Showing papers on "Stress concentration published in 1999"

Factors influencing the mechanism of superlong fatigue failure in steels

Abstract: When the fatigue life N f of a specimen of 10 mm in thickness is longer than 10 8 cycles, the average fatigue crack growth rate is much less than the lattice spacing (∼0.1 A or 0.01 nm) that is 10 -11 to 10 -12 m/cycle. In the early stage of the fatigue process, the crack growth rate should be much less than the average growth rate, and accordingly we cannot assume that crack growth occurs cycle by cycle. In this paper, possible mechanisms for extremely high cycle fatigue are discussed. Of some possible mechanisms, a special focus was put on a newly found particular fatigue fracture morphology in the vicinity of the fracture origin (non-metallic inclusions) of a heat-treated alloy steel, SCM435, which was tested to N ≥ 10 8 . The particular morphology observed by SEM and AFM was presumed to be influenced by the hydrogen around inclusions. The predictions of the fatigue limit by the √area parameter model are ∼ 10% unconservative for a fatigue life of N f = ∼10 8 , though it successfully predicts the conventional fatigue limit defined for N = 10 7 . Thus, the fatigue failure for N ≥ 10 8 is presumed to be caused by a mechanism which induces breaking or releasing of the fatigue crack closure phenomenon in small cracks. In the vicinity of a non-metallic inclusion at the fracture origin, a dark area was always observed inside the fish-eye mark for those specimens with a long fatigue life. Specimens with a short fatigue life of N f = ∼10 5 do not have such a dark area in the fish-eye mark. SEM and AFM observations revealed that the dark area has a rough surface quite different from the usual fatigue fracture surface in a martensite lath structure. Considering the high sensitivity of high-strength steels to a hydrogen environment and the high hydrogen content around inclusions, it may be concluded that the extremely high cycle fatigue failure of high-strength steels from non-metallic inclusions is caused by environmental effects, e.g. hydrogen embrittlement coupled with fatigue.

Fundamentals of Machine Elements

Abstract: Part I - Fundamentals Introduction What is Design? Design of Mechanical Systems Design as a Multidisciplinary Endeavor Design of Machine Elements Computers in Design Catalogs and Vendors Units Unit Checks Significant Figures Summary Load, Stress, and Strain Introduction Critical Section Load Classification and Sign Convention Support Reactions Static Equilibrium Free-Body Diagram Supported Beams Shear and Moment Diagrams Stress Stress Element Stress Tensor Plane Stress Mohr's Circle Three-Dimensional Stresses Octahedral Stresses Strain Strain Tensor Plane Strain Summary Introduction to Materials and Manufacturing Introduction Ductile and Brittle Materials Classification of Solid Materials Stress-Strain Diagrams Properties of Solid Materials Stress-Strain Relationships Two-Parameter Materials Charts Effects of Manufacturing Summary Stresses and Strains Introduction Properties of Beam Cross Sections Normal Stress and Strain Torsion Bending Stress and Strain Transverse Shear Stress and Strain Summary Deformation Introduction Moment-Curvature Relation Singularity Functions Method of Superposition Strain Energy Castigliano's Theorem Summary Failure Prediction for Static Loading Introduction Stress Concentration Fracture Mechanics Modes of Crack Growth Fracture Toughness Failure Prediction for Uniaxial Stress State Failure Prediction for Multiaxial Stress State Summary Fatigue and Impact Introduction Fatigue Cyclic Stresses Strain Life Theory of Fatigue Fatigue Strength Fatigue Regimes Stress Concentration Effects The Modified Endurance Limit Cumulative Damage Influence of Nonzero Mean Stress Influence of Multi-Axial Stress States Fracture Mechanics Approach to Fatigue Linear Impact Stresses and Deformations Summary Lubrication, Friction, and Wear Introduction Surface Parameters Conformal and Nonconformal Surfaces Hertzian Contact Bearing Materials Lubricant Rheology Regimes of Lubrication Friction Wear Summary Part II - Machine Elements Columns Introduction Equilibrium Regimes Concentrically Loaded Columns End Conditions Euler's Buckling Criterion Johnson's Buckling Criterion AISC Criteria Eccentrically Loaded Columns Summary Stresses and Deformations in Cylinders Introduction Tolerances and Fits Pressurization Effects Rotational Effects Press Fits Shrink Fits Summary Shafting and Associated Parts Introduction Design of Shafts for Static Loading Fatigue Design of Shafts Additional Shaft Design Considerations Critical Speed of Rotating Shafts Keys, Roll Pins, Splines and Set Screws Retaining Rings and Pins Flywheels Couplings Summary Hydrodynamic and Hydrostatic Bearings Introduction The Reynolds Equation Thrust Slider Bearings Journal Slider Bearings Squeeze Film Bearings Hydrostatic Bearings Summary Rolling-Element Bearings Introduction Historical Overview Bearing Types and Selection Geometry Kinematics Separators Static Load Distribution Elastohydrodynamic Lubrication Fatigue Life Variable Loading Summary General Gear Theory Spur Gears Introduction Types of Gears Gear Geometry Gear Ratio Contact Ratio and Gear Velocity Tooth Thickness and Backlash Gear Trains Gear Manufacture and Quality Gear Materials Loads Acting on a Gear Tooth Bending Stresses in Gear Teeth Contact Stresses in Gear Teeth Elastohydrodynamic Film Thickness Gear Design Synthesis Summary Helical, Bevel, and Worm Gears Introduction Helical Gears Bevel Gears Worm Gears Summary Fasteners, Connections, and Power Screws Introduction Thread Terminology, Classification, and Designation Power Screws Threaded Fasteners Riveted Fasteners Welded, Brazed, and Soldered Joints Adhesive Bonding Integrated Snap Fasteners Summary Springs Introduction Spring Materials Helical Compression Springs Helical Extension Springs Helical Torsion Springs Leaf Springs Gas Springs Belleville Springs Wave Springs Summary Brakes and Clutches Introduction Thermal Considerations Thrust Pad Clutches and Brakes Cone Clutches and Brakes Block or Short-Shoe Brakes Long-Shoe, Internal, Expanding Rim Brakes Long-Shoe, External, Contracting Rim Brakes Symmetrically Loaded Pivot-Shoe Brakes Band Brakes Slip Clutches Summary Flexible Machine Elements Introduction Flat Belts Synchronous Belts V-Belts Wire Ropes Rolling Chains Summary Appendices Index

