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This paper reports on a new method for the measurement of sheet fracture toughness. In this method, samples cut in DENT geometry are cyclically loaded. The maximum load for each cycle is incremented after each cycle until the sample fractures. The work in the final cycle is then the work required to fracture the sample. The fracture toughness determined using the new cyclic technique is compared with that determined using the Essential Work of Fracture (EWF) technique, for samples with a wide range of fracture toughness, and it is shown that cyclic technique gives a fracture toughness around 8% lower than the EWF technique. For 3 samples, cyclic fracture toughness values were measured for ligament lengths from 3.3 to 14.0 mm and compared with the EWF fracture toughness in each case. The cyclic fracture toughness was found to be independent of the ligament length, except for very weak samples, and to be 5–10% lower than the EWF fracture toughness. The differences between the EWF and cyclic fracture toughnesses were probably due to the development of damage zones around the crack tips before the fracture. The advantages of the new cyclic technique over the EWF technique are that it requires less sample area as only one ligament length is required, is quicker and can be readily automated. [ABSTRACT FROM AUTHOR]

Many metal materials possess the transition from strain localization to fracture, the so-called post-necking behavior, during large deformation under tensile load. It is crucial to understand and characterize the transition for the application of these materials. In this paper, the stress state dependence of the transition from strain localization to fracture of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy is characterized and analyzed by carrying out experiments and phase-field modeling. Firstly, tensile tests for smooth and notched round bars were conducted, in which the notched specimens have different notch radius. It was observed in the tests that the sharper the notch, the shorter the transition process, which can be explained as that high stress triaxiality would shorten the transition process. To further quantify the effects of stress triaxiality in the transition process, the phase-field fracture model involving the nucleation, growth and coalescence of micro-voids is developed to simulate and characterize the damage evolution observed in experiments. The simulations show that as the stress triaxiality increases, the material undergoes less plastic deformation, whether in the initiation of strain localization or the transition process. More interestingly, it is found that there exists a critical value of stress triaxiality, which can be considered the characteristic point of brittle-ductile transition. Above this point, the material has almost no plastic deformation before localization, and brittle fracture occurs directly. This work is meaningful for evaluating the safety of metal structures under complex loads. [ABSTRACT FROM AUTHOR]

When multiple fractures are propagating simultaneously, the fracture spacing may coarsen gradually resulting from loss of stability of the fracture system, which can also occur during the propagation of multiple hydraulic fractures (HFs). In this paper, the stability of the propagation of periodic parallel HFs in brittle solids is investigated based on a representative unit cell consisting two HFs. The fractures are driven to propagate by the inside fluid flow and fluid-solid coupling effect is involved. Both the stress interaction acting in the solid medium and the flow of fluid medium can influence the stability. Stability criterions are given based on the variations of the rates of change of the stress intensity factor with respect to facture velocities. Stability results are obtained by solving the system with fully coupled numerical method which considers the deformation of solid medium, fracture propagation, fluid flow in fractures, fluid partitioning into each fracture. Based on the numerical results, the influences of propagation regimes, fracture lengths and the fracture distance on the stability of HFs are investigated. [ABSTRACT FROM AUTHOR]

This paper describes research on the prediction of necking and failure in metals at very high strain rates. The model developed in this paper uses a total Lagrangian SPH formulation with a normalised kernel. The detailed data from electromagnetically driven ring experiments by Zhang and Ravi-Chandar (Int J Fract 142:183-217, ) is used to evaluate the accuracy of the model predictions. In order to correctly model fracture in the total Lagrangian SPH formulation a visibility criterion based on a truncated cone has been implemented to remove particles obscured by a failed particle. A Johnson-Cook plasticity model is used in combination with a Lemaitredamage model to describe the plastic deformation and fracture of the rings. The effect of Joule heating due to the current induced in the ring is taken into account in the constitutive model. The acceleration due to the ring currents was implemented in the SPH code as a body force. The results demonstrate that this type of model is capable of predicting the number of fragments as well as the time of fracture. In agreement with experimental data, the model also predicts arrested necks and bending in the fragments. [ABSTRACT FROM AUTHOR]

