Maximum Normal Stress Criterion Research Articles

Numerical Simulation of Rock Breaking by High-Temperature and High-Pressure Water under Thermal Driving

To solve the difficult problems in the field of unconventional oil and gas extraction and hard rock excavation in urban underground spaces, this paper proposes a rock-breaking technique with high-temperature and high-pressure water under thermally driven conditions and establishes a coupled thermal-fluid-solid model with COMSOL Multiphysics (COMSOL Co., Ltd. Shanghai, China). Different simulation groups are established by controlling variables to explore the effects of the surrounding rock load, heat source power, and Biot coefficient on the damage evolution during thermally driven rock breaking. To make the results relevant to practical engineering, the damage evolution results under the maximum normal stress criterion, maximum normal strain criterion, and Coulomb-Navier damage criterion are considered, and a comparative analysis is performed. The results of this study show that an increase in unilateral load and heat source power accelerates the damage evolution rate, while an increase in bilateral load and Biot coefficient has the opposite effect. The damage evolution rate controlled by the maximum normal stress criterion is the fastest under general conditions. Finally, the advantages in rock breaking provided by the established method are verified by a comparison of results from the proposed model and a conventional hydraulic fracturing model.

Research on size effect of fracture toughness of sandstone using the center-cracked circular disc samples

In order to investigate the size effect and reason of rock fracture toughness, the split loading test was carried out in the GCTS rock mechanics testing machine using the center-cracked circular disc (CCCD) samples with diameters of 50 mm, 100 mm, 150 mm and 205 mm, respectively. The lengths of fracture process zone (lFPZ) were determined by the maximum normal stress criterion. The size effect of the lFPZ , fracture toughness test value (KIc), and fracture energy (Gf) were analyzed. The influence of the lFPZ on the size effect of the KIc was revealed. The crack growth paths and failure characteristics of the samples were discussed. The results show that the lFPZ and the KIc increase linearly with the sample size, and there is obvious size effect within the range of the test. The KIc and the lFPZ do not always increase linearly with the size in a larger size range, but gradually stabilize by extrapolation analysis. The lFPZ increases with the size, which means the release of stored energy increases with the size corresponding to the size effect of the Gf, and in turn leads to the size effect of the KIc. It is helpful to deeply understand the cause of the size effect reason of rock fracture toughness.

Ultimate pressure determination in hydraulic fracturing of boreholes for different rock failure criteria

The problem on elastoplastic deformation and rock failure around boreholes under the action of internal pressure is considered. The stress state in the intact rock mass is assumed to be hydrostatic. The hydraulic fracturing pressure is conventionally determined by the maximum normal stress criterion. However, the experimental studies described in scientific articles show that this criterion is not consistent with the results obtained in the course of laboratory tests on failure of cylindrical and spherical cavities made in rock samples. It has been known that test results on complex loading for solid samples of various materials are not confirmed by the theory of maximum normal stress both in terms of ultimate load value and direction of failure surface propagation. In this case, for the complex stress state of rocks, it is proposed to determine the ultimate pressure by the experimentally substantiated fracture criteria which are in good agreement with the results of laboratory tests on hydraulic fracturing of boreholes.

Improvement of DDA with a New Unified Tensile Fracture Model for Rock Fragmentation and its Application on Dynamic Seismic Landslides

Discontinuous deformation analysis (DDA) method is a discrete element method, presenting a great advantage in modelling deformation and rigid body movements, and it is also an alternative approach for problems involving the fracturing process from continuity to discontinuity if the failure mechanism in DDA is well constituted. This paper presents a new united tensile fracture model (UTFM) for the two-dimensional DDA method to simulate the fracture behaviors of various brittle materials (e.g., rock, soil, and concrete). The new fracture model unifies four classical failure modes, including the maximum normal stress criterion, Tresca criterion, Mohr–Coulomb criterion, and the von Mises criterion, for tensile fracture. By incorporating UTFM into the original DDA frame, the improved DDA (I-DDA) can predict the crack initiation and propagation paths in Brazil disc and simulate rock fracture of various brittle materials. Numerical examples of the direct tensile test and the Brazil disc split tests are investigated to verify the accuracy and validity of the I-DDA method. The simulated results agree well with those obtained from physical tests and other numerical analyses, suggesting that the I-DDA has obvious advantage in simulating the fracture behaviors of the Brazil disc split test. Further, the I-DDA is applied to analyze the failure process of a practical earthquake-induced landslide with consideration of the tensile strength of the rock mass. The results indicate that the I-DDA is more feasible to analyze the slope failure, which can consider both the tensile and shear characteristics simultaneously compared with the original DDA.

