Showing papers on "Stress concentration published in 1980"

Tensile Cracks in Creeping Solids

Abstract: The aim of the paper is to answer the question: which loading parameter determines the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions? As candidates for relevant loading parameters, the stress intensity factor K I , the path-independent integral C*, and the net section stress σ n e t have been proposed in the literature. The answer, which is attempted in this paper, is based on the time-dependent stress analysis of a stationary crack in Mode I tension. The material behavior is modeled as elastic-nonlinear viscous, where the nonlinear term describes power law creep. At the time t = 0, load is applied to the cracked specimen, and in the first instant the stress distribution is elastic. Subsequently, creep deformation relaxes the initial stress concentration at the crack tip, and creep strains develop rapidly near the crack tip. These processes may be analytically described by self-similar solutions for short times t. An important result of the analysis is that small-scale yielding may be defined. In creep problems, this means that elastic strains dominate almost everywhere except in a small "creep zone" which grows around the crack tip. If crack growth ensues while the creep zone is still small compared with the crack length and the specimen size, the stress intensity factor governs crack growth behavior. If, however, the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can be neglected. In this limiting case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity that has been treated in the literature. The loading parameter that determines the near tip fields uniquely is then the path-independent integral C*. It should be emphasized that K 1 and C* characterize opposite limiting cases. Which case applies in a given situation can be decided by comparing the creep zone size with the specimen size and the crack length. Criteria for small-scale yielding are worked out in several alternative forms. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived also, which characterizes the transition from small-scale yielding to extensive creep of the whole specimen.

Crack blunting mechanisms in polymers

Abstract: A quantitative model has been developed to account for the degree of blunting that occurs at crack tips in epoxy materials prior to the onset of crack propagation. This mechanism controls the subsequent mode of crack growth and, to a large extent, the toughness as defined by the stress intensity factor for crack initiation. From this model a unique fracture criterion is derived which is applicable over all modes of crack propagation.

Microcrack closure in rocks under stress: Direct observation

Abstract: Direct observations of the closure of microcracks in rocks under increasing stress are reported. Uniaxial stresses up to 300 bars were applied to untreated and previously heated samples of Westerly granite and Frederick diabase by a small hydraulic press which fit entirely within a scanning electron microscope. Crack closure characteristics are found to depend on crack orientation, with cracks perpendicular to the applied stress closing and those parallel tending to open, as well as crack aspect ratio, crack intersection properties, stress concentrations and surface roughness. Uniaxial and hydrostatic stress measurements are found to be strongly dependent on fracture content as observed by SEM, and the observed hysteresis in strain measurements in the first stress cycles is also related to microscopic processes

Materials Science Comparative Evaluation of Ceramic-metal Bond Tests Using Finite Element Stress Analysis

Abstract: Eleven porcelain-fused-to-metal bond tests were analyzed for interfacial shear stress distribution using finite-element stress analysis. Stress concentration effects are significant in ten of the 11 tests. A high probability of tensile failure within porcelain or the interfacial region was found in eight of the 11 tests analyzed.

The effects of confining pressure and stress difference on static fatigue of granite

Abstract: Samples of Barre granite were creep tested at room temperature at confining pressures up to 2 kilobars. The time to fracture increased with decreasing stress difference at every pressure, but the rate of change of fracture time with respect to the stress difference increased with pressure. At 87% of the short-term fracture strength, the time to fracture increased from about 4 minutes at atmospheric pressure to longer than one day at 2 Kb of pressure. The inelastic volumetric strain at the onset of tertiary creep, delta, was constant within 25% at any particular pressure but increased with pressure in a manner analogous to the increase of strength with pressure. At the onset of tertiary creep, the number of cracks and their average length increased with pressure. The crack angle and crack length spectra were quite similar, however, at each pressure at the onset of tertiary creep.

