A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Dynamic Phase Field Description on Ductile Fracture Process

In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

Comparative efficacy of proximal femoral nail vs dynamic condylar screw in treating unstable intertrochanteric fractures

BACKGROUND Among the most frequent hip fractures are trochanteric fractures,which usually occur from low-energy trauma like minor falls,especially in older people with osteoporotic bones.AIM To evaluate the treatment efficacy of dynamic condylar screws(DCS)and proximal femoral nails(PFN)for unstable intertrochanteric fractures.METHODS To find pertinent randomized controlled trials and retrospective observational studies comparing PFN with DCS for the management of unstable femoral intertrochanteric fractures,a thorough search was carried out.For research studies published between January 1996 and April 2024,PubMed,EMBASE,Scopus,Web of Science,Cochrane Library,and Google Scholar were all searched.The complete texts of the papers were retrieved,vetted,and independently examined by two investigators.Disputes were settled by consensus,and any disagreements that persisted were arbitrated by a third author.RESULTS This study included six articles,comprising a total of 173 patients.Compared to the DCS,the PFN had a shorter operation time[mean difference(MD):-41.7 min,95%confidence interval(95%CI):-63.04 to-20.35,P=0.0001],higher success rates with closed reduction techniques[risk ratio(RR):34.05,95%CI:11.12-104.31,P<0.00001],and required less intraoperative blood transfusion(MD:-1.4 units,95%CI:-1.80 to-1.00,P<0.00001).Additionally,the PFN showed shorter fracture union time(MD:-6.92 wk,95%CI:-10.27 to-3.57,P<0.0001)and a lower incidence of reoperation(RR:0.37,95%CI:0.17-0.82,P=0.01).However,there was no discernible variation regarding hospital stay,implant-related complications,and infections.CONCLUSION Compared to DCS,PFN offers shorter operative times,reduces the blood transfusions requirements,achieves higher closed reduction success,enables faster fracture healing,and lowers reoperation incidence.

Mixed-mode fracture behavior in deep shale reservoirs under different loading rates and temperatures

In the last years,shale gas has gradually substituted oil and coal as the main sources of energy in the world.Compared with shallow shale gas reservoirs,deep shale is characterized by low permeability,low porosity,strong heterogeneity,and strong anisotropy.In the process of multi-cluster fracturing of horizontal wells,the whole deformation process and destruction modes are significantly influenced by loading rates.In this investigation,the servo press was used to carry out semi-circular bend(SCB)mixedmode fracture experiments in deep shales(130,160,190℃)with prefabricated fractures under different loading rates(0.02,0.05,0.1,0.2 mm/min).The fracture propagation process was monitored using acoustic emission.The deformation characteristics,displacementeload curve,and acoustic emission parameters of shale under different loading rates were studied during the mixed-mode fracture propagation.Our results showed that during the deformation and fracture of the specimen,the acoustic emission energy and charge significantly increased near the stress peak,showing at this point the most intense acoustic emission activity.With the increase in loading rate,the fracture peak load of the deep shale specimen also increased.However,the maximum displacement decreased to different extents.With the increase in temperature,the effective fracture toughness of the deep shale gradually decreased.Also,the maximum displacement decreased.Under different loading rates,the deformation of the prefabricated cracks showed a nonlinear slow growthelinear growth trend.The slope of the linear growth stage increased with the increase in loading rate.In addition,as the loading rate increased,an increase in tension failure and a decrease in shear failure were observed.Moreover,the control chart showing the relationship between tension and the shear failure under different temperatures and loading rates was determined.

