Showing papers on "Deformation (engineering) published in 2007"

Fundamentals of Materials Science and Engineering : An Integrated Approach

Abstract: Chapter 1 - Introduction. 1.1 Historical Perspective 1.2 Materials Science and Engineering 1.3 Why Study Materials Science and Engineering? 1.4 Classification of Materials Materials of Importance-Carbonated Beverage Containers 1.5 Advanced Materials 1.6 Modern Materials Needs 1.7 Processing/Structure/Properties/Performance Correlations Chapter 2 - Atomic Structure and Interatomic Bonding. 2.1 Introduction 2.2 Fundamental Concepts 2.3 Electrons in Atoms 2.4 The Periodic Table 2.5 Bonding Forces and Energies 2.6 Primary Interatomic Bonds 2.7 Secondary Bonding or van der Waals Bonding Materials of Importance-Water (Its Volume Expansion Upon Freezing) 2.8 Molecules Chapter 3 - Structures of Metals and Ceramics 3.1 Introduction 3.2 Fundamental Concepts 3.3 Unit Cells 3.4 Metallic Crystal Structures 3.5 Density Computations-Metals 3.6 Ceramic Crystal Structures 3.7 Density Computations-Ceramics 3.8 Silicate Ceramics 3.9 Carbon Materials of Importance-Carbon Nanotubes 3.10 Polymorphism and Allotropy Material of Importance-Tin (Its Allotropic Transformation) 3.11 Crystal Systems 3.12 Point Coordinates 3.13 Crystallographic Directions 3.14 Crystallographic Planes 3.15 Linear and Planar Densities 3.16 Close-Packed Crystal Structures 3.17 Single Crystals 3.18 Polycrystalline Materials 3.19 Anisotropy 3.20 X-Ray Diffraction: Determination of Crystal Structures 3.21 Noncrystalline Solids Chapter 4 - Polymer Structures 4.1 Introduction 4.2 Hydrocarbon Molecules 4.3 Polymer Molecules 4.4 The Chemistry of Polymer Molecules 4.5 Molecular Weight 4.6 Molecular Shape 4.7 Molecular Structure 4.8 Molecular Configurations 4.9 Thermoplastic and Thermosetting Polymers 4.10 Copolymers 4.11 Polymer Crystallinity 4.12 Polymer Crystals Chapter 5 - Imperfections in Solids 5.1 Introduction 5.2 Point Defects in Metals 5.3 Point Defects in Ceramics 5.4 Impurities in Solids 5.5 Point Defects in Polymers 5.6 Specification of Composition 5.7 Dislocations-Linear Defects 5.8 Interfacial Defects Materials of Importance-Catalysts (and Surface Defects) 5.9 Bulk or Volume Defects 5.10 Atomic Vibrations 5.11 Basic Concepts of Microscopy 5.12 Microscopic Techniques 5.13 Grain Size Determination Chapter 6 - Diffusion 6.1 Introduction 6.2 Diffusion Mechanisms 6.3 Steady-State Diffusion 6.4 Nonsteady-State Diffusion 6.5 Factors That Influence Diffusion 6.6 Diffusion in Semiconducting Materials Material of Importance-Aluminum for Integrated Circuit Interconnects 6.7 Other Diffusion Paths 6.8 Diffusion in Ionic and Polymeric Materials Chapter 7 - Mechanical Properties 7.1 Introduction 7.2 Concepts of Stress and Strain 7.3 Stress-Strain Behavior 7.4 Anelasticity 7.5 Elastic Properties of Materials 7.6 Tensile Properties 7.7 True Stress and Strain 7.8 Elastic Recovery after Plastic Deformation 7.9 Compressive, Shear, and Torsional Deformation 7.10 Flexural Strength 7.11 Elastic Behavior 7.12 Influence of Porosity on the Mechanical Properties of Ceramics 7.13 Stress-Strain Behavior 7.14 Macroscopic Deformation 7.15 Viscoelastic Deformation 7.16 Hardness 7.17 Hardness of Ceramic Materials 7.18 Tear Strength and Hardness of Polymers 7.19 Variability of Material Properties 7.20 Design/Safety Factors Chapter 8 - Deformation and Strengthening Mechanisms 8.1 Introduction 8.2 Historical 8.3 Basic Concepts of Dislocations 8.4 Characteristics of Dislocations 8.5 Slip Systems 8.6 Slip in Single Crystals 8.7 Plastic Deformation of Polycrystalline Metals 8.8 Deformation by Twinning 8.9 Strengthening by Grain Size