Plastic deformation of silver chloride. II. Photoelastic study of the internal stresses in glide packets

1949 ◽  
Vol 200 (1060) ◽  
pp. 47-66 ◽  
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Silver Chloride ◽  
Relative Orientation ◽  
Internal Stresses ◽  
Middle Plane ◽  
Pure Bending ◽  
State Of Stress ◽  
Electrical Analogy ◽  
Point To Point

The pattern of birefringence caused by glide in silver chloride is most clearly resolved when the glide planes are observed edge on. It is then possible to sketch the two orthogonal sets of curves giving the directions of polarization at each point of the pattern and, by means of a compensator, to find how the magnitude of the birefringence varies from point to point. The stress distribution can be deduced from the distribution of birefringence, provided that the important influence of the relative orientation of stress axes and crystal axes is taken into account. The state of stress in each plastically deformed grain can be resolved into two parts. (1) Each glide packet is subject to pure bending about two perpendicular axes lying in the glide plane (but with a neutral plane that is not always the middle plane of the packet). This gives stresses that vary discontinuously with a period equal to the spacing of the glide zones. (2) There is also a continuously varying stress distribution which changes only slightly in distances equal to the glide zone spacing. The curvature of the glide packets means either that all the dislocations in one glide zone have the same sign or that positive and negative dislocations are present there in unequal numbers. It is found that, throughout any one grain, the ‘ dislocation charge ’ on each zone (to use an obvious electrical analogy) has the same sign and is never more than about twice the average for the grain.

scholarly journals Plastic deformation of silver chloride I. Internal stresses and the glide mechanism

1949 ◽  
Vol 198 (1053) ◽  
pp. 190-204 ◽  
Keyword(s):  
Crystal Structure ◽  
Plastic Deformation ◽  
Single Crystals ◽  
Cross Section ◽  
Optical Method ◽  
Silver Chloride ◽  
Maximum Shear Stress ◽  
Internal Stresses ◽  
Simple Extension ◽  
Set Up

The experiments of Obreimow & Schubnikoff (1927) on the birefringence produced by the plastic deformation of single crystals of rock salt have been extended to a polycrystallirie material. Rolled sheets of silver chloride have been recrystallized and then deformed plastically in various ways—by simple extension and by bending, for example. The sheets are transparent and very ductile and, since silver chloride is cubic in structure, the birefringence patterns observed under the microscope provide a picture of the distribution of the internal stresses uncomplicated by natural double refractions. It is suggested that results obtained with this optical method are applicable to metals. Silver chloride appears to deform by glide, and when the glide packets are observed on edge the glide plane and glide direction to the crystal structure has been studied by making observations upon these bands and upon the glide lines formed on the surfaces of bars of square cross-section consisting effectively of chains of single crystals. The orientations of the fifteen sets of glide bands examined in this way were all consistent with glide movements in a <110> direction; the glide plane, however, was not always a crystallographic plane of low indices. In the six cases in which the measurement was possible, it lay within 9° of the plane in the.<110> zone on which the maximum shear stress, resolved in the <110> direction, acted. It is concluded that silver chloride deforms by ‘pencil glide’, the mechanism postulated by Taylor & Elam in 1926 to explain the plastic behaviour of a-iron. The transmission of pencil glide across grain boundaries is discussed. The residual stresses observed by the optical method in polycrystalline sheets may be divided into three groups: (1) A system of stresses set up between the glide zones of each grain and alternating with a period equal to the spacing of the glide zones. A detailed analysis of these is given in the second paper (part II). (2) Alternating stresses produced when a system of glide zones meets a grain boundary. (3) ‘Heyn stresses’ produced by the nonuniformity of plastic deformation from grain to grain.

scholarly journals On the stresses induced by flexure in a deep rectangular beam

1934 ◽  
Vol 143 (849) ◽  
pp. 271-284 ◽  
Keyword(s):  
Stress Distribution ◽  
Practical Importance ◽  
Sufficient Accuracy ◽  
Elastic Instability ◽  
Theoretical Interest ◽  
Close Approximation ◽  
Rectangular Section ◽  
Apparent Paradox ◽  
State Of Stress ◽  
Radial Forces

