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Mixed-mode fracture is a common failure phenomenon of materials, while its experiment requires at least a material test machine, test materials and special machining procedures. In this paper, a simple but effective mixed-mode fracture experiment using office paper is proposed, so one can easily conduct the mixed-mode fracture experiment and understand its fracture criteria such as the maximum tensile stress (MTS) criterion. [ABSTRACT FROM AUTHOR]

Creep failure of hierarchical materials is investigated by simulation of beam network models. Such models are idealizations of hierarchical fibrous materials where bundles of load-carrying fibers are held together by multi-level (hierarchical) cross-links. Failure of individual beams is assumed to be governed by stress-assisted thermal activation over local barriers, and beam stresses are computed by solving the global balance equations of linear and angular momentum across the network. Disorder is mimicked by a statistical distribution of barrier heights. Both initially intact samples and samples containing side notches of various length are considered. Samples with hierarchical cross-link patterns are simulated alongside reference samples where cross-links are placed randomly without hierarchical organization. The results demonstrate that hierarchical patterning may strongly increase creep strain and creep lifetime while reducing the lifetime variation. This is due to the fact that hierarchical patterning induces a failure mode that differs significantly from the standard scenario of failure by nucleation and growth of a critical crack. Characterization of this failure mode demonstrates good agreement between the present simulations and experimental findings on hierarchically patterned paper sheets. [ABSTRACT FROM AUTHOR]

The dynamics of a “peeling front” or an elastic line is studied under creep (constant load) conditions. Our experiments show in most cases an exponential dependence of the creep velocity on the inverse force (mass) applied. In particular, the dynamical correlations of the avalanche activity are discussed here. We compare various avalanche statistics to those of a line with non-local elasticity, and study various measures of the experimental avalanche-avalanche and temporal correlations such as the autocorrelation function of the released energy and aftershock activity. From all these we conclude, that internal avalanche dynamics seems to follow “line depinning”-like behavior, in rough agreement with the depinning model. Meanwhile, the correlations reveal subtle complications not implied by depinning theory. Moreover, we also show how these results can be understood from a geophysical point of view. [ABSTRACT FROM AUTHOR]

Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated. [ABSTRACT FROM AUTHOR]

When plates with edge cracks in the rolling process is straightened by cyclic tensile and compressive stress, the tip of edge crack always accompanied by stress concentration, which leads to crack propagation. In this paper, damage parameters are imported into the plate straightening model based on determining the GTN damage parameters of magnesium alloy materials by inverse finite element calibration method, the influence of different straightening process schemes and prefabricated V-shaped crack geometry on crack growth is analyzed through the way of the combination of simulation and straightening experiment. The results show that the peak values of equivalent stress and equivalent strain under each straightening roll appear at the crack tip. The value of longitudinal stress and equivalent stain decrease with the distance to crack tip becomes larger. The peak value of longitudinal stress appears when the crack circumferential angle is about 100°, and the crack tip is easy to form crack propagation; when the plate passes roll 2 and roll 4, the equivalent stress and strain concentration at the crack tip are most obvious; when the reduction reaches a certain degree, the void volume fraction (VVF) reaches the VVF of the material breaking; with the increase of the entrance reduction, the number of VVF at the crack tip which reaches the material fracture increases, and the length of crack propagation increases; the stress concentration at the tip of V-shaped crack with large length–width ratio is obvious, and the VVF is more likely to reach the VVF at the time of material fracture, crack initiates and propagates easily. [ABSTRACT FROM AUTHOR]

Frost crack evolution induced by cyclic freeze–thaw is responsible for rock deterioration in cold regions and poses major threats to public safety, engineering structures, and alpine slope stability. This paper presents experimental and numerical works aimed at investigating the frost crack evolution in fissured rock masses, as well as the interaction between frost cracks. A series of laboratory freezing experiments are conducted on rock-like specimens with various pre-existing fissures. Experimental results show that frost cracks initiate at the pre-existing fissure tips and propagate under the freeze–thaw treatment. Moreover, the frost crack evolution is significantly influenced by external stress conditions and frost crack interactions, forming several typical propagation patterns (e.g., deflection, coplanar and butterfly shape, etc.). Then, numerical simulations with a low-temperature thermal–mechanical coupled model, where the water/ice phase transition and hence volume expansion are explicitly simulated, are conducted to reproduce the experimental observation. The numerical results are consistent with the experimental observations and help to reveal the underlying mechanisms of the frost crack growth and frost crack interaction. This experimental and numerical investigation helps to improve the understanding of frost cracking mechanisms that can inform engineering design in cold regions with fissured rock masses. Highlights: Frost crack propagation and interaction under freeze-thaw cycles are investigated. Frost heaving pressure induced by ice expansion is large enough to drive crack propagation. Confining stresses alter the stress field around the crack tips, inducing crack orientation. Mutual interaction between adjacent frost cracks significantly affects the cracking pattern. Novel low-temperature thermal-mechanical coupling model is developed for frost cracking problems. [ABSTRACT FROM AUTHOR]