Reduction 8.10 Solid-Solution Strengthening 8.11 Strain Hardening 8.12 Recovery 8.13 Recrystallization 8.14 Grain Growth 8.15 Crystalline Ceramics 8.16 Noncrystalline Ceramics 8.17 Deformation of Semicrystalline Polymers 8.18 Factors That Influence the Mechanical Properties of Semicrystalline Polymers Materials of Importance-Shrink-Wrap Polymer Films 8.19 Deformation of Elastomers Chapter 9 - Failure 9.1 Introduction 9.2 Fundamentals of Fracture 9.3 Ductile Fracture 9.4 Brittle Fracture 9.5 Principles of Fracture Mechanics 9.6 Brittle Fracture of Ceramics 9.7 Fracture of Polymers 9.8 Fracture Toughness Testing 9.9 Cyclic Stresses 9.10 The S-N Curve 9.11 Fatigue in Polymeric Materials 9.12 Crack Initiation and Propagation 9.13 Factors That Affect Fatigue Life 9.14 Environmental Effects 9.15 Generalized Creep Behavior 9.16 Stress and Temperature Effects 9.17 Data Extrapolation Methods 9.18 Alloys for High-Temperature Use 9.19 Creep in Ceramic and Polymeric Materials Chapter 10 - Phase Diagrams 10.1 Introduction 10.2 Solubility Limit 10.3 Phases 10.4 Microstructure 10.5 Phase Equilibria 10.6 One-Component (or Unary) Phase Diagrams 10.7 Binary Isomorphous Systems 10.8 Interpretation of Phase Diagrams 10.9 Development of Microstructure in Isomorphous Alloys 10.10 Mechanical Properties of Isomorphous Alloys 10.11 Binary Eutectic Systems Materials of Importance-Lead-Free Solders 10.12 Development of Microstructure in Eutectic Alloys 10.13 Equilibrium Diagrams Having Intermediate Phases or Compounds 10.14 Eutectoid and Peritectic Reactions 10.15 Congruent Phase Transformations 10.16 Ceramic Phase Diagrams 10.17 Ternary Phase Diagrams 10.18 The Gibbs Phase Rule 10.19 The Iron-Iron Carbide (Fe-Fe3C) Phase Diagram 10.20 Development of Microstructure in Iron-Carbon Alloys 10.21 The Influence of Other Alloying Elements Chapter 11 - Phase Transformations 11.1 Introduction 11.2 Basic Concepts 11.3 The Kinetics of Phase Transformations 11.4 Metastable versus Equilibrium States 11.5 Isothermal Transformation Diagrams 11.6 Continuous-Cooling Transformation Diagrams 11.7 Mechanical Behavior of Iron-Carbon Alloys 11.8 Tempered Martensite 11.9 Review of Phase Transformations and Mechanical Properties for Iron-Carbon Alloys Materials of Importance-Shape-Memory Alloys 11.10 Heat Treatments 11.11 Mechanism of Hardening 11.12 Miscellaneous Considerations 11.13 Crystallization 11.14 Melting 11.15 The Glass Transition 11.16 Melting and Glass Transition Temperatures 11.17 Factors That Influence Melting and Glass Transition Temperatures Chapter 12 - Electrical Properties 12.1 Introduction 12.2 Ohm's Law 12.3 Electrical Conductivity 12.4 Electronic and Ionic Conduction 12.5 Energy Band Structures in Solids 12.6 Conduction in Terms of Band and Atomic Bonding Models 12.7 Electron Mobility 12.8 Electrical Resistivity of Metals 12.9 Electrical Characteristics of Commercial Alloys Materials of Importance-Aluminum Electrical Wires 12.10 Intrinsic Semiconduction 12.11 Extrinsic Semiconduction 12.12 The Temperature Dependence of Carrier Concentration 12.13 Factors that Affect Carrier Mobility 12.14 The Hall Effect 12.15 Semiconductor Devices 12.16 Conduction in Ionic Materials 12.17 Electrical Properties of Polymer 12.18 Capacitance 12.19 Field Vectors and Polarization 12.20 Types of Polarization 12.21 Frequency Dependence of the Dielectric Constant 12.22 Dielectric Strength 12.23 Dielectric Materials 12.24 Ferroelectricity 12.25 Piezoelectricity Chapter 13 - Types and Applications of Materials 13.1 Introduction 13.2 Ferrous Alloys 13.3 Nonferrous Alloys Materials of Importance-Metal Alloys Used for Euro Coins 13.4 Glasses 13.5 Glass-Ceramics.

