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Fracture geometry is important when stimulating low-permeability reservoirs for natural gas or oil production. The geological layer (GL) properties and contrasts in in-situ stress are the two most important parameters for determination of the vertical fracture growth extent and containment in layered rocks. However, the method for assessing the cumulative impact on growth in height remains ambiguous. In this research, a 3D model based on the cohesive zone method is used to simulate the evolution of hydraulic fracture (HF) height in layered reservoirs. The model incorporates fluid flow and elastic deformation, considering the friction between the contacting fracture surfaces and the interaction between fracture components. First, an analytical solution that was readily available was used to validate the model. Afterwards, a quantitative analysis was performed on the combined impacts of the layer interface strength, coefficient of interlayer stress difference, and coefficient of vertical stress difference. The results indicate that the observed fracture height geometries can be categorized into three distinct regions within the parametric space: blunted fracture, crossed fracture, and T-shaped fracture. Furthermore, the results explained the formation mechanism of the low fracture height in the deep shale reservoir of the Sichuan Basin, China, as well as the distinction between fracture network patterns in mid-depth and deep shale reservoirs. [ABSTRACT FROM AUTHOR]

Computer modeling and numerical simulation are essential for understanding the progression of aortic dissection. However, tear propagation has not been properly modeled and simulated. The in‐plane dissection propagation between concentrically distributed elastic lamellae is modeled using the cohesive zone method with a bilinear traction‐separation law. The parameters of cohesive elements are calibrated for the three modes of interfacial damage in the media, enabling quantitative predictions of in‐plane tear propagation. An idealized cylindrical tube‐shaped bilayer thick‐wall model of the aorta is employed to elucidate the influence of geometrical parameters, loading conditions and residual stress on the tear propagation. While the model is capable of replicating that deeper, larger tears are associated with lower critical pressure, new findings include: (i) Larger axial stretch leads to lower critical pressure; (ii) Increased magnitude of residual stress is associated with higher critical pressure; (iii) Pressure difference between true and false lumen alters the critical pressure; (iv) The interfacial damage is mostly opening mode in the axial direction, but shear‐dominated in the circumferential direction; (v) Damage due to the opening mode is associated with smaller fracture energy, which makes it easier to propagate than the shear and the mixed modes. (vi) The deformed shape of the tear, which is related to its geometrical features and loading conditions, modulates the critical pressure via two pathways: (a) deformed shapes are associated with specific modes of damage, which influences the critical pressure, and (b) deformed shapes modulate the critical pressure directly via geometrical constraints. [ABSTRACT FROM AUTHOR]

In quasi-brittle materials such as concrete, numerical methods are frequently used to simulate the crack propagation for monotonic loading. However, further research and action are required to better understand the fracture properties under cyclic loading. For this purpose, in this study, we present numerical simulations of mixed-mode crack propagation in concrete using the scaled boundary finite element method (SBFEM). The crack propagation is developed based on a cohesive crack approach combined with the thermodynamic framework of a constitutive concrete model. For validation, two benchmark crack-mode examples are modelled under monotonic and cyclic loading conditions. The numerical results are compared against the results from available publications. Our approach revealed good consistency compared to the test measurements from the literature. The damage accumulation parameter was the most influential variable on the load-displacement results. The proposed method can provide a further investigation of crack growth propagation and damage accumulation for cyclic loading within the SBFEM framework. [ABSTRACT FROM AUTHOR]

The Jurassic Badaowan formation of the tight oil reservoir in northwest Xinjiang, China, is featured by a complex in situ stress pattern, leading to an unclear understanding of the orientation and geometry of a propagated hydraulic fracture. In this regard, a three-dimensional (3-D) in situ stress field was first configured based on a detailed mechanical earth model of the region of concern. Secondly, a fluid-solid-damage coupling model was established to explore the influences of the in situ stresses and the engineering parameters on fracture propagation. Finally, a systematic approach was proposed to characterize the updated stress field and the fracture morphology reconfigured by the in situ stress. The findings disclose that the reservoir is mainly controlled by reverse faults that generate horizontal fractures in most parts of the region. The in situ stress follows the strike-slip fault pattern where vertical fractures are dominant in the central and southeastern part of the reservoir, where the vertical fracture tends to be constrained in the oil layer when the interlayer minimum stress difference ∆Sh becomes greater than 4 MPa in the southeast. In addition, as the injection rate increases, the width of a fracture increases, whereas its height decreases. The viscosity has negligible effect on the fracture height, but its increase can enlarge the fracture width and decrease the length. Here, the cross-dipole shear wave logging record in a field well was used to verify the proposed method, showing that the predicted fracture morphology was consistent with the field test result. The research can aid field engineers in predicting fracture morphology for optimizing a fracturing scheme. [ABSTRACT FROM AUTHOR]

