Engineering Transactions, 3, 2, pp. 287-322, 1955

Przypadek Jednoczesnego Rozciągania i Skręcania Pręta o Przekroju Kołowym w Zakresie Sprężysto-Plastycznym

M. Życzkowski
Instytut Podstawowych Problemów Techniki PAN
Poland

The problem is solved on the basis of Hencky's theory of plastic deformations. General equations are derived and boundary conditions stated. The general equations are integrated in an exact manner in the case of an incompressible material having Poisson's ratio equal to 1/2. In the case of a compressible material an approximate integration is carried out together with the evaluation of error.
The problem of simultaneous tension and torsion of a bar can be characterized by means of five parameters: torque Ms, longitudinal force N, radius c of the boundary separating the plastic region from the elastic region, unit elongation ε and unit angle of twist p. The relations between these parameters are considered in detail. The stresses can be expressed in terms of strains by means of elementary functions. The inverse relations however have not this property. They are expressed graphically and numerically.
The results permit to determine any three parameters in the elasto-plastic and plastic range, when two other parameters have a known value.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

N. I. Biezuchow, Tieorja uprugosti plasticznosti, Gostiechizdat, Moskwa 1953.

L. Collatz, Eigenwertaufgaben mit technischen Anwendungen, Akad Verlagsges., Lipsk 1949.

F. A. Gaydon, On the Combined Torsion and Tension of a. Purtly Plastic Circular Cylinder, Journ. Mech. Appl. Math. 1 (1952) Oksford.

R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oksford 1950.

M. T. Huber, Teoria sprężystości, t. 1, PAU, Kraków 1948.

L. S. Lejbienzon, Kurs tieorji uprugosti, Gostiechizdat, Moskwa-Leningrad 1947.

R. A. Miezlumjan, O funkej popieriecznoj dieformacji, Prikt. Mat. Miech., t. 16, Moskwa 1952, str. 491.

A. Nádai, Trans. Am. Soc. Mech. Eng. 52 (1930), str. 193; cyt. wedlug [4].

A. Nádai, Plasticity, Mc Graw-Hill. New York Londyn 1931.

J. Nowiński i W. Olszak, O podstawach teorii sprężystości ciał fizykalnie nieliniowych, Arch. Mech. Stos. 1 (1954).

A. R. Rzanicyn, Rasczot sooruzenig s uczotom ptasticzeskich swojstw matieriatow, Strojwojenmorizdat, Moskwa 1949.

W. Sierpiński, Zasady algebry wyższej, Monogr. Matem., Warszawa-Wroclaw 1946.

M. Sokołowski, Zastosowania metody małych parametrów w zagadnieniach płyt, Arch. Mech. Stos. 3 (1953).

W. W. Sokołowski, Tieorja plasticznosti, Gostiechizdat, Moskwa-Leningrad 1950.