Showing papers on "Stress concentration published in 2007"

The damage tolerance of elastic–brittle, two-dimensional isotropic lattices

Abstract: The fracture toughness of elastic–brittle 2D lattices is determined by the finite element method for three isotropic periodic topologies: the regular hexagonal honeycomb, the Kagome lattice and the regular triangular honeycomb. The dependence of mode I and mode II fracture toughness upon relative density is determined for each lattice, and the fracture envelope is obtained in combined mode I–mode II stress intensity factor space. Analytical estimates are also made for the dependence of mode I and mode II toughness upon relative density. The high nodal connectivity of the triangular grid ensures that it deforms predominantly by stretching of the constituent bars, while the hexagonal honeycomb deforms by bar bending. The Kagome microstructure deforms by bar stretching remote from the crack tip, and by a combination of bar bending and bar stretching within a characteristic elastic deformation zone near the crack tip. This elastic zone reduces the stress concentration at the crack tip in the Kagome lattice and leads to an elevated macroscopic toughness. Predictions are given for the tensile and shear strengths of a centre-cracked panel with microstructure given explicitly by each of the three topologies. The hexagonal and triangular honeycombs are flaw-sensitive, with a strength adequately predicted by linear elastic fracture mechanics (LEFM) for cracks spanning more than a few cells. In contrast, the Kagome microstructure is damage tolerant, and for cracks shorter than a transition length its tensile strength and shear strength are independent of crack length but are somewhat below the unnotched strength. At crack lengths exceeding the transition value, the strength decreases with increasing crack length in accordance with the LEFM estimate. This transition crack length scales with the parameter of bar length divided by relative density of the Kagome grid, and can be an order of magnitude greater than the cell size at low relative densities. Finally, the presence of a boundary layer is noted at the free edge of a crack-free Kagome grid loaded in tension and in shear. Deformation within this boundary layer is by a combination of bar bending and stretching whereas remote from the free edge the Kagome grid deforms by bar stretching (with a negligible contribution from bar bending). The edge boundary layer degrades both the macroscopic stiffness and strength of the Kagome plate. No such boundary layer is evident for the hexagonal and triangular honeycombs.

Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes

Abstract: The fracture strengths and elastic moduli of arc-grown multi-walled carbon nanotubes (MWCNTs) were measured by tensile loading inside of a scanning electron microscope (SEM). Eighteen tensile tests were performed on 14 MWCNTs with three of them being tested multiple times (3×, 2×, and 2×, respectively). All the MWCNTs fractured in the “sword-in-sheath” mode. The diameters of the MWCNTs were measured in a transmission electron microscope (TEM), and the outer diameter with an assumed 0.34 nm shell thickness was used to convert measured load-displacement data to stress and strain values. An unusual yielding before fracture was observed in two tensile loading experiments. The 18 outer shell fracture strength values ranged from 10 to 66 GPa, and the 18 Young's modulus values, obtained from a linear fit of the stress–strain data, ranged from 620 to 1,200 GPa, with a mean of 940 GPa. The possible influence of stress concentration at the clamps is discussed.

Dislocation nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation

Abstract: Molecular dynamics simulations are used to evaluate the primary interface dislocation sources and to estimate both the free enthalpy of activation and the critical emission stress associated with the interfacial dislocation emission mechanism. Simulations are performed on copper to study tensile failure of a planar Σ5 {2 1 0} 53.1° interface and an interface with the same misorientation that contains a ledge. Simulations reveal that grain boundary ledges are more favorable as dislocation sources than planar regions of the interface and that their role is not limited to that of simple dislocation donors. The parameters extracted from the simulations are utilized in a two-phase composite mesoscopic model for nanocrystalline deformation that includes the effects of both dislocation emission and dislocation absorption mechanisms. A self-consistent approach based on the Eshelby solution for grains as ellipsoidal inclusions is augmented by introduction of stress concentration in the constitutive law of the matrix phase to account for more realistic grain boundary effects. Model simulations suggest that stress concentration is required in the standard continuum theory to activate the coupled grain boundary dislocation emission and absorption mechanisms when activation energy of the dislocation source is determined from atomistic calculation on grain boundaries without consideration of impurities or other extrinsic defects.