Many concrete structures, such as bridges and wind turbine towers, fail mostly due to the fatigue rapture and bending, where the cracks are initiated and propagate under cyclic loading. Modeling the fracture process zone (FPZ) is essential to understanding the cracking behavior of heterogeneous, quasi-brittle materials such as concrete under monotonic and cyclic actions. The paper aims to present a numerical modeling approach for simulating crack growth using a scaled boundary finite element model (SBFEM). The cohesive traction law is explored to model the stress field under monotonic and cyclic loading conditions. In doing so, a new constitutive law is applied within the cohesive response. The cyclic damage accumulation during loading and unloading is formulated within the thermodynamic framework of the constitutive concrete model. We consider two common problems of three-point bending of a single-edge-notched concrete beam subjected to different loading conditions to validate the developed method. The simulation results show good agreement with experimental test measurements from the literature. The presented analysis can provide a further understanding of crack growth and damage accumulation within the cohesive response, and the SBFEM makes it possible to identify the fracture behavior of cyclic crack propagation in concrete members. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing is a popular method used in the petroleum industry to increase the well performance by improving the permeability of the reservoir. However, while there has been extensive research on the development of the length of the fracture, the fractured height has been frequently assumed to be equal to the reservoir thickness. The objective of this paper is to study the influence of formation rock characteristics and the impact of underground stress state on the development of the fracture height. To achieve this objective, a finite element model was built using a cohesive zone method to predict the development of fracture height in time and space. Different scenarios were then effectuated by varying the values of the primary formation variables which are the Young's modulus, the porosity, the Poisson ratio, the fracture energy, and the maximum horizontal stress of the reservoir and of the beddings. This research therefore covered principally uncontrolled factors which are the formation properties and stress state underground, which contribute mostly to the erroneous prediction in fracture height. The findings revealed that the fracture height was strongly influenced by the properties of the formation and of the adjacent layers. However, the influence levels are not the same for different kinds of properties. This study showed that the most influential mechanical property of the rock on the fracture height is the Young's modulus. Regarding the porosity, its effect on the fracture height is extremely small. However, it is worth noting that the porosity is still an important parameter in hydraulic fracturing because it can be used to estimate others parameters and to model the development of fracture geometry which are width, length, and height. Practical suggestions for real-life hydraulic fracturing jobs can be deduced from this study, in order to control the fracture height as accurately as possible, and to decrease financial cost by concentrating mostly on the high influential factors instead of doing all kinds of tests for other less influential mechanical properties of the rock. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing in combination with horizontal well has been widely used to stimulate shale oil and gas from reservoirs. Numerical simulation of hydraulic fracturing is a great challenge due to the geological complexity of reservoirs. In this paper, a fully coupled fluid flow, plastic deformation and fracture propagation model is presented based on cohesive zone method. An implicit algorithm to discretize and integrate the fully coupled differential equations is presented. Plastic deformation is observed in the vicinity of hydraulic fracture during the stimulation process. The effect of plastic and stimulation parameters on fracture propagation behaviors has been investigated. The energy dissipation induced by the plastic deformation increases the fracture width. The fracture propagation behaviors both in viscosity and toughness dominated regimes are discussed. The evolution formula of non-dimensional fracture length at different regimes is presented by fitting numerical results. [ABSTRACT FROM AUTHOR]

• Finite-element analysis offers insights into needle-TM interactions for middle-ear interventions. • Combined 2D and 3D FE modeling strategy reveals TM deformation during needle insertion. • First-order Ogden hyperelastic model accurately captures TM mechanical nonlinearity. • TM thickness, needle geometry, and material impact needle insertion force and success. • Methodology aids in developing therapeutic and diagnostic technologies for hearing and balance pathologies. The tympanic membrane (TM) is one of the most common routes to access the middle ear and inner ear for the treatment of hearing and balance pathologies. Since the TM is a soft thin biological tissue with small dimensions, using needles seems to be among the most practical interventional approaches. In this study, we proposed a finite-element (FE) analysis of needle-TM interactions that combines a 3D model of the TM and other main middle-ear structures in gerbil, and a 2D model of needle insertion into the TM based on the cohesive zone method (CZM). The TM was modelled using a 1st-order Ogden hyperelastic material and its properties were obtained by fitting to the experimental force-displacement plots of large deformation in the TM under needle indentation. The cohesive parameters were also acquired by calibrating the puncture force against the experimental data of needle insertion into the TM. These FE models were then used to obtain the deformation behaviour of the TM and other middle-ear structures due to the insertion force applied at different locations on the TM. Moreover, we investigated the effect of the TM thickness, the geometry of the needle (i.e., diameter and tip angle), and needle material on the insertion of needles into the TM. We also studied the penetration success of deformable needles. [ABSTRACT FROM AUTHOR]

Various numerical models are developed that seek to reproduce, in a simulation instance, the formation and evolution of cracks in the claddings of nuclear fuel elements. The algorithms are based on the cohesive zone method within the finite element framework. When applied to simulations involving fracture mechanics, cohesive elements have various advantages, such as not needing to know the stress state in advance, representing the nucleation of the crack, and being able to reproduce the contact between the crack surfaces after fracture, with numerous application examples for ductile materials, including metals. The models developed were included in the DIONISIO 3.0 nuclear fuel code and compared with analytical test cases, controlled tests of nuclear materials, and a large set of experimental exercises with rods subjected to steep power ramps where breakages are caused due to contact with the pellets. Similarly, these new models were used in controlled experiments where the conditions of an accident type such as a loss-of-coolant accident are reproduced, analyzing the variation of the thermohydraulic, thermomechanical, and structural parameters of a rod. [ABSTRACT FROM AUTHOR]

