Maximum Circumferential Stress Criterion Research Articles

Numerical simulation study on propagation mechanism of fractures in tight oil vertical wells with multi-stage temporary plugging at the fracture mouth

The multi-stage temporary plugging and diverting fracturing technique stands as a pivotal method for enhancing production in tight oil reservoirs. At present, fracture propagation models in temporary plugging and diverting fracturing primarily focus on single-stage temporary plugging, disregarding intricate mechanisms influenced by multi-stage temporary plugging and inter-fracture interference on the redirection and propagation of artificial fractures. To address this gap, this study employs the extended finite element method and establishes a mechanical model for the propagation of multi-stage temporary plugging fractures in tight oil reservoirs based on the maximum circumferential stress criterion. Relevant numerical simulations are conducted, considering key factors such as horizontal stress differences, fracturing fluid viscosity, injection rate, and initial fracture angle, all of which influence the morphology of diversion fracture propagation. The study rigorously analyzes and compares characteristics such as the radius of diversion fractures, diversion angle, and fracture width profile corresponding to different numbers of temporary plugging stages. Numerical simulations reveal that the primary controlling factor influencing the extension of fractures is the horizontal stress difference. A smaller horizontal stress difference makes fracture diversion easier, resulting in larger redirection radii. The impact of fracturing fluid viscosity on the diversion radius and diversion angle of fractures can be deemed negligible. Larger injection rates during construction facilitate easier diversion, leading to larger diversion radii. Furthermore, when the initial fracture angle exceeds 90°, the diversion radius of fractures is significantly larger compared to cases where the initial fracture angle is less than 90°, indicating a more facile diversion of fractures.

An adaptive extended finite element based crack propagation analysis method

In this paper, a method of crack propagation analysis based on adaptive extension finite element is proposed. This method combines adaptive mesh reconstruction technology with extended finite element method (XFEM). Firstly, the model of engineering structure is discretized with the help of mesh generation software, and the initial mesh is divided. Secondly, Construction of XFEM model, and the tip of crack strengthening function is introduced to describe the physical field properties of the crack tip. The integral equation is solved to obtain the crack tip parameters. Then, the adaptive mesh reconstruction technology is built to refine the mesh of crack tip area through the error estimation of crack tip. Finally, the SIFs at the crack tip were calculated using the interaction integral, and the path direction of crack growth was determined using the maximum circumferential tensile stress criterion. Thus, the propagation path can be well traced.

Investigating the Influence of Holes as Crack Arrestors in Simulating Crack Growth Behavior Using Finite Element Method

The primary focus of this paper is to investigate the application of ANSYS Workbench 19.2 software’s advanced feature, known as Separating Morphing and Adaptive Remeshing Technology (SMART), in simulating the growth of cracks within structures that incorporate holes. Holes are strategically utilized as crack arrestors in engineering structures to prevent catastrophic failures. This technique redistributes stress concentrations and alters crack propagation paths, enhancing structural integrity and preventing crack propagation. This paper explores the concept of using holes as crack arrestors, highlighting their significance in increasing structural resilience and mitigating the risks associated with crack propagation. The crack growth path is estimated by applying the maximum circumferential stress criterion, while the calculation of the associated stress intensity factors is performed by applying the interaction integral technique. To analyze the impact of holes on the crack growth path and evaluate their effectiveness as crack arrestors, additional specimens with identical external dimensions but without any internal holes were tested. This comparison was conducted to provide a basis for assessing the role of holes in altering crack propagation behavior and their potential as effective crack arrestors. The results of this study demonstrated that the presence of a hole had a significant influence on the crack growth behavior. The crack was observed to be attracted towards the hole, leading to a deviation in its trajectory either towards the hole or deflecting around it. Conversely, in the absence of a hole, the crack propagated without any alteration in its path. To validate these findings, the computed crack growth paths and associated stress intensity factors were compared with experimental and numerical data available in the open literature. The remarkable consistency between the computational study results for crack growth path, stress intensity factors, and von Mises stress distribution, and the corresponding experimental and numerical data, is a testament to the accuracy and reliability of the computational simulations.