The effect of oxide coatings on fatigue properties of 7475-T6 aluminium alloy.

Abstract: The effect of hard anodic oxide and plasma electrolytic oxide coatings on the fatigue strength of 7475-T6 aluminium alloy has been investigated. The coated aluminium alloy was tested using constant load uniaxial tensile fatigue machine. Hard anodising led to an appreciable reduction in the fatigue strength of 7475-T6 alloy of about 75% for a 60 μm thick coating. Further, plasma electrolytic oxidation resulted in reduction of the fatigue strength of about 58% for a 65 μm thick oxide coating. The decrease in fatigue strength of the hard anodic oxide coatings was associated with the stress concentration at the microcracks in the coating. The better fatigue performance of the PEO coatings was attributed to the development of the compressive residual internal stress within the coatings. The reduction in the fatigue strength of the PEO coatings as compared to the uncoated material was associated with the development of the tensile residual internal stress within the substrate. This may cause an early crack initiation in the substrate adjacent to the coating.

Suppression of fatigue crack growth in carbon nanotube composites

Abstract: Fatigue is one of the primary causes for catastrophic failure in structural materials. Here, we report an order-of-magnitude reduction in the fatigue crack propagation rate for an epoxy system with the addition of ∼0.5wt.% of carbon nanotube additives. Using fractography analysis and fracture mechanics modeling, we show that the crack suppression is caused by crack bridging, which results in an effective crack-closing stress due to the pull out of nanotube fibers in the wake of the crack tip. Carbon nanotubes therefore show potential to significantly enhance the reliability and operating life of structural polymers that are susceptible to fatigue failure.

Stress analysis of thermal fatigue fracture of brake disks based on thermomechanical coupling

Abstract: This paper develops a three-dimensional (3D) thermal-structure coupling model, implements transient stress analysis of thermoelastic contact of disk brakes with a frictional heat variation and identifies the source of the thermal fatigue. This thermostructure model allows the analysis of the effects of the moving heat source (the pad) with a variable speed and integrates the heat flux coupling between the sliding surfaces. To obtain the transient stress/temperature fields of the brake under an emergency braking, the thermoelastic problem under this 3D model is solved by the finite element method. The numerical results from the analysis and simulation show the temperature/stress of the disk presenting periodic sharp fluctuation due to the continuous cyclic loading; its varying frequency corresponds to the rotated cycle times of the braking disk. The results demonstrate that the maximum surface equivalent stress may exceed the material yield strength during an emergency braking, which may cause a plastic damage accumulation in a brake disk, while a residual tensile hoop stress is incurred on cooling. These results are validated by experimental observation results available in the literature. Based on these numerical results, some suggestions for avoiding fatigue fracture propagation are further presented.

Towards a new model of crack tip stress fields

Abstract: This work introduces a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of plasticity through an analysis of their shielding effects on the applied elastic field. The ability of the model to characterize plasticity-induced effects of cyclic loading on the elastic stress fields is assessed and demonstrated using full-field photoelasticity. The focus is on determining the form of the shielding stress components (induced by compatibility requirements at the elastic–plastic interface along the crack flank and via the crack tip plastic zone) and how they influence the crack tip elastic stress fields during a load cycle. The model is successfully applied to the analysis of a fatigue crack growing in a polycarbonate CT specimen.