During the operation of entrained‐flow gasifiers, the ash deposits located on the wall tubes in the radiant syngas coolers (RSC) reduce the heat transfer efficiency. Syngas sootblowing is an effective method to remove the slag deposits in the RSC. In this study, a 3D numerical model was developed by combining the cohesive zone method (CZM) and the coupled Eulerian–Lagrangian analysis to investigate the deposit fracture process in RSC during sootblowing. The quasi‐static analysis using ABAQUS obtained the stress–strain curve of the slag sample, which agreed well with the experimental tests and provided the detailed mechanical parameters to the CZM model. The dynamic characteristics of deposit fracture were discovered. The main fracture occurred between 1.0 and 1.5 ms, and the shape of the fracture area was not round but elliptical. The RSC operating pressure (P) was also investigated. The study found that higher pressure led to lower fracture speed, longer sootblowing time, and more syngas consumption. Based on the same extent of deposit fracture, syngas consumption increased when P < 3.5 MPa, and the density of syngas (ρsyngas) has a more significant influence on the syngas consumption than the velocity of sootblowing syngas flow (vavg), especially when the sootblowing time is small. [ABSTRACT FROM AUTHOR]

A progressive interlaminar damage model, based on the Northwestern University theory and a trapezoidal trilinear traction-separation law, is presented to predict the initiation and propagation of delamination in layered composites under Mode I and Mode II loadings. The capability and reliability of the damage model proposed is assessed by comparing its results with experimental data. It was found that the model was able to accurately predict the maximum load and postfailure behavior of composite laminates. The model proposed was also compared with the Abaqus inbuilt cohesive surface model, which is also based on a bilinear tractionseparation law, and our model was found to give more accurate results. [ABSTRACT FROM AUTHOR]

A 3D simulation model of graphene toughened Al 2 O 3 ceramic materials had been developed to study the fracture behaviour. Voronoi tessellation was used owing to its high similarity to the ceramic grain distribution. In addition, a new method to automatically generate nano-graphene along the Al 2 O 3 grain boundaries was proposed. The Al 2 O 3 /graphene interface properties were characterised by the cohesive zone method, wherein cohesive elements along grain boundaries and in grains were generated using Python. Furthermore, the effects of phase interface bonding strength and graphene content on the fracture behaviour were analysed. The results clearly showed the occurrence of both intergranular and transgranular fractures. In addition, some toughening mechanisms induced by nano-graphene such as crack guiding, crack bridging, crack branching, microcracks, and pull-out of graphene have been discussed. The finite element simulation results were consistent with the experimental ones. Therefore, the results presented in this study would be beneficial for improving the design efficiency of Al 2 O 3 /graphene ceramic materials. [ABSTRACT FROM AUTHOR]

In this paper, the size effect in unidirectional (UD) laminated glass-fibre reinforced plastic (GFRP) composites subjected to quasi-static bending loading was investigated: the sensitivity of a specimen's mechanical behaviour and failure mechanism to its geometry was studied. Composite beams with different numbers of 0° unidirectional plies were tested and their post-deformation structures were analysed microscopically. In the subsequent simulations, the intraply damage was modelled using continuum damage mechanics, implemented as a user-defined VUMAT subroutine in ABAQUS/Explicit, while cohesive zone elements were employed to characterize the delamination between different plies. It was observed that the flexural failure triggered the multiple delaminations; their location was studied. The influence of the size effect on the bending response of the UD composite beams was analysed in depth. The findings of the current study can be used to design modern structures made of composite materials. [ABSTRACT FROM AUTHOR]

The migration and leakage of formation fluid along the cement plug/formation interface negatively affects the integrity of open-hole temporary abandoned wells. A 3-D numerical model is developed based on the cohesive zone method for analyzing the initiation and propagation of fractures along the cement plug/formation interface. The model is validated by comparison with an existing microannulus model to demonstrate its reliability. The relationship between fracture development, propagation pressure, and fluid migration time in the damage evolution of the interface is quantitatively analyzed, and the influences of different mechanical parameters on fracture propagation pressure and debonding height are studied, including cement plug mechanical parameters, formation mechanical parameters, horizontal in-situ stress, and interface cementation strength. The simulation results indicate that (1) high interface cementation strength, cement plug elastic modulus, and formation elastic modulus tend to increase fracture propagation pressure and decrease fracture debonding height, which helps to mitigate debonding failure of the cement plug/formation interface. (2) Large horizontal in-situ stress can constrain fracture propagation when the stress is uniform. For a non-uniform horizontal stress, a large in-situ stress difference is more likely to cause fracture extension. (3) The fracture propagation pressure and fracture debonding height of the cement plug/formation interface are less affected by the Poisson's ratio than the elastic modulus of the formation and the cement plug. The numerical model established in this study provides an effective method to evaluate the well integrity failure of open-hole temporary abandoned wells due to debonding failure of the cement plug/formation interface. A 3-D numerical model of fracture debonding of the cement plug/formation interface was developed. The potential of debonding failure can be mitigated by improving interface cementation strength and increasing the elastic modulus of the cement plug and formation. Large non-uniform horizontal in-situ stress and small uniform horizontal in-situ stress tend to result in fracture extension. The Poisson's ratios of the formation and the cement plug have little effect on interface bonding failure. [ABSTRACT FROM AUTHOR]

