Shear Crack Research Articles

Propagation and complex morphology of hydraulic fractures in lamellar shales based on finite-discrete element modeling

We explore the controls of stress magnitude and orientation relative to bedding on the resulting morphology/topology of hydraulic fractures using a combined finite-discrete element method (FDEM). Behavior is shown conditioned by the ratio of principal stresses λ=σ3/σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ={\\sigma }_{3}/{\\sigma }_{1}$$\\end{document} and relative inclination of the bedding. When the lateral pressure coefficient (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) is less than 0.67, hydraulic fractures predominantly initiate as tensile fractures along the wellbore, aligning with the maximum principal stress direction. Conversely, for λ≥0.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\ge 0.67$$\\end{document}, shear cracks are favored to initiate for the minor stress difference, leading to a less predictable initiation and extension direction. Simultaneously, diminished stress differences correspond to elevated reservoir breakdown pressures, displaying a linear correlation with lateral pressure coefficients and little influenced by equivalent bedding orientation. Bedding plane orientation significantly impacts the mode and morphology of hydraulic fracture propagation. Bedding parallel to the direction of the minimum principal stress (σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{3}$$\\end{document}) favors layer-penetrating and bifurcated fractures, whereas inclined bedding facilitates the emergence of numerous steering-type and capture-type fractures. Especially at steeper inclinations (β=60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =60^\\circ$$\\end{document}), hydraulic fractures readily extend along the bedding surface, inducing macroscopic shear slip failure. Under high-stress disparities, the breakdown pressure exhibits greater sensitivity to bedding inclination, and its influence pattern aligns with the variations in tensile strength, typically reaching maximum and minimum values at bedding inclination angles of 0° and 60°, respectively.

Reinforced ECC-UHPC-SCC composite modular framed shear wall systems under lateral cyclic loading

The shear strength and deformability of high performance reinforced composite framed shear wall systems made of Engineered Cementitious Composite (ECC), Ultra-High-Performance Concrete (UHPC) and Self-Consolidating Concrete (SCC) subjected to lateral cyclic shear loading to failure were investigated. A total of seven framed shear wall specimens were constructed using combinations of ECC or SCC wall, SCC frame and ECC or UHPC frame joints. The performance of such novel modular forms of walling systems were compared based on experimental results in terms of cracking, failure mode, hysteretic shear load-deformation response, shear load capacity, ductility, bearing capacity degradation, stiffness degradation, dissipated energy, viscous damping capacity, induced wall shear stresses and strain development characteristics. ECC walling system exhibited better structural performance compared to their SCC counterparts showing up to 40% higher load capacity forming significantly higher number of closely spaced diagonal cracks with up to 72% lower crack shear stress, 14% to 21% higher ductility, up to 2 times higher energy dissipation capacity and lower rate of stiffness/bearing capacity degradation through both hysteretic and damping actions. The incorporation of ECC and ECC or UHPC joint in frame significantly improved shear strength capacity of infill wall and overall framed shear wall system. ECC incorporated framed shear walls even with frames made of SCC and UHPC joints also exhibited superior performance. This study confirmed the superior performance of ECC material for the construction of reinforced framed shear wall with boundary frame made of ECC/SCC/UHPC combinations for better seismic resistance.

The behaviour of Reinforced Concrete Beams by Using Expanded Polystyrene Beads and Palm Oil Fuel Ash as Replacement Materials

The Reinforced Concrete (RC) beams containing Expanded Polystyrene Beads (EPS) and Palm Oil Fuel Ash (POFA) as sand and cement replacement with a percentage between 10% and 30% were studied in terms of load-deflection behaviour. RC beam’s size was 1000×150×150 mm and simply supported at spaced 750 mm apart. The 10% of POFA without EPS shows a slight increase which is 0.26% higher than normal concrete in compressive strength. The ultimate load and flexural performance of RC beams with EPS and POFA exhibited a decreasing trend. All beams’ ultimate load exceeds the design value. The cracks of the RC beam may be classified as vertical flexural cracks, and some of the cracks can be classified as shear cracks based on the crack angle. As the percentage of EPS and POFA increases above 20% for all specimens, cracking starts to change to shear cracking.

