Showing papers on "Paris' law published in 2002"

Principles of Fracture Mechanics

Abstract: Most chapters include an Introduction, Summary, References and Exercises. 1. Introduction to Fracture Mechanics. Historical Overview of Brittle Fracture. Elementary Brittle-Fracture Theories. Crack Extension Behavior. 2. Elements of Solid Mechanics. Concepts of Stress and Strain. Equations of Elasticity in Cartesian Coordinates. Equations of Elasticity in Polar Coordinates. Solution of the Biharmonic Equation. The Problem of the Elliptical Hole. 3. Elasticity of Singular Stress Fields. Overview. The Williams Problems. The Generalized Westergaard Approach. The Central Crack Problem. Single-Ended Crack Problems. The Effect of Finite Boundaries. Determining the Geometric Stress Intensity Factor. The Three-Dimensional Crack Problem. 4. Numerical Methods for K Determination. Boundary Collocation. The Finite Element Method. 5. Experimental Methods for K Determination. Overview. Classical Photoelesatic Methods. The Method of Caustics. Strain Gages. Multi-Parameter Full-Field Methods: Local Collocation. Interference Patterns. Moire Patterns. Photoelasticity. 6. A Stress Field Theory of Fracture. The Critical Stress-State Criterion. Crack-Tip Plasticity. The Effect of Variables on Fracture Toughness. R-Curves. 7. The Energy of Fracture. Griffith's Theory of Brittle Fracture. A Unified Theory of Fracture. Compliance. 8. Fracture Toughness Testing. Fracture Toughness Standards. Nonstandard Fracture-Toughness Tests. 9. Fatigue. Stages of Fatigue Crack Growth. Mathematical Analysis of Stage II Crack Growth. The Effects of Residual Stress on Crack Growth Rates. Life Prediction Computer Programs. Measuring Fatigue Properties: ASTM. 10. Designing against Fracture. Fracture Mechanics in Conventional Design. The Role of NDE in Design. U.S. Air Force Damage-tolerant Design Methodology. Designing by Hindsight: Case Studies. 11. Elastoplastic Fracture. Nonlinear Elastic Behavior. Characterizing Elastoplastic Behavior. Comments on the J-Integral in Elastoplastic Fracture Mechanics. Appendix A: Comprehensive Exercises. General Comments. Appendix B: Complex Variable Method in Elasticity. Complex Numbers. Complex Functions. Appendix C: An Abbreviated Compendium of Westergaard Stress Functions. Appendix D: Fracture Properties of Engineering Materials. Appendix E: NASGRO 3.0 Material Constants for Selected Materials. Index.

Particle impact on metal substrates with application to foreign object damage to aircraft engines

Abstract: Foreign object damage (FOD) occurs when hard, millimeter-sized objects such as gravel or sand are ingested into aircraft jet engines Particles impacting turbine blades at velocities up to about 300 m=s produce small indentation craters which can become sites for fatigue crack initiation, severely limiting the lifetime of the blade A framework for analyzing FOD and its e5ect on fatigue cracking is established in this paper Finite element analysis is used to determine the residual stresses and geometric stress concentration resulting from FOD The roles of material rate sensitivity and inertia are delineated The most important non-dimensional parameters governing impact indents are identi7ed, signi7cantly reducing the set of independent parameters The second step in the analysis focuses on the potency of cracks emerging from critical locations at the indents The results have been used to address the question: When and to what extent do the residual stresses and stress concentration caused by FOD reduce the critical crack size associated with threshold fatigue crack growth? For deep indents, it is found that elastic stress concentration is the dominant factor in reducing critical crack threshold when the applied cyclic load ratio, R, is large, otherwise the residual stresses are also important Comparisons with a set of experiments conducted in parallel with the theory show that the numerical approach can account for various phenomena observed in practice ? 2002 Elsevier Science Ltd All rights reserved

Computational model for analysis of bending fatigue in gears

Abstract: A computational model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. The fatigue process leading to tooth breakage is divided into crack initiation (Ni) and crack propagation (Np) period, where the complete service life is defined as N=Ni+Np . The strain-life method in the framework of the FEM method has been used to determine the number of stress cycles Ni required for the fatigue crack initiation. Gear tooth crack propagation was simulated using a FEM method based computer program which uses principles of linear elastic fracture mechanics. Paris equation is then used for the further simulation of the fatigue crack growth. The presented model is used for determination of service life of real spur gear made from through-hardened steel 42CrMo4.

Fatigue crack growth behavior of rail steel under mode I and mixed mode loadings

Abstract: It is necessary to evaluate the fatigue behavior of rail steel under mixed mode loadings to assure the safety of railway vehicles. For this purpose, the stress analysis to investigate static failure and fatigue behavior under mixed mode loadings is performed. The stress analysis results show that the K I / K II tends to increase as the transverse crack below the surface propagates. For the mixed mode, the fatigue crack growth behavior was evaluated using various comparative stress intensity factor ranges Δ K V . Fatigue crack growth rate under the condition of mixed mode is slower than that under mode I, and this difference decreases with the increase of the stress ratio R .

