An Upper Bound Solution for Upsetting of Two-Layer Cylinder

2006 ◽  
Vol 505-507 ◽  
pp. 1303-1308 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Load ◽  
Equivalent Strain ◽  
Industrial Applications ◽  
Upper Bound Theorem ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Plastic Materials

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

An Upper Bound Solution for a Two-Layer Cylinder Subject to Compression and Twist

2007 ◽  
Vol 345-346 ◽  
pp. 37-40 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Additional Condition ◽  
Velocity Fields ◽  
Upper Bound Theorem ◽  
Predictive Capacity ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Bound Theorem ◽  
Formal Requirements

The choice of a kinematically admissible velocity field has a great effect on the predictive capacity of upper bound solutions. It is always advantageous, in addition to the formal requirements of the upper bound theorem, to select a class of velocity fields satisfying some additional conditions that follow from the exact formulation of the problem. In the case of maximum friction law, such an additional condition is that the real velocity field is singular in the vicinity of the friction surface. In the present paper this additional condition is incorporated in the class of kinematically admissible velocity fields chosen for a theoretical analysis of two - layer cylinders subject to compression and twist. An effect of the angular velocity of the die on process parameters is emphasized and discussed.

Criteria for the Prevention of Split Ends

1988 ◽  
Vol 110 (2) ◽  
pp. 162-172 ◽  
Author(s):  
Y. D. Zhu ◽  
B. Avitzur
Keyword(s):  
Rigid Body ◽  
Upper Bound ◽  
Strip Rolling ◽  
Deformation Region ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Rotational Motions ◽  
Split Ends

A criterion for the prevention of split ends (alligatoring) is expressed mathematically. This criteria, t0/R0>1.81×(t0/tf−1) is derived through the extension of an earlier upper bound solution for strip rolling of a perfectly plastic mises material. The treatment is based on the division of the deformation region to a series of triangles, undergoing rigid body rotational motions.

An Upper Bound Solution Analysis of Equal Channel Angular Pressing

2005 ◽  
Vol 23 ◽  
pp. 109-112
Author(s):  
Wei Wei ◽  
Guang Chen
Keyword(s):  
Equal Channel Angular Pressing ◽  
Upper Bound ◽  
Maximum Load ◽  
Equivalent Strain ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Angular Pressing ◽  
Good Agreement

The purpose of this study is to obtain an upper bound solution of ECAP at 0 = ψ and φ=90 deg, which aims at analysis of the relations between ECAP upper bound pressure and the die angles of φ and ψ. The results show that the value of pressing load and the equivalent strain, e ε , decreases as the angle ψ increases at φ=90 deg, but the equivalent strain, e ε , decreases rapidly and no less than 0.90. The measured maximum load required for ECAP is in good agreement with the values obtained from the upper bound solution.

scholarly journals An Accurate Limit Load Solution for an Anisotropic Highly Undermatched Tension Specimen with a Crack

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1941
Author(s):  
Sergei Alexandrov ◽  
Yun-Che Wang ◽  
Lihui Lang
Keyword(s):  
Upper Bound ◽  
Yield Criterion ◽  
Thickness Distribution ◽  
Plastic Anisotropy ◽  
Base Material ◽  
Limit Load ◽  
Orthotropic Materials ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Principal Axes

Plastic anisotropy significantly influences the behavior of structures subjected to various loading conditions. The extremum principles in the theory of rigid plastic solids are convenient and reliable tools for plastic design. The present paper combines the upper bound theorem and Hill’s quadratic yield criterion for orthotropic materials to evaluate the plastic collapse load of a highly undermatched welded tensile panel with a crack in the weld. The base material is supposed to be rigid. The shape of the crack is quite arbitrary. The orientation of the principal axes of anisotropy varies through the thickness of the weld. The upper bound solution is based on an exact solution for a layer of an anisotropic material. This feature of the upper bound solution is advantageous for increasing its accuracy. A numerical treatment is only necessary to find the solution for the uncracked specimen. This specimen has two axes of symmetry, which simplifies the solution. Simple analytic formulae transform this solution into a solution for the cracked specimens with one axis of symmetry and no symmetry. It is shown that the through-thickness distribution of anisotropic properties significantly affects the limit load.

scholarly journals An Upper Bound Solution for the Compression of an Orthotropic Cylinder

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5253
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Yun-Che Wang
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Yield Criterion ◽  
Limit Load ◽  
Compression Force ◽  
Orthotropic Cylinder ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Bound Theorem ◽  
Quick Estimate

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

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