A numerical critical shear crack model and its application to post‐peak behavior assessment of RC and SFRC beams

AbstractIn this paper, a numerical critical shear crack model, in which the shear‐flexural coupling effect is considered and the full process of stress and strain is captured, is proposed to evaluate the post‐peak behavior of reinforced concrete (RC) and steel fiber reinforced concrete (SFRC) beams. The shape of critical shear crack is identified by combining the modified compression field theory considering the bridge effect of steel fibers and the section analysis method. Based on the shape of critical shear crack, the shear capacity of beam members is provided by the shear tension zone and the shear compression zone. The shear capacity of the shear tension zone is calculated by the modified compression field theory and that of the shear compression zone is determined by multiaxial strength criterion of concrete. The vertical displacements caused by the flexure deformation and shear deformation are deduced by the moment area method and integration of shear strain. To verify the proposed numerical approach, a test database of 486 RC beams and 313 SFRC beams was established to predict the shear strength, and the force‐displacement relationships of twelve beam members are used to validate the feasibility for full process analysis. The stochastic analysis of beams with different failure modes is conducted via GF‐discrepancy‐based point selection method and probability density evolution method. The limitation between different failure modes is defined according to the degradation percent of shear capacity and it is taken as threshold value of failure domain, and the failure probability analysis indicates that the designed flexure beam member suffered severe degradation of shear capacity, resulting in a significant decline in safety probability.

Strength, Deformation and Fracture Properties of Hard Rocks Embedded with Tunnel-Shaped Openings Suffering from Dynamic Loads

In rock engineering, the dynamic loads caused by mechanical action and rock blasting have an extremely significant influence on the stableness of surrounding rock masses. To examine the impact of dynamic load on the mechanical properties and fracturing characteristics of hard rocks as well as the failure responses of underground openings, a number of prismatic samples with holes of different numbers and configurations were prepared for dynamic tests employing an SHPB loading device. The experimental results demonstrate that the order of dynamic compressive strength of each group of samples under the impact nitrogen pressure of 0.45 MPa is: G3 > G2 > G5 > G4 > G7 > G6, and the dynamic deformation process of the samples is parted into three phases: linear elastic deformation, plastic deformation and post-peak deformation. A total of three categories of cracks, i.e., spalling cracks, shear cracks and tensile cracks, occur in the specimens. The failure mode of the samples having one or two holes arranged in a vertical direction is controlled by shear cracks, whilst that of the rest groups of pre-holed specimens belongs to tensile-shear failure. The existence of the fabricated holes in the samples significantly weakens the mechanical properties and affects the fracture evolution characteristics, which rely on the quantity and layout of the cavities in the specimens. The interesting results are also discussed and explained, and could supply some insight in the mechanisms of tunnel surrounding rock failure and rock dynamic hazards such as rock burst.

Experimental investigation on the mixture optimization and failure mechanism of cemented backfill with coal gangue and fly ash

Using coal gangue and fly ash for mining backfill materials can create a win-win situation for safe mining and waste disposal, with the critical challenge being the optimization of coal gangue grading and fly ash proportions. Uniaxial compression tests and scanning electron microscopy (SEM) observation were conducted on backfill specimens with different coal gangue grading and fly ash proportions, and in-situ monitoring of acoustic emission (AE) parameters and infrared radiation temperatures (IRT) was carried out. The elastic modulus, uniaxial compressive strength (UCS), failure pattern, infrared temperature, AE ringing count and energy evolution of the backfill were discussed. Further, the b-value and entropy-value of AE during the loading were analyzed. The results show that the UCS and elastic modulus decrease with the increase in the proportions of fly ash and large-size gangue. Tensile cracks generally dominate the failure of specimen under unaxial compressive load but shear cracks are more prone to occur for specimens with high proportions of fly ash and large-size gangue. The inner defects and weak interfaces between large-size gangue and cement pastes significantly affect the mechanical performance for specimens with high proportions of fly ash and large-size gangue. A sudden drop of the b-value occurs before the peak stress while the AE entropy-value reaches maximum at the peak stress. The methods and findings can guide the mixture optimization and mechanical failure analysis for backfill mining.

Shear Banding and Cracking in Unsaturated Porous Media through a Nonlocal THM Meshfree Paradigm

The mechanical behavior of unsaturated porous media under non-isothermal conditions plays a vital role in geo-hazards and geo-energy engineering (e.g., landslides triggered by fire and geothermal energy harvest and foundations). Temperature increase can trigger localized failure and cracking in unsaturated porous media. This article investigates the shear banding and cracking in unsaturated porous media under non-isothermal conditions through a thermo–hydro–mechanical (THM) periporomechanics (PPM) paradigm. PPM is a nonlocal formulation of classical poromechanics using integral equations, which is robust in simulating continuous and discontinuous deformation in porous media. As a new contribution, we formulate a nonlocal THM constitutive model for unsaturated porous media in the PPM paradigm in this study. The THM meshfree paradigm is implemented through an explicit Lagrangian meshfree algorithm. The return mapping algorithm is used to implement the nonlocal THM constitutive model numerically. Numerical examples are presented to assess the capability of the proposed THM mesh-free paradigm for modeling shear banding and cracking in unsaturated porous media under non-isothermal conditions. The numerical results are examined to study the effect of temperature variations on the formation of shear banding and cracking in unsaturated porous media.