Fatigue crack-growth behavior of Sn-Ag-Cu and Sn-Ag-Cu-Bi Lead-free solders

Abstract: Fatigue crack-growth behavior and mechanical properties of Sn-3Ag-0.5Cu, Sn-3Ag-0.5Cu-1Bi, and Sn-3Ag-0.5Cu-3Bi solders have been investigated at room temperature (20 °C). The tensile strength and hardness of the solders increased with increasing Bi content. However, the yield strengths of Sn-3Ag-0.5Cu-1Bi and Sn-3Ag-0.5Cu-3Bi solders were nearly similar, but the 3Bi solder exhibited the lowest ductility. Fatigue crack-growth behavior of the solders was dominantly cycle dependent in the range of stress ratios from 0.1-0.7 at a frequency of 10 Hz, except for the Sn-3Ag-0.5Cu solder tested at a stress ratio of 0.7. Mixed intergranular/transgranular crack propagation was observed for the Sn-3Ag-0.5Cu solder tested at the stress ratio of 0.7, indicating the importance of creep in crack growth. The Sn-3Ag-0.5Cu-1Bi and Sn-3Ag-0.5Cu-3Bi solders had higher resistance to time-dependent crack growth, resulting from the strengthening effect of the Bi constituent. It appears that the addition of Bi above a certain concentration is harmful to the mechanical properties of Sn-3Ag-0.5Cu.

The influence of microstructure and environment on the crack growth behavior of Powder Metallurgy nickel superalloy RR1000

Abstract: A study of crack growth in vacuum and air at 725 °C (T/T m=06) highlights the relative importance of creep and environmental crack-tip damage mechanisms in Powder Metallurgy (P/M) disc alloy RR1000 Both of these mechanisms are associated with a transition to intergranular fracture during fatigue crack growth at 025 Hz Crack growth under sustained loads reveals the precise nature of these mechanisms in RR1000 The severity of creep and environmental mechanisms is controlled by the grain-boundary microstructure and the crack-tip stress Near-tip cavitation leads to fracture in vacuum Sigma-phase precipitation causes an increase in crack growth rate through increased crack-tip cavity nucleation Rapid near-tip stress relaxation induced by γ′ coarsening has a beneficial effect on the severity of this type of damage In air, increases in crack growth rates are associated with near-tip intergranular oxidation It is proposed that the extent of this damage and subsequent growth rates are increased by sigma-phase precipitation through enhanced oxidation due to chromium depletion and subsequent decreased passivation Again, a beneficial effect of rapid near-tip stress relaxation due to selective γ′ coarsening is apparent and environmental damage is reduced under these conditions

Step loading for very high cycle fatigue

Abstract: The conventional method for determining fatigue strength at high cycle counts is to either extrapolate S-N data from lower cycle counts or to generate S-N data in the high cycle count regime using special high frequency test machines. In the process of generating S-N data, runout tests often occur where no failure is obtained within the allotted time for a test. Such data points are normally indicated on an S-N plot with an arrow, but no information is available as to whether failure would ever occur. As an alternative, and as a method for getting a data point for every test, a step-loading method may be employed. In this paper, some of the unique test equipment being applied to the study of high cycle fatigue in our laboratory are reviewed. Data are presented on the long-life fatigue behaviour of Ti-6Al-4V which validate both the step-loading methodology and indicate the trend of fatigue strength as a function of cycle number in the very high cycle fatigue regime. The absence of coaxing is demonstrated by comparing S-N data with step-loading data. Applicability of high frequency testing to the determination of fatigue crack growth thresholds is also demonstrated.

Crack closure and the fatigue-crack propagation threshold as a function of load ratio

Abstract: The phenomenon of crack closure, which involves the premature closing of fatigue cracks during the unloading portion of a fatigue cycle resulting in the development of crack-tip shielding due to crack wedging, has become widely accepted as a critical mechanism influencing many aspects of the behaviour of fatigue cracks in metallic materials; these include effects of load ratio, variable-amplitude loading, crack size, microstructure, environment and the magnitude of the fatigue threshold. Recently, however, the significance of crack closure has been questioned and alternative suggestions made for many of these phenomena, e.g. the effect of the load ratio (i.e. the ratio R of the minimum to maximum loads) on threshold behaviour. In the light of this, the present paper provides evidence to rebut the assertion that crack closure is an insignificant process. Particular attention is given to the effect of crack closure on the threshold level as a function of load ratio.

