, N2, N3, and N4, were developed based on type 316LN as a cryogenic structural material. By extrapolating the proportional relationship between carbon plus nitrogen content (C + N) and 0.2 % proof stress (σ0.2) in the range of approximately 0.10–0.25 mass% C + N content, the C + N content was successfully designed to achieve the target σ0.2. To suppress the degradation of the plane-strain fracture toughness (KIC(J)) while increasing the nitrogen solid-solution content, the alloying level was designed by considering the stability of the austenite phase and stacking fault energy. The steel forgings showed a good balance of strength and toughness at 4.2 K, i.e., N2 (σ0.2 = 1142 MPa, KIC(J) = 228 MPa√m), N3 (σ0.2 = 1226 MPa, KIC(J) = 219 MPa√m) and N4 (σ0.2 = 1296 MPa, KIC(J) = 215 MPa√m). The σ0.2 and KIC(J) of ITER-grade 316LN (316LNL, 316LNM, and 316LNH) thick plates with low interstitial (C + N) content of 0.13–0.17 mass% were also evaluated at 4.2 K. Then, the effects of nitrogen content on strength and fracture toughness were successfully clarified in the full range of interstitials concentrations. An alloy design with higher Ni, Mn, and Mo contents in the chemical composition range of 316LN would be desirable for improving the fracture toughness by increasing σ0.2 due to the higher nitrogen content.

Coalescence of thermal fractures initiated at parallel cooling surfaces

PurposeThermal fractures initiated under cooling at the surfaces of a 2-D or 3-D structure propagate, arrest and coalesce, leading to its structural failure and material-property changes, while the same processes can happen in the rock mass between parallel hydraulic fractures filled with cold fluid, leading to enhanced fracture connectivity and permeability.Design/methodology/approachThis study used a 2-D plane strain fracture model for mixed-mode thermal fractures from two parallel cooling surfaces. Fracture propagation was governed by the theory of linear elastic fracture mechanics, while the displacement and temperature fields were discretized using the adaptive finite element method. This model was validated using two numerical benchmarks with strong fracture curvature and then used to simulate the propagation and coalescence of thermal fractures in a long rock mass.FindingsModeling results show two regimes: (1) thermal fractures from a cooling surface propagate and arrest by following the theoretical solutions of half-plane fractures before the unfractured portion decreases to 20% rock-mass width and (2) some pairs of fractures from the opposite cooling surfaces tend to eventually coalesce. The fracture coalescence time is in a power law with rock-mass width.Originality/valueThese findings are relevant to both subsurface engineering and material engineering: structure failure is a key concern in the latter, while fracture coalescence can enhance the connectivity of thermal and hydraulic fractures and thus reservoir permeability in the former.

Characterization and Prediction of Plane Strain Bendability in Advanced High-Strength Steels

The rapid development of new classes of automotive steels such as the 3rd generation of advanced high-strength steels has created the need for the efficient characterization of their mechanical properties in loading scenarios other than uniaxial tension. The VDA 238-100 tight radius bend test has gained widespread acceptance in recent years for characterizing performance in plane strain bending, but there is uncertainty surrounding the use of the bend angle and its interrelation with the test parameters. The objective of the present study is to investigate the intertwined effects of the sheet thickness, bend radius, and tensile properties upon the bendability of seven advanced high-strength steels in different thicknesses for a total of 83 conditions. Practical correlations are developed to predict the bend angle and plane strain fracture strain as functions of the bending conditions and tensile mechanical properties. An extensive dataset comprising 26 additional advanced high-strength steel test cases was compiled from the literature to evaluate the proposed correlation for the plane strain fracture strain.

Effect of bimodal microstructure on the tensile properties and fracture toughness of extruded Mg-9Gd-4Y-0.5Zr alloy

The effects of bimodal microstructure on the tensile properties and fracture toughness of Mg-9Gd-4Y-0.5Zr alloys were investigated. The Mg-9Gd-4Y-0.5Zr alloy was extruded at different temperatures to produce samples with bimodal and fully dynamic recrystallized (DRXed) grain structures. The results show that the bimodal grain structure exhibits a better combination of yield strength (YS of 277 MPa) and plane strain fracture toughness (KIc = 21.5 MPa m1/2), compared to the fully DRXed microstructure (YS of 207 MPa, KIc = 16.3 MPa m1/2). The fracture mechanisms for the bimodal and fully DRXed microstructures are the ductile fracture mode and quasi-cleavage fracture mode, respectively. Both hetero-deformation induced (HDI) strengthening effect and strong basal texture can contribute to high tensile strength in the bimodal grain structured sample. As compared to the sample with fully DRXed microstructure, the stronger strain hardening capacity and larger hardened region around the crack tip in the bimodal grain structured sample can bring about the improvement in the fracture toughness. The tortuous crack propagation path and the hindrance of propagating crack by the un-DRXed grains result in larger fracture resistance and more energy dissipation. The increase of geometrically necessary dislocation (GND) density and the activation of non-basal dislocations also have positive effects on the fracture toughness of the samples with bimodal grain structure. The fracture toughness is effectively improved via intrinsic and extrinsic toughening mechanisms associated with the bimodal microstructure.