Crack Arrest and Multiple Cracking in Glass Through the Use of Designed Residual Stress Profiles.

Abstract: A processing approach has been identified and reduced to practice in which a residual stress profile can be designed such that cracks in a brittle material are arrested or grow in a stable manner. In the approach, cracks in the body encounter an increase in the magnitude of residual compression as the crack propagates. If correctly designed, the process increases strength and significantly decreases strength variability. This approach was demonstrated for a silicate glass, and multiple cracking was observed as a forewarning of the final failure. Normally, such glasses would fail catastrophically with the propagation of a dominant crack.

Small defects and Inhomogeneities in fatigue strength: experiments, models and statistical implications

Abstract: The method explained in this paper for quantitative evaluation of fatigue limit for materials containing defects is based on the experimental evidences that inhomogeneities and micro-notches can be treated like cracks. First, the basic concept of the √area parameter model is explained introducing the various data obtained by the first author's group for over last 15 years. Evidences are shown that small cracks, defects and nonmetallic inclusions having the same value of the square root of projection area, √area, have the identical influence on the fatigue limit regardless of different stress concentration factors. Various applications of these concepts to various defect types and microstructural inhomogeneities are shown. Since the estimation of fatigue strength is related to the estimation of the size of maximum defects occurring in a piece, the methods for searching the defects and the quality control of materials with respect to inclusion or defect rating as well as their statistical implications are discussed.

Technical note High-cycle fatigue crack initiation and propagation behaviour of high-strength sprin steel wires

Abstract: An attempt has been made to characterize high-cycle fatigue behaviour of high-strength spring steel wire by means of an ultrasonic fatigue test and analytical techniques. Two kinds of induction-tempered ultra-high-strength spring steel wire of 6.5 mm in diameter with a tensile strength of 1800 MPa were used in this investigation. The fatigue strength of the steel wires between 106 and 109 cycles was determined at a load ratio R = −1. The experimental results show that fatigue rupture can occur beyond 107 cycles. For Cr–V spring wire, the stress–life (S–N ) curve becomes horizontal at a maximum stress of 800 MPa after 106 cycles, but the S–N curve of the Cr–Si steel continues to drop at a high number of cycles (>106 cycles) and does not exhibit a fatigue limit, which is more correctly described by a fatigue strength at a given number of cycles. By using scanning electron microscopy (SEM), the crack initiation and propagation behaviour have been examined. Experimental and analytical techniques were developed to better understand and predict high-cycle fatigue life in terms of crack initiation and propagation. The results show that the portion of fatigue life attributed to crack initiation is more than 90% in the high-cycle regime for the steels studied in this investigation.