1. When a straight cylindrical rod is bent into a circle by couples applied at its ends, the resulting state of stress is given, with sufficient accuracy for practical purposes, by the well-known theory of St. Venant. In that theory qunatities of the second and higher orders in therms of strain are neglected, and the resulting solution asserts that the stress is purely longitudinal, so that the rod may be thought of as an assembly of cylindrical fibres, each of which behaves independently of its neighbours. It is evident that this description cannot be exact; for a fibre bent into a circle cannot be kept in tension unless radial forces operate to maintain equilibrium, and in the case considered such forces can come only from actions between adjacent fibres. The apparent paradox is explained by the consideration that those action are of the second order in terms of the curvature, and accordingly are neglected in St. Venant's theory. In connection with a certain problem of elastic instability it was thought desirable to attempt a more accurate description for a particular case, namely, a rod of deep and thin rectangular section. It was found that the equations of equilibrium can be integrated independently of any simplifying assumption, and the stress-distribution determined for curvature of any magnitude. The results have no great practical importance, sice they show that St. Venant's theory gives a close approximation to the facts within that range of strains which actual materials can sustain elastically; but they have some theoretical interest, and accordingly are presented in this paper.

Numerical Solution of Elastoplastic Torsion of a Shaft of Rotational Symmetry

1949 ◽  
Vol 16 (2) ◽  
pp. 139-148
Author(s):  
R. P. Eddy ◽  
F. S. Shaw
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Numerical Solution ◽  
Rotational Symmetry ◽  
Relaxation Methods ◽  
Elastoplastic Boundary ◽  
Sufficient Magnitude ◽  
Elastoplastic Torsion ◽  
Von Mises

Abstract Using relaxation methods, an approximate numerical solution is found of the stress distribution in a shaft of rotational symmetry, which is subjected to a torque of sufficient magnitude to cause portions of the material to yield. It is assumed that the material of which the shaft is composed is isotropic and yields according to the condition of von Mises. The particular problem investigated is a shaft with a collar; results are presented showing the elastoplastic boundary, and the stress distribution, for two different amounts of plastic deformation.

Experimental and numerical investigation of Armox 500T armor steel perforation process

2021 ◽  
Vol 70 (1) ◽  
pp. 43-61
Author(s):  
Arkadiusz Popławski
Keyword(s):  
Plastic Deformation ◽  
Strain State ◽  
Numerical Study ◽  
Stress And Strain ◽  
Failure Model ◽  
Modes Of Failure ◽  
State Of Stress ◽  
Computational Code ◽  
Armor Steel ◽  
Plate Perforation

This paper presents the results of an experimental and numerical study of the perforation of Armox 500T armoured steel. The plate perforation was performed with a pneumatic gun using three types of penetrators. Sharp, spherical and blunt penetrators were used. The use of different geometries of penetrators causes the process of perforation and destruction of plates in a different state of stress and strain, which leads to the appearance of three basic modes of failure. Numerical analyses of the perforation process have been carried out using the Ls-Dyna computational code with an advanced constitutive model of the material and the integrated failure model. The obtained experimental and numerical results were analysed and compared. The failure shape, the level of plastic deformation and the parameters of stress and strain state were analysed.

Design with Nonhomogeneous Materials—Part I: Pure Bending of Prismatic Bars

1987 ◽  
Vol 109 (1) ◽  
pp. 82-86 ◽  
Author(s):  
V. K. Stokes
Keyword(s):  
Tensile Test ◽  
Material Properties ◽  
Elastic Moduli ◽  
Mechanical Response ◽  
Mechanical Design ◽  
Beam Theory ◽  
Pure Bending ◽  
Strongly Coupled ◽  
Point To Point ◽  
Nonhomogeneous Materials

