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In the paper, new hybrid (numerical-analytical) methods to calculate the J-integral, the CTOD, and the load line displacement are presented. The proposed solutions are based on FEM calculations which were done for SEN(B) specimens dominated by plane strain condition. The paper includes the verification of the existing limit load solution for SEN(B) specimen with proposal of the new analytical formulae, which were used for building hybrid equations for determining three selected fracture mechanics parameters. [ABSTRACT FROM AUTHOR]

Connection (adhesive layer, welded seam, etc.) of solid bodies at the macro-level looks like a zero-thickness object (surface or line). At the micro-level, the connection is a three- or two-dimensional zone of complex geometry. Often it has no recognizable boundaries and/or inhomogeneous structure. Nevertheless [1-2], there exists a general relationship between the microscopic stress–strain state in the connecting zone and the stress–strain state at the macroscopic interface surfaces. It was demonstrated in [1-2] that independently of the specific form of this relationship, the microscopic stress–strain state does not influence the macroscopic interface conditions. It is the so-called erasing of the individual properties of the connection. In other words, the connection has no own properties and does not appear as an independent object in the interface elasticity theory problem. The opposite situation takes place if we address the strength properties of the connected bodies. Based on the same relationships [1-2], we demonstrate the interface surface demonstrates on the macro-level the own strength property. Namely, there exists a macroscopic strength criterion for the interface that differs from the strength criteria for the connected bodies. Thus, the interface is an independent object for the fracture mechanics. Both the features of the joint noted above are phenomena of asymptotic nature. In reality, the thickness of the joint is small but nonzero. In this case, the asymptotic provides us with the so-called leading terms. It means that in reality the microstructural properties of the connection slightly influence the macroscopic model and the macroscopic strength criterion may be used in practice as an approximation. Additional mathematical analysis is required to estimates of the accuracy of these approximations. It is impossible to obtain a simple relationship between the micro- and macroscopic stress–strain fields. However, the theoretical technique [1-2] can be implemented using the FEM software (with some additional programming). An example of the construction of the strength criterion of explosive welding seam is presented. [ABSTRACT FROM AUTHOR]

It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second-order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three-point reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to 1, occurring often in mode I crack propagation problems, is finally discussed. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded).Design/methodology/approach The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification.Findings Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments.Originality/value A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation. [ABSTRACT FROM AUTHOR]

This paper aims at understanding and predicting how pressurized cracks propagate in anisotropic brittle solids, a situation frequently encountered in hydraulic fracturing. Special attention is paid to transverse isotropy, often used to model shale. Although the theory of linear elastic fracture mechanics of anisotropic solids is well established at present, this paper shows that the application of Muskhelishvili's formalism to Lekhnitskii's anisotropic complex potentials provides a powerful tool to extend the validity of the classical tools of isotropic fluid-driven crack models to the anisotropic case, provided that the appropriate elastic constants are used. These elastic constants are identified and derived in closed form for transversely isotropic solids. The constants are shown to be directly related to quantities easily measured in a laboratory at macroscopic scale through indentation tests and acoustic measurements. Moreover, several crack-kinking criteria are compared. Contrary to the isotropic case, the crack-kinking criteria are not consistent among themselves, even in the case of a pure pressure loading. The orientation at which it is easier to propagate an already existing crack is sought. A critical crack length, below which this crack orientation is the one of minimal stiffness felt by the crack, is identified. [ABSTRACT FROM AUTHOR]

Peeling is a physical mechanics involved in the detachment of many natural and industrial applications. In this paper, we investigate the double peeling of an endless elastic pre-stressed tape adhering to a flat smooth rigid substrate. Solutions are given in closed form and their stability is discussed. Critical pull-off force needed to detachment is shown to be higher for pre-stressed tapes. However, when a pre-stress is high, tapes behave differently and may spontaneously detach from the rigid substrate. [ABSTRACT FROM AUTHOR]

In the case of sufficiently brittle material the use of stress intensity factor as a fracture parameter alone is well justified within the Linear-Elastic Fracture Mechanics. This is because the singular stress field associated with the stress intensity factor is dominant near the crack tip. However, there are numerous experimental evidences that the critical stress intensity factor to cause fracture initiation (or fracture toughness) can be affected by the specimen geometry as well as loading conditions. To address this issue a number of twoparameter criteria have been proposed in the past, which often utilise non-singular terms of the classical asymptotic expansion of the stress field near the crack tip. Therefore, there is a problem of the selection of an appropriate parameter in addition to the stress intensity factor, which could account for various effects induced by the specimen geometry and loading on initiation of brittle fracture. This short paper demonstrates that brittle fracture conditions can be successfully predicted with various two-parameter criteria, and there are no clear advantages in the use of T-stress as the additional parameter in fracture criterion, in comparison with the next non-singular term, A1, of the asymptotic expansion. [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]