The effect of particle shape on ductility of SiCp reinforced 6061 Al matrix composites

Abstract: To study the effect of particle shape on thermal residual stress and strain distributions in composites, five two-dimension SiCp/6061Al model composites reinforced with spherical, hexagon, square, triangle and shuttle-shaped particles, respectively were analyzed by finite element method (FEM). The results showed that the particle shape has a great effect on thermal residual stress and strain fields in composites. There are a residual plastic strain concentration in the matrix around a pointed particle corner and a serious residual stress concentration in the pointed particle corner. The two concentrations increase with decreasing pointed corner degree. When an external stress is applied, the plastic strain concentration in the matrix around the pointed particle corner and the serious stress concentration in the pointed particle corner which will fracture on a relative low level of applied stress can decrease ductility of the composite. Two 6061 aluminium alloy matrix composites reinforced with general SiC particles and blunted SiC particles were studied on the basis of the FEM analyses. It was found that most very pointed particle corners are eliminated after SiC particles being blunted. Replacing general SiC particles with blunted ones can reduce residual plastic strain concentrations in the matrix and serious residual stress concentration in the particle. Therefore, blunted SiC particles reinforced composite shows a higher ductility than general one. (C) 1999 Elsevier Science S.A. All rights reserved.

Edge fracture in cone-plate and parallel plate flows

Abstract: Edge fracture is an instability of cone-plate and parallel plate flows of viscoelastic liquids and suspensions, characterised by the formation of a `crack' or indentation at a critical shear rate on the free surface of the liquid. A study is undertaken of the theoretical, experimental and computational aspects of edge fracture. The Tanner-Keentok theory of edge fracture in second-order liquids is re-examined and is approximately extended to cover the Criminale-Ericksen-Filbey (CEF) model. The second-order theory shows that the stress distribution on the semi-circular crack is not constant, requiring an average to be taken of the stress; this affects the proportionality constant, K in the edge fracture equation −N 2c = KΓ/a, where N 2c is the critical second normal stress difference, Γ is the surface tension coefficient and a is the fracture diameter. When the minimum stress is used, K = 2/3 as found by Tanner and Keentok (1983). Consideration is given to the sources of experimental error, including secondary flow and slip (wall effect). The effect of inertia on edge fracture is derived. A video camera was used to record the inception and development of edge fracture in four viscoelastic liquids and two suspensions. The recorded image was then measured to obtain the fracture diameter. The edge fracture phenomenon was examined to find its dependence on the physical dimensions of the flow (i.e. parallel plate gap or cone angle), on the surface tension coefficient, on the critical shear rate and on the critical second normal stress difference. The critical second normal stress difference was found to depend on the surface tension coefficient and the fracture diameter, as shown by the theory of Tanner and Keentok (1983); however, the experimental data were best fitted by the equation −N 2c = 1.095Γ/a. It was found that edge fracture in viscoelastic liquids depends on the Reynolds number, which is in good agreement with the inertial theory of edge fracture. Edge fracture in lubricating grease and toothpaste is broadly consistent with the CEF model of edge fracture. A finite volume method program was used to simulate the flow of a viscoelastic liquid, obeying the modified Phan-Thien-Tanner model, to obtain the velocity and stress distribution in parallel plate flow in three dimensions. Stress concentrations of the second normal stress difference (N 2) were found in the plane of the crack; the velocity distribution shows a secondary flow tending to aid crack formation if N 2 is negative, and a secondary flow tending to suppress crack formation if N 2 is positive.

