Stress–strain curve

About: Stress–strain curve is a research topic. Over the lifetime, 11351 publications have been published within this topic receiving 251437 citations. The topic is also known as: Stress-strain curve & Stress-strain diagram.

Hyperbolic Stress-Strain Response: Cohesive Soils

Abstract: The divergent concepts of a stability analysis, as compared with a load-deformation approach to soil mechanics, are shown to be compatible within the framework of a hyperbolic stress-strain relation. The two-constant hyperbolic form of the stress-strain response is such that the ultimate shear strength of the soil is contained within the general formulation and appears in the mathematical limit of the stress as the strain becomes excessive. This is quantiatively demonstrated for a remolded cohesive soil tested in consolidated-undrained triaxial compression. The variables contained in the hyperbolic stress-strain relation include the preconsolidation pressure, rebound stress, lateral pressure during the test, vertical normal stress, strain, and rate of strain. History effects are included in terms of the overconsolidation ratio. The general formulations obtained for the consolidated-undrained triaxial tests are compared with the results reported in the literature by other investigators for both drained and undrained consolidated triaxial tests under various conditions.

Constitutive analysis in hot working

Abstract: Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Abstract: A nalyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J -integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J -integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

Mechanical properties of ceramics

Abstract: Preface. Acknowledgments. 1 Stress and Strain. 1.1 Introduction. 1.2 Tensor Notation for Stress. 1.3 Stress in Rotated Coordinate System. 1.4 Principal Stress. 1.4.1 Principal Stresses in Three Dimensions. 1.5 Stress Invariants. 1.6 Stress Deviator. 1.7 Strain. 1.8 True Stress and True Strain. 1.8.1 True Strain. 1.8.2 True Stress. Problems. 2 Types of Mechanical Behavior. 2.1 Introduction. 2.2 Elasticity and Brittle Fracture. 2.3 Permanent Deformation. 3 Elasticity. 3.1 Introduction. 3.2 Elasticity of Isotropic Bodies. 3.3 Reduced Notation for Stresses, Strains, and Elastic Constants. 3.4 Effect of Symmetry on Elastic Constants. 3.5 Orientation Dependence of Elastic Moduli in Single Crystals and Composites. 3.6 Values of Polycrystalline Moduli in Terms of Single-Crystal Constants. 3.7 Variation of Elastic Constants with Lattice Parameter. 3.8 Variation of Elastic Constants with Temperature. 3.9 Elastic Properties of Porous Ceramics. 3.10 Stored Elastic Energy. Problems. 4 Strength of Defect-Free Solids. 4.1 Introduction. 4.2 Theoretical Strength in Tension. 4.3 Theoretical Strength in Shear. Problems. 5 Linear Elastic Fracture Mechanics. 5.1 Introduction. 5.2 Stress Concentrations. 5.3 Griffith Theory of Fracture of a Brittle Solid. 5.4 Stress at Crack Tip: An Estimate. 5.5 Crack Shape in Brittle Solids. 5.6 Irwin Formulation of Fracture Mechanics: Stress Intensity Factor. 5.7 Irwin Formulation of Fracture Mechanics: Energy Release Rate. 5.8 Some Useful Stress Intensity Factors. 5.9 The J Integral. 5.10 Cracks with Internal Loading. 5.11 Failure under Multiaxial Stress. Problems. 6 Measurements of Elasticity, Strength, and Fracture Toughness. 6.1 Introduction. 6.2 Tensile Tests. 6.3 Flexure Tests. 