Showing papers on "Stress concentration published in 1986"

Mechanics of engineering materials

Abstract: Preface to second edition. Preface to first edition. Notation. 1. Statically Determinate Force Systems. 2. Statically Determinate Stress Systems. 3. Stress-Strain Relations. 4. Statically Indeterminate Stress Systems. 5. Torsion. 6. Bending Stress. 7. Bending: Slope and Deflection. 8. Statically Indeterminate Beams. 9. Energy Methods. 10. Buckling Instability. 11. Stress and Strain Transformations. 12. Yield Criteria and Stress Concentration. 13. Variation of Stress and Strain. 14. Application of the Equilibrium and Strain-Displacement. 15. Elementary Plasticity. 16. Thin Plates and Shells. 17. Finite Element Method. 18. Tension, Compression, Torsion and Hardness. 19. Fracture Mechanics. 20. Fatigue. 21. Creep and Viscoelasticity.

Small Fatigue Cracks

Abstract: This book contains over 30 papers. Some of the titles are: Overview of the Small Crack Problem; Fatigue Crack Initiation along Slip Bands; Small Crack-Environment Interactions: The Hydrogen Embrittlement Perspective; High Resolution Techniques for the Study of Small Cracks; and Crack Inititiation and Growth Under Far-Field Cyclic Compression: Theory, Experiments and Applications.

Shear fracture tests of concrete

Abstract: Symmetrically notched beam specimens of concrete and mortar, loaded near the notches by concentrated forces that produce a concentrated shear force zone, are tested to failure. The cracks do not propagate from the notches in the direction normal to the maximum principal stress but in a direction in which shear stresses dominate. Thus, the failure is due essentially to shear fracture (Mode II). The crack propagation direction seems to be governed by maximum energy release rate. Tests of geometrically similar specimens yield maximum loads which agree with the recently established size effect law for blunt fracture, previously verified for tensile fracture (Mode I). This further implies that the energy required for crack growth increases with the crack extension from the notch. The R-curve that describes this increase is determined from the size effect. The size effect also yields the shear fracture energy, which is found to be about 25-times larger than that for Mode I and to agree with the value predicted by the crack band model. The fracture specimen is simple to use but not perfect for shear fracture because the deformation has a symmetric component with a non zero normal stress across the crack plane. Nevertheless, these disturbing effects appear to be unimportant. The results are of interest for certain types of structures subjected to blast, impact, earthquake, and concentrated loads.

Non‐damaging notches in fatigue*

Abstract: The fact that very small notches (cavities, holes, scratches, etc.) have no effect on the fatigue limit of metallic materials is well known. This paper presents both a qualitative explanation for the existence of non-damaging notches and a quantitative derivation of their critical sizes. The condition for a notch (characterized by the stress concentration factor Kt and the notch root radius ρ) to be non-damaging in a metallic material (characterized by a critical crack size l0) is (K2t− 1)ρ≤ 4.5 l0. The critical crack size can be expressed with good approximation in terms of the threshold stress intensity for fatigue crack growth and the plain fatigue limit. Therefore the above relation can be applied for an engineering evaluation of non-damaging notches. Test results obtained for copper and a pressure vessel steel demonstrate the applicability of the proposed method.

The Bauschinger and Hardening Effect on Residual Stresses in an Autofrettaged Thick-Walled Cylinder

Abstract: : Most of the earlier solutions for residual stresses were based on the assumption of elastic unloading and only a few considered reverse yielding. In this report a new theoretical model for a high strength steel is proposed and a closed-form solution for calculating residual stresses in autofrettaged tubes has been obtained. The new results indicate that the influence of the combined Bauschinger and hardening effects on the residual stress distribution is significant.

Mechanical property changes in sapphire by nickel ion implantation and their dependence on implantation temperature

Abstract: Sapphire plates, cut parallel to an {0001} plane, have been implanted with 300 keV nickel ions to doses ranging from 5×1012 to 1×1017 Ni cm−2 at specimen temperatures of 100, 300 and 523 K, in order to investigate the effect of implantation temperature on the mechanical property changes in sapphire caused by ion implantation. The measured changes in surface hardness, surface fracture toughness and bulk flexural strength were found to depend strongly on the implantation temperature, and were largely correlated with the residual surface compressive stress measured by using a cantilever beam technique. The surface amorphization that occurred only by the implantation at 100 K and at doses larger than ∼2×10s15 Ni cm−2 reduced the hardness to ∼0.6 relative to the value of the unimplanted sapphire, and considerably increased the surface plasticity. Furthermore, the amorphization was found to involve a large volume expansion of ∼30% and to change drastically the apparent shape and size of a Knoop indentation flaw made prior to implantation. This effect was suggested to reduce stress concentrations at surface flaws and hence to increase the flexural strength.