In this paper we derive the theory of multiple peeling, extending the pioneering energy-based single peeling theory of Kendall, including large deformations and pre-stretching. We can thus treat a complex system of films, adhering over a substrate and having a common hinge where the pulling force is applied. Two case studies are investigated: the asymmetric V-shape double peeling and the symmetric cone-shape configuration with N peeling tapes, both requiring the solution of six nonlinear coupled equations (instead of the one needed in the simpler single peeling problem). Remarkable implications emerge: (1) for moderate deformations, the critical strain of a tape is identical to that of the single peeling; (2) an optimal peeling angle, at which adhesion is maximal, is discovered; (3) an additional optimization, even for hierarchical structures, is introduced by imposing the delamination force equal to the intrinsic fracture of the tape. Also, the length of the peeling process zone is calculated, suggesting different optimal values for flaw-tolerant peeling at different angles. Applications to gecko adhesion, for which the flaw-tolerant peeling is demonstrated, and spider silk anchors, that we are going to discuss in details in subsequent papers, are envisioned (including a new pre-stretching mechanism for adhesion control) and suggested by the evidence of a smart mechanism capable of maximizing adhesion simply by increasing the applied tension. [ABSTRACT FROM AUTHOR]

Since the pioneering paper by Mandelbrot (Nature, 308:721–722, 1984) on the fractal character of the fracture surfaces in metals, the fractal aspects in the deformation and failure of materials have been investigated by several Researchers (see the reviews by Bouchaud (J Phys Condens Matter, 9:4319–4344) and Carpinteri et al. (Appl Mech Rev, 59:283–305, 2006)) and the attempts to apply fractals to fracture have grown exponentially. Aim of this paper is 2-fold: on one hand, it summarizes in a detailed yet concise fashion the major results of the fractal approach to the scaling of mechanical properties in solid mechanics; on the other hand, it reports some recent results concerning the size effect in the failure of reinforced concrete (RC) beams. These recent findings clearly show that the picture of the size-scale effects is much more complex when interaction among different collapse mechanisms occurs. The consequences on the size-scale effects are discussed in detail. [ABSTRACT FROM AUTHOR]

This paper deals with energy based r-adaptivity in finite hyperelastostatics. The focus lies on the development of a numerical solution strategy. Although the concept of improving the accuracy of a finite element solution by minimizing the discrete potential energy with respect to the material node point positions is well-known, the numerical implementation of the underlying minimization problem is difficult. In this paper, energy based r-adaptivity is defined as a minimization problem with inequality constraints. The constraints are introduced to restrict the maximum distortion of the finite element mesh. As a solution strategy for the constrained problem, we use a classical barrier method. Beside the theoretical aspects and the implementation, a numerical experiment is presented. We illustrate the performance of the proposed r-adaptivity in the case of a cracked specimen. [ABSTRACT FROM AUTHOR]

In Wang et al. (2002), the mode I crack problem has been analyzed for a functionally graded material strip with arbitrarily distributed properties. For the completeness of the research, this paper provides an analysis method for the mode II in plane and mode III anti-plane elastic crack problems for a functionally graded material (FGM) strip containing a crack along the gradient direction. In the analysis, the gradient region is treated as a number of homogeneous layers stacked along the gradient direction. The analytical models developed in this paper for the modes II and III problems, together with the model developed in Wang et al. (2002) for the mode I crack problem complete the analysis of the mixed-mode crack problem for functionally graded materials with a crack parallel the gradient direction. Those analytical models allow the material properties be any continuous functions along the thickness direction of the strip. [ABSTRACT FROM AUTHOR]

Devices in modern technologies often have complex architectures, dissimilar materials, and small features. Their long-term reliability relates to inelastic, time-dependent mechanical behavior of such structures. This paper analyzes a three-layer structure consisting of, from top to bottom, an elastic film, a power-law creep underlayer, and a rigid substrate. The layers are bonded. Initially, the film is subject to a uniform biaxial tensile stress. A channel crack is introduced in the elastic film. As the underlayer creeps, the stress field in the film relaxes in the crack wake, but intensifies around the crack tip. We formulate nonlinear diffusion-like equations that evolve the displacement field. When the crack is stationary, the region in which the stress field relaxes increases with time. We identify the length scale of the region as a function of time. The stress intensity factor is proportional to the square-root of the length scale. For the power-law creep underlayer, this newly identified length depends on the film stress, and corrects an error in a previous paper by Huang, Prévost and Suo (Acta Materialia50, 4137, 2002). When the crack advances, its velocity can reach a steady state. We identify the scaling law for the steady velocity. An extended finite element method (X-FEM) is used to simultaneously evolve the creep strain and crack length. Numerical results are presented for the stress intensity factors of stationary cracks, and the steady velocities of advancing cracks. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of interaction of a semi-infinite crack (propagating in elastic material) with a random array of small defects (e.g. inclusions, voids). This interaction manifests itself in changes of the crack orientation and, overall in randomly varying curvilinear crack trajectories. Making use of the asymptotic results proposed in (Movchan, 1991, 1995) the procedure for configurational averaging is presented which yields the mean crack path and the standard deviation from the mean. The general formulae for the mean crack path can serve as a basis for effective quantitative analysis for specific situations of practical interest. The illustrative examples elaborated in the paper show dependence of the shape of crack trajectory on the probabilistic characteristics of random locations of inclusions and on their elastic parameters. The analysis performed in the paper can be directly used in prediction of failure mechanisms of brittle materials containing small randomly distributed inclusions/voids. [ABSTRACT FROM AUTHOR]

