Summary
Hypothesis of local determinabilily predicting the behavior of the angles between a stress vector and a Frenet's frame established on a strain trajectory in a five-dimensional vector space of strain deviator is discussed to formulate a plastic constitutive equation of metals under complex loadings. Namely, a set of equations giving the rates of angles at the relevant instant for arbitrary five-dimensional curved strain trajectories is derived first on the basis of the previously reported experiments for the deformation along three-dimensional orthogonal trilinear strain trajectories. Then, a simple constitutive equation is formulated by employing the above equations together with the relation between the magnitude of stress vector and the arc-length of strain trajectory for pure torsion. It is found that the resulting equation reproduced well the above experimental results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Phillips, A.: Experimental plasticity. Some thoughts on its present status and possible future trends. In: Problems of Plasticity (Sawczuk, A., ed.), pp. 193–233. Leyden: Noordhoff 1974.
Michno, M. J., Findley, W. N.: An historical perspective of yield surface investigations for metals. Int. J. Non-Linear Mech.11, 59–82 (1976).
Hecker, S. S.: Experimental studies of yield phenomena in biaxially loaded metals. In: Constitutive Equations in Viscoplasticity (Stricklin, J. A., Saczalski, K. J., eds.), AMD-20, 1–33. New York: ASME 1976.
Ikegami, K.: Experimental plasticity on the anisotropy of metals. In: Mechanical Behavior of Anisotropic Solids (Boehler, J. P., ed.), pp. 201–242. The Hagŭe: Martinus Nijhoff 1983.
Mróz, Z.: An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model. Acta Mechanica7, 199–212 (1969).
Dafalias, Y. F., Popov, E. P.: A model of nonlinearly hardening materials for complex loading. Acta Mechanica21, 173–192 (1975).
Mróz, Z., Shrivastava, H. P., Dubey, R. N.: A non-linear hardening model and its application to cyclic loading. Acta Mechanica25, 51–61 (1976).
Chaboche, J. L., Rousselier, G.: On the plastic and viscoplastic constitutive equations. In: Inelastic Analysis and Life Prediction in Elevated Temperature Design (Baylac, G., ed.), PVP-59, 33–55. New York: ASME 1982.
Ilyushin, A. A.: Plasticity, foundation of general mathematical theory. Moscow: Izd. Akad. Nauk 1963.
Ohashi, Y., Tokuda, M., Yamashita, H.: Effect of third invariant of stress deviator on plastic deformation of mild steel. J. Mech. Phys. Solids23, 295–323 (1975).
Lensky, V. S.: Hypothesis of local determinability in the theory of plasticity. Izd. Akad. Nauk, Otn. Mekh. Mashinostr5, 154–158 (1962).
Ohashi, Y., Kurita, Y., Suzuki, T., Tokuda, M.: Experimental examination of the hypothesis of local determinability in the plastic deformation of metals. J. Mech. Phys. Solids29, 51–67 (1981).
Ohashi, Y., Tanaka, E., Gotoh, Y.: Effect of pre-strain on the plastic deformation of metals along orthogonal bilinear strain trajectories. Mechanics of Material1, 297–305 (1982).
Tokuda, M., Ohashi, Y., Iida, T.: On the hypothesis of local determinability and a concise stress-strain relation for curved strain path. Bulletin of Japan Society of Mechanical Engineers26, 1475–1480 (1983).
Ziegler, H.: A modification of Prager's hardening rule. Quart. App. Math.17, 55–65 (1959).
Ohashi, Y., Tanaka, E.: Plastic deformation behavior of mild steel along orthogonal trilinear strain trajectories in three-dimensional vectors pace of strain deviator. Trans. ASME, J. Eng. Mater. Technol.103, 287–292 (1981).
Author information
Authors and Affiliations
Additional information
With 4 Figures
Rights and permissions
About this article
Cite this article
Tanaka, E. Hypothesis of local determinability for five-dimensional strain trajectories. Acta Mechanica 52, 63–76 (1984). https://doi.org/10.1007/BF01175965
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01175965