The method of backfill in underground mining is important for ground control as well as material recycling and energy efficiency. Even though extensive testing and field studies of backfill have been conducted, less is known about the detailed damage and fracturing that occurs directly at the rock/backfill interface. In this paper, cylindrical specimens containing an inner diameter of backfill and an outer diameter of rock (RB) were tested under triaxial compression. Acoustic emissions (AE) were used throughout testing, and X-ray computed tomography (CT) scanning was conducted before loading was applied and after the specimens had failed. The high-resolution CT images were then converted into point clouds to isolate the fractures and visualize them in three dimensions. The point clouds clearly show that fracturing occurred both in the rock and along with the contact between rock and backfill, while very little fracturing was found to occur in the backfill. Based on the point cloud and AE results, a unique evolution of fracturing is found to occur that includes two stages of shear fracturing in the rock, tensile fracturing along with the rock/backfill interface, and final tensile fracturing in the rock after delamination from the backfill, all of which contributed to the nonlinear stress–strain response. This paper presents a novel approach for investigating the initiation and propagation of 3D fractures in laboratory testing and can offer a useful reference for further studies on the mechanics of bi-material structures. [ABSTRACT FROM AUTHOR]

The creep-fatigue behaviors of P92 steel under strain range of 0.3 %–0.5 % and test temperature of 600–650 °C was studied carefully in this paper. With the increase of temperature, the creep-fatigue life is significantly reduced, and more vulnerable to temperature than strain amplitude. In addition, the dislocation density decreases with increasing creep fatigue, and the martensite laths become coarser. Furthermore, the increase of strain amplitude leads to more significant secondary cracks and fatigue striation. The higher temperature causes much deeper and larger dimples. During the test, the growth and accumulation of precipitates inevitably lead to stress concentration, resulting in material fracture and destruction. Finally, the linear cumulative damage (LCD), the modified ductility exhaustion (MDE) and the frequency separation life (FSL) model are used to predict the creep-fatigue life of P92 steel, and it is found that the frequency separation life model had the highest prediction accuracy among the threes. [ABSTRACT FROM AUTHOR]

Open circular holes are an important design feature, for instance in bolted joint connections. However, stress concentrations arise whose magnitude depends on the material anisotropy and on the defect size relative to the outer finite plate dimensions. To design both safe and light-weight optimal structures, precise means for the assessment are crucial. These can be based on analytical methods providing efficient computation. For this purpose, the focus of the present paper is to provide a comprehensive stress and failure analysis framework based on analytical methods, which is also suitable for use in industry contexts. The stress field for the orthotropic finite-width open-hole problem under uniform tension is derived using the complex potential method. The results are eventually validated against Finite-Element analyses revealing excellent agreement. Then, a failure analysis to predict brittle crack initiation is conducted by means of the Theory of Critical Distances and Finite Fracture Mechanics. These failure concepts of different modelling complexity are compared to each other and validated against experimental data. The size effect is captured, and in this context, the influence of finite width on the effective failure load reduction is investigated. [ABSTRACT FROM AUTHOR]

The disposal of high-level radioactive waste (HLW) is one of the most challenging issues globally, and granite is considered an ideal host rock. In this paper, we present an experimental study on the transmissivity of fractured granite filled with different materials. A series of tests were carried out to study the effects of different factors (filling material, confining stress, and fracture roughness) on fracture transmissivity. Our results show that the properties of the filling material play a critical role in the transmissivity of fractured granite. Specifically, quartz sand significantly increases the transmissivity of the fractured granite, but the larger the sand particle size, the slower the transmissivity increases. Conversely, compared with fractured samples without any filling material, bentonite as a filling material decreases fracture transmissivity. Furthermore, confining stress also exhibits a great effect on transmissivity, and high stress compresses the filling material, resulting in a reduction in transmissivity. In addition, confining stress has a larger impact on the transmissivity of sand-filled fractured samples than others. We quantify the roughness of the fractures to examine its impact on the transmissivity. The results show that larger roughness reduces transmissivity for the unfilled fractures, but has an opposite effect on sand-filled fractures, while the results of bentonite-filled fractures are scattered. This study could provide an important guidance for evaluating the safety of HLW repositories. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

In this paper, the effect of creep-fatigue loading condition on crack tip deformation and stress fields of Grade 91 steel at 600 °C at crack initiation and growth is studied. By using finite element debond analysis method, creep-fatigue crack growth tests using C(T) specimens under various load ratios and hold times are simulated, and the effect of creep-fatigue load ratio and hold time on the crack opening profile, equivalent stress, crack-opening stress and triaxiality at crack initiation and growth is presented. It is found that the crack tip deformation and stress fields under tension–compression creep-fatigue loading are overall different from those under tension-tension creep-fatigue and pure creep loading, due to re-sharpening of the crack tip. [ABSTRACT FROM AUTHOR]

