Showing papers on "Stress concentration published in 1989"

Global patterns of tectonic stress

Abstract: Regional patterns of present-day tectonic stress can be used to evaluate the forces acting on the lithosphere and to investigate intraplate seismicity. Most intraplate regions are characterized by a compressional stress regime; extension is limited almost entirely to thermally uplifted regions. In several plates the maximum horizontal stress is subparallel to the direction of absolute plate motion, suggesting that the forces driving the plates also dominate the stress distribution in the plate interior.

Sandwich test specimens for measuring interface crack toughness

Abstract: A crack lying along one interface on an elastic sandwich structure is analyzed. When the thickness of the middle layer is small compared with the other length scales of the structure, a universal relation is found between the actual interface stress intensity factors at the crack tip and the apparent mode I and mode II stress intensity factors associated with the corresponding problem for the crack in the homogeneous material. Therefore, if the apparent stress intensity factors are known, for example calculated from the applied loads as if the structure was homogeneous, this information can be immediately converted into the interface stress intensity factors with the universal relation. This observation provides the theoretical basis for developing sandwich specimens for measuring interface crack toughness. The universal relation reveals the extent to which the asymmetry inherent to a bimaterial interface induces asymmetry in the near tip crack field. In particular, the result of the study can be used to infer whether stress intensity factors for a homogeneous body can be used with good approximation in place of the actual interface stress intensity factors. A proposal for simplifying the approach to interfacial fracture is made which plays down the role of the so-called oscillatory interface singularity stresses.

Micromechanics of the brittle to plastic transition in Carrara marble

Abstract: Samples of Carrara marble were deformed at room temperature to varying strains at confining pressures spanning the range in mechanical behavior from brittle to plastic. Volumetric strain was measured during the experiments, and the stress-induced microstructure was characterized quantitatively using optical and transmission electron microscopy. The range of confining pressure over which transitional (or semibrittle) deformation occurs is 30–300 MPa. The macroscopic initial yield stress is constant for confining pressures greater than 85 MPa, whereas the differential stress at the onset of dilatancy increases with pressure up to 300 MPa. The dilatancy coefficient decreases rapidly with increasing pressure up to 100 MPa, and then asymptotically approaches zero for pressures up to 300 MPa. The work hardening coefficient increases with pressure up to 450 MPa; the pressure sensitivity is greatest for pressures up to 100 MPa. Active deformation mechanisms include microcracking, twinning, and dislocation glide. Transmission electron microscopy observations indicate that dislocation glide occurs, at least on a local scale, in samples deformed in the semibrittle field at pressures as low as 50 MPa and applied differential stress well below the critical resolved shear stress for glide on the easiest slip system. Cracks and voids frequently nucleate at sites of stress concentration at twin boundaries, at twin terminations, and at the intersection of twin lamallae. Geometries suggestive of crack tip shielding by dislocations are also observed. Stereological measurements indicate that at constant strain in the semibrittle field, the stress-induced crack density and anisotropy decrease with increasing pressure. Crack density and anisotropy in samples deformed to strains of 3–5% in the semibrittle field at pressures up to 120 MPa are comparable to those in the prefailure brittle sample, although an analysis of the energetics of deformation suggests that the ratio of brittle energy dissipation to total energy dissipation is at least 60% lower. We also detect a qualitative difference in the characteristic length of the cracks in the brittle and semibrittle fields. The mean dislocation density at constant differential stress increases significantly for samples deformed at pressures of 230 MPa and greater. Our results suggest that although semibrittle flow occurs over a wide range of pressure, the most marked changes in strain partitioning, and hence the style of deformation occur over a small range in pressure.