Mechanically-Fastened Joints for Advanced Composites — Phenomenological Considerations and Simple Analyses

Abstract: The various factors affecting the strength of bolted or riveted joints in advanced composites are discussed qualitatively. The mechanisms associated with each failure mode — tension, bearing, shearout, cleavage, and pull-through — are explained. The work is based mainly on experimental observations, from which conclusions have been drawn to integrate the study. A simple theory to account for the elastic stress concentrations at loaded bolt holes, in terms of the various geometric parameters, is deduced from experimental and analytical evidence for isotropic materials. Further tests on composite materials are used to deduce correlation factors which relate this theory to the limited, but significant, stress concentration relief observed prior to failure. The combination of these theories permits a considerable generalization from limited test data to geometries for which no test data are available, but does need some testing for that specific composite material and fiber pattern. The interaction of stress concentration factors caused by bearing and bypass loads is explained. The theories above are shown to cover such combined load cases, as at multi-row bolted joints, and along spar caps and consistency with test data is shown. Not all load cases are usually covered by test programs, so the use of this theory to extend results to such cases as bearing loads applied orthogonally to the bypass load is explained, along with cautions about known limits on such techniques. No attempt is made to compile a comprehensive data bank of test data, but the examples presented do cover a sufficiently diverse range of fiber patterns to elucidate the known failure phenomena. The need to consider advanced composites not as homogeneous orthotropic materials but as two-phase mixtures of fibers and resin is highlighted by the observations on the benefits and problems associated with interference-fit fasteners in composites. The sequence of first failure of the resin (by delamination or disbonding of the fibers) and second of the fibers (by tension) is shown to explain the strength increases resulting from nonlinearity.

Grain Boundary Segregation and Intergranular Fracture in Molybdenum

Abstract: The refractory group VIA metals generally exhibit intergranular brittleness when they are in the recrystallized condition. This causes severe problems in their fabrication and places major limitations on their practical application. The phenomenon, generally referred to as recrystallization embrittlement, results in large increases in the ductile-to-brittle transition temperature and a change in fracture mode in the lower shelf regime from cleavage to intergranular with a significant decrease in ductility. The embrittlement is widely considered to be associated with interstitial impurities but there have been few systematic studies to elucidate their effects. The present paper reports results from a systematic study of segregation and intergranular embrittlement in binary molybdenum-oxygen and ternary molybdenum-oxygen-carbon alloys. The experiments were carried out on ‘bamboo’ specimens containing a series of identical single grain boundaries traversing their cross-sections. Measurements have been made of the activation energy for oxygen segregation to grain boundaries in the binary molybdenum-oxygen alloys. The influence of carbon additions on the level of oxygen segregation has also been determined. In addition, the influence of oxygen segregation on the energy to fracture has been studied and this has involved quantitative measurements of the work of fracture and the contribution made by plastic deformation. Results from metallographic studies are also presented, showing the effects of segregation on fracture surface topography and dislocation structures immediately adjacent to the fracture surfaces. In discussing the results we consider the thermodynamics of oxygen segregation to grain boundaries and the role played by carbon in inhibiting segregation. It is proposed that carbon either increases the effective solubility of oxygen in molybdenum or acts as a trap for oxygen atoms. In either case the effect is to reduce the driving force for segregation. We also consider the influence of segregation on the work of fracture and show that the reduction in oxygen segregation resulting from the addition of carbon produces small increases in fracture energy. This increases the local stress to propagate a crack sufficiently to promote plastic deformation which blunts the crack tip. The consequent change in geometry reduces the stress concentration at the crack tip, thereby resulting in a large increase in the applied fracture stress and the work to fracture.

The effect of particle shape on the mechanical properties of filled polymers

Abstract: The existing models for predicting the elastic moduli of polymers dispersed with particles of shape other than spheres and continuous fibres are reviewed. The applicability and limitation of these equations are discussed. The emphasis of the review is to seek a unified understanding and approach to the effect of particle shape at finite concentration on the elastic moduli, thermal expansion coefficient, stress concentration factor, viscoelastic relaxation modulus and creep compliance of filled polymers. The effects of anisotropic particle shape on mechanical properties of polymeric composites are clearly illustrated. Attention is also drawn to the relationship between elastic moduli, thermal expansion, creep elongation and stress relaxation moduli.

