Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Systematic prediction of the gas content, fractures, and brittleness in fractured shale reservoirs with TTI medium

The main objective is to optimize the development of shale gas-rich areas by predicting seismic sweet spot parameters in shale reservoirs. We systematically assessed the fracture development, fracture gas content, and rock brittleness in fractured gas-bearing shale reservoirs. To better characterize gas-bearing shale reservoirs with tilted fractures, we optimized the petrophysical modeling based on the equivalent medium theory. Based on the advantages of shale petrophysical modeling, we not only considered the brittle mineral fraction but also the combined effect of shale porosity, gas saturation, and total organic carbon(TOC) when optimizing the brittleness index. Due to fractures generally functioning as essential channels for fluid storage and movement, fracture density and fracture fluid identification factors are critical geophysical parameters for fractured reservoir prediction. We defined a new fracture gas indication factor(GFI) to detect fracture-effective gas content. A new linear PP-wave reflection coefficient equation for a tilted transversely isotropic(TTI) medium was rederived, realizing the direct prediction of anisotropic fracture parameters and the isotropic elasticity parameters from offset vector tile(OVT)-domain seismic data. Synthetic seismic data experiments demonstrated that the inversion algorithm based on the L_P quasinorm sparsity constraint and the split-component inversion strategy exhibits high stability and noise resistance. Finally, we applied our new prediction method to evaluate fractured gas-bearing shale reservoirs in the Sichuan Basin of China, demonstrating its effectiveness.

A Non-Intrusive Stochastic Phase-Field for Fatigue Fracture in Brittle Materials with Uncertainty in Geometry and Material Properties

Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications.This is all the more important when elements composed of brittle materials are exposed to dynamic environments,resulting in catastrophic fatigue failures.The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables.Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading.Crack growth is modelled using a phase-field approach within a finite element framework.For modelling fatigue,fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function.Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties.Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method.This proposed approach can accurately predict results typically obtained through 105 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs.The independent random variables’sensitivity to the system response is determined using Sobol’indices.The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace,nuclear and biomedical engineering.The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing.

Pulp health and calcific healing of a complicated crown–root fracture with additional root fracture in a maxillary incisor: A case report

BACKGROUND Complicated crown–root fracture (CRF) involves severe injury to the crown, root,and pulp, and may be accompanied by multiple root fractures. The loss of a toothhas lifelong consequences for children and teenagers, but the maintenance of pulphealth and the calcific healing of multiple root fractures are rarely reported in theliterature.CASE SUMMARY This case reports healing of a permanent tooth with complicated crown–root andadditional root fractures, in which pulp health was maintained. A 10-year-old girlfell and fractured the root of her maxillary left central incisor at the cervical level.After the coronal fragment was repositioned, the tooth was splinted until thetooth was no longer mobile, 2 years later. Eight years after treatment, the toothhas remained asymptomatic with vital pulp and localized gingival overgrowth.Cone-beam computed tomography revealed not only calcified healing of the CRFbut also spontaneous healing in an additional undiagnosed root fracture. Thefracture line on the enamel could not be healed by hard tissue and formed agroove in the cervical crown. It was speculated that the groove was related to thelocalized gingival overgrowth.CONCLUSION This case provides a clinical perspective of the treatment of a tooth with acomplicated CRF and an additional root fracture.

Correlation between anxiety, depression, and social stress in young patients with thoracolumbar spine fractures

