Crack Angle Research Articles

Crack evolution and fractal characteristics of fractured red sandstone based on acoustic emission parameters

Rock is a widely used engineering material, and accurate understanding of its internal microcrack evolution process during loading can provide a theoretical basis for preventing instability and failure in rock engineering. The rock pressure test system and acoustic emission equipment were used to carry out uniaxial loading and acoustic emission monitoring tests on fractured red sandstone. Based on the RA and AF values of acoustic emission and the fractal theory, the internal crack patterns and evolution rules of red sandstone with different crack angles were explored. The results show that the compressive strength of red sandstone varies with the crack Angle in the shape of “U”, and there is an obvious stress drop after the elastic stage of 30° and 45° crack red sandstone, which has a good correspondence with the acoustic emission ringing count rate. During the loading process, the damage mainly caused by tension cracks first appears inside the rock, and then the tension cracks increase steadily and the shear cracks gradually increase, indicating that the rock enters the stage of fracture instability development. With the development of shear cracks, the peak strength is finally reached and the instability failure occurs. During the loading process of 30° fracture red sandstone, the corresponding stress drop phenomenon of “shear crack group” appears. According to the D/S statistical analysis of different crack samples based on acoustic emission ringing count, the fractal dimension presents a decreasing-rising-decreasing trend with the increase of crack inclination, which corresponds to the change of the complexity of crack development in rock.

Study on non-destructive visualization identification of concrete internal cracks based on SH array ultrasound

Ultrasonic nondestructive testing (NDT) technology was one of the most frequently used and fastest-developing NDT techniques in detection field. This method had high detection sensitivity, more accurate defect localization, and was harmless to the human body. With the development of ultrasonic testing technology, modern ultrasonic imaging technology generally had automatic data acquisition and processing functions, which allowed for intuitive and clear recognition of internal defects by the human eyes. The overall purpose of this study was to visualize the cracks in concrete by synthetic aperture focusing technique (SAFT) and full-waveform inversion (FWI) algorithms on the basis of ultrasonic nondestructive testing technology. At present, there have been studies on the use of ultrasonic instruments to detect the internal defects of concrete. However, the accuracy and authenticity of this method have not been compared in previous studies. Therefore, in this experiment, four concrete specimens with different buried depths, angles, shapes, and thicknesses of cracks were designed. Based on SH ultrasonic wave NDT technology, two types of operations were performed on the collected ultrasonic wave data: one was the application of SAFT method, and the other was the first application of FWI method for detecting internal cracks in concrete. The study found that both algorithms were most accurate in determining the burial depth of cracks, with error results not exceeding 10 %. They also showed good recognition effects for the angle, shape, and thickness of the buried cracks. This proved that both identification methods had the capability to recognize internal cracks. The Introview software bundled with the ultrasonic instrument could identify cracks using SAFT directly and quickly. When FWI was used with MATLAB computation, the results were more precise and intuitive. The overall purpose of this study was to detect cracks in concrete by SAFT and FWI algorithms on the basis of ultrasonic nondestructive testing technology. Combining the two crack identification techniques could be of great significance for ensuring the long-term safety and stability of concrete structures, providing strong support for structural maintenance and reinforcement.

Crack propagation behavior and failure prediction of rocks with non-parallel conjugate flaws: Insights from the perspective of acoustic emission and DIC

Rock-like containing non-parallel conjugate flaws specimens (NPCFS) were prepared and uniaxial compression crack propagation tests were conducted employing acoustic emission (AE) and digital image correlation (DIC) techniques. The results show that: the angle of conjugate unilateral cracks increases, the average load-bearing capacity of the rock rises. Dominant frequencies from different conjugate defect angles exhibit distinct bimodal characteristics (low-frequency: 80–140 kHz, intermediate-frequency: 260–320 kHz). The concept of AE dominant frequency ratio β is proposed and introduced to quantify the strength of macro-scale failure of the specimens. The AE multiparameter is proposed to predict the failure load, and the mean value of failure load is predicted to be in the range of 86–93 % (failure load), the prediction interval of Ib value is in the range of 95–99 %, the prediction interval of critical slowing down variance value is in the range of 90–95 %, while the prediction interval of autocorrelation coefficient is in the range of 83–90 %. A favorable correlation was observed between AE events in NPCFS and surface deformations observed through DIC technology. Both ends of the conjugate flaw cannot propagate simultaneously; once one extends, the other ceases further expansion, forming a primary failure line that propagates towards the direction of the primary compressive stress.