Fatigue Crack Propagation in Metals and Alloys: Microstructural Aspects and Modelling Concepts

Abstract: Foreword. Preface. Symbols and Abbreviations. 1 Introduction. 2 Basic Concepts of Metal Fatigue and Fracture in the Engineering Design Process. 2.1 Historical Overview. 2.2 Metal Fatigue, Crack Propagation and Service-Life Prediction: A Brief Introduction. 2.2.1 Fundamental Terms in Fatigue of Materials. 2.2.2 Fatigue-Life Prediction: Total-Life and Safe-Life Approach. 2.2.3 Fatigue-Life Prediction: Damage-Tolerant Approach. 2.2.4 Methods of Fatigue-Life Prediction at a Glance. 2.3 Basic Concepts of Technical Fracture Mechanics. 2.3.1 The K Concept of LEFM. 2.3.2 Crack-Tip Plasticity: Concepts of Plastic-Zone Size. 2.3.3 Crack-Tip Plasticity: The J Integral. 3 Experimental Approaches to Crack Propagation. 3.1 Mechanical Testing. 3.1.1 Testing Systems. 3.1.2 Specimen Geometries. 3.1.3 Local Strain Measurement: The ISDG Technique. 3.2 Crack-Propagation Measurements. 3.2.1 Potential-Drop Concepts and Fracture Mechanics Experiments. 3.2.2 In Situ Observation of the Crack Length. 3.3 Methods of Microstructural Analysis and Quantitative Characterization of Grain and Phase Boundaries. 3.3.1 Analytical SEM: Topography Contrast to Study Fracture Surfaces. 3.3.2 SEM Imaging by Backscattered Electrons and EBSD. 3.3.3 Evaluation of Kikuchi Patterns: Automated EBSD. 3.3.4 Orientation Analysis Using TEM and X-Ray Diffraction. 3.3.5 Mathematical and Graphical Description of Crystallographic Orientation Relationships. 3.3.6 Microstructure Characterization by TEM. 3.3.7 Further Methods to Characterize Mechanical Damage Mechanisms in Materials. 3.4 Reproducibility of Experimentally Studying the Mechanical Behavior of Materials. 4 Physical Metallurgy of the Deformation Behavior of Metals and Alloys. 4.1 Elastic Deformation. 4.2 Plastic Deformation by Dislocation Motion. 4.3 Activation of Slip Planes in Single- and Polycrystalline Materials. 4.4 Special Features of the Cyclic Deformation of Metallic Materials. 5 Initiation of Microcracks. 5.1 Crack Initiation: Definition and Significance. 5.1.1 Influence of Notches, Surface Treatment and Residual Stresses. 5.2 Influence of Microstructual Factors on the Initiation of Fatigue Cracks. 5.2.1 Crack Initiation at the Surface: General Remarks. 5.2.2 Crack Initiation at Inclusions and Pores. 5.2.3 Crack Initiation at Persistent Slip Bands. 5.3 Crack Initiation by Elastic Anisotropy. 5.3.1 Definition and Significance of Elastic Anisotropy. 5.3.2 Determination of Elastic Constants and Estimation of the Elastic Anisotropy. 5.3.3 FE Calculations of Elastic Anisotropy Stresses to Predict Crack Initiation Sites. 5.3.4 Analytical Calculation of Elastic Anisotropy Stresses. 5.4 Intercrystalline and Transcrystalline Crack Initiation. 5.4.1 Influence Parameters for Intercrystalline Crack Initiation. 5.4.2 Crack Initiation at Elevated Temperature and Environmental Effects. 5.4.3 Transgranular Crack Initiation. 5.5 Microstructurally Short Cracks and the Fatigue Limit. 5.6 Crack Initiation in Inhomogeneous Materials: Cellular Metals. 6 Crack Propagation: Microstructural Aspects. 6.1 Special Features of the Propagation of Microstructurally Short Fatigue Cracks. 6.1.1 Definition of Short and Long Cracks. 6.2 Transgranular Crack Propagation. 6.2.1 Crystallographic Crack Propagation: Interactions with Grain Boundaries. 6.2.2 Mode I Crack Propagation Governed by Cyclic Crack-Tip Blunting. 6.2.3 Influence of Grain Size, Second Phases and Precipitates on the Propagation Behavior of Microstructurally Short Fatigue Cracks. 6.3 Significance of Crack-Closure Effects and Overloads. 6.3.1 General Idea of Crack Closure During Fatigue-Crack Propagation. 6.3.2 Plasticity-Induced Crack Closure. 6.3.3 Influence of Overloads in Plasticity-Induced Crack Closure. 6.3.4 Roughness-Induced Crack Closure. 6.3.5 Oxide- and Transformation-Induced Crack Closure. 6.3.6 &delta K/K max Thresholds: An Alternative to the Crack-Closure Concept. 6.3.7 Development of Crack Closure in the Short Crack Regime. 6.4 Short and Long Fatigue Cracks: The Transition from Mode II to Mode I Crack Propagation. 6.4.1 Development of the Crack Aspect Ratio a/c. 6.4.2 Coalescence of Short Cracks. 6.5 Intercrystalline Crack Propagation at Elevated Temperatures: The Mechanism of Dynamic Embrittlement. 6.5.1 Environmentally Assisted Intercrystalline Crack Propagation in Nickel-Based Superalloys: Possible Mechanisms. 6.5.2 Mechanism of Dynamic Embrittlement as a Generic Phenomenon: Examples. 6.5.3 Oxygen-Induced Intercrystalline Crack Propagation: Dynamic Embrittlement of Alloy 718. 6.5.4 Increasing the Resistance to Intercrystalline Crack Propagation by Dynamic Embrittlement: Grain-Boundary Engineering. 7 Modeling Crack Propagation Accounting for Microstructural Features. 7.1 General Strategies of Fatigue Life Assessment. 7.2 Modeling of Short-Crack Propagation. 7.2.1 Short-Crack Models: An Overview. 7.2.2 Model of Navarro and de los Rios. 7.3 Numerical Modeling of Short-Crack Propagation by Means of a Boundary Element Approach. 7.3.1 Basic Modeling Concept. 7.3.2 Slip Transmission in Polycrystalline Microstructures. 7.3.3 Simulation of Microcrack Propagation in Synthetic Polycrystalline Microstructures. 7.3.4 Transition from Mode II to Mode I Crack Propagation. 7.3.5 Future Aspects of Applying the Boundary Element Method to Short-Fatigue-Crack Propagation. 7.4 Modeling Dwell-Time Cracking: A Grain-Boundary Diffusion Approach. 8 Concluding Remarks. References. Subject Index.