Mechanical properties and damage evolution features in uniaxial compression with non-coincident interlayer contact in double-block ballastless track

As interlayer cracking has become as a significant issue in ballastless tracks, investigating the mechanical properties and damage characteristics during uniaxial compression with non-coincident contact is vital for enhancing the operational performance of ballastless tracks. This study conducted experiments on interlayer non-coincident contact damage in double-block ballastless tracks with nominal normal pressures of 0.666 MPa, 1.244 MPa, 2.489 MPa, and 3.733 MPa. The research explored the relationship between normal load and normal deformation stiffness, analyzed the interlayer contact damage mechanism of concrete, and investigated the damage evolution mechanism under non-coincident contact conditions based on Acoustic Emission (AE) signals. The findings indicate that: I) When the nominal pressure is respectively less than and greater than 1.333 MPa, the normal deformation stiffness and normal load satisfy linear and power function relationships, respectively. II) The interaction of interlayer protrusions under non-coincident contact, combined with the outward expansion resulting from interlayer mutual compression deformation, are two significant factors contributing to the formation of tensile cracks, while the presence of significant shear stresses directly beneath the interlayer contact points is the primary cause of shear cracks. III) After loading, The ballastless track slab matrix remains undamaged, while the supporting layer matrix may experience comprehensive cracking when the nominal pressure exceeds 1.333 MPa. IV) During the stage of only interlayer interface damage, both tensile and shear cracks are the primary causes of concrete damage. In the stage where damage occurs to both the interlayer interface and matrix, tensile cracks play a dominant role. However, when comprehensive matrix cracking occurs, shear cracks take on a dominant role. The outcomes of this study contribute to a deeper understanding of the damage mechanisms of ballastless tracks under train loads following interlayer cracking. Particularly focusing on the evolution characteristics of damage under high interlayer pressure.

Failure evolution and instability prediction of fiber-reinforced polymer-confined cement mortar specimens under axial compression.

In geotechnical engineering, a large number of pillars are often left in underground space to support the overlying strata and protect the surface environment. To enhance pillar stability and prevent instability, this study proposes an innovative technology for pillar reinforcement. Specifically, local confinement of the pillar is achieved through fiber-reinforced polymer (FRP) strips, resulting in the formation of a more stable composite structure. In order to validate the effectiveness of this structural approach, acoustic emission characteristics and surface strain field characteristics were monitored during failure processes, while mathematical models were employed to predict specimen instability. The test results revealed that increasing FRP strip confinement width led to heightened activity in acoustic emission events during failure processes, accompanied by a decrease in shear cracks but an increase in tensile cracks. Moreover, ductility was improved and deformation resistance capacity was enhanced within specimens. Notably, initial crack generation occurred within unconfined regions of specimens during failures; however, both length and width as well as overall numbers of cracks significantly decreased due to implementation of FRP strips. Consequently, specimen failure speed was slowed down accordingly. Finally, the instability of the partial FRP-confined cement mortar could be more accurately predicted based on the model of FRP-confined concrete. It was verified by the test results.

Iron ore grade's impact on uniaxial compression behavior and acoustic emission characteristics

