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About: Necking is a(n) research topic. Over the lifetime, 5280 publication(s) have been published within this topic receiving 113945 citation(s).

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TL;DR: In this article, a theory is suggested which describes the yielding and plastic flow of an anisotropic metal on a macroscopic scale and associated relations are then found between the stress and strain-increment tensors.
Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

3,097 citations

Journal ArticleDOI
TL;DR: In this article, a set of elastic-plastic constitutive relations that account for the nucleation and growth of micro-voids is used to model the failure of a round tensile test specimen.
Abstract: Necking and failure in a round tensile test specimen is analysed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of micro-voids. Final material failure by coalescence of voids, at a value of the void volume fraction in accord with experimental and computational results, is incorporated in this constitutive model via the dependence of the yield condition on the void volume fraction. In the analyses the material has no voids initially; but high voidage develops in the centre of the neck where the hydrostatic tension peaks, leading to the formation of a macroscopic crack as the material stress carrying capacity vanishes. The numerically computed crack is approximately plane in the central part of the neck, but closer to the free surface the crack propagates on a zig-zag path, finally forming the cone of the cup-cone fracture. The onset of macroscopic fracture is found to be associated with a sharp “knee” on the load deformation curve, as is also observed experimentally, and at this point the reduction in cross-sectional area stops.

2,645 citations

22 Dec 2003
TL;DR: In this paper, the second-rank tensors of a tensor were modeled as tensors and they were used to model the deformation of polycrystalline materials and their properties.
Abstract: Chapter 1. Introduction.1.1 Strain1.2 Stress.1.3 Mechanical Testing.1.4 Mechanical Responses to Deformation.1.5 How Bonding Influences Mechanical Properties.1.6 Further Reading and References.1.7 Problems.Chapter 2. Tensors and Elasticity.2.1 What Is a Tensor?2.2 Transformation of Tensors.2.3 The Second Rank Tensors of Strain and Stress.2.4 Directional Properties.2.5 Elasticity.2.6 Effective Properties of Materials: Oriented Polycrystals and Composites.2.7 Matrix Methods for Elasticity Tensors.2.8 Appendix: The Stereographic Projection.2.9 References.2.10 Problems.Chapter 3. Plasticity.3.1 Continuum Models for Shear Deformation of Isotropic Ductile Materials.3.2 Shear Deformation of Crystalline Materials.3.3 Necking and Instability.3.4 Shear Deformation of Non Crystalline materials.3.5 Dilatant Deformation of Materials.3.6 Appendix: Independent Slip Systems.3.7 References.3.8 Problems.Chapter 4. Dislocations in Crystals.4.1 Dislocation Theory.4.2 Specification of Dislocation Character.4.3 Dislocation Motion.4.4 Dislocation Content in Crystals and Polycrystals.4.5 Dislocations and Dislocation Motion in Specific Crystal Structures.4.6 References.4.7 Problems.Chapter 5. Strengthening Mechanisms.5.1 Constraint Based Strengthening.5.2 Strengthening Mechanisms in Crystalline Materials.5.3 Orientation Strengthening.5.4 References.5.5 Problems.Chapter 6. High Temperature and Rate Dependent Deformation.6.1 Creep.6.2 Extrapolation Approaches for Failure and Creep.6.3 Stress Relaxation.6.4 Creep and Relaxation Mechanisms in Crystalline Materials.6.5 References.6.6 Problems.Chapter 7. Fracture of Materials.7.1 Stress Distributions Near Crack Tips.7.2 Fracture Toughness Testing.7.3 Failure Probability and Weibull Statistics.7.4 Mechanisms for Toughness Enhancement of Brittle Materials.7.5 Appendix A: Derivation of the Stress Concentration at a Through Hole.7.6 Appendix B: Stress Volume Integral Approach for Weibull Statistics.7.7 References.7.8 Problems.Chapter 8. Mapping Strategies for Understanding Mechanical Properties.8.1 Deformation Mechanism Maps.8.2 Fracture Mechanism Maps.8.3 Mechanical Design Maps.8.4 References.8.5 Problems.Chapter 9. Degradation Processes: Fatigue and Wear.9.1 Cystic Fatigue of materials.9.2 Engineering Fatigue Analysis.9.3 Wear, Friction, and Lubrication.9.4 References.9.5 Problems.Chapter 10. Deformation Processing.10.1 Ideal Energy Approach for Modeling of a Forming Process.10.2 Inclusion of Friction and Die Geometry in Deformation Processes: Slab Analysis.10.3 Upper Bound Analysis.10.4 Slip Line Field Analysis.10.5 Formation of Aluminum Beverage Cans: Deep Drawing, Ironing, and Shaping.10.6 Forming and Rheology of Glasses and Polymers.10.7 Tape Casting of Ceramic Slurries.10.8 References.10.9 Problems.Index.

