The New Theory of Plasticity, Strain Hardening, and Creep, and the Testing of the Inelastic Behavior of Metals

1933 ◽  
Vol 1 (4) ◽  
pp. 151-155
Author(s):  
H. Hencky
Keyword(s):  
Strain Hardening ◽  
Elastic Energy ◽  
Inelastic Behavior ◽  
Analytical Treatment ◽  
Very Old ◽  
Theory Of Plasticity

Abstract The knowledge of the inelastic behavior of metals has experienced considerable growth in the last few years. To draw all the advantages possible from the experiments, frequently very difficult, an effort has been made to bring the entire development under some dominating physical ideas. These ideas are in fact very old, and deal mainly with the proper conception of the hidden elastic energy that is responsible for the statical component of the strain hardening. The analytical treatment of the inelastic behavior gives promise of being valuable not only in the testing of materials, but even for the designer of machines used in the forming of metals.

Finite Deflections of a Rigid-Viscoplastic Strain-Hardening Annular Plate Loaded Impulsively

1968 ◽  
Vol 35 (2) ◽  
pp. 349-356 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Strain Rate Sensitivity ◽  
Annular Plate ◽  
Dominant Role ◽  
Plate Thickness ◽  
Rate Sensitivity ◽  
Finite Deflections ◽  
Analytical Treatment ◽  
Rigid Plastic

A relatively simple analytical treatment of the behavior of a rigid-plastic annular plate subjected to an initial linear impulsive velocity profile is presented. The influence of finite deflections has been included in addition to strain-hardening and strain-rate sensitivity of the plate material. It is shown, for deflections up to the order of twice the plate thickness, that strain-hardening is unimportant, strain-rate sensitivity has somewhat more effect, while membrane forces play a dominant role in reducing the permanent deflections.

Assessment of Different Steel Material Characteristics on Shear Links Performance

2019 ◽  
Vol 1154 ◽  
pp. 150-160
Author(s):  
Sara Ansari ◽  
Javad Tashakori ◽  
Javad Razzaghi
Keyword(s):  
Strain Hardening ◽  
Local Buckling ◽  
Cyclic Stress ◽  
Inelastic Behavior ◽  
Plastic Rotation ◽  
Material Characteristics ◽  
Steel Material ◽  
Steel Grades ◽  
Element Approach ◽  
Shear Links

The inelastic behavior of shear links depends on their material ductility. In order to investigate the effect of cyclic characteristics of steel on shear links behavior, five experimental links constructed of various steel grades are modeled by finite element approach. These models are verified using experimental shear links results. Moreover, cyclic stress-strain material curve is used for simulating links behavior and the models can simulate strength degradation of flange and web local buckling appropriately. The overstrength and plastic rotation of the links are modified due to the influence of test setup configuration once the buckling occurs. It can be concluded that the links material characteristics can affect the overstrength and plastic rotation. In this study, the various strain hardening of different grades of steel are evaluated and the amplitudes of strain which can simulate strain hardening of links are determined for five materials.

Strain Hardening of a Porous Limestone

1967 ◽  
Vol 7 (03) ◽  
pp. 229-234 ◽  
Author(s):  
J.B. Cheatham
Keyword(s):  
Yield Strength ◽  
Mechanical Behavior ◽  
Strain Hardening ◽  
Rock Mechanics ◽  
Mathematical Theory ◽  
Confining Pressure ◽  
Plasticity Theory ◽  
Single Type ◽  
Microscopic Structure ◽  
Theory Of Plasticity