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]

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]

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 presents the fatigue behavior of interface bond between red maple wood and phenolic FRP substrates. Using linear elastic fracture mechanics concepts, the influence of load ratio on fatigue crack propagation rate is studied. A contoured double cantilever beam (CDCB) specimen is adopted in this study in order to obtain constant strain energy release rate independent of crack length. The compliance method is used for measuring the crack growth rate. A modified Paris Law equation based on strain energy release rate range, ΔG, and mean value of strain energy release rate, Gmean, is proposed in this study for efficient evaluation of load ratio effect on fatigue crack propagation of the bonded interfaces. Follow-up environmental effects are being examined by means of the same energy parameters of the present study and without the need to consider crack closure. The proposed approach can further be extended to characterization of other bonded interfaces for dissimilar materials. [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]

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This paper is the sequel of a companion Part I paper devoted to dislocation-based antiplane fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type. In the present paper, the inplane analysis is carried out to study cracks of Modes I and II. Generalized continua including nonlocal elasticity of bi-Helmholtz type and gradient elasticity of bi-Helmholtz type (second strain gradient elasticity) offer nonsingular frameworks for the discrete dislocations. Consequently, the dislocation-based fracture mechanics within these frameworks is expected to result in a regularized fracture theory. By distributing the (climb and glide) edge dislocations, (Modes I and II) cracks are modeled. Distinctive features are captured for crack solutions within second-grade theories (nonlocal and gradient elasticity of bi-Helmholtz type) comparing with solutions within first-grade theories (nonlocal and gradient elasticity of Helmholtz type) as well as classical elasticity. Other than the total stress tensor, all of the field quantities are regularized within second-grade theories, while first-grade theories give singular double stress and dislocation density and classical elasticity leads to singularity in the stress field and dislocation density. Similar to gradient elasticity of Helmholtz type (first strain gradient elasticity), crack tip plasticity is captured in gradient elasticity of bi-Helmholtz type without any assumption of the cohesive zone. [ABSTRACT FROM AUTHOR]

An overview of past research on T-stress is presented in this paper, we provides some critical review of the history and state of two elastic fracture mechanics and relationship to crack paths stability. The importance of the global approach with two parameters (K-T) or (K-A3) in the analysis of the linear elastic fracture mechanics, based on the effect of confinement according to the work of Williams, is presented in the field of CT specimen in mode I for the API X52 steel. The objective is to propose a numerical study, defining the T-stress, by applying the finite element method, in 2D, using the software ANSYS 15.0. Thereafter, we propose the method inspired from the volumetric approach developed by Pluvinage, this method is based on the determination of the effective stress Tef over an effective distance Xef ahead of the crack tip. Finally, it concludes with a discussion critical of methods of calculated the T-stress. [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]

Little understanding exists between the early-age stress developments in a wellbore cement sheath and its risk of impairment. During hydration, the cement morphology and pore-pressure changes induce eigenstresses in the solid and pore volumes. Utilizing these stresses as the driving mechanism of fracture, this paper formalizes the inspection of a radial crack in an elastic cement sheath constrained by an inner steel casing and an outer rock formation. The solution is constructed in the framework of analytic function theory and seeks the Green’s function for an edge dislocation in the intermediate cement phase. A dislocation pile-up along the line of fracture constructs a singular integral equation for the crack opening displacement derivative, from which the energy release rate is readily deduced. Under the uniform development of eigenstresses, the stiffness ratios of steel-to-cement and rock-to-cement generally predict the crack to initiate along the steel-cement interface. Here, the impacts of (i) a rigid bond and (ii) a sliding interface with no shear are assessed. This leads to the primary result of the paper: the potential for radial fracture is substantially mitigated by ensuring the shear connection between the steel casing and the cement sheath. [ABSTRACT FROM AUTHOR]

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couplestress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip. [ABSTRACT FROM AUTHOR]