Damage index correlation in massive granite-porous backfills under hydromechanical triaxial cyclic loading using acoustic emissions and X-ray computed tomography

The characterization accuracy of damage indices in massive and porous composite biomaterials under complex osmotic conditions has long been a challenge in engineering materials science. Establishing correlations between damage indices calculated using different methodologies is crucial to validate and improve defects characterizations. In this study, we investigated the damage index correlation of cylindrical massive granite-porous backfill structural composites under both dry and seepage conditions. A series of triaxial cyclic loading and unloading tests were conducted on specimens under hydromechanical conditions with varying osmotic pressures (0, 1, 3, 5, 7, and 9 MPa) and a confining pressure of 9 MPa involving acoustic emission monitoring and phase-based 3D nondestructive CT scanning. The results revealed the AE energy was lower under osmotic conditions compared to dry conditions. The AE Damage Index (DAE), defined by separating tensile and shear microcracking signals, significantly increased from 0.32 to 0.55 with rising osmotic pressure. 3D mesoscopic fracture visualization provided detailed insights into the fractures in granite and backfill interfaces. The number of small-angle cracks increased with osmotic pressure, and the crack inclination distribution range expanded from 63°- 85° to 49°–80°. The average crack angle showed a significant monotonic decrease with increasing osmotic pressure. An Energy Dissipation Damage Index (DED) was defined, and its correlation with the DAE under dry conditions was modeled using a reciprocal function DED=a/(DAE+bσ3)+c. This novel approach offers insights into the transition points between tensile and shear-dominated failure stages. Furthermore, an exponential function DV=aDAEb(b<0) was used to model the correlation between AE Damage Index and Visual Damage Index (DV) under osmotic conditions. The damage indices derived from different methods can be mathematically correlated, providing a comprehensive evaluation of material damage states. The study found the flow transition between different natural-human medias results in different damage mechanisms, which are all obey the correlation law. These damage mechanisms offered constructive recommendations for engineering applications based on varying ratios of osmotic pressure to confining pressure.

Effect of aggregate size on the slump and uniaxial compressive strength of concrete: a DEM study

The aggregate size and particle-size distribution (PSD) can change the packing density, slump, and strength of concrete. The micromechanical effects of aggregate size on the slump and strength remain unclear. The current numerical study examined concrete behavior using slump and uniaxial compressive strength (UCS) tests considering the aggregate size distribution using the discrete element method. The effect of the aggregate size on the packing density, UCS, and slump of the concrete was analyzed. To accomplish this, we evaluated how variations in the uniformity and curvature coefficients of the PSD, as well as the specific surface area of the samples, were affected by changes in aggregate size. Although the simulations were based on standard specimens from the laboratory, the results showed good agreement with the documented experimental results. Briefly, at a 40–60% fine aggregate content, the packing density and compressive strength of the concrete reached their peaks and caused a decrease in the height of the slump. The uniformity and curvature coefficients did not influence the slump height. The induced shear band could be tracked during the UCS tests and the crack angles could be measured. At the optimum fine content (40–60%), the shear bands were primarily localized and propagated through the samples having different fine contents.

Microstructure and mechanical properties of TiB2/Al-5Cu composites fabricated by multi-material laser powder bed fusion

This study compares the fabrication of aluminum matrix composites (AMCs) using multi-material laser powder bed fusion (MM-LPBF) with that of conventional methods. The MM-LPBF AMCs exhibit a lamellar structure with a microhardness of 90±2 HV0.05 in the soft zone and 126±2 HV0.05 in the hard zone. The microhardness of the LPBF AMCs is 97±1 HV0.05. Compression tests show that the MM-LPBF AMCs have anisotropic properties with a compressive yield strength of 155±2 MPa along the building direction and 186±4 MPa along the scanning direction. In comparison, the LPBF AMCs have a compressive yield strength of 171±4 MPa. The fracture morphology shows that a single crack in the lamellar composite is accompanied by a deflection of the crack angle. In summary, this work showcases the potential of the MM-LPBF technique for tailoring material properties on demand.

