Showing papers on "Stress concentration published in 1991"
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TL;DR: In this article, the cyclic deformation and fatigue crack initiation in polycrystalline ductile solids was studied and a total-life approach was proposed to deal with the problem.
Abstract: Preface 1. Introduction and overview Part I. Cyclic Deformation and Fatigue Crack Initiation: 2. Cyclic deformation in ductile single crystals 3. Cyclic deformation in polycrystalline ductile solids 4. Fatigue crack initiation in ductile solids 5. Cyclic deformation and crack initiation in brittle solids 6. Cyclic deformation and crack initiation in noncrystalline solids Part II. Total-Life Approaches: 7. Stress-life approach 8. Strain-life approach Part III. Damage-Tolerant Approach: 9. Fracture mechanics and its implications for fatigue 10. Fatigue crack growth in ductile solids 11. Fatigue crack growth in brittle solids 12. Fatigue crack growth in noncrystalline solids Part IV. Advanced Topics: 13. Contact fatigue: sliding, rolling and fretting 14. Retardation and transients in fatigue crack growth 15. Small fatigue cracks 16. Environmental interactions: corrosion-fatigue and creep-fatigue Appendix References Indexes.
4,158 citations
TL;DR: In this article, a two-dimensional electroelastic analysis is performed on a transversely isotropic piezoelectric material containing defects, and a general solution is provided in terms of complex potentials, with emphasis being placed on stress concentrations that arise in the vicinity of circular and elliptical holes.
386 citations
TL;DR: In this paper, the authors investigated the gains in structural efficiency that can be achieved by aligning the fibers in some or all of the layers in a laminate with the principal stress directions in those layers.
Abstract: 'I'his paper investigates the gains in structural efficiency that can be achieved by aligning the fibers in some or all of the layers in a laminate with the principal stress directions in those layers. The name curvilinear fiber format is given to this idea. The problem studied is a plate with a central circular hole subjected to a uniaxial tensile load. An iteration scheme is used to find the fiber directions at each point in the laminate. Two failure criteria are used to evaluate the tensile load capacity of the plates with a curvilinear format, and for comparison, counterpart plates with a conventional straightline fiber format. The curvilinear designs for improved tensile capacity are then checked for buckling resistance. It is concluded that gains in efficiency can be realized with the curvilinear format.
293 citations
TL;DR: In this article, a progressive failure model for laminated composites containing stress concentrations subjected to in-plane loading is developed for a damaged lamina using a damaged ply constitutive relation in a simplified manner.
Abstract: A progressive failure model is developed for laminated composites containing stress concentrations subjected to in-plane loading. The fundamental approach is to model a damaged lamina using a damaged ply constitutive relation in a simplified manner. The environmental effects including the thermal residual stresses and hygroscopic stresses arc taken into consideration. Parametric studies show that load increment only has little effect on the ultimate strength. When the number of elements for the finite element mesh increases to a certain value, the predicted ultimate strength approaches a stable value. The predictions for the ultimate strength, stress-strain behavior and the damage progression agree reasonably well with the experimental result.
280 citations
01 Jan 1991
TL;DR: In this paper, a generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips, which is accomplished by introducing a "crack function" into the beam's compatibility relations.
Abstract: Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.
230 citations
TL;DR: In this article, the size-adjusted Paris law is combined with size-effect law for fracture under monotonic loading, which leads to a size adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of size adjusted stress intensity factor.
Abstract: Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of size-adjusted stress intensity factor. The crack growth is also characterized in terms of the nominal stress amplitude.
202 citations
TL;DR: In this article, a spatial rescaling has been used to reduce the orthotropic problems to equivalent problems in materials with cubic symmetry, and solutions for orthotropic materials can be constructed approximately from isotropic material solutions or rigorously from cubic ones.
187 citations
TL;DR: In this article, a sliding crack model is proposed to predict the dependence of the stress-strain curve on the applied strain rate, and the model is able to predict both transient and tertiary creep in brittle rocks.
176 citations
TL;DR: Contact stress distributions were studied in vitro for 13 dog knees, with full‐thickness osteochondral defects drilled in the weight‐bearing area of both femoral condyles, and the radial component of the gradient of contact stress was consistently elevated by an order of magnitude above that for intact, condyle articular cartilage.
169 citations
TL;DR: In this article, an algorithm for the prediction of fatigue lives to initiation of cracks of technical sizes in case of variable amplitude loading is presented. But the results of the investigations have been merged to build an algorithm to predict the initiation of crack of technical size and the improvement in accuracy of life prediction compared to results of an existing damage accumulation concept is demonstrated for two materials and two load sequences.
