Theoretical and Applied Fracture Mechanics

Papers
(The TQCC of Theoretical and Applied Fracture Mechanics is 14. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-12-01 to 2025-12-01.)
ArticleCitations
Solutions of crack constraint parameter in 3D models − I: Through curve shape similarity101
Investigation of the compression-shear fracture characteristics of flaw-filled sandstone under confining pressure94
Relevance of displacement softening model in discrete element method to investigate structural and grain size scaling effect92
Foreword – Special issue on Notch Mechanics88
An implicit adaptive finite volume-based phase-field model for dynamic fracture86
Study on the static critical stress intensity factors of sandstone in a water environment based on semicircular bending specimens78
A comparison between FEM predictions and DIC results of crack tip displacement field in CT specimens made of titanium73
Isogeometric boundary element method for isotropic damage elastic mechanical problems71
The influence of SC-CO2 on the shales’ fracture behavior described by using ultra-fast time resolution method and the damage fracture constitutive model: A case study of the Cretaceous Qingshankou for68
Photoelastic analysis of crack terminating at an arbitrary angle to the bimaterial interface under four point bending66
Effects of adhesive layer thickness on the fracture properties of a concrete-epoxy resin interface63
Experimental investigation on open-hole CFRP laminate under combined loading using acoustic emission and digital image correlation62
Mechanical behavior and fracture mechanism of red-bed mudstone under varied dry-wet cycling and prefabricated fracture planes with different loading angles61
Optimization scheme of the precision separation process of the notched bar based on the acoustic emission hit energy angle61
Predicting sulfide stress cracking in a sour environment: A phase-field finite element study59
Effect of prefabricated flaw angle on the mechanical properties and failure characteristics of stratified cemented tailings backfill59
Crack propagation and strength characteristic of sandstone with structural defects under extensive true triaxial tests by using DEM simulation58
Study on fracture characteristics of 3D-ILC brittle solids under high-temperature loading in three-point bending58
Frozen effect of microcrack growth on compressive fracture in saturated brittle rocks57
Numerical investigation on the fracture and mechanical behaviors of marble containing two parallel fissures under triaxial compression conditions using FDEM57
Sustainable crumb rubber modified asphalt mixtures based on low-temperature crack propagation characteristics using the response surface methodology55
Mode II fracture properties of parallel neosinocalamus affinis bamboo strand lumber54
Ultra-low cycle fatigue (ULCF) in fibre-reinforced concrete beams53
Experimental investigation on mechanical properties and failure mechanism of rock-like specimens containing an arc-shaped ice-filled flaw under uniaxial compression52
Fracture mechanics analysis of bimaterial interface cracks using an enriched method of fundamental solutions: Theory and MATLAB code51
Investigation on the interaction evolution and growth behavior of multiple cracks under fatigue loading51
Crack initiation and slow growth in soda-lime glass from a self-healed crack51
Cohesive element-based chemo-thermo-mechanical multi-field coupled cracking simulation of early-age concrete50
Experimental study on compression characteristics of fractured soft rock and its Mohr-Coulomb criterion50
Research on the mechanism and dip angle effect of grouting reinforcement for fractured rock mass with expansive slurry50
Numerical & experimental assessment of mixed-modes (I/II) fracture of PMMA/hydroxyapatite nanocomposite50
Analysis and prediction of dynamic stress concentration in jointed coal using boundary element method48
Evolution of acoustic emission activity throughout fine recycled aggregate earth concrete under compressive tests47
Support vector regression-assisted finite element method for mode I-II fatigue crack growth path prediction47
Mixed mode fracture of polyolefin fibre reinforced concrete47
Stress intensity factors and T-stress for an edge cracked Brazilian disk specimen under diametrically distributed load46
Experimental investigation of the coupled effects of bedding planes and flaws on fracture evolution of soft bedded rocks based on 3D printing and DIC technologies46
On crack tip localisation in quasi-statically loaded, adhesively bonded double cantilever beam specimens by acoustic emission46
Computations of J-integral and T*-integral in elastic–plastic fracture by the quadrature element method46
A displacement-spatial co-adaptive strategy for the meshfree simulation of brittle phase-field fracture44
Comparative analysis of the effects of aggregates and fibres on the fracture performance of lightweight aggregate concrete based on types I and II fracture test methods44
