Showing papers on "Stress concentration published in 1983"

Crack deflection: Implications for the growth of long and short fatigue cracks

Abstract: The influences of crack deflection on the growth rates ofnominally Mode I fatigue cracks are examined. Previous theoretical analyses of stress intensity solutions for kinked elastic cracks are reviewed. Simple elastic deflection models are developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates. Experimental data are presented for intermediate-quenched and step-quenched conditions of Fe/2Si/0.1C ferrite-martensite dual phase steel, where variations in crack morphology alone influence considerably the fatigue crack propagation rates and threshold stress intensity range values. Such results are found to be in good quantitative agreement with the deflection model predictions of propagation rates for nonlinear cracks. Experimental information on crack deflection, induced by variable amplitude loading, is also provided for 2020-T651 aluminum alloy. It is demonstrated with the aid of elastic analyses and experiments that crack deflection models offer a physically-appealing rationale for the apparently slower growth rates of long fatigue cracks subjected to constant and variable amplitude loading and for the apparent deceleration and/or arrest of short cracks. The changes in the propagation rates of deflected fatigue cracks are discussed in terms of thelocal mode of crack advance, microstructure, effective driving force, growth mechanisms, mean stress, slip characteristics, and crack closure.

Stress in elastic plates reinforced by fibres lying in concentric circles

Abstract: W e Consider fibre-reinforced elastic plates with the reinforcement continuously distributed in concentric circles ; such a material is locally transversely isotropic, with the circumferential direction as the preferred direction. For an annulus bounded by concentric circles, the exact solution of the traction boundary value problem is obtained. When the extension modulus in the fibre direction is large compared to other extension and shear moduli, the material is strongly anisotropic. For this case a simpler approximate solution is obtained by treating the material as inextensible in the fibre direction. It is shown that the exact solution reduces to the inextensible solution in the appropriate limit. The inextensible theory predicts the occurrence of stress concentration layers in which the direct stress is infinite ; for materials with small but finite extensibility these layers correspond to thin regions of high stress and high stress gradient. A boundary layer theory is developed for these regions. For a typical carbon fibre-resin composite, the combined boundary layer and inextensible solutions give an excellent approximation to the exact solution. The theory is applied to the problem of an isotropic plate, under uniform stress at infinity, containing a circular hole which is strengthened by the addition of an annulus of fibre-reinforced material.

Propagation and non-propagation of short fatigue cracks at a sharp notch

Abstract: — Sharply notched specimens of a structural low-carbon steel were fatigued under several ratios of the maximum to minimum loads. The growth behavior of a short fatigue crack near the notch tip was analyzed based on crack closure measurements. A fatigue crack first decelerates with increasing crack length, and then accelerates or becomes non-propagating depending on the applied stress. A similar deceleration is seen when the rate is correlated to the stress intensity range. The effective stress intensity range is a unique parameter in correlating the growth rate of a short crack for all the stress levels examined, and the relation is identical to that obtained for a long crack. By considering the increase in crack closure with crack length, a quantitative method is proposed for predicting the non-propagating crack length and the fatigue limit of notched specimens as a function of the applied stress and the notch geometry.

Roughness-Induced Crack Closure: An Explanation for Microstructurally Sensitive Fatigue Crack Growth

Abstract: The concept of roughness-induced crack closure is utilized to explain the role of prior austenite grain size and pearlite interlamellar spacing on near-threshold fatigue crack propagation in fully pearlitic eutectoid steel tested at low and high stress ratio in lab air and purified helium. It is shown that at low load ratios, near-threshold growth rates are significantly reduced for coarse-grained microstructures, compared to fine-grained at constant yield strength, due to roughness-induced crack closure. Using roughness-profile microscopy, it was found that fracture surface roughness near threshold scaled with grain size and inversely with yield strength, macroscopic roughnesses at threshold being considerably larger than the conventionally calculated cyclic crack tip opening displacement. Auger analysis of near-threshold corrosion products showed it to be iron oxide; the oxide thickness was seen to be decreased by increased stress ratio. The significance of this model to near-threshold fatigue crack growth behavior, in terms of load ratio, microstructure, and environment is discussed.