BACKGROUND Traumatic injuries,such as falling,car accidents,and crushing mostly cause spinal fractures in young and middle-aged people,and>50%of them are thoracolumbar fractures.This kind of fracture is easily combined with serious injuries to peripheral nerves and soft tissues,which causes paralysis of the lower limbs if there is no timely rehabilitation treatment.Young patients with thoracolumbar fractures find it difficult to recover after the operation,and they are prone to depression,low self-esteem,and other negative emotions.AIM To investigate the association between anxiety,depression,and social stress in young patients with thoracolumbar spine fractures and the effect on rehabilitation outcomes.METHODS This study retrospectively analyzed 100 patients admitted to the orthopedic department of Honghui Hospital,Xi’an Jiaotong University who underwent thoracolumbar spine fracture surgery from January 2022 to June 2023.The general data of the patients were assessed with the Hamilton anxiety scale(HAMA),Hamilton depression scale(HAMD),life events scale,and social support rating scale(SSRS)to identify the correlation between anxiety,depression scores,and social stress and social support.The Japanese Orthopedic Association(JOA)was utilized to evaluate the rehabilitation outcomes of the patients and to analyze the effects of anxiety and depression scores on rehabilitation.RESULTS According to the scores of HAMD and HAMA in all patients,the prevalence of depression in patients was 39%(39/100),and the prevalence of anxiety was 49%(49/100).Patients were categorized into non-depression(n=61)and depression(n=39),non-anxiety(n=51),and anxiety(n=49)groups.Statistically significant differences in gender,occupation,Pittsburgh Sleep Quality Index(PSQI)score,and monthly family income were observed between the non-depression and depression groups(P<0.05).A significant difference in occupation and PSQI score was found between the non-anxiety and anxiety groups.Both depression(r=0.207,P=0.038)and anxiety scores(r=0.473,P<0.001)were significantly and positively correlated with negative life events.The difference in negative life event scores as well as SSRS total and item scores was statist-ically significant between patients in the non-depression and depression groups(P<0.05).The difference between the non-anxiety and anxiety groups was statistically significant(P<0.05)in the negative life event scores as well as the total SSRS scores.Additionally,JOA scores were significantly lower in both anxious and depressed patients.CONCLUSION Young patients with thoracolumbar fractures are prone to anxiety and depression.Patients’anxiety and depression are closely associated with social pressure,which reduces the life pressure of young patients with thoracolumbar fractures,enhances social support,and improves the psychology of anxiety and depression.,which affects patients’recovery.

Teriparatide as a non-surgical salvage therapy for prolonged humerus fracture nonunion:A case report and literature review

BACKGROUND Fracture nonunion represents a challenging complication during fracture repair,often necessitating surgical intervention.Teriparatide,a recombinant human parathyroid hormone,has demonstrated promise in enhancing fracture healing,although its efficacy in treating established nonunion remains under investigation.CASE SUMMARY We report a case of a 27-year-old male who presented with a right humerus fracture following a traffic accident.Despite undergoing open reduction and internal fixation,the fracture resulted in a delayed union and subsequent nonunion.After 4 years of conservative management,teriparatide treatment was initiated due to persistent nonunion.Teriparatide injections were administered daily for 6 months,resulting in complete fracture healing and resolution of pain.CONCLUSION Our case demonstrates the successful use of teriparatide in treating a prolonged nonunion of a humerus fracture.Teriparatide may provide a valuable therapeutic option for established bone nonunion,even in cases that have not responded to conservative treatments.

Microstructure effect of mechanical and cracking behaviors on brittle rocks using image-based fast Fourier transform method

The internal microstructures of rock materials, including mineral heterogeneity and intrinsic microdefects, exert a significant influence on their nonlinear mechanical and cracking behaviors. It is of great significance to accurately characterize the actual microstructures and their influence on stress and damage evolution inside the rocks. In this study, an image-based fast Fourier transform (FFT) method is developed for reconstructing the actual rock microstructures by combining it with the digital image processing (DIP) technique. A series of experimental investigations were conducted to acquire information regarding the actual microstructure and the mechanical properties. Based on these experimental evidences, the processed microstructure information, in conjunction with the proposed micromechanical model, is incorporated into the numerical calculation. The proposed image-based FFT method was firstly validated through uniaxial compression tests. Subsequently, it was employed to predict and analyze the influence of microstructure on macroscopic mechanical behaviors, local stress distribution and the internal crack evolution process in brittle rocks. The distribution of feldspar is considerably more heterogeneous and scattered than that of quartz, which results in a greater propensity for the formation of cracks in feldspar. It is observed that initial cracks and new cracks, including intragranular and boundary ones, ultimately coalesce and connect as the primary through cracks, which are predominantly distributed along the boundary of the feldspar. This phenomenon is also predicted by the proposed numerical method. The results indicate that the proposed numerical method provides an effective approach for analyzing, understanding and predicting the nonlinear mechanical and cracking behaviors of brittle rocks by taking into account the actual microstructure characteristics.

