Showing papers on "Stress concentration published in 1984"
TL;DR: A review of the experimental data on subcritical crack growth in geological materials is presented in this article, where the main parameters describing subcritical cracking growth are the critical stress intensity factor Kc, the sub critical crack growth limit Ko, and the relationship between Ko and Kc.
Abstract: A review is presented of the experimental data on subcritical crack growth in geological materials. The main parameters describing subcritical crack growth are the critical stress intensity factor Kc, the subcritical crack growth limit Ko, and the stress intensity factor-crack velocity (K-v) relationship between Ko and Kc. The K-v data are presented in terms of an equation in which the crack velocity depends on stress intensity factor raised to a power n because this is common practice in experimental studies. These data are presented as tables and in synoptic diagrams. For silicates the value of n increases as the environment becomes depleted in hyroxyl species and with increase in the microstructural complexity of the solid. Values of n as low as 9.5 have been found for tensile cracking of quartz in basic environments and as high as 170 for tensile cracking of basalt in moist air. Insufficient experimental data are available to predict subcritical crack growth behavior at depth in the earth's crust without major extrapolations of the data base. Schematic outlines are presented, therefore, of the probable influence on subcritical crack growth of some key parameters in the crustal environment. These include stress intensity factor, temperature, pressure, activity of corrosive environmental agent, microstructure, and residual strains. In addition, a discussion is presented of the likely magnitude of the subcritical crack growth limit. For stress corrosion tensile crack growth of quartz a limit of approximately 0.2 of the critical stress intensity factor is inferred from theoretical calculations. Further problems discussed with regard to the extrapolation of experimental data to crustal conditions include the choice of a suitable equation to describe crack growth and the magnitude of parameters in these equations. A brief discussion of the double torsion testing method is presented in order to aid the interpretation of experimental results because it is almost the sole method used to study subcritical cracking in rocks.
1,184 citations
TL;DR: In this paper, a general crack opening stress equation is presented which may be used to correlate crack growth rate data for various materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined.
Abstract: A general crack opening stress equation is presented which may be used to correlate crack growth rate data for various materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined. The constraint factor, alpha, is a constraint on tensile yielding; the material yields when the stress is equal to the product of alpha and sigma. Delta-K (LEFM) is plotted against rate for 2024-T3 aluminum alloy specimens 2.3 mm thick at various stress ratios. Delta-K sub eff was plotted against rate for the same data with alpha = 1.8; the rates correlate well within a factor of two.
761 citations
TL;DR: In this paper, an approximate theory was established to derive the stress and strain state of constituent phases, stress concentrations at the interface, and the elastic energy and overall moduli of the composite.
593 citations
TL;DR: In this article, the authors examined the problem of dynamic crack propagation experimentally in large thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated.
Abstract: This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.
529 citations
TL;DR: In this paper, the authors examined crack initiation and arrest in thin sheets of Homalite-100 and showed that cracks can propagate rapidly with constant velocity even though the stress intensity factor varies considerably during this propagation.
Abstract: Problems of dynamic crack propagation are examined experimentally in a series of four papers. In this paper, the first of this series, crack initiation and arrest are investigated in thin sheets of Homalite-100. It is found that as the rate of loading increases to as high as 105 MPa/sec, the stress intensity factor required to initiate crack growth increases markedly. Crack arrest resulting from a simulated pressurized semi-infinite crack in an unbounded medium was found to occur abruptly. There was no continuous deceleration and the crack always stopped at a constant value of the stress intensity factor, which value was lower than the stress intensity factor required for quasi-static crack growth initiation. The second paper in this series deals with the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching. The third contribution establishes the hitherto unreported occurrence that cracks can propagate rapidly with constant velocity even though the stress intensity factor varies considerably during this propagation. This velocity is determined by the initial stress wave loading on the crack tip, and is changed, within limits, only by stress pulses of sufficient magnitude and brevity of rise time. The final paper in the series deals with the effect of stress waves on the behavior of running cracks, in particular with the influence of stress waves on the branching phenomenon. Also, crack curving under transient stress waves is examined. These results are believed to apply to materials other than Homalite 100 and the reasons for this belief are discussed in this first contribution.
