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Showing papers in "International Journal of Fracture in 2001"


Journal ArticleDOI
TL;DR: In this article, an energetic approach is proposed to predict the static and fatigue behavior of components weakened by sharp reentrant corners, where the energy in a small volume of material surrounding the notch tip has a finite value and such a value is thought of as the entity that controls the failure.
Abstract: The paper presents an energetic approach useful to predict of the static and fatigue behavior of components weakened by sharp re-entrant corners. Despite the fact that stresses and strain energy density tend toward infinity at the point of singularity, the energy in a small volume of material surrounding the notch tip has obviously a finite value and such a value is thought of as the entity that controls the failure. The energy, averaged in a volume of radius R (which depends on the material properties), is a precise function of the Notch Stress Intensity Factors and is given in closed form for plane stress and plane strain conditions, the material being thought of as isotropic and linear elastic. The method is validated taking into account experimental data already reported in the literature, concerning both static tests carried out on polymethyl metacrylate (PMMA)and Duraluminium specimens and fatigue tests on welded joints and notched components in structural steels. As a matter of fact, the method proposed here is the re-formulation, on one hand, of some recent area/volume criteria (in which averaged values of the maximum principal stress are used to predict component fatigue limits) and, on the other, of N-SIF-based criteria, where the Notch Stress Intensity Factors are thought of as the parameters that control static and fatigue failures.

722 citations


Journal ArticleDOI
TL;DR: In this article, the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction is investigated.
Abstract: We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.

417 citations


Journal ArticleDOI
TL;DR: In this article, a mode-dependent embedded process zone (EPZ) model has been developed and used to simulate the mixed-mode fracture of plastically deforming adhesive joints, which can provide quantitative predictions of the deformation and fracture of mixedmode geometries.
Abstract: A mode-dependent embedded-process-zone (EPZ) model has been developed and used to simulate the mixed-mode fracture of plastically deforming adhesive joints. Mode-I and mode-II fracture parameters obtained from previous work have been combined with a mixed-mode failure criterion to provide quantitative predictions of the deformation and fracture of mixed-mode geometries. These numerical calculations have been shown to provide excellent quantitative predictions for two geometries that undergo large-scale plastic deformation: asymmetric T-peel specimens and single lap-shear joints. Details of the deformed shapes, loads, displacements and crack propagation have all been captured reasonably well by the calculations.

308 citations


Journal ArticleDOI
TL;DR: In this article, an edge crack in a strip of a functionally graded material (FGM) was studied under transient thermal loading conditions, where the FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip.
Abstract: An edge crack in a strip of a functionally graded material (FGM) is studied under transient thermal loading conditions. The FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip. Thus the material is elastically homogeneous but thermally nonhomogeneous. This kind of FGMs include some ceramic/ceramic FGMs such as TiC/SiC, MoSi2/Al2O3 and MoSi2/SiC, and also some ceramic/metal FGMs such as zirconia/nickel and zirconia/steel. A multi-layered material model is used to solve the temperature field. By using the Laplace transform and an asymptotic analysis, an analytical first order temperature solution for short times is obtained. Thermal stress intensity factors (TSIFs) are calculated for a TiC/SiC FGM with various volume fraction profiles of the constituent materials. It is found that the TSIF could be reduced if the thermally shocked cracked edge of the FGM strip is pure TiC, whereas the TSIF is increased if the thermally shocked edge is pure SiC.

191 citations


Journal ArticleDOI
TL;DR: In this paper, a micromechanical model for a viscoelastic cohesive zone is formulated, and an incrementalized form of this traction-displacement law is integrated numerically and placed within an implicit finite element program designed to predict crack propagation in viscous media.
Abstract: A micromechanical model for a viscoelastic cohesive zone is formulated herein. Care has been taken in the construction of a physically-based continuum mechanics model of the damaged region ahead of the crack tip. The homogenization of the cohesive forces encountered in this region results in a damage dependent traction-displacement law which is both single integral and internal variable-type. An incrementalized form of this traction-displacement law has been integrated numerically and placed within an implicit finite element program designed to predict crack propagation in viscoelastic media. This research concludes with several example problems on the response of this model for various displacement boundary conditions.