Effect of extended nursing based on self-efficacy theory on the anxiety of patients with intertrochanteric fracture

BACKGROUND Extended care based on self-efficacy theory to elderly patients with intertrochanteric fractures will provide data reference to optimize the care plan of these patients,reduce patients’concurrent mental diseases,and improve prognosis.AIM To analyze the value of extended nursing based on the self-efficacy theory in older patients with intertrochanteric fractures.METHODS Older patients with intertrochanteric fractures(n=88)admitted to our hospital between January 2021 and December 2024 were randomly divided into two groups-the control group(n=44,routine nursing)and the observation group(n=44,extended nursing)-via balloting and treated for 12 weeks.The mental state,pain severity,limb function,and self-nursing ability of all patients before and after nursing were analyzed.RESULTS After nursing,the Hamilton Anxiety Scale and General Self-Efficacy Scale scores of patients in the two groups improved.Notably,Hamilton Anxiety Scale and General Self-Efficacy Scale scores in the observation group were lower and higher,respectively,than those in the control group(P<0.05).The pain severity in the observation group(2.64±0.22)was lower than that in the control group(2.85±0.41)(P<0.05).The recovery rate of limb function was higher in the observation group than in the control group(P<0.05).In addition,the self-nursing ability scores of the patients in both groups increased,with a significantly higher score in the observation group(P<0.05).CONCLUSION Extended nursing based on the self-efficacy theory can significantly improve mental state,relieve pain,and promote the recovery of limb function and self-nursing ability in older patients with intertrochanteric fractures.

An adjustable bio-sealing method for rock fracture leakage mitigation

This study proposed a repeated adjustable mixture injection strategy(RAM)based microbial induced carbonate precipitation(MICP)for efficient mitigation of rock fracture leakage.Granite fractures with small apertures were investigated,and bio-sealing experiments were conducted using five different cementation solution(CS)concentrations(0.25−2 M).The results showed that the RAM-based bio-sealing method can seal and bond the small aperture rock fractures with high efficiency and uniform precipitation by adjusting the CS concentration.The RAM-based bio-sealing mechanism is attributed to the following four stages:(1)fixation of bacterial flocs onto the fracture surfaces,(2)precipitation of CaCO3 onto the fracture surfaces,(3)growth of pre-precipitated CaCO3 and adhesion of new-suspended CaCO3,and(4)bridging and clogging processes.The optimal CS concentration of 1 M resulted in a fracture filling rate up to 85%,a transmissivity reduction of 4 orders of magnitude,and a shear strength ranging from 512 kPa to 688 kPa.The bio-sealing effect was found to be influenced by the CS concentration on bacterial attachment,calcium carbonate yield and calcium carbonate bulk density.The CS concentration of 1 M promoted bacterial attachment,and increased calcium carbonate yield as well as calcium carbonate bulk density,while concentrations above 1 M had the opposite effect.The bulk density of calcium carbonate played a crucial role in the sealing and bonding performance of bio-sealed fractures,particularly at comparable filling ratios and bridging areas.The bulk density was regulated by the size of calcium carbonate crystals and was determined by Ca2+concentration in the CS.This study provides valuable insights into the RAM-based bio-sealing method,highlighting its potential for efficient rock fracture leakage mitigation through precise control of CS concentration and understanding the underlying mechanisms.