Because material properties vary from point to point in nonhomogeneous materials, there is some question as to what “properties” are measured in tests such as the tensile test, and how such “properties” can be used in the mechanical design process. In this paper, the mechanical response of nonhomogeneous prismatic bars in pure bending has been shown to depend on parameters that are strongly coupled combinations of geometry and material properties. The purely geometry based inertia tensor in homogeneous beam theory is replaced in the nonhomogeneous case by the rigidity tensor, which combines geometry and material properties. Interpretations for the average elastic moduli, which would be determined by tests on nonhomogeneous materials, have been explored. Also discussed is the usefulness of such average moduli for predicting the mechanical response of nonhomogeneous bars.

scholarly journals Model Calculations of Elastic Moduli in Highly Deformed Composites

1989 ◽  
Vol 10 (2) ◽  
pp. 153-164 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Plastic Deformation ◽  
Simple Model ◽  
Elastic Moduli ◽  
Opposite Sign ◽  
Internal Stresses ◽  
Minor Importance ◽  
High Increase ◽  
Two Phase ◽  
Linear Elasticity Theory ◽  
Model Calculations

Young's modulus of heavily deformed two-phase composites shows an unusually high increase after plastic deformation. It is assumed that this is due to two reasons, i.e. texture changes and changes of the moduli of the constitutive phases on the basis of non-linear elasticity theory and internal stresses of opposite sign in the phases. Expressions of the two contributions are given on the basis of simple model assumptions. It is estimated that the changes of shape and arrangement of the phases and shape and arrangement of the crystallites in the phases are only of minor importance.

Characterization of Microstructure and Mechanical Properties of 6060 Aluminum Alloy Processed by ECAP

2018 ◽  
Vol 275 ◽  
pp. 81-88
Author(s):  
Monika Karoń ◽  
Marcin Adamiak
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Plastic Deformation ◽  
Aluminum Alloy ◽  
Internal Stresses ◽  
Refined Grains ◽  
Angular Pressing ◽  
Heat Treated ◽  
Evolution Of Microstructure

The purpose of this paper is to present the microstructure and mechanical behavior of 6060 aluminum alloy after intense plastic deformation. Equal Channel Angular Pressing (ECAP) was used as a method of severe plastic deformation. Before ECAP part of the samples were heat treated to remove internal stresses in the commercially available aluminium alloy. The evolution of microstructure and tensile strength were tested after 1, 3, 6 and 9 ECAP passes in annealed and non annealed states. It was found that intensely plastically deformed refined grains were present in the tested samples and exhibited increased mechanical properties. Differences were noted between samples without and after heat treatment

Applications of Creep Tests

1933 ◽  
Vol 1 (3) ◽  
pp. 87-97
Author(s):  
Gleason H. MacCullough
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Analytical Solutions ◽  
Practical Interest ◽  
Creep Data ◽  
Pure Bending ◽  
Creep Tests ◽  
Circular Shaft ◽  
Pipe Joint

Abstract Analytical solutions of problems which involve creep phenomena and which are of practical interest are at present very limited in number. This paper discusses four specific problems for which solutions have been presented: namely, the problem of the flanged and bolted pipe joint under creep conditions, and the three problems of stress distribution and creep in thick-walled cylinders under internal pressure, in a beam subjected to pure bending, and in a solid circular shaft under torsion. These solutions will illustrate the kind of creep data which the designer desires the experimenter to furnish.

Stress Distributions in Nonsymmetric Rotating Rays

1955 ◽  
Vol 22 (3) ◽  
pp. 311-316
Author(s):  
P. G. Hodge
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Large Scale ◽  
Bending Moment ◽  
Rotating Disk ◽  
Longitudinal Force ◽  
Maximum Speed ◽  
Stress Distributions ◽  
Centrifugal Forces

Abstract The centrifugal forces acting upon a rotating ray will produce longitudinal stresses along the ray. If the ray is not symmetric, these stresses will result not only in a longitudinal force, but also in a bending moment. A technique for finding the stress distribution in this case is developed and illustrated by means of simple examples. The limiting elastic speed and the maximum speed before large-scale plastic deformation commences are computed. An indication is given of how similar methods may be used to analyze a rotating disk with no plane of symmetry perpendicular to the axis.

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