In this paper Digital Image Correlation (DIC) is used to study the evolution of the plastic zone close to a crack tip. A modified CT-specimen was used in order to fulfill the plane stress condition. The strain field around the crack tip was measured using two cameras and stereo DIC, so that out-of-plane movements are taken into account. Then, the Virtual Fields Method was used to identify the plastic zone, looking at the parts of the specimen which deviates from the linear elastic behavior. With such approach, it was possible to individuate the onset of plasticity close to the crack tip and follow its evolution. A comparison with FEM results is also provided. [ABSTRACT FROM AUTHOR]

In this paper the so-called Theory of Critical Distances is reformulated to make it suitable for estimating the strength of notched metals subjected to dynamic loading. The TCD takes as its starting point the assumption that engineering materials' strength can accurately be predicted by directly post-processing the entire linear-elastic stress field acting on the material in the vicinity of the stress concentrator being assessed. In order to extend the used of the TCD to situations involving dynamic loading, the hypothesis is formed that the required critical distance (which is treated as a material property) varies as the loading rate increases. The accuracy and reliability of this novel reformulation of the TCD was checked against a number of experimental results generated by testing notched cylindrical bars of Al6063-T5. This validation exercise allowed us to prove that the TCD (applied in the form of the Point, Line, and Area Method) is capable of estimates falling within an error interval of ±20%. This result is very promising especially in light of the fact that such a design method can be used in situations of practical interest without the need for explicitly modelling the non-linear stress vs. strain dynamic behaviour of metals. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate a value of the critical applied stress for a crack initiation from a sharp V-notch tip. The classical approach of the linear elastic fracture mechanics (LELM) was generalized, because the stress singularity exponent differs from 0.5 in the studied case. The value of the stress singularity exponent depends on the V-notch opening angle. The finite element method was used for a determination of stress distribution in the vicinity of the sharp V-notch tip and for the estimation of the generalized stress intensity factor depending on the V-notch opening angle. Critical value of the generalized stress intensity factor was obtained using stability criteria based on the opening stress component averaged over a critical distance d from the V-notch tip and generalized strain energy density factor. Calculated values of the critical applied stresses were compared with experimental data from the literature and applicability of the LEFM concept is discussed. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes simplified methods to estimate the elastic–plastic J-integral, J, related to the crack growth rate in elastic–plastic situations. Estimating this parameter under general conditions entails costly detailed elastic–plastic FEA modelling of the cracked component concerned, and thus, some simplified methods that do not involve complex numerical calculations are required, particularly, for use in situations where plastic strains are produced by secondary stresses. For mechanical primary stresses, the reference stress method may provide reasonable estimates of J. The direct use of the reference stress method for secondary stresses, however, has not yet been fully established. The method presented in this paper is based on the enhanced reference stress method, which leads to more accurate estimates of J than the original method, and elastic follow-up factors for approximating the inelastic response of the component from the elastic FEA. The present method has been validated by performing detailed elastic–plastic FEA of cracked plates subjected to displacement-controlled loading and of a circumferentially cracked cylinder subjected to thermal loads. [Copyright &y& Elsevier]

The paper deals with the three-dimensional nature and the multi-parametric representation of the stress field ahead of cracks and notches of different shape. Finite thickness plates are considered, under different loading conditions. Under certain hypotheses, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to some notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE models. [ABSTRACT FROM AUTHOR]

Abstract: In a companion paper, proposals for the shape of a strain-based failure assessment diagram (FAD) have been made. The developments in that paper and in related works on strain-based fracture assessment have largely been for remotely applied strains, such as those produced by welding. This paper re-writes existing methods for treating secondary stresses within stress-based FADs in the framework of the proposed strain-based FAD. It is shown that residual strains must be included fully in the elastic regime but at large applied strains their contribution to fracture can be relaxed considerably. Practical methods for inclusion of secondary strains within the strain-based FAD are then developed and shown to be conservative relative to some detailed finite element calculations. [Copyright &y& Elsevier]

Results related to the buckling delamination of elastic and viscoelastic composite plates are reviewed and analyzed. They have been obtained during the last fifteen years by the author and his students. The plates contain cracks whose faces have initial infinitesimal imperfections. The evolution of the imperfections under compression of the plates is studied, and the values of critical parameters are determined from a criterion of initial imperfection. The study is performed with the use of 3D geometrically nonlinear field equations. In the present paper, the historical background of the problems is outlined considered, general remarks about the field equations and solution method are made, and problems related to the plane strain state are reviewed. [ABSTRACT FROM AUTHOR]