Growth behavior of surface cracks in the circumferential plane of solid and hollow cylinders

Abstract: Experiments were conducted to study the growth behavior of surface fatigue cracks in the circumferential plane of solid and hollow cylinders. In the solid cylinders, the fatigue cracks were found to have a circular arc crack front with specific upper and lower limits to the arc radius. In the hollow cylinders, the fatigue cracks were found to agree accurately with the shape of a transformed semiellipse. A modification to the usual nondimensionalization expression used for surface flaws in flat plates was found to give correct trends for the hollow cylinder problem.

Plastic near-tip fields for branched cracks

Abstract: A procedure is outlined whereby the plastic near-tip stress and deformation fields for branched cracks are determined under plane strain and small scale yielding conditions. This method utilizes the known elastic stress intensity factor solutions and the universal mixed-mode plastic near-tip fields to determine the stress and deformation conditions at the tip of a kinked or forked crack. The plastic near-tip fields are characterized by an amplitude and a mixity parameter. We examine the influence of crack tip plasticity and material strain hardening characteristics on the local stress and strain states. Possible beneficial effects of crack branching and crack tip plasticity on fracture toughness and crack growth resistance are discussed in the light of these results.

Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites

Abstract: An elasticity solution is utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness (C-rr) is greater than the hoop stiffness (C-theta-theta). Conversely, if C-rr is less than C-theta-theta the maximum stress in the composite is finite and occurs at the fiber-matrix interface. In both cases the stress distributions are radically different than those predicted assuming the fiber to be transversely isotropic (C-rr = C-theta-theta). It is also shown that fiber volume fraction greatly influences the stress distribution for transversely isotropic fibers, but has little effect on the distribution if the fibers are transversely orthotropic.

The growth of small fatigue cracks in a low carbon steel; the effect of microstructure and limitations of linear elastic fracture mechanics

Abstract: The growth characteristics of small fatigue cracks were studied under rotary bending in a low carbon steel prepared with two ferrite grain sizes of 24 and 84 μm, and were compared with the growth characteristics of large through cracks in fracture mechanics type specimens. The effect of microstructure on crack growth rates and the interaction in growth behaviour between two neighboring small cracks were examined experimentally, and also the critical crack lengths above which linear elastic fracture mechanics (LEFM) is applicable were evaluated for small crack growth and for fatigue crack thresholds. It is found that small cracks grow much faster than large ones and also show growth rate perturbations due to grain boundaries. It is indicated that the critical crack lengths for fatigue crack thresholds are significantly shorter than those for small crack growth.

Response of Quasi-Isotropic Carbon/Epoxy Laminates to Biaxial Stress

Abstract: The results of biaxial tension tests on AS4/3501-6 carbon/epoxy are presented for a quasi-isotropic [90, ±45,0]s laminate. These tests were performed using a tubular spec imen subjected to internal pressure and axial tension. The specimen design appears to minimize stress concentrations in the gage section. The measured stress-strain response shows a small but definite reduction in stiffness associated with progressive matrix failure. The failure stresses and strains are consistent with a maximum fiber strain failure criterion, and are most accurately modeled with a progressive failure model that incor porates ply stiffness changes.

Transient crack growth under creep conditions

Abstract: Transient crack growth in an elastic/power-law creeping material is investigated under antiplane shear loading and small-scale-yielding conditions. At time t = 0 the solid is suddenly loaded far from the crack by tractions that correspond to the elastic crack-tip stress distribution. At that time the crack begins to propagate at a constant velocity. The stress fields evolve in a complex manner as the crack propagates due to the competing effects of stress relaxation due to constrained creep and stress elevation due to the instantaneous elastic material response to crack growth. From detailed finite element calculations it is shown that these fields can be approximated by a simple matching of three asymptotic singular crack-tip solutions. A characteristic stress, distance and time are defined for this problem which provide a normalization that accounts for any crack velocity, loading and all material properties for a given creep exponent n . Results are presented for crack-tip stresses, strains, crack opening displacements and creep zones.