151 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical fracture model for brittle piezoelectric and dielectric materials is developed consistent with standard features of elasticity and Dielectricity, and the influence of electric field and mechanical loading is considered in this approach.
Abstract: A theoretical fracture mechanics for brittle piezoelectric and dielectric materials is developed consistent with standard features of elasticity and dielectricity. The influence of electric field and mechanical loading is considered in this approach and a Griffith style energy balance is used to establish the relevant energy release rates. Results are given for a finite crack in an infinite isotropic dielectric and for steady state cracking in a piezoelectric strip. In the latter problem, the effect of charge separation in the material and discharge in the crack are considered. Observations of crack behavior in piezoelectrics under combined mechanical and electrical load are discussed to assess which features of the theory are useful.

143 citations


Journal ArticleDOI
TL;DR: In this article, linear elastic inclusions and voids embedded in an elasto-plastic matrix material are modeled with both kinematic and isotropic hardening laws cast in a hardening minus recovery format.
Abstract: Monotonic and cyclic finite element simulations are conducted on linear-elastic inclusions and voids embedded in an elasto-plastic matrix material The elasto-plastic material is modeled with both kinematic and isotropic hardening laws cast in a hardening minus recovery format Three loading amplitudes (Δe/2=010%, 015, 020%) and three load ratios (R=−1, 0, 05) are considered From a continuum standpoint, the primary driving force for fatigue crack formation is assumed to be the local maximum plastic shear strain range, Δγmax, with respect to all possible shear strain planes For certain inhomogeneities, the Δγmax was as high as ten times the far field strains Bonded inclusions have Δγmax values two orders of magnitude smaller than voids, cracked, or debonded inclusions A cracked inclusion facilitates extremely large local stresses in the broken particle halves, which will invariably facilitate the debonding of a cracked particle Based on these two observations, debonded inclusions and voids are asserted to be the critical inhomogeneities for fatigue crack formation Furthermore, for voids and debonded inclusions, shape has a negligible effect on fatigue crack formation compared to other significant effects such as inhomogeneity size and reversed loading conditions (R ratio) Increasing the size of an inclusion by a factor of four increases Δγmax by about a factor of two At low R ratios (−1) equivalent sized voids and debonded inclusions have comparable Δγmax values At higher R ratios (0, 05) debonded inclusions have Δγmax values twice that of voids

114 citations


Journal ArticleDOI
TL;DR: In this paper, a 3D, interface-cohesive finite element model is proposed to predict quasi-static, ductile crack extension in thin aluminum panels for mode I loading and growth.
Abstract: This work describes the formulation and application of a 3-D, interface-cohesive finite element model to predict quasi-static, ductile crack extension in thin aluminum panels for mode I loading and growth. The fracture model comprises an initially zero thickness, interface element with constitutive response described by a nonlinear traction-separation relationship. Conventional volumetric finite elements model the nonlinear (elastic-plastic) response of background (bulk) material. The interface-cohesive elements undergo gradual decohesion between faces of the volumetric elements to create new traction free crack faces. The paper describes applications of the computational model to simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Parameters of the cohesive fracture model (peak opening traction and local work of separation) are calibrated using measured load vs. outside surface crack extensions of high constraint (T-stress > 0) C(T) specimens. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and outside surface crack extensions. The models capture accurately the strong 3-D effects leading to various degrees of crack front tunneling in the C(T) and M(T) specimens. The predicted crack growth response shows rapid convergence with through-thickness mesh refinement. Adaptive load increment procedures to control the rate of decohesion in the interface elements leads to stable, rapidly converging iterations in the globally implicit solution procedures.