This paper deals with the study of thermal stresses due to a plane crack lying on an interface in a microperiodic two-layered composite under a uniform perpendicular heat flow. An approximate analysis is carried out within the framework of linear stationary thermoelasticity with microlocal parameters. Taking this approach, a general method of solving the resulting boundary-value problem is presented. Effective results have been achieved through the use of suitable potential solutions and reducing the thermal crack problem to its skew-symmetric isothermal mechanical counterpart. An illustrative example is given in the paper by considering an insulated stress-free penny-shaped crack. For this problem the solution is obtained in terms of elementary functions and discussed from the point of view of fracture theory. [ABSTRACT FROM AUTHOR]

Cyclic cohesive zone models represent powerful numerical tools to describe and predict different phenomena of fatigue. In the present paper a review is given about the state of the art of cyclic cohesive zone modelling. Firstly, a commented survey of the history of cyclic cohesive zone models is presented starting from the strip-yield models of Dugdale and Barenblatt and ending with the modern creep-fatigue models. Next, the paper focuses on the thermodynamically consistent formulation of cyclic cohesive zone models. In particular, the formulation of cohesive zone potentials, the choice of appropriate deformation and damage measures as well as the assembly of damage evolution equations are discussed in detail. In this context, established models are critically compared with a model recently proposed by the authors. Finally, some numerical examples are presented for illustration, dealing with fatigue crack growth, uniaxial fatigue life prediction, and intergranular fatigue damage. These simulations demonstrate the wide range of applications of cyclic cohesive zone models. [ABSTRACT FROM AUTHOR]

Deformation and failure processes of crystalline materials are governed by complex phenomena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propagation relations of crystalline materials containing atomic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi-scale model incorporates a finite temperature atomistic region containing the crack, a continuum region represented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atomistic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic potential function. An efficient, staggered solution scheme with parallel implementation is designed for the coupled problem. The atomistic-continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantitative analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simulation results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results. [ABSTRACT FROM AUTHOR]

This paper analyzes the role of microstructural anisotropy generated by cold drawing in the hydrogen-assisted fracture of progressively drawn pearlitic steel notched bars. Very different notched geometries were used to generate quite distinct stress triaxiality distributions (and thus very different constraint levels) in the vicinity of the notch tip, and fracture surfaces were classified in accordance with three micromechanical models of hydrogen-assisted micro-damage on the basis of the micro-fracture maps assembled by scanning electron microscopy over the fractured area of the notched specimens. [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]