The Tensile Properties and Fracture Toughness of a Cast Mg-9Gd-4Y-0.5Zr Alloy

Low fracture toughness has been a major barrier for the structural applications of cast Mg-Gd-Y-Zr alloys. In this work, the tensile properties and fracture toughness of a direct-chill-cast Mg-9Gd-4Y-0.5Zr (VW94K) alloy were investigated in different conditions, including its as-cast and as-homogenized states. The results show that the tensile properties of the as-cast VW94K alloy are greatly improved after the homogenization treatment due to the strengthening of the solid solution. The plane strain fracture toughness values KIc of the as-cast and as-homogenized VW94K alloys are 10.6 ± 0.5 and 13.8 ± 0.6 MPa·m1/2, respectively, i.e., an improvement of 30.2% in KIc is achieved via the dissolution of the Mg24(Gd, Y)5 eutectic phases. The initiation and propagation of microcracks in an interrupted fracture test are observed via an optical microscope (OM) and scanning electron microscope (SEM). The fracture surfaces of the failed samples after the fracture toughness tests are examined via an SEM. The electron backscatter diffraction (EBSD) technique is adopted to determine the failure mechanism. The results show that the microcracks are initiated and propagated across the Mg24(Gd, Y)5 eutectic compounds in the as-cast VW94K alloy. The propagation of the main cracks exhibits an intergranular fracture pattern and the whole crack propagation path displays a zigzag style. The microcracks in the as-homogenized alloy are initiated and propagated along the basal plane of the grains. The main crack in the as-homogenized alloy shows a more tortuous fracture characteristic and a trans-granular crack propagation behavior, leading to the improvement of the fracture toughness.

Exceptional fracture toughness in a high-strength Mg alloy with the synergetic effects of bimodal structure, LPSO, and nanoprecipitates

Addressing the strength-toughness trade-off issue has been highly desirable for high strength Mg alloys. Herein, an Mg-9Gd-4Y-1Zn-0.5Zr (wt %) alloy is designed, and a yield strength of 430 MPa and plane-strain fracture toughness KIc of 23.1 MPa·m1/2 are achieved. Intrinsically, significant stress dissipation is induced by interactions between the tensile twinning and the kinking of the lamellar γ' phase, leading to increased KIc. Owing to the residual stress release, the fracture resistance is remarkably improved by the non-basal 〈a〉 and 〈c + a〉 dislocations activated in the fine dynamic recrystallized (DRXed) grains. Extrinsically, the microcracks initiated along the interfaces between lamellar γ' phase and α-Mg matrix facilitate the reduction of local crack-driving forces, resulting in an enhanced KIc. Moreover, the underlying toughening mechanisms were revealed, including the crack propagation path deflection caused by coarse deformed grains and microcrack shielding by the long-period stacking ordered (LPSO) and lamellar γ' phases.

Development of a low-carbon carbide-free nanostructured bainitic steel with extremely high strength and toughness

High-carbon carbide-free nano-bainitic steels show extremely high strength but relatively poor fracture toughness and welding prospects. Therefore, an attempt has been made to develop a strong and damage tolerant low-carbon bainitic steel in the current study by taking recourse to two-step austempering at 350 °C for 20 min and 250 °C for 7 h (20min-TS) and the properties have been compared with another block prepared using a single step transformation for 3 h at 350 °C (3hr-SS). Two stage heat-treatment leads to lath thickness refinement in addition to block refinement as compared to a single step transformation. Moreover, a NW misorientation developed in 20min-TS as compared to KS in a single-stage transformation. An average bainitic lath thickness below 100 nm in a steel having 0.26 wt% carbon has been obtained in 20min-TS which in turn results in an ultimate tensile strength of 1.5 GPa, percentage elongation of 18.5, impact energy of 31 J and plane-strain fracture toughness of 82 MPam−1/2. This is an around two and a half times increase in toughness without significantly compromising on the strength when compared to nanostructured bainitic steels produced in a similar duration of austempering for high carbon steels.