6.4 Double-Cantilever-Beam Test. 6.5 Double-Torsion Test. 6.6 Indentation Test. 6.7 Biaxial Flexure Testing. 6.8 Elastic Constant Determination Using Vibrational and Ultrasonic Methods. Problems. 7 Statistical Treatment of Strength. 7.1 Introduction. 7.2 Statistical Distributions. 7.3 Strength Distribution Functions. 7.4 Weakest Link Theory. 7.5 Determining Weibull Parameters. 7.6 Effect of Specimen Size. 7.7 Adaptation to Bend Testing. 7.8 Safety Factors. 7.9 Example of Safe Stress Calculation. 7.10 Proof Testing. 7.11 Use of Pooled Fracture Data in Linear Regression Determination of Weibull Parameters. 7.12 Method of Maximum Likelihood in Weibull Parameter Estimation. 7.13 Statistics of Failure under Multiaxial Stress. 7.14 Effects of Slow Crack Propagation and R-Curve Behavior on Statistical Distributions of Strength. 7.15 Surface Flaw Distributions and Multiple Flaw Distributions. Problems. 8 Subcritical Crack Propagation. 8.1 Introduction. 8.2 Observed Subcritical Crack Propagation. 8.3 Crack Velocity Theory and Molecular Mechanism. 8.4 Time to Failure under Constant Stress. 8.5 Failure under Constant Stress Rate. 8.6 Comparison of Times to Failure under Constant Stress and Constant Stress Rate. 8.7 Relation of Weibull Statistical Parameters with and without Subcritical Crack Growth. 8.8 Construction of Strength-Probability-Time Diagrams. 8.9 Proof Testing to Guarantee Minimum Life. 8.10 Subcritical Crack Growth and Failure from Flaws Originating from Residual Stress Concentrations. 8.11 Slow Crack Propagation at High Temperature. Problems. 9 Stable Crack Propagation and R -Curve Behavior. 9.1 Introduction. 9.2 R-Curve (T-Curve) Concept. 9.3 R-Curve Effects of Strength Distributions. 9.4 Effect of R Curve on Subcritical Crack Growth. Problems. 10 Overview of Toughening Mechanisms in Ceramics. 10.1 Introduction. 10.2 Toughening by Crack Deflection. 10.3 Toughening by Crack Bowing. 10.4 General Remarks on Crack Tip Shielding. 11 Effect of Microstructure on Toughness and Strength. 11.1 Introduction. 11.2 Fracture Modes in Polycrystalline Ceramics. 11.3 Crystalline Anisotropy in Polycrystalline Ceramics. 11.4 Effect of Grain Size on Toughness. 11.5 Natural Flaws in Polycrystalline Ceramics. 11.6 Effect of Grain Size on Fracture Strength. 11.7 Effect of Second-Phase Particles on Fracture Strength. 11.8 Relationship between Strength and Toughness. 11.9 Effect of Porosity on Toughness and Strength. 11.10 Fracture of Traditional Ceramics. Problems. 12 Toughening by Transformation. 12.1 Introduction. 12.2 Basic Facts of Transformation Toughening. 12.3 Theory of Transformation Toughening. 12.4 Shear-Dilatant Transformation Theory. 12.5 Grain-Size-Dependent Transformation Behavior. 12.6 Application of Theory to Ca-Stabilized Zirconia. Problems. 13 Mechanical Properties of Continuous-Fiber-Reinforced Ceramic Matrix Composites. 13.1 Introduction. 13.2 Elastic Behavior of Composites. 13.3 Fracture Behavior of Composites with Continuous, Aligned Fibers. 13.4 Complete Matrix Cracking of Composites with Continuous, Aligned Fibers. 13.5 Propagation of Short, Fully Bridged Cracks. 13.6 Propagation of Partially Bridged Cracks. 13.7 Additional Treatment of Crack-Bridging Effects. 13.8 Additional Statistical Treatments. 13.9 Summary of Fiber-Toughening Mechanisms. 13.10 Other Failure Mechanisms in Continuous, Aligned-Fiber Composites. 13.11 Tensile Stress-Strain Curve of Continuous, Aligned-Fiber Composites. 13.12 Laminated Composites. Problems. 