426 citations
01 Apr 1984
TL;DR: In this paper, the stress intensity factor equations for an embedded elliptical crack, a semielliptical surface crack and a quarter elliptical corner crack are presented for three dimensional finite element analyses of these cracks.
Abstract: Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.
367 citations
TL;DR: In this article, the second of a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite 100 simulating crack growth in an unbounded plate.
Abstract: This is the second of a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite 100 simulating crack growth in an unbounded plate. In the first paper crack initiation resulting from stress wave loading to the crack tip and crack arrest were investigated. It was found that for increasing rates of loading in the micro second range, the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity below that value which causes initiation under quasi-static loading.
365 citations
TL;DR: In this article, the authors analyzed the time dependent sintering of a bi-modal powder compact, consisting of two regions which sinter at different rates, and obtained complete solutions for the internal stress and for the densification rate.
214 citations
TL;DR: In this article, the authors evaluate static stress condition, especially stress ratio effects on the low-amplitude dynamic shear modulus, G0, of three clean, dry sands.
Abstract: Resonant column tests involving anisotropic confining conditions were conducted to evaluate static stress condition, especially stress ratio effects on the low‐amplitude dynamic shear modulus, G0, of three clean, dry sands. Six static stress paths, involving both triaxial compression and triaxial extension, developed the desired ranges of stress ratios and stress histories. The results of these tests determined that increasing the stress ratio decreased G0, up to 20%–30%, but the reduction was not significant for stress ratios below about 2.0. Stress history caused a reduction in G0, but when the final stress ratio was the maximum value attained, the loading, unloading, and reloading path followed to develop this maximum value had little influence. The results also indicated that G0, depends about equally on the static principal stresses in the direction of wave propagation and in the direction of particle motion. The effect of the third principal stress appears to be unimportant. Two empirical equations ...
210 citations
TL;DR: In this article, a series of four papers dealing with experimental observations of dynamic crack propagation in thin, large sheets of a Homalite 100 plastic material which allow simulation of crack growth in unbounded plates.
Abstract: This is the last in a series of four papers dealing with experimental observations of dynamic crack propagation in thin, large sheets of a Homalite 100 plastic material which allow simulation of crack growth in unbounded plates. In the first paper crack initiation resulting from stress wave loading was examined as well as crack arrest. It was found that for increasing rates of loading in the microsecond range the stress intensity factor required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.
207 citations
TL;DR: In this article, the role of microstructure and environment in influencing ultra-low fatigue crack propagation rates has been investigated in 7075 aluminum alloy heat-treated to underaged, peak-aged, and overaged conditions and tested over a range of load ratios.
Abstract: The role of microstructure and environment in influencing ultra-low fatigue crack propagation rates has been investigated in 7075 aluminum alloy heat-treated to underaged, peak-aged, and overaged conditions and tested over a range of load ratios. Threshold stress intensity range, ΔK0, values were found to decrease monotonically with increasing load ratio for all three heat treatments fatigue tested in 95 pct relative humidity air, with ΔK
0 decreasing at all load ratios with increased extent of aging. Comparison of the near-threshold fatigue behavior obtained in humid air with the data forvacuo, however, showed that the presence of moisture leads to a larger reduction in ΔK0 for the underaged microstructure than the overaged condition, at all load ratios. An examination of the nature of crack morphology and scanning Auger/SIMS analyses of near-threshold fracture surfaces revealed that although the crack path in the underaged structure was highly serrated and nonlinear, crack face oxidation products were much thicker in the overaged condition. The apparent differences in slow fatigue crack growth resistance of the three aging conditions are ascribed to a complex interaction among three mechanisms: the embrittling effect of moisture resulting in conventional corrosion fatigue processes, the role of microstructure and slip mode in inducing crack deflection, and crack closure arising from a combination of environmental and microstructural contributions.
TL;DR: In this article, the authors investigated the influence of a preferred crystallographic orientation on mechanical properties of textured Ti-6Al-4V material and found that high cycle fatigue and fatigue crack growth were performed in vacuum, laboratory air, and a 3.5 pct NaCl solution.