Fracture toughness evolution and failure mechanisms of two-dimensional SiCf/SiC composites at temperatures up to 1500 °C in air44
Mechanical behavior of anchored rock with an infilled joint under uniaxial loading revealed by AE and DIC monitoring44
Experimental study on anchorage mechanical effect of rock bolts on cross-jointed rock mass using DIC and AE44
Bayesian analysis of acoustic emission data for prediction of fatigue crack growth in concrete43
Influence of load ratio on fatigue life assessment of AZ31B magnesium alloy under different temperatures43
Retraction notice to “Effects of tensile overload on fatigue crack growth in AM60 magnesium alloys” [Theor. Appl. Fract. Mech. 122 (2022) 103573]43
Influence of chopped basalt fibers on the fracture performance of concrete subjected to calcium leaching43
Characterization of eccentric internal crack expansion in brittle materials at low temperature43
Experimental and numerical estimation of complex stress intensity factor for the completely debonded anti-crack embedded into a weak matrix using domain integral method43
A local stress criterion to assess the effects of hydrogen embrittlement on the fracture strength of notched tensile specimens42
Foreword to ‘Special issue on small scale specimen testing’42
Analysis of mixed-mode Compact-Tension-Shear (CTS) specimens with slanted propagating cracks42
Weak interface-induced repeated kinking of a central crack in a brittle multilayered plate under remote shear loading42
Effects of bamboo waste biochar on fracture behavior of cementitious materials42
Fracture analysis of seawater sea-sand recycled aggregate concrete beams: Experimental study and analytical model41
Evaluation of the structural integrity of solid rocket propellant by means of the viscoelastic fracture mechanics approach at low and medium strain rates41
Influence of arch shaped notch angle, length and opening on the failure mechanism of rock like material and acoustic emission properties: Experimental test and numerical simulation41
Effect of micro-hole shape and arrangement on the impact properties of three-dimensional isotropic brittle structures41
Experimental studies on the extent of 3D and 2D stress–strain states at sharp V-notches40
Determining singular and non-singular Williams’ expansion terms from full-field measurements: Consideration of structural effects on fracture behavior40
Corrigendum to “Numerical investigation of the effects of the micro-parameters of the transgranular contact on the mechanical response of granite” [Theoret. Appl. Fract. Mech. 118 (2022) 103259]40
Damage assessment for steel structures subjected to cyclic pre-strain Part2: SEM in-situ observations clarifying the effect of stress state on damage evolution during plastic deformation40
Probabilistic fatigue life prediction of small sample properties notched specimens under multiaxial loading39
Fatigue life prediction of welded joints at sub-zero temperatures using modified Paris–Erdogan parameters39
Mode I and mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity39
The coupling effects of strain gradient and damage on Mode I crack tip stress fields39
Investigating failure modes and Micro-Crack classification in Mao phyllite under notched Semi-Circular bend testing39
Assessment of macroscopically inhomogeneous fracture toughness data sets using the simplified and multimodal master curve methods39
Research on fracture toughness of X80 pipeline girth welds based on quantitative assessment of fractal characteristics of fracture surfaces38
Influence of ultrasonic rolling on crack growth behavior of TC4 titanium alloy under various tensile overload conditions38
Enhanced hyperbolic Drucker-Prager criterion-based phase-field model for the brittle-ductile transition in rock under varying confining pressures38
Effect of external magnetic field on electric current-induced fracture of notched thin metallic conductors: Part 1 – Low magnetic fields38
Experimental and numerical investigation of the fracture behavior in granite specimens with two co-planar side flaws under biaxial loading38
Numerical study on roadway stress relief of surrounding rock through hydraulic fracturing-induced roof cracking based on phase-field theory37
Critical and subcritical cracking of high-strength wires obtained by cold-drawing of pearlitic and duplex stainless steels37
Experimental analysis of influence of pouring interval on fracture performance of concrete structures with cold joints37
Mixed Class I/Class II post-peak curves of mortar models of rock samples37
Determination of approximate point load weight functions and fatigue crack growth analysis for U-rib-to-deck joints36
Fracture toughness and fatigue crack growth in DMLS Co-Cr-Mo alloy: Unraveling the role of scanning strategies36
Identification of crack initiation and damage thresholds in sandstone using 3D digital image correlation36