Separate layer fracturing (SLF) technique is the prevailing method for stimulating multi-thin layered reservoirs (MTLRs) whereas the production record reveals that not all wells show good performance after being fractured. The primary cause for this phenomenon can be attributed to the complex geometry of the created hydraulic fractures. For better understanding the problem, we establish a new geomachanical model based on the extended finite element method (XFEM) and cohesive zone method (CZM), to investigate the fracture propagation in MTLRs under SLF. Reverse faulting stress regime is considered. In the simulation procedure, horizontal hydraulic fractures (HHFs) are created sequentially from the bottom up along a vertical wellbore. The results show that later created HHFs will propagate out of the pay zones or probably enter the water or gas-bearing layers if the fracturing time is not reasonably controlled. The fracture initiation pressure (FIP) and fracture propagation pressure (FPP) present larger values when stimulating the upper formations, and the deviation of later created HHFs can lead to the building up of FPP. Parametric studies indicate that larger injection rate and shallower reservoir depth yields longer and wider HHFs while smaller injection rate, shallower reservoir depth and thicker barriers results in lower FIP and FPP. [ABSTRACT FROM AUTHOR]

The effect of delamination on the stiffness reduction of composite pipes is studied in this research. The stiffness test of filament wound composite pipes is simulated using cohesive zone method. The modeling is accomplished to study the effect of the geometrical parameters including delamination size and its position with respect to loading direction on stiffness of the composite pipes. At first, finite element results for stiffness test of a perfect pipe without delamination are validated with the experimental results according to ASTM D2412. It is seen that the finite element results agree well with experimental results. Then the finite element model is developed for composite pips with delaminated areas with different primary shapes. Thus, the effect of the size of delaminated region on longitudinal and tangential directions and also its orientation with respect to loading direction on delamination propagation and stiffness reduction of the pipes is assessed. [ABSTRACT FROM AUTHOR]

Interfacial delamination in semiconductor packages during their lifetime is a reliability risk. For the realisation of a "Design for Reliability" approach, the whole product needs to be studied virtually using Finite Element simulations. Only this approach allows for the evaluation of possible failure mechanisms, which is an integral part of risk analyses in reliability assessments. The Cohesive Zone Method enables the prediction of interfacial damage initiation and damage evolution in the simulation model. For accurate simulation results, not only material models need to be chosen carefully, but also the parameters for the cohesive zone. A new experimental method was proposed for the calibration of these so-called damage models, utilising the experimental setup of the Advanced Button Shear Test. Critical adhesion energies are determined based on sub-sequent shear loading, and thus, sub-critical damage evolution at the interface of the test vehicle. This paper summarises the method itself and investigations regarding the main influences on experimental results. Influences are categorised as test setup inherent, and sample inherent. Setup inherent influences can be taken into account using a new calibration routine. Sample inherent influences need to be subtracted from measurement results, or prevented with the aid of design optimisations. • New method to determine critical adhesion energies of material interfaces with the Advanced Button Shear Test setup • Subcritical crack growth at the interface induced by subsequent loading and unloading • Main influences during testing are identified • Temperature-dependent measurement results are given for a moulding compound/lead frame interface [ABSTRACT FROM AUTHOR]

Models for fluid-driven fractures in a poroelastic medium involve the simultaneous simulation of multiple physical processes—diffusion of pore pressure, poroelastic stresses, fluid injection into a fractured porous medium, and fracture propagation. To simulate the above-mentioned physics, many algorithms and discretization techniques have been used in the past. The finite volume method has been gaining popularity for simulating solid mechanics problems. The discretization algorithms discussed in the past have used a segregated method for solving the poroelastic momentum balance, where iterations are necessary to obtain a converged solution for each component of the displacement vector. This segregated approach, when coupled with fluid-driven fracture propagation, can lead to excessive simulation times because of the coupled nature of the problem. In this study, an implicit formulation was designed to construct a linear system of equation for the components of the displacement vector to solve the poroelastic momentum balance equation (without iterating between components). Within this formulation, a fluid-driven fracture propagation model was implicitly incorporated using a cohesive zone approach. This methodology provided accurate solutions as shown by the validations in this paper where simulated results were compared with various well-known analytical solutions. The implicitness of the new model allowed significant improvements in computation speed when solving multi-physics problems. The simulation speed-ups were found to be 2 to 8 times when compared with the segregated method. [ABSTRACT FROM AUTHOR]