Dynamic fracture of Ti-6Al-4V alloy in Taylor impact test

The dynamic fracture behaviors of Ti-6Al-4V alloy at high strain rate loading were investigated systemically through Taylor impact test, over the range of impact velocities from 145 m/s to 306 m/s. The critical impact velocity of fracture ranges from 217 m/s to 236 m/s. Smooth surfaces and ductile dimple areas were observed on the fracture surfaces. As the impact velocity reached 260 m/s, the serious melting regions were also observed on the fracture surfaces. Self-organization of cracks emerges when the impact velocity reaches 260 m/s, while some special cracks whose ＂tips＂ are not sharp but arc and smooth, and without any evidence of deformation or adiabatic shear band were also observed on the impact end surfaces. Examination of the sections of these special cracks reveals that the cracks expand along the two maximum shear stress directions respectively, and finally intersect as a tridimensional ＂stagger ridge＂ structure.

Caustics study of the effect of glass fibres on dynamic fracture of hardened cement paste

The reflected optical caustics method is applied to study dynamic fracture problems in hardened cement paste. First both the unreinforced cement paste and the glass fibres reinforced cement paste specimens were fabricated and the reflective coating on the surface of the specimen was prepared. Secondly the crack path and the shadow spot patterns during the crack propagation process for the two specimens were recorded by using a multi-spark high speed camera.Thirdly some dynamic parameters of two cement paste specimens including crack onset time the dynamic stress intensity factor and crack growth velocity were determined and analyzed comparatively.This indicates that the glass fibres can improve the fracture resistance and delay fracture time.These results will play an important role in evaluating the dynamic fracture properties of cement paste.

Laboratory visualization of damage asymmetry formation of rock fracture via acoustic emission and digital imaging correlation

Rock fracture mechanics and accurate characterization of rock fracture are crucial for understanding a variety of phenomena interested in geological engineering and geoscience.These phenomena range from very large-scale asymmetrical fault structures to the scale of engineering projects and laboratory-scale rock fracture tests.Comprehensive study can involve mechanical modeling,site or post-mortem investigations,and inspection on the point cloud of the source locations in the form of earthquake,microseismicity,or acoustic emission.This study presents a comprehensive data analysis on characterizing the forming of the asymmetrical damage zone around a laboratory mixed-mode rock fracture.We substantiate the presence of asymmetrical damage through qualitative analysis and demonstrate that measurement uncertainties cannot solely explain the observed asymmetry.The implications of this demonstration can be manifold.On a larger scale,it solidifies a mechanical model used for explaining the contribution of aseismic mechanisms to asymmetrical fault structures.On a laboratory scale,it exemplifies an alternative approach to understanding the observational difference between the source location and the in situ or post-mortem inspection on the rock fracture path.The mechanical model and the data analysis can be informative to the interpretations of other engineering practices as well,but may face different types of challenges.

DETERMINING CRITICAL TIME OF ROCK DYNAMIC FRACTURE BY DYNAMIC MOIRE METHOD

An effective Dynamic Moire method was presented to determine the critical time of crack instable propagation in rock dynamic fracture. Two pieces of grating were installed near the notch of Short Rod specimen to form the Moire fringes, then the COD versus time could be monitored from the movement of the Moire fringes, and finally the critical time could be determined from the velocity of COD. This method was also compared with another one.It could be concluded that the critical time determined by Dynamic Moire method corresponds with that of the Transmitted Wave method at the loading rates from 103 to 104 MPa·m(1/2)·S(-1).

Watson-Jones Anatomical Approach for Open Reduction and Internal Fixation of Proximal Femoral Fractures without Image Intensifier in a Low-Resource Setting