Crack growth leads to roller failure and damages other parts. The three-dimensional modeling of crack growth, the effect of different factors on the fatigue life of roller, and the effect of stress distribution are important factors that should be considered. The purpose of this paper is to investigate the failure and modeling of three-dimensional fatigue crack growth and fatigue life prediction of high chromium steel (HCS) rollers in hot rolling to minimize the failure of rollers by practical solutions. This article uses boundary element method for fatigue crack growth under the influence of stress field. The proposed method allows modeling each of the components involved separately in the contact area. As a result, this method is faster than finite element models with contact components. In this regard, the types and causes of cracks in the roller are analyzed with the effect of residual stresses on the roller. By selecting the HCS roller and sheet, modeling and stress analysis are performed by finite element method. This study includes the effect of crack growth factors such as load ratio, length, and initial crack angle. The results of the numerical model showed a good agreement with the results obtained in the field observations. [ABSTRACT FROM AUTHOR]

This paper describes the conditions leading to a sustained, low-rate, heave phenomenon affecting a building founded on hard Keuper anhydritic rock. The building was located in an abandoned gypsum quarry. Monitoring data as well as vertical profiles of gypsum and anhydrite content indicate that swelling was associated with the presence of a shallow level of anhydritic clay rock. This paper concludes that the initial quarry excavation as well as the additional building foundation work modified the original stress state and contributed to opening fractures at depth. It also resulted in a facilitated access of water to the upper rock levels, immediately under the foundation footings. Measured heave rates are substantially lower than other rates recorded in a few recent cases. An explanation is provided for the difference. This paper describes a comforting solution for the building. [ABSTRACT FROM AUTHOR]

Pipe bends, often referred to as 'elbows', are special pipeline components, widely used in onshore buried steel pipelines. They are sensitive to imposed deformations and their structural behavior is quite flexible and associated with the development of significant stress and strain, which may lead to failure. In the present paper, the mechanical performance of buried steel pipeline bends is investigated first, using rigorous finite element models that account for the pipe-soil interface. Three 36-inch-diameter pipe elbows are considered, subjected to pull-out force and embedded in cohesive soils. The elbows have bend angles equal to 90°, 60° and 30°, and bend radius-over-diameter ratio ( R/ D) equal to 5. The results show the increased flexibility of the pipeline bend with respect to the straight pipe, and are reported in the form of force-displacement diagrams. Furthermore the deformation limits of each elbow are identified in terms of appropriate performance criteria. The second part of the paper investigates the effect of pipe bends on the response of pipelines crossing active faults using a three-dimensional rigorous finite element model. The numerical results refer to a 36-inch-diameter pipeline crossing a strike-slip fault, and show that the unique mechanical response of pipe bends, in terms of their flexibility, may offer an efficient tool for reducing ground-induced deformations. The three-dimensional model employs the load-displacement curves of the first part of the paper as end conditions through nonlinear springs. Furthermore, the results show that there exist an optimum distance of the elbow from the fault plane, which corresponds to the maximum allowable ground displacement. Therefore, pipeline elbows, if appropriately placed, can be employed as 'mitigating devices', reducing ground-induced action on the pipeline at fault crossings. [ABSTRACT FROM AUTHOR]

On the basis of Reissner's plate theory, the stress singularities at the tip of an arbitrarily inclined semiinfinite crack terminating at the interface of two dissimilar materials are investigated in the present paper. Using the eigenfunction expansion method, the eigenequation of the corresponding problem is derived explicitly by directly solving the governing equations of Reissner's plate theory in terms of three generalized displacement components. In this paper, the focus is on the calculation of the singularity order as a fundamental quantity in fracture mechanics. The singularity orders of the moments and shear force at the crack tip are determined by the dominant eigenvalues whose real parts lie between 0 and 1. The influences of the bi-material parameters and the crack inclination angle on the moment and shear force singularity orders are discussed in detail. Specifically, the variations of the shear force singularity order with the bi-material parameter and the crack inclination angle are examined in detail. It is proved that the shear force singularity order is a completely monotonic function of the bi-material parameter and the inclination angle. Some numerical results are given in order to prove the validity of the present study. [ABSTRACT FROM AUTHOR]

The paper presents the results of experiments that were conducted to determine the influence of a triaxial stress state on the evolution of the permeability of an argillaceous limestone. The limestone rock is found in the Ordovician rock formations above the Precambrian basement located in southern Ontario, Canada, which is being considered as a potential host rock for the construction of a deep ground repository for storing low- and intermediate-level nuclear waste. The paper presents the results of an extensive series of hydraulic pulse tests and steady-state tests that were conducted to determine the permeability alterations in zones that can experience levels of damage that can be present in vicinity of an excavated underground opening. A 'state-space' relationship is developed to describe permeability evolution with the triaxial stress in the pre-failure regime. The permeability evolution in extensively damaged post-failure states of the rock is also investigated. It is shown that permeability alterations were four orders of magnitude higher as a result of significant damage to the material, which is an important consideration in establishing the efficiency of the host rock formation as a barrier for the long-term containment of radionuclide migration. [ABSTRACT FROM AUTHOR]

The paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex micro-structures. This approach can be categorized as a semi-concurrent model using the representative volume element concept. A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: (i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); (ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point. Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE $$^2$$ approach) are described: (i) finite elements with embedded strong discontinuities are used for the macro-scale simulation, and (ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale. The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale. [ABSTRACT FROM AUTHOR]