Ultrasonic characterization of defects in polycrystalline materials based on TFM image reconstruction using denoising diffusion probabilistic models

This paper presents a refined ultrasonic total focusing method (TFM) for accurately characterizing key defect parameters including size, orientation, and location in complex materials. The proposed approach aims to accurately reconstruct the defect shape in images compromised by grain interference. First, a TFM image database was generated with varying defect parameters and grain noise levels by adopting a custom forward modeling process based on superposition of defect and grain scattering data. Second, a new architecture called TFM-DDPM was then proposed which incorporates TFM and the conditional denoising diffusion probabilistic model (DDPM). Third, pixel-level uncertainty can be quantified through repeated sampling of noise which follows a standard normal distribution. An acceptance criterion for the reconstruction was further established by analyzing the quantified uncertainty. In simulation, the median Dice coefficient between the de-noised TFMs of 30° cracks and their corresponding ground truth images increased from 0.5585 to 0.9137 using the proposed approach, and the median IoU metric rose from 0.3875 to 0.8408. By applying the 6-dB drop approach to the reconstructed images, the root mean squared errors (RMSEs) of size, angle and location were decreased by 93.59%, 86.90% and 86.25%, respectively. It is also demonstrated that our method can reject 69.19% of incorrect characterization results caused by high levels of noise and/or images with steeply inclined (e.g., 45°) cracks, while accepting 97.29% accurate results. Experimental results obtained on nickel-based alloy K403 specimens also exhibited significant improvements. For 2–3 mm cracks, the average sizing error reduced from 0.46 mm to 0.13 mm, and the error in crack angle decreased from 28.63° to 1.50°. Comparable performance enhancements were observed for 4–5 mm cracks using the proposed approach.

Free vibration of functionally graded graphene platelets reinforced porous composite plate with a diamond-shaped hole and two cracks

This paper investigates the free vibration of the functionally graded graphene platelets reinforced porous composite (FG-GPLRPC) plate with a diamond-shaped hole and two cracks. Based on the Mindlin-Reissner plate theory and Hamilton principle, the governing equations and boundary conditions are derived. These equations are discretized using the generalized differential quadrature finite element method (GDQFEM), and the natural frequency is obtained by numerical solutions. The effects of the hole size, crack length and crack angle on the natural frequency are discussed. The results show that the natural frequency decreases with increasing crack angle and crack length.

Influence of collapsible shape of Loess Foundation on high-speed railway subgrade under train vibration loading

Collapsible loess has special sensitivity to water, and its engineering mechanical properties deteriorate significantly after immersion in water, causing the foundation to sink, which seriously threatens the safety and stability of the high-speed railway subgrade under train vibration loading. Studying this effect is essential to prevent and control the disasters of high-speed railway subgrades. In this study, a model with the function of simulating foundation settlement is established to conduct disaster testing of high railway subgrade under train vibration loading. The results indicate that when different foundation shapes are settled, the surface of the subgrade under static load is gradually settled in a short time, and the settlement value of the track surface is lower than that of the corresponding subgrade surface. Under train vibration load, the maximum dynamic settlement occurs at the middle of the subgrade slope, which is smaller than the corresponding settlement under static load. The number of stabilization times required from different monitoring positions on the subgrade surface is different under different excitation forces, and the number of stabilization times required is more in the middle of the subgrade slope and the slope shoulder. The influence of train speed on subgrade has a critical respond speed that increases with increasing vibration times. There are horizontal, vertical and 45° angle cracks in the middle of subgrade slope. It is qualitatively assessed that the slope of the high-speed railway subgrade in the collapsible loess area is unstable under the effect of train load. The data and rules provided in this document provide some reference values for the construction of a high-speed railway in the collapsible loess area.

Crack coalescence and failure behaviors in slate specimens containing a circular cavity and a pre-existing flaw pair under uniaxial compression

The flaws (fractures) widely existing in rock mass pose a threat on the stability of many underground cavities. This study aims at investigating the failure process of a cavity affected by adjacent flaws. A number of slate specimens containing a circular cavity and a pre-existing flaw pair were tested under uniaxial compression. Varied flaw configurations were obtained by changing the flaw inclination angle with respect to horizontal and the spacing between flaw pair and cavity. Three main types of cracks emanated from the pre-existing flaw tips, and played a dominant role in the failure process of cavity, comprising primary wing cracks (tensile cracks) and two types of secondary cracks (quasi-coplanar shear cracks and oblique shear cracks). The initiation and propagation of these cracks were highly dependent on the flaw pair configurations. When the pre-existing flaw pairs were non-parallel to the loading direction, (1) mostly, coalescence occurred both in the tensile and compressive stress concentration regions around cavity; (2) in most cases, the quasi-coplanar and oblique shear cracks were the predominant cracks leading to the coalescence between the compressive stress concentration regions of cavity and the pre-existing flaw pair tips. When the pre-existing flaws were parallel to the loading direction, the combination of inclined shear cracks and tensile cracks or inclined shear cracks only dominated the failure of cavity. The initiation angles of wing cracks, quasi-coplanar shear cracks and oblique shear cracks agreed well with the theoretical predictions by the maximum tangential strain criterion (MTSN), Mohr-Coulomb criterion (M−C) and maximum shear stress criterion (MSS), respectively.