Fracture mechanics investigation for 2D orthotropic materials by using ordinary state-based peridynamics

Fracture behaviors of orthotropic plates are studied by using ordinary state-based peridynamic (OSPD) theory. Based on OSPD, a novel nonlocal formulation of interaction integral is proposed by considering the material orthogonality for the fracture parameter evaluation. By employing peridynamic differential operator, the partial differential terms in the formulation can be transformed into corresponding spatial integral form, which contributes to the calculations of stress intensity factors within the framework of OSPD. It has built up a relationship between classical theory and peridynamic theory. Static and dynamic fracture parameters are carefully evaluated. The crack propagation directions are predicted by prototype microelastic brittle (PMB) criterion in OSPD and maximum circumferential stress (MCS) criterion in classical theory. Several pre-cracked plates with orthotropic material are examined, and results are validated by comparing against the reference solutions. The relationship between fiber orientation and crack inclined angle are also examined. Meanwhile, the crack inclination determined by PMB criterion and MCS criterion are compared and discussed. Accuracy of the peridynamic orthotropic model and proposed nonlocal interaction integral are discussed in detail.

Cracking direction in graphene under mixed mode loading

Crack branching in graphene under complex stresses is investigated by molecular dynamics simulations and boundary-layer models. Using the maximum energy release rate (MERR) criterion, an analogy of Wulff curve is plotted considering the anisotropic fracture toughness of hexagonal graphene, which shows the direction of crack kinking (local bump on the curve) is consistent with that of the weak fracture toughness (along zigzag edge). The angle of crack kinking prefers 0°/30°/60°, rather than the angle predicted by maximum circumferential stress criterion. The T-stress along crack front, obtained by the over-deterministic method, can indicate the possibility of kink by its transformation between positive and negative, especially for zigzag cracks. This study incorporates Wulff-like curve and MERR criterion to provide an accurate prediction of nanocrack paths in graphene.

Study on Theoretical Prediction Method of PBXs Uniaxial Tensile Compressive Strength Ratio based on Microcrack Model

Strength is an important characteristic of material mechanical properties. Based on the microcrack model and considering the internal friction effect between the crack surfaces, the uniaxial tensile and compressive strength theoretical model which can reflect the tensile and compressive anisotropy of materials is derived and established by using the crack initiation criteria of maximum circumferential stress and maximum circumferential strain, considering the internal friction coefficient and Poisson’s ratio. By introducing the TATB based PBXs parameters, the tension compression ratio of PBXs calculated by using the maximum circumferential stress and strain criteria are 0.293 and 0.471 respectively, with errors of -10% and 44% respectively compared with the experimental value of 0.326; The calculated failu re angles are 29.52 ° and 19.44 ° respectively. Compared with the experimental values of 24 ° and 30 ° (average 27 °), the errors are 9% and -28%, respectively. The analysis shows that the maximum circumferential stress criterion is more suitable for the construction of PBXs strength criterion based on microcrack model.

An extended multiphase hybrid-stress finite element method for modelling interface crack propagation between two dissimilar materials

In this work, an extended multiphase hybrid-stress finite element method (X-MHSFEM) is developed to investigate the stress intensity factor, kinking angle, and propagation path of an interface crack. Further, we have simulated the propagation of the interface crack by using the X-MHSFEM. Several types of element models containing the interface and matrix cracks are introduced in the propagation process of the interface crack. The derivation of the functional of the element containing the two materials, one interface, and all types of cracks, is performed. Stress functions are enriched by the asymptotic singular items that accounts for the oscillatory behavior to describe the stress concentration in the vicinity of the interface crack-tip, and the stress concentration near the matrix crack-tip are also captured by inserting certain singular stress terms of Williams expansion into the physical field of whole model. The stress intensity factors of the tips of the interface and matrix cracks are calculated by the least square method. The maximum and relative maximum circumferential stress criterion are employed as the fracture criteria for predicting the interface crack propagation along the interface or the deflection into layers. Further, the matrix crack propagation angle within the layers is determined by the maximum energy release rate criterion. A remeshing algorithm is employed to implement the propagation of the interface and matrix cracks. The effectiveness and accuracy of the present method are validated by comparing the results, obtained by the new method, with the experimental observation and other numerical results. Therefore, the extended multiphase hybrid-stress finite element method can provide an effective medium to deal with the interface crack fracture problems.

Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics

Mixed-mode fatigue crack propagation analysis is studied using ordinary state-based peridynamics. By introducing the concept of “remaining life”, the fatigue crack nucleation and propagation can be simulated in the PD framework. The PD fatigue modelling and the crack path prediction is carefully investigated. For the comparison purpose, the maximum circumferential stress criterion is introduced. The interaction integral and the peridynamic differential operator is employed to evaluate the fracture mechanics parameters. Two pre-cracked structures under mixed-mode loading conditions are provided with the validations from reference solutions.

Dynamic crack propagation under thermal impact

This paper addresses the dynamic crack growth in an isotropic media subjected to a non-classical thermal shock by implementing the Green-Naghdi (GN) generalized thermoelasticity theory in the eXtended Finite Element Method (XFEM). To satisfy the crack tip singularity for modeling dynamic crack growth via XFEM, proper enrichment functions for field variables are needed, which are extracted from the asymptotic fields for a dynamically growing crack in a thermoelastic media. These near tip fields of a dynamically moving crack are also used in the formulations of the maximum circumferential stress criterion and the equivalent stress intensity factor. Finally, numerical examples of the dynamic crack propagation under thermal shock are given out, and the effect of the dissipation coefficient in the GN model and the thermal shock amplitude on the crack growth path is studied in detail. In addition, the crack propagation under GN thermal shock is compared with that under classic thermal shock. The main difference between them is discussed in a numerical example.

Research on the propagation mechanism of hydraulic fractures in infill horizontal wells

In recent years, infill horizontal well technology has been used to develop oil and gas in the remaining oil areas of unconventional low-permeability reservoirs. However, the initial fractures in parent wells will affect the hydraulic fractures formed by fracturing infilling horizontal wells. The interaction mechanisms between initial fractures and artificial fractures in infill horizontal wells are still unclear. Combined with the boundary element method and the maximum circumferential tensile stress criterion, a numerical model of hydraulic fracturing that can simulate the evolution of fracture trajectory and stress field was established. The analytical solution of the hydraulic fracture-induced stress field was used to verify the accuracy of the model. Using this model, propagation of hydraulic fractures in infill horizontal wells under different conditions was analyzed. Simulation results show that both the fracture spacing and well spacing have a significant impact on the propagation trajectory of hydraulic fractures in infill horizontal wells. The shorter the fracture spacing and well spacing is, the stronger the inter-fracture stress interference between the initial fractures and hydraulic fractures is. Reasonable fracture spacing and well spacing can enhance the induced stress field and form a complex fracture network in the reservoir. Too small well spacing may cause artificial fractures to communicate with initial fractures, thereby reducing hydraulic fracturing efficiency and limiting the stimulation volume of the reservoir.

Dynamic crack propagation under generalized thermal shock based on Lord-Shulman model

In this paper, dynamic crack propagation in a 2D isotropic medium under a generalized thermal shock in the framework of eXtended Finite Element Method (XFEM) is studied. A new set of tip enrichment functions for displacement and temperature based on the near tip fields for a moving crack is proposed. In addition, the maximum circumferential stress criterion is developed using the stress field near the moving crack to determine the crack propagation direction. The fully coupled generalized thermoelasticity equations based on the Lord-Shulman model are considered as the governing equations. The effect of the thermal wave magnitude on the crack propagation path as well as on the crack speed is discussed in details.

Effect of edge cracks on critical current degradation in REBCO tapes under tensile stress

The slitting process for manufacturing REBa2Cu3O7-δ (REBCO, RE = Rare earth) tapes of required width significantly improves the production efficiency and reduces production costs. However, edge cracks induced by the slitting process of wide REBCO tapes may cause premature degradation under high tensile stress in high-field magnets. Therefore, it is necessary to evaluate the effect of edge cracks of REBCO tapes on the critical current (Ic) degradation. Firstly, Ic degradation under artificial cracks was measured to validate the applicability of linear elastic fracture mechanics for the REBCO layer. The maximum circumferential stress criterion was used to derive the mixed-mode stress intensity factor of multiple oblique edge cracks. A semi-analytical model considering edge crack properties such as angle β, spacing d, and length a, was built to evaluate the critical load and critical crack. We found that when the stress intensity factor at the crack tip is below KIC=2.3 MPam, edge cracks did not propagate. We examined commercial REBCO tapes manufactured by two different processes, concluding that edge cracks in these tapes will not cause premature degradation.