The mechanical properties of iron ore are influenced by various factors, including its grade, which consequently impacts stope stability and equipment efficiency in the mining process. In order to explore the influence and mechanism of grade on these properties, handheld XRF testing was conducted to determine the grade of iron ore samples ranging from 28% to 40%. Subsequently, the acoustic emission method was employed to acquire signals during the uniaxial compression tests. Additionally, scanning electron microscopy was utilized to examine the fracture surface, for performing a microscopic analysis of the influence mechanism of grade on the mechanical properties of iron ore. The results revealed that lower-grade iron ore exhibited larger transverse deformation, with a corresponding dominance of tensile failure. This observation aligned with the AF-RA value (Parameters of reaction crack type), which depicted a shift in the types of microcracks generated during the compression process from tensile cracks to shear cracks with the increasing grade. The content of gangue minerals diminishing as the grade increased. Consequently, the location of the cracks transitioned from the primary failure Through the gangue minerals to the primary microcracks in metallic minerals, resulting in a higher occurrence of acoustic emission events during the early loading stage and the development speed of microcracks accelerates during the loading process. The dominant frequency (Parameters of reaction crack size) of the acoustic emission signal increased from 150 kHz at a grade of 28% to 264 kHz at a grade of 40%, accompanied by a linear decrease in the proportion of low-frequency signals. The b value (indicator for quantifying the degree of damage) demonstrates a decrease with increasing grade. Overall, the content of metal minerals in the iron ore increased with the grade, resulting in polymerization. However, the influence of crack propagation on the overall strength of iron ore remained relatively minor. Macroscopically, the uniaxial compressive strength increased almost linearly with the iron ore grade.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Softened membrane model for shear of ultra-high-performance concrete (SMM-UHPC)

Understanding the shear behavior of Ultra-High-Performance (UHPC) is crucial to prevent undesired responses that could be induced by diagonal shear cracks. Hence, the ability of analytical models to predict shear responses of UHPC members is of paramount importance, which is addressed in this paper by the Softened Membrane Model (SMM). Since the SMM is a two-dimensional shear modeling framework developed for reinforced concrete, a parametric investigation was conducted to assess its suitability for UHPC, namely SMM-UHPC. Through this assessment, a softening coefficient for the biaxial behavior of UHPC was developed and new constitutive laws were integrated in SMM. Comparisons with shear panel tests were used to evaluate the accuracy of SMM-UHPC and quantify the significance of key model parameters. Sensitivity analyses showed that the decomposition between biaxial and uniaxial strain fields, which is used in SMM to capture the Poisson effect, has a negligible influence on UHPC shear. Combining experimental and analytical data, the tensile localization strain was identified to be of most significance for predicting the shear stress-strain response of UHPC.

Punching shear tests in flat slabs supported on re-entrant corner columns

The punching strength and deformation capacity of slab-column connections is governing for design at ultimate limit state of flat slabs. This phenomenon has been investigated since decades with experimental programmes in an effort to derive empirical or mechanical design approaches. Such efforts, due to the complexity of the phenomena, have mostly been addressed to axisymmetric inner slab-column connections, which correspond to the simplest academic case and are not directly covering a large variety of practical situations. Although some tests are also available for other configurations, such as edge or corner connections, no experimental evidence is found on relevant cases for practice such as re-entrant corner columns. The lack of experimental data in this latter case raises questions on the design of such connections, as extrapolating results from other cases is not a simple task due to the complexity of the phenomena implied (such as redistributions in the shear field and moment transfer between slab and column). In order to advance the knowledge on the response of re-entrant connections and to provide a sound design approach for them, this paper presents the results of an investigation specifically addressed at this case. To that aim, seven specimens were tested under different conditions, varying the load eccentricity, flexural reinforcement and shear reinforcement arrangement at the edges. The tests were instrumented with refined measurements, allowing to understand in a detailed manner the response of the slabs during testing in the shear-critical region. The experimental results are later compared to current design codes, leading to a number of conclusions with practical relevance. Finally, on the basis of the knowledge acquired from the tests, a mechanical approach is proposed based on the Critical Shear Crack Theory to assess the punching response. This approach is shown to lead to accurate and reliable predictions of the punching strength, improving those of current design codes.

Investigating the toppling failure of anti-dip rock slopes containing non-persistent cross-joints via a strength-based fracture method

The toppling failure of anti-dip rock slopes is significantly affected by crack propagation from non-persistent cross-joints (NPCJs). In this study, a strength-based localized maximum stress (SLMS) criterion is adopted to model the toppling failure process caused by crack propagation in anti-dip rock slopes containing a set of NPCJs via the finite element method. The crack initiation sequence from NPCJs and the toppling evolution of anti-dip slopes under different stratum dips and slope angles, as well as the influences of stratum dips and slope angles on toppling evolution, are investigated. Variations in the displacements during the toppling of the slope and the influence of toppling on the displacements are analyzed. Additionally, variations in the magnitude and distribution area of interlayer friction between rock layers during the toppling evolution process and the effects of toppling on the evolution of interlayer friction are examined. The results indicate that the toppling process of the anti-dip slope containing NPCJs involves three stages: crack initiation and propagation from the NPCJs, the development of interlayer tensile and shear cracks, and toppling failure of the rock layers. The stability of anti-dip slopes containing NPCJs is greatly affected by the stratum dip and slope angle. The horizontal displacements and interlayer crack aperture increase nonlinearly with the development of toppling evolution, and the magnitude of the increase gradually increases. Moreover, the magnitude and distribution area of interlayer friction vary with the development of toppling evolution. The maximum interlayer friction gradually increases, but the distribution area of friction decreases.