From a local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints

Abstract: This paper investigates the possibility of unifying different criteria concerned with the fatigue strength of welded joints In particular, it compares estimates based on local stress fields due to geometry (evaluated without any crack-like defect) and residual life predictions in the presence of a crack, according to LEFM Fatigue strength results already reported in the literature for transverse non-load-carrying fillet welds are used as an experimental database Nominal stress ranges were largely scattered, due to large variations of joint geometrical parameters The scatter band greatly reduces as soon as a 03-mm virtual crack is introduced at the weld toe, and the behaviour of the joints is given in terms of ΔK I versus total life fatigue Such calculations, not different from residual life predictions, are easily performed by using the local stress distributions determined near the weld toes in the absence of crack-like defects More precisely, the analytical expressions for K I are based on a simple combination of the notch stress intensity factors K N 1 and K N 2 for opening and sliding modes Then, fatigue strength predictions, as accurate as those based on fracture mechanics, are performed by the local stress analysis in a simpler way

Fatigue life assessment of nodular cast iron containing casting defects

Abstract: The fatigue behaviour of a a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical clastic-plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10 6 cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10 6 cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (> 10 6 cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.

Present-day stress field and deformation in eastern Austria

Abstract: We analysed fault plane solutions and borehole breakouts in the eastern part of the Eastern Alps and found a heterogeneous stress field which we interpret as a transition zone of three different stress provinces: the western European stress province with NW to NNW SH orientation and mainly strike-slip faulting regime; the Adriatic stress province with a radial stress pattern and thrust faulting to strike-slip faulting regime; and the Dinaric-Pannonian stress province with NE SH orientation and strike-slip faulting regime. The western Pannonian basin seems to be a part of the transition zone with WNW to NW SH orientation. A stress regime stimulating strike-slip faulting prevails in the Eastern Alps. The south Bohemian basement spur as a major tectonic structure with a high rheological contrast to surrounding units has a strong influence on the stress field and exhibits the highest seismicity at its tip due to stress concentration. From a constructed vertical stress orientation profile we found stress decoupling of the Northern Calcareous Alps from the underlying European foreland. Both the Molasse and the Flysch-Helvetic zone are considered as candidates for decoupling horizons due to stress orientation observations and due to their rheological behaviour. From seismological and rheological data, we suggest a horizontal stress decoupling across the Eastern Alps caused by a weakened central Alpine lithosphere.

The influence of cross‐sectional thickness on fatigue crack growth

Abstract: For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.

The mechanical behavior of foamed aluminum

Abstract: Experiments have been carried out to investigate the mechanical behavior of foamed aluminum with different matrixes and states. It is found that the matrix composition has a significant influence over the deformation, failure and fracture of foamed aluminum. Like other cellular solid materials, Al foam shows a smooth compression stress–strain curve with three regions characteristic of plastic foams: linear elastic, plastic collapse and densification. AlMg10 foam has a serrated plateau and no densification, characteristic of brittle foams. AlMg10 foam has higher compressive and tensile strength but lower ductility than Al foam. The difference in the mechanical properties between Al foam and AlMg10 foam decreases as the relative density decreases, and when it is lower than roughly 0.15, no difference can be discerned. The mechanical properties in compression are clearly higher than those in tension, which can be explained in terms of dislocation theory and stress concentration behavior.

Concrete Beams with Openings: Analysis and Design

Abstract: Introduction General Classification of Openings Elastic Stress Distribution around Openings Design Considerations Beams with Small Openings General Pure Bending Bending and Shear Effect of Torsion Design for Torsion Effect of Coring Beams with Large Rectangular Openings General Analysis at Collapse Design for Ultimate Strength Crack Control Calculation of Deflection Multiple Openings Torsion in Beams with Large Rectangular Openings General Pure Torsion Torsion Combined with Bending Combined Torsion, Bending and Shear Analysis and Design of Continuous Beams General Elastic Analysis Design Procedure and Recommendations Design Example Effect of Prestressing General Stress Concentration and Stress Distribution Types of Cracking and Crack Control Deflections Design and Detailing for Ultimate Strength Appendices References Index

Interfacial fatigue crack growth in foam core sandwich structures

Abstract: This paper deals with the experimental measurement of face/core interfacial fatigue crack growth rates in foam core sandwich beams. The so-called ‘cracked sandwich beam’ specimen is used, slightly modified, which is a sandwich beam that has a simulated face/core interface crack. The specimen is precracked so that a more realistic crack front is created prior to fatigue growth measurements. The crack is then propagated along the interface, in the core material, during fatigue loading, as is assumed to occur in a real sandwich structure. The crack growth is stable even under constant amplitude testing. Stress intensity factors are obtained from the FEM which, combined with the experimental data, result in standard da/dN versus ΔK curves for which classical Paris’ law constants can be extracted. The experiments to determine stress intensity factor threshold values are performed using a manual load-shedding technique.