113 citations


Journal ArticleDOI
TL;DR: In this article, the authors extended the Kitagawa diagram to blunt cracks (U-shaped notches) and presented the simple expression (a*/a0)05 = Kt in which a0 is the El-Haddad's length parameter and a* is a particular blunt crack depth corresponding to the intersection between the ΔKth and δσ0/Kt curves.
Abstract: Notch sensitivity and defect sensitivity are two different aspects of the fatigue behavior of materials The paper extends the Kitagawa diagram to blunt cracks (U-shaped notches) and presents the simple expression (a*/a0)05 = Kt In such an expression a0 is the El-Haddad's length parameter and a* is a particular blunt crack depth corresponding to the intersection between the ΔKth and δσ0/Kt curves The new expression provides an explicit bridging between the notch sensitivity and the sensitivity to defects

102 citations


Journal ArticleDOI
TL;DR: In this paper, the fracture mechanisms in single crystal and polycrystalline Ti-50.8at%Ni shape memory alloys containing Ti3Ni4 precipitates were studied using the scanning electron microscope (SEM).
Abstract: The fracture mechanisms in single crystal and polycrystalline Ti-50.8at%Ni shape memory alloys containing Ti3Ni4 precipitates are studied using the scanning electron microscope (SEM). Aged materials with three different precipitate sizes (50 nm, 150 nm, and 400 nm), which have interfaces ranging from semi-coherent to incoherent, are considered. The mechanisms of material fracture identified in the single crystal NiTi are: 1. Nucleation, growth, and coalescence of voids from the Ti3Ni4 precipitates, 2. Cleavage fracture on {100} and {110} crystallographic planes, 3. Nucleation, growth, and coalescence of voids from fractured Ti-C inclusions. Cleavage and ductile tearing mechanisms also operate in polycrystalline NiTi, however, since the Ti-C inclusions are an artifact of single crystal growth processes, mechanism 3 was not discovered in the polycrystalline materials. Cleavage fracture and ductile tearing are found to act in conjunction, with the relative dominance of one over the other depending on the local precipitate size and concentration. As the Ti3Ni4 precipitate size increases to about 400 nm, the overall fracture is dominated by failure mechanism 1, and the cleavage markings become diffuse. Finally, we assert that the high tensile ductility of drawn NiTi polycrystals is due partially to the fact that drawn bar and wire stock usually have a strong {111} fiber texture. Such a texture promotes the initiation of the transformation at low stresses and concurrently prevents primary cleavage on the {100} or {110} planes.

96 citations


Journal ArticleDOI
TL;DR: In this article, a particular form of a probabilistic model for materials under fatigue which embodies Weibull features and the size effect in a weakest-link framework is derived, which can be justified as being consistent with experimental features of fatigue and the mathematics of extreme value theory.
Abstract: A particular form of a probabilistic model for materials under fatigue which embodies Weibull features and the size effect in a weakest-link framework is derived. The parametric and functional form of the model arises from a certain set of assumptions, as the weakest-link principle, stability, limit behavior, limited range and compatibility, which can be justified as being consistent with experimental features of fatigue (mainly of highly drawn steel wires) and the mathematics of extreme value theory. These assumptions, which are discussed, can be used to rule out other possible forms as being fundamentally inconsistent. The authors also discuss estimation procedures for the parameters based on two steps: a non-linear regression step, in which the threshold lifetime and stress range values are determined, and a second step in which the Weibull parameters are estimated by pooling data from different stress levels and using a probability-weighted moments approach or the Castillo-Hadi estimators. Next, the damage accumulation problem is dealt with and two different proposals for the damage index are given. The model, originally developed to handle a fixed load parameter (such as the stress range in cyclic fatigue), is extended to handle a block load sequence involving many load levels, as well as random load programs. Some formulas for calculating the accumulated damage index for constant, block and random loading are given. Finally, the model and methods are applied to a particular fatigue program on concrete to illustrate all concepts and the practical use of formulas.

Journal ArticleDOI
Shicheng Zhang1
TL;DR: In this article, an approximate stress formula for structural stress, notch stress, and equivalent stress intensity factor is given for common spot-welded specimens, which can also facilitate the transfer of test data across different specimens.
Abstract: Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.