A novel atomic J-integral concept beyond conventional fracture mechanics36
Determination of fatigue crack growth in the near-threshold regime using small-scale specimens36
Mechanical behaviors and failure mechanism of flawed sandstone containing infillings under freeze-thaw cycles and uniaxial compression36
A novel super symplectic analytical singular element for crack propagation along a bimaterial interface36
Dynamic mechanical properties and failure mechanisms of rock-like materials containing main and auxiliary holes with various arrangement inclinations and spacing ratios36
Investigations on the fracture mechanisms of Z-shaped fissured rock-like specimens35
Fatigue life prediction of AA2524 thin plate strengthened using compound laser heating and laser shot peening method35
Influence of distinct testing methods on the mode-I fracture toughness of Longmaxi shale35
Extended Voronoi cell finite element methods for fracture analysis of composites35
Investigation on stress intensity factor and fracture characteristics of SCB sandstone containing prefabricated cracks35
Development of a design method for the fracture performance of steel fiber-reinforced concrete by considering steel fiber characteristics and aggregate gradation35
An FFT-based homogenization scheme for cohesive zones with an application to adhesives and the core material of thin metal sandwich plates35
Experimental study on seepage-stress coupling failure characteristics and fracture fractal characteristics of cemented gangue-fly ash backfill with defects34
Quasi-brittle fracture analysis of large and small wedge splitting concrete specimens with size from 150 mm to 2 m and aggregates from 10 to 100 mm34
Effect of confining pressure on shear fracture behavior and surface morphology of granite by the short core in compression test34
A coupling algorithm of ordinary and non-ordinary state-based peridynamic models for fracture analysis in brittle and ductile materials34
Quantitative investigation of crack propagation and fracture mechanism of fissured granite from the mesoscopic perspective33
Dynamic compressive micro-macro fracture mechanism with the water-saturated strengthening and weakening effect in brittle rocks33
Evaluation of existing and introduction of new incremental crack propagation approaches in FEM33
Analysis of fracture process zone of coral reef limestone under dynamic impact33
A new method for predicting multi-crack fracture mechanism in the finite plate of red sandstone33
Shear fracture behavior and damage constitutive model of rock joints considering the effect of pre-peak cyclic loading33
Mechanical aspects of semi-circular sandstone fractured specimens with U-notch in the presence of various bedding angles33
Modeling crack propagation in heterogeneous granite using grain-based phase field method32
Determining Norton creep properties from small punch creep tests by using the representative stress–strain method and inverse approach32
Enhancement fracture behavior of sustainable cementitious composites using synergy between fly ash (FA) and nanosilica (NS) in the assessment based on digital image processing procedure32
Loading rate dependence of staged damage behaviors of granite under uniaxial compression: Insights from acoustic emission characteristics32
A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface32
Experimental study on the energy evolution law during crack propagation of cracked rock mass under impact loads32
Fracture properties prediction of Ultra-High-Performance Concrete (UHPC) after High-Temperature exposure based on Meso-Scale finite element analysis and artificial neural network32
Fracture and structural performance of adhesively bonded 3D-printed PETG single lap joints under different printing parameters32
An analytical model for determining realistic tensile strength and fracture toughness of fired clay bricks32
Stress evolution in rocks around tunnel under uniaxial loading: Insights from PFC3D-GBM modelling and force chain analysis32
Surface fatigue characterization and its enhancement by the engineered ultrasonic rolling process for 300 M ultrahigh strength steel32
Mixed mode (I&III) fracture behavior of cement emulsified asphalt mortar under freeze and thaw cycles32
Effect of loading rate on mode I fracture behavior of red sandstone: Insights from AE and DIC techniques31
Modelling of cracks with frictional contact based on peridynamics31
Vibration-induced crack tip flipping: A closer look at an unfamiliar phenomenon in pipeline failure analysis31
Interference study of double cracks on the inner surface of pipe bends with axial misalignment weld defects31
Phase-field ductile fracture analysis of multi-materials and functionally graded composites through numerical and experimental methods30
Experiment on progressive failure mechanism and anisotropic mechanical properties of differentially brittle-fractured sandstone under uniaxial compression30