A phase-field model for mixed-mode fracture based on a unified tensile fracture criterion

Different fracture patterns can be observed because of different material properties, even the geometry and loading are the same. However, most of the known phase-field fracture models have only considered the tensile failure and may not be directly applicable to the shear fracture. In this paper, a phase-field model for mixed-mode fracture is proposed based on a unified tensile fracture criterion. The proposed model is developed from the unified phase-field theory and the original unified phase-field model can be recovered as a particular case. General softening laws for cohesive zone models can also be considered. The unified tensile fracture criterion is embedded in the proposed mixed-mode phase-field model and different fracture patterns can be obtained in the simulation according to the material properties, including failures based on both maximum normal stress and maximum shear stress criteria. The crack propagation direction can be easily determined by the unified tensile fracture criterion. Compared with the classical phase-field model, two additional material parameters are needed, i.e., the failure tension strength and the ratio of the critical shear failure stress to the critical normal fracture stress. Numerical examples have shown that the proposed model has the ability to model mixed-mode fractures, and can also be applied to rock-like brittle materials under compression.

Adhesive class I restorations in sound molar teeth incorporating combined resin-composite and glass ionomer materials: CAD-FE modeling and analysis

ObjectivesTo investigate the influence of different resin composite and glass ionomer cement material combinations in a “bi-layer” versus a “single-layer” adhesive technique for class I cavity restorations in molars using numerical finite element analysis (FEA). Materials and MethodsThree virtual restored lower molar models with class I cavities 4mm deep were created from a sound molar CAD model. A combination of an adhesive and flowable composite with bulk fill composite (model A), of a glass ionomer cement with bulk fill composite (model B) and of an adhesive with bulk fill composite (model C), were considered. Starting from CAD models, 3D-finite element (FE) models were created and analyzed. Solid food was modeled on the occlusal surface and slide-type contact elements were used between tooth surface and food. Polymerization shrinkage was simulated for the composite materials. Physiological masticatory loads were applied to these systems combined with shrinkage. Static linear analyses were carried out. The maximum normal stress criterion was adopted as a measure of potential damage. ResultsAll models exhibited high stresses principally located along the tooth tissues–restoration interfaces. All models showed a similar stress trend along enamel–restoration interface, where stresses up to 22MPa and 19MPa was recorded in the enamel and restoration, respectively. A and C models showed a similar stress trend along the dentin-restoration interface with a lower stress level in model A, where stresses up to 11.5MPa and 7.5MPa were recorded in the dentin and restoration, respectively, whereas stresses of 17MPa and 9MPa were detected for model C. In contrast to A and C models, the model B showed a reduced stress level in dentin, in the lower restoration layer and no stress on the cavity floor. SignificanceFE analysis supported the positive effect of a “bi-layer” restorative technique in a 4mm deep class I cavities in lower molars versus “single-layer” bulk fill composite technique.