Fatigue crack propagation in Ni-base superalloy single crystals under multiaxial cyclic loads

Abstract: The effects of crystallographic orientation and stress state on the multiaxial fatigue behavior of MAR-M200* single crystals were examined Using notched tubular specimens subjected to combined tension/torsion cyclic loads, crack growth rates were determined at ambient temperature as functions of stress intensity range, the shear stress range-to-normal stress range ratio, and crystallographic orientation Comparison of crack growth data at the same effective ΔK reveals a weak dependence of the crack growth rate on both the tube axis and the notch orientation For a given set of tube axis and notch orientation, the crack growth rate might or might not vary with the applied stress state, depending on whether roughness-induced crack closure is present In most cases, subcritical cracking occurs either along a single 111 slip plane or on ridges formed with two 111 slip planes Neither fracture mode is altered by a change in the applied stress state This complex crack growth behavior will be discussed in terms of the crack-tip stress field, slip morphology, and crack closure

An assessment of the small-crack effect for 2024-T3 aluminum alloy

Abstract: Data on small-crack behavior were obtained for a single-edge-notched tensile specimen made of 2024-T3 Al alloy and used to evaluate the capability of a semiempirical crack-growth and closure model to predict the fatigue life of notched specimens. Fatigue tests were conducted under either constant-amplitude loading (with stress ratios of 0.5, 0, -1, and -2) or spectrum loading, using a replication technique to record growth. It was found that small cracks exhibited the 'small-crack' effect in that they grew faster than large cracks when subjected to the same stress intensity factor range. Experimental small-crack growth rates agreed well with the model predictions. For making predictions of fatigue life, an initial surface defect void size of 3 x 12 x 0.4 microns was used in all calculations; predicted fatigue lives agreed well with experimentally determined values obtained in all tests. The crack-closure model indicated that the 'small-crack' effect on fatigue life was greatest in tests involving significant compressive loads.

Stress corrosion cracking of Lac du Bonnet granite in tension and compression

Abstract: Rocks subjected to long-term loading have been known to suffer microcracking. The rate of cracking is sensitive to the type of the applied stress (tensile or compressive), and the magnitude of the stress relative to the instantaneous strength. In addition, crack growth is influenced by the environment (pressure and temperature) including the presence or absence of moisture. For tensile loading, the sensitivity of granite to time-dependent cracking is demonstrated through a fracture mechanics test known as double torsion. The crack velocity versus stress intensity function is established for two environments, room temperature and humidity and room temperature and 100 percent humidity. For compressive loading, time dependent cracking is evaluated from creep tests conducted in uniaxial compression in the same two environments. The rate of cracking is defined by finding the functional relationship between the rate of crack growth, expressed as the rate of crack volume strain, and uniaxial compressive stress. A variety of mathematical functions has been fitted to the obtained data. The traditionally-used power and exponential relationships give good correlation for both crack velocity and crack volume strain rate. The crack volume strain rate versus stress function can be integrated to obtain a lifetime estimate for Lac du Bonnet granite. After 1 000 years of loading in uniaxial compression at room temperature and 100 percent humidity, the strength of this granite could reduce from 225 MPa to 90–100 MPa.

Thermal Expansion of Elastic-Plastic Composite Materials.

Abstract: : Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stifness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also the local instantaneous thermal strain and stress concentration factors are related in an exact way to the corresponding mechanical concentration factors. The results depend on instantaneous thermoelastic constants and volume fractions of the phases. They are found for fibrous composites with two distinct elastically isotropic or transversely isotropic phases, and for any binary composite with elastically isotropic phases. The results indicate that in the plastic range the thermal and mechanical loading effects are coupled even if the phase properties of not depend on changes in temperature. The derivation is based on a novel decomposition procedure which indicates that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase eigen-strains with local strains caused by piecewise uniform strss fields which are in equilibrium with prescribed surface tractions. The method is extended to discretized microstructures, and also to analysis of moisture absorption and phase transformation effects on overall response and on local fields in the two composite materials. (Author)