New insights into fracture and cracking simulation of quasi-brittle materials based on the NMMD model

The simulation of crack-induced failure is of vital importance for the safety and integrity assessment of solids and structures but still challenging. Being the foremost approach, fracture mechanics is plagued by the logical inconsistency in dealing with crack and non-cracked region, and to make matters worse, it has been contradicted by the ongoing experiments that the fracture energy is not a material constant irrelevant to geometry even for the unsophisticated situations. In this paper, based on the recently proposed nonlocal macro-meso-scale consistent damage (NMMD) model, it is demonstrated that the logical consistency of governing equations either on crack-tip or off crack-tip plays a crucial role in the complete solution of cracking problems. To this end, the central themes of fracture mechanics, including the definition of an idealized crack, the separated equilibrium laws and the cracking criteria attached to crack-tip, are firstly revisited. Then, after a concise description of NMMD model with emphasis on the geometrical transmission form micro- to macro-scale and the physical–mechanical translation from geometry to energy, it is theoretically proved that the geometry-based damage zone reproduces idealized crack as a limit when the nonlocal characteristic length, i.e., the influence radius in NMMD model, tends to zero. As a result, the separated equilibrium laws of fracture mechanics can be covered by NMMD model with a unified set of governing equations that does not distinguish between points at crack surface and at non-cracked region. This advantage permits NMMD model to be well-suited to analyze both crack-induced failure problems with and without pre-existing cracks in the absence of additional cracking criteria. In contrast, owing to its macro-meso-scale consistent feature, a new criterion for kinking angle of crack, the maximum stress intensity factor (SIF) of mode-I, can be derived from NMMD model. Some representative numerical examples are also presented to further confirm the above intrinsic link to fracture mechanics. In particular, the superiority of the NMMD model is demonstrated by capturing not only the non-constant fracture parameters (especially the fracture energy) but also the cracking initiation not from the pre-existing crack-tips, which are revealed by experimental results but contradict fracture mechanics. These investigations imply that the NMMD model could provide a potential avenue to understand when and how cracks nucleate and propagate based on a two-scale perspective.

Unveiling solid-solid contact states in all-solid-state lithium batteries: An electrochemical impedance spectroscopy viewpoint

All-solid-state lithium batteries (ASSLBs) are strongly considered as the next-generation energy storage devices for their high energy density and intrinsic safety. The solid-solid contact between lithium metal and solid electrolyte plays a vital role in the performance of working ASSLBs, which is challenging to investigate quantitatively by experimental approach. This work proposed a quantitative model based on the finite element method for electrochemical impedance spectroscopy simulation of different solid-solid contact states in ASSLBs. With the assistance of an equivalent circuit model and distribution of relaxation times, it is discovered that as the number of voids and the sharpness of cracks increase, the contact resistance Rc grows and ultimately dominates the battery impedance. Through accurate fitting, inverse proportional relations between contact resistance Rc and (1 − porosity) as well as crack angle was disclosed. This contribution affords a fresh insight into clarifying solid-solid contact states in ASSLBs.

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.

Reactive molecular dynamics of the fracture behavior in geopolymer: Crack angle effect

Reactive molecular dynamics was applied in this study to construct the sodium aluminosilicate hydrate (N-A-S-H) and tensile fracture models with various crack angles. The impact of crack angle on the behavior of N-A-S-H fractures was explored while considering structural mechanical properties and energy evolution. Furthermore, the fracture toughness and brittleness index for various crack angle models were calculated. The findings indicated that the ultimate strength and elastic modulus of the fracture models grew linearly with the increase in crack angle. The fracture toughness value progressively grew while the model’s elastic energy efficiency and new surface energy efficiency decreased simultaneously. The 45° crack model possessed the largest oblique crack development surface in the fracture process due to the coupling effect of tensile and shear stress. Its elastic energy efficiency decreased as well the most, while the new surface energy efficiency increased and the fracture toughness value dropped sharply. It is crucial to place a stronger emphasis on spotting cracks both in the in-service structures or structures being demolished. This ensures optimal performance and safety by enabling more effective adjustments to the direction of external forces and energy input.

