Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

The Study of Elastic-Plastic Fatigue Behavior of Nigerian-Rolled NST 37-2 Steel

2010 ◽  
Vol 3 ◽  
pp. 28-41
Author(s):  
B.O. Malomo ◽  
S.A. Ibitoye ◽  
L.O. Adekoya
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Fatigue Behavior ◽  
Numerical Results ◽  
Test Material ◽  
Flow Rule ◽  
Static Fatigue ◽  
Elastic Plastic

The NST 37-2 steel represents about 75% volume of Nigerian-produced steel which is yet to be fully characterized for its fatigue behavior. Thus, its suitability for many applications is questionable. This paper presents a framework based on the theory of elasto-plasticity in order to make appropriate recommendations in this regard. Experimentally, tensile tests were carried out on test specimens to establish the baseline material properties of the steel in annealed, as-rolled, normalized and hardened/tempered conditions. Fatigue tests were then conducted at 60% Su; 70% Su and 80% Su of the test material and fractographic examinations on the test specimens were subsequently carried out. The frequency harmonic fatigue analysis was implemented in the ANSYS software environment for the numerical study. The elastic-plastic material property was described by the von Mises yield criterion, the flow rule of Prandtl-Reuss, and the kinematic hardening rule of Prager. The numerical results indicate with respect to rate-dependence fatigue behavior that the annealed test specimen is most resilient under cyclic deformation as compared with the normalized, hardened/tempered and as-rolled specimens respectively. The experimental and numerical results were found to be in close agreement and based on the general performance, the steel material is recommended for use in low cycle, quasi-static fatigue applications.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

Asymptotic Crack-Tip Fields for Mixed Stationary Crack under Plane Stress Conditions in Pressure Sensitive and Elastic-Plastic Materials

2010 ◽  
Vol 146-147 ◽  
pp. 611-614
Author(s):  
Chen Hua Lu ◽  
Su Fang Xing ◽  
Wen Jia Wang ◽  
Jian Bing Sang ◽  
Bo Liu
Keyword(s):  
Plane Stress ◽  
Yield Criterion ◽  
Crack Tip ◽  
Flow Rule ◽  
Basic Solution ◽  
Crack Tip Field ◽  
Plane Stress Condition ◽  
Elastic Plastic ◽  
Pressure Sensitive ◽  
Elastic Plastic Materials

Based on the parabolic yield criterion reflected by pressure sensitive and the SD effect, the material constitutive equation is given by orthogonal flow rule. In the plane stress condition, a basic solution in elastic-plastic crack tip field is given. The different structures of solutions with different plastic mixity are analyzed. Different parameters in crack-tip stress field and the singularity in the strain field are discussed. These results provide a theoretical reference for engineering applications.

Ultimate Carrying Capacity of Elastic-Plastic Plates on a Pasternak Foundation

2014 ◽  
Vol 81 (5) ◽  
Author(s):  
L. Lanzoni ◽  
E. Radi ◽  
A. Nobili
Keyword(s):  
Yield Criterion ◽  
Plastic Region ◽  
Closed Form Solution ◽  
Form Solution ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Plastic Mechanism ◽  
Pasternak Elastic Foundation ◽  
Loaded Area

In the present work, the problem of an infinite elastic perfectly plastic plate under axisymmetrical loading conditions resting on a bilateral Pasternak elastic foundation is considered. The plate is assumed thin, thus making it possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen's yield criterion with associative flow rule. A uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elastic-plastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, a further increase of the load may originate two or three different elastic-plastic regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows us to estimate the elastic-plastic behavior of the plate up to the onset of collapse, here defined by the formation of a plastic mechanism within the plate. The corresponding collapse load and the sizes of the elastic-plastic regions are thus found by imposing the boundary and continuity conditions between the different regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.

The Shrink Fit with Nonlinearly Hardening Elastic-Plastic Hub

1987 ◽  
Vol 54 (2) ◽  
pp. 474-476 ◽  
Author(s):  
Udo Gamer
Keyword(s):  
Yield Criterion ◽  
Elastic Region ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Hardening Law ◽  
Elastic Disk ◽  
Shrink Fit ◽  
Associated Flow Rule ◽  
Nonlinear Hardening

Based on Tresca’s yield criterion and the associated flow rule, stresses and displacement in a rotating shrink fit consisting of an elastic disk and a partially plasticized annulus are calculated for an arbitrary nonlinear hardening law. It is shown that the elastic-plastic border radius and the stresses in the elastic region of the hub do not depend on the hardening law.

On the plastic flow of metals under conditions of axial symmetry

1955 ◽  
Vol 233 (1193) ◽  
pp. 267-287 ◽  
Keyword(s):  
Stress Field ◽  
Plastic Flow ◽  
Plane Surface ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Principal Stresses ◽  
Infinite Body ◽  
Plastic Stress

This paper is concerned with the axially symmetric plastic flow of a rigid-plastic nonhardening material which obeys the Tresca yield criterion of constant maximum shearing stress and the associated flow rule. A general discussion of the basic equations is given. The discussion shows that the hypothesis of Haar and von Kármán is likely to be of great importance in the solution of axially symmetric problems. This conclusion is substantiated by the remainder of the work which considers problems in which the hypothesis is satisfied, i.e. problems in which the circumferential stress is equal to one of the principal stresses in the meridional planes. Possible plastic velocity fields in a circular cylindrical bar stressed to yielding in compression or tension are obtained in §3. Section 4 examines plastic stress fields in the neighbourhood of stress-free conical surfaces. In the final sections of the paper, the plastic stress field and a permissible deformation mode for the problem of the indentation of the plane surface of a semi-infinite body by a circular flat-ended rigid punch are obtained. It is shown that the plastic stress field near the punch can be extended into the rigid region without violating the yield criterion.

Elastic-Plastic Plane-Strain Solutions With Separable Stress Fields

1969 ◽  
Vol 36 (3) ◽  
pp. 528-532
Author(s):  
D. B. Bogy
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Yield Criterion ◽  
A Priori ◽  
Equivalent Plastic Strain ◽  
Uniaxial Stress ◽  
Stress Fields ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Elastic Plastic

A stress field σij(χ, t) depending on position χ and time t will be called separable if the time-dependence enters only through a scalar multiplier; i. e., if σij(χ,t)=s(χ,t)σˆij(χ). It is shown here that elastic-plastic plane-strain solutions in the infinitesimal (flow) theory of plasticity satisfying Tresca’s yield criterion and associated flow rule with linear isotropic hardening, based on either equivalent plastic strain or total plastic work, can occur with separable stress fields only in the following instances: (a) solutions with uniaxial stress fields, as in bending, (b) solutions with stress fields such that the entire domain changes from elastic to plastic at the same time, and (c) solutions with stress fields for which the elastic-plastic boundary coincides with a principal shear stress trajectory. Whether or not a plasticity solution has a separable stress field can be determined a priori by examining the corresponding elasticity solution.

The Elastic-Plastic Stress Distribution Within a Wide Curved Bar Subjected to Pure Bending

1955 ◽  
Vol 22 (3) ◽  
pp. 305-310
Author(s):  
Bernard W. Shaffer ◽  
Raymond N. House
Keyword(s):  
Stress Distribution ◽  
Convex Surface ◽  
Plastic Material ◽  
Circumferential Stress ◽  
Yield Condition ◽  
Bending Moment ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Stress

Abstract Analytical expressions are obtained for the radial and circumferential stress distributions within a wide curved bar made of a perfectly plastic material when it is subjected to a uniformly distributed bending moment. The elastic stress distributions are based on the use of the Airy stress function, whereas the plastic stress distributions in this problem of plane strain are based on the use of the Tresca yield condition. It is found that as the bending moment increases in the direction which tends to straighten the initially curved bar, an elastic-plastic boundary develops first around the concave surface. It meets a second boundary, which starts sometime later around the convex surface, when the bar is completely plastic. The elastic region within the bar decreases at a fairly uniform rate as the bending moment increases to within approximately 90 per cent of the fully plastic bending moment but then it degenerates very much more rapidly until it no longer exists when the bar is completely plastic. The position of the neutral surface is independent of the applied bending moment when the stress distribution is within the completely elastic and the completely plastic ranges. Within the elastic-plastic range, however, it moves away from and then toward the center of curvature as the bending moment increases.

Elastic-Plastic Contact Analysis of Materials with Gradient Yield Strength

2006 ◽  
Vol 532-533 ◽  
pp. 881-884
Author(s):  
Qin Xie ◽  
Geng Liu ◽  
Tian Xiang Liu ◽  
Jane Q. Wang
Keyword(s):  
Yield Strength ◽  
Yield Criterion ◽  
Contact Model ◽  
Von Mises Stress ◽  
Stress Distributions ◽  
Initial Stiffness ◽  
Programming Technique ◽  
Elastic Plastic ◽  
Von Mises ◽  
Yield Strength Variation

Reported in the paper is an elastic-plastic contact model developed to analyze the contact performance characteristics of materials with gradient yield strength. Plastic yielding and the strain-hardening properties of the materials are taken into account. The finite element method, the initial stiffness method, and a mathematical programming technique are utilized to solve the contact model. The von Mises yield criterion is used to determine the inception of plastic deformation. Results indicate that nitrided material with appropriate gradient of yield strength may greatly alter the distributions of contact stress, contact pressure as compared with untreated material in contact. The effects of different yield strength variation path of material on von Mises stress distributions are numerically investigated and discussed.

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