Present paper focuses on the cross-property connection between the changes in electrical resistivity and work hardening coefficient in the process of plastic deformation. The possibility of the cross-property connection is provided by the fact that both quantities are governed by the same parameter - growth of the dislocation density caused by the applied stresses. Experimental measurements on stainless steel 304 are in a good agreement with analytical estimates. [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 series of papers, we investigate the mechanics and physics of localization and fragmentation in ductile materials. The behavior of ductile metals at strain rates of about 4,000–15,000 per second is considered. The expanding ring experiment is used as the vehicle for examining the material behavior in this range of strain rates. In Parts I–III, we examined the response of rings with cross-sectional aspect ratios in the range of 1–10, exhibiting a transition from diffuse necking to sheet-mode localization. In the present paper we report on experimental observations of high strain-rate expansion of Al 6061-O tubes. Through an innovative use of high-speed imaging aided with a conical mirror we determine the sequence of deformation and failure in the expanding tube. In particular, the conical mirror provides information of surface deformation on the tube. Forming limit diagrams at high strain rates are obtained from post-mortem measurement of the deformed tubes or fragments and are compared with analysis from quasi-static analysis. Numerical simulations are used to explain the experimental observations. [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 series of papers, we investigate the mechanics of deformation localization and fragmentation in ductile materials. The behavior of ductile metals at strain rates between 4000 and 15,000 s−1 is considered. The expanding ring experiment is used as the primary tool for examining the material behavior in this range of strain rates. In Part I, the details of the experiment and the experimental observations on Al 6061-O were reported. Statistics of necking and fragmentation were evaluated and the process was modeled through the idea of the Mott release waves both from necking and fragmentation. Finally, it was shown that the strain in the ring in regions that strained uniformly never exceeded the necking strain. In the present paper, Part II, we address the issue of strain hardening and strain-rate sensitivity. Specifically, we examine different materials—Al 1100-H14, and Cu 101—in order to determine the role of material constitutive property on the dynamics of necking. These experiments reinforce the conclusion presented in Part I that the onset of necking essentially terminates the possibility of further straining in other parts of the ring and even more importantly that there is no influence of material inertia on the strain at the onset of necking in this wide range of materials. Furthermore, the effect of aspect ratio of the specimen is evaluated; this reveals that as the aspect ratio increases beyond about five, in addition to or instead of diffuse necking, localization into the sheet necking mode is observed; in this mode, the effect of ring expansion speeds is demonstrated to result in an increase of the strain at the onset of localization. In addition, an absolute size effect is observed: larger specimens exhibit localization at larger strain levels. These observations are explained in terms of plastic wave propagation and reproduced with finite element simulations. In future contributions as part of this sequel, we will explore the effect of other geometrical constraints and the effect of a compliant cladding or coating on the development of necking and fragmentation. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical model for the electromagnetic radiation (EMR) emissions during plastic deformation and crack propagation in metallic materials. It is shown that under an externally applied stress, edge dislocations within the plastic zone ahead of a crack tip form accelerated electric line dipoles which give rise to the EMR emissions. The dynamic motion of these dislocations becomes overdamped, underdamped or critically damped, depending upon the material/microstructural properties such as mass per unit length of dislocation, line tension, damping coefficient, and distance between the dislocation pinning points. The nature of the EMR signals, viz. exponential decay or damped sinusoidal, is decided essentially by these damping characteristics. The EMR emissions are followed by crack propagation in metallic materials. The EMR has a continuous frequency spectrum with a frequency bandwidth ranging from 108 to 1012 radians s−1, depending upon the properties of the metals. Screw dislocations do not contribute to the EMR emissions. The paper also presents some experimental results on the EMR emissions in ASTM B265 grade 2 titanium sheets. The nature (damped sinusoidal and exponential decay), amplitude and frequency of the observed EMR emissions are in conformity with the predictions of the theoretical model. [ABSTRACT FROM AUTHOR]

Cold-drawn prestressing steel wires exhibit strength anisotropy in the form of fracture path deflection towards a direction approaching the wire axis, or cold drawing line, as a consequence of the pearlitic microstructure orientation induced by the manufacturing procedure. Such a crack path deflection is initiated at certain nuclei (fracture origins) at which axial cracking appears in the cold drawing direction (or wire axis) in the form of micro-cleavage units that produce in the load-displacement curve a macroscopic phenomenon of pop-in. This paper shows that such fracture initiators appear at a certain distance from the fatigue pre-crack tip at which a local maximum of the cleavage stress is located. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the static problem of model III crack of a functionally graded coating-substrate system with an internal crack perpendicular to the interface under antiplane shear loading when the coating layer and substrate have finite thickness. After the Fourier transform method is employed, the expressions of the displacement components can be obtained. Integral transforms are employed to reduce the problem to a singular integral equation that can be solved numerically. The influences of the nonhomogeneity constant, relative crack length and thickness ratio are quantitatively studied. [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]

Following an extensive and critical review of fractals and size effects models, this paper seeks to generalize Bažant’s size effect law to fractal cohesive cracks. This is achieved through a Newtonian approach in which the cohesive and far field stress intensity factors of fractal cracks (derived by Yavari) are set equal. It will be shown that the fractal size effect law is a generalization of the one of Bažant (derived in Euclidian space). In light of the derived equation, the multi-fractal model of Carpinteri and the size effect law of Bažant are revisited. Finally, the paper will conclude with some general considerations pertaining to the so-called “New Kind of Science” developed by Wolfram, and its applicability to fracture mechanics. [ABSTRACT FROM AUTHOR]