1,450 citations

Journal ArticleDOI
TL;DR: In this article, an equiatomic CoCrFeMnNi high-entropy alloy, which crystallizes in the face-centered cubic (fcc) crystal structure, was produced by arc melting and drop casting.
Abstract: An equiatomic CoCrFeMnNi high-entropy alloy, which crystallizes in the face-centered cubic (fcc) crystal structure, was produced by arc melting and drop casting. The drop-cast ingots were homogenized, cold rolled and recrystallized to obtain single-phase microstructures with three different grain sizes in the range 4–160 μm. Quasi-static tensile tests at an engineering strain rate of 10−3 s−1 were then performed at temperatures between 77 and 1073 K. Yield strength, ultimate tensile strength and elongation to fracture all increased with decreasing temperature. During the initial stages of plasticity (up to ∼2% strain), deformation occurs by planar dislocation glide on the normal fcc slip system, {1 1 1}〈1 1 0〉, at all the temperatures and grain sizes investigated. Undissociated 1/2〈1 1 0〉 dislocations were observed, as were numerous stacking faults, which imply the dissociation of several of these dislocations into 1/6〈1 1 2〉 Shockley partials. At later stages (∼20% strain), nanoscale deformation twins were observed after interrupted tests at 77 K, but not in specimens tested at room temperature, where plasticity occurred exclusively by the aforementioned dislocations which organized into cells. Deformation twinning, by continually introducing new interfaces and decreasing the mean free path of dislocations during tensile testing (“dynamic Hall–Petch”), produces a high degree of work hardening and a significant increase in the ultimate tensile strength. This increased work hardening prevents the early onset of necking instability and is a reason for the enhanced ductility observed at 77 K. A second reason is that twinning can provide an additional deformation mode to accommodate plasticity. However, twinning cannot explain the increase in yield strength with decreasing temperature in our high-entropy alloy since it was not observed in the early stages of plastic deformation. Since strong temperature dependencies of yield strength are also seen in binary fcc solid solution alloys, it may be an inherent solute effect, which needs further study.

1,449 citations

Journal ArticleDOI
TL;DR: In this article, a rate dependent constitutive model is developed for polycrystals subjected to arbitrarily large strains, and the model is used to predict deformation textures and large-strain strain hardening behavior following various stressstrain histories for single phase f.c. aggregates that deform by crystallographic slip.
Abstract: A new rate dependent constitutive model is developed for polycrystals subjected to arbitrarily large strains. The model is used to predict deformation textures and large-strain strain hardening behavior following various stress-strain histories for single phase f.c.c. aggregates that deform by crystallographic slip. Examples involving uniaxial and plane strain tension and compression are presented which illustrate how texture influences polycrystalline strain hardening, in particular these examples demonstrate both textural strengthening and softening effects. Input to the model includes the description of single crystal strain hardening and latent hardening along with strain rate sensitivity, all properties described on the individual slip system level. The constitutive formulation used for the individual grains is essentially that developed by Peirce et al . [6, Acta metall . 31, 1951 (1983)] to solve rate dependent boundary value problems for finitely deformed single crystals. Inclusion of rate dependence is shown to overcome the long standing problem of nonuniqueness in the choice of active slip systems which is inherent in the rate independent theory. Because the slipping rates on all slip systems within each grain are unique in the rate dependent theory, the lattice rotations and thus the textures that develop are unique. In addition, the model makes it possible to study how strain rate sensitivity on the slip system, and single grain, levels is manifested in polycrystalline strain rate sensitivity. The model is also used to predict “constant offset plastic strain yield surfaces” for materials that are nearly rate insensitive—these calculations describe the development of rounded “yield surface vertices” and the resulting softening of material stiffness to a change in loading path that vertices imply. For our rate dependent solid this reduction in stiffness occurs after small but finite loading increments. Finally the model is used to carry out an imperfection-based sheet necking analysis both for isotropic and strongly textured sheets. The results show that larger strain hardening rates, and strain rate sensitivity, on the slip system level both increase the failure strains, as expected, but also demonstrate a strong influence of texture on localized necking.

1,421 citations

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