Showing papers in "International Journal of Fracture in 1996"

High cycle fatigue in aircraft gas turbines—an industry perspective

Abstract: The largest single cause of component failures in modern military aircraft gas turbine engines is high cycle fatigue (HCF), exceeding the number attributed to low cycle fatigue, corrosion, overstress, manufacturing processes, mechanical damage, and materials. The HCF problem is a pervasive one, affecting all engine sections and a wide range of materials. In addition to the impact on engine component reliability, HCF problems cause significant economic impacts through field inspection and maintenance actions, and reduced readiness reliability.

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

Abstract: The problem of evaluating linear elastic stress fields in the neighborhood of cracks and notches is considered. An analytical solution valid for cracked and notched components is given in general terms, according to Muskhelishvili's method based on complex stress functions. The solution is particularly useful for V-shape notches in wide and finite plates under uniform tensile loading. It will be demonstrated that some remarkable solutions of fracture mechanics and notch analysis already reported in the literature can be considered special cases of this general solution, as soon as appropriate values of the free parameters are adopted.

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis

Abstract: Fracture toughness of re-entrant foam materials with a negative Poisson's ratio is explored experimentally as a function of permanent volumetric compression ratio, a processing variable. J IC values of toughness of negative Poisson's ratio open cell copper foams are enhanced by 80 percent, 130 percent, and 160 percent for permanent volumetric compression ratio values of 2.0, 2.5, and 3.0, respectively, compared to the J IC value of the conventional foam (with a positive Poisson's ratio). Analytical study based on idealized polyhedral cell structures, approximating the shape of the conventional and re-entrant cells, disclose for re-entrant foam, toughness increasing as Poisson's ratio becomes more negative. The increase in toughness is accompanied by an increase in compliance, a combination not seen in conventional foam, and which may be useful in some applications such as sponges.

Strengthening of concrete prisms using the plate-bonding technique

Abstract: This paper presents the use of fracture mechanics for the plate bonding technique. Plates of steel or carbon-fibre reinforced plastic are bonded with an epoxy adhesive to rectangular concrete prisms and loaded in shear up to failure, what is normally known in fracture mechanics as mode II failure. In this special application a linear and a nonlinear approach are presented. The nonlinear equation derived for a realistic shear-deformation curve can only be used for numerical calculations. However, for simplified shear-deformation curves, the derived formula can be solved analytically. Results from tests, which are compared with the theory, are also presented.

Numerical simulations of dynamic crack growth along an interface

Abstract: Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.

Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens

Abstract: A study of mixed-mode crack propagation in bending-based interlaminar fracture specimens is here presented. A numerical scheme to simulate full crack propagation is proposed which makes use of interface laws relating interlaminar stresses to displacement discontinuities along the plane of crack propagation. The relation between interface laws and mixed-mode failure loci in terms of critical energies is discussed and clarified. Numerical simulations are presented and compared with analytical and experimental results.

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

Abstract: This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J c , δc). Our approach adopts the Weibull stress σw as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of σw which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of σw on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness J c of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured J c -values.

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Abstract: Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised ‘in-plane’ constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide ‘effective’ thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised η-plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.

Numerical modeling of ductile crack growth in 3-D using computational cell elements

Abstract: This study describes a 3-D computational framework to model stable extension of a macroscopic crack under mode I conditions in ductile metals. The Gurson-Tvergaard dilatant plasticity model for voided materials describes the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer at the crack plane provide an explicit length scale for the continuum damage process. Outside this layer, the material remains undamaged by void growth, consistent with metallurgical observations. An element vanish procedure removes highly voided cells from further consideration in the analysis, thereby creating new tractionfree surfaces which extend the macroscopic crack. The key micro-mechanics parameters are D, the thickness of the computational cell layer, and f 0 , the initial cell porosity. Calibration of these parameters proceeds through analyses of ductile tearing to match R-curves obtained from testing of deep-notch, through-crack bend specimens. The resulting computational model, coupled with refined 3-D meshes, enables the detailed study of non-uniform growth along the crack front and predictions of specimen size, geometry and loading mode effects on tearing resistance, here described by J-Δa curves. Computational and experimental studies are described for shallow and deep-notch SE(B) specimens having side grooves and for a conventional C(T) specimen without side grooves. The computational models prove capable of predicting the measured R-curves, post-test measured crack profiles, and measured load-displacement records.

Basic issues in the mechanics of high cycle metal fatigue

Abstract: Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach. Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.

Three-dimensional cell model analyses of void growth in ductile materials

Abstract: Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.