Abstract: Opening and closure of short cracks has been examined experimentally using small strain gauges fixed to unnotched specimens very close to short fatigue cracks. The results of completely reversed tension-compression constant amplitude tests are that crack opening stresses decrease with increasing stress amplitude and that crack closure occurs at nearly the same strain as crack opening. In variable amplitude loading the crack is subjected to a low crack opening level resulting from larger cycles. Based on the results of this experimental investigation some simple approximation formulas are proposed with which decrease as well as increase of crack opening levels can be described. Using these formulas it is possible to compute crack opening strains for any load sequence. The findings of the investigations have been merged to build an algorithm for the prediction of fatigue lives to initiation of cracks of technical sizes in case of variable amplitude loading. The improvement in accuracy of life predictions compared to results of an existing damage accumulation concept is demonstrated for two materials and two load sequences.
165 citations
TL;DR: In this paper, a first order diffraction analysis of an optical interferometer, Coherent Gradient Sensor (CGS), for measuring surface gradients is presented, which has potential for the study of deformation fields near a quasi-statically or dynamically growing crack.
Abstract: A first order diffraction analysis of an optical interferometer, Coherent Gradient Sensor (CGS), for measuring surface gradients is presented. Its applicability in the field of fracture mechanics is demonstrated by quantitatively measuring the gradients of out-of-plane displacements around a crack tip in a three point bent fracture specimen under static loading. This method has potential for the study of deformation fields near a quasi-statically or dynamically growing crack.
TL;DR: In this paper, the surface and the deepest point of a semi-elliptical crack in a finite thickness plate were derived from a general weight function and two references stress intensity factors.
TL;DR: In this article, a strip crack closure model based on the original Dugdale-Barenblatt model was investigated for various aspects of fatigue crack growth behavior, and a variable constraint factor was introduced into the model to account for the 3D effect at the crack tip.
TL;DR: In this paper, a first-order perturbation analysis of the stress concentration effects caused by slightly undulating surfaces is presented, where the perturbations are treated as being perturbed from a reference state in which the surface is perfectly flat.
Abstract: T his paper presents a first-order perturbation analysis of the stress concentration effects caused by slightly undulating surfaces. The perturbation approach that we use treats the undulating surfaces as being perturbed from a reference state in which the surface is perfectly flat. The magnitude of the perturbation is assumed to be sufficiently small compared to other length scales of the bulk material so that a half-plane model can be used for simplification. First-order-accurate perturbation solutions have been derived for the stress distribution along a sinusoidally wavy surface and for the attenuation of the stress concentration away from the undulating surface. The interactions among different surface perturbation waves are investigated by comparing the result of stress concentration factor at the trough of a single wave perturbation along an otherwise flat surface to that for periodically wavy surface. We also examine some of the 3-D effects by using the perturbation algorithm to calculate the stress concentration at undulating surfaces of elastic half-spaces. In all cases, it is found that wavy surfaces can magnify the bulk stress easily by a factor of 2 or 3 when the surface profile does not deviate substantially from flatness. This stress concentration effect is significant especially for already highly stressed heteroepitaxial semiconductor thin films, suggesting that the surface morphology of the film surfaces can play an important role in nucleating dislocations and crack-like surface flaws before the bulk stress reaches a critical level.
TL;DR: In this article, mixed mode crack growth direction criteria have been applied to calculations of the loading experienced by surface-initiated rolling contact fatigue cracks growing at a shallow angle to the surface, and it was demonstrated that cracks grow on the plane of the maximum shear stress rather than perpendicular to the maximum tangential stress as occurs during conventional fatigue testing.
TL;DR: In this paper, the tensile and impact behavior of CaCO3-filled polypropylene was studied in the composition range 0-60 wt % filler and showed that tensile modulus increased while tensile strength and breaking elongation decreased with an increase in caCO3 content.
Abstract: Tensile and impact behavior of CaCO3-filled polypropylene was studied in the composition range 0–60 wt % filler. Tensile modulus increased while tensile strength and breaking elongation decreased with increase in CaCO3 content. The modulus increase and elongation decrease were attributed to increased filler–polymer interaction resulting in reduction in molecular mobility, while increased amorphization and obstruction to stress transfer accounted for the tensile strength decrease. Analysis of tensile strength data showed introduction of stress concentration in the composites. Izod impact strength at first increased up to a critical CaCO3 content, beyond which the value decreased. Surface treatment of CaCO3 with a titanate coupling agent LICA 12 enhances the adhesion of the filler and polymer, which further modifies the strength properties. Scanning electron microscopic studies indicated better dispersion of CaCO3 particles upon surface treatment, which effected the changes in the strength properties of the composites.