Journal ArticleDOI
TL;DR: In this article, the first five terms of the crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are computed using a hybrid crack element.
Abstract: The coefficients of the first five terms of the crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are computed using a hybrid crack element (HCE), which has the potential to directly calculate not only the stress intensity factor (SIF) but also the coefficients of the higher order terms of the crack tip asymptotic field. The general approximate closed-form expression for SIF proposed by Guinea et al. (1998) and the available numerical results for the second T-term are calibrated by the results of the HCE. Approximate analytical expressions for the second, third, fourth and fifth terms for a TPB with a span to depth ratio of 4 and for a single edge notched beam subjected to pure bending are obtained by fitting the computed data. These approximations are then used to predict the general expressions for coefficients of the higher order terms of a TPB with arbitrary span to depth ratio β. The accuracy of these general expressions is studied for TPBs with β=6, 8 and 12.

Journal ArticleDOI
TL;DR: In this paper, the authors present a complete set of measurements for critical COD during crack growth under nominal tension-torsion loading, the evolution of crack path with crack growth and the crack surface shape as a function of loading.
Abstract: To assess the viability of using a critical COD criterion for flaws in 2024-T3 aluminum experiencing tension stresses (SP) and torsion stresses (ST), the enclosed work presents (a) a complete set of measurements for critical COD during crack growth under nominal tension-torsion loading, (b) the evolution of crack path with crack growth and (c) crack surface shape as a function of loading. Data from this work will provide an important experimental database for use in assessing the predictive capability of advanced, three-dimensional, crack growth simulation tools. Results for COD during crack growth under tension-torsion loading indicates that the measured critical COD for tension-torsion loading is constant during crack growth. In addition, the value of COD measured using image correlation methods is approximately 8% larger than observed for in-plane tension-shear, with much of the increase apparently due to specimen deformations in the crack tip vicinity. In addition, crack path evolution data for the range of ST/SP considered in this work show that the crack experiences both tunneling and slant fracture during loading, with tunneling rapidly decreasing (a) as crack growth progresses for all ST/SP values or (b) as ST/SP increases. Furthermore, results indicate that tearing during tension-torsion loading always occurs in a manner so that the crack surfaces tend to interfere during growth. Finally, crack surface shape data indicates that, with the exception of a small secondary transition, the direction of crack growth remains stable along a straight line oriented along the initial fatigue crack direction for the range of ST/SP being considered.

Journal ArticleDOI
TL;DR: In this paper, two path independent integrals for T-stress computations, one based on the Betti-Rayleigh reciprocal theorem and the other based on Eshelby's energy momentum tensor are studied.
Abstract: Two path independent integrals for T-stress computations, one based on the Betti-Rayleigh reciprocal theorem and the other based on Eshelby's energy momentum tensor are studied. Analytical as well as numerical equivalence between the two integrals is found. To quantify and assess the accuracy of computed values, error analysis for the proposed numerical computation of the T-stress is presented. Specifically, it is found that the error of the computed T-stress is proportional to the ratio of the stress intensity factor divided by the square root of the characteristic dimension of the integration domain where the path independent integral is evaluated. Using a highly accurate hierarchical p-version finite element method, the convergence and accuracy of computed values are easily monitored, and it is shown for numerical examples that the error of the computed T-stress complies with the described error analysis. We conclude that path independent integrals, in conjunction with hierarchical p-version finite element methods, provide a powerful and robust tool to obtain highly accurate numerical results for the T-stress.

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface, where the central part of the joint is detached and the remaining part is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap.
Abstract: The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.