Stress intensity factors and COD in an orthotropic strip

Abstract: The elasticity problem for an orthotropic strip or a beam with an internal or an edge crack under general loading conditions is considered. The numerical results are given for four basic loading conditions, namely, uniform tension, pure bending, three point bending, and concentrated surface shear loading. For the strip with an edge crack additional results regarding the crack opening displacements are obtained by using the plastic strip model. A critical quantity which is tabulated is the maximum compressive stress in the plane of the crack. It is shown that this stress may easily exceed the yield limit in compression and hence may severely limit the range of application of the plasticity results.

Stress analysis of a semi-infinite plate with an oblique edge crack

Abstract: A semi-infinite plate with an oblique edge crack is analyzed as a thin plate bending problem and a plane elastic problem. The rational mapping function of the sum of fractional expressions and the complex variable method are used. Closed solutions are obtained for these respective problems. Stress distributions, stress intensity factors are investigated for loads causing transverse bending, twisting and uniform tension. The relations between the stress intensity factors and the angle of the oblique edge crack are also investigated.

Appraisal of biaxial strength testing

Abstract: Three biaxial strength tests (ring-on-ring, piston-on-3 ball, and ball-on-ring) were evaluated using finite element analysis. Although in all three tests some uncertainties exist regarding the calculation of fracture stresses from the analytical equation, if fracture occurs within the loading ring, the ring-on-ring loading is thought to give the most accurate measure of strength. In addition, it was found that specimen shape (square vs. circular) had no effect on the stress distribution within the supports and that the stress at the edge of the specimen was less than 10% of the maximum stress for an overhang greater than about 40%. Fracture strength measurements on soda-lime glass gave support to these finite element results.

Incomplete self‐similarity of fatigue in the linear range of crack growth

Abstract: —The application of dimensional analysis and similarity methods to the study of the speed of fatigue crack growth is considered. It is shown that the Paris range of the crack propagation diagram is an intermediate-asymptotic stage of the crack growth process. Over this stage the influence of the initial conditions on the process of fatigue crack growth has disappeared but the influence of the instability has not yet intruded. So-called incomplete self-similarity prevails at this stage with respect to a basic similarity parameter, equal to the ratio of the stress intensity factor amplitude to the fracture toughness. It is shown that for a certain material under fixed external loading conditions the exponent in the Paris power law is a universal function of the ratio of specimen thickness to the ultimate size of the cyclic plastic zone. Processing of available experimental data confirmed the results obtained by this approach.

Crack velocity dependence of longitudinal fracture in bone

Abstract: An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G c) and critical stress intensity factor (K c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10−5 m sec−1 produced increases in G c (from 1736 to 2796 J m−2), K c (from 4.46 to 5.38 MN m−3/2) and W. At crack velocities >23.6×10−5 m sec−1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec−1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.

Tensile First Cracking Strain and Strength of Hybrid Composites and Laminates

Abstract: A hybrid like a multidirectional laminate contains at least two major load-bearing components whose failure strains are different. The failure strain of the higher elongation component is invariably reduced by the presence of the other, but the ultimate strain of the lower elongation component may remain the same or can be increased by decreasing its dimensions. The relevant dimension may be the diameter of a bundle or of separate fibres or the thickness of the transverse ply in a 0 degrees /90 degrees laminate. Our previous theory of multiple cracking and constrained failure is reviewed and applied to simple laminates and laminated hybrids. We also demonstrate that it can be applied to preventing cracking due to thermal strain. It is pointed out that, in 0 degrees /90 degrees /0 degrees laminates, longitudinal splitting of the 0 degrees plies may occur owing to the constraint imposed by the 90 degrees plies, whether these have cracked or not. Simple rules are given to account for the longitudinal ultimate strength and ultimate fracture strain of intermingled glass and carbon hybrids in epoxy resin. In this system, stress concentrations due to failure of the low elongation component do not appear to be very important.