Fault slip and seismic source response characteristics under induced stress wave

As coal mining depth and structural complexity increase, the failure severity of mining-induced fault activation leading to rock bursts escalates. Fault fracture zones, consisting of various secondary structures, are essential for understanding tectonic evolution and seismic wave propagation. The interaction between mining-induced stress waves and in-situ stress complicates the dynamics and activation markers of fault fracture zones. This paper aims to clarify the patterns of stick–slip instability and stress evolution in these zones under coal mining-induced stress waves. Using theoretical models and continuous-discrete coupling simulations, the study explores the dynamic response of fault fracture zones in the meta-instability stage, the micro-scale fracture force chain structure, and the distribution and synergistic instability of fault plane seismic sources. The research shows that fault fracture zones changes stress wave propagation path and energy redistribution due to its heterogeneity leads to multiple times decomposition of wave field. Minor delamination between the hanging wall and footwall can trigger unstable slip. Tensional seismic sources with extensive failure drive fault slip. Dynamic stress waves disrupt force chains near seismic sources, increasing hazard levels. Static in-situ stress affects shear seismic sources by influencing porosity and crack angles. Seismic sources along the fault strike transition from divergent to concentrated, trending horizontally. In the meta-instability stage, the initial fracture area locks, with strong structures causing cohesive fractures in the middle of the fault zone, releasing strain energy and forming a sudden increase in slip intensity. These findings provide crucial insights into fault fracture-development-activation markers, fault region stress deformation evolution mechanisms, and risk control of fault-induced rock bursts.

Phase field thermal shock analysis of rotating porous cracked pretwisted FGM microblade using exact shear correction factor

The present work is an attempt to develop a simple and accurate finite element formulation for the thermal shock analysis of the rotating porous cracked pretwisted functionally graded material (FGM) microblade using modified coupled stress theory in conjunction with phase-field and first-order shear deformation theory (FSDT). The physical neural surface is taken as the reference plane and the exact value of the shear correction factor is calculated from the shear stiffness. The elastic properties are assumed to be temperature-dependent and the upper ceramic layer is subjected to a high thermal shock whereas the bottom metallic layer is maintained at room temperature or is thermally insulated. The governing differential equation for the present analysis is derived using Hamilton’s principle and Newmark average acceleration method is used to obtain the transient response of the rotating porous cracked pretwisted FGM microblade subjected to thermal shock. The results obtained from the present finite element formulation are first validated with several benchmark examples available in the literature. New results are presented investigating the effect of crack depth, crack location, crack angle, rotational velocity and material scale ratio on the transient response of the cracked rotating porous pretwisted FGM microblade subjected to thermal shock. It is shown here that the parameters like crack depth, crack location and crack angle have a significant influence on the transient response of the rotating porous cracked pretwisted FGM microblade.

Experimental and numerical study on the effect of friction between crack faces on fracture parameters of hot mix asphalt concrete

This article investigates the effect of friction between crack faces in ASCB (asymmetric semi-circular bend) specimen on fracture parameters of hot mix asphalt concrete. To achieve this, fracture tests were conducted on ASCB specimens containing cracks with different angles (0, 10, 20, 30, and 40°). In addition to the fracture tests, friction tests were also performed by designing a simple fixture. Subsequently, finite element analyses were carried out, and friction coefficients between crack faces were calculated based on the results of fracture and friction tests. Furthermore, two fracture criteria, ASED (average minimum strain energy density) and MTS (maximum tangential stress), were examined under two different scenarios: assuming zero-friction and non-zero friction between crack faces to predict fracture load and fracture strength. The fracture tests showed that with an increase in the crack angle, the fracture load initially decreased up to the crack angle of 20°, and then increased. Furthermore, the friction tests revealed that an increase in the normal load led to an increase in the friction coefficient. As per finite element results, the crack face contact occurred at a crack angle of 13.1°. Hence, crack faces in the ASCB specimens with the crack angles of 20, 30, and 40° had friction, which significantly affected the fracture parameters. The results also indicated that the average error values for the MTS and ASED criteria compared to the experimental results were 22.8 % and 18.8 %, respectively, when the friction` between crack faces is ignored, and 12.4 % and 4.0 % for the scenario that the friction effect is taken into account. The ASED criterion demonstrated higher accuracy than MTS criterion. Additionally, the average error value of fracture strength predicted by the ASED criterion with assuming non-zero friction was 4 %, indicating good predictive accuracy for fracture strength.