This paper presents a combined continuous-discontinuous modeling technique for the dynamic ductile fracture analysis using an interactive particle enrichment algorithm and a strain-morphed nonlocal meshfree method. The strain-morphed nonlocal meshfree method is a nodel-integrated meshfree method which was recently proposed for the analysis of elastic-damage induced strain localization problems. In this paper, the strain-morphed nonlocal meshfree formulation is extended to the elastic-plastic-damage materials for the ductile fracture analysis. When the ductile material is fully degraded, the interactive particle enrichment scheme is introduced in the strain-morphed nonlocal meshfree formulation that permits a continuous-to-discontinuous failure modeling. The essence of the interactive particle enrichment algorithm is a particle insertion-deletion scheme that produces a visibility criterion for the description of a traction-free crack and leads to a better presentation of the ductile fracture process. Several numerical benchmarks are examined using the explicit dynamics analysis to demonstrate the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A masonry dome cracks when the tension stresses in the hoop rings near the springing reach the masonry's weak tensile strength. These meridional cracks arrive and spread along the dome. In this condition, the pressure surface with zero hoop stresses represents the extension to the three-dimensional case of the problem of the catenary. This analytical approach is adopted in the paper first to develop an accurate description of the minimum thrust state for the hemispherical masonry dome and the corresponding configuration of the pressure surface. Furthermore, the minimum thickness state is studied. Contributions of the paper are either an analytical formulation of the minimum thrust, depending on the geometrical thickness-radius ratio, or a modification of the minimum thickness-radius ratio with respect to the commonly accepted value. In this last geometrical configuration, the pressure surface has to touch the intrados of the dome at the crown, instead of passing through the extrados at the springing. [ABSTRACT FROM AUTHOR]

The Callovo Oxfordian clay-rock (COx) is studied in France for the disposal of radioactive waste, because of its extremely low permeability. This host rock is governed by a hydromechanical coupling of high complexity. This paper presents an experimental study into the mechanisms of water uptake in small, unconfined, prismatic specimens of COx, motivated by the comprehension of cracking observed during concrete/COx interface sample preparation. Water uptake is monitored using both X-ray tomography and neutron radiography, the combination of these imaging techniques allowing material deformation and water arrival to be quantified, respectively. Given the speed of water entry and crack propagation, relatively fast imaging is required: 5-min X-ray tomographies and 10-s neutron radiographs are used. In this study, pairs of similar COx samples from the same core are tested separately with each imaging technique. Two different orientations with respect to the core are also investigated. Analysis of the resulting images yields with micro- and macro-scale insights into hydromechanical mechanisms to be obtained. This allows the cracking to be interpreted as a rapid breakdown in capillary suction (supposed large both to drying and rebound from in situ stress state) due to water arrival, which in turn causes a loss of effective stress, allowing cracks to propagate and deliver water further into the material. [ABSTRACT FROM AUTHOR]

This paper focuses on evaluating stress intensity factors (SIFs), for a curved beam of circular cross section with an external ring crack, applying an approach on the basis of estimating the strain energy release rate. The out of plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach namely differential quadrature element method (DQEM) to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam. [ABSTRACT FROM AUTHOR]

The unconventional fracture model can simulate complex fracture network propagation in a formation with pre-existing natural fractures. The interaction between hydraulic fracture branches, or stress shadowing effect, could be modeled by 2D or 3D displacement discontinuity method (DDM). In this paper, we concentrate on a hydraulic fracture model that integrates 3D DDM for computing the induced 3D stress field around the propagating hydraulic fractures and incorporates the changes in induced stress into the fracture height calculations and propagation criterion. Examples show that for parallel fractures, the height growth may be promoted or suppressed depending on the relative fracture height. For fractures initiated from different formation layers, the fracture growth into the layer occupied by the other fractures is reduced due to the vertical stress shadowing effect. [ABSTRACT FROM AUTHOR]

This paper considers the thermodynamically substantiated derivation of the scalar and vector forms of the J-integral for the Biot elastic porous medium model representing a permeable deformable matrix saturated with a fluid, which is described as a double continuum and whose behavior is determined by coupled equations of elasticity and filtration theory. [ABSTRACT FROM AUTHOR]

The ability of fracture propagation (fracability) is a key parameter of evaluating the fracture network generation during hydraulic fracturing. In order to consider the in situ conditions of the shale formation, four factors should be taken into consideration, which are brittleness, fracability, in situ stresses and natural fractures. The current shale brittleness and fracability evaluation methods rarely involve all the above factors. In this paper, coupling brittleness, stress-strain data and fracture morphology, a new shale fracability evaluation method is proposed. The brittleness is calculated by the mineral components and elastic parameters; the stress-strain data obtained by triaxial compression experiments are used to describe the shale breaking process; and the fracture morphology is evaluated by the fractal dimension method. This method is used to calculate the fracability index of the Longmaxi shale in Sichuan, China. The results show that: (1) the shale fracability under 5 MPa confining pressure is higher than that of under 20 MPa confining pressure; (2) the fracability in 7 coring angles shows a significant difference under the same confining pressure, the highest fracability is at 15∘ and the lowest is from 60∘ to 75∘. Compared with Jin and Rickman’s models, our model matches to the fracture morphologies and the fragments distribution closely. [ABSTRACT FROM AUTHOR]