Fracture of titanium plates used for mandibular reconstruction following ablative tumor surgery

Abstract: Purpose The purpose of this study was to identify reasons for fracture of titanium mandibular reconstruction plates, when used to bridge lateral mandibular defects after ablative tumor surgery. Materials and Methods Sixteen titanium reconstruction plates from sheep mandibles were examined to identify reasons for the plate fractures. The broken plates and the seemingly unbroken plates were examined separately. The plates were removed from the mandibular bone and inspected by dye penetrant examination, metallography, optical microscope, scanning electron microscope, and energy dispersive X-ray spectrometer. Furthermore, axial load fatigue tests were performed in two different environments, air and physiologic salt solution, 0.9% NaCl, to compare titanium behavior in air and the human body. Results The site of crack initiation was the inner curvature of the reconstruction plate, and the cracks initiated as a result of stress concentration in the shoulder fillet of the plate. The cracks grew in a cyclic manner under masticatory loading of the mandible and the plate. The plate fracture occurred by means of fatigue. The corrosive environment did not affect the failure of the titanium plate, and the fracture was not caused by hydrogen embrittlement. The results revealed that the fatigue properties of the plates may have been impaired by the residual stresses generated in plate bending. Conclusions Adjustive bending of the plates, in the surgical operation, may thus be an important cause of fracture of the reconstruction plates, because of generated residual stresses, which affect the mean stress in fatigue loading. To make the plates function without failure the plates should match closely with the three-dimensional shape of the mandible, to avoid any bending in the operative phase. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2007