This paper presents an alternative criterion (simplified method) to determine the cohesion () and internal angle of friction () properties for two granular materials lightly stabilized with slag lime and general blend (GB) cement-fly ash using indirect diametral tensile (IDT) strength and unconfined compressive strength (UCS). The and values of the stabilized materials obtained on the basis of this criterion were related to the IDT strength and UCS. The results suggest that the and can be estimated using this criterion and the can be accurately related to either the IDT strength or UCS for lightly cementitiously stabilized granular materials. However, the IDT strength is a better characteristic than the UCS to estimate the . To validate the criterion, the and obtained from the proposed criterion were input in the numerical analyses of IDT testing with Mohr-Coulomb failure criterion using FLAC2D finite difference software. The predicted tensile stress-horizontal diametrical deformation numerical results were compared with the corresponding experimental results. On the basis of this numerical analysis, the and parameters estimated from this method could predict the experimental results well in the elastic region but over-predicted the ultimate stress. [ABSTRACT FROM AUTHOR]

This paper reports an experimental study on the use of carbon fiber-reinforced polymer (CFRP) sheets to strengthen non-load-carrying cruciform welded joints subjected to fatigue loading. Failure modes and corresponding fatigue lives were recorded during tests. Scatter of test results was observed. Thereafter, a series of numerical analyses were performed to study the effects of weld toe radius, the number of CFRP layers and Young's modulus of reinforced materials on local stress concentration at a weld toe. It was found that fatigue life of such welded connections can be enhanced because of the reduction of stress concentration caused by CFRP strengthening. Parametric study indicates that the weld toe radius and the amount of CFRP are the key parameters influencing the stress concentration factors and stress ranges of the joint. Enhancement of modulus for adhesive and CFRP sheets can also be beneficial to the fatigue performance to some extent. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes an efficient numerical procedure for computing T-stresses of cracks in three-dimensional, linearly elastic, infinite media. The technique is established in a broad framework allowing a medium made of generally anisotropic materials and cracks of arbitrary shape and under general loading conditions to be treated. A pair of weakly singular, weak-form, displacement and traction boundary integral equations is utilized to formulate the key equations governing the unknown crack-face fields. Besides the basic benefits such as the reduction of spatial dimensions of the solution space and the efficient treatment of unbounded domains and remote boundary data, use of such integral equations in the formulation offers additional positive features including the computational simplicity resulting from the weakly singular nature of all involved integrals and the involvement of a complete set of crack-face displacement fields. A weakly singular symmetric Galerkin boundary element method together with the special near-front approximation is utilized to solve for the unknown relative crack-face displacement whereas the sum of the crack-face displacement is obtained from the displacement boundary integral equation for cracks via the Galerkin technique. The latter step is one of the essential aspects of the present study that provides the direct means for determining the T-stress data in terms of the sum of the crack-face displacement in the neighborhood of the crack-front. An extensive numerical study is conducted for various scenarios and a selected set of results is reported to demonstrate both the accuracy and capability of the proposed technique. Highlights • A numerical method is established to determine T-stress for cracks in 3D media. • The formulation is based on a pair of weakly singular weak-form integral equations. • A special element is used for the near-front relative crack-face displacement. • Explicit formulae are used to extract the T-stress from the crack-face data. • Highly accurate T-stress results are obtained using relatively coarse meshes. [ABSTRACT FROM AUTHOR]

Shear banding represents a local failure mechanism of a soil structure as a response to shear loading. In soil structures of different spatial scales systems of regularly spaced shear bands can be observed as a consequence of extensional loading. The phenomenon of single shear bands, defined as thin zones of localized deformation with a discontinuity of the strain field at its boundaries, is well understood. Inside the shear band the material undergoes inelastic strain softening accompanied by shearing and dilation, whereas the material outside the shear band unloads accompanied by elastic contraction in extension tests. Despite numerous experimental and numerical investigations, the physical mechanisms and parameters determining the spacing of parallel shear bands remained unknown. The paper in hand presents an analytical solution for the spacing of the shear bands and a comparison with a large base of experimental data gained from 1 g and ng (geotechnical centrifuge) model experiments. The analytical solution is based on the assumption that the elastic energy rate in the unloaded zone between the shear bands tends to a minimum value. The spacing was calculated as the energetically preferred solution for a broad range of cohesive-frictional granular materials. The dependency of the calculated spacing on initial and boundary conditions as well as on material parameters was found to be in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of two equal coplanar cracks with allowance for the crack faces contact interaction was investigated. The problem of the cracks located in homogeneous, isotropic, and linearly elastic solid subjected to normally incident tension-compression wave is solved by the boundary integral equations method. The influence of the distance between two cracks on the stress intensity factors (opening mode and transverse shear mode) is studied for a range of wave numbers. The results are compared with those obtained neglecting cracks' closure. [ABSTRACT FROM AUTHOR]