The Erdogan fundamental solutions are derived from an infinite plane containing a crack. When they are used in the formulation of the boundary element method (BEM), the stress boundary conditions on the crack surface are automatically satisfied and the singular behavior at the crack tip can be naturally reflected. Using the multi-domain technique, the multi-crack problem can be transformed into a series of single-crack problems involving displacement continuity conditions along common boundaries. In this paper, the displacements which are expressed in terms of the integral of a complex function in the Erdogan fundamental solutions are derived in closed-form expressions. Then, the multi-domain spline fictitious boundary element method (SFBEM) based on the above fundamental solutions is proposed and formulated for analyzing multi-crack problems. The computational accuracy and stability of the proposed method are verified by comparing the stress intensity factor (SIF) results of a double-inner crack problem with different inclined angles and crack lengths against those calculated by the finite element method. Also, the SIF results of a double-edge crack problem with different crack lengths are compared with those obtained from studies. Finally, the proposed method is applied to the analysis of the triple-crack problem, in which the shielding effects of multi-crack and stress contours are studied with different crack lengths and locations. [ABSTRACT FROM AUTHOR]

In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic-orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass-epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass-epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading. [ABSTRACT FROM AUTHOR]

Brittle failure of adhesively bonded single lap joints is considered in this paper. A coupled stress and energy criterion in the framework of finite fracture mechanics is employed to study crack initiation by means of a numerical model presented by Hell et al. (Eng Fract Mech 117:112-126, ). Two different formulations of the coupled criterion are compared and the effect of geometrically nonlinear bending deformation of the adherends is analysed. A comparison to experimental results on the effect of the overlap length for single lap joints with composite adherends is given, showing a very good agreement of the failure load predictions. A detailed study of the effects of the geometrical and material parameters of a single lap joint configuration is given. As the energy release at crack formation is considered, the size effect of the adhesive layer thickness is covered correctly. The paper closes with an analysis of the effect of the unbonded adherend length. An approximate explicit expression for a minimum unbonded adherend length is given, which is required to optimize joint designs and to allow for the study of individual parameter effects in numerical and experimental studies. [ABSTRACT FROM AUTHOR]

Calibration functions, used to determine crack extension from potential drop measurements, are not readily available for many common crack growth specimen types. This restricts testing to a limited number of specimen types, typically resulting in overly conservative material properties being used in residual life assessments. This paper presents a unified calibration function which can be applied to all common crack growth specimen types, mitigating this problem and avoiding the significant costs associated with the current conservative approach. Using finite element analysis, it has been demonstrated that Johnson’s calibration function can be applied to the seven most common crack growth specimen types: C(T), SEN(T), SEN(B), M(T), DEN(T), CS(T) and DC(T). A parametric study has been used to determine the optimum configuration of electrical current inputs and PD probes. Using the suggested configurations, the error in the measurement of crack extension is <6% for all specimen types, which is relatively small compared to other sources of error commonly associated with the potential drop technique. [ABSTRACT FROM AUTHOR]

The paper presents results from experimental studies on the influence of loading-unloading processes on the mechanical, linear, and nonlinear properties of the strain-hardening polycrystalline aluminum alloy AMg6 (Rus). The stress-strain curve is measured for AMg6 samples under high-cycle loading-unloading up to fracture of a sample. The microhardness of the sample is measured before and after its fracture. It has been found that the loading-unloading process leads to strain hardening of the AMg6 alloy. The influence of strain hardening of AMg6 on its linear and nonlinear elastic properties is studied by an ultrasonic method. To study the nonlinear elastic properties for different domains of the loading curve, we used the Thurston-Brugger method and spectral method by studying the efficiency of second acoustic harmonic generation. The experimental results are discussed. [ABSTRACT FROM AUTHOR]

Most of the engineering materials are faced with fracture phenomenon that needs to be controlled. There are several methods for controlling crack growth such as hole technique, using locks etc. In order to predict crack growth, stress intensity factor can be conducted as a useful tool. In this paper, the photoelasticity method is conducted as an experimental stress analysis tool in order to calculate the stress intensity factor (SIF). The investigations were conducted to find the effects of holes and locks on the fracture resistance and the SIF. This research is specially focused on the crack stitch as a unique technique to control crack propagation. In this technique, holes of locks are drilled close to each other in rows perpendicular to the crack then keys are inserted into the holes. Three batches including six different edge crack samples of polymethyl methacrylate rectangular plates were used for fracture tests. In the present study, the effects of locks in various geometries were investigated on the SIF. The results were obtained using a polariscope and the tensile load was applied to the specimens on the mode fracture (I) strength; then, the fracture forces were measured. The results showed that the samples with lock and hole have more fracture strength and thus their SIF decreases in comparison with the lock-less or hole-less samples. [ABSTRACT FROM AUTHOR]