Introduction: Standard procedures for surgical fixation of proximal femoral fractures (PFF) require an image intensifier which in developing countries remains a luxury. We hypothesized that, with a well-codified technique, the Watson Jones approach (WJA) without image intensifier nor traction table, can allow open reduction and internal fixation (ORIF) of PFF using Dynamic hip screw (DHS), with satisfactory outcome. Patients and methods: Forty one consecutive patients (mean age 59.5 ± 21.6 years, 61% males) who were followed in a Teaching Hospital for PFF treated by ORIF using the WJA and DHS from January 2016 to December 2020 were reassessed. The outcome measures were the quality of the reduction, the positioning of the implants, the tip-apex distance (TAD), the rate and delay of consolidation, the functional results using Postel Merle d’Aubigné (PMA) score, the rate of surgical site infection (SSI) and the overall mortality. Logistic regression was used to determine factors associated with mechanical failure. Results: The mean follow-up period was 33.8 ± 15.0 months. Fracture reduction was good in 31 (75.6%) cases and acceptable in 8(19.5%) cases. Implant position was fair to good in 37 (90.2%) patients. The mean TAD was 26.1 ± 3.9 mm. Three patients developed SSI. Consolidation was achieved in 38 (92.6%) patients. The functional results were good to excellent in 80.5% of patients. The overall mortality rate was 7.3%. There were an association between mechanical failure and osteoporosis (p = 0.04), fracture reduction (p = 0.003), and TAD (p = 0.025). In multivariate logistic regression, no independent factors were predictive of mechanical failure. Conclusion: This study shows that ORIF using DHS for PFF via the Watson-Jones approach without an image intensifier can give satisfactory anatomical and functional outcomes in low-resource settings. It provides and validates a reliable and reproducible technique that deserves to be diffused to surgeons in austere areas over the world.

Analytic Expression of Meso-Criterion on Dynamic Fracture

This study presents a meso-criterion of dynamic fracture, on the basis of stress in integral form In such way the difficulty due to the singularity of stress distribution at the crack tip is overcome. A micro-parameter, the atom radius, is introduced into the criterion.Meanwhile a characteristic time concept is taken into account for describing the inertia effect of material. The criterion reveals The criterion reveals the effects of loading rate, defect and sample geometry,material constants including the micro-structure parameter.

Molecular dynamics simulation of fracture behaviors of <110> tilt grain boundaries in γ-TiAl

Molecular dynamics(MD) simulations were carried out to study the fracture behaviors of several symmetric tilt grain boundaries in γ-Ti Al bicrystals with <110> misorientation axes. Tensile deformation along direction perpendicular to grain boundary was simulated under various strain rates and temperatures. The results indicate that the relative orientation of the grains and the presence of certain atom units are two critical factors of the interface structure affecting the stress required for dislocation nucleation. Dislocations nucleate and extend at or near the symmetric tilt grain boundaries during the tensile deformation of Σ3(111) 109.5°, Σ9(221) 141.1° and Σ27(552) 148.4° interfaces. For Σ27(115) 31.6° and Σ11(113) 50.5° interfaces, the interfaces fractured directly in a cleavage manner due to no dislocation emitted from the boundary. The tensile fracture mechanisms of the bicrystals are that micro-cracks nucleate at the grain boundary and propagate along the interface. The variance of crack propagation is whether there is accommodation of plastic region at the crack tips.

Dynamic notched semi-circle bend(NSCB) method for measuring fracture properties of rocks:Fundamentals and applications

Rocks are increasingly used in extreme environments characterised by high loading rates and high confining pressures.Thus the fracture properties of rocks under dynamic loading and confinements are critical in various rock mechanics and rock engineering problems.Due to the transient nature of dynamic loading,the dynamic fracture tests of rocks are much more challenging than their static counterparts.Understanding the dynamic fracture behaviour of geomaterials relies significantly on suitable and reliable dynamic fracture testing methods.One of such methods is the notched semi-circle bend(NSCB)test combined with the advanced split Hopkinson pressure bar(SHPB)system,which has been recommended by the International Society for Rock Mechanics and Rock Engineering(ISRM)as the standard method for the determination of dynamic fracture toughness.The dynamic NSCB-SHPB method can provide detailed insights into dynamic fracture properties including initiation fracture toughness,fracture energy,propagation fracture toughness and fracture velocity.This review aims to fully describe the detailed principles and state-of-the-art applications of dynamic NSCB-SHPB techniques.The history and principles of dynamic NSCB-SHPB tests for rocks are outlined,and then the applications of dynamic NSCB-SHPB method(including the measurements of initiation and propagation fracture toughnesses and the limiting fracture velocity,the size effect and the digital image correlation(DIC)experiments)are discussed.Further,other applications of dynamic NSCB-SHPB techniques(i.e.the thermal,moisture and anisotropy effects on the dynamic fracture properties of geomaterials,and dynamic fracture toughness of geomaterials under pre-loading and hydrostatic pressures)are presented.