Tensile ductility and necking of metallic glass

Abstract: Metallic glasses have a very high strength, hardness and elastic limit. However, they rarely show tensile ductility at room temperature and are considered quasi-brittle materials(1,2). Although these amorphous metals are capable of shear flow, severe plastic instability sets in at the onset of plastic deformation, which seems to be exclusively localized in extremely narrow shear bands similar to 10nm in thickness(3-13). Using in situ tensile tests in a transmission electron microscope, we demonstrate radically different deformation behaviour for monolithic metallic-glass samples with dimensions of the order of 100 nm. Large tensile ductility in the range of 23-45% was observed, including significant uniform elongation and extensive necking or stable growth of the shear offset. This large plasticity in small-volume metallic-glass samples did not result from the branching/deflection of shear bands or nanocrystallization. These observations suggest that metallic glasses can plastically deform in a manner similar to their crystalline counterparts, via homogeneous and inhomogeneous flow without catastrophic failure. The sample-size effect discovered has implications for the application of metallic glasses in thin films and micro-devices, as well as for understanding the fundamental mechanical response of amorphous metals.

Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale

Abstract: Under stress, many crystalline materials exhibit irreversible plastic deformation caused by the motion of lattice dislocations. In plastically deformed microcrystals, internal dislocation avalanches lead to jumps in the stress-strain curves (strain bursts), whereas in macroscopic samples plasticity appears as a smooth process. By combining three-dimensional simulations of the dynamics of interacting dislocations with statistical analysis of the corresponding deformation behavior, we determined the distribution of strain changes during dislocation avalanches and established its dependence on microcrystal size. Our results suggest that for sample dimensions on the micrometer and submicrometer scale, large strain fluctuations may make it difficult to control the resulting shape in a plastic-forming process.

Ductile crystalline–amorphous nanolaminates

Abstract: It is known that the room-temperature plastic deformation of bulk metallic glasses is compromised by strain softening and shear localization, resulting in near-zero tensile ductility. The incorporation of metallic glasses into engineering materials, therefore, is often accompanied by complete brittleness or an apparent loss of useful tensile ductility. Here we report the observation of an exceptional tensile ductility in crystalline copper/copper–zirconium glass nanolaminates. These nanocrystalline–amorphous nanolaminates exhibit a high flow stress of 1.09 ± 0.02 GPa, a nearly elastic-perfectly plastic behavior without necking, and a tensile elongation to failure of 13.8 ± 1.7%, which is six to eight times higher than that typically observed in conventional crystalline–crystalline nanolaminates (<2%) and most other nanocrystalline materials. Transmission electron microscopy and atomistic simulations demonstrate that shear banding instability no longer afflicts the 5- to 10-nm-thick nanolaminate glassy layers during tensile deformation, which also act as high-capacity sinks for dislocations, enabling absorption of free volume and free energy transported by the dislocations; the amorphous–crystal interfaces exhibit unique inelastic shear (slip) transfer characteristics, fundamentally different from those of grain boundaries. Nanoscale metallic glass layers therefore may offer great benefits in engineering the plasticity of crystalline materials and opening new avenues for improving their strength and ductility.