Development of an improved limit pressure solution for shape-distorted 90o pipe bends with through-wall circumferential cracks

PurposeThis paper presents the approximate limit pressure solution for shape-imperfect and through-wall circumferential cracked (TWCC) 90° pipe bends at the intrados region. Finite element (FE) limit analysis was used to estimate the limit pressure by considering the small geometrical change effects.Design/methodology/approachThree-dimensional (3D) geometric linear FE methodology was implemented to investigate the limit pressure of structurally deformed TWCC 90° pipe bends. The material considered in the analysis is elastic perfectly plastic (EPP). The limit pressure of TWCC shape-distorted pipe bends was predicted from the corresponding internal pressure when von-Mises stress was equal to or just exceeded the material’s yield strength for all the models. The theoretical solution which was published in the literature was used to evaluate the current FE approach.FindingsOvality Co and TWCC at the intrados region caused a considerable impact on pipe bends, while the thinning? Ct produced a negligible effect and hence was not included in the analysis. With the combined effect, the bend portion of pipe bend experiences substantial influence, and the TWCC effect consequently increases with 45o, 60o and 90o crack angles and decreases the limit pressure of pipe bends. An improved closed-form empirical limit pressure solution was proposed for TWCC shape-distorted pipe bends at the intrados region.Originality/valueIn the limit pressure analysis of 90° pipe bends, the implications of structural irregularities (ovality and thinning) and TWCC have not been examined and reported.

Investigation on fatigue parameters in railway wheels using a critical plane model

The contact areas between rail and wheel are critical in determining the performance of rail vehicles. Analyzing the mechanics, materials, tribology, and geometry of the interface is important to understand the contact damage mechanisms, fatigue parameter and fatigue life. Developing a simplified and novel approach to predict crack initiation and fatigue life is key for investigating contact fatigue of rail wheel interaction. This study aims to investigate rolling contact fatigue (RCF) cracks and fatigue life in railroad wheels using Finite Element Model (FEM). Using a proper material model that accounts for plastic shakedown, ratchetting, and cyclic hardening for both the rail and wheel materials, the FEM model is analyzed with the help of Abaqus 2020 tool. The submodelling technique was implemented to reduce computation demand. Stress and strain history outputs extracted from the submodel (at 0 mm, 1.3 mm, 2.6 mm, and 3.6 mm depths) were used to predict critical plane orientation, crack initiation and fatigue life using critical plane models. The orientation of critical (crack) plane was found using a novel MATLAB algorithm by searching for a plane with maximum fatigue parameter (FPmax). The investigation reveals that the location of maximum damage is the subsurface and the crack angles fall within the range of (0°, 40°), (62°, 123°) and (143°, 180°) with a 5 % margin and at a depth of 2.6 mm below the wheel surface. The determined fatigue crack initiation and life at this specific location were 6178 and 7174 cycles, respectively. Predicting the critical zone which is susceptible to shorter crack initiation and fatigue life is a crucial to prevent wheel failure.

Analysis of tensile failure mechanism in intact, foliated, and cracked rocks using distinct element method: Influence of anisotropy

A thorough numerical analysis was conducted to understand the failure mechanisms and behaviour in intact rocks, foliated rocks and rocks with pre-existing cracks using the Brazilian tensile strength tests. The dominant anisotropy in rocks, especially foliated rocks like phyllites, slates and schists, as well as sedimentary rocks like sandstone, limestones and shale, leads to complex failure mechanism. The presence of cracks leads to anisotropy causing different mechanisms of failure and variation in tensile strengths of rock mass. Numerical simulations were conducted based on experimental studies of foliated phyllite and dolomitic limestone from the Tejam Group, Lesser Himalaya. The variations in failure behaviour and strength of foliated rocks were studied for samples at different foliation angle using the particle distinct element model. The simulation results show that with increase in foliation angle to the loading direction (from 0° to 90°), the peak tensile strength of rocks remains almost same for specimens with θ = 0° to 30° and then increases linearly till 90°. The influence of cracks as anisotropy was also studied by changing crack length (from 5 mm to 30 mm) and angle (from 0° to 90°). The development of failure patterns in rocks with pre-existing cracks leads to a better understanding of the failure modes and makes it possible to interpret failure behavior, pattern, and strength parameters. With increase in crack length, the tensile strength of rocks decreases. Overall, this study depicts the influence of anisotropy and microparameters on failure modes and behavior in Brazilian tensile strength tests on foliated and pre-cracked rocks.