14 Mechanical Properties of Whisker-, Ligament-, and Platelet-Reinforced Ceramic Matrix Composites. 14.1 Introduction. 14.2 Model for Whisker Toughening. 14.3 Combined Toughening Mechanisms in Whisker-Reinforced Composites. 14.4 Ligament-Reinforced Ceramic Matrix Composites. 14.5 Platelet-Reinforced Ceramic Matrix Composites. Problems. 15 Cyclic Fatigue of Ceramics. 15.1 Introduction. 15.2 Cyclic Fatigue of Metals. 15.3 Cyclic Fatigue of Ceramics. 15.4 Mechanisms of Cyclic Fatigue of Ceramics. 15.5 Cyclic Fatigue by Degradation of Crack Bridges. 15.6 Short-Crack Fatigue of Ceramics. 15.7 Implications of Cyclic Fatigue in Design of Ceramics. Problems. 16 Thermal Stress and Thermal Shock in Ceramics. 16.1 Introduction. 16.2 Magnitude of Thermal Stresses. 16.3 Figure of Merit for Various Thermal Stress Conditions. 16.4 Crack Propagation under Thermal Stress. Problems. 17 Fractography. 17.1 Introduction. 17.2 Qualitative Features of Fracture Surfaces. 17.3 Quantitative Fractography. 17.4 Fractal Concepts in Fractography. 17.5 Fractography of Single Crystals and Polycrystals. Problems. 18 Dislocations and Plastic Deformation in Ductile Crystals. 18.1 Introduction. 18.2 Definition of Dislocations. 18.3 Glide and Climb of Dislocations. 18.4 Force on a Dislocation. 18.5 Stress Field and Energy of a Dislocation. 18.6 Force Required to Move a Dislocation. 18.7 Line Tension of a Dislocation. 18.8 Dislocation Multiplication. 18.9 Forces between Dislocations. 18.10 Dislocation Pileups. 18.11 Orowan's Equation for Strain Rate. 18.12 Dislocation Velocity. 18.13 Hardening by Solid Solution and Precipitation. 18.14 Slip Systems. 18.15 Partial Dislocations. 18.16 Deformation Twinning. Problems. 19 Dislocations and Plastic Deformation in Ceramics. 19.1 Introduction. 19.2 Slip Systems in Ceramics. 19.3 Independent Slip Systems. 19.4 Plastic Deformation in Single-Crystal Alumina. 19.5 Twinning in Aluminum Oxide. 19.6 Plastic Deformation of Single-Crystal Magnesium Oxide. 19.7 Plastic Deformation of Single-Crystal Cubic Zirconia. Problems. 20 Creep in Ceramics. 20.1 Introduction. 20.2 Nabarro-Herring Creep. 20.3 Combined Diffusional Creep Mechanisms. 20.4 Power Law Creep. 20.5 Combined Diffusional and Power Law Creep. 20.6 Role of Grain Boundaries in High-Temperature Deformation and Failure. 20.7 Damage-Enhanced Creep. 20.8 Superplasticity. 20.9 Deformation Mechanism Maps. Problems. 21 Creep Rupture at High Temperatures and Safe Life Design. 21.1 Introduction. 21.2 General Process of Creep Damage and Failure in Ceramics. 21.3 Monkman-Grant Technique of Life Prediction. 21.4 Two-Stage Strain Projection Technique. 21.5 Fracture Mechanism Maps. Problems. 22 Hardness and Wear. 22.1 Introduction. 22.2 Spherical Indenters versus Sharp Indenters. 22.3 Methods of Hardness Measurement. 22.4 Deformation around Indentation. 22.5 Cracking around Indentation. 22.6 Indentation Size Effect. 22.7 Wear Resistance. Problems. 23 Mechanical Properties of Glass and Glass Ceramics. 23.1 Introduction. 23.2 Typical Inorganic Glasses. 23.3 Viscosity of Glass. 23.4 Elasticity of Inorganic Glasses. 23.5 Strength and Fracture Surface Energy of Inorganic Glasses. 23.6 Achieving High Strength in Bulk Glasses. 23.7 Glass Ceramics. Problems. 24 Mechanical Properties of Polycrystalline Ceramics in General and Design Considerations. 24.1 Introduction. 24.2 Mechanical Properties of Polycrystalline Ceramics in General. 24.3 Design Involving Mechanical Properties. References. Index.