Frequency response analysis of edge-cracked magneto-electro-elastic functionally graded plates using extended finite element method30
RETRACTED: Effects of tensile overload on fatigue crack growth in AM60 magnesium alloys30
Experimental and numerical investigation on mode I fracture properties of bedded rocks30
Influence of hot-spot on crack path and lifetime estimation of fretting-affected steel components30
An effective free-meshing and linear Step-Wise procedure to predict crack initiation and propagation30
The influence of impacting orientations and tunnel filled on the fracture characteristic of crack29
Structural integrity and life assessment of railway and aeronautical components – Review of four case studies29
Harnessing waste for sustainable construction: A novel synthesizing activators from waste for one-part geopolymer concrete and evaluating its fracture toughness29
Stress intensity factors of elliptical cracks at the weld toe29
Dislocation-based entropy as a criterion for fracture29
A new small punch test method to predict tensile properties of steels: Representative stress–strain method29
Effects of fissure inclination and spacing on crack evolution and mechanical behavior of 3D-printed horseshoe tunnel models: Experiments and SPH simulations29
A modified semi-weight function method for SIF calculation of arbitrary inclined interface crack with both single complex-root and double real-root singularities29
An improved photoelastic method for determining stress intensity factors of rock-like material29
Verification of stress transfer mechanism in fatigue crack growth under overload29
Effects and optimization of biomimetic laser shock peening on residual fatigue life improvement of aluminum alloy used in aircraft skin29
EcoBlends’up: PLA/BioPA blends composites, microfibrillated “in situ” through additive manufacturing28
Cohesive and gradient damage coupling applied to the propagation of microcracks in layered materials28
Fatigue crack propagation performance of Q690 high-strength steel and butt welds28
Mechanism in strength enhancement and fracture mode change of oscillating laser-arc hybrid fillet welding of Al alloy28
Investigating the effects of different temperatures on the mixed-mode fracture parameters in adhesively bonded joints considering cohesive zone modeling28
Numerical analysis for characterizing hydrogen embrittlement behaviors induced in STS316L stainless steel using an in-situ small-punch test28
An analytical method for determining Mode I initiation fracture toughness in multidirectional composite Laminates: Interlaminar fiber ply angle effects28
Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method28
Investigation of cracking resistance of rubberized epoxy asphalt mixture using semi-circular bending (SCB) test28
Study on dynamic loading characteristics and energy evolution of sandstone with double cracks28
Study on the influence of hydraulic pressure on the bilinear softening curve of concrete28
Effect of interlayer carbon nanotube films on the quasi-static and dynamic mode Ⅰ fracture behavior of laminated composites – An experimental and numerical investigation28
Mechanical responses and stress distribution of rock-like specimen containing a spherical defect under uniaxial compression28
Influences of matrix strength and weak planes on fracture response of recycled aggregate concrete28
Study on crack propagation behaviors of three-point bending concrete beams with small span-depth ratios28
Coherence analysis of the crack strain field in coal rock with borehole-crack composite defects27
A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO27
Dual-horizon peridynamics-based variational damage modeling for complex dynamic fractures27
Evaluation of effect of spheroidization heat treatment on mechanical properties via small punch test27
Mean stress effect on crack propagation threshold at high stress ratios27
A computationally efficient Element Edge point numerical integration scheme in the meshless method framework for solving fracture problems27
Nondimensional size dependent fracture model of concrete based on boundary effect theory27
Experimental investigation of mixed mode I-II fracture property of thermally treated granite under dynamic loading27
Investigation of stress-wave-induced crack penetration behavior at the rock-Ultra-High-Performance Concrete (UHPC) interface27
Prediction on residual flexural fatigue life of rock-concrete interface based on a deformation-controlled fatigue crack propagation criterion27
Assessment of freezing and thawing cycle (FTC) effects on mixed mode I/III fracture toughness and work of fracture of HMA asphalt mixtures26
Extended wavelet Galerkin method for mixed-mode cracked FGM plate under static and dynamic loads26
Experimental characterization of fracture toughness of X52 pipe steel using CT, SENB, and SENT specimens26
Mechanical behaviour of weakly filled granite and a unified evaluation method for macro-fine-micro multi-scale fracture characteristics26