A microcrack model for the deformation and failure of brittle rock

Abstract: A continuum model derived from the mechanics of tensile microcracks is presented which describes the deformation of brittle rock. The model employs the assumption that stress and time-dependent microcrack growth is responsible for the inelastic deformation. Microcrack growth is assumed to occur by two mechanisms: stress-induced crack growth (time independent) and stress corrosion (stress and time dependent). From the analysis of individual cracks a criterion for the initiation of damage (crack growth) is derived. This results in the specification of initial and subsequent damage surfaces in stress space which are similar to yield surfaces in the theory of plasticity. When the stress state is below the damage surface, no stress-induced crack growth can take place. For stress states on the damage surface, crack growth accompanies any increase in loading, thus expanding the damage surface. By generalizing the results obtained from the analysis of single cracks, a continuum description of the behavior of an ensemble of cracks in an otherwise elastic body is derived. The resulting constitutive equation is essentially elastic but accounts for material behavior due to microcrack growth through the inclusion of an internal state variable which is a measure of the crack state. The form of the evolutionary equation for the crack state parameter is determined from the fracture mechanics analysis of single cracks and experimental results on time-dependent crack growth in rock. Model simulations of quasi-static uniaxial and triaxial compression tests are presented, and the results are compared to the results of a similar laboratory test on Westerly granite.

Grain boundary sliding and stress concentration during creep

Abstract: Importance of grain boundary sliding to creep intergranular fracture is focussed. Previous metallographic and fractographic studies of creep intergranular fracture on metal bicrystals and polycrystals are briefly reviewed in order to show the close relationship between grain boundary sliding and fracture. Deformation ledge and migration irregularity are shown to be potential sites of stress concentration and crack nucleation on sliding grain boundaries without particles. The effect of grain boundary structure on creep intergranular fracture is discussed on the basis of the effect of grain boundary structure on sliding, the contribution of sliding to the overall creep deformation, and a sliding-fracture diagram. Recent observations of the effect of grain boundary structure on creep intergranular fracture on alpha iron-tin alloy polycrystals are shown.

Breaking of a single asperity: Rupture process and seismic radiation

Abstract: The problem of spontaneous shear rupture of a single circular asperity on an infinite fault plane is studied. Initially, the fault plane is broken everywhere except at a circular asperity. An applied displacement at infinity results in a stress concentration along the bounding edge of the asperity. The frictional stress on the broken part of the fault plane is taken to be a constant. Once a point on the asperity breaks, the stress there drops to the same value as on the ‘main’ fault surface. The rupture is started by relaxing the shear stress at a point on the asperity edge and is then allowed to propagate spontaneously, using a critical stress level fracture criterion. The rupture process is calculated numerically. It is found that for asperities of constant strength, the rupture first propagates around the edge of the asperity and then inward, a phenomenon best described by the well-known term of classic military maneuver: ‘the double encircling pincer movement.’ In the appendix, the expressions for the far-field seismic radiation due to the rupture of such an asperity are derived. It is shown that the nth Cartesian component of the far-field displacement at (x, t) for P, SV, and SH waves, using the notation of Aki and Richards (1980), is given by un(x, t) = (Dni/4πρc2R)∫∫s0τi3{ξ, t − [(R − ξ · γ)/c]} dS(ξ). Thus the far-field pulses can be directly found from the stress drops on the fault plane. This formula is also true for ‘crack’ or ‘dislocation’ problems. The directivity function Dni for displacement for the asperity problem is found to be that for the double couple, modified by some factor. In particular, the fault plane is a nodal plane for SV waves. For the rupturing of asperities on a finite fault, these directivity functions are applicable only to the initial part of observed pulses at a receiver, provided the receiver is not located on the fault plane outside the broken part of the main crack edge, in which case it is inapplicable for all time.

Crack and cavity nucleation at interfaces during creep

Abstract: Athermal nucleation of microcracks and thermal nucleation of cavities during creep deformation are reviewed with an emphasis on effects of solute segregation to grain boundaries and cavity surfaces. The magnitude and the duration of stress concentration at a triple grain junction or at a grain boundary inclusion are estimated for transient Coble creep and steady state power-law creep conditions. Stable configurations of wedge-type microcracks are predicted by a Griffith-like crack model. The rate for thermal nucleation of cavities is obtained by the Fokker-Planck equation for vacancy clusters. Cracks and cavities are interdependent, and cavity nucleation occurs continuously throughout the three creep stages. The local stress concentration enhances microcrack and cavity nucleation. The cavity nucleation rate is generally increased as a result of solute segregation to the surfaces and interfaces and/or gas precipitation into cavity volume. This enhanced nucleation is more effective in a system with mobile solutes than with immobile solutes. Immobile solute or trace elements may affect the nucleation rate also by changing the grain boundary diffusivity. Experimental techniques for quantitative analyses of cavity nucleation processes are discussed.