Using fracture mechanics method to analyze the failure mechanism and equilibrium equation of interfacial loess-mudstone landslides

Loess-mudstone landslides are common in the Loess Plateau.Investigations into the mechanical theory of loess-mudstone landslides have become a challenging undertaking due to the distinctive interfacial properties of loess-mudstone and the unique water sensitivity characteristics of mudstone.Hence,it is imperative to develop innovative mechanical models and mathematical equations specifically tailored to loess-mudstone landslides.In this study,we analyze the fracture mechanism of the loess-mudstone sliding zone using plastic fracture mechanics and develop a unique fracture yield model.To calculate the energy release rate during the expansion of the loess-mudstone interface tip region,the shear fracture energy G is applied,which reflects both the yield failure criterion and the fracture failure criterion.To better understand the instability mechanism of loess-mudstone landslides,equilibrium equations based on G are established for tractive,compressive,and tensile loess-mudstone landslides.Based on the equilibrium equation,the critical length Lc of the sliding zone can be used for the safety evaluation of loess-mudstone landslides.In this way,this study proposes a new method for determining the failure mechanism and equilibrium equation of loessmudstone landslides,which resolves their starting mechanism,mechanical equilibrium equations,and safety evaluation indicators,thus justifying the scientific significance and practical value of this research.

High cycle fatigue performance at 650℃and corresponding fracture behaviors of GH4169 joint produced by linear friction welding

GH4169 joints manufactured by Linear Friction Welding(LFW)are subjected to tensile test and stair-case method to evaluate the High Cycle Fatigue(HCF)performance at 650℃.The yield and ultimate tensile strengths are 582 MPa and 820 MPa,respectively.The HCF strength of joint reaches 400 MPa,which is slightly lower than that of Base Metal(BM),indicating reliable quality of this type of joint.The microstructure observation results show that all cracks initiate at the inside of specimens and transfer into deeper region with decrease of external stress,and the crack initiation site is related with microhardness of matrix.The Electron Backscattered Diffraction(EBSD)results of the observed regions with different distances to fracture show that plastic deformation plays a key role in HCF,and the Schmid factor of most grains near fracture exceeds 0.4.In addition,the generation of twins plays a vital role in strain concentration release and coordinating plastic deformation among grains.

An extended discontinuous deformation analysis for simulation of grouting reinforcement in a water-rich fractured rock tunnel

Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength.Nevertheless,there is a lack of potent numerical tools for assessing the grouting effectiveness in water-rich fractured strata.In this study,the hydro-mechanical coupled discontinuous deformation analysis(HM-DDA)is inaugurally extended to simulate the grouting process in a water-rich discrete fracture network(DFN),including the slurry migration,fracture dilation,water plugging in a seepage field,and joint reinforcement after coagulation.To validate the capabilities of the developed method,several numerical examples are conducted incorporating the Newtonian fluid and Bingham slurry.The simulation results closely align with the analytical solutions.Additionally,a set of compression tests is conducted on the fresh and grouted rock specimens to verify the reinforcement method and calibrate the rational properties of reinforced joints.An engineering-scale model based on a real water inrush case of the Yonglian tunnel in a water-rich fractured zone has been established.The model demonstrates the effectiveness of grouting reinforcement in mitigating water inrush disaster.The results indicate that increased grouting pressure greatly affects the regulation of water outflow from the tunnel face and the prevention of rock detachment face after excavation.

Deformation mechanism and NPR anchor cable truss coupling support in tunnel through fault fracture zone

To address the issue of extensive deformation in the Tabaiyi Tunnel caused by the fault zone,nuclear magnetic resonance(NMR)technology was employed to analyze the physical and mechanical properties of waterabsorbing mudstone.This analysis aimed to understand the mechanism behind the significant deformations.Drawing from the principle of excavation stress compensation,a support scheme featuring NPR anchorcables and an asymmetric truss support system was devised.To validate the scheme,numerical analysis using a combination of the Discrete Element Method(DEM)-Finite Element Method(FEM)was conducted.Additionally,similar material model tests and engineering measurements were carried out.Field experiments were also performed to evaluate the NPR anchor-cable and truss support system,focusing on anchor cable forces,pressures between the truss and surrounding rock,pressures between the initial support and secondary lining,as well as the magnitude of settlement and convergence deformation in the surrounding rock.The results indicate that the waterinduced expansion of clay minerals,resulting from damage caused by fissure water,accelerated the softening of the mudstone's internal structure,leading to significant deformations in the Tabaiyi Tunnel under high tectonic stress.The original support design fell short as the length of the anchor rods was smaller than the expansion depth of the plastic zone.As a result,the initial support structure bore the entire load from the surrounding rock,and a non-coupled deformation contact was observed between the double-arch truss and the surrounding rock.The adoption of NPR asymmetric anchor-cable support effectively restrained the expansion and asymmetric distribution characteristics of the plastic zone.Considering the mechanical degradation caused by water absorption in mudstone,the rigid constraint provided by the truss proved crucial for controlling the stability of the surrounding rock.These research findings hold significant implications for managing large deformations in soft rock tunnels situated within fractured zones under high tectonic stress conditions.