EXPERIMENTAL INVESTIGATION AND NUMERICAL MODELING OF ELASTIC PROPERTIES AND STRENGTH OF POROUS CERAMICS

Received: 22 June 2015 Accepted: 13 October 2015 Published: 25 December 2015 Advanced ceramics are widely used in responsible structures that work at conditions of high temperature changes, strong electrical fields and impact loads. Sintered ceramics are usually porous which affects their strength and elastic properties. In the first part of this work the results of experimental and numerical strength investigations of hot-pressed alumina ceramic are presented. The disk-shaped specimens with different (4- 23 %) were subjected to Piston-on-Ring bending test up to failure. Ultimate tensile strength is varied in the range of 180…490 MPa. Finite element method was used for stress state analysis of ceramic disk during bending test. Elastic properties of porous ceramic for numerical simulations were determined by using the known approximation of dependences property - porosity and some experimental data. In the second part of this work three-dimensional numerical micro-model was created in ANSYS. This model is a cube with set pores up to 160 of spherical forms. The diameter of sphere is given by Weibull distribution with mean value m = 0,139 ‡m and standard deviation s = 0,075 ‡m (defined by SEM analysis of fracture surfaces). Scale parameter „ = 0,156 ‡m and shape parameter k = 1,919 of the Weibull distribution was determined by the least squares method. The authors generated three to six models with a random distribution of pores for each average porosity; and analyzed stress state under axial tension for each case. The maximum normal stress, stress concentration factor, elastic modulus and Poisson's ratio are dependent on the average porosity. The values of the tensile strength were defined for different according to the Rankine criterion (maximum normal stress criterion). These values are in a good agreement with the experimental results.

Mechanical behavior of endodontically restored canine teeth: Effects of ferrule, post material and shape

ObjectiveTo assess the effect of a ferrule design with specific post material-shape combinations on the mechanical behavior of post-restored canine teeth. MethodsMicro-CT scan images of an intact canine were used to create a 3-D tessellated CAD model, from which the shapes of dentin, pulp and enamel were obtained and geometric models of post-endodontically restored teeth were created. Two types of 15mm post were evaluated: a quartz fiber post with conical–tapered shape, and a carbon (C) fiber post with conical–cylindrical shape. The abutment was created around the coronal portion of the posts and 0.1mm cement was added between prepared crown and abutment. Cement was also added between the post and root canal and a 0.25mm periodontal ligament was modeled around the root. Four models were analysed by Finite Element (FE) Analysis: with/without a ferrule for both types of post material and shape. A load of 50N was applied at 45° to the longitudinal axis of the tooth, acting on the palatal surface of the crown. The maximum normal stress criterion was adopted as a measure of potential damage. ResultsModels without a ferrule showed greater stresses (16.3MPa) than those for models with a ferrule (9.2MPa). With a ferrule, stress was uniformly distributed along the abutment and the root, with no critical stress concentration. In all models, the highest stresses were in the palatal wall of the root. Models with the C-fiber post had higher stress than models with the quartz fiber posts. The most uniform stress distribution was with the combination of ferrule and quartz fiber post. SignificanceThe FE analysis confirmed a beneficial ferrule effect with the combination of ferrule and quartz fiber post, with tapered shape, affording no critical stress concentrations within the restored system.

Comment on “Generalization of the Lame problem for three-stage decelerated corrosion process of an elastic hollow sphere”

There were questions about the variation range of pressures and vessel size when the analytical solutions for the corrosion of an elastic thick-walled sphere under pressure in terms of the maximum principal stress can be applied. In the paper the conditions are presented under which the maximum (in absolute value) principal stress in the sphere both inside and outside is the circumferential one. Moreover, these conditions are satisfied for the entire corrosion process. These conditions must be met when applying the mentioned solution and/or the maximum normal stress criterion with respect to the hoop stress for a pressurized spherical vessel. The weakened conditions of the constancy of the sign of the circumferential stress are also given.

An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks

The cracked chevron notched semi-circular bending (CCNSCB) method for measuring mode I fracture toughness of rocks has many favorable properties similar to those of the notched semi-circular bending (NSCB) method, which has been suggested by the International Society for Rock Mechanics (ISRM). In this study, the lengths of fracture process zones (FPZs) in the NSCB and CCNSCB tests with representative specimen geometries were theoretically estimated using the maximum normal stress criterion, and their effects on these fracture toughness tests were evaluated according to the effective crack model. The CCNSCB method was found to be less affected by the existence of FPZ and the measured fracture toughness was not that conservative as that using the NSCB method. Furthermore, even relatively small-size CCNSCB specimen could obtain the fracture toughness value that might require the use of a much larger sample size in the NSCB method. Subsequently, to further verify these theoretical results, laboratory tests using a total of 36 CCNSCB and NSCB specimens of three different sizes were conducted. For the same specimen size, the NSCB test always produced conservative fracture toughness value compared with the CCNSCB test. Additionally, even the toughness value measured using the NSCB specimen with a 75mm radius was still lower than that using the 25-mm-radius CCNSCB specimen. Given the experimental and theoretical results, the CCNSCB method is demonstrated to be less influenced by the presence of FPZ than the NSCB method for mode I fracture toughness measurements.

