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Torsion testing is used to determine the quality of steel wire used for motor tire beads in pneumatic tires. These steel wires must have good-tensile strength so that the tire bead can support the finished tire safely, and yet retain adequate ductility to deform easily around the forming wheel. The present paper highlights premature failure of bead wire which failed during torsion test. Torsion property is one of the important parameters of tire bead as it monitors both the metallurgical soundness and surface quality of a drawn wire. From the analysis, it has been concluded that probable reason for premature failure is due to strain aging (dynamic and static) caused by interstitial atoms which bounds the mobile dislocations resulting in increases yield strength and decreases bead formability. Moreover, the microstructural study indicates that failed specimen has misaligned and broken lamella of pearlite with globular cementite which creates the array of voids. These voids hinder the rotation of pearlite during torsion test thus leading to brittle fracture. [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]

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]

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]

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]

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]

In the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates. [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]

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]

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]

Fracture occurs at interface corners due to stress singularity which generates as a result of material discontinuity and geometrical configuration. In elastic stress field near a bimaterial notch tip, eigenvalues extracted from Airy’s stress function approach determine the order of singularity. In this paper, the characteristic equation of elastic stress field near bimaterial notches is investigated. The study is done on singular eigenvalues as well as the first non-singular eigenvalue which has not been well studied before. First, different combination of materials and geometrical configurations for two of the most applicable paths in the Bogy diagram (β = 0, β = α/4) were studied and the results were comprehensively discussed. It was shown that the geometrical and materials configurations near a bimaterial notch tip can significantly affect on the stress singularity near these corners. Finally, the areas between two lines β = 0 and β = α/4 in the Bogy diagram with high stress singularities were determined and discussed for both the first and second singular eigenvalue. [ABSTRACT FROM AUTHOR]

This paper investigated the mechanism of fracture in concrete due to the deflagration phenomenon. For this purpose, the electric discharge impulse crushing method was selected, with liquid nitromethane (NM) taken as the deflagration agent. Employing this technique, NM is set inside charge holes and initiated by electric discharge. The pressure generated by the deflagration of NM in a steel chamber was modeled using the Jones-Wilkins-Lee equation of state. The modeled and measured pressures agreed well and the applicability of the pressure model was validated. Then, assuming controlled splitting along the expected fracture surface in concrete, dynamic fracture process analysis (DFPA) based on two-dimensional dynamic finite element method was conducted. The results showed that fracture patterns predicted in the DFPAs agreed well with those obtained from experiments. The mechanism of fracture in concrete due to deflagration was then discussed in terms of the fracture process in the controlled splitting. Owing to stress interference from each charge hole, compressive stress zones (CSZs) formed above and below the middle regions between charge holes where maximum and minimum principle stresses were both in compression. The CSZs was found to be important in obtaining a flatter fracture surface in the case of controlled splitting. In conclusion, the proposed method was shown to be useful for the investigation of the fracture mechanism in the case of the use of deflagration agents and could be useful for the design optimization of such controlled splitting. [ABSTRACT FROM AUTHOR]

For carrying out the precise cropping of metal bar with different geometrical sizes, it is very important to obtain the reasonable stress intensity factor of V-shaped notch tip rapidly and accurately. At first, a new precise cropping method, which is the high-speed peripheral low-stress bending fracture cropping is presented in the paper, and its working mechanism is also given in detail. The stress field near V-shaped notch tip is analyzed, and the stress extrapolation method is presented to compute the stress intensity factor of V-shaped notch tip. Based on it, the correctional expression of theoretical stress intensity factor in a handbook of stress intensity factor is also given. The contrasts between stress intensity factor results obtained by means of the stress extrapolation method and the corresponding theoretical results in the handbook of stress intensity factor are also carried out in detail. The results show that the two errors are not more than 5 % and are within a reasonable engineering range. The cropping experimental results for initial loading force and crack propagation life have also confirmed that the correctional expression of theoretical stress intensity factor is feasible. [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]

For composite materials, two quantities that are useful for characterizing the contribution of inhomogeneities in a matrix material to the overall properties are (1) the individual H-tensor, H, which describes the contribution of a single inhomogeneity and (2) the overall strain concentration tensor, which describes the relationship between the overall volumetric strain to the average strain of all of the inhomogeneities. In this paper, we develop a relationship expressing the overall H-tensor, $${\mathcal{H}}$$ , in terms of the overall strain concentration tensor. An important feature of the derivation is that it allows for rigorous upper and lower bounds on the overall H-tensor. In the special case that the inhomogeneities are all the same, with the same orientation, then $${\mathcal{H} = {\bf H}_i}$$ , and the results derived for $${\mathcal{H}}$$ also hold for H. [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]

