On the concept of relative and plastic spins and its implications to large deformation theories. II: Anisotropic hardening plasticity. (English) Zbl 0667.73032
By resorting to both microscopic and macroscopic considerations, including the concept of single slip, dislocation stress, and a scale invariance argument we show that the notion and formalism of the “relative spin” introduced in part I [see the summary above (Zbl 0667.73031)] reduces to that of “plastic spin” previously recognized in the literature. The central feature of this reduction is the possibility of obtaining physically based constitutive equations for the plastic spin along with appropriate evolution equations for the dislocation or back stress. When these constitutive models are incorporated in the analysis of existing data on tension-torsion tests, we find satisfactory agreement between theory and experiment. In particular, a theoretical interpretation of the torsionally induced axial strain is provided. Moreover, recent experiments on torsionally induced axial stresses are discussed in the light of the presently proposed models of large inelastic deformation inelasticity accounting for anisotropy and texture effects.
MSC:
| 74B99 | Elastic materials |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
| 74A20 | Theory of constitutive functions in solid mechanics |
| 74A60 | Micromechanical theories |
| 74M25 | Micromechanics of solids |
Citations:
Zbl 0667.73031References:
| [1] | Zbib, H. M., Aifantis, E. C.: The concept of relative spin and its implications to large deformation theories. Part I: hypoelasticity and vertex-type plasticity. MM Report No. 13, MEEM, MTU, Houghton, Michigan 1987. · Zbl 0667.73031 |
| [2] | Dafalias, Y. F.: A missing link in the macroscopic constitutive formulation of large plastic deformations. In: Plasticity today (Sawczuk, A., Bianchi, G., eds.), pp. 135-151. Symposium of Current Trends and Results in Plasticity, CISM, Udine, Italy, June 1983, Elsevier 1985. |
| [3] | Loret, B.: On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mechanics of Materials2, 287-304 (1983). · doi:10.1016/0167-6636(83)90021-2 |
| [4] | Onat, E. T.: Shear flow of kinematically hardening rigid-plastic materials. In: Mechanics of material behavior (Dvorak, G. J., Shield, R. T., eds.) pp. 311-323. Elsevier 1984. |
| [5] | Aifantis, E. C.: On the microstructural origin of certain inelastic models. Trans. ASME, J. Eng. Mat. Tech.106, 326-330 (1984). · doi:10.1115/1.3225725 |
| [6] | Aifantis, E. C.: Continuum models for dislocated states and media with microstructures. In: The mechanics of dislocations (Aifantis, E. C., Hirth, J. P., eds.) pp. 127-146. American Society of Metals, 1983. |
| [7] | Aifantis, E. C.: Mechanics of microstructures I?III. In: Mechanical properties and behaviour of solids-plastic instabilities (Bottani, C., Balakrishnan, V., eds.) pp. 314-353. [International Centre for Theoretical Physics, Enrico Fermi School of Theoretical Physics, Trieste 1986] World Scientific, Singapore 1986. |
| [8] | Aifantis E. C.: On the structure of single slip and its implications to inelasticity. In: Physical modelling of finite deformations of aggregates (Gittus, J., Nemat-Nasser, S., Zarka, J., eds.) pp. 283-323. [Jean Mandel in Memoriam, Paris 1985], Elsevier 1987. |
| [9] | Dafalias, Y. F., Aifantis, E. C.: On the microscopic origin of the plastic spin. MM Report No. 8, MEEM, MTU, Houghton, Michigan 1984. |
| [10] | Melan, E.: Zur Plastizität des räumlichen Kontinuums. Ing. Arch.9, 116-121 (1938). · JFM 64.0840.01 · doi:10.1007/BF02084409 |
| [11] | Prager, W.: A new method of analyzing stresses and strains in work-hardening of plastic solids. J. Appl. Mech.23, 493-496 (1956). · Zbl 0074.41003 |
| [12] | Ziegler, H.: A modification of Prager’s hardening rule. Quart. Appl. Math.17, 55-65 (1959). · Zbl 0086.18704 |
| [13] | Armstrong, P. J., Frederick, C. O.: A mathematical representation of the multiaxial Bauschinger effect. C. E. G. B. Report RD/B/N731 (1966). |
| [14] | Nagtegaal, J. C., de Jong, J. E.: Some aspects of non-isotropic work-hardening in finite strain plasticity. In: Plasticity of