A single leg bending test for interfacial fracture toughness determination

Abstract: A single leg bending test is described and its suitability for interfacial fracture toughness testing is evaluated. The test specimen consists of a beam-type geometry comprised of two materials, one ‘top’ and one ‘bottom’, with a split at one end along the bimaterial interface. A portion of the bottom material in the cracked section of the beam is removed and the geometry is loaded in three-point bending. Thus, the reaction force of the support at the cracked end is transmitted only into the material comprising the top portion of the beam. The test is analyzed by a crack tip element analysis and the resulting expressions for energy release rate and mode mixity are verified by comparison with finite element results. It is shown that, by varying the thicknesses of the two materials, the single leg bending test can be used to determine the fracture toughness of most bimaterial interfaces over a reasonably wide range of mode mixities.

Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media

Abstract: A complete form of stress and electric displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic piezoelectric media, is derived by using the complex function theory. New definitions of real-valued stress and electric displacement intensity factors for the interfacial crack are proposed. These definitions are extensions of those for cracks in homogeneous piezoelectric media. Closed form solutions of the stress and electric displacement intensity factors for a semi-infinite crack as well as for a finite crack at the interface between two dissimilar piezoelectric media are also obtained by using the mutual integral.

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

Abstract: A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.

Fracture mechanics of a shaft-loaded blister of thin flexible membrane on rigid substrate

Abstract: A shaft-loaded blister test has been developed to measure the interfacial energy W of a thin flexible polymeric film adhered to a rigid substrate. A theoretical analysis is given of an axisymmetric debond (‘blister’) in terms of an external applied load P, tensile stretching modulus E and thickness h of the adhering layer. The fracture mechanics model presented considers both elastic and elastoplastic deformations in the thin film. The intrinsic stable interface debonding process provides an attractive alternative to the conventional adhesion measurement techniques.

Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Abstract: Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.

On the use of the Goodman diagram for high cycle fatigue design

Abstract: Materials in rotating machinery are typically subjected to vibratory loading from a number of sources which, in turn, is superimposed on mean stresses which result primarily from steady-state centrifugal loads. In addition, components subjected to vibratory stresses can sustain damage during manufacturing, break-in cycles, or during service such as from foreign objects, fretting, or other types of wear. The combination of vibratory and ‘steady’ stress levels can, for certain load levels, produce low cycle fatigue damage in addition to the damage produced from the high frequency (HCF) vibratory loading since the ‘steady’ stresses are actually low cycle fatigue (LCF) which results in one cycle for every startup and shutdown operation. Design for HCF is generally based on a Goodman diagram which takes into account the vibratory as well as the steady stress amplitudes for fatigue runout or fatigue under a given number of cycles. It does not, however, take into account the combined effects of LCF and HCF. In this investigation, the combined effects are demonstrated analytically by numerical examples which consider both the initiation and propagation phases of fatigue. In addition to the analysis of LCF/HCF interactions, considerations which must be accounted for in design are reviewed in light of a number of failures of components in service in U.S. Air Force fighter engines. A critical assessment of the concepts embedded in the use of the Goodman diagram is presented. Comments on the limitations on the use of a Goodman diagram for design are provided. Some suggestions are offered for the improvement of the design methodology for HCF which involve both damage tolerance considerations and methods for assessing and improving the margin of safety.

Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method

Abstract: A new formulation of the boundary element method (BEM) is proposed in this paper to calculate stress intensity factors for cracked 2-D anisotropic materials. The most outstanding feature of this new approach is that the displacement and traction integral equations are collocated on the outside boundary of the problem (no-crack boundary) only and on one side of the crack surfaces only, respectively. Since the new BEM formulation uses displacements or tractions as unknowns on the outside boundary and displacement differences as unknowns on the crack surfaces, the formulation combines the best attributes of the traditional displacement BEM as well as the displacement discontinuity method (DDM). Compared with the recently proposed dual BEM, the present approach doesn't require dua elements and nodes on the crack surfaces, and further, it can be used for anisotropic media with cracks of any geometric shapes. Numerical examples of calculation of stress intensity factors were conducted, and excellent agreement with previously published results was obtained. The authors believe that the new BEM formulation presented in this paper will provide an alternative and yet efficient numerical technique for the study of cracked 2-D anisotropic media, and for the simulation of quasi-static crack propagation.