Influence of Poisson’s ratio and stress triaxiality on fracture behavior based on elastic strain energy density

The present study highlighted a new homenergic ellipse criterion to describe the fracture behavior of bulk metallic glass materials (BMGs) as well as a variety of other materials due to the inappropriate classical failure criteria of depicting the fracture behavior of BMGs, such as the maximum normal stress criterion, Tresca criterion, Mohr–Coulomb criterion, and von Mises criterion. Specifically, the fracture angles, revealing the fracture property, were discussed through studying the critical fracture stresses of uniaxial tension. In addition, based on elastic strain energy density, the fracture angles in uniaxial tension were uniquely depended on Poisson’s ratio. Further study found that fracture angles in complex stress-states not only depended on Poisson’s ratio, but also on stress triaxiality.

A universal fracture criterion for high-strength materials

Recently developed advanced high-strength materials like metallic glasses, nanocrystalline metallic materials, and advanced ceramics usually fracture in a catastrophic brittle manner, which makes it quite essential to find a reasonable fracture criterion to predict their brittle failure behaviors. Based on the analysis of substantial experimental observations of fracture behaviors of metallic glasses and other high-strength materials, here we developed a new fracture criterion and proved it effective in predicting the critical fracture conditions under complex stress states. The new criterion is not only a unified one which unifies the three classical failure criteria, i.e., the maximum normal stress criterion, the Tresca criterion and the Mohr-Coulomb criterion, but also a universal criterion which has the ability to describe the fracture mechanisms of a variety of different high-strength materials under various external loading conditions.

Numerical Simulation on Interface Crack Propagation for Non-Uniform Welded Joint

Maximum normal stress criterion can be used to determine the cracking angle in the uniform and non-uniform zone. According to this theory, the propagating process of the crack in non-uniform composite material is simulated based on the finite element method. The results show that the crack advances wave-like and basically along the direction perpendicular to the maximum normal stress, which is of great guiding significance for the fracture resistance of such kind of structure.

Cleavage fracture behavior of a C–Mn vessel steel at various loading rates in notched specimens

In this paper, the cleavage fracture behavior of a C–Mn vessel steel at various loading rates was studied by experiments and FEM calculations. The results show the cleavage fracture mechanism of this steel in two types of notched specimens loaded in two loading modes (four-point bending and three-point bending) at a temperature of −110 °C does not change with loading rates. This leads to the independence of the measured the local cleavage fracture stress σ f and the macroscopic cleavage fracture stress σ F on loading rate, notch geometry and loading mode. The macroscopic notch toughness characterized by the ratio of fracture load to general yield load ( P f/ P gy) of the notched specimens with two notch geometries loaded in the two loading modes at various loading rates can be predicated by the maximum normal stress criteria ( σ yymax⩾ σ F). The σ F can be regarded as an engineering notch toughness parameter of materials, and may be used for assessing integrity of structures with notch defects by the criteria σ yymax⩾ σ F. The σ F values of steels can be simply measured by the Griffiths–Owen's notched specimens loaded in four-point bending or three-point bending at a test temperature and a loading rate.

Determination of Growing Direction of Fatigue Crack

The stress field of an interfacial crack in non-homogeneous materials is computed using the semi-analytical method of arbitrary lines (MAL). Then, the eigen-functions of stress, strain and displacement, i.e. the angular distribution functions near a crack tip, are analyzed based on our wedge-shape non-homogeneous model. Finally, the growing direction of the interfacial crack is determined according to the relevant maximum normal stress criterion accurately. Therefore, the effective approach is provided for solving the complicated crack growing directions of an interfacial crack in non-homogeneous materials.