Journal ArticleDOI
TL;DR: In this article, two efficient numerical procedures in conjunction with the finite element method (FEM) for the stress intensity factor (SIF) analysis of interface cracks under thermal stresses are presented.
Abstract: Thermal stresses, one of the main causes of interfacial failure between dissimilar materials, arise from different coefficients of linear thermal expansion. Two efficient numerical procedures in conjunction with the finite element method (FEM) for the stress intensity factor (SIF) analysis of interface cracks under thermal stresses are presented. The virtual crack extension method and the crack closure integral method are modified using the superposition method. The SIF analyses of some interface crack problems under mechanical and thermal loads are demonstrated. Very accurate mode separated SIFs are obtained using these methods.

Journal ArticleDOI
TL;DR: In this paper, the authors explored crack growth initiation and subsequent resistance to propagation for regular and irregular hexagonal honeycomb structures made from ductile cell walls, and the dependence of the crack growth behavior upon the cell wall material parameters and geometric imperfections of the structure was investigated.
Abstract: Crack growth initiation and subsequent resistance to propagation are explored numerically for regular and irregular hexagonal honeycomb structures made from ductile cell walls. The elasto-plastic response of the cell walls is described by a bilinear uniaxial stress-strain law, with fracture of the cell walls characterised by the fracture energy per unit area. Estimates for the macroscopic toughness and the associated plastic zone shape are derived analytically on the basis of simple considerations. Crack propagation is simulated numerically by fracturing elements within a finite element model and K-resistance curves are calculated under the assumption of small-scale yielding. The dependence of the crack growth behaviour upon the cell wall material parameters and geometric imperfections of the structure is investigated.

Journal ArticleDOI
Abstract: This paper analyzes the propagation of a cohesive crack through a reinforcement layer and gives a solution that can be used for any specimen and loading condition. Here it faces the case of a reinforced prismatic beam loaded at three points. Reinforcement is represented by means of a free-slip bar bridging the cracked section, anchored at both sides of the crack at a certain distance that is called the effective slip length. This length is obtained by making the free-slip bar mechanically equivalent to the actual adherent reinforcement. With this model, the crack development depends on three parameters (apart from those that represent the specimen geometry): the size of the specimen, the cover thickness of the layer and the reinforcement strength. The latter depends on the reinforcement ratio and its adherence to the matrix while the reinforcement is in the elastic regime; otherwise, on the reinforcement ratio and its yielding strength. The thickness of the reinforcement cover influences the first stages of the development of the cohesive crack, and thus it also affects the value of the load peak. The computed load-displacement curves display a noticeable size effect, as real cohesive materials do. Finally, the model is able to fit the available experimental results, and accurately reproduces the influence of size, amount of reinforcement and adherence variations in the tests.

Journal ArticleDOI
TL;DR: In this paper, the authors show that there is a boundary layer effect associated with lein MSG plasticity, and the thickness of the boundary layer is on the order of l2ebig/l.
Abstract: The theory of mechanism-based strain gradient (MSG) plasticity involves two material length parameters, namely the intrinsic material length land the mesoscale cell size le, which are on the order of a few microns and 0.1 μm, respectively. Prior studies suggest that lehas essentially no effect on the macroscopic quantities, but it may affect the local stress distribution. We demonstrate in this paper that there is a boundary layer effect associated with lein MSG plasticity, and the thickness of the boundary layer is on the order of l2ebig/l. By neglecting this boundary layer effect, a stress-dominated asymptotic field around a crack tip in MSG plasticity is obtained. This asymptotic field is valid at a distance to the crack tip between leand l(i.e., from 0.1 μm to a few microns). The stress in this asymptotic field has an approximate singularity of r−2/3, which is more singular than not only the HRR field in classical plasticity but also the classical elastic Kfield (r−1/2). The stress level in this asymptotic field is two to three times higher than the HRR field, which provides an alternative mechanism for cleavage fracture in ductile materials observed in experiments.

Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of the failure of metallic thin films used for device interconnections in integrated circuits is presented based on surface mass transport modeling coupled with the electrostatic and elastic deformation problems in the metallic films.
Abstract: A theoretical analysis is presented of the failure of metallic thin films used for device interconnections in integrated circuits. Failure is mediated by void dynamics, which is driven by surface electromigration and processing related residual thermal stresses in the films. The analysis is based on surface mass transport modeling coupled strongly with the electrostatic and elastic deformation problems in the metallic films. Special emphasis is placed on the combined effects on void dynamics of anisotropy both in surface diffusivity along a void surface and in the applied stress tensor. A systematic parametric study is carried out based on self-consistent numerical simulations of surface morphological evolution. Void dynamics is analyzed and results are presented for void morphological stability in terms of critical stress levels as a function of stress state and surface mobility anisotropy. Finally, the role of plastic deformation is discussed around crack-like features emanating from void surfaces in ductile metallic films based on results of molecular-dynamics simulations in Cu.

Journal ArticleDOI
TL;DR: In this article, uniform asymptotic solutions (UAS) for displacement discontinuities (DDs) that lie within the middle layer of a three layer elastic medium are presented for both 2D and 3D elastic media.
Abstract: We present uniform asymptotic solutions (UAS) for displacement discontinuities (DD) that lie within the middle layer of a three layer elastic medium. The DDs are assumed to be normal to the two parallel interfaces between the leastic media, and solutions will be presented for both 2D and 3D elastic media. Using the Fourier transform (FT) method we construct the leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three layer medium. Although a closed form solution will require an infinite series solution, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We present an explicit UAS for elements in which the DD fields are assumed to be piecewise constant throughout a line segment in 2D and a rectangular element in 3D. We demonstrate the usefulness of this UAS by providing a number of examples in which the UAS is used to solve problems in which cracks just touch or cross an interface. The accuracy and efficiency of the algorithm is demonstrated and compared with other numerical methods such as the finite element method and the boudary integral method.

Journal ArticleDOI
TL;DR: In this paper, the interaction problem between a coated circular inclusion and a near-by line crack has been investigated, where the crack and the inclusion are embedded in an infinitely extended isotropic matrix, with the crack being along the radial direction of the inclusion.
Abstract: Stress investigation for the interaction problem between a coated circular inclusion and a near-by line crack has been carried out. The crack and the coated inclusion (a coated fiber) are embedded in an infinitely extended isotropic matrix, with the crack being along the radial direction of the inclusion. Two loading conditions, namely, the tensile and shear loading ones are considered. During the solution procedure, the crack is treated as a continuous distribution of edge dislocations. By using the solution of an edge dislocation near a coated fiber as the Green's function, the problem is formulated into a set of singular integral equations which are solved by Erdogan and Gupta (1972) method. The expressions for the stress intensity factors of the crack are then obtained in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Several numerical examples are given for various material and geometric parameters. The solutions obtained from the integral equations have been checked and confirmed by the finite element analysis results.

Journal ArticleDOI
TL;DR: In this paper, the size effect of fatigue crack growth near threshold in the high cycle fatigue regime and associated fracture processes was studied. But the authors focused on the effect of the size of the crack on the fracture process.
Abstract: Metallic thin foils are essential structural parts in microsystems ,which may be subjected to fatigue loading caused by thermal fluctuations and mechanical vibrations influencing their reliability in numerous engi- neering applications. It is well known that the fatigue properties of bulk material cannot be adopted for small scaled structures. For a better understanding of the 'size-effect' in the present investigation fatigue crack growth near threshold in the high cycle fatigue regime and associated fracture processes were studied. Free- standing rolled and electrodeposited Cu-, Mo- and Al foils of thickness from 20m to 250m in different conditions have been tested in a special experimental set up operating at RD 1 and a testing frequency of 20 kHz. At a given constant strain value the fatigue crack growth behaviour has been recorded accompanied by intermittent observation of the change of the dislocation structure in the vicinity of the growing crack by use of the electron channeling contrast imaging (ECCI)-technique in a scanning electron microscope (SEM). In a load shedding technique fatigue threshold stress intensity factor values have been derived and compared with data of bulk material. Typical crack growth features were detected depending on thickness and grain sizes of the foils. Various criteria (compliance , extent of plastic zones and plastic strain gradients) were selected for the explanation of this anomalous behaviour. Additionally fractomicrographs of uniaxial strained and fatigued foils have been studied to obtain further insight of the effect of dimensional constraint.