Abstract In the last decades, composite materials have been increasingly used in advance engineering fields such as aerospace and automobile industries due to their advantages in terms of stress concentrations, structural weight and manufacturing. Joining composite parts in such applications has been increasingly achieved by adhesives compared to welded, riveted or bolted connections. Mechanical testings of adhesively bonded composite joints are often time consuming and expensive due to a number of parameters involved and their analytical modellings are complicated. Therefore, numerical analysis is increasingly used in recent years to overcome these limitations. In this work three-dimensional FE modelling of the single lap joints (SLJs) of angle ply composite adherends subjected to tensile loading was developed using ABAQUS/Explicit. Cohesive zone model was adopted for the modelling of damage in the adhesive layer. The continuum damage mechanic model implemented via a user defined VUMAT subroutine was used to model the intraply damage in composite adherends. The model accounted for the damage initiation, the damage evolution, and the nonlinear shear behaviour of the material. Experiments of the SLJs of [±10] 5s , [±20] 5s , [±45] 5s and [±55] 5s adherends under tensile loading were performed. The adherends were manufactured from glass reinforced polymer matrix and the adhesive layer was AF163-2K. For verification of the developed model, numerical results were compared with those of the experiments mentioned above. The SLJs of [±10] 5s and [±20] 5s adherends failed due to failure in the adhesive layer and those of [±45] 5s and [±55] 5s failed mainly due to failure in the adherends. The peel and shear deformation modes in the adhesive layer were invoked in different ways for different SLJ configurations. The effects of adhesive layer thickness and the overlap length on the response of the SLJ were investigated in detail. [ABSTRACT FROM AUTHOR]

Optical glass scratching can induce various types of cracks, among which median cracks are extremely detrimental and penetrate deeply under the surface. Due to deep-scratching process complexity, it is challenging to devise a method to predict median crack depth. Indentation testing has been examined comprehensively in prior research works. It has been found that using the correlation between scratch and indentation testing can simplify predictive method development. In this research, a numerical method based on indentation testing is proposed to determine median crack depth during deep scratching. In the first step, an FE model is configured to simulate the indentation testing process and the Cohesive Zone Method is applied to describe median crack behavior. The cohesive parameters calibrated through experimental indentation testing are implemented in the FE scratch model, and the results are compared with the experimental scratch test results. According to the results, the FE scratch model was enhanced by mode II fracture energy and the modeled friction coefficient. The indentation and scratch experiments were conducted with BK7, F2, Fused silica, K5, Pyrex, Quartz, SF6, and SF19. The experimental results prove that the nonlinearity of the median crack depth curve correlates with K Ic . A comparison of the experimental and numerical results demonstrates the model is virtually functional for materials with K Ic below 1000 kPa m 1/2 . Comparisons between the current findings and other studies infer the model and experimental results are accurate and reliable. [ABSTRACT FROM AUTHOR]

The influence of transformation induced plasticity (TRIP) on materials mechanical behaviours, as well as failure phenomena including crack propagation and phase boundary debonding in multiphase steels (e.g. dual phase steels, TRIP steels) are studied by using an advanced crystal plasticity finite element method. We have coupled the crystal plasticity model Ma and Hartmaier (2015), which explicitly considers elastic-plastic deformation of ferrite and austenite, austenite-martensite phase, with a cohesive zone model designed for crack propagation, to study the deformations of several representative microstructural volume elements (RVE). Results shows that, the transformation induced plasticity enhances materials strength and ductility, hinders crack propagation and influences interface debonding. Furthermore, the martensitic transformation kinetics in TRIP steels was found depending on the crystallographic orientation and the stress state of a retained austenite grain. The current simulation results helps to investigate and design multiphase steels with improved mechanical properties. [ABSTRACT FROM AUTHOR]

Refracturing can effectively enhance hydrocarbon production from hydraulically fractured wells. Using self-degradable diverting agents, people can temporarily plug previously generated fractures, and generate a new pair of fractures perpendicular to the direction of the original maximum principle stress (i.e., near-wellbore temporary plugging and diverting technique). To simulate the plugging and diverting process, a numerical model is established using the cohesive zone model (CZM) based on the extended finite element method (XFEM). After this model is verified by the published laboratory testing results, it is applied to understand the influences of stress contrast, formation permeability, rock tensile strength, Young's modulus and injection rate, so as to improve the applicability of temporary plugging and diverting technique under various reservoir conditions. Furthermore, “deflection angle” is proposed to quantitatively analyze the simulation results. This new concept enables the comparison among various cases without the restrictions of fracture length and simulation time. Simulation results indicate that: (1) with increases of stress contrast, rock permeability and Young's modulus, the diverting fractures reorient to the direction of the preferred fracture plane (PFP) more rapidly, which reduces the effectiveness of this technique; (2) propping previously-formed fractures can create higher defection angles of the diverting fractures, which enhances the effectiveness of this technique; (3) enhancing the injection rate can also enhance the effectiveness of this technique, yet there is one optimal injection rate for a given reservoirs. This study provides a systematic guideline for optimizing the temporary plugging and diverting technique under different reservoir conditions. [ABSTRACT FROM AUTHOR]

• A 3D hydro-mechanical coupled model is presented to study hydraulic fracturing interaction with bedding planes. • Cohesive zone method is employed to represent the bedding planes explicitly. • Fracture propagation behaviors are analyzed under different patterns. Bedding planes are abundant in the continental shale oil reservoirs, but their impact on hydraulic fracturing is still not fully understood. To investigate the effects of stress condition, bedding plane's properties and layer lithology on hydraulic fracture propagation in layered formation, a 3D hydro-mechanical coupled model is presented. The bedding planes are explicitly represented by cohesive elements with degraded properties compared to the rock. The results show that increasing the stress difference ratio of the vertical principal stress to horizontal principal stress promotes the hydraulic fracture propagating across bedding planes, and the critical value of vertical principal stress required for hydraulic fracture crossing rises with the decrease of bedding plane's critical traction. Furthermore, when the critical traction ratio of bedding plane to rock drops below 0.7, the fracture propagation pattern changes from crossing to deflecting. Additionally, the extension pressure increases slightly, the fracture length decreases and the area of opening bedding planes rises. As the permeability of bedding plane increases, the fracture cannot cross the bedding planes and even stops extension. The layer lithology contrast also affects fracture propagation patterns. This study examines the fracture propagation behaviors under different patterns, including the opening morphology of bedding plane and the evolution of injection pressure and strain energy. The simulation results may provide useful insights for hydraulic fracturing design in layered formations. [ABSTRACT FROM AUTHOR]