Elastic-Plastic Mixed-Mode Fracture Criteria and Parameters

Abstract: I. Mixed-mode crack behavior under plane stress and plane strain small scale yielding.- 1.1 Governing equations.- 1.1.1 Plane strain.- 1.1.2 Plane stress.- 1.1.3 Boundary conditions for different types of dominating fracture mechanism.- 1.2 Numerical iterative method for solving the nonlinear eigenvalue problems.- 1.3 Application of J-integral to plastic stress intensity factor determination.- 1.3.1 Plane strain.- 1.3.2 Plane stress.- 1.4 Family of crack-tip fields characterized by dominating fracture mechanism.- 1.4.1 Plane strain.- 1.4.2 Plane stress.- 1.5 Finite element analysis of stress distributions at the crack tip.- 1.6 Conditions of existence for mixed mode fracture.- II. Modeling of crack growth by fracture damage zone.- 2.1 A modified strain-energy density approach.- 2.1.1 Elastic strain energy density.- 2.1.2 Plastic strain energy density.- 2.2 Strain energy density distributions.- 2.3 Fracture damage zone.- 2.3.1 A brief review.- 2.3.2 Fracture damage zone size.- 2.4 Relation between cracks growth resistance and fracture process parameters in elastic-plastic solids.- 2.5 Elastic-plastic approach for modeling of fatigue crack behavior.- 2.6 Some aspects of the fatigue crack path prediction.- III. Experimental investigation of fatigue crack propagation.- 3.1 Specimens for study of fatigue and fracture processes and material properties.- 3.2 Method of interpretation for cyclic crack resistance characteristics.- 3.3 Effect of biaxial stress on fatigue crack growth in aluminum alloys.- 3.4 Influence of mixed mode loading on fatigue fracture of high strength steels.- 3.5 Fatigue crack growth trajectories for the aluminum alloys and steels.- IV. Models for predicting crack growth rate and fatigue life.- 4.1 Crack growth direction criterion.- 4.2 Criteria of equivalent plastic strain under a complex stress state.- 4.3 A model for predicting crack growth rate under biaxial loads.- 4.4 An analysis of crack growth under complex stress state with taking into account their orientation.- V. Practical applications.- 5.1 Fracture analysis of gas turbine engine disks and simulation modeling of operational conditions.- 5.1.1 Stress state analysis.- 5.1.2 Crack growth model.- 5.1.3 Full size disk experiments.- 5.2 Modeling fatigue crack behavior in a pressurized cylinder.- 5.2.1 Crack growth model.- 5.2.2 Results and discussion.- Reference.

Fatigue performance of high-pressure waterjet-peened aluminum alloy

Abstract: An experimental study of high-pressure waterjet peening on 7075-T6 aluminum alloy was conducted to investigate the effects of waterjet on high-cycle fatigue life and fatigue crack growth. Unnotched hourglass-shaped circular cross section test specimens were fatigue tested in completely reversed rotating bending (R =S min /S max = -1) to determine fatigue life behavior (S-N curves). Single-edge-notched flat tensile test specimens were tested in the tension-tension fatigue crack growth tests (R=S min /S max =0.1) to determine fatigue crack propagation behavior (da/dN versus AK). Surface characteristics and fracture surfaces were evaluated by scanning electron microscopy (SEM). Results show that waterjet peening can increase high-cycle fatigue life, delay fatigue crack initiation, and decrease the rate of fatigue crack propagation.

Residual strain measurement by synchrotron diffraction

Abstract: Third generation synchrotron X-ray sources such as the European Synchrotron Radiation Facility and the Advanced Photon Source (USA) have made very intense beams of very high energy X-rays available for the first time. At energies in excess of 60 keV penetration lengths of the order of centimetres are possible in most engineering materials. The associated low scattering angles limit the strain measurement directions available at depth. Gauge dimensions as small as microns and sub-second measurement times give the technique unique characteristics, making 2 and 3 dimensional strain mapping economically feasible. The current state of the art is reviewed and the potential assessed, primarily using illustrative case studies made at the ESRF. These include the measurement of near surface strains caused by peening, TIG welding stresses for the development of finite element models, the mapping of crack bridging during fatigue crack growth in Ti/SiC fibre composites and crack field mapping in 3D.

Effect on fatigue crack growth of interactions between overloads

Abstract: Various types of interactions between overloads were studied in a 0.38% C low carbon steel. The retarding effect due to consecutive overloads is found to increase with the number of overloads, until it reaches a maximum. Similarly, it is found that a critical distance between overloads ensures the highest retarding effect, while shorter or longer spacing are less efficient for retarding crack growth. These effects are successfully explained using FEM calculations of the effective stress intensity factor. The kinematic hardening of the alloy, which is very efficient in ferritic-pearlitic steels, is shown to be mostly responsible for those effects. Taking into account the amplitude of kinematic hardening allows qualitative explanation of the observed effects. The order of application of the cycles during variable amplitude fatigue is thus important and should be taken into account for predicting fatigue lives.

Thermally stable aluminum-lithium alloy 1424 for application in welded fuselage

Abstract: Sheets of Al – Li alloy 1424 have high fracture toughness and diminished rate of fatigue crack growth, high corrosion resistance, and excellent weldability. The chemical composition and the regime of the hardening heat treatment of alloy 1424 are shown to provide good thermal stability of the sheets with respect to fracture toughness (K c f) and growth rate of fatigue cracks (GRFC) after a hold of up to 3000 h at 85°C. These characteristics decrease only after a hold of 4000 h and only in the L – T direction. The suggested process for manufacturing sheets diminishes the anisotropy of the strength characteristics and the elongation due to the formation of a partially recrystallized structure.