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/δ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from `complete slip before opening' to `opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks. [ABSTRACT FROM AUTHOR]

This paper shows how the cohesive zone model can help in predicting fracture loads of brittle components with blunted V-notches. Linear Elastic Fracture Mechanics cannot be applied in such cases because there are no singularities; there is no crack, and neither is the notch sharp. Numerical predictions based on the cohesive zone model were checked succesfully against experimental measurements for PMMA at -60 °C (made by the authors) and steel, zirconia, silicon nitride and alumina by other researchers. The concept of a critical stress concentration factor, well established for sharp V-notches, is generalized, under certain circumstances, to blunted V-notches, and a non dimensional formulation of the fracture criterion is proposed. [ABSTRACT FROM AUTHOR]

In Part I of this paper, the static problem of a functionally graded coating-substrate system with an internal or edge crack perpendicular to the interface has been studied. In this part, the transient response of the structure is considered under an in-plane impact. Laplace and Fourier transforms are applied to reduce the mixed boundary value problem to a singular integral equation which is solved in the Laplace domain numerically. The dynamic stress intensity factors (DSIFs) are obtained by numerical Laplace inversion technique. The influences of material constants and geometry parameters on the dynamic stress intensity factors are studied. It is found that the DSIFs for an internal crack rise rapidly to a peak and then tend to the steady value without obvious oscillations, but the DSIFs for an edge crack have more obvious oscillations after rising to a peak with the increasing of the nonhomogeneity constant. [ABSTRACT FROM AUTHOR]

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings. [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 stress-deformation relation i.e. cohesive law representing the fracture process in an almost incompressible adhesive tape is measured using the double cantilever beam specimen. As in many ductile materials, the fracture process of the tape involves nucleation, growth and coalesce of cavities. This process is studied carefully by exploiting the transparency of the used materials and the inherent stability of the specimen configuration. Utilising the path independence of the J-integral, the cohesive law is measured. The law is compared to the results of butt-joint tests. The law contains two stress peaks-the first is associated with nucleation of cavities at a stress level conforming to predictions of void nucleation in rubber elasticity. The second stress peak is associated with fracture of stretched walls between fully-grown cavities. After this second peak, a macroscopic crack is formed. The tape suffers at this stage an engineering strain of about 800%. A numerical analysis with the determined cohesive law recreates the global specimen behaviour. [ABSTRACT FROM AUTHOR]

This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the so-called EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young's modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio $${\delta }/{\varDelta X}=3$$ for a wide range of materials, if an error of 5 % is acceptable. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of symmetric and skew-symmetric weight functions for in-plane interfacial crack problems in piezoelectric bimaterials. The symmetric weight function matrix is obtained by means of the solution of a Wiener-Hopf functional equation and the skew-symmetric weight function matrix is developed by the construction of a corresponding full field solution. The explicit expressions for the symmetric and skew-symmetric weight functions are given and applied to in-plane deformation problems for a semi-infinite crack between two dissimilar piezoelectric materials. The validity of the present method in the determination of the field intensity factors is demonstrated by illustrative examples, in which both piezoelectric bimaterials and piezoelectric/elastic bimaterials are considered. It is shown that, for the present interfacial crack problem, both symmetric and skew-symmetric weight function matrices are necessary in the general integral formula for the evaluation of field intensity factors, and that the contribution of the skew-symmetric element of the applied load is not negligible in fracture analysis. [ABSTRACT FROM AUTHOR]