Abstract: Tensile properties, high cycle fatigue strength, and fatigue crack propagation behavior were evaluated on highly textured Ti-6Al-4V material to investigate the influence of a preferred crystallographic orientation on mechanical properties. Thermomechanical treatments were used to develop three different textures: a basal, basal/transverse, and transverse type, all of which exhibited the same homogeneously equiaxed microstructure. The Young’s modulus was found to vary between 107 and 126 GNm-2, and yield strength changed from 1055 to 1170 MNm-2. Ductility was only slightly affected by texture. High cycle fatigue and fatigue crack growth measurements were performed in vacuum, laboratory air, and a 3.5 pct NaCl solution. It is shown that laboratory air can be regarded as a quite corrosive environment. In vacuum the highest fatigue strength values were measured whenever loads were perpendicular to basal planes. However, these conditions had the highest susceptibilities to air and 3.5 pct NaCl solution environments. Nearly no influence of texture on fatigue crack propagation was found in vacuum, but in a corrosive environment crack growth parallel to (0002)-planes was much faster than perpendicular to these planes. To explain the corrosive effect on the fatigue properties of the textured material hydrogen is thought to play a key role.
TL;DR: In this article, the authors considered the conditions leading to both the initiation and the cessation of fracture propagation and found that the final geometry of the fracture set is a function of the remote strain history and the initial crack geometry.
Abstract: Naturally occurring extension fractures, including some joints and veins, form sets consisting of numerous subparallel fractures, each with well-defined ends. In order to correctly interpret these fractures in the field, it is necessary to determine which factors control the geometries of fracture sets. This requires consideration of the conditions leading to both the initiation and the cessation of fracture propagation. A fracture begins to propagate when the crack extension force reaches a critical value, which is a property of the rock and of environmental conditions. After propagation initiates, the crack extension force varies owing to: (1) increase in crack length, (2) change in remote strain, (3) elastic interaction with nearby cracks, (4) change in internal fluid pressure, and (5) stress relaxation due to growth of cracks in the surrounding rock. Each fracture continues to propagate as long as its crack extension force exceeds the critical value and terminates when this condition is no longer met. Neglecting fluid effects, the final geometry of the fracture set is a function of the remote strain history and the initial crack geometry, which can be characterized by the initial crack density. For low initial densities, large increases in crack length occur with little or no increase in remote strain. However, for large initial densities, crack lengths increase only if the applied strain increases. This analysis is used to estimate the variation in remote strain during formation of a fracture set in granitic rock from observations of the final fracture geometry.
TL;DR: In this paper, Fatigue crack growth rates have been determined on standard specimens containing long cracks and on specimens containing two-dimensional short cracks (∼0.10-0.50mm).
Abstract: Fatigue crack growth rates have been determined on standard specimens containing long cracks (∼5–10mm) and on specimens containing two-dimensional short cracks (∼0.10–0.50mm). Large differences have been observed indicating that at a given stress intensity factor short cracks propagate much faster than long cracks. Mouth opening displacement measurements for both specimen geometries have shown that the crack closure effect is largely responsible for the observed effect. These results are used to rationalize the behaviour of short cracks initiated from natural sites which were either graphite nodules or microshrinkage pores. The three-dimensional aspect of these natural small cracks is analysed and discussed in detail.
TL;DR: In this paper, the authors derived a specific internal state variable constitutive law relating uniaxial stress to crack density and crack propagation rate, which is based on the instantaneous crack extension force.
Abstract: Quasi-static propagation and dilation of macroscopic mode I cracks is considered as a source of inelastic strain in crustal rocks undergoing extensional deformations. The approach here is to first characterize the propagation of a single dilating crack and then to consider how a large two-dimensional array of similar, parallel cracks accomodates an applied deformation. The driving force for propagation of each crack, Gi, is found as a function of the applied strain and the instantaneous crack lengths ci. The rate of crack propagation is taken to be a function of the instantaneous crack extension force ċi = ċ (Gi). A specific propagation rate extension force relation is developed that both fits the available experimental data and has vanishing propagation rate at a finite value of G. From these results a specific internal state variable constitutive law is derived relating uniaxial stress to the instantaneous uniaxial strain and crack density. For strains less than those necessary to cause crack propagation, the rock is predicted to behave like a linear elastic solid. Following the onset of propagation, the average stress may continue to increase if the strain rate accommodated by crack growth is slow in comparison to the applied strain rate. For constant strain rate boundary conditions the solutions exhibit strain softening, leading to peak stress and then a stress decrease. The peak stress increases nearly logarithmically with increasing applied strain rate. The response to unloading depends strongly on whether or not cracks heal. Unloading that follows sealing of the cracks with mineral precipitates causes the rock to undergo a permanent nonrecoverable strain.