Critical loads of columns under compressive follower forces have been widely discussed in the literature. By means of shape optimization, improvements by factors of more than eight could be achieved. However, the obtained solutions turn out to be not robust against perturbations of shape ormaterial parameters. The aim of this paper is to explain this sensitivity effect, basing on a study of eigenforms. Further, a robust alternative to the classical optimization approach is proposed. [ABSTRACT FROM AUTHOR]

The plastic zones of crack tips play a significant role in the fracture behavior of material. This paper proposes a semi-analytic solution for the plastic zones and stress distribution of an infinite space with multiple cracks and inhomogeneous inclusions under remote stress. In this solution, cracks can be treated as a distribution of edge dislocations with unknown densities according to the distributed dislocation technique, while inhomogeneous inclusions can be modeled as homogeneous inclusions with initial eigenstrain plus the unknown equivalent eigenstrain by using the equivalent inclusionmethod. These unknowns can be obtained by using the conjugate gradient method. The plastic zones ahead of crack tips are one-dimensional slender strips, and their sizes can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the applied load based on the Dugdale model of small-scale yielding. It is found that the plastic zones of crack tips are significantly affected by Young's modulus and the positions of inhomogeneous inclusions. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of cracking behaviour of rock-like disc containing one circular inclusion subjected to diametral compression, which is validated by physical tests in terms of the crack patterns and stress–strain responses. The numerical results indicate that if the inclusion strength is higher or close to the matrix strength, one dominated crack can form to split the disc into two parts. Otherwise, the crack branches can be observed besides the dominated crack. The inclusion eccentricity has important influences on the crack pattern of the rock disc. If the inclusion strength is lower than the matrix strength, the horizontal eccentricity can induce to a horizontal crack. The length of the horizontal crack is close related to the eccentricity that a higher eccentricity can lead to a longer horizontal crack. The vertical eccentricity can result in crack branch, which becomes shorter as the eccentricity increases. If the inclusion strength is higher than the matrix, the horizontal and vertical eccentricity cannot lead to crack branches and only one dominated crack can be observed. The disc nominal strength increases by increasing the horizontal or vertical eccentricity both for cases of the inclusion strength lower and greater than the matrix. [ABSTRACT FROM AUTHOR]

In this paper, an extension to a modified Gurson porous ductile material model, namely the Dung’s model, is introduced to investigate ductile fracture processes of AA6061-T6 aluminum alloy sheets. The combined Dung–Hill48 model accounts for anisotropic hardening effects of the matrix material. The constitutive model is implemented as a user-defined material subroutine in ABAQUS/Explicit to predict ductile fracture and formability of the aluminum alloy sheets. Ductile fracture predictability of the model comes from the description of void growth in an anisotropic strain hardening material. After being calibrated the model is applied to establish a fracture plastic strain–triaxiality relation using only tensile test data of smooth and R-notched specimens. Calculations of forming limits from seven deep drawing simulations with Nakajima specimens estimate the formability of the material. Influence of the material anisotropy on the obtained forming limit diagram is discussed. [ABSTRACT FROM AUTHOR]

The goal of this paper is to predict how the properties of the constituent phases and microstructure of dual phase steels (consisting of ferrite and martensite) influence their fracture resistance. We focus on two commercial low-carbon dual-phase (DP) steels with different ferrite/martensite phase volume fractions and properties. These steels exhibit similar flow behavior and tensile strength but different ductility. Our experimental observations show that the mechanism of ductile fracture in these two DP steels involves nucleation, growth and coalescence of micron scale voids. We thus employ microstructure-based finite element simulations to analyze the ductile fracture of these dual-phase steels. In the microstructure-based simulations, the individual phases of the DP steels are discretely modeled using elastic-viscoplastic constitutive relations for progressively cavitating solids. The flow behavior of the individual phases in both the steels are determined by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Chen et al. in Acta Mater 65:133–149, 2014) while the damage parameters are determined by void cell model calculations. We then determine microstructural effects on ductile fracture of these steels by analyzing a series of representative volume elements with varying volume fractions, flow and damage behaviors of the constituent phases. Our simulations predict qualitative features of the ductile fracture process in good agreement with experimental observations for both DP steels. A ‘virtual’ DP microstructure, constructed by varying the microstructural parameters in the commercial steels, is predicted to have strength and ductile fracture resistance that is superior to the two commercial DP steels. Our simulations provide guidelines for improving the ductile fracture resistance of DP steels. [ABSTRACT FROM AUTHOR]

Numerical simulations based on the bifurcation and imperfection versions of the strain localization theory are used in this paper to predict the failure loci of metals and applied to an advanced high strength steel subjected to proportional loading paths. The results are evaluated against the 3D unit cell analyses of Dunand and Mohr (J Mech Phys Solids 66(1):133–153, 2014. doi:10.1016/j.jmps.2014.01.008) available in the literature. The Gurson porous plasticity model (Gurson in J Eng Mater Technol 99(1):2–15, 1977. doi:10.1115/1.344340) is used to induce strain softening and drive the localization process. The effects of the void growth, void nucleation and void softening in shear are investigated over a large range of stress triaxialities and Lode parameters. A correlation between the imperfection and bifurcation results is established. [ABSTRACT FROM AUTHOR]