Mechanical Properties of Bulk Metallic Glasses

Abstract: In the absence of dislocation-mediated crystallographic slip, room-temperature deformation in metallic glasses occurs in thin shear bands initially only ~10 nm thick. A sharp drop in viscosity (shear softening) occurs in deformed glassy matter and facilitates additional flow in existing shear bands. This further localization of plastic flow leads to shearing-off failure without any significant macroscopic plasticity. However, whereas most bulk metallic glasses fail in this manner, some undergo surprisingly extensive plastic deformation (in some cases, up to 50% or more) in compression or bending. When this occurs, the flow is “jerky,” as indicated by serrated stress–strain curves. Each serration may correspond to the emission of a shear band that then ceases to operate, at least temporarily, despite the predicted shear softening. As elastic energy is converted to heat during shear, temperatures rise sharply at or near shear bands. This heating may lead to the growth of nanocrystals that then block propagation of shear bands and cracks. The understanding of the dependence of mechanical response of metallic glasses on intrinsic (elastic constants, chemistry) and extrinsic factors (shapes, flaws) is the subject of intense current interest.

Shape and Temperature Memory of Nanocomposites with Broadened Glass Transition

Abstract: Shape-memory polymers can revert to their original shape when they are reheated. The stress generated by shape recovery is a growing function of the energy absorbed during deformation at a high temperature; thus, high energy to failure is a necessary condition for strong shape-memory materials. We report on the properties of composite nanotube fibers that exhibit this particular feature. We observed that these composites can generate a stress upon shape recovery up to two orders of magnitude greater than that generated by conventional polymers. In addition, the nanoparticles induce a broadening of the glass transition and a temperature memory with a peak of recovery stress at the temperature of their initial deformation.

Electromechanical hysteresis and coexistent states in dielectric elastomers

Abstract: When a voltage is applied to a layer of a dielectric elastomer, the layer reduces in thickness and expands in area. A recent experiment has shown that the homogeneous deformation of the layer can be unstable, giving way to an inhomogeneous deformation, such that regions of two kinds coexist in the layer, one being flat and the other wrinkled. To analyze this instability, we construct for a class of model materials, which we call ideal dielectric elastomers, a free-energy function comprising contributions from stretching and polarizing. We show that the free-energy function is typically non-convex, causing the elastomer to undergo a discontinuous transition from a thick state to a thin state. When the two states coexist in the elastomer, a region of the thin state has a large area, and wrinkles when constrained by nearby regions of the thick state. We show that an elastomer described by the Gaussian statistics cannot stabilize the thin state, but a stiffening elastomer near the extension limit can. We further show that the instability can be tuned by the density of cross links and the state of stress.

Localized Deformation due to Portevin-LeChatelier Effect in 18Mn-0.6C TWIP Austenitic Steel

Abstract: The thermo-mechanical properties of low stacking fault energy austenitic Fe18Mn0.6C steel exhibiting twinning-induced plasticity were investigated during uniaxial tensile deformation using infrared thermography. Over a wide strain range, the plastic deformation was by the movement of very few well-defined localized deformation bands. The formation and propagation of Portevin–LeChatelier (PLC) bands lead to type A and type B serrated stress–strain curves, exhibiting a negative strain rate sensitivity. The PLC band properties were analyzed in detail: strain, strain rate and mobile dislocation density within the bands were determined. The microstructures of the un-deformed and deformed Fe18Mn0.6C TWIP steel were studied by transmission electron microscopy. The possible dynamic strain aging processes causing the localized deformation are reviewed.