TL;DR: In this paper, the total potential energy for a body composed of an anisotropic micropolar linear elastic material is developed and used to formulate a displacement type finite element method of analysis.
TL;DR: In this paper, the initiation stage and short crack behavior in torsional fatigue of a 0.4% C steel was investigated by a replication technique, and it was proposed that crack growth rate depends on the extent and intensity of plasticity at the tip of the crack.
Abstract: The initiation stage and short crack behaviour in torsional fatigue of a 0.4% C steel was investigated by a replication technique.
The fatigue cracks initiated and propagated in the ferrite phase which is located at the prior austenite grain boundaries in the form of long allotriomorphs. At this stage of crack development it is proposed that crack growth rate depends on the extent and intensity of plasticity at the tip of the crack. Crack growth per cycle is correspondingly proportional to the strength of the slip band. The ferrite-pearlite boundaries are strong barriers to crack propagation, which is manifested by a deceleration of growth and possible arrest. On raising the stress level the previously non-propagating cracks may continue to grow by branching or joining with other cracks in the ferrite phase. This process is repeated until the stress fields of one or more dominant cracks attain a critical value to sustain continued growth that leads to failure.
TL;DR: In this paper, local crack tip opening micromechanics have been characterized for both crack size regimes in a high strength aluminum alloy, and it was found that crack tip displacement, crack opening load, and crack opening mode all differ widely for large and small cracks at equivalent cyclic stress intensities (ΔK).
Abstract: In order to rationalize observed differences in the growth behavior of large and small cracks, local crack tip opening micromechanics have been characterized for both crack size regimes in a high strength aluminum alloy. It is found that crack tip opening displacement, crack tip opening load, and crack opening mode all differ widely for large and small cracks at equivalent cyclic stress intensities (ΔK). High crack tip opening displacements and relatively low, approximately constant, crack opening loads for microcracks account both for their rapid rate of growth relative to large cracks and the absence of a microcrack threshold stress intensity. Crack tip plastic zone sizes also were measured, and it was found that the ratio of plastic zone size to crack length for small cracks is ∼ 1.0, while for large cracks the same ratio is ≪ 1. Simple empirical corrections to ΔK are found inadequate to correlate the growth of large and small cracks. It is concluded that for small cracks, linear elastic fracture mechanics similitude does not apply, and that an alternative crack driving force must be formulated.
TL;DR: In this article, microstructures containing fine globular or coarse martensite in a coarse-grained ferritic matrix demonstrated exceptionally high resistance to crack growth without loss in strength properties.
Abstract: microstructures with maximum resistance to fatigue crack extension while maintaining high strength levels. A wide range of crack growth rates has been examined, from ~10-8 to 10-3 mm per cycle, in a series of duplex microstructures of comparable yield strength and prior austenite grain size where intercritical heat treatments were used to vary the proportion, morphology, and distribution of the ferrite and martensite phases. Results of fatigue crack propagation tests, conducted on “long cracks” in room temperature moist air environments, revealed a very large influence of microstructure over the entire spectrum of growth rates at low load ratios. Similar trends were observed at high load ratio, although the extent of the microstructural effects on crack growth behavior was significantly less marked. Specifically, microstructures containing fine globular or coarse martensite in a coarse-grained ferritic matrix demonstrated exceptionally high resistance to crack growth without loss in strength properties. To our knowledge, these microstructures yielded the highest ambient temperature fatigue threshold stress intensity range ΔK0 values reported to date, and certainly the highest combination of strength and ΔK0 for steels (i.e., ΔK0 values above 19 MPa√m with yield strengths in excess of 600 MPa). Such unusually high crack growth resistance is attributed primarily to a tortuous morphology of crack path which results in a reduction in the crack driving force from crack deflection and roughness-induced crack closure mechanisms. Quantitative metallography and experimental crack closure measurements, applied to currently available analytical models for the deflection and closure processes, are presented to substantiate such interpretations.
