Closure to “Discussion of ‘A New Upper-Bound Method for Analysis of Some Steady-State Plastic Deformation Processes’” (1969, ASME J. Eng. Ind., 91, pp. 741–742)

1969 ◽  
Vol 91 (3) ◽  
pp. 742-742
Author(s):  
E. R. Lambert ◽  
H. S. Mehta ◽  
S. Kobayashi
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Upper Bound ◽  
Upper Bound Method ◽  
Deformation Processes

A New Upper-Bound Method for Analysis of Some Steady-State Plastic Deformation Processes

1969 ◽  
Vol 91 (3) ◽  
pp. 731-741 ◽  
Author(s):  
E. R. Lambert ◽  
H. S. Mehta ◽  
S. Kobayashi
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Plane Strain ◽  
Velocity Component ◽  
Velocity Fields ◽  
Flow Lines ◽  
Upper Bound Method ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Deformation Processes

A method of obtaining admissible velocity fields without velocity discontinuities is described, and applied to plane-strain extrusion, tube extrusion, and axisymmetric piercing. In plane-strain extrusion, the flow lines, grid distortions, and extrusion pressures were obtained and the values were compared with those found in previous solutions. For tube extrusion and axisymmetric piercing, the solutions are presented as examples in terms of flow lines and velocity component distributions; these solutions await experimental confirmation.

Extension of the Upper Bound Method to Include Estimation of Stresses

1991 ◽  
Vol 58 (2) ◽  
pp. 493-498 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Plastic Deformation ◽  
Stress Field ◽  
Upper Bound ◽  
Plastic Material ◽  
Approximate Solutions ◽  
Incompressible Material ◽  
Bulk Deformation ◽  
Upper Bound Method ◽  
Convenient Tool ◽  
Perfectly Plastic

The upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. Since the rate of work for an incompressible material depends only on the deviator portion of the stress, the hydrostatic portion does not enter the formulation and the stress field is not determined. Here we show that this limitation can be overcome by adding a relatively simple postprocessing procedure. We then apply this technique to examples of rigid asperities penetrating a plastic material undergoing subsurface bulk deformation and compare our results with previous approximate solutions.

Upper Bound Analysis of the ECAE Process by Considering Circular Cross-Section and Strain Hardening Materials

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
C. J. Luis Pérez ◽  
R. Luri
Keyword(s):  
Plastic Deformation ◽  
Severe Plastic Deformation ◽  
Strain Hardening ◽  
Cross Section ◽  
Upper Bound ◽  
Equal Channel Angular Extrusion ◽  
Circular Cross Section ◽  
Experimental Tests ◽  
Extrusion Force ◽  
Deformation Processes

Severe plastic deformation processes have a great deal of importance because of the improvement in mechanical properties of the processed parts as a consequence of the grain size reduction in the material due to the accumulation of deformation. One of the main severe plastic deformation (SPD) processes is called the equal channel angular extrusion (ECAE). Although a large amount of studies, which deal with experimental analysis of processed parts exist, few studies dealing with the force required to perform the process have been developed. In this study, an analytical modeling of the force required to perform the ECAE process has been developed using the upper bound method (UBM). The analytical equations developed take into account the material strain hardening and the ECAE dies with circular cross-section. Moreover, the experimental tests have been performed and the extrusion force has been measured. The UBM and experimental results have been compared showing a great deal of agreement.

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