How to obtain a more accurate maximum energy release rate for mixed mode fracture

Energy release rate (ERR) is considered one of the most widely employed fracture criteria. However, for mixed mode fracture situations, the exact computation of ERR for an infinitesimal branch crack is challenging. With some assumptions, Nuismer's theoretical expression (Int. J. Fracture. 11 (1975)) has been used to determine the ERR. In this work, we investigate its deviation. Based on St. Venant's theorem, it is first proved that the stress intensity factor (SIF) of a branch crack is almost independent of its length when the branch crack is small enough as compared to the main crack, which enables us to more accurately obtain the ERR and SIF of an infinitesimal branch crack by simulating a finitely short branch crack in finite element simulations. More accurate curves for the maximum ERR and the corresponding branch angle under any mixed mode are provided. From results of more accurate simulation, we find that Nuismer's model has the maximum difference of 11.2% in the maximum ERR and the 7.1% difference in the branch angle prediction. These are also the differences of predictions between the maximum circumferential stress criterion and the maximum energy release rate criterion.

Finite Element Simulation of a Crack Growth in the Presence of a Hole in the Vicinity of the Crack Trajectory.

The aim of this paper was to present a numerical simulation of a crack growth path and associated stress intensity factors (SIFs) for linear elastic material. The influence of the holes’ position and pre-crack locations in the crack growth direction were investigated. For this purpose, ANSYS Mechanical R19.2 was introduced with the use of a new feature known as Separating Morphing and Adaptive Remeshing Technology (SMART) dependent on the Unstructured Mesh Method (UMM), which can reduce the meshing time from up to several days to a few minutes, eliminating long preprocessing sessions. The presence of a hole near a propagating crack causes a deviation in the crack path. If the hole is close enough to the crack path, the crack may stop at the edge of the hole, resulting in crack arrest. The present study was carried out for two geometries, namely a cracked plate with four holes and a plate with a circular hole, and an edge crack with different pre-crack locations. Under linear elastic fracture mechanics (LEFM), the maximum circumferential stress criterion is applied as a direction criterion. Depending on the position of the hole, the results reveal that the crack propagates in the direction of the hole due to the uneven stresses at the crack tip, which are consequences of the hole’s influence. The results of this modeling are validated in terms of crack growth trajectories and SIFs by several crack growth studies reported in the literature that show trustworthy results.

Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.

A new method for calculating the direction of fracture propagation by stress numerical search based on the displacement discontinuity method

In the traditional, displacement discontinuity method (DDM) simulation of hydraulic fracturing, the stress intensity factor (SIF) method is usually employed to calculate the fracture propagation angle (FPA). However, the SIF method is not suitable for real formation rock stress conditions. Considering the real stress condition of the formation under far-field bidirectional compression, we proposed a stress numerical search method (SNSM) that is based on the maximum circumferential stress criterion at the fracture tip to predict the FPA. Moreover, we compared the results from this model with indoor experiments and numerical simulation results to verify the model. The computation results of the model show that the traditional SIF method simplifies the rock stress, which will cause a large error and that the SNSM method is more consistent with the real situation. The sensitivity parameter analysis shows that the SNSM method can be utilized to predict the fracture propagation trajectory with different rock and construction parameters and to simulate the competitive growth of multiple fractures with the effect of a “stress shadow”. The results of this paper supplement and improve the existing hydraulic fracturing model and can provide guidance for the fracture parameter design of field fracturing construction.