Stress distributions along a short fibre in fibre reinforced plastics

Abstract: This paper develops an analysis for predicting the normal stress and interfacial shearing stress distribution along a single reinforcing fibre of a randomly oriented chopped-fibre composite, such as sheet moulding compound (SMC), from a knowledge of the constituent properties and the length-to-diameter ratio of the fibres. The analysis is useful in analysing the tensile strength of SMC, and as a guide to increasing the tensile strength by altering the elastic characteristics. The model is based on a generalized shear-lag analysis. Numerical values of the normal stress and interfacial shearing stress are presented as functions of various parameters. It is observed that the maximum normal stress occurs at the middle of the fibre and the maximum shear stress occurs at the end. The analysis is restricted to loading which does not result in buckling of the fibre; i.e., axial loads on the fibre can be at most only slightly compressive.

The influence of grain orientation on the mode and rate of fatigue crack growth in α -titanium

Abstract: The high cycle fatigue crack growth characteristics of coarse grainedα-titanium have been studied in vacuum, air, water and brine. Tests were carried out on single-edge-notch tension test-pieces at anR ratio of 0.35, a frequency of 130 Hz, and a ΔK range of 5 to 25 MPa-√m. The use of channelling patterns in the SEM permitted detailed crystallographic information to be correlated with fatigue fracture morphologies. Three distinct modes of fatigue crack growth were identified. Cleavage-like facets on the basal planes (0002); the formation of which was encouraged by increasing severity of environment and increasing stress normal to (0002), striations on planes normal to (0002) consistent with a mechanism involving intersecting prism slip systems, and furrows in the [0001] direction associated with fine lines parallel to the 1123 direction. It is shown how the relationships between grain orientation, stress geometry and testing environment may be presented in the form of Grain Orientation Control Maps. The rate of fatigue crack growth in individual grains was dominated by the mode of growth; below a ΔK of 10 MPa√m the cleavage-like mode was up to 10 times more rapid than the other modes of growth.

The effect of fretting and environment on fatigue crack initiation and early propagation in a quenched and tempered 4130 Steel

Abstract: Fretting fatigue studies were performed on quenched and tempered 4130 steel in laboratory air and in argon as functions of relative slip displacement, normal pressure and applied cyclic stress. Significant reductions in fatigue resistance were observed at all stress levels and increased with increasing normal pressures. However, a minimum in resistance was observed for relative slip magnitudes of 20 to 30 μm. Inert environments improve fatigue resistance under fretting conditions. Metallographic observations indicated that subsurface cracking was generally observed and that stress concentrations associated with this cracking resulted in deviations to and away from the faying surfaces. Fretting cracks which deviated into the alloy become initiated fatigue cracks. A mechanical model is proposed for fretting induced fatigue crack initiation which suggests that this phenomenon is a simple extension of the basic fretting process.

Fatigue crack growth in polymers

Abstract: A number of fatigue crack propagation laws applied in the study of polymers is described. Consideration of the stress field distribution at the crack tip leads to the application of fracture mechanics. It is shown that a simplified relationship of the form da/dN =Fλα, whereφ is a function ofKIC,Kmax,Kmin andKTH appears to be a convenient expression for cyclic crack growth. The effect of mean stress is more complicated than that in the field of metals, the compressive component of cyclic stress may delay the crack growth. Cyclic tests in tension performed on PMMA and PVC are dependent on ΔK and its mean value,K m . The threshold value,KTH, is also influenced byK m but a more complicated behaviour due to strain rate effects may be observed. Other differences, such as the position of upper and lower transition points and growth rate changes with frequence, are noted. The effect of biaxial cyclic loading of PMMA and PVC plates is compared and some differences highlighted. The results available so far indicate little effect of the crack curving on its growth. However, it is shown that, while the increasing biaxiality can substantially retard the crack growth in PMMA, no such effect was recorded in PVC. Finally, it is shown that at very high stress levels (region III), the cyclic crack growth consists of two propagation modes, namely, a pure cyclic propagation, together with slow growth. At lower stress levels, slow growth disappears and the crack propagates in pure fatigue (region II). In region I, the propagation is very slow, without the usual correspondence between cycles and striations. The results recently obtained on glass reinforced plastics (GRP) are also presented and differences highlighted.