Evaluation of the delayed hydride cracking mechanism for transgranular stress corrosion cracking of magnesium alloys

Abstract: This paper evaluates the important elements of delayed hydride cracking (DHC) for transgranular stress corrosion cracking (TGSCC) of Mg alloys. A DHC model was formulated with the following components: (i) transient H diffusion towards the crack tip driven by stress and H concentration gradients; (ii) hydride precipitation when the H solvus is exceeded; and (iii) crack propagation through the extent of the hydride when it reaches a critical size of similar to 0.8 mu m. The stress corrosion crack velocity, V-c, was calculated from the time for the hydride to reach the critical size. The model was implemented using a finite element script developed in MATLAB. The input parameters were chosen, based on the information available, to determine the highest possible value for Vc. Values for Vc of similar to 10(-7) m/s were predicted by this DHC model. These predictions are consistent with measured values for V, for Mg alloys in distilled water but cannot explain values for V, of similar to 10(-4) m/s measured in other aqueous environments. Insights for understanding Mg TGSCC are drawn. A key outcome is that the assumed initial condition for the DHC models is unlikely to be correct. During steady state stress corrosion crack propagation of Mg in aqueous solutions, a high dynamic hydrogen concentration would be expected to build up immediately behind the crack tip. Stress corrosion crack velocities similar to 10(-4) m/s, typical for Mg alloys in aqueous solutions, might be predicted using a DHC model for Mg based on the time to reach a critical hydride size in steady state, with a significant residual hydrogen concentration from the previous crack advance step. (c) 2007 Elsevier B.V. All rights reserved.

Microstructure effects on high temperature fatigue crack initiation and short crack growth in turbine disc nickel-base superalloy Udimet 720Li

Abstract: An assessment of the effects of microstructure on fatigue crack initiation and short crack growth in a turbine disc nickel-base superalloy at 650 °C in air is presented. U720Li and microstructural variants of U720Li, i.e. U720Li-LG (large grain variant) and U720Li-LP (large intragranular coherent γ′ precipitate variant) have been assessed by uninterrupted and replicated short crack tests in polished U-notch specimens using a 1-1-1-1 trapezoidal loading cycle at nominal stress levels ranging between 700 and 850 MPa (calculated in the uncracked ligament). Crack initiation was primarily due to porosity on or near the surface but also due to grain boundary oxidation. Initial transgranular crack growth across four to six grains in air was noted at short crack lengths before oxidation-assisted intergranular crack growth modes were established at larger crack lengths. At a nominal applied stress of 840 MPa, U720Li and U720Li-LP show similar fatigue lifetimes while U720Li-LG demonstrates a significantly improved fatigue lifetime, particularly when lifetimes are compared on a local strain range basis. A larger grain size gave the most significant performance benefits in terms of overall fatigue lifetime under these test conditions.

Toughening polymeric composites using nanoclay: Crack tip scale effects on fracture toughness

Abstract: Fracture behavior of vinyl ester resin and the methods that can be used to toughen vinyl ester resin were studied. Neat resin, 5% by weight nanoclay, 5% by weight core shell rubber (CSR) and hybrid system (3% nanoclay and 2% CSR by weight) were the material systems considered for comparing fracture toughness. Three types of cracks were used to determine the stress intensity factors at failure, viz., sharp crack, blunt crack and notch. The critical stress intensity factor in the case of sharp cracks improved significantly when compared to neat resin. In the case of notched and blunt cracked specimens, a reduction in stress intensity factors (at failure) was observed for reinforced systems. However, for notched and blunt cracked specimens, it was shown from the morphology of the fracture surface that the stress intensity factor calculated by assuming a notch or a blunt crack as an ideal crack was not the controlling parameter for fracture. A method for quantifying the crack tip sharpness using fracture surface roughness has been proposed.