Abstract: An exact solution for stresses in cracked composite laminates with lay-up [] is developed in this paper. The inter-laminar shear stresses between the 90° and 0° plies are assumed to be in the form of series expansion of sinusoidal functions. This leads to the stress components in laminates having corresponding series expressions from the equilibrium equations together with boundary conditions for inter-laminar stresses. The principle of minimum potential energy is used to derive algebraic equations for the unknown coefficients. Furthermore, cyclic differential function is introduced to express analytically the resulting stresses in the laminates. As an application, reduction of Young’s modulus and change in Poisson’s ratio for different laminates are evaluated and compared with available experimental and predicted results. Distributions of inter-laminar stresses are also presented in this paper, with results showing that the present solution is accurate and suitable for the analysis of characteristic damage state for composite laminates. [Copyright &y& Elsevier]

Crack penetration through the bimaterial interface of two polymers is investigated numerically. Due to the practical importance of the problem, a crack in a three-layer pipe consisting of a main and two, inner and outer, protective layers is analyzed in this paper. The prime aim is to formulate the conditions under which the crack stays arrested at the interface between the protective layer and the main pipe or penetrates into the interface and causes failure of the main pipe and consequently of the entire pipe system. The crack tip stress field is described by using a generalized stress intensity factor for cases where the crack touches the interface and the stress singularity exponent differs from 1/2. In the case of short-term applications, the stress state on the interface is given simply by a combination of the elastic properties of materials of the main pipe and the protective layers. In long-term applications, the time-dependent properties of the materials can significantly influence the stress state of the interface and can lead to considerable changes in failure conditions. The results presented here may contribute to a more accurate estimation of the residual lifetime of multilayer pipes. [ABSTRACT FROM AUTHOR]

This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. [ABSTRACT FROM AUTHOR]

Abstract: It is evident that the carbon-fiber-reinforced cementitious composites are being used in the structural and construction works owing to the synergetic action from two components viz. fiber and mortar matrix. Incorporation of a very nominal percentage of carbon fibers into a mortar mixture produces a strong and durable composite that leads the product of smart material properties. Flexural behavior of cement-based matrices carrying carbon fibers reinforcement of different percentage and size is studied in this paper. Influence of fiber content and length of the fiber is quantified using load–deflection curves. Specimens containing fiber of 0.0, 0.5, 1.0 and 1.5% with 3mm (0.12in.), 6mm (0.36in.), and their combination are prepared and tested. It is demonstrated that combination of 3mm (0.12in.) and 6mm (0.36in.) fibers enhances the bearing capacity to crack- and ultimate-stresses as well as the Young’s modulus of the fiber reinforced cement composites. The paper emphasizes the desired performances after the initiation of cracks and discusses the pre- and post-cracking load–deflection characteristics of the composites. [ABSTRACT FROM AUTHOR]

The paper establishes a correspondence between the solutions for rectilinear cracks located in a piezoceramic plane at a right angle to the polarization axis and smoothly (no friction) opened with rigid wedges and the solutions for cracks in a purely elastic isotropic plane. This correspondence can be used to calculate the SIFs for cracks in a piezoceramic plane from the expressions for cracks in an elastic isotropic plane, without the need to solve the electroelastic problem. The following problems are solved as examples: opening of a semi-infinite crack with a semi-infinite rounded wedge, a truncated wedge, and a wedge of constant thickness; opening of two semi-infinite cracks with hyperbolic wedges and wedges of constant thickness [ABSTRACT FROM AUTHOR]

In this paper we consider a crack of arbitrary shape in a homogeneous elastic media in the absence of body forces, formulate variational Dirichlet and Neumann crack problems in a linear three-dimensional elasticity in Sobolev spaces and prove the existence and uniqueness of the corresponding (weak) solutions. [ABSTRACT FROM PUBLISHER]