In the paper, a model of a hydraulic fracture with a tip cohesive zone according to the Barenblatt's approach is considered. The particular case of inviscid fracturing fluid and impermeable rock is studied analytically. Dependencies on time of the fracture length, injection pressure, and fracture opening at the wellbore are obtained, and compared with the corresponding dependencies for a brittle (elliptic-tip) hydraulic fracture. It is proved that on the assumption of finiteness of the cohesive stresses action range, the cohesive zone length cannot also exceed a certain limit value. The limit form of the cohesive zone is obtained, and the limit fracture toughness is evaluated. It is shown that effective fracture toughness tends to the limit value as power function of fracture length with index −1/2. [ABSTRACT FROM AUTHOR]

The long-term performance of engineering structures is typically discussed in terms of such concepts as structural integrity, durability, damage tolerance, fracture toughness, etc. These familiar concepts are usually addressed by considering balance equations, crack growth relationships, constitutive equations with constant material properties, and constant or cyclically applied load conditions. The loading histories are represented by changing stress (or strain) states only. For many situations, especially for those associated with high-performance engineering structures, the local state of the material may also change during service, so that the properties used in the equations are functions of time and history of applied conditions. For example, the local values of stiffness, strength, and conductivity are altered by material degradation to create "property fields" that replace the global constants, and introduce time and history into the governing equations. The present paper will examine a small set of such problems, which involve the accumulation of distributed damage and the development of an eventual fracture path leading to failure. Specifically, the paper discusses this problem in the context of material state changes measured by impedance variations as a method of following the details of fracture path development. An analysis and interpretations of observations will be presented, and limitations and opportunities associated with this general concept will be discussed. [ABSTRACT FROM AUTHOR]

In order to avoid the post-processing in micro-tensile tests, a directly strain measuring method is presented in this paper. The nickel tensile test specimen was electroplated in Watts solution under certain conditions. The measured Young’s modulus, ultimate tensile strength and elongation are 171.5 GPa, 2.18 GPa and 13.8%, respectively. By comparing these results to that obtained by the traditional method, this new approach has been proved reliable. Furthermore, the mean grain size of the nickel specimen measured by TEM images is about 160 nm with wide distribution. The XRD results show that nickel thin film in our experiment has no preferred orientation in the growth direction. The dimple rupture with small microvoids has been observed after the fracture of specimen. [ABSTRACT FROM AUTHOR]

Asymmetric four point bend specimens are often used for determination mode II fracture toughness. Different corrections were proposed to classical solution of Stress Intensity Factors for this specimen. This paper provides a solution for a bi-material four point specimen with sub-interface crack. The solutions were obtained using Finite Element Analysis, and the effect of crack distance to interface, crack length and materials combination were investigated. [ABSTRACT FROM AUTHOR]

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement ( m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons. We also analyze the influence of the particular shape of the micro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well as it obtains crack propagation speeds that compare well, qualitatively and quantitatively, with experimental results published in the literature. The branching patterns also correlate remarkably well with tests published in the literature that show several branching levels at higher stress levels reached when the initial notch starts propagating. We notice the strong influence reflecting stress waves from the boundaries have on the shape and structure of the crack paths in dynamic fracture. All these computational solutions are obtained by using the minimum amount of input information: density, elastic stiffness, and constant fracture energy. No special criteria for crack propagation, crack curving, or crack branching are used: dynamic crack propagation is obtained here as part of the solution. We conclude that peridynamics is a reliable formulation for modeling dynamic crack propagation. [ABSTRACT FROM AUTHOR]