Sandia National Laboratories have carried out the Sandia Fracture Challenge in order to evaluate ductile damage mechanics models under conditions which are similar to those in the industrial practice. In this challenge, the prediction of load-deformation behavior and crack path of a sample that is designed for the competition under two loading rates is required with given data: the material Ti-6Al-4V, and raw data of tensile tests and V-notch tests under two loading rates. Within the stipulated time frame 14 teams from USA and Europe gave their predictions to the organizer. In this work, the approach applied by Team Aachen is presented in detail. The modified Bai-Wierzbicki (MBW) model is used in the framework of the Second Blind Sandia Fracture Challenge (SFC2). The model is made up by a stress-state dependent plasticity core that is extended to cope with strain rate and temperature effects under adiabatic conditions. It belongs to the group of coupled phenomenological ductile damage mechanics models, but it assumes a strain threshold value for the instant of ductile damage initiation. The initial guess of material parameters for the selected material Ti-6Al-4V was taken from an in-house database available at the authors' institutes, but parameters are optimized in order to meet the validation data provided. This paper reveals that the model predictions can be improved significantly compared to the original submission of results at the end of SFC2 by two simple measures. On the one hand, the function to express the critical damage as well as the amount of energy dissipation between ductile damage initiation and complete ductile fracture were derived more carefully from the data provided by the challenge's organizer. On the other hand, the experimental set-up of the challenge experiment was better described in the geometrical representation used for the numerical simulations. These two simple modifications allowed for a precise prediction of crack path and estimation of force-displacement behavior. The improved results show the general ability of the MBW model to predict the strain rate sensitivity of ductile fracture at various states of stress. [ABSTRACT FROM AUTHOR]

In the present paper, the roles of a linear spring interface and a membrane shell interface on the mechanical behaviour of a bimaterial are investigated by using a simplified matrix-inhomogeneity elastic system. The system consists of a circular inhomogeneity embedded in an unbounded matrix and is in shear deformation, either coming from a remote uniform stress applied in the matrix, or from a uniform shear transformation in the inhomogeneity. It was shown that, if a perfect interface of the system is transformed to a spring-type one, while the system is stressed by the above loadings, the change in the total potential energy is negative. The opposite occurs, if a membrane shell interface is formed in the stressed system. The elastic energies stored in the system constituents are determined by considering the interface as a separate phase of the system. [ABSTRACT FROM AUTHOR]

Slip localization is widely observed in metallic polycrystals undergoing cyclic deformation or post-irradiation tensile deformation, whatever their crystallographic structure. Hence, strong strain localization occurs in thin slip bands (SBs) inducing by the way local stress concentrations at their intersections with grain boundaries (GBs). Many GB stress field formulae based on the dislocation pile-up theory have been proposed since the pionnering work of Stroh and others. These allow the use of the Griffith criterion for prediction GB fracture initiation. However, recent observations show that assuming that slip is localized on a single atomic plane leads to unrealistic results. In fact, a large number of slip planes are plastically activated and then finite slip band thickness should be accounted for. Numerous crystalline finite element (FE) computations have been carried out using considering a slip bands with low critical resolved shear stress embedded in an elastic matrix. The computed GB normal and shear stress fields: are considerable lower than the pile-up ones and exhibit strong dependency on the slip band thickness close to the SB corner but are in fair agreement with the solution predicted by the pile-up theory far away. Since the pile-up theory leads to the overestimation of the local GB stress fields, the main goal of the current paper is to perform analytical model of GB stress components based upon FE calculations. The effect of various parameters can be understood in the framework of matching asymptotic expansions which is usually applied to cracks with V notches of finite thickness. Finally, the predicted remote stresses to GB fracture in pre-irradiated austenitic stainless steels subjected to tensile loading in various environment are compared to experimental data and the pile-up based predictions. [ABSTRACT FROM AUTHOR]

Interfacial delamination is a key reliability challenge in composites and micro-electronic systems due to (high density) integration of dissimilar materials. Predictive finite element models require the input of interface properties, often determined with an interface delamination growth experiment with (nearly) constant process zone, relying on the assumption of no permanent deformation in the sample structure layers. However, much evidence in the literature exists that plasticity often does occur in the sample structure during delamination experiments, which should be adequately dealt with to obtain the real interface fracture toughness that is independent of the thickness of the two sample arms. This paper presents a practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment on a double-cantilever beam specimen involving only small-scale plasticity at the interface. The procedure does not require knowledge of the constitutive behavior of the adherent layers. It only deals with the separation of structural plasticity in the adherents, whereas small-scale plasticity in connection with ductile interface fracture is lumped into the interface fracture toughness. The proposed approach was numerically verified for one set of parameters. Experimental assessment of the approach on industrially-relevant copper lead frame-molding compound epoxy interface structures showed a correction of the interface fracture toughness of more than a factor of two, demonstrating the potentially significant errors induced by plastic deformation of the sample structure during delamination experiments. [ABSTRACT FROM AUTHOR]