Gpgpu-parallelized FDEM modelling of mode-I fracturing during the NSCB test under quasi-static and dynamic loading conditions26
Evaluation of fracture energy, toughness, brittleness, and fracture process zone properties for lightweight concrete exposed to high temperatures26
The role of minimum principal stress in tunnel strainburst considering spatial structure effect26
Twin and phase boundaries synergistic effect on multiscale dynamic fracture in Ni-based deformed superalloy26
Mechanical and failure characteristics of flawed granite after high-temperature cycling: An experimental study using biaxial compression26
Fracture testing and estimation of critical loads in a PMMA-based dental material with nonlinear behavior in the presence of notches25
Prediction model of S-N curve under mean stress without fatigue test or with a minimum number of fatigue tests25
Investigation on the size effect of compacted clay mode I fracture based on NDB specimens25
An averaged strain energy density based approach to predict the static notch effect in short fibre composites. Part 1: Theoretical formulation25
Sizing limitations of ultrasonic array images for non-sharp defects and their impact on structural integrity assessments25
Editorial Board25
Preface to the special issue of Theoretical and applied fracture mechanics - fatigue crack growth - multiscale modelling and crack path analysis in engineering materials25
Analysis of stress intensity factor for a crack emanating from elliptical hole subjected to compressive stress and shear stress25
Toughening and toughness degradation of concrete under varying volume fractions of coarse aggregate25
Notch sensitivity on post-cracking behaviour of ultra-high performance fibre-reinforced concrete25
Fracture toughness resistance curves for a delamination in CFRP MD laminate composites, Part II: Mixed-mode deformation25
Investigation of plastic and slipping regions at the edge of an adhered complete contact of elastically dissimilar materials25
Simulation of delamination propagation in laminated composites under Mode-I and Mixed-Mode bending with LCZ-Based R-curve cohesive zone modeling25
Quantitative visualization of 3D stress field evolution during hydraulic fracturing in reservoir rocks using 3D-printed models and digital photoelasticity techniques25
Determination of mode I fracture toughness of rocks with field fitting and J-integral methods25
Effects of initial unloading level on the mechanical, micro failure and energy evolution characteristics of stratified rock mass under triaxial unloading confining pressure25
Pseudo energy-based crack initiation criterion for asphalt-filler composite system under a fatigue shear load25
Influences of the burden on the fracture behaviour of rocks by using electric explosion of wires25
Editorial Board25
Weld crack detection in spiral-welded pipes by direct current potential drop method and backpropagation neural network25
Geometrical effect of a notch tip on fracture toughness test25
Research on the propagation characteristics of multiple cracks in steel bridge joints24
A new method for determining mode-II fracture toughness of composite curved laminates24
On formulations for modeling pressurized cracks within phase-field methods for fracture24
Numerical prediction and experiments for 3D crack propagation in brittle materials based on 3D-generalized maximum tangential strain criterion24
Effects of initial overload on the fatigue crack initiation and growth in notched plates24
Critical plane based method for multiaxial fatigue analysis of 316 stainless steel24
Degradation response of mode I and mode III fracture resistance of sandstone under wetting–drying cycles with an acidic solution24
Fracture propagation characteristics of pre-cracked red clay in roadbed filling under three-point bending24
Fracturing behavior and damage model of spatial-rotation fissured sandstone: An experimental study on freeze–thaw and fatigue loads coupling24
Prediction of the influence of loading rate and sugarcane leaves concentration on fracture toughness of sugarcane leaves and epoxy composite using artificial intelligence24
Discrete element simulation on failure mechanical behavior of transversely isotropic shale under two kinds of unloading paths24
Multiscale modelling of fracture in graphene sheets24
An accelerated phase-field model for high-cycle fatigue behaviour in quasi-brittle materials24
Mode I fracture behavior of rubber-modified unsaturated polyester resin concrete under impact loads: The effects of loading rate, rubber content and curing age24
Prediction of fracture toughness using small specimens based on machine learning23
New insights into the fracture evolution and instability warning predication for fissure-contained hollow-cylinder granite with different hole diameter under multi-stage cyclic loads23