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con-ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors (SIFs) in rotating disks containing three-dimensional (3D) semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop-erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen-trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as me-chanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature. [ABSTRACT FROM AUTHOR]

This paper describes the results of an experimental study on deformation and fracture of a Zr-1% Nb zirconium alloy in the case of multiple loads at low temperatures (-80°C). Samples cut out of pipes and applied as shells of nuclear fuel elements of fuel assemblies of nuclear reactors are used to conduct a series of experiments on low-cycle stretching and compression at low temperatures and study the effect of low temperature on stress relaxation in the material under different numbers of preliminary loads. [ABSTRACT FROM AUTHOR]

In this paper, four kinds of characteristic length parameters used in a local notch fracture criterion are presented: (1) a characteristic length $${\uprho }_{\mathrm{c}}$$ generally connecting to the notch radius, (2) a characteristic distance $$\hbox {X}_{\mathrm{c}}$$ considered as intrinsic to material and connected to the microstructure, (3) a critical distance $$\hbox {d}_{0}$$ considered as intrinsic to material and connected to the fracture process zone, (4) an effective distance $$\hbox {X}_{\mathrm{ef}}$$ considered as a characteristic of the stress distribution. Each approach is discussed. The paper ends with the author's opinion about the different methods. [ABSTRACT FROM AUTHOR]

The paper presents the theoretical part of a method for the identification of the modified Cockroft-Latham ductile fracture criterion at elevated temperature. Quite a general viscoplastic model is adopted to describe material behavior. The original criterion is path-dependent and involves stresses. Therefore, the identification of constitutive parameters of this criterion, as well as many other ductile fracture criteria, is rather a difficult task that usually includes experimental research and numerical simulation. The latter is impossible without a precisely specified material model and boundary conditions. It is shown in the present paper that for a wide class of material models usually used to describe the behavior of materials at elevated temperatures, the criterion is significantly simplified when the site of fracture initiation is located on traction-free surfaces. In particular, this reduced criterion solely depends on two in-surface logarithmic strains. Since there are well-established experimental procedures to measure surface strains, the result obtained can be considered as a theoretical basis for the efficient method for the identification of the modified Cockroft-Latham ductile fracture criterion at elevated temperature. [ABSTRACT FROM AUTHOR]

In the present paper a sheet of material is considered. It is loaded by uniaxial tensile stress and contains a random distribution of flaw orientations, with the flaws thought of as flat pre-cracks of comparable length, and with all crack planes being oriented perpendicular to the faces of the sheet. Intuition suggests that the most likely flaw to initiate fracture, which will be termed the 'most dangerous defect', lies orthogonally to the major load axis. The purpose of the present paper is to show that such an assumption is incorrect. Neither the most dangerous defect nor the first increments of crack growth will be oriented perpendicularly to the stress direction (nor will they be co-planar with the orientation of the most critical flaw). [ABSTRACT FROM AUTHOR]

The purpose of this paper consists in developing a probabilistic approach for predicting fatigue life improvement of 7075-T6 cracked Single Edge Notch Tension (SENT) specimen repaired by high interference fit bushing. The developed approach is carried out by coupling FE-analysis and Monte Carlo reliability method. In this context, a 2D- finite element analysis of the cracked SENT specimen using ABAQUS commercial software is established to: (i) simulate the interference fit process and (ii) to predict the fatigue life improvement after repair. The non-linear isotropic/kinematic hardening model embedded in ABAQUS is used to characterize the material behavior. Different stress levels, different interference fit sizes and different expanded hole diameters are investigated. As a result, crack arrest hole diameter equals to 6 mm with larger interference fit size (IFS = 0.2 mm) provides higher beneficial compressive residual stress distribution and higher fatigue life improvement than drilling hole near the crack tip. The iso-probabilistic S-N curves and the Reliability-Life curves after repair can be determined for different interference fit sizes and different expanded hole diameters. This probabilistic approach can be used with the interference fit process as an interesting and practical tool to ensure an optimal maintenance planning for cracked structures and to improve the fatigue lives of these cracked components that cannot be replaced as soon as the cracks are observed, especially in the aeronautical filed. [ABSTRACT FROM AUTHOR]

The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress-strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity. [ABSTRACT FROM AUTHOR]

This paper studies propagation criteria in three-dimensional fracture mechanics within the extended finite element framework (XFEM). The crack in this paper is described by a hybrid explicit-implicit approach as proposed in Fries and Baydoun (Int J Numer Methods Eng, ). In this approach, the crack update is realized based on an explicit crack surface mesh which allows an investigation of different propagation criteria. In contrast, for the computation of the displacements, stresses and strains by means of the XFEM, an implicit description by level set functions is employed. The maximum circumferential stress criterion, the maximum strain energy release rate criterion, the minimal strain energy density criterion and the material forces criterion are realized. The propagation paths from different criteria are studied and compared for asymmetric bending, torsion, and combined bending and torsion test cases. It is found that the maximum strain energy release rate and maximum circumferential stress criterion show the most favorable results. [ABSTRACT FROM AUTHOR]