Analysis of multi-crack propagation by using the extended boundary element method

A new way is proposed to simulate the crack propagation paths of the multi-cracked structure. Firstly, the complete displacement and stress fields of the multi-cracked structure are calculated by the extended boundary element method (XBEM) coupled with characteristic analysis of the crack tip. Secondly, based on the maximum circumferential stress criterion by considering the contribution of the non-singular stress terms, the crack initiation angles are obtained. Thirdly, the cracks propagate forward along the crack initiation angles to form a new multi-cracked structure. During this process, boundary element adaptive mesh technique is established and the XBEM is used to analyze the newly formed multi-cracked structure repeatedly. Finally, the crack propagation paths of the multi-cracked structure are obtained. Numerical examples show that the results obtained by the XBEM are in good agreement with the experimental results.

Evaluation of the fracture mechanisms and criteria of bedding shale based on three-point bending experiment

Shale has remarkable bedding characteristics, and the key technology of shale gas extraction engineering is garnering great interest in the influence of bedding on the fracture mechanisms and fracture criteria of shale. Three-point bending tests combined with digital image correlation (DIC) were carried out on semicircular bend (SCB) specimens of shale with different bedding angles to investigate the influence of bedding on crack evolution. The results showed that the strain field of each bedding shale exhibited three stages during the three-point bending : uniform strain distribution, damage accumulation, and strain localization. In the stage of strain localization, each specimen first showed considerable tensile strain localization along a straight line extending from the tip of the prefabricated crack. With increasing loading, except for in the localized bands of the tensile strain, the maximum shear strain became aligned with the bedding orientation in the shale specimens, indicating that the original mode I cracks of the specimens were transformed into mixed-mode I/II cracks due to the influence of the bedding. A new fracture criterion (the generalized maximum circumferential stress criterion based on shale bedding, GMTS-SB) was deduced for predicting the propagation of a prefabricated mode I crack in bedding shale. The results calculated from the GMTS-SB were compared with the experimental results to evaluate the accuracy of the criterion. In the established GMTS-SB, the stress intensity factor is related to the specimen size, the load magnitude, and the bedding angle. This criterion also considers the influence of T-stress on the calculated result. For bedding shale, the GMTS-SB can effectively describe the crack angle and fracture resistance of a crack initiating along the bedding orientation.

Computational Simulation of 3D Fatigue Crack Growth under Mixed-Mode Loading

The purpose of this research was to present a simulation modelling of a crack propagation trajectory in linear elastic material subjected to mixed-mode loadings and investigate the effects of the existence of a hole and geometrical thickness on fatigue crack growth and fatigue life under constant amplitude loading. For various geometry thickness, mixed-mode (I/II) fatigue crack growth studies were carried out to utilize a single edge cracked plate with three holes and compact tension shear specimens with various loading angles. Smart Crack Growth Technology, a new feature in ANSYS, was used in ANSYS Mechanical APDL 19.2 to predict the cracks’ propagation trajectory and their consequent fatigue life associated with evaluating the stress intensity factors. The maximum circumferential stress criterion is implemented as a direction criterion under linear elastic fracture mechanics (LEFM). According to the hole position, the results demonstrate that the fatigue crack grows towards the hole due to the unbalanced stresses on the hole induced crack tip. The results of this simulation are verified in terms of crack growth paths, stress intensity factors, and fatigue life under mixed-mode load conditions, with several crack growth studies published in the literature showing consistent results.

Numerical simulation of direct shear test on granular materials composed of breakable angular particles: A DEM-XFEM approach

A combined DEM-XFEM novel approach is used to simulate the direct shear test on assemblies of breakable two-dimensional angular particles in order to study the macro- and micro-mechanical behavior of granular materials and the effect of particle breakage phenomenon on it. Therefore, the direct shear test simulations are conducted on two different particle assemblies, a breakage-disabled (BD) sample and a breakage-enabled (BE) one, and the results are analyzed and compared. In this approach, the particle assembly under direct shear loading is simulated through DEM, while the fracture within individual particles is modeled using XFEM, in which the Hoek-Brown criterion (HB) and an interaction-integral-based LEFM maximum circumferential tensile stress criterion are utilized to model the crack initiation and its propagation, respectively. Overall, the presented results demonstrate that particle breakage in granular materials reduces the amount of anisotropy, the dilative behavior, and the mobilized friction angle of the sample.