TL;DR: In this article, a model for fatigue crack propagation was developed which incorporates mechanical, cyclic and fatigue properties as well as a length parameter, which can be associated with the microstructure of the material.
TL;DR: In this paper, a tubular lap joint comprised of a steel tube adhesively bonded to a composite tube subjected to torsion is considered and a finite element method is employed to characterize the stress concentration associated with the boundary layer effect in the end region of the adhesive layer.
Abstract: This analysis considers a tubular lap joint comprised of a steel tube adhesively bonded to a composite tube subjected to torsion. A finite element method is employed to characterize the stress concentration associated with the boundary layer effect in the end region of the adhesive layer. Through the selective perturbation of geometric and material properties, a parametric evaluation is conducted in which the peak stress and its gradient are reduced. A number of design guidelines are subsequently drawn based on the results of this evaluation.
TL;DR: In this article, Biaxial fatigue tests were conducted on Inconel 718 thin-walled tubular specimens to quantify the effect of mean stress on crack growth and distribution of cracks.
Abstract: Biaxial fatigue tests were conducted on Inconel 718 thin-walled tubular specimens to quantify the effect of mean stress. The specimens were loaded in combined tension and torsion in strain control at room temperature. Fatigue lives ranged from 3000 to 15,000 cycles depending on the mean stress. These data were correlated with a parameter based on the maximum plastic shear strain amplitude, normal strain amplitude and mean normal stress on the plane of maximum shear strain amplitude. This parameter was combined with the Coffin-Manson equation for estimating fatigue lives. Observations of the cracking behavior show that mean stress affects the rate of crack growth and distribution of cracks.
TL;DR: In this article, the stress concentration of a cylindrical bar with a V-shaped circumferential groove is analyzed by the body force method, and the stress field due to a ring force in an infinite body is used to solve this problem.
TL;DR: In this article, the authors summarized the results of classical nucleation theory applied to the nucleation of creep cavities at hard second-phase particles and concluded that cavities cannot be nucleated by the considered mechanism of vacancy condensation unless the nuclei have a narrow, rather than spherical, shape.
01 Apr 1984
TL;DR: In this paper, the authors predicted crack growth patterns and crack growth lives for aluminum alloys using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior, using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest.
Abstract: Fatigue crack growth patterns and lives for surface cracks, surface cracks at holes, and corner cracks at holes in three dimensional bodies were predicted using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior. The predictions were made by using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest. The crack configurations were subjected to constant-amplitude fatigue loading under either remote tension or bending loads. The predicted crack growth patterns and crack growth lives for aluminum alloys agreed well with test data from the literature.
TL;DR: In this article, experiments on various palliatives are reported and their relevant merits compared, and the data derived are also reviewed in the light of a companion document considering stress distributions associated with contact conditions.
TL;DR: In this article, the authors considered the problem of a hollow sphere subjected to uniform internal and external pressure within the equilibrium theory of finite elasticity, and obtained closed-form solutions for the deformation and stress fields.
TL;DR: In this paper, the early stages of plastic deformation in stainless steel with a small grain size have been studied by in situ straining of a thin foil inside the electron microscope, and the shear stresses acting in each deformation stage have been calculated using data based on the geometry of the pile-ups observed in thin foil.
TL;DR: In this article, an eigenvector expansion method is used to solve the governing equations of shear-lag analyses. But this method has two effects on the stress concentrations in an intermingled hybrid composite.
Abstract: This paper first treats the stress concentrations in an intermingled hybrid composite. An eigenvector expansion method is used to solve the governing equations of shear-lag analyses. Two effects on...
TL;DR: In this article, the micromechanical theory of fatigue crack nucleation is applied to stage I fatigue crack growth observed in high-strength alloys, and it is further extended to the near-threshold growth of a long fatigue crack.