Effect of martensite plasticity on the deformation behavior of a low-carbon dual-phase steel

Abstract: An experimental study has been conducted to quantify the effects of martensite plasticity on the mechanical properties of a commercial low-carbon (0.06 wt pct) dual-phase steel. The volume fraction and morphology (banded and more equiaxed) of the martensite second phase were systematically varied by control of the intercritical annealing temperature and the heating rate to this temperature. It was observed that the yield and tensile strengths were dependent on the volume fraction of martensite but not on the morphology. In contrast, the true uniform strain, fracture strain, and fracture stress were found to have a significant dependence on martensite morphology. These results were rationalized by considering an Eshelby-based model, which allowed for the calculation of the stress in the martensite islands for different morphologies and volume fractions. By comparing the stress in the martensite with an estimate of its yield stress, it was possible to rationalize the conditions under which martensite plasticity occurs. The implications of martensite plasticity affect the work hardening of the steels but most importantly the fracture properties. For conditions where martensite codeforms with the ferrite matrix, void nucleation is suppressed and the final fracture properties are dramatically improved.

Low-Temperature in Situ Large Strain Plasticity of Ceramic SiC Nanowires and Its Atomic-Scale Mechanism

Abstract: Large strain plasticity is phenomenologically defined as the ability of a material to exhibit an exceptionally large deformation rate during mechanical deformation. It is a property that is well established for metals and alloys but is rarely observed for ceramic materials especially at low temperature ( approximately 300 K). With the reduction in dimensionality, however, unusual mechanical properties are shown by ceramic nanomaterials. In this Letter, we demonstrated unusually large strain plasticity of ceramic SiC nanowires (NWs) at temperatures close to room temperature that was directly observed in situ by a novel high-resolution transmission electron microscopy technique. The continuous plasticity of the SiC NWs is accompanied by a process of increased dislocation density at an early stage, followed by an obvious lattice distortion, and finally reaches an entire structure amorphization at the most strained region of the NW. These unusual phenomena for the SiC NWs are fundamentally important for understanding the nanoscale fracture and strain-induced band structure variation for high-temperature semiconductors. Our result may also provide useful information for further studying of nanoscale elastic-plastic and brittle-ductile transitions of ceramic materials with superplasticity.

Textile-Reinforced Mortar versus Fiber-Reinforced Polymer Confinement in Reinforced Concrete Columns

Abstract: Poorly detailed reinforced concrete (RC) columns have limited deformation capacity under seismic loads due to buckling of the longitudinal bars. This study experimentally investigates the effectiveness of textile-reinforced mortar (TRM) jackets as a means of confining these columns. The effectiveness of TRM is evaluated by comparing TRM jackets with fiber-reinforced polymer (FRP) jackets of equal stiffness and strength. Tests were carried out both on short prisms under concentric compression and on nearly full-scale, nonseismically detailed, RC columns subjected to cyclic uniaxial flexure under constant axial load. The compression tests on 15 RC prisms show that TRM jackets provide a substantial gain in compressive strength and deformation capacity by delaying buckling of the longitudinal bars. This gain increases with the volumetric ratio of the jacket. Compared with their FRP counterparts, TRM jackets used in this study are slightly less effective in terms of increasing strength and deformation capacity by approximately 10%. Tests on nearly full-scale columns under cyclic uniaxial flexure show that TRM jacketing is very effective (and equal to the FRP jacketing) as a means of increasing the cyclic deformation capacity and the energy dissipation of RC columns with poor detailing by delaying bar buckling.

Paleowattmeters: A scaling relation for dynamically recrystallized grain size

Abstract: During dislocation creep, mineral grains often evolve to a stable size, dictated by the deformation conditions. We suggest that grain-size evolution during deformation is determined by the rate of mechanical work. Provided that other elements of microstructure have achieved steady state and that the dissipation rate is roughly constant, then changes in internal energy will be proportional to changes in grain-boundary area. If normal grain-growth and dynamic grain-size reduction occur simultaneously, then the steady-state grain size is determined by the balance of those rates. A scaling model using these assumptions and published grain-growth and mechanical relations matches stress–grain-size relations for quartz and olivine rocks with no fitting. For marbles, the model also explains scatter not rationalized by assuming that recrystallized grain size is a function of stress alone. When extrapolated to conditions typical for natural mylonites, the model is consistent with field constraints on stresses and strain rates.