Separation of crack extension modes in orthotropic delamination models

Abstract: In modeling a crack along a distinct interface between dissimilar elastic materials, the ratio of mode I to mode II stress intensity factors or energy release rates is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. Although methods have been developed for comparing mode mixes for isotropic interfacial fracture problems, this behavior currently limits the applicability of interfacial fracture mechanics in predicting delamination in layered materials without isotropic symmetry. The virtual crack closure technique (VCCT) is a method used to extract mode I and mode II energy release rate components from numerical fracture solutions. Energy release rate components extracted from an oscillatory solution using the VCCT are not unique due to their dependence on the virtual crack extension length, Δ. In this work, a method is presented for using the VCCT to extract Δ-independent energy release rate quantities for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior and it is similar to existing methods for extracting a mode mix from isotropic interfacial fracture models. Knowledge of near-tip fields is used to determine the explicit Δ dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Δ. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Δ-independent energy release rate quantities result. The modified technique has potential as a consistent method for extracting a mode mix from numerical solutions. The Δ-independent energy release rate quantities extracted using this technique can also aid numerical modelers, serving as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

Abstract: A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.

A boundary element method for two dimensional linear elastic fracture analysis

Abstract: A boundary element method is developed for the analysis of fractures in two-dimensional solids. The solids are assumed to be linearly elastic and isotropic, and both bounded and unbounded domains are treated. The development of the boundary integral equations exploits (as usual) Somigliana's identity, but a special manipulation is carried out to ‘regularize’ certain integrals associated with the crack line. The resulting integral equations consist of the conventional ordinary boundary terms and two additional terms which can be identified as a distribution of concentrated forces and a distribution of dislocations along each crack line. The strategy for establishing the integral equations is first outlined in terms of real variables, after which complex variable techniques are adopted for the detailed development. In the numerical implementation of the formulation, the ordinary boundary integrals are treated with standard boundary element techniques, while a novel numerical procedure is developed to treat the crack line integrals. The resulting numerical procedure is used to solve several sample problems for both embedded and surface-breaking cracks, and it is shown that the technique is both accurate and efficient. The utility of the method for simulating curvilinear crack propagation is also demonstrated.

Elastic-plastic stress-strain calculation in notched bodies subjected to non-proportional loading

Abstract: An analytical method for calculating notch tip stresses and strains in elastic-plastic isotropic bodies subjected to non-proportional loading sequences is presented. The key elements of the two proposed models are generalized relationships between elastic and elastic-plastic strain energy densities, and the material constitutive relations. These two models form the lower and the upper limits of the actual energy densities at the notch tip. Each method consists of a set of seven linear algebraic relations that can easily be solved for elastic-plastic strain and stress increments, knowing the hypothetical notch tip elastic stress history and the material stress-strain curve. Results of the validation show that the proposed methods compare well with finite element data and each solution set forms the limits of a band within which actual notch tip strains fall.

The effect of residual stresses on brittle and ductile fracture initiation predicted by micromechanical models

Abstract: The effect of a realistic residual stress field on the predicted initiation of brittle and ductile fracture in a pressure and axially loaded circumferentially cracked pipe is examined using finite element analysis, micromechanical models of fracture initiation, andJ-Q theory. The study confirms that residual stresses contribute to the driving force and reduce fracture loads early in the loading history. In addition, results show that the residual stresses severely alter theJ-value (i.e., fracture toughness) predicted for the onset of brittle fracture. The reason for this decrease is found to be the increase in constraint generated by the residual stress field. In contrast, the effect of residual stresses on the ductile fracture initiation toughness is shown to be negligible. kw]Key words kw]residual stress kw]fracture initiation kw]micromechanics

Cracks in gradient elastic bodies with surface energy

Abstract: In the present paper the effect of higher order gradients on the structure of line-crack tips is determined. In particular we introduce in the constitutive equations of the linear deformation of an elastic solid a volumetric energy term, which includes the contribution of the strain gradient, and a surface energy gradient dependent term and then determine the effect of these terms on the structure of the mode-III crack tip and the associated stress and strain fields. By making use of the solution in terms of Fourier transform of the equation of elastic equilibrium we solve the half-plane boundary value problems of: (a) specified tractions, and (b) prescribed displacements, along the crack surface, respectively.

Recent advances in fatigue crack growth modeling

Abstract: Recent advances in our understanding of fatigue crack growth processes and respective crack growth modeling techniques are reviewed. Much of the observed experimental behavior (such as the effects of notches, maximum applied stress, crack length, in-plane biaxiality, out-of-plane constraint, and transient loadings) can be explained based on crack closure concepts. Both Dugdale based models and finite element techniques have been utilized. However, so far neither approach has accounted for crystallographic slip effects, grain orientation effects, or microstructural barriers. A model for crack closure with two microscopic crystallographic slip directions is used to model microscopic cracks. The model predicts variations in closure levels as the orientations of the two slip directions, with respect to the crack growth direction, are changed. In addition, a solution is proposed for the asperity micro-contact problem through a unique roughness induced closure model using a statistical description of asperity heights, asperity densities, and material flow properties.