Experimental and numerical investigation on effects of gas adsorption pressures on damage behaviors, failure characteristics, and energy evolution of coals

Coal and gas outbursts are anthropogenic hazards that can be divided into four stages: preparation, occurrence, development, and termination. Studying the influence of gas on coal damage and energy changes during the formation of outbursts is highly important for investigating the entire hazard. In this paper, laboratory experiments were performed on samples. The energy changes and failure mechanism of coal under different gas pressures were revealed, and a seepage model was established based on compressibility and adsorption to investigate gas-induced coal damage. The results demonstrated that gas pressure caused initial damage within the coal, resulting in nonlinear deformation and strength deterioration of the coal. Gas-induced damage affected the energy evolution mechanism of coal under loading, as pressure caused the premature release of energy at the tips of internal microcracks and reduced the ability to accumulate energy. These changes increased the proportion of dissipative energy under unstable conditions. The combined acoustic emission (AE) parameters—rising angle (RA) and average frequency (AF)—were used to study the fracture mode of gas-containing coal. As the gas pressure increased from 0 to 4 MPa, the RA–AF distribution pattern changed from tensile failure to tensile–shear composite failure, with the proportion of shear cracks increasing from 0.30% to 25.44%. As the complexity of the crack network increased, the randomness of crack propagation increased, and the fracture surface roughness parameters, arithmetic mean height Sa, root mean square height Sq, and maximum height Sz increased by 90.33%, 94.02%, and 81.70%, respectively. These findings could contribute to a comprehensive understanding of the underlying mechanism of coal and gas outbursts and guide for predicting and preventing these hazards.

Experimental study on mechanical behavior of precast large-cantilevered UHPC bent caps with π-shaped cross-sections

To reduce the self-weight of the precast bent caps with large cantilevers commonly used in municipal bridge construction, an innovative thin-walled bent cap scheme made of ultra-high-performance concrete (UHPC) was proposed in this paper. Six scaled bent cap specimens, characterized by a scale ratio of 1:2.5, were subjected to static loading tests, encompassing both bending-shear and bending-shear-torsion combinations. Throughout the loading process, careful observations were made regarding the progressive development of crack patterns, stress distribution within various materials, and the identification of ultimate failure modes. It was observed that for the UHPC cap beams with small shear span-to-depth ratios, both the web shear cracks and flexural cracks were fully developed, leading to a combined shear and bending failure mode. With shear span-to-depth ratio increased, the effect of bending behavior became more and more dominate, resulting in an increased ductility. When subjected to a combined bending-shear-torsion loading, the UHPC bent caps exhibited conspicuous diagonal shear failure attributes, indicating that the torsion presented in the bent caps should be limited. In summary, the adoption of a π-shaped section for the UHPC bent caps with large cantilevers results in an impressive weight reduction of 40%∼50% compared to the conventional solid cap beam design. Moreover, the proposed design not only aligns with specifications in terms of cracking strength and ultimate bearing capacity but also facilitates monolithic precast, making it exceptionally well-suited for practical engineering applications.

Role of Crack Interaction on Shear Localization in Porous Granular Rocks Deformed in the Brittle and Ductile Fields

AbstractCrack interactions leading to shear localization were quantified using microstructural analysis for brittle faults and high‐temperature ductile faults formed during experiments on quartz sandstone. In both faulting regimes, the nucleation of macroscopic faults results from the interactions of microfractures at two length scales in ensemble. Brittle faults nucleate when the longest mesoscale shear fractures and transgranular tensile cracks critically interact. In contrast, ductile faults nucleate when the longest mesoscale shear fractures and multi‐grain scale intergranular shear cracks critically interact. For both faulting regimes, we conclude the interaction and coalescence of the longest mesoscale shear fractures is the fundamental process responsible for fault nucleation. Hence, mesoscale shear fractures, which accommodate the majority of axial strain prior to shear localization in both faulting regimes, also serve as the nucleus of macroscopic faults. Locally, the growth of the mesoscale shear fractures is promoted by the interaction and coalescence of the multi‐grain scale cracks in both faulting regimes. We hypothesize that attainment of a critical microstructure for shear localization (i.e., local clustering of the longest microfractures) requires a characteristic amount of plastic axial strain, which depends on deformation conditions. In brittle faulting, distributed microfracturing is confined within limited regions of the rock volume, which expedites crack clustering and fault nucleation at low characteristic strains. In ductile faulting, distributed microfracturing occurs more uniformly throughout the rock volume, delaying shear localization to high characteristic strains. Accurate prediction of shear localization requires models that describe crack interactions of the largest flaws that account for crack clustering.