In this paper the contact fatigue resistance of gearwheel teeth, subjected to shot-peening treatment, was investigated experimentally and analytically. The main objective was the evaluation and prediction of fatigue crack initiation, propagation, direction, and rate. A specially designed experimental rig was used to test a number of spur gears with the following characteristics: (a) unhardened, thermally untreated unpeened surfaces, (b) thermally treated unpeened surfaces, (c) unhardened peened surfaces, and (d) thermally treated peened surfaces. The theoretical model assumed initiation and propagation of surface cracks of gears operating in the elastohydrodynamic lubrication regime while loading was due to simultaneous rolling and sliding. Finite element modeling was used for the calculation of the stress field at the gear teeth. Comparison of the experimental and analytical results showed considerable improvement in the contact fatigue strength of thermally treated gear teeth and especially those that underwent shot peening, which increased surface durability. The residual stresses induced by shot peening are mainly effective in stopping microcrack propagation. When shot peening is applied on thermally untreated gear teeth surface, it increases the contact fatigue life of the material by 17% at 7 × 105 loading cycles. If shot peening is applied on carburized gear teeth surfaces, it increases the surface fatigue life by approximately 8% at 106 cycles. Contact fatigue and eventual pitting are treated as a normal consequence of the operation of machine elements. To study this failure process different types of testing machines have been designed. The purpose of this paper is the presentation and evaluation of a new design experimental rig for studying contact fatigue damage of gear teeth subjected to different load patterns. [ABSTRACT FROM AUTHOR]

Abstract  This paper studies the depth variability of uniaxial compressive laboratory test results on intact Toki granite (i.e., sound rock without macroscopic fractures) from the Shobasama and Mizunami Construction Sites, Japan. Some of the depth variability observed in the laboratory results can be indirectly attributed to the high fracture frequency of the “upper highly fractured rock domain” from which some of the samples were taken. For samples taken from the “lower sparsely fractured rock domain,” however, the uniaxial compressive strength of the granite seems to be very strongly correlated to the level of in situ rock stress (i.e., maximum shear stress) determined by measurement results obtained from hydrofracturing tests. The correlation between the laboratory results and the level of in situ stress is explained by the damage due to the complex stress path that the cores undergo during drilling, besides the stress concentrations at the drill-bit/rock contact, which can also affect the microcracking of the samples. An attempt to adjust laboratory test results to estimate the in situ intact rock strength of Toki granite based on its correlation with in situ stresses was carried out. [ABSTRACT FROM AUTHOR]

Recently, authors(Cao et al., Acta Aeronautica et Astronautica Sinica 25(5): 470–472, 2004) extended the singular crack element originally introduced by Wang et al. (Eng Fract Mech 37(6):1195–1201, 1990) for evaluating the stress intensity factors (SIFs). Extensive studies have proved the versatility and accuracy of the element. This study is to show the versatility of the element for piezoelectric materials. In this paper, electric potential and displacement fields near a crack tip of piezoelectric materials are first used to construct a finite element version for directly determining intensity factors of piezoelectric materials with cracks. A singular finite element is constituted and a new method to calculate intensity factors of piezoelectric materials with cracks is obtained without any post-processing procedures. Detailed derivations are given and the results obtained with present method are good agreement with those of theoretical results, the FEM data by ANSYS and singular electromechanical crack tip elements. The results to the different selections of the structural dimensions are carried out. Numerical examples demonstrate the accuracy and validity of the novel element of present method. [ABSTRACT FROM AUTHOR]

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved. [ABSTRACT FROM AUTHOR]

In this paper, an accurate formula for calculating the thermal residual stress field in a particle-reinforced composite are presented. Numerical examples are given to show r-variations of the thermal residual stresses. The increase in fracture toughness of matrix predicted by the thermal residual stress field is compared well with the experimentally measured increase. [ABSTRACT FROM AUTHOR]

In order to avoid introduction of an error when a local crack growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction is proposed in connection with crack growth analyzed by the Dual Boundary Element Method (DBEM). The proposed correction procedure and a reference correction procedure already described in the literature are evaluated by solving two different computational crack growth examples. In the two examples it is found that analyses of the crack paths performed with the proposed crack correction procedure using big increments of crack extension are in excellent agreement with analyses of the crack paths performed by using very small increments of crack extension. Furthermore, it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not calibrated in each new crack growth analysis. [ABSTRACT FROM AUTHOR]

In order to investigate the causes of material fracture, a new method is proposed that uses only the fracture surfaces for determining the fracture parameters in terms of the Cract-tip opening angle (CTOA) and the J integral. This method is based on the principle of fracture-surface topography analysis (FRASTA). In FRASTA, the fracture surfaces are scanned by laser microscope and the elevation data is recorded. Based on this recorded elevation data, the J integral can be calculated. The J integral calculated by the new method agrees well with that calculated by the elastic compliance method. FRASTA allows easy determination of the crack opening deformation (CTOA and COA) and the variation in CTOA and COA through specimen thickness. [ABSTRACT FROM AUTHOR]