Journal ArticleDOI
TL;DR: In this paper, the authors determined the stress intensity factor K and the elastic T-stress for corner cracks using domain integral and interaction integral techniques, and showed that the T-stress reaches its maximum value at the mid-plane where the K-stressing reached its maximum, though negative, value in all cases.
Abstract: The stress intensity factor K and the elastic T-stress for corner cracks have been determined using domain integral and interaction integral techniques Both quarter-circular and tunnelled corner cracks have been considered The results show that the stress intensity factor K maintains a minimum value at the mid-plane where the T-stress reaches its maximum, though negative, value in all cases For quarter-circular corner cracks, the K solution agrees very well with Pickard's (1986) solution Rapid loss of crack-front constraint near the free surfaces seems to be more evident as the crack grows deeper, although variation of the T-stress at the mid-plane remains small Both K and T solutions are very sensitive to the crack front shape and crack tunnelling can substantially modify the K and T solutions Values of the stress intensity factor K are raised along the crack front due to crack tunnelling, particularly for deep cracks On the other hand, the difference in the T-stress near the free surfaces and at the mid-plane increases significantly with the increase of crack tunnelling These results seem to be able to explain the well-observed experimental phenomena, such as the discrepancies of fatigue crack growth rate between CN (corner notch) and CT (compact tension) test pieces, and crack tunnelling in CN specimens under predominantly sustained load

Journal ArticleDOI
TL;DR: In this paper, the effects of relative lamellae misorientation and offsets between neighboring colonies on crack growth are investigated computationally through an idealized microstructure of multiple colonies.
Abstract: In-situ compact tension tests on binary lamellar titanium aluminide (TiAl) possessing the colony ``polycrystalline'' microstructure illustrate a range of damage phenomena and toughening mechanisms including crack nucleation across colony boundaries, plastic deformation of bridging ligaments, and multiple cracking within colonies. Here, the effects of relative lamellae misorientation and offsets between neighboring colonies on crack growth are investigated computationally through an idealized microstructure of multiple colonies. Within each colony, the brittle Ti3Al lamellae are represented as parallel planes of comparatively low toughness embedded in a matrix of ductile TiAl lamellae that are collectively modeled as an elastic-viscoplastic solid with higher fracture toughness. Plane strain calculations of crack growth are carried out on a compact tension geometry. The calculations are in good qualitative agreement with the in-situ observations, capturing many features of crack growth such as multiple microcrack nucleation and plastic deformation of residual ligaments. Experiments and numerical analyses show that changes in lamellar orientation and alignment across a colony boundary can contribute significantly to the fracture resistance. The numerical results demonstrate that the fracture resistance of these alloys is determined by an intricate interplay between matrix ductility, Ti3Al and TiAl fracture toughnesses, and colony boundary toughness. This suggests the possibility of computationally-guided material optimization through microstructural control of these material properties.

Journal ArticleDOI
TL;DR: In this article, a finite element analysis is used to identify three relevant regimes of foreign object damage related to the depth of penetration into the substrate, and to determine the residual stresses, which are used to address the question: To what extent do residual stresses caused by the FOD reduce the critical crack size associated with threshold fatigue crack growth?
Abstract: Foreign Object Damage (FOD) usually happens when objects are ingested into jet engines powering military or civil aircraft. Under extreme conditions, FOD can lead to severe structural damage. More commonly it produces local impacted sites of the fan and compressor airfoils, lowering fatigue life of these components. FOD is a prime cause for maintenance and repair in aircraft engines. In this paper, a framework for analyzing FOD and its effect on fatigue cracking is established. A finite element analysis is used to identify three relevant regimes of FOD related to the depth of penetration into the substrate, and to determine the residual stresses. Most of the emphasis in this paper focuses on fatigue cracks emerging from shallow indentations, which are generally expected to be of most practical concern. Full three-dimensional finite element solutions are obtained for semi-circular surface cracks emerging from specific locations at the indentation revealing the influence of the residual stress on the stress intensity factor distribution. For shallow indents, a relatively simple dimensionless formula for the relation between the residual stress intensity factor, the crack size, and the indentation width are developed. These results, together with results for the intensity factor variations due to cyclic loading, have been used to address the question: To what extent do the residual stresses caused by the FOD reduce the critical crack size associated with threshold fatigue crack growth? Formulas for the critical crack size are obtained. Specific results are presented for the blade alloy, Ti-6Al-4V, revealing that FOD can reduce the critical crack size by as much as 60%.