Experimental investigation on influence of vertical stirrup legs to shear failure behavior in RC beams

Conventional close stirrup has been widely used in RC beams to avoid shear failure behavior but the effect of internal vertical stirrup legs on the shear strength and the initiation of three-dimensional diagonal shear crack in RC beams is still debatable. In this study, three-dimensional crack evaluation was conducted to determine the shear failure mechanism of RC beams with different (two, three and four) vertical stirrup legs across beam width, with almost same stirrup contribution in design equation, using three-point loading test. The load displacement relationship, surface crack initiation and propagation, internal cracking patterns in cross section, vertical stirrup leg strain and concrete strain relationships, shear resistance components were discussed in detail. It was concluded that the presence of two equally spaced internal vertical stirrup legs with conventional close stirrup restricts the initiation and propagation of internal cracks to side surfaces of tested RC beams and influenced the shear strength.

Experimental and simulation research on rupture behavior of coal-based solid waste material backfilling column under non-uniformly distributed load with different loading ratios

Artificial construction backfilling columns underground based on coal-based solid waste materials is an important method to slow down surface subsidence and reduce the environmental pollution caused by coal gangue hills and fly ash. Taking the Xinyang coal mine as an example, based on a self-developed non-uniform load application device, acoustic emission (AE) and digital image correlation (DIC) monitoring technology, the evolution law of rupture behavior of coal-based solid waste material backfilling columns under different loading ratios was revealed. When the loading ratios are 1, 1.1319, 1.3585, 1.6371, and 2.0631, the average compression strength with the same material ratio is 3.96 MPa, 4.05 MPa, 4.22 MPa, 4.57 MPa, and 3.94 MPa, respectively. It is indicated that an increase in the loading ratio within the critical range is beneficial for stimulating the collaborative bearing of different parts inside the backfilling columns. From the perspective of the internal rupture behavior of the backfilling columns, the increase in loading ratio promotes a significant increase in the proportion of shear cracks, which has increased from 17.07% to 37.02%, resulting in the shear failure of backfilling columns. Meanwhile, as the loading ratio increases, the crack initiation position gathers from the left and right sides to the middle, and the final crack shape gradually transitions from two inclined and parallel main cracks to an inverted "V" shaped intersecting main cracks. The research is of great significance for improving the understanding of the failure law of backfilling columns and the safety evaluation of engineering-bearing structures under non-uniform loads.

A Review of Sheet Metal Forming Evaluation of Advanced High-Strength Steels (AHSS)

This paper presents a review on the formability evaluation of AHSS, enhancing necking-based failure criteria limitations. Complementary fracture/damage constitutive modeling approaches specifically tailored to formability evaluation, validated through numerical and experimental methods, are also subjects of research. AHSS are widely processed through sheet metal forming processes. Although an excellent choice when lightweight, high-strength, and ductility are critical factors, their multi-phase microstructure accentuates forming challenges. To accurately model forming behavior, necking-based failure criteria as well as direct fracture models require improvements. As a necking-based failure model, the conventional forming limit diagram/curve (FLD/FLC) presents limitations in estimating direct fracture (surface cracks, edge cracks, shear cracks), as well as deformation histories under non-linear strain paths. Thus, significant research efforts are being made towards the development of advanced fracture constitutive models capable of predicting fracture scenarios without necking, which are more frequently observed in the realm of AHSS. Scientific community research is divided into several directions aiming at improving the forming and fracture behavior accuracy of parts subjected to sheet metal forming operations. In this review paper, a comprehensive overview of ductile fracture modeling is presented. Firstly, the limitations of FLD/FLC in modeling fracture behavior in sheet metal forming operations are studied, followed by recent trends in constitutive material modeling. Afterwards, advancements in material characterization methods to cover a broad range of stress states are discussed. Finally, damage and fracture models predicting failure in AHSS are investigated. This review paper supplies relevant information on the current issues the sheet metal forming community is challenged with due to the trend towards AHSS employment in the automotive industry.