TL;DR: In this article, a first-order boundary perturbation method based on Muskhelishvilli's complex variable representations is formulated for the two-dimensional elasticity problem of a nearly-circular inclusion embedded in an infinite dissimilar material.
TL;DR: In this article, a simple method for determining the stress intensity factors for small notch-emanating cracks is presented, which can be used for a variety of central and edge notches with through-thickness of semi-elliptical cracks.
Abstract: This paper presents a simple method for determining the stress intensity factors for small notch-emanating cracks. The proposed method is based on similarities between elastic notch-tip stress fields described by two parameters; the stress concentration factor K1, and the notch-tip radius ρ. The method developed here is rather general, and can be used for a variety of central and edge notches with through-thickness of semi-elliptical cracks. The predicted values are in good agreement with the available numerical data.
TL;DR: In this article, the authors investigated the fatigue behavior of 3-mol%yttria-stabilized tetragonal zirconia polycrystals and found that microcracking is the dominant mechanism of fatigue damage, and that nucleation of fatigue crack is usually not necessary.
Abstract: ~Uniaxial tension-compression fatigue behavior of 3-mol%yttria-stabilized tetragonal zirconia polycrystals was investigated. Hysteresis in the stress-plastic strain curve featured cumulative plastic strain and weakened elastic stiffness. Fracture statistics in terms of cycle-to-failure depends strongly on the maximum stress and less on the stress amplitude. Preexisting processing flaws were identified as the fracture origins in all cases. We suggest that microcracking is the dominant mechanism of fatigue damage, that nucleation of fatigue crack is usually not necessary, and that fatigue lifetime is primarily controlled by crack propagation, which is most sensitive to the maximum stress. [Key words: fatigue, fracture, zirconia, cracks, stress.]
TL;DR: In this paper, an elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip.
Abstract: — An elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip. Forward plastic zone widths for fatigue cracks and stationary, monotonically loaded cracks are compared and found to be similar. The width of the forward plastic zone at the tip of a fatigue crack is not significantly influenced by closure. The traditional Irwin-Rice estimate for crack tip plastic zone size in plane stress is found to be generally consistent with the finite element results. The width of the reversed plastic zone at the tip of a growing fatigue crack in plane stress is found to be considerably less than one-fourth the size of the forward plastic zone, the traditional Rice estimate. This decrease appears to be due to fatigue crack closure. A simple model is developed which permits estimation of the reversed plastic zone size for any stress ratio from information about maximum and minimum stresses and the closure stress. The predictions of this model agree closely with plastic zone sizes calculated by the finite element analysis. These observations appear to be consistent with experimental measurements of forward and reversed plastic zones sizes reported in the literature.
TL;DR: In this article, a number of modifications are introduced to the linear elastic approach to establish a new parameter which is capable of correlating both long crack and short crack fatigue crack growth data.
TL;DR: In this paper, a finite element simulation of growing fatigue cracks in both plane stress and plane strain is used as an aid to visualization and analysis of the crack closure phenomenon, where residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs.
Abstract: Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction Finite element analyses indicate that crack closure does occur under pure plane strain conditions The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction This in-plane contraction also leads to the generation of complex residual stress fields The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain
TL;DR: In this paper, a unique growth law strongly dependent on the maximum stress intensity factor and quadratically dependent on amplitude of the range of stress intensity factors was established for fatigue crack propagation in 3Y-TZP.
Abstract: Fatigue crack propagation in 3Y-TZP was investigated using controlled surface flaws. A unique growth law strongly dependent on the maximum stress intensity factor and quadratically dependent on the amplitude of the range of stress intensity factor was established. This growth law was found to apply for both surface flaws and internal flaws and could be used to predict fatigue lifetime. The presence of residual stress altered the growth mechanics so that an inverse growth rate dependence on the applied stress, reminiscent of the so-called "short-crack behavioe was manifested. Fatigue striations resulting from alternate overload fracture and fatigue fracture during stress cycling were observed. The appearance of striations varied with the R ratio and was very sensitive to the loading condition and crack geometry.
TL;DR: In this paper, a new theory is presented to interpret the breakdown pressure which is the wellbore pressure at fracture initiation in hydraulic fracturing tectonic stress measurements, and the theory is able to explain the effects of well-bore diameter and pressurization rate on breakdown pressure.
01 Nov 1991
TL;DR: In this article, a finite element procedure is presented for the analysis of the buckling and postbuckling behavior of cracks in plates loaded in tension, where the loading direction is perpendicular to the crack faces.
Abstract: A finite element procedure is presented for the analysis of the buckling and postbuckling behavior of cracks in plates loaded in tension. The procedure proposed is applied to the problem of the centrally cracked plate in tension where the loading direction is perpendicular to the crack faces. The results of the analysis show that the buckling deformations can cause a considerable amplification of the stress intensity around the crack tip. This effect, which is due to a redistribution of the stress field in the plate, increases with the length of the crack.