Abstract: Notched plates are often found in various applications ranging from microelectronic devices to large-scale civil structures. Stress analysis of plate components wherein the loading is uniformly distributed over the thickness, parallel to the plane of the plate, is normally based on plane stress or plane strain assumptions. Three-dimensional effects, such as the influence of the plate thickness on stress components, are largely ignored or considered as negligible for all practical purposes. This paper summarizes recent theoretical and numerical studies and discusses some important features of the three-dimensional singular solutions for sharp notches obtained within linear elasticity. Taking into account dimensionless considerations, the relationships between the intensities of the singular stress states corresponding to the three-dimensional linear elastic solutions and the plate thickness are established. The obtained relationships have many intriguing implications for the failure assessment of notched plates made of sufficiently brittle material. For example, based on a similar argument to the one used in classical linear-elastic fracture mechanics, it can be shown that a sufficiently thick plate with a sharp re-entrant corner should have virtually zero strength when subjected to antisymmetric (or mixed mode) loading. The theoretical conclusions drawn in this paper have direct applications to fracture testing and fracture assessment of plate components, and they set new goals for further experimental studies. [Copyright &y& Elsevier]

Abstract: In the given paper, rotating polygonal plate of the theory of elasticity is considered. From the solution of only elementary simple dynamic problems of the theory of elasticity are known. Solutions of dynamic problems of the theory of elasticity for multi-connected polygonal plates, as well as for the plates with rectilinear cuts are still waiting for their exhaustive answer. For complex domains, especially in the availability of linear cracks, such problems are considered for the first time. Mainly, this was connected with the lack of conformably mapping functions which, for the first time in the scientific world, were discovered by the author of the given manuscript. Owing to the papers , many questions connected with conformably mapping functions may be settled. Stress state of a polygonal isotropic plate weakened by two linear crack elliptic holes () is considered. The centers of elliptic holes are on a real axis , the linear cracks reaching the ellipses are symmetrically arranged along a real axis. End points of the crack have the coordinates. Two point masses have been fixed on an imaginary axis at distances from the center of a plate. The plate revolves with constant angular velocity around the axis passing through the center of the plate and perpendicular plane. The origin is at the centre of a polygonal plate. The contours of the plate are free from external forces. We shall obtain the solution of the considered problem by applying the solutions of indicated two problems (two cases of acting loads). Solving each of indicated problems by Muskheleshvili method (determining the functions and that are regular in the plate’s domain for each case) we find the stress fields, and at characteristic points of cuts at the end points of cracks. From these values of stress we can determine the stress intensity coefficient (K) at the end points of cracks, and then to define a critical load at which the fracture of a plate begins. Knowing we find a limiting angular velocity (or limiting member of revolutions per minute). Numerical examples are considered. [Copyright &y& Elsevier]

Abstract: The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same. [Copyright &y& Elsevier]

Bi-material interfaces are studied with cracks that end perpendicular to the interface. As is well-known, singularities in the stresses appear when classical elasticity is used. Moreover, the nature of the singularity depends on the difference in elastic constants of the two materials. In this paper, the gradient elasticity theory of Aifantis is used to remove these singularities. This is demonstrated for a range of ratios between the two Young’s moduli. [ABSTRACT FROM AUTHOR]

Abstract: Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value −1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, the near tip stresses are oscillatory due to the order of singularity being −1/2±iε and −1/2. The oscillation index ε is a constant related to the elastic properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the elastic properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials. [Copyright &y& Elsevier]

A new approach to computing sub-surface stresses in an elastic half-space subjected to a line loading is presented. The approach is based on the discrete element method (DEM) in which the material continuum is replaced by a set of convex, rigid, interacting elements connected through visco-elastic fibers. A Hertzian pressure profile with, and without surface traction is applied to a semi-infinite domain created by gluing together discrete elements. Stresses are calculated from the inter-element joint forces that develop due to relative motion of the elements. Newton’s laws are employed to simulate the motion of each element. The stress distribution obtained from the discrete element model compares very well with that obtained from continuum elasticity models. The paper illustrates the applicability of the DEM to analysis of contacts at the microlevel and serves as a foundation to further studies in fracture and fatigue of bearing materials. [ABSTRACT FROM AUTHOR]