Journal ArticleDOI
TL;DR: In this paper, the authors derived the stresses around a crack in an interfacial layer between two dissimilar elastic half-planes by expanding the differences of the crack face displacements into a series.
Abstract: The stresses around a crack in an interfacial layer between two dissimilar elastic half-planes are obtained. The crack is parallel to the interfaces. The material constants of the layer vary continuously within a range from those of the upper half-plane to those of the lower half-plane. An internal gas pressure is applied to the surfaces of the crack. To derive the solution, the nonhomogeneous interfacial layer is divided into several homogeneous layers with different material properties. The boundary conditions are reduced to dual integral equations, which are solved by expanding the differences of the crack face displacements into a series. The unknown coefficients in the series are determined using the Schmidt method, and a stress intensity factor is calculated numerically for epoxy-aluminum composites.

Journal ArticleDOI
TL;DR: In this article, the authors developed a fracture mechanics-based methodology for predicting the limiting threshold stress of high-cycle fretting fatigue in structural alloys, where the contact stress field for two flat surfaces under fretting was analyzed via an integral equation technique.
Abstract: An integrated analytical and experimental approach was taken to develop a fracture mechanics-based methodology for predicting the limiting threshold stress of high-cycle fretting fatigue in structural alloys. The contact stress field for two flat surfaces under fretting was analyzed via an integral equation technique. The local fretting stress field of the uncracked body was then utilized to obtain the stress intensity factor of an arbitrarily oriented fatigue crack using a continuum dislocation formulation. The limiting threshold stress ranges for the nonpropagation of fretting fatigue cracks were predicted on the basis that the fretting fatigue cracks are small cracks that exhibit a size-dependent growth threshold and propagate at stress intensity ranges below the large-crack threshold. In part I, the development of the worst-case fret (WCF) model is described. The influence of the limiting high-cycle fatigue (HCF) threshold stress on a variety of fretting fatigue parameters such as bearing pressure, pad geometry, shear stress, mode mixity, and coefficient of friction are elucidated by parametric calculations. In part II, the WCF model is applied to treating HCF of Ti-6Al-4V where model predictions are compared against critical experiments performed on a kilohertz fretting-fatigue rig.

Journal ArticleDOI
TL;DR: In this article, the authors presented a two-terms asymptotic analysis of the near-tip stress fields of sharp V-shaped notches having the bisector inclined with respect to remotely applied tensile stress.
Abstract: The paper presents a two-terms asymptotic analysis of the near-tip stress fields of sharp V-shaped notches having the bisector inclined with respect to remotely applied tensile stress Due to their geometry, mixed-load conditions are present at the notch tip The governing of equations result in a leading order system and a second order system As known, one of the most significant characteristics of singular stress fields in nonlinear materials is that the solution for mixed-mode loading cannot be expressed as a linear combination of mode I and mode II solutions When the included angle is greater than 90° (as it generally happens in most welded joints, for example) a satisfactory description of the stresses at the notch tip can be obtained by imposing boundary conditions of the symmetric type in the leading-order system, and boundary conditions of antisymmetric type in the second order system Finally, simple expressions of the plastic Notch Stress Intensity Factors are reported for a particular geometry, with the aim to explicitly describe the influence of scale effect, nominal stress and material properties on the intensities of the asymptotic stress distribution under nonlinear conditions