Plastic Collapse of a Thin Annular Disk Subject to Thermomechanical Loading

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeau-Ren Jeng
Keyword(s):  
Analytic Solution ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
The Other ◽  
Collapse Mechanism ◽  
Plastic Collapse ◽  
Thermomechanical Loading ◽  
Annular Disk ◽  
Collapse Mechanisms ◽  
Inner Radius

A semi-analytic solution for plastic collapse of a thin annular disk subject to thermomechanical loading is presented. It is assumed that the yield criterion depends on the hydrostatic stress. A distinguished feature of the boundary value problem considered is that there are two loading parameters. One of these parameters is temperature and the other is pressure over the inner radius of the disk. The general qualitative structure of the solution at plastic collapse is discussed in detail. It is shown that two different plastic collapse mechanisms are possible. One of these mechanisms is characterized by strain localization at the inner radius of the disk. The entire disk becomes plastic according to the other plastic collapse mechanism. In addition, two special regimes of plastic collapse are identified. According to one of these regimes, plastic collapse occurs when the entire disk is elastic, except its inner radius. According to the other regime, the entire disk becomes plastic at the same values of the loading parameters at which plastic yielding starts to develop.

scholarly journals Effect of Plastic Anisotropy on the Collapse of a Hollow Disk under Thermal and Mechanical Loading

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 909
Author(s):  
Elena Lyamina
Keyword(s):  
Plastic Anisotropy ◽  
Plastic Region ◽  
Finite Size ◽  
Analytic Solutions ◽  
Outer Radius ◽  
The Other ◽  
Plastic Collapse ◽  
Essential Difference ◽  
Plastic Yielding ◽  
Inner Radius

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and preliminary design of such structures. The present paper is devoted to describing the plastic collapse of a thin orthotropic hollow disk inserted into a rigid container. The disk is subject to a uniform temperature field and a uniform pressure is applied over its inner radius. The condition of axial symmetry in conjunction with the assumption of plane stress, permits an exact analytic solution. Two plastic collapse mechanisms exist. One of these mechanisms requires that the entire disk is plastic. According to the other mechanism, plastic deformation localizes at the inner radius of the disk. Additionally, two special solutions are possible. One of these solutions predicts that the entire disk becomes plastic at the initiation of plastic yielding (i.e., plastic yielding simultaneously initiates in the entire disk). The other special solution predicts that the plastic localization occurs at the inner radius of the disk with no plastic region of finite size. An essential difference between the orthotropic and isotropic disks is that plastic yielding might initiate at the outer radius of the orthotropic disk.

Effect of Pressure-Dependency of the Yield Criterion on the Development of Plastic Zones and the Distribution of Residual Stresses in Thin Annular Disks

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng ◽  
Evgenii Lomakin
Keyword(s):  
Stress Distribution ◽  
Residual Stresses ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
The Other ◽  
Plastic Yielding ◽  
Annular Disk ◽  
Effect Of Pressure ◽  
Other Hand ◽  
Pressure Dependency

The main objective of the present paper is to show an effect of pressure-dependency of the yield criterion on the development of the plastic zone and the distribution of residual stresses in a thin annular disk subject to a pressure over its inner edge during the loading stage. The Drucker–Prager yield criterion is adopted to account for the effect of the hydrostatic pressure on plastic yielding. The state of stress is supposed to be plane and the material model is perfectly plastic. A semi-analytical stress solution to the problem formulated is given and its qualitative features are emphasized. It is shown that the pressure at which plastic yielding starts and the pressure at which the entire disk becomes plastic are weakly affected by the pressure-dependency of the yield criterion. On the other hand, this dependency has a significant effect on the maximum possible pressure that can be supported by the disk. The minimum pressure at which reverse yielding occurs is also affected by the pressure-dependency of the yield criterion. In general, the residual radial stress distribution is more influenced by the pressure-dependency of the yield criterion than the residual circumferential stress distribution, although the magnitude of circumferential stresses is larger than the magnitude of radial stresses. On the other hand, the effect of pressure-dependency of the yield criterion on the residual circumferential stress distribution is pronounced in the vicinity of the inner edge of the disk, where this stress is important for improving fatigue performance of structures.

scholarly journals X-ray variability of the HMXB Cen X-3: evidence for inhomogeneous accretion flows.

2020 ◽  
Author(s):  
G Sanjurjo-Ferrín ◽  
J M Torrejón ◽  
K Postnov ◽  
L Oskinova ◽  
J J Rodes-Roca ◽  
...  
Keyword(s):  
Equivalent Width ◽  
Compact Star ◽  
Timing Analysis ◽  
Roche Lobe ◽  
The Other ◽  
Emission Lines ◽  
High Mass ◽  
X Ray ◽  
Accretion Flows ◽  
Inner Radius