A theoretical analysis for the mechanism of ductile chip formation in the cutting of brittle materials is presented in this paper. The coexisting crack propagation and dislocation in the chip formation zone in the cutting of ductile materials are examined based on an analysis of the geometry and forces in the cutting region, both on Taylor’s dislocation hardening theory and the strain gradient plasticity theory. It was found that the ductile chip formation was a result of large compressive stress and shear stress in the chip formation zone, which shields the growth of pre-existing flaws by suppressing the stress intensity factor K I . Additionally, ductile chip formation in the cutting of brittle materials can result from the enhancement of material yield strength in the chip formation zone. The large compressive stress can be generated in the chip formation zone with two conditions. The first condition is associated with a small, undeformed chip thickness, while the second is related to the undeformed chip thickness being smaller than the radius of the tool cutting edge. The analysis also shows that the thrust force F t is much larger than the cutting force F c . This indicates that large compressive stress is generated in the chip formation zone. This also confirms that the ductile chip formation is a result of large compressive stress in the chip formation zone, which shields the growth of pre-existing flaws in the material by suppressing the stress intensity factor K I . The enhancement of material yield strength can be provided by dislocation hardening and strain gradient at the mesoscale, such that the workpiece material can undertake the large cutting stresses in the chip formation zone without fracture. Experiments for ductile cutting of tungsten carbide are conducted. The results show that ductile chip formation can be achieved as the undeformed chip thickness is small enough, as well as the undeformed chip thickness is smaller than the tool cutting edge radius. [ABSTRACT FROM AUTHOR]

This paper presents the experimental results of high-speed tests using PVB sheets and PVB laminated glass. PVB showed a non-linear visco-elastic property in the low-speed tests. The non-linear visco-elastic property could be described using a simple spring-dashpot model including a non-linear spring. The visco-elastic parameters were determined by comparing the experimentally obtained stress-strain curves to the simulated model in which the various visco-elastic parameters are used. The strain-stress curves of PVB under high strain rates are elasto-plastic and those under the low strain rates are non-linear visco-elastic. The phenomenon can be explained from the phase transition from rubbery phase to glassy phase. Considering the results of PVB tensile tests, a simple fracture-mechanical model of PVB laminated glass was formulated to determine energy release rate G. Fracture toughness GC of the PVB laminated glass specimens were calculated from both the experimental results and the energy release rate. Potential energy UC was defined and also compared to the fracture toughness. Nevertheless, the critical loads increase with respect to the increase of tensile speed; potential energy and the fracture toughness remain the same order in all of the chosen tensile speeds. [ABSTRACT FROM AUTHOR]

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data. [ABSTRACT FROM AUTHOR]

The fracture strength of PMMA is studied using columns with rectangular cross- section that contain a central hole and are subjected to axial compression. Samples with geometries such that the width is 2, 3, 4, and 5 times the diameter of the hole are investigated. Cracks are initiated by introducing sharp notches in the axial direction at the crowns of the hole in each sample. The sample is then subjected to axial compression such that the axial cracks grow in a stable manner until a critical compression is attained, after which the cracks extend rapidly in the sample but do not reach its ends. To predict the experimental results, we have first sought to use several published models, but discovered that none would produce results in accord with our data, as they seem not to address the essential features of our beam-column experiments. We have then developed a simple model that consists of a suitably modified version of an elasticity solution based on a short-crack in an infinite plate, combined with a beam-column solution for a long-crack. This model yields results in good accord with our data and also gives reasonable values for the fracture toughness of the material. A comparative discussion of several published models is presented at the end of the paper, pointing out that linear elasticity is not an appropriate tool for solving the present beam-column problem. [ABSTRACT FROM AUTHOR]

The importance of a two-parameter approach in the fracture mechanics analysis of many cracked components is increasingly being recognized in engineering industry. In addition to the stress intensity factor, the T stress is the second parameter considered in fracture assessments. In this paper, the path-independent mutual M- integral method to evaluate the T stress is extended to treat plane, generally anisotropic cracked bodies. It is implemented into the boundary element method for two-dimensional elasticity. Examples are presented to demonstrate the veracity of the formulations developed and its applicability. The numerical solutions obtained show that material anisotropy can have a significant effect on the T stress for a given cracked geometry. [ABSTRACT FROM AUTHOR]

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes. RC for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of RC might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [19]. We consider the case ofn-dimensional nonlinear elasticity, for an arbitraryn?1, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. [ABSTRACT FROM AUTHOR]