Dynamic fracture analysis in nonhomogeneous piezoelectric materials with a new domain-independent interaction integral23
Study on shear resistance and crack resistance and toughening mechanism of fiber reinforced cement stabilized aeolian sand23
Experimental studies on the effect of cyclic thermal shock and cooling methods on the mechanical properties and fracture behavior of prefabricated fissured sandstone23
Investigation on fracture properties and FPZ evolution of concrete/rock bi-material interface after low-level fatigue loading23
Several cracks in a rectangular bar reinforced by a piezoelectric layer subjected to torsion23
Effect of the Lüders plateau on the relationship between fracture toughness and constraint for pipeline steels23
Fatigue performance of Hastelloy X at elevated temperature via small punch fatigue test23
Investigation of the compression–shear fracture propagation for rocks accounting for confining pressure and crack surface friction23
Discontinuous deformation analysis (DDA) simulations of crack propagation, branching and coalescence in brittle materials under dynamic loading23
A comparative study on characterizing the fracture toughness variations in thick-wall hydrogenation reactor welded joint by spherical indentation tests23
A novel boundary tracing method without enrichment for modeling cracks and their propagation23
Three-dimensional weight function analyses and stress intensity factors for two unsymmetric surface cracks and surface-corner cracks at a circular hole23
Effects of multiple overloads and high-low sequence loading on the fatigue crack propagation of AZ31B magnesium alloy23
Numerical simulation of frost heaving deformation of fractured rocks considering heat-force coupling23
Fracture properties of the gold mine tailings-based geopolymer under mode I loading condition through semi-circular bend tests with digital image correlation23
Analysis of tooth root three-dimensional fatigue crack initiation, propagation, and fatigue life for spur gear transmission23
Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory23
Investigation of energy-based interlayer debonding of open-graded friction course pavement under mode I fracture test23
Modeling structure-dependent fracture behaviors of anisotropic cracked chevron notched Brazilian disc shale samples: Laboratory scale testing22
Mechanical behavior of mixed-mode I-II fracture in deep laminated shale based on finite discrete element method22
A closed-form solution for thermoelastic stress analysis of perforated asymmetric functionally graded nanocomposite plates22
Effect of cork powder concentration and service temperature on strength characteristics and failure modes of tubular adhesively bonded joints22
Interfacial debonding in a thin plate bonded to a rigid substrate with a circular hole22
Reliability-based approach for structural integrity assessment of a bucket wheel excavator22
Adaptive scaled boundary finite element method for hydrogen assisted cracking with phase field model22
Phase field study of the thermo-electro-mechanical fracture behavior of flexoelectric solids22
Crack propagation mechanisms in plain woven CFRP: A focus on intralaminar fracture under mixed-mode loading22
A finite similitude approach to fatigue crack growth across the scales22
Damage and energy evolution characteristics of pre-cracked sandstone under multi-stage amplitude-increasing cyclic loading22
Remaining fatigue life estimation under varying amplitude cyclic loading conditions combining ultrasonic waves and relative strain measurements for aluminum 6061-T6 plates with a notch22
Experimental and numerical investigations on rate-dependent fracture behavior of concrete-rock interface22
Artificial neural network and YUKI algorithm for notch depth prediction in X70 steel specimens22
Research on local cyclic plastic behavior and fatigue life prediction of notched components based on digital image correlation22
Quasi-static tensile and fatigue behaviour of a metastable austenitic stainless Cr-Ni-Cu-N steel22
Mechanical behaviour and spatial fracture characteristics of granite containing weak inclusions under uniaxial loading revealed by 3D DIC and AE monitoring: The influence of extension length of planar22
Crack propagation characteristics of coal body around the borehole under different loading rates22
Effect of cyclic heating-rapid cooling on fracture behavior of notched semi-circular bend granite22
Influence of uniaxial and equi-biaxial tensile pre-straining on the high cycle and notch fatigue behaviour of AA2024-T4 aluminium alloy21
Experimental study on dynamic mechanical characteristics and fracture behaviors of coal under water–gas-temperature coupling conditions21
Long-term Freeze–thaw effect on fracture performance of asphalt mixture with reclaimed asphalt pavement, glass fiber and rejuvenator21
Acoustic emission characteristics and failure mode analysis of rock failure under complex stress state21
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