Abstract Applications of the mathematical theory of plasticity promises to lead to the solution of many drilling and rock mechanics problems. Because of mathematical considerations, the inelastic behavior of rock has frequently been represented by a perfectly plastic model in conjunction with a yield criteria of the Coulomb or Mohr type. The totality of all stress states for which a solid ceases to behave elastically can be represented as a limit surface in stress space. Probing of such limit surfaces indicates details of strain hardening which are not provided by the standard triaxial testing procedure. Probing tests of the limit surfaces have been performed on Cordova Cream limestone to provide data for extending plasticity theory to cover situations in which consolidation and strain hardening are present. Test results indicate that this highly porous limestone undergoes a permanent volume decrease when it is subjected to hydrostatic pressures in excess of 3,500 psi. A virgin sample tested under a confining pressure of 1,500 psi has a yield strength of 1,700 psi; however, if the sample is subjected to a consolidation pressure of 5,000 psi, before testing at 1,500 psi, the yield strength is raised to 2,300 psi. Thus, both consolidation and strain hardening are important considerations in describing the mechanical behavior of this limestone. Tests conducted with the axis of the core having different orientations indicate that this rock is also anisotropic. Portions of the initial and subsequent limit surfaces are determined for samples loaded either perpendicular or parallel to the bedding planes. INTRODUCTION Previous experimental work in rock mechanics indicates that no mathematically tractable constitutive theory is inclusive enough to describe the mechanical behavior exhibited by all types of rocks under all conditions of stress and temperature. Indeed, the type of deformation encountered in a single type of rock is known to depend upon the stress and temperature conditions in the rock during deformation.1-5 Certain rocks and minerals, notably those minerals composed of ionic salts, have been shown to exhibit plastic deformation when tested under conditions of high confining pressure.2 Since the mathematical theory of plasticity provides simplifications over the theory of elasticity in certain types of problems, such as those in which limit analysis can be applied, it is of interest to know under what conditions plasticity theory may be applied to rock mechanics problems. The following factors determine the nature of the deformation a particular specimen will undergo:the microscopic structure of the rock, i.e., the structure visible under an optical microscope, including number of phases, porosity, distribution of phases,the mineralogical structure of the solid phases,the conditions of stress and the rate of change of stress andthe temperature. Extensive experiments on Yule marble, Carthage marble, Solenhofen limestone and other calcerous rocks indicate that these relatively nonporous rocks deform plastically under certain conditions of loading, and creep under other conditions of loading.1-3 This study is concerned with the behavior of Cordova Cream limestone (Austin chalk) which is also composed almost entirely of calcite and thus has the same mineralogical composition but, because of a rather large porosity, it possesses a different microscopic structure. This investigation was undertaken to learn if Cordova Cream limestone deforms plastically despite the embrittling effect of the pore spaces, and to provide data which can be used to determine whether the mathematical theory of plasticity can describe the mechanical behavior of Cordova Cream limestone.

scholarly journals Some comments on reinforced concrete structures forming column hinge mechanisms

1977 ◽  
Vol 10 (4) ◽  
pp. 186-195 ◽  
Author(s):  
T. E. Kelly
Keyword(s):  
Energy Dissipation ◽  
Computer Program ◽  
Strain Hardening ◽  
Elastic Energy ◽  
Static Loading ◽  
Wall Structure ◽  
Reinforced Concrete Structures ◽  
Base Shear ◽  
Input Design ◽  
Incremental Collapse

Three buildings relying on column hinge mechanisms for post-elastic energy dissipation were studied using an inelastic dynamic computer program. The structures were an eight storey wall structure with ground storey columns, an eight storey frame with rigid, non-yielding beams, and a single storey frame with rigid, non-yielding beams. Parameters varied were earthquake input, design base shear and strain hardening ratio. All structures exhibited deformations far in excess of deflections under code static loading. The eight storey structures showed a tendency towards incremental collapse from P-delta effects when low, probably realistic, strain hardening ratios were used.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 260-265 ◽  
Author(s):  
C. L. Chow ◽  
M. Jie ◽  
S. J. Hu
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Yield Criterion ◽  
Strain Ratio ◽  
Yield Function ◽  
Forming Limit ◽  
Sheet Metals ◽  
Theory Of Plasticity ◽  
Von Mises Yield Criterion ◽  
Von Mises

This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Sto¨ren and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

Sign in / Sign up

Export Citation Format

Share Document