Analysis of borehole breakouts

Abstract: Boreholes drilled into rock, which is subjected to stresses that amount to a significant fraction of the strength of the rock, may cause the rock to fail adjacent to the borehole surface. Often this results in the elongation of the cross section of the borehole in the direction of the minimum principal (compressive) stress orthogonal to the borehole axis. Such breakouts are valuable indicators of the direction of the minimum compressive stress orthogonal to the axis of the borehole. Their shapes may provide information about the magnitudes of both the maximum and minimum stresses relative to the strength of the rock. Borehole breakouts also may be impediments to drilling and to in situ measurement techniques, such as hydraulic fracturing. Observations and analyses of borehole breakouts raise three important questions. First, how does the shape of the borehole breakout evolve? Second, why are breakout shapes stable despite the very high compressive stress concentrations that they produce? Third, how is the shape of the breakout related to the magnitudes of the stresses in the rock? In this paper, extensile splitting of rock in unconfined, plane strain compression is assumed to be the process of rock failure adjacent to the circumference of the borehole, by which a breakout forms. To simulate the evolution of a borehole breakout, this process is combined with a numerical boundary element analysis of the stresses around a borehole as its cross section evolves from the originally circular shape to that of a stable breakout. The tangential stresses around a stable breakout cross section are found to be everywhere less than the unconfined, plane strain tensile or compressive strength of the rock. The stresses outside the stable breakout are found to be everywhere less than the limiting values of shear strength given by a Mohr-Coulomb criterion. In the regions of great stress concentrations at the ends of a breakout cross section, which have a pointed shape, the state of stress approaches that of equal biaxial compression in plane strain, as it does ahead of a mathematical crack or notch. The fact that the stresses around a breakout are less than the relevant strength establishes both the stability of the final breakout cross section and the appropriateness of an elastic analysis of the stresses. According to this model, the cross-sectional shapes of stable breakouts are not related uniquely to the state of stress and the strength of the rock. For example, stable breakouts created instantly in rock already subjected to stress are much larger than stable breakouts created in the same rock with a preexisting borehole by subsequently increasing the stresses to the same values. The results of drilling into an actual rock probably lie between these extremes. Modest changes in borehole cross section as a result of breakout do not alter significantly the minimum tangential (tensile) stress around a borehole with internal pressure from that given by the Kirsch solution for a circular hole subjected to the same stresses. Therefore hydraulic fracturing interpretations based on the Kirsch solution give the correct values for the far-field stresses.

Cyclic Fatigue Crack Propagation in Alumina under Direct Tension—Compression Loading

Abstract: Cyclically induced crack propagation occurs in alumina subjected to direct tension—compression loading. The crack increment per cycle (da/dN) has a power-law dependence on the peak stress intensity factor (Kmax). Cyclic crack growth can occur at lower values of Kmax than are required to produce static fatigue effects. Subcritical crack-growth behavior was found to be dependent on specimen geometry: it is suggested that direct compressive loads and crack length are both factors that affect cyclic fatigue behavior, and that the use of K alone to characterize fatigue crack growth in ceramics may be questionable.

High‐Temperature Failure of an Alumina‐Silicon Carbide Composite under Cyclic loads: Mechanisms of Fatigue Crack‐Tip Damage

Abstract: Experimental results are presented on the mechanisms of tensile cyclic fatigue crack growth in an A1203-33-vol%-SiC-whisker composite at 1400°C. The ceramic composite exhibits subcritical fatigue crack propagation at stress-intensity-fator values far below the fracture toughness. The fatigue characterized by the stressintensity-factor range, ΔK, and crack propagation rates are found to be strongly sensitive to the mean stress (load ratio) and the frequency of the fatigue cycle. Detailed transmission electron microscopy of the fatigue crack-tip region, in conjunction with optical microscopy, reveals that the principal mechanism of permanent damage ahead of the advancing crack is the nucleation and growth of interfacial flaws. The oxidation of Sic whiskers in the crack-tip region leads to the formation of a silica-glass phase in the 1400°C air environment. The viscous flow of glass causes debonding of the whisker-matrix interface; the nucleation, growth, and coalescence of interfacial cavities aids in developing a diffuse microcrack zone at the fatigue crack tip. The shielding effect and periodic crack branching promoted by the microcracks result in an apparently benefcial fatigue crack-growth resistance in the A1203—SiC composite, as compared with the unreinforced alumina with a comparable grain size. A comparison of static and cyclic load crack velocities is provided to gain insight into the mechanisms of elevated temperature fatigue in ceramic composites.

Application of the Paris Equation to the Fatigue Growth of Transverse Ply Cracks

Abstract: A model based on a stress intensity factor for a growing transverse ply crack is outlined. The model is applied to experimental observations of crack growth in a trans parent 0/90/0 glass fibre/epoxy laminate under fatigue loading. The crack growth rate is found to be independent of crack length but to depend on the spacing between cracks. Under static loading and fatigue loading at high maximum stress, cracks grow by fast frac ture. Slow crack growth is observed at lower maximum fatigue stresses and in the later stages of fatigue tests at higher stresses when the crack spacing is small. Crack growth rates can be described using a Paris relation.

