scholarly journals Analysis of Strain-Hardening Viscoplastic Wide Sheets Subject to Bending under Tension

Metals ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 118
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina
Keyword(s):  
Strain Hardening ◽  
Thickness Distribution ◽  
Tensile Force ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Equivalent Strain ◽  
Accurate Solution ◽  
Viscoplastic Material ◽  
Rigid Plastic ◽  
Bending Under Tension

The present paper provides an accurate solution for finite plane strain bending under tension of a rigid/plastic sheet using a general material model of a strain-hardening viscoplastic material. In particular, no restriction is imposed on the dependence of the yield stress on the equivalent strain and the equivalent strain rate. A special numerical procedure is necessary to solve a non-standard ordinary differential equation resulting from the analytic treatment of the boundary value problem. A numerical example illustrates the general solution assuming that the tensile force vanishes. This numerical solution demonstrates a significant effect of the parameter that controls the loading speed on the bending moment and the through-thickness distribution of stresses.

Compression of Viscoplastic Material Between Rotating Plates

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng
Keyword(s):  
Friction Surface ◽  
Thickness Distribution ◽  
Numerical Procedure ◽  
Equivalent Strain ◽  
Two Dimensional ◽  
Accurate Approximation ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Two Dimensional Flow ◽  
Rotating Plates

An analysis is conducted of the two-dimensional flow of Bingham solids between two rotating plates. The maximum friction law is adopted at the plate surface. An asymptotic analysis of the solution is performed in the vicinity of the friction surface. Its results are used in a numerical procedure to obtain an accurate approximation of the solution near the friction surface. The through thickness distribution of velocities, the equivalent strain rate, and stresses is illustrated. Qualitative features of the solution are emphasized. The results are compared with the solution for rate-independent materials.

A Semi-Analytical 3-D Solution for Bending Under Tension

2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Bending Under Tension ◽  
Associated Flow Rule

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

scholarly journals Rigid-Plastic Approximations for Predicting Plastic Deformation of Cylindrical Shells Subject to Dynamic Loading

1996 ◽  
Vol 3 (3) ◽  
pp. 169-181 ◽  
Author(s):  
Michelle S. Hoo Fatt ◽  
Tomasz Wierzbicki ◽  
Minos Moussouros ◽  
John Koenig
Keyword(s):  
Plastic Deformation ◽  
Tensile Force ◽  
Bending Moment ◽  
Expansion Method ◽  
Rigid Plastic ◽  
Closed Form Solutions ◽  
Eigenfunction Expansion Method ◽  
Longitudinal Bending ◽  
Final Deformation ◽  
String State

A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

scholarly journals Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1166
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Kinematic Hardening ◽  
Tensile Force ◽  
Plastic Region ◽  
Equivalent Plastic Strain ◽  
Isotropic Hardening ◽  
Finite Plane ◽  
Present Solution ◽  
Bending Under Tension ◽  
Elastic Unloading

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Three-Dimensional Finite Element Analysis of Pipe Flange Connections: The Case of Using Compressed Asbestos Sheet Gasket

2002 ◽  
Author(s):  
Tomohiro Takaki ◽  
Toshimichi Fukuoka
Keyword(s):  
Contact Pressure ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Bending Moment ◽  
Elastic Interaction ◽  
Bearing Surface ◽  
Element Analysis ◽  
Bolt Stress ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The most important factor for the leakage problem of pipe flange connections is considered to be contact pressure distribution at the gasket bearing surface in service. In this study, the mechanical behaviors of the pipe flange connection are evaluated using FEM as a three-dimensional contact problem, in which a gasket is modeled as a nonlinear one-dimensional gasket element. Here, the contact pressure distributions at the gasket bearing surface and the variations of the bolt stress are estimated under uniform bolt preloads or nonuniform ones due to the elastic interaction during bolting up. The numerical procedure proposed here can successively deal with the processes of bolt-up, applying inner pressure and applying bending moment. The analytical objects are pipe flanges specified in JIS B 2238 with compressed asbestos sheet gaskets being inserted. The validity of the numerical method is ascertained by experiment.

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.

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