Force chain buckling, unjamming transitions and shear banding in dense granular assemblies

Abstract: Force chain buckling, leading to unjamming and shear banding, is examined quantitatively via a discrete element analysis of a two-dimensional, densely-packed, cohesionless granular assembly subject to quasistatic, boundary-driven biaxial compression. A range of properties associated with the confined buckling of force chains has been established, including: degree of buckling, buckling modes, spatial and strain evolution distributions, and relative contributions to non-affine deformation, dilatation and decrease in macroscopic shear strength and potential energy. Consecutive cycles of unjamming–jamming events, akin to slip–stick events arising in other granular systems, characterize the strain-softening regime and the shear band evolution. Peaks in the dissipation rate, kinetic energy and local non-affine strain are strongly correlated: the largest peaks coincide with each unjamming event that is evident in the concurrent drops in the macroscopic shear stress and potential energy. Unjamming nucleates from...

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

Abstract: In this paper, by capturing the atomic informa- tion and reflecting the behaviour governed by the nonlin- ear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single- walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's. of CNT's. The Young's modulus of CNT's was found to be about 1 TPa (2-5). Many theories of mechanics have also been proposed to study the mechanical properties of CNT's. Zhang et al. (6) developed a continuum mechanics approach to model elastic properties of single-walled carbon nanotubes (SWCNT's), and the Young's modulus of SWCNT's was pre- dicted to be 0.705 TPa. Li and Chou (7) presented a structural mechanics approach to model the deformation of CNT's, and calculated the Young's moduli for CNT's with different radii. A similar approach was presented by Chang and Gao (8), and the chirality- and size-dependent elastic properties such as Young's modulus, Poisson's ratio and shear modulus were predicted (9,10). Moreover, the nonlinear effect of SWCNT's was taken into account (11) recently. In view of the unrealistic demand of computational power to study materials of practical size, atomistic simulations are deemed unsuitable for the study of large scaled nanometer materials in large time spans. Therefore, various attempts have been made by researchers to introduce atomic character- istics into the mechanical theory. For example, the molecular mechanics originally developed by chemical scientists (12) can be considered one of the successful attempts. According to the definition of Burkert and Allinger (12), the total potential energy, U , is constitutive of several individual energy terms corresponding to bond stretching, angle bend- ing, torsion, and van der Waals interactions, respectively: U = � Ustretch + � Ubend

An FEM investigation into the behavior of metal matrix composites: tool-particle interaction during orthogonal cutting

Abstract: An analytical or experimental method is often unable to explore the behavior of a metal matrix composite (MMC) during machining due to the complex deformation and interactions among particles, tool and matrix. This paper investigates the matrix deformation and tool–particle interactions during machining using the finite element method. Based on the geometrical orientations, the interaction between tool and particle reinforcements was categorized into three scenarios: particles along, above and below the cutting path. The development of stress and strain fields in the MMC was analyzed and physical phenomena such as tool wear, particle debonding, displacements and inhomogeneous deformation of matrix material were explored. It was found that tool–particle interaction and stress/strain distributions in the particles/matrix are responsible for particle debonding, surface damage and tool wear during machining of MMC.

Dislocation structures. Part I. Grain orientation dependence

Abstract: To clarify the effect of grain orientation on the evolution of dislocation structures in metals of medium-to-high stacking fault energy, detailed TEM characterization of structures was carried out for more than 350 individual grains in Al and Cu deformed in tension or by cold rolling up to moderate strain levels (ϵvM ≤ 0.8). Efforts were made to obtain a precise description of the three-dimensional arrangement of the dislocation structures and to determine the crystallographic plane of extended dislocation boundaries (geometrically necessary boundaries). A universal pattern of structural evolution characterized by a formation of three types of structure was found in both metals, irrespective of material parameters (stacking fault energy, grain size and impurity) and deformation conditions (deformation mode, strain and strain rate). The key parameter controlling the formation of the different structural types was found to be grain orientation with respect to the deformation axis (axes) and a clear relation...

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.

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.