Integrated microseismic and geomechanical analysis of hydraulic fracturing induced fault reactivation: a case study in Sichuan Basin, Southwest China

Because of the special geographical location adjacent to the Tibetan Plateau, the geological setting of the Sichuan Basin is very complex, which brings a great challenge to shale gas development. In this study, we conducted an integrated microseismic and geomechanical analysis on a refracturing well in the Sichuan Basin. We observed that casing deformation occurred in the area of fault reactivation. However, the reactivation of pre-existing faults does not always cause casing deformation. In addition, a cluster of high-magnitude microseismic events will be triggered during the fault reactivation, which is also helpful to recognize the reactivated faults. Furthermore, according to the definition of b-value in the Gutenberg–Richter law, a group of high-magnitude microseismic events usually shows a low b-value and vice versa. Based on the analysis of treatment data and microseismicity, we found that there is a positive relationship between b-value and instantaneous shut-in pressure (ISIP): lower b-value represents lower ISIP. The investigation of the stress shadow effect based on the theoretical solution of a plane strain fracture is also convincing to prove the relationship between b-value and ISIP. Therefore, a significant relationship between hydraulic fracturing, microseismicity, and fault reactivation is established. Importantly, some useful implications of this relationship could be utilized for early warning of fault reactivation (probably casing deformation) and optimization of refracturing design for unconventional shale plays.

Early-Time Shut-In for Plane-Strain Hydraulic Fractures

One investigates the post-shut-in growth of a plane-strain hydraulic fracture in an impermeable medium while accounting for the possible presence of a fluid lag. After the stop of fluid injection, the fracture may present three distinct propagation patterns: an immediate arrest, a temporary arrest with delayed propagation, and a continuous fracture growth. These three patterns are all followed by a final fracture arrest yet the fracture behaviour prior to that results from the interplay between the dimensionless toughness mathcal {K}_m, the shut-in time t_s/t_{om}, and the propagation time t/t_s. mathcal {K}_m characterizes the energy dissipation ratio between fracture surface creation and viscous fluid flow under constant rate injection. t_s and t_{om} represent respectively the timescale of shut-in and the coalescence of the fluid and fracture fronts. The immediate arrest occurs when the fracture toughness dominates the fracture growth at the stop of injection (mathcal {K}_m gtrapprox 4.3). It may also occur upon an early shut-in at low dimensionless toughness associated with an overshoot of fracture extension and a significant fluid lag. For intermediate values of mathcal {K}_m and t_s/t_{om}, the fracture may experience a temporary arrest followed by a restart of fracture propagation. The period of the temporary arrest becomes shorter with higher dimensionless toughness and later shut-in until it drops to zero. The fracture behaviour after shut-in then transitions from temporary arrest to continuous propagation. These propagation patterns result in different evolution of fracture dimensions which possibly explains the various emplacement scaling relations reported in magmatic dikes.

Two-dimensional models for waterflooding induced hydraulic fracture accounting for the poroelastic effects on a reservoir scale

This work focuses on the developing of a computationally efficient numerical model for a waterflooding induced planar hydraulic fracture in a poroelastic medium. In particular, under certain assumptions it is possible to decouple the fully coupled model into poroelastic reservoir and purely elastic fracture subproblems. Further, the general 3D problem formulation for a planar fracture is reduced to two dimensions for early time plane strain fracture and late time constant height fracture. Noticeably, the division of the problem into two subproblems allows us to use the displacement discontinuity approach for the fracture related part, and finite element method for the reservoir related part. The latter is especially important for the constant height fracture, which cannot be modeled using exclusively the finite element approach in two dimensions. The algorithm is benchmarked against the available analytical solutions, as well as compared to other numerical codes. The developed numerical method is used to study the influence of the heterogeneous pore pressure and the corresponding stress for different waterflooding fracturing situations. We consider the cases with both injection and production wells operating nearby. With the presence of such wells, the fracture growth becomes asymmetrical and both the well type and location are important. The qualitatively different fracture behavior is observed for various cases. Other numerical examples include the simulation of a step-rate test as well as investigation of the possibility of fracture control by altering the injection rate.

Effects of velocity-dependent apparent toughness on the pre- and post-shut-in growth of a hydraulic fracture

We investigate the growth of a plane-strain/radial hydraulic fracture in an infinite impermeable medium driven by a constant injection rate assuming that the apparent toughness scales with the decreasing fracture growth rate in a power-law relation. The viscosity dominated regime always governs the fracture growth at large time for the plane-strain geometry. For a radial hydraulic fracture, we report a transition from early-time fracture growth dominated by viscous fluid flow to large-time propagation dominated by fracture toughness. Such a transition results from an overall increase of the energy dissipation by fracture surface creation. After shut-in, both plane-strain and radial fractures propagate at a lower velocity with decreasing fracture toughness. The fracture growth then depends on the dimensionless toughness at the stop of fluid injection and transitions towards a self-similar pulse-viscosity solution when viscous fluid flow dominates the energy dissipation. The fracture arrests when fulfilling two conditions — the apparent toughness reaching its minimum, and viscous forces being negligible in the fluid flow. The fracture dimension at arrest is independent of the velocity-dependent power-law relation.