Mesoscopic fracture damage evolution and fractal damage constitutive model of heat-treated red sandstone under direct tensile impact loadings

Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.

Fracture evolution around pre-existing cylindrical cavities in brittle rocks under uniaxial compression

The development of fracture around pre-existing cylindrical cavities in brittle rocks was examined using physical models and acoustic emission technique. The experimental results indicate that when granite blocks containing one pre-existing cylindrical cavity are loaded in uniaxial compression condition, the profiles of cracks around the cavity can be characterized by tensile cracking （splitting parallel to the axial compression direction） at the roof-floor, compressive crack at two side walls, and remote or secondary cracks at the perimeter of the cavity. Moreover, fracture around cavity is size-dependent. In granite blocks containing pre-existing half-length cylindrical cavities, compressive stress concentration is found to initiate at the two sidewalls and induce shear crack propagation and coalescence. In granite blocks containing multiple parallel cylindrical cavities, the adjacent cylindrical cavities can influence each other and the eventual failure mode is determined by the interaction of tensile, compressive and shear stresses. Experimental results show that both tensile and compressive stresses play an important role in fracture evolution process around cavities in brittle rocks.

Nonequilibrium Statistical Nature of Intergranular Brittle Fracture in Polycrystal

The brittle fracture probability and reliability are obtained in terms of dislocation mechanism of microcrack evolution. The statistical distribution functions and statistical deviations of elongation, strength, plastic work, crack extension force, fracture foughness, critical and crack length, can be derived in a unified fashion.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

PROBABILISTIC MODELING OF BRITTLE FRACTURE WITH PRIOR DUCTILE CRACK EXTENSION

A computation framework for brittle fracture which incorporates weakest link statistics and a microme- chanics model reflecting reflecting local damage of the material is described.The Weibull stress W emerges as a probabilistic fracture parameter to define the condition leading material failure. Unstable crack propa- gation occurs at a critical value of W which may be attained paior to or following some amount of duc- tile crack extension. A realistic model of ductile crack growth using the computation cell methodology is used to define the evolution of near tip stress fields during crack extension. An application of proposed framework to predict the measured geometry and ductile tearing effects on the statistical distributio of fracture toughness for the pipe line steel welded joint is described.

Effect of weld microstructure on brittle fracture initiation in the thermallyaged boiling water reactor pressure vessel head weld metal

Effects of the weld microstructure and inclusions on brittle fracture initiation are investigated in a thermally aged ferritic high-nickel weld of a reactor pressure vessel head from a decommissioned nuclear power plant.As-welded and reheated regions mainly consist of acicular and polygonal ferrite,respectively.Fractographic examination of Charpy V-notch impact toughness specimens reveals large inclusions(0.5-2.5μm)at the brittle fracture primary initiation sites.High impact energies were measured for the specimens in which brittle fracture was initiated from a small inclusion or an inclusion away from the V-notch.The density,geometry,and chemical composition of the primary initiation inclusions were investigated.A brittle fracture crack initiates as a microcrack either within the multiphase oxide inclusions or from the debonded interfaces between the uncracked inclusions and weld metal matrix.Primary fracture sites can be determined in all the specimens tested in the lower part of the transition curve at and below the 41-J reference impact toughness energy but not above the mentioned value because of the changes in the fracture mechanism and resulting changes in the fracture appearance.

ANALYSIS OF BRITTLE FRACTURE DUE TO COMPRESSIVE LOADING USING CENTER-CRACKED BRAZILIAN DISK

The center cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode Ⅰ and mode Ⅱ stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R . This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode Ⅱ crack growth (crack coplanar extension) and any combination of K Ⅰ and K Ⅱ by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.