The thermal deformation appearing in indium antimonide infrared focal plane arrays (InSb IRFPAs) subjected to thermal shock tests, will easily incur the fracture of InSb chip, this phenomenon restricts the final yield of InSb IRFPAs. In light of the proposed equivalent method, the three dimensional structural modeling of InSb IRFPAs is developed, and the simulated strain distributions are consistent with the buckling pattern, the shallow groove and the local flatness, appearing on the top surface of InSb IRFPAs at the corresponding regions. After comparing the deformation profiles at different regions, we deduce that the top surface flatness of InSb IRFPAs will be improved with frustum pyramid indium bump arrays, and this deduction is verified by the subsequent simulation results. That is, when the top surface area of indium bump is smaller than its bottom surface area, in this paper, the diameter of indium bump bottom surface is set with 24 μm, the simulated Z-components of strain is uniformly covering the whole top surface of InSb IRFPAs, and the deformation amplitude is decreased slowly with the decreasing top surface area of indium frustum pyramid arrays. These findings are beneficial to further improve the flatness of InSb IRFPAs, correspondingly, to lengthen its temperature cycling life. [ABSTRACT FROM AUTHOR]

The complex behaviours of rocks and rock masses have presented paradoxes to the rock engineer, including the fracturing of seemingly strong rock under low stress conditions, which often occurs near excavation boundaries. The extension strain criterion was presented as a fracture initiation criterion under these conditions (Stacey in Int J Rock Mech Min Sci 18:469-474, 1981). This criterion has been used successfully by some and criticised by others. In this paper, we review the literature on the extension strain criterion and present a case for the correct interpretation of the criterion and the conditions suitable for its use. We argue that the extension strain criterion can also be used to provide an indication of damage level under conditions of relatively low confining stress. We also present an augmentation of the criterion, the ultimate extension strain, which is applicable under extensional loading conditions when σ is similar in magnitude to σ . [ABSTRACT FROM AUTHOR]

A non-local formulation of the classical continuum mechanics theory called peridynamics is used to study initiation and propagation of dynamic fractures. The purpose of this study is twofold. First, we introduce a new post-processing technique to estimate stress intensity factors using peridynamic data. Second, the peridynamic stress intensity factors are used to study the influence of loading rate on key aspects of dynamic fracture. In particular attention is focused on examining the influence of loading rate and material properties on time to fracture and the local stress state at the fracture tip during initiation and propagation. In the first part of the paper emphasis is placed on using stress intensity factors to verify the numerical method. Simulations are performed on simplified test cases and the results are compared to relevant experimental and numerical studies found in the literature. Peridynamic stress intensity factors are then used to demonstrate the influence of loading rate on fracture initiation and propagation. To this end simulations are performed by partially loading the internal surfaces of a notch at various loading rates and monitoring the stress intensity at the tip of the notch. For each loading rate, the stress intensity factor increases smoothly to a value above the input fracture toughness at which point initiation occurs. After initiation, the stress intensity factor remains nearly constant in time. It is shown that the stress intensity factor at initiation and the time to fracture depend on the loading rate. Predictions show that the critical stress intensity is insensitive to loading rate when the fracture initiation time is below a material-dependent characteristic time scale. As loading rate increases, the time to fracture decreases and stress intensity at initiation increases markedly. The characteristic time-scale is shown to be only dependent on the material stiffness and independent of the strength of the singularity at the fracture tip. In our simulations, increasing the loading rate resulted in fracture branching. Also, the fracture speed increases with loading rate. However, the dynamic stress intensity factor of a propagating fracture is shown to be independent of loading conditions for a linear peridynamic solid with rate-independent input fracture toughness. [ABSTRACT FROM AUTHOR]

In this paper, the stresses near the tip of interface corners are expressed in matrix power function form. To make this matrix power function form valid for all possible cases of interface corners, all kinds of singularities including oscillatory and logarithmic singularity are discussed in this paper. The coefficient vector of this matrix power function form solution is then defined as a vector of stress intensity factors along the radial direction. Since the stress intensity factors are functions of radial direction, the maximum stress intensity factor of a certain radial direction may be useful for the fracture prediction of interface corners. This new definition of stress intensity factors is applicable for all possible singular orders-repeated or distinct, real or complex, and keeps the same unit for all possible interface corners. Therefore, it will be helpful for bridging the problems of cracks, corners, interface cracks and interface corners. Finally, the matrix form solutions are reduced to the scalar form solutions for two special cases. One is a special case of corner angles-cracks, and the other is a special case of anisotropic materials-isotropic materials. Through this reduction, new scalar form analytical solutions are obtained and specialized further to compare with the existing analytical solutions. [ABSTRACT FROM AUTHOR]

The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out. [ABSTRACT FROM AUTHOR]