Mechanics of fault junctions

Abstract: A sharp bend in a fault must be part of a triple junction, and slip on the three fault segments at the junction must have a vector sum of zero, in order to avoid an unphysical 1/r stress singularity. Accompanying the slip, a volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The energy absorbed due to the volume change is proportional to the slip increment times the total past slip accumulated at the junction. At a new junction the energy absorbed is a small fraction of the energy released by slip on the fault system, but after a number of earthquakes (proportional to shear modulus over confining stress) the junction becomes a strong barrier to further slip. Although slip occurs more easily on old rupture surfaces than on fresh fractures, the growing barrier strength of junctions requires that there be some fresh fracture in earthquakes. Perhaps a small fraction of the surface that slips in any earthquake is fresh fracture, which could provide the instability needed to explain earthquakes. A numerical model in two-dimensional static plane strain shows, even without accounting for energy absorbed at the junction, that a bend in a fault acts as a barrier if slip is impeded on the associated fault spur. The stress concentration at the bend will tend to induce slip on the spur. Slip occurring on the spur unstably (with a drop in the coefficient of friction) can induce increased slip on the main fault segments with no change in the coefficient of friction. A fault junction provides a natural realization of barrier and asperity models without appealing to arbitrary variations of fault strength. The location of the fresh fracture that occurs after a junction becomes a strong barrier remains an unanswered question. It is likely to be initiated near the stress concentration at the old junction. A model simulating the effect of fresh fracture near old junctions might explain earthquakes without appealing to an unstable friction law anywhere.

Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes

Abstract: Porous or clastic rocks often have elastic moduli which are not constant but increase with increasing minor principal stress. The use of classical constant modulus linear elasticity in these cases can lead to erroneous predictions of the deformations and of the initiation and extent of failure around underground excavations. To illustrate these effects, solutions are developed for axisymmetric excavations in infinite media having power law and exponential variations of elastic modulus with minor principal stress. The maximum stress concentrations do not occur at the excavation boundaries and are less than the constant value of 2.0 given by constant modulus elasticity. When modified slightly to allow for test boundary conditions, the theory gives predictions that are consistent with aspects of the results obtained in hydrostatic compression tests on thick walled cylinders of three sedimentary rocks.

A boundary element approach for recovery of shape sensitivities in three-dimensional elastic solids

Abstract: A boundary element formulation for design sensitivities has been developed for application in three-dimensional shape optimization of elastic solids. Both displacement and stress sensitivities can be determined, at any stage of the design process, by relatively straightforward numerical integration procedures. Further simplification in calculating displacement sensitivities is accomplished by using a special rigid-body integral identity to remove singularities. The issue of accuracy was addressed by analyzing the problem of an infinite elastic solid with a triaxial ellipsoidal cavity. It turns out that this test case is considerably more general than the usual axisymmetric examples employed in prior elastostatic error analyses. Furthermore, the stress concentration can be increased indefinitely by decreasing the two aspect ratios that define the cavity surface. More importantly, the availability of an analytical solution makes it possible to obtain an exact measure of error. For completeness, stresses and stress sensitivities were obtained for three progressively eccentric cavity shapes, using three different singular integration schemes. Generally, the numerical predictions and exact results were in excellent agreement. In the worst case, with a stress concentration of about 4.1, the best stress sensitivity prediction was within 2 percent of the exact value. This is remarkably accurate, given that the corresponding cavity model consisted of only twelve elements per octant.

Notch size effect in fatigue

Abstract: — The notch size effect (i.e. the decrease of the notched fatigue limit with increasing notch size for the same stress concentration factor) was quantitatively derived by describing the threshold conditions for the propagation of a short semi-elliptical crack nucleated at the notch root. A close relation between the Kitagawa—Takahashi diagram for the short crack threshold stress and the dependence of the notched fatigue limit on the notch size was shown. The derived relation for the notch size effect was experimentally verified for several specimen/notch geometries in the cases of pressure vessel steel and copper.

Fatigue of thick‐section cold‐expanded holes with and without cracks

Abstract: — Fatigue tests under spectrum loading were conducted to evaluate hole cold-expansion in thick-section open-hole aluminium alloy specimens, some of which contained residual fatigue cracks before cold expansion. Cold expansion resulted in an increase in life by a factor of about 7. Small residual fatigue cracks did not inhibit the effectiveness of the cold-expansion process, indicating that it may not be essential to remove such cracks prior to hole cold-expansion. The increase in life is primarily associated with a reduced crack propagation rate compared with that for cracks from non-cold-expanded holes. Cold-expanded hole fractures displayed a marked disparity in crack depths adjacent to the two faces of the specimens. Considerable differences were evident in crack depths and fatigue crack areas at failure between cold-expanded and non-cold-expanded hole specimens. These findings have ramifications in the damage tolerance assessment of aircraft structures.

Thermo-viscoelastic analysis of composite materials

Abstract: The thermo-viscoelastic boundary value problem for anisotropic materials is formulated and a numerical procedure is developed for the efficient analysis of stress and deformation histories in composites. The procedure is based on the finite element method and therefore it is applicable to composite laminates containing geometric discontinuities and complicated boundary conditions. Using the present formulation, the time-dependent stress and strain distributions in both notched and unnotched graphite/epoxy composites have been obtained. The effect of temperature and ply orientation on the creep and relaxation response is also studied.