The paper gives some closed form expressions for the strain energy averaged in a finite size volume surrounding the root of blunt V-shaped notches under Mode I loading. The control volume, reminiscent of Neuber’s concept of elementary structural volumes, is thought of as dependent on the ultimate tensile strength and the fracture toughness K IC in the case of brittle or quasi-brittle materials subjected to static loads. Expressions for strain energy density under plane strain conditions and Mode I loading have been derived from an analytical frame recently reported in the literature, which matches Williams and Creager-Paris’ solutions in the particular cases of plates weakened by sharp V-notches or blunt cracks (U-notches), respectively. In order to validate a local-strain-energy based approach, a well-documented set of experimental data recently reported in this journal by Gómez and Elices has been used. Data refer to blunt and sharp V-specimens of PMMA subjected to static tension loads and characterised by a large variability of notch root radius (from 0 to 4.0 mm) and notch angle (from 0° to 150°). Critical loads obtained experimentally have been compared with the theoretical ones, estimated here by keeping constant the mean value of the strain energy in a well-defined small size volume. [ABSTRACT FROM AUTHOR]

This paper considers isotropic and orthotropic nonlinear constitutive relations for brittle materials in the case of plane stresses. Numerical solution algorithms based on the finite-element method are developed. The resulting material models are incorporated in the PIONER software. The correctness of crack path determination is examined by solving a test problem of crack propagation. The isotropic model gives mesh-dependent results, whereas the orthotropic model provides an adequate solution. It is shown that solutions obtained for the isotropic model are close to those obtained by eliminating failed elements. [ABSTRACT FROM AUTHOR]

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a ``generalized isoparametric formulation'' and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions. [ABSTRACT FROM AUTHOR]

The objective of this paper is to show the advantages of the cohesive crack model for predicting fracture of V-notched components. Critical values of the generalized stress intensity factor can be obtained from the knowledge of the material softening function and the elastic parameters, avoiding a cumbersome experimental work. The results were checked successfully against experimental ones, from other authors, in different materials: steel, aluminium, PMMA and PVC. A non dimensional formulation of the fracture criterion for sharp V-notched components was obtained and a simple approximate expression derived for easy appication. [ABSTRACT FROM AUTHOR]

A criterion to predict crack onset at a sharp notch in homogeneous brittle materials has been presented in a previous paper of one of the authors. It is reviewed and improved herein. It fulfils both the energy and the strength criteria and takes an Irwin-like form involving the generalized intensity factor of the singularity governing the elastic behaviour in the vicinity of a notch tip. The prediction agrees fairly well with the experiments although it slightly underestimates the experimental measures. A cause of this discrepancy can be that a small notch tip radius blunts the sharp corner. It is analysed in this paper by means of matched asymptotics involving 2 small parameters: a micro-crack increment length and the notch tip radius. A correction is brought to the initial prediction and a better agreement is obtained with experiments on PMMA notched specimens. Experiments performed on a stiffer material (Alumina/Zirconia) show that it is less sensitive to small notch tip radii. A remaining small discrepancy between experiments and predictions can be due to some non linear behaviour of the materials near the notch tip. In addition, without new developments, the method allows to determine the stress intensity factor at the tip of a short crack emanating from a sharp or a rounded v-notch. [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 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]

The paper studies fatigue and fracture behavior of aluminum alloy AA 7085. Fatigue crack growth, low cycle fatigue (LCF), and High cycle fatigue tests have been performed at room temperature. Material's performance against the crack growth has been evaluated at load ratio of 0.1 and 0.3, parameters that govern crack growth are calculated using Paris and Walker model. XFEM has been used for the simulation of fatigue crack growth. Heaviside function is used for the modeling of crack surface while crack front is modeled by branch enrichment function. The simulation result presents a good match with experimental results. In LCF, cyclic softening was observed at higher strain amplitude. Fractographic features of the fracture surfaces obtained from the tests are examined by scanning electron microscopy. [ABSTRACT FROM AUTHOR]