Multistage hydraulic fracturing is a highly effective method for creating multiple transverse fractures to improve gas and oil reservoir production. It is critical to minimize the fracture spacing while also ensuring transverse propagation of fractures in multi-fractured horizontal wells. In this paper, a 3D fully coupled pore pressure-stress model based on the extended finite element method (XFEM) combined with the cohesive zone method is established to simulate five different fracturing scenarios in close spacing. The sensitivity of mesh size and the integration method are optimal, which are verified by the highly accurate traditional cohesive zone method. Then, the effect of five different fracturing scenarios on fracture geometries is compared. It is shown that spacing is a key parameter controlling fracture geometries in all fracturing scenarios. Alternative sequential and modified two-step fracturing can significantly reduce the influence of stress shadowing to generate more transverse fractures and form longer effective fractures. The sequential and two-step fracturing see an obvious improvement with increased fracture effective length when the spacing increases. The simultaneous fracturing technique can result in excessive closure of the middle fractures, which causes serious insertion of proppants. These results offer a new insight on optimization of hydraulic fracturing and can be a guidance for typical field cases.

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a nonlocal elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model. The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation. [ABSTRACT FROM AUTHOR]

Complex hydraulic fractures are often reported in layered formations as the existence of a geological discontinuity. A seepage-stress-damage coupled finite element model was built to study the hydraulic fracture propagation behavior of the X5 sandstone and shale layered reservoir in the western Sichuan basin. The cohesive zone method (CZM) based on damage mechanics was used to simulate hydraulic fracture initiation and propagation. The influence of geologic parameters and fracturing execution parameters on hydraulic fracture morphology were studied. The results show that hydraulic fractures are mainly penetrating the interface and extending along the interface to generate a branched fracture, while others are forming normal bi-wing fractures. [ABSTRACT FROM AUTHOR]

Z-pin technology, as a promising through-thickness reinforcement, offers an efficient solution for the weak composite parts joints, especially for large integrated composite structures. This paper presents a two-dimensional finite element model to analyze the enhancing efficiency of Z-pins for composite T-joints. The modeling used a new parameter definition method for delamination growth simulation in Z-pinned joining interface via a regional cohesive zone model. The finite element model was validated by experiments for unpinned and Z-pinned T-joints under web pullout tension. The parametric analysis on the structural configuration shows that shear stress ratio in Z-pins declines with the span ratio increasing and the skin thickness ratio decreasing, which leads to the failure mode change of a single pin from pull-out to shear fracture so that the improvement on the out-of-plane tension declines gradually. Within 1.7–2.1 span ratio (the constant 4 mm skin thickness) or 1.8–2.5 thickness ratio (the 200 mm constant span), the ultimate tension is improved by at least 15%, where Z-pins exhibit the best efficiency. When span ratio is above 2.4 or thickness ratio below 1.2 within the range studied herein, Z-pinned T-joints fail by skin fracture rather than the bonding interface in which cases further increasing of Z-pin reinforcements becomes unfavorable. [ABSTRACT FROM AUTHOR]

A new model for prediction of fatigue-driven delamination in laminated composites is proposed using cohesive interface elements. The presented model provides a link between cohesive elements damage evolution rate and crack growth rate of Paris law. This is beneficial since no additional material parameters are required and the well-known Paris law constants are used. The link between the cohesive zone method and fracture mechanics is achieved without use of effective length which has led to more accurate results. The problem of unknown failure path in calculation of the energy release rate is solved by imposing a condition on the damage model which leads to completely vertical failure path. A global measure of energy release rate is used for the whole cohesive zone which is computationally more efficient compared to previous similar models. The performance of the proposed model is investigated by simulation of well-known delamination tests and comparison against experimental data of the literature. [ABSTRACT FROM AUTHOR]

Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests. [ABSTRACT FROM AUTHOR]

In this study, a low-velocity impact test of glass fiber-reinforced polypropylene (GFPP) composites was simulated considering interlaminar fracture toughness. In the simulation, intralaminar and interlaminar damage were modeled using the continuum damage mechanics (CDM) and cohesive zone method (CZM) models, respectively. The B-K criterion was used for the interlaminar damage model along with experimental results, which were obtained from fracture toughness tests of modes I and II and the mixed mode. Low-velocity impact tests were performed to verify the developed damage model, and various characteristics such as delamination and the force–displacement were evaluated. Finally, it was found that the developed damage model with interlaminar fracture toughness can be used to accurately predict the impact behavior of GF/PP composites, including interlaminar delamination. [ABSTRACT FROM AUTHOR]