Mode I stress intensity factors induced by fracture surface roughness under pure mode III loading: Application to the effect of loading modes on stress corrosion crack growth

Abstract: A model to estimate the reduction of effective crack tip Mode III stress intensity factors by frictional and asperity interaction of an idealized fracture surface is described An extension of the model is used to calculate the Mode I stress intensity factors due to the crack tip opening displacement induced by the mismatch of the fracture surface asperities The results of calculations based on a “reasonable” fracture surface profile are used to analyze experimental studies designed to determine the relative significance of hydrogen embrittlement and crack tip dissolution in stress corrosion crack growth in Al alloys by comparison of Mode I and Mode III stress corrosion cracking (SCC) resistance It is concluded that a pure Mode III stress state is not possible for cracks with microscopically rough surfaces and that the magnitude of the induced Mode I stress intensity factor is sufficient to cause stress corrosion crack growth

The role of crack tip strain rate in the stress corrosion cracking of high strength steels in water

Abstract: Creep tests have been performed on fracture mechanics specimens of as-quenched 4340 and 3.5NiCrMoV rotor steel to confirm the importance of crack tip strain rate in causing stress corrosion cracking. By allowing creep in a noncracking environment, dry air for the high strength steels tested, cracking did not occur when water, the corrosive solution, was later added to the system. Thus, it is possible to inhibit stress corrosion in spite of conditions otherwise conducive to crack growth. Conditions necessary to restart cracking were also tested. The importance of this result in terms of the mechanism of stress corrosion and difficulties in measuring KISCC is discussed.

Fracture and fatigue crack propagation in a nickel-base metallic glass

Abstract: This work is an investigation of fracture and fatigue in thin ribbons of a nickel-base metallic glass: Ni78Si10B12. The fracture and fatigue crack propagation behavior of this high tensile strength and high toughness amorphous alloy is of interest for two reasons: (1) the alloy, has no normal microstructure, and (2) the alloy shows an unusual form of plastic deformation which proceeds by nucleation and propagation of localized shear bands. On uniaxial tensile loading, failure of uniform ribbons occurs instantaneously at the yield stress by shear rupture through an intense shear band inclined at 55 deg to the loading axis. The development of a local plastic zone at the crack tip in single edge-notched specimens under monotonic tensile loading has been studied by a replication technique. Under plane stress conditions, these plastic zones are dominated by shear bands elongated in the direction of crack extension. Dugdale's “strip yield” model offers a reasonable description of the plastic zone sizes and displacements at the crack tip. The relationship between fatigue crack growth per, cycle,da/dN, and the alternating stress intensity factor, ΔK, has been determined atR=0.1. For growth rates in the range 10−6 through 5×10−4 mm/cycle, the Paris law (with an exponentm∼-2) is obeyed. The mechanism of fatigue crack extension is shown to depend on the deformation microstructure of the alloy. At intermediate growth rates, the plastic zone consists of a number of shear bands similar in shape to the Prandtl slip line field for nonhardening materials. Decohesion along these bands produces undulating fracture morphologies. At near threshold values of ΔK, growth rates deviate from the Paris law producing an extremely low ΔK TH (=0.5 MPa { % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpiZxe9LqFHe9Lq% pepeea0xd9q8as0-LqLs-Jirpepeea0-as0Fb9pgea0lrP0xe9Fve9% Fve9qapdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaie% aacaWFTbaaleqaaaaa!396B! $$\sqrt m $$ }). This is attributed to the ease of shear band nucleation, and a simple geometrical model of crack growth at low ΔK levels is proposed.

Crack growth in transforming ceramics under cyclic tensile loads

Abstract: The mechanisms of stable growth of short fatigue cracks (crack length up to 1 mm) at room temperature in magnesia-partially stabilized zirconia subjected to cyclic tensile loads were investigated. Single edge-notched specimens were fractured in the four-point bend configuration under cyclic and quasi-static tensile loads. At a load ratio of 0.1, the threshold stress intensity factor range, ΔK, for fracture initiation in cyclic tension is as low as 3.4 M Pam1/2, and catastrophic failure occurs at ΔK=6.6 M Pam1/2. For crack length less than 1 mm and for plane strain conditions, growth rates are highly discontinuous, and periodic crack arrest is observed after growth over distances of the order of tens of micrometres. Crack advance could only be resumed with an increase in the far-field stress intensity range. The mechanisms of short crack advance in cyclic tension are similar to those observed under quasi-static loads, and the tensile fatigue effect appears to be a manifestation of “static failure modes”. A model is presented to provide an overall framework for the tensile fatigue crack growth characteristics of partially stabilized zirconia. Experimental results are also described to demonstrate the possibility of stable room temperature crack growth under cyclic tension in fine-grained tetragonal zirconia polycrystals, partially stabilized with Y2O3. The growth of cracks in transformation-toughened ceramics is found to be strongly influenced by the crack size and shape, stress state and specimen geometry.