Residual stresses are usually not considered in engineering calculations of components and structures, however, they are present more or less in most of components, such as castings, welded components, components produced by rolling, bending, etc. The main objective of presented research is to determine the residual stresses in seamless thin-walled pipes, i.e. in ring specimens cut out from hot-rolled pipes. Pipe Ring Notched Bend specimens cut out from a pipe are considered as an alternative to the standardized Single Edge Notched Bend specimen used for determination of pipe material fracture toughness. In this research, residual stresses in ten ring specimens are measured by two methods: Incremental Hole Drilling Method (IHDM) and X-Ray Diffraction (XRD). Hoop residual stress is considered as the most important one in pipes. Principal stresses, as well as orientation of principal coordinate system, are determined by IHDM, and subsequently, hoop residual stress is calculated. Direct residual stress in hoop direction is measured by XRD. All results are shown on diagrams up to the depth of 1 mm from outer surface of each ring. Direct comparison of results referring to residual stresses obtained by both methods of measurement is presented to conclude that measurement with XRD shows uncertainty at some depths of measurement, since that method of measurement gives results with some large local oscillations. [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 a comprehensive investigation is carried out with regard to the state of the stress and strain in the neighbourhood of notches in bodies subjected to an anti-plane state of shear stress, within the context of a strain limiting theory of elasticity. Taking advantage of a unified analytical framework, the strain-limiting theory of elasticity is used to determine the full stress and strain field close to a pointed or radiused notch with any notch opening angle. An extensive discussion is provided that highlights the main features of stress and strain distributions, and the implications of the new theory for fracture assessments. In particular, it is proved that the obtained stress and strain solution predicts finite strains at the notch tip and allows the intensity of the stress field to be written as a function of the elastic Notch Stress Intensity Factor $$K_{3}$$ , as in the case of conventional linearized elasticity theory. This makes the strain limiting elasticity an excellent vehicle for justifying theoretically a K based-approach to the fracture of brittle elastic solids, within the context of a self consistent theory, unlike the classical linearized theory that predicts singularities for the strain at crack tips. [ABSTRACT FROM AUTHOR]

In the 1920s, a closed-form solution of the moving Griffith crack was first obtained by Yoffe. Based on Yoffe's solution, the Dugdale model for the moving crack case gives a good result. However, the Dugdale model fails when the crack speed is closed to the Rayleigh wave speed because of the discontinuity occurred in the crack opening displacement (COD). The problem is solved in this paper by introducing a restraining stress zone ahead of the crack tip and two velocity functions. The restraining stresses are linearly distributed and related to the velocity of the moving crack. An analytical solution of the problem is obtained by use of the superposition principle and a complex function method. The final result of the COD is continuous while the crack moves at a Rayleigh wave speed. The characteristics of the strain energy density (SED) and numerical results are discussed, and conclusions are given. [ABSTRACT FROM AUTHOR]

This paper considers several finite moving cracks in an orthotropic half-plane with non-homogenous coating subjected to anti-plane deformation. The distributed dislocation technique is used to carry out stress analysis in the medium containing moving cracks under anti-plane loading. By utilizing the complex Fourier transformation technique, the stress fields are obtained for an orthotropic half-plane containing a screw dislocation. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. Stress fields are derived in the medium under anti-plane point forces. These solutions are Cauchy singular at the location of dislocations and the point of application of forces. The solution is employed to derive integral equations for a half-plane weakened by moving cracks. Numerical results are provided to show the effects of material properties, the crack length and the speed of the crack propagating upon the stress intensity factor. [ABSTRACT FROM AUTHOR]

This paper presents a new method for direct measurement of Mode-I stress intensify factor of cracks using BaSrTiO flexoelectric strain gradient sensors. Firstly, strain gradient field around the opening mode crack tip was analyzed, followed by the derivation of induced flexoelectric polarization in the strain gradient sensors attached in the vicinity of a crack tip. It was found that the constant stress term makes no contribution to the strain gradient, thus the flexoelectric output directly reflects the singular effect. This unique property eliminates the special requirement for sensor placement coordinates and improves the accuracy of the stress intensify factor predication. A specimen with Mode-I crack was then prepared with two strain gradient sensors (4.7 mm × 0.9 mm × 0.3 mm) attached close to the crack tip to verify the analytical model for measurements of stress intensity factor. The experimental results matched well with the empirical estimation confirming that flexoelectric strain gradient sensing can be a convenient and accurate avenue for measuring the stress intensify factor. [ABSTRACT FROM AUTHOR]

The subject of the paper is the capabilities and problems of simulation in computational and experimental fracture mechanics as applied to description of the stress-strain state in the neighborhood of the crack tip and the fracture mechanics parameters considering specific features of the local deformation fixity (stress triaxiality). Simulation techniques are illustrated by evaluation of fracture mechanics parameters of substandard cracked or notched specimens by numerical and experimental methods. [ABSTRACT FROM AUTHOR]