In linear elastic fracture mechanics the path-independent J-integral is a loading quantity equivalent to stress intensity factors (SIF) or the energy release rate. Concerning plane crack problems, $$J_k$$ is a 2-dimensional vector with its components $$J_1$$ and $$J_2$$ . These two parameters can be related to the mode-I and mode-II SIFs $$K_{\mathrm{I}}$$ and $$K_{\mathrm{II}}$$ . To guarantee path-independence for curved crack geometries, an integration path along the crack faces must be considered. This paper deals with problems occurring at the numerical calculation of the J-integral in connection with the FE-method. Two new methods for accurately calculating values of $$J_2$$ for arbitrary cracks are presented. [ABSTRACT FROM AUTHOR]

This paper proposes a compliance-based approach to determine the fracture resistance $$J$$- $$R$$ curve for surface cracks in high-strength steel (S690) plate specimens in a four-point-bend set up. This study extends the $$\eta $$-approach used in the fracture test for the typical specimens with a through-thickness crack, to the surface cracks in plate specimens in calculating the energy release rate from the area below the measured moment versus the crack-plane rotation. The energy release rate, computed from the detailed finite element models using the domain integral approach, confirms a constant $$\eta $$ value for surface cracked steel plates. Coupled with the post-test sectioning, the unloading compliance method quantifies the extended crack-front profiles ahead of the fatigue pre-cracked surface notch, using the crack-size versus the compliance relationship derived from linear-elastic finite element analyses. The fracture resistance curves thus obtained remain similar at different locations along the crack front and comparable with the fracture resistance measured using a standard side-grooved compact tension specimen at a finite crack extension. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to study the effects of plastic anisotropy and evolution in crystallographic texture with deformation on the ductile fracture behaviour of polycrystalline solids. To this end, numerical simulations of multiple void growth and interaction ahead of a notch tip are performed under mode I, plane strain, small scale yielding conditions using two approaches. The first approach is based on the Hill yield theory, while the second employs crystal plasticity constitutive equations and a Taylor-type homogenization in order to represent the ductile polycrystalline solid. The initial textures pertaining to continuous cast Al-Mg AA5754 sheets in recrystallized and cold rolled conditions are considered. The former is nearly-isotropic, while the latter displays pronounced anisotropy. The results indicate distinct changes in texture in the ligaments bridging the voids ahead of the notch tip with increase in load level which gives rise to retardation in porosity evolution and increase in tearing resistance for both materials. [ABSTRACT FROM AUTHOR]

In this paper bond-line cracks in assembled plate structures are investigated. A multi-region boundary element formulation is used to model the assembly and to perform the analysis. Once the solution at the boundary has been obtained, energy methods are used to extract relevant fracture parameters from the boundary values. The energy release rate (G) method and a new J- integral formulation are implemented for interlaminar cracks in shear deformable plates. The energy release rate and the J- integral are then decomposed into stress intensity factors and their value along the bond-line is computed by means of a displacement discontinuity method. [ABSTRACT FROM AUTHOR]

This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE) towards a discontinuity enriched framework. The classical homogenization approaches typically rely on the separation of scales principle, which is violated as soon as a strain localization band develops within a microstructural volume element (MVE). The newly developed scheme resolves this limitation by considering the bifurcation of the microscale deformation into a continuum 'bulk' part and a localization related part. The most distinct feature of the proposed framework is that both, the local macroscale traction-opening response of the cohesive crack and the stress-strain response of the surrounding 'bulk', are obtained from a single MVE analysis. The discontinuity enriched macroscale description is formulated to accommodate for the micro-macro coupling. The macroscale boundary value problem and the corresponding implementation are detailed for the use within the embedded discontinuities approach. The presented multi-scale method is demonstrated on a numerical example of a cohesive crack propagation in a macroscopic double notch specimen, with underlying voided microstructure. [ABSTRACT FROM AUTHOR]