Numerical Investigation of Interface Debonding of Particle Reinforced Composites by Unit Cell Model

Abstract Due to its high specific stiffness and strength, good damage tolerance capabilities, and good fatigue resistance with respect to the traditional materials, metal matrix composite materials (MMCs) have attracted much research interests in recent years. It is known that interface debonding plays an important role in the thermo-mechanical behavior of the MMCs. In the present study, the effect of interface debonding on the mechanical properties of MMCs has been studied by a new periodic unit cell model, the multi-particle cubic (MPC) model, which is proposed with the consideration of the inhomogeneous structures within the MMCs. The representative cell is constructed by several randomly distributed elastic spheres, matrix material and interfacial region with the perfect bonding initially. And the onset of damage was assumed to follow a maximum normal stress criterion. The simulated results agree well with the experimental results. It is found that with the decrease of interfacial strength, the degradation of the composite resulted from the initiation and propagation of interfacial damage becomes severe. Damage evolution of the interface is further investigated with the increase of plastic strain. In additions, the predictions from the MPC model have also been compared with those from the single particle cubic (SPC) model.

Finite element simulation of stress intensity factors in elastic-plastic crack growth

A finite element program developed elastic-plastic crack propagation simulation using Fortran language. At each propagation step, the adaptive mesh is automatically refined based on a posteriori h-type refinement using norm stress error estimator. A rosette of quarter-point elements is then constructed around the crack tip to facilitate the prediction of crack growth based on the maximum normal stress criterion and to calculate stress intensity factors under plane stress and plane strain conditions. Crack was modelled to propagate through the inter-element in the mesh. Some examples are presented to show the results of the implementation.

Comparison of Fuzzy logic and Neural Network in life prediction of boiler tubes

The life prediction of equipments guarantees reliable, safe, efficient and continuous operation of thermal power plants. In this paper wall thickness of reheater tubes of boiler number 3 of Neka power plant in north of Iran are measured at several points during maintenance shut down periods. Thickness dependency vs. time has been investigated. Artificial Neural Network (ANN) as a tool has been acquired to determine this dependency. Extrapolation of thickness function vs. time applying maximum normal stress criteria results in corresponding thickness. The maximum wall reduction rates have been calculated by two schemes namely Fuzzy function (FF) and Neural Network (ANN) applying numerical calculation and Genetic Algorithm. Results have been compared with the existing relevant data from the literature and measured data of the plant in order to determine the accuracy and verify the validity of the methods.

A new triangular layered plate element for the non-linear analysis of reinforced concrete slabs

A new 3-node, 18-DOF triangular layered plate element is developed in this paper for the geometric and material non-linear analysis of isotropic plates and reinforced concrete slabs under service loads. The proposed model is a combination of Allman's 3-node, 9-DOF triangular membrane element with drilling degrees of freedom and the refined non-conforming 3-node, 9-DOF triangular plate-bending element RT9 in order to account for the coupling effects between membrane and bending actions. The element is modelled as a layered system of concrete and equivalent smeared steel reinforcement layers, and perfect bond is assumed between the concrete layers and the smeared steel layers. The maximum normal stress criterion is employed to detect cracking of the concrete, and a smeared fixed crack model is assumed. Both geometric non-linearity with large displacements but moderate rotations and material non-linearity, which incorporates tension, compression, concrete cracking and tension stiffening, are included in the model. An updated Lagrangian approach is employed as a solution strategy for the non-linear finite element analysis and a numerical example of reinforced concrete slab is given to demonstrate the efficacy of this robust element. Copyright © 2005 John Wiley & Sons, Ltd.

Edge-chipping reduction in rotary ultrasonic machining of ceramics: Finite element analysis and experimental verification

Rotary ultrasonic machining (RUM) is one of the machining processes for advanced ceramics. Edge chipping (or chamfer), commonly observed in RUM of ceramic materials, not only compromises geometric accuracy but also possibly causes an increase in machining cost. In this paper, a three-dimensional finite element analysis (FEA) model is developed to study the effects of three parameters (cutting depth, support length, and pretightening load) on the maximum normal stress and von Mises stress in the region where the edge chipping initiates. Two failure criteria (the maximum normal stress criterion and von Mises stress criterion) were used to predict the relation between the edge chipping thickness and the support length. Furthermore, a solution to reduce the edge chipping is proposed based upon the FEA simulations and verified by experiments.