A NOVEL METHOD FOR MEASURING AND CHARACTERIZING DYNAMIC FRACTURE-INITIATION TOUGHNESS OF ELASTIC-PLASTIC MATERIALS

The characterization and testing methods of the dynamic fractureinitiation toughness of elas- tic-plastic materials under tensileimpact are studied. By using the self-designed bar-bar tensile impactappa- ratus, a novel test method for studying dynamicfracture-initiation ahs been proposed based on the one-di- mensionaltest principle. The curve of average load v. s. displacement (P-δ)is smooth until unstable crack propagation, and the kinetic energywhich does not contribute to the crack growth can be removed fromtotal work done by external-force to the specimen.

DETERMINATION OF THE DYNAMIC STRESS INTENSITY FACTORS,K_Ⅰ~d AND K_Ⅱ~d,FOR A MIXED-MODE PROPAGATING CRACK

In this paper,the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics.The initial curve and caustic equations were derived un- der the mixed-mode dynamic condition.A multi-point measurement method for determining the dy- namic stress intensity factors,K_Ⅰ~d and K_Ⅱ~d,and the position of the crack tip was developed.Several other methods were adopted to check this method,and showed that it has a good precision.Finally, the dynamic propagating process of a mixed-mode crack in a three-point bending beam specimen was investigated with our method.

Dynamic Fracture Analysis for Shale Material by Peridynamic Modelling

In this work,a bond-based peridynamics(PD)model was built to analyze the dynamic fracture of shale material.Both the the convergence studies and the result of dynamic crack propagation were presented.As well-known,crack propagation,aggregation,and bifurcation play an critical role in the failure analysis of brittle materials such as shale.The dynamic crack propagation and branching analysis of shale by using the PD method were discussed.Firstly,the valid and accuracy of the PD model for the rock materials was verified by comparing with the existed numerical results.Secondly,we discussed the convergence both with uniform grid refinement(m-convergence)and decreasing the peridynamics horizon(δ-convergence).Then the shale material with two pre-crack under uniaxial compression using the present PD model were discussed,and the influence of the different angle of flaws on the behavior of crack propagation was also analyzed.The results shows that both the loading conditions and the angle of flaws can influences the crack propagation in shale.

Spalling fracture mechanism of granite subjected to dynamic tensile loading

Rocks are likely to undergo spalling failure under dynamic loading.The fracture development and rock failure behaviours were investigated during dynamic tensile loading.Tests were conducted with a split-Hopkinson pressure bar(SHPB)in four different impact loading conditions.Thin sections near failure surfaces were also made to evaluate the growth patterns of fractures observed by polarizing microscope.Scanning electron microscopy(SEM)was used to observe mineral grains on failure surfaces and to evaluate their response to loading and failure.The results indicate that the number of spalling cracks increases with increase in peak impact loads and that quartz sustains abundant intergranular fracturing.Cleavage planes and their direction relative to loading play a vital role in rock strength and fracturing.Separation along cleavage planes perpendicular to loading without the movement of micaceous minerals parallel to loading appears to be unique to the rock spalling process.

EXPERIMENTAL AND THEORETICAL STUDY OF STATIC-DYNAMIC MIXED MODE BRITTLE FRACTURE OF ROCK

A new criterion of static dynamic state mixed mode brittle fracture initiation in rock is suggested, i.e. the distortion strain energy criterion.When t →∞, the static state distortion strain energy criteria and the formula for determiming static state fracture angle are obtained. The new static state criterion, suggested by authors, is in good agreement with the author′s experimental results. In addition, the relative accuracy of three current fracture theories and the new criterion in predicting static state mixed mode initiation fracture loading and fracture angle in rock have been evaluated experimentally.