This paper deals with high cycle fatigue delamination in composite materials. The cohesive zone approach along with the level set method is used to simulate fatigue-driven delamination growth. The cohesive zone method is used for calculation of the energy release rate at the crack front because of its superiority over the virtual crack closure technique (VCCT) for bi-material interfaces and non self-similar crack growth. Evolution of the crack front in 3D during fatigue growth is handled with the level set method. The damage variable in the cohesive zone formulation is changed according to the updated level set field. Benchmarks are used to evaluate the performance of the proposed approach in simulation of 3D delamination growth under fatigue loading. [ABSTRACT FROM AUTHOR]

Combining multistage hydraulic fracturing and horizontal drilling is a highly effective method of increasing the production rates of unconventional reservoirs. The openings of propped transverse fractures in horizontal wells cause the reorientation of the stress in their neighborhood. This, in turn, affects the direction of propagation of the subsequent fractures. It is desirable to minimize the fracture spacing while also ensuring the growth of transverse fractures in multi-fractured horizontal wells, in order to improve reservoir drainage. In this paper, we present a two-dimensional fully coupled pore pressure-stress model based on the extended finite element method in conjunction with the cohesive zone method for simulating consecutive fracturing and alternate fracturing for a typical field case corresponding to low-permeability reservoirs. It is shown that the stress interference increases with the number of fractures created and also depends on the sequence of fracturing. The in-situ stress difference has a significant impact on the extent of the stress interference zone. The magnitude of in-situ stress affects the fracture length and width. The local in-situ stress in the near-tip region is redistributed with fracture propagation. In contrast to the consecutive fracturing method, the alternate fracturing method allows for the fracture spacing to be lowered, owing to the propagation of a middle fracture between the previous two fractures. These results offer new insights on the optimization of fracture spacing and should act as a guide for fracture design, helping improve the production rates in unconventional reservoirs. [ABSTRACT FROM AUTHOR]

Composite sandwich structural joints, such as T-joints, are used in many different composite applications to transfers the load orthogonally between two sandwich elements. However, these joints connecting the sections can represent the weakest link in sandwich composite structures due to the lack of reinforcement in the out-of-plane direction. Therefore, this paper presents a new methodology for the design and analysis of composite sandwich T-joints using new biomimetic fabrication methods. The fabricated idea comes from biological fixed joints as an evolutionary alteration processes of trunk-branches of trees. It offers unique attributes to optimize the continuous fiber paths for minimum stress concentrations and multi-sandwich layers to increase the bending stiffness and strength. The focus is on how the biomimetic technique can improve sandwich T-joint structures by increasing their strength and load carrying capability without adding a significant weight penalty. The major attention is to investigate the comprehensive failure modes in the joint numerically and verified by experiments. Investigations were conducted on three different designs of biomimetic composite sandwich T-joints under tension and bending loads. The results show significant improvements to the ultimate load up to 68% in the case of bending load and 40% in the case of pull-off load in the biomimetic sandwich T-joints compared to the reference conventional T-joint design. The final failure was significantly deferred in both load status. The FE models provided important insights into the core failure and delamination of multi-interface biomimetic T-joints. [ABSTRACT FROM AUTHOR]

The involvement of the dynamic embrittlement phenomenon during tensile tests of a Cu Ni Si alloy leads to decohesion of grain boundaries, which is dependent on the energy decrease at grain boundaries caused by sulfur segregation. The severity of dynamic embrittlement increases with the increasing of temperature and/or the decreasing of straining rate. A crystal plasticity approach associated with the cohesive zone method is used in order to analyze the fracture caused by dynamic embrittlement. A cohesive zone model is used to describe the grain boundary cracking and one of its main parameters is identified using a homogenization scheme for the nonlinear response of a polycrystal in presence of degradable grain boundaries. Numerical simulations are carried out in order to simulate the mechanical behavior related to dynamic embrittlement under different conditions of strain rate and temperature. The obtained results such as tensile stress-strain curves and intergranular crack distribution are compared with experimental observations. [ABSTRACT FROM AUTHOR]

Purpose – Since failure of laminated composites by delaminations is common, the purpose of this paper is to present a numerical procedure to check the stability of delaminations in fiber metal laminate (Glare), with different possible damage configurations, under uni-axial tension. Deformation behavior of the laminate is also examined. Influence of the type and the extent of damage, represented by varying sizes and number of delaminations, on delamination driving force and laminate deformation is found. Design/methodology/approach – Delaminated Glare is modeled by finite element method. Interface cohesive elements are used to model the delaminations. Finite element results provide the deflection/deformation characteristics of the laminate. Driving forces of delaminations are estimated by J integrals that are numerically obtained over cyclic paths near delamination tips. Laminates with different types of delaminations are also fabricated and externally delaminated for measurement of their interlaminar fracture toughness. The delamination is considered to be stable if its driving force is less than corresponding interlaminar fracture toughness of the laminate. Findings – Delaminations are found to be stable in laminates with lower number of delaminations and unstable in laminates with higher number of delaminations. Increase in size of delaminations increases the deformations but reduces the delamination driving force whereas increase in number of delaminations increases both deformations and driving forces. The trends change in case of laminates with symmetrical damage. Shape of delamination is also found to influence the deformations and driving forces. The finite element model is validated. Research limitations/implications – There is scope for validating the numerical results reported in the paper by theoretical models. Practical implications – Checking the stability of delaminations and their effect on deformation behavior of the laminate helps is assessment of safety and remaining life of the laminate. If failure is predicted, preemptive action is taken by using repair patch ups at identified critical locations in order to avoid failures in service conditions. Originality/value – The paper offers the following benefits: use of cohesive zone method that is readily possible in finite element procedures and is relatively simple, fast and reasonably accurate is demonstrated; suitability of using J integrals over paths crossing non-homogeneous and property mismatched material layers is tested; and influence of the type and the extent of damage in the laminate on its deformation behavior and delamination driving forces is found. This type of work has not been reported so far. [ABSTRACT FROM AUTHOR]