Interaction of a dislocation with a crack

Abstract: A solution is given of the field equations of nonlocal elasticity for a line crack interacting with a screw dislocation in an elastic plane under antiplane shear loading. Displacement and stress fields are determined throughout the core region and beyond. In the case when the dislocation is absent, the circumferential stress is shown to vanish at the crack tip, increasing to a maximum along the crack line afterwards decreasing to its classical value at large distances from the crack tip. This is in contradiction with the classical elasticity solutions which predicts stress singularity at the crack tip and it is in accordance with the physical condition that the crack tip surface must be free of surface tractions. The presence of the dislocation alters the stress distribution considerably when it is close to the crack tip. The stress distributions in the core region are displayed. A fracture criterion based on the maximum stress is established and used to determine the theoretical strengths of pure crystals that contain a line crack. Results are in good agreement with those based on the atomic theories and experiments.

Mode III and Mode I fatigue crack propagation behaviour under torsional loading

Abstract: Fatigue crack growth rates have been measured under cyclic torsional loading (R = −1, 1 Hz loading frequency) in AISI 4340 steel tempered at 650° C, with circumferentiallynotched specimens (12.7 mm specimen diameter). The Mode III fatigue crack growth curve for macroscopically flat fracture surface — being obtained by an extrapolation procedure which eliminates the “Mode III crack closure” influence — has higher crack growth rates and shows a greater slope than Mode I results in the stress intensity range of ΔKIIIeff = 18 to 50 MPa m1/2. In the range of ΔKIIIeff < 18 MPa m1/2, the fracture surface has “factory roof” morphology (Mode I). The difference between fatigue crack growth behaviour in Mode III and Mode I as well as mechanisms that can lead to a fracture mode change are discussed. A comparison of the Mode III crack closure influence for specimen diameters of 12.7 mm (this study) and of 24.5 mm (an earlier study) shows that this influence is not only dependent on the depth of the crack and applied torque but also on the specimen diameter. The extrapolated crack growth rates show good agreement with measurements for various specimen diameters.

A Griffith crack shielded by a dislocation pile-up

Abstract: The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.

Near-threshold fatigue crack propagation: a perspective on the role of crack closure

Abstract: In recent years, mechanistic and continuum studies on fatigue crack propagation, particularly at near-threshold levels, have highlighted a dominant role of crack closure in influencing growth rate behavior In this paper we review and model the various sources of closure induced by cyclic plasticity, corrosion deposits, irregular fracture morphologies, viscous fluids and metallurgical phase transformations It is shown that many of the commonly observed effects of mechanical factors, such as load ratio, microstructural factors, such as strength and grain size, and certain environmental conditions can be traced to the extrinsic influence of closure in modifying the effective driving force for crack extension The implications of such closure mechanisms are discussed in the light of constant and variable amplitude fatigue behavior, the existence of a threshold stress intensity for no fatigue crack growth and the validity of such threshold concepts for the case of short fatigue cracks 106 references, 21 figures

The cyclicJ-integral as a criterion for fatigue crack growth

Abstract: The definition of the cyclic J-integral is offered and its physical significance for fatigue crack growth is discussed using the Dugdale model on the assumption that the crack closure, cycle dependent creep deformation, and crack extension under cycling can be neglected. It is shown that the cyclic J-integral for small scale yielding is equivalent to theJ-integral for linear elastic crack independent of loading processes, while the value for large scale yielding varies with the loading processes. However, in both cases, the cyclicJ-integral remains constant during the reversal of loading under a constant stress range, if the first monotonic loading stage is excluded. In this situation, the cyclicJ-integral can be applied as a criterion for fatigue crack growth, since it is evaluated as a generalized force on dislocations to be moved or the energy flow rate to be dissipated to heat by the dislocation movements in an element just attached to the fatigued crack tip during one cycle of loading. It is suggested that the available experimental data of different materials for fatigue crack growth can be generalized to a unified formulation on the basis of the energy criterion. It is also deduced that the threshold ΔJ corresponding to ΔKth should be larger than 4γ where γ is the surface energy of the material. Finally the operational definition of the cyclicJ-integral on single loadversus displacement curves is given for center cracked plate with wide uncracked ligaments in tension.

Short crack propagation and closure effects in a508 steel

Abstract: — Fatigue crack growth measurements are usually made on standard specimens containing long cracks (∼10 mm) although in most practical situations, a large part of the fatigue life is spent with much shorter dimensions. The purpose of the present study is a comparison of crack growth behaviour for long cracks (∼13–16 mm) in CT specimens and smaller ones (∼0.3–0.5 mm) in four point bend specimens. Large effects are noticed indicating that, at a given stress intensity factor amplitude, the crack growth rate is significantly higher in specimens with short cracks. Mouth displacement measurements for both specimen configurations show that the crack closure phenomenon accounts for the observed effect. Crack closure is likely to be associated with fracture surface roughness as shown by partly machining the material left behind the crack tip in CT specimens.