Standardized complex and logarithmic eigensolutions for n -material wedges and junctions

Abstract: The Airy stress eigenfunction expansion of Williams [1] has been used to obtain simple expressions for the angular variations of the stress and displacement fields for n-material wedges and junctions subjected to inplane loading. This formulation applies to real and complex roots, as well as the special transition case giving rise to r −ω singular behavior. The asymptotic behavior of the general problem is similar to that of the bi-material interface crack. In the case of real roots, the stress and displacement expressions can be determined to within a multiplicative real constant (amplification), while for the complex case, the fields are determined to within a multiplicative complex constant (amplification plus rotation). Because of the rotation in the complex case, there are an infinite number of equivalent ways to express the angular variations (eigenfunctions) of the stress and displacement fields. Therefore, the fields are standardized in terms of ‘generalized stress intensity factors’ that are consistent with the bi-material interface crack and the homogeneous crack problems. As in the bi-material crack problem, for the complex case there are two stress intensity factors for each admissible order of the stress singularity. For specific n-material wedges and junctions, a small variation of material properties and/or geometry can change the eigenvalues from a pair of complex conjugate roots to two distinct real roots or vice-versa. An r −ω singularity associated with a nonseparable solution in υ and θ exists at this point of bifurcation. Such behavior requires an adjustment in the standard eigenfunction approach to insure bounded stress intensity factors. The proper form of the solution is given both at and near this special material combination, and the smooth transition of the eigenfunctions as the roots change from real to complex is demonstrated in the results. Additional eigenfunction results are provided for particular cases of 2 and 3-material wedges and junctions.

An invariance property of local energy release rate in a strip saturation model of piezoelectric fracture

Abstract: The strip saturation model hase been solved using a simplified electroelasticity formulation in which only three material constants and two degrees of freedom are considered; the local energy release rate hase been shown to give predictions which are in brad agreement with experimental observations

Bridged versus cohesive crack in the flexural behavior of brittle-matrix composites

Abstract: A nonlinear fracture mechanics model, which explains and reproduces the constitutive flexural behavior of a brittle-matrix composite, is proposed. It embraces in a unified dimensionless formulation two peculiar models, i.e., the cohesive-crack and the bridged-crack, which are used to analyze the composite failure process. Dimensionless parameters, which depend on the mechanical and geometrical properties, characterize the structure in flexure. It is shown that, based on the assumptions of the bridged-crack model, which simulates the composite as a multiphase material, the flexural response is controlled by two dimensionless parameters, whereas, based on the assumptions of the cohensive-crack model, which simulates the composite as a homogeneous material, the parameters reduce to one. The influence of the dimensionless parameters on the behavior is studied, along with the size-scale effects on the structural ductility. It is also shown how the matrix toughness affects the response. The two theoretical models are compared through the simulation of an experimental test on a fiber-reinforced beam, and it is shown that both the models can predict approximately the same overall behavior.

Crack-resistance behavior as a consequence of self-similar fracture topologies

Abstract: The effect of the invasive fractality of fracture surfaces on the toughness characteristics of heterogeneous materials is discussed. It is shown that the interplay of physics and geometry turns out to be the non-integer (fractal) physical dimensions of the mechanical quantities involved in the phenomenon of fracture. On the other hand, fracture surfaces experimentally show multifractal scaling, in the sense that the effect of fractality progressively vanishes as the scale of measurement increases. From the physical point of view, the progressive homogenization of the random field, as the scale of the phenomenon increases, is provided. The Griffith criterion for brittle fracture propagation is deduced in the presence of a fractal crack. It is shown that, whilst in the case of smooth cracks the dissipation rate is independent of the crack length a, in the presence of fractal cracks it increases with a, following a power law with fractional exponent depending on the fractal dimension of the fracture surface. The peculiar crack-resistance behavior of heterogeneous materials is therefore interpreted in terms of the self-similar topology of the fracture domains, thus explaining also the stable crack growth occurring in the initial stages of the fracture process. Finally, extrapolation to the macroscopic size-scale effect of the nominal fracture energy is deduced, and a Multifractal Scaling Law is proposed and successfully applied to relevant experimental data.

Determination of the fracture toughness by automatic image processing

Abstract: We determine the fracture toughness of a duplex stainless steel using the COD-concept (crack tip opening displacement). The CODi values are obtained by stereophotogrammetric reconstruction of fracture surfaces. This is done by analyzing stereoscopic scanning electron microscope (SEM) images of the surfaces with an automatic image processing system. This system allows the automatic generation of a digital elevation model (DEM) with approximately 50000 points for each fracture surface image. Height-profiles at the point of crack initiation can be obtained from this DEM. The examination of corresponding profiles from both specimen-halves leads to CODi.