Solution to the Rolling Problem for a Strain-Hardening Material by the Method of Discontinuities

1951 ◽  
Vol 18 (1) ◽  
pp. 90-94
Author(s):  
Alice Winzer
Keyword(s):  
Strain Hardening ◽  
Method Of Characteristics ◽  
Continuous Solution ◽  
Discontinuous Solution ◽  
Yield Condition ◽  
Hardening Material ◽  
Discontinuity Surfaces ◽  
Plane Plastic ◽  
Thin Plastic ◽  
Good Agreement

Abstract The problem of drawing and rolling of a thin plastic sheet between cylindrical guides was investigated recently by H. I. Ansoff, under the assumption that the material is in a state of plane plastic flow and obeys the Saint Venant-Mises yield condition (1, 2). He determined the stress distribution along the sheet by the method of characteristics and also by the method of discontinuity surfaces and found good agreement between these results as well as with experimental data. Since the computations required for the discontinuous solution are considerably less laborious than those necessary for the continuous solution, the same type of problem, but now under the assumption that the material displays strain-hardening, will be analyzed by the method of discontinuities. It seems reasonable to expect that the results so found constitute a close approximation to results based upon a continuous solution.

MANUFACTURE INVESTIGATION OF CARTRIDGE WITH BOTTOM-MOST PART FLANGE BY DIRECT EXTRUSION WITH COUNTERPUNCH. REPORT 18. EXPERIMENTAL CHECK OF THEORETICAL RESULTS FOR DIFFERENT HOLLOW RADIUSES AND BOTTOM-MOST PART THICKNESSES

2020 ◽  
Vol 0 (9) ◽  
pp. 16-23
Author(s):  
A. L. Vorontsov ◽  
◽  
I. A. Nikiforov ◽  
Keyword(s):  
Strain Hardening ◽  
Theoretical Calculations ◽  
High Accuracy ◽  
Geometric Parameters ◽  
Strength Characteristics ◽  
Experimental Check ◽  
Hardening Material ◽  
Direct Extrusion ◽  
Theoretical Results

The results of an experimental check of the obtained theoretical formulae allowing us to determine the most important parameters of extrusion cartridges with a counterpunch for different hollow radiuses and bottom-most part thicknesses are presented. Characteristics of used tools, geometric parameters of extrusion experiments, strength characteristics of deformed materials and lubricants are described in detail. Both strain-hardening material and strain-unhardening material were studied. Methodology of the theoretical calculations is demonstrated in detail. High accuracy of the obtained design formulae was confirmed.

Stress Intensity Factors for Radial Cracks in a Pre-Stressed, Thick-Walled Cylinder of Strain-Hardening Materials

1983 ◽  
Vol 105 (2) ◽  
pp. 117-123 ◽  
Author(s):  
S. L. Pu ◽  
P. C. T. Chen
Keyword(s):  
Stress Intensity ◽  
Strain Hardening ◽  
Yield Condition ◽  
Function Technique ◽  
Maximum Pressure ◽  
Simple Method ◽  
Fatigue And Fracture ◽  
Useful Life ◽  
Radial Cracks ◽  
High Internal Pressure

A simple method which combines the weight function technique and finite element results is used to obtain mode I stress intensity factor solutions for radially cracked cylinders subjected to a high internal pressure. The method is especially effective for cylinders having residual stresses due to a manufacturing pre-stress process to increase the maximum pressure the cylinder can contain and to improve the cylinder’s useful life against fatigue and fracture. The method is quite general for various assumptions involving the plastic stress-strain relations, the yield condition, the strain-hardening, and the compressibility of the cylinder material.

scholarly journals On Computational Modelling Of Strain-Hardening Material Dynamics

2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski
Keyword(s):  
Relaxation Time ◽  
Stress Relaxation ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Computational Modelling ◽  
Constitutive Models ◽  
Successful Implementation ◽  
Hardening Material ◽  
Dislocation Mechanics

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

Torsion of a conical rod made of a strain-hardening material

1985 ◽  
Vol 17 (6) ◽  
pp. 801-805 ◽  
Author(s):  
A. A. Ostsemin ◽  
V. A. Lupin
Keyword(s):  
Strain Hardening ◽  
Hardening Material ◽  
Conical Rod

Comparative Evaluation of Analytical Methods for the Determination of Coefficients of Friction and Stresses when Wire Rod Drawing

2018 ◽  
Vol 284 ◽  
pp. 247-252 ◽  
Author(s):  
Sergei I. Platov ◽  
V.A. Nekit ◽  
Nikolay N. Ogarkov
Keyword(s):  
Plastic Deformation ◽  
Comparative Evaluation ◽  
Method Of Characteristics ◽  
Circular Cross Section ◽  
Wire Drawing ◽  
Work Piece ◽  
Relative Height ◽  
Plane Plastic ◽  
Special Case

The article discusses the process of wire drawing of circular cross-section. The study of stresses of wire drawing in conditions of plane plastic flow was held. As theoretical framework the study was adopted the method of characteristics, a special case, having the definitive decision. Stresses during wire drawing are defined by decomposing the decision into two components of plane strain and the superposition of these decisions. The results of theoretical solution of the problem of wire drawing were used to determine the coefficients of friction on the surface of contact of the tool and the work piece during the deformation of steel with a diameter of 5.5 mm. It is recommended to use two-dimensional methods of solution in the analysis of the process of wire drawing in conditions with a high hearth of plastic deformation (with the relative height of the hearth of plastic deformation 2 and bigger). The theoretical dependences between the friction coefficients at the contact surface of the work piece and the tool was obtained. The obtained values of coefficients of friction can be used over solving the task of the wire drawing in conditions with a high hearth of plastic deformation.

On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

1955 ◽  
Vol 6 (1) ◽  
pp. 31-45
Author(s):  
H. K. Zienkiewicz
Keyword(s):  
Method Of Characteristics ◽  
Order Theory ◽  
Stagnation Pressure ◽  
Slender Body Theory ◽  
Pressure Losses ◽  
The Method Of Characteristics ◽  
Curvature Approximation ◽  
Body Theory ◽  
Theory And Experiment ◽  
Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

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