TL;DR: In this paper, a fatigue criterion based on an average stress formulation of composite materials derived from the Mori-Tanaka method is established, which addresses the failure of all the constituents of the composite and represents the interactions between the constituents by involving the volume fraction, properties of the constituents and the interfacial bond.
TL;DR: In this article, the influence of applied stress, crack length, and stress intensity factor on crack closure is compared and evaluated using both experimental data and the results of numerical closure simulations, particularly original finite element (FE) analyses.
Abstract: Experimental and analytical evidence for the influence of applied stress, crack length, and stress intensity factor on crack closure is critically compared and evaluated. Fatigue crack opening behaviors are broadly catalogued into three classes. Class I comprises “near-threshold” behavior, where crack closure levels increase with decreasing stress intensity factor. In class II, the “stable” regime, the crack opening level is independent of the stress intensity factor and crack length but is influenced by the applied stress. Class III is characterized by the loss of elastic constraint accompanying extensive yielding at the crack tip or in the remaining ligament, especially with further crack growth. Here, the crack opening level decreases with increasing crack length until little or no closure occurs. These three different classes of closure behavior are extensively illustrated with both experimental data and the results of numerical closure simulations, particularly original finite element (FE) analyses. No single relationship between crack opening levels and the fundamental fatigue parameters is found to hold universally, due to the wide range of mechanisms which cause or influence closure.
TL;DR: In this article, a numerical multiple-crack interaction model is developed to simulate the failure process in brittle solids containing significant populations of flaws, which allows for the growth of microcracks on a regular array of potential crack sites.
Abstract: A numerical multiple-crack interaction model is developed to simulate the failure process in brittle solids containing significant populations of flaws. The model, which is two dimensional, allows for the growth of microcracks on a regular array of potential crack sites. Individual cracks may be oriented vertically, horizontally, or at 45° to the sample axes. Quasi-static equilibrium equations are expressed in terms of finite difference approximations and are solved by applying a Renormalization Group theory approach. More than 5800 potential crack sites are included in the current version of the model. We have successfully duplicated a variety of brittle fracture phenomena observed in laboratory rock mechanics studies by employing a limited number of parameters and relations in the model. Included in the model are (1) Lame constants λ and μ for intact material, (2) a coefficient of friction for friction on cracks, (3) a normal stress-dependent crack closure algorithm and (4) an initial crack population. A fracture mechanics approach is used to determine crack growth. Approximate stress intensity factors are computed for all cracks, and when critical values are exceeded, cracks are allowed to grow in either mode I (tension) or mode II (in-plane shear). Simulations are performed by specifying a combination of stress and strain boundary conditions. The model is capable of duplicating experimentally observed features such as elastic moduli, dilatancy, acoustic velocities, peak strength, Mohr-Coulomb failure envelope and, to a limited degree, crack coalescence. A mode II critical stress intensity factor was required to produce a concave failure envelope, as is observed in laboratory experiments. This curvature in the failure envelope reflects a transition from mode I crack growth at low confining pressure to mode II growth at high confining pressure.
TL;DR: In this article, a mechanism based on out-of-plane plastic strain component, e z p, in plane strain is shown not to be adequate in explaining crack closure, and a third model based on compressive strain accumulation in the x-direction, e x p, is studied.
Abstract: A mechanism based on out-of-plane plastic strain component, e z p , in plane strain is shown not to be adequate in explaining closure. In the second model, partial relief of compressive stresses in front of the crack tip upon crack advance is forwarded as responsible for crack closure in plane strain. A third model based on compressive strain accumulation in the x-direction, e x p , is studied. Stress-strain history and material displacements as crack advances are presented for plane strain conditions that lend further support to the third model
TL;DR: In this paper, the influence of stress ratio on the tensile fatigue behavior of a unidirectional SiC-fiber/Si,N.,-matrix composite was investigated at 1200°C.
Abstract: The influence of stress ratio on the tensile fatigue behavior of a unidirectional SiC-fiber/Si,N.,-matrix composite was investigated at 1200°C. Tensile stress ratios of 0.1, 0.3, and 0.5 were examined. Fatigue testing was conducted in air, at a sinusoidal loading frequency of 10 Hz. For peak fatigue stresses below the proportional limit of the composite (approximately 195 MPa at 1200°C) specimens survived 5 X lo6 cycles, independent of stress ratio. At peak stresses above the proportional limit, fatigue failures were observed; fatigue life decreased significantly as the stress ratio was lowered from 0.5 to 0.1. Creep appears to be the predominant damage mechanism which occurs during fatigue below the pro