With the increasingly wide use of hydraulic fracturing in the petroleum industry, it is essential to accurately predict the behavior of fracture propagations based on the understanding of fundamental mechanisms governing the process. For unconventional resources exploration and development, hydraulic fracture pattern, geometry and associated dimensions are critical in determining well stimulation efficiency. In shale formations, non-planar, complex hydraulic fractures are often observed, due to the activation of pre-existing natural fractures. The propagating of turning non-planar fractures due to re-fracturing treatment and unfavorable perforation conditions have also been reported. Current numerical simulation of hydraulic fracturing generally assumes planar crack geometry and weak coupling behaviors, which severely limits the applicability of these methods in predicting fracture propagation under complex subsurface conditions. In addition, the prevailing approach for hydraulic fracture modeling also relies on Linear Elastic Fracture Mechanics (LEFM), which uses stress intensity factor at the fracture tip as fracture propagation criteria. Even though LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in ductile rocks, such as poorly consolidated/unconsolidated sands and clay-rich ductile shales, even in the form of simple planar geometry. In this study, a fully coupled non-planar hydraulic fracture propagation model in permeable medium based on the Extended Finite Element Method (XFEM), Cohesive Zone Method (CZM) and Mohr-Coulomb theory of plasticity is developed for the first time, which is able to model fracture initiation and propagation in both brittle and ductile formations. To illustrate the capabilities of the presented model, example simulations are presented on both near wellbore and far field scale. The results indicate that the in-elastic deformations induced by propagating hydraulic fracture have significant impact on propagation pressure and fracture geometry, and the prediction of fracture propagation behaviors can be extremely erroneous if ductile formations are simply treated as soft rocks with lower Young's modulus. The method discussed in this article represents a useful step towards the prediction of non-planar, complex hydraulic fractures and can provide us a better guidance of completion design and optimizing hydraulic fracture treatment that will better drain reservoir volume in formations with complex stress conditions and heterogeneous properties. [ABSTRACT FROM AUTHOR]

In practical offshore structure/icebreaker designs, it is critical to capture the salient failure modes of the ice feature. The dominant failure modes are influenced by the structural properties, interaction process, and characteristics of the ice features. For an ice feature of finite size with relatively small lateral confinement, splitting failure has been frequently observed during ice-structure interactions. In literature, the splitting failure of an ice floe has been studied using several different methods, ranging from strength theory to methods based on fracture mechanics. One contribution of this paper is that these various methods are compiled and evaluated collectively. Another contribution of this paper is the construction of an analytical framework to obtain solutions for the splitting process of an ice floe upon serious considerations of relevant fundamental theories. The framework developed for its calculations is presented but not limited these two base cases (i.e., rectangular and circular ice floes). Specifically, because of the complexity of the splitting failure scenario (particularly the ice floe geometry) and our pursuit of analytical solutions, within the presented framework, two different approaches have been proposed: the fracture mechanics approach and plasticity theory approach. All of the employed methods are validated against data from previous field tests or numerical results. Recommendations and discussion were presented for each of these methods’ respective application range. It was found that most of the floe sizes under engineering interests can be accurately described by linear elastic fracture mechanics. The cohesive zone method, which is one type of the nonlinear fracture mechanics based approaches, is found to be potentially applicable in extrapolating laboratory-scale measurements to the field scale. Worth mentioning, the weight function method was effectively used to calculate the fracture properties of an ice floe under various symmetric loading conditions (e.g., boundary confinement). The boundary confinement can easily prevent splitting failure or increase the ice splitting load. As one type of the lateral confinement, the inertia-induced body force, is also studied and compared with previous numerical results. Comparatively, the plasticity theory based approach (i.e., the plastic upper/lower limit theory) enables us to effectively attain a conservative estimation of the ice splitting load in an analytical form. It can serve as a supplementary tool to the fracture mechanics based approach. [ABSTRACT FROM AUTHOR]

In this paper, we present a general partition of unity-based cohesive zone model for fracture propagation and nucleation in saturated porous materials. We consider both two-dimensional isotropic and orthotropic media based on the general Biot theory. Fluid flow from the bulk formation into the fracture is accounted for. The fracture propagation is based on an average stress approach. This approach is adjusted to be directionally depended for orthotropic materials. The accuracy of the continuous part of the model is addressed by performing Mandel's problem for isotropic and orthotropic materials. The performance of the model is investigated with a propagating fracture in an orthotropic material and by considering fracture nucleation and propagation in an isotropic mixed-mode fracture problem. In the latter example we also investigated the influence of the bulk permeability on the numerical results. [ABSTRACT FROM AUTHOR]