This paper presents a new mechanism controlling the acceleration of fatigue crack growth of a hydrogen-charged high-strength steel (bearing steel SAE52100, σ > 1, 900MPa, HV = 569). Three- dimensionally complicated shape of a primary crack and secondary cracks were observed in hydrogen- charged specimens. Marked acceleration of fatigue crack growth in the presence of hydrogen was observed particularly at low test frequency, and was attributed to the initiation and successive coalescence of secondary cracks formed ahead of primary crack. These secondary cracks were produced along prior-austenite grain boundaries and carbide boundaries, or by direct cracking of carbides. Surprisingly, secondary cracks were observed outside the ordinary plastic zone ahead of the crack tip. TEM observation elucidated that the secondary cracks outside the crack tip plastic zone were produced by hydrogen-induced deformation twins impinging on grain boundaries and carbides. These results suggest a new mechanism of the acceleration of fatigue crack growth rates in high-strength steels caused by hydrogen-induced deformation twins, rather than due to hydrogen- enhanced localized plasticity. The phenomena associated with time dependent fatigue crack growth are presumed to be correlated with the initiation and coalescence of secondary cracks in the presence of hydrogen. [ABSTRACT FROM AUTHOR]

In the paper, the elastic-plastic fracture behavior of an interface crack between two dissimilar materials is investigated. The mixed-mode Dugdale model is applied to examine the plastic zone size and the crack tip opening displacement. In numerical examples, the plastic zone size and the crack tip opening displacement of an interface crack under uniform loads are studied in detail. Two formulae are proposed to calculate the plastic zone size and the crack tip opening displacement of an interface crack under small scale yielding conditions. [ABSTRACT FROM AUTHOR]

Several groups have studied experimentally the deformation of the front of mode I cracks propagating quasistatically along the interface between bonded plates. The theoretical interpretation of such experiments has always been based up to now on a formula of Rice (ASME J Appl Mech 52:571-579, ); this formula provides the first-order variation of the local mode I stress intensity factor resulting from some small, but otherwise arbitrary coplanar perturbation of the front of a semi-infinite crack in an infinite body. To be applicable to bonded plates, this formula requires that the characteristic distance of variation of this perturbation in the direction of the crack front be small compared to all other characteristic dimensions of the problem, and first of all the thickness of the plates. This condition is unfortunately frequently violated in practice. The purpose of this paper is therefore to provide a more exact formula for the variation of the local stress intensity factor, for the specific cracked geometry and boundary conditions used in experiments; this should allow for more accurate theoretical interpretations. This is done in two steps. The first one consists in adapting Rice's (ASME J Appl Mech 52:571-579, ) treatment, applicable to the extreme case of plates of infinite thickness, to the other extreme one of plates of infinitesimal thickness, using the standard Love-Kirchhoff plate theory. An interesting outcome of the analysis is that the distance from the crack front to the boundary of the plate acts as a 'cutoff length', in the sense that when the distance between two points on the crack front gets larger than it, the influence of the crack advance at the first point upon the stress intensity factor at the second diminishes quickly; the plate thickness, however, plays no similar role. The second step consists in supplementing the theoretical expressions applicable to extreme values of the plate thickness with finite element computations providing results for intermediate values. These computations lead to the definition of a simple, approximate but accurate 'interpolation formula' for the variation of the local stress intensity factor, applicable to plates of arbitrary thickness. [ABSTRACT FROM AUTHOR]

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions. [ABSTRACT FROM AUTHOR]

The paper deals with elasto-plastic materials, whose structural damage is produced by lattice defects, within the constitutive framework of finite elasto-plasticity with second order deformations. For second order deformations, which are represented by distortions and connections, we adopt the decomposition rule into second order elastic and plastic components. The split of the plastic connection into independent components, which involve Bilby’s connection type and a second order tensor, called disclination, plays a fundamental role in defining kinematical variables. The lattice defects are modeled by dislocations and disclinations, which are introduced within the finite deformation formalism and based on the differential geometry arguments. The constitutive framework is compatible with the free energy imbalance, postulated in the configuration with torsion, in such a form to include the presence of the disclinations. The model includes macro forces, which are power conjugated with the appropriate rate of the second order elastic deformations, and micro forces which are related with the plastic behaviour, as well as with the disclinations. The micro balance equations which are associated with the presence of disclinations are derived from a virtual power principle relative to the disclination mechanism. As a consequence of the principle of the free energy imbalance, the free energy function becomes potential for the macro forces. The viscoplastic type equations for micro forces are proposed in such a way to be compatible with the resulting dissipation inequality. Finally, we determine within the proposed constitutive framework, the disclinations as a solution of the micro balance equation associated with the disclination and satisfying the appropriate evolution equation. We suppose that the plastic simple shear deformation is the source for the evolution of disclination. After our knowledge this is a new framework for the mathematical description of disclinations. [ABSTRACT FROM AUTHOR]