Abstract Cen X-3 is a compact high mass X-ray binary likely powered by Roche lobe overflow. We present a phase-resolved X-ray spectral and timing analysis of two pointed XMM-Newton observations. The first one took place during a normal state of the source, when it has a luminosity LX ∼ 1036 erg s−1. This observation covered orbital phases φ = 0.00 − 0.37, i.e. the egress from the eclipse. The egress lightcurve is highly structured, showing distinctive intervals. We argue that different intervals correspond to the emergence of different emitting structures. The lightcurve analysis enables us to estimate the size of such structures around the compact star, the most conspicuous of which has a size ∼0.3R*, of the order of the Roche lobe radius. During the egress, the equivalent width of Fe emission lines, from highly ionized species, decreases as the X-ray continuum grows. On the other hand, the equivalent width of the Fe Kα line, from near neutral Fe, strengthens. This line is likely formed due to the X-ray illumination of the accretion stream. The second observation was taken when the source was 10 times X-ray brighter and covered the orbital phases φ = 0.36 − 0.80. The X-ray lightcurve in the high state shows dips. These dips are not caused by absorption but can be due to instabilities in the accretion stream. The typical dip duration, of about 1000 s, is much longer than the timescale attributed to the accretion of the clumpy stellar wind of the massive donor star, but is similar to the viscous timescale at the inner radius of the accretion disk.

A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

1990 ◽  
Vol 57 (1) ◽  
pp. 40-49 ◽  
Author(s):  
F. Z. Li ◽  
J. Pan
Keyword(s):  
Plane Strain ◽  
Effective Stress ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Crack Tip ◽  
Flow Rule ◽  
Pressure Sensitivity ◽  
Crack Tip Fields ◽  
Pressure Sensitive ◽  
Plane Strain Crack

Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

Plastic Collapse of Orthotropic Plates

1982 ◽  
Vol 26 (04) ◽  
pp. 286-295
Author(s):  
John C. Christodoulides ◽  
Joao G. de Oliveira
Keyword(s):  
Limit Analysis ◽  
Lateral Pressure ◽  
Yield Criterion ◽  
Plastic Collapse ◽  
Orthotropic Plates ◽  
Perfectly Plastic ◽  
Technical Theory ◽  
Orthotropic Shells ◽  
Theory Of Shells

A yield criterion for thin orthotropic shells expressed in terms of generalized stresses is first derived. This yield criterion is based on the yield criterion proposed by Hill for anisotropic continua and it is consistent with all the assumptions usually adopted in the technical theory of shells. As an example of application of this criterion the collapse of perfectly plastic rectangular orthotropic plates subjected to a uniform lateral pressure is studied using the Theorems of Limit Analysis.

Plastic collapse mechanisms of lifeguards for the class 465 EMU bogies

2000 ◽  
pp. 311-317
Author(s):  
E.C. Chirwa ◽  
E.J. Searancke ◽  
A. Hoe ◽  
S.M.P. Wong
Keyword(s):  
Plastic Collapse ◽  
Collapse Mechanisms

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.

Experimental Study for Proximity Rule of Multiple Flaws for Ductile Fracture

2004 ◽  
Author(s):  
Katsumasa Miyazaki ◽  
Kunio Hasegawa ◽  
Takeshi Shimamura
Keyword(s):  
Aspect Ratio ◽  
Ductile Fracture ◽  
Fracture Behavior ◽  
Maximum Load ◽  
Tensile Tests ◽  
Fracture Pattern ◽  
The Other ◽  
Plastic Collapse ◽  
Intensity Factors ◽  
Class 1

The proximity rule of multiple flaws in ASME B&PV Code Section XI 2003 addenda was mainly determined by the evaluation of stress intensity factors from the viewpoint of brittle fracture. Since the austenitic steel and carbon steel for class 1 piping shows a ductile manner in fracture, a new proximity rule for ductile fracture is required. To understand the fracture behavior of multiple flaws, tensile tests, using flat plate specimens made of Type 304SS with twin flaws, were conducted. When the shapes of twin flaws were semi-circular with aspect ratio, a/l = 0.5, the effect of the space of multiple flaws on maximum load is clear. On the other hand, the effect of flaw spacing on maximum load was insignificant for flat multiple flaws with 0.167 in a/l. The effect of space of multiple flaws, aspect ratio of multiple flaws on ductile fracture pattern was discussed. Finally, the proximity rule for plastic collapse was proposed in this paper.

Seismic Vulnerability of Ancient Churches: I. Damage Assessment and Emergency Planning

2004 ◽  
Vol 20 (2) ◽  
pp. 377-394 ◽  
Author(s):  
Sergio Lagomarsino ◽  
Stefano Podestà
Keyword(s):  
Damage Assessment ◽  
Seismic Behavior ◽  
Seismic Vulnerability ◽  
Collapse Mechanism ◽  
Damage Level ◽  
Bell Tower ◽  
Collapse Mechanisms ◽  
Damage Grades ◽  
Definition Of ◽  
The Church

This paper describes a new methodology used to assess seismic damage in the churches of Umbria and the Marches, which is based on 18 indicators, each representative of a possible collapse mechanism for a macroelement. The subdivision of the church into macroelements consists of the identification of architectonic elements in which the seismic behavior is almost independent from the rest of the structure (façade, apse, dome, bell tower, etc.). For each macroelement, by considering its typology and connection to the rest of the church, it is possible to identify the damage modes and the collapse mechanisms. During inspection operations, the surveyors must indicate: (a) the actual macroelements; (b) the damage level; and (c) the vulnerability of the church to that mechanism, related to some specific details of construction. From these data a damage score is defined, which is a number from 0 to 1, obtained as a normalized mean of the damage grades in each mechanism. The analysis of the collected data (more than 1,000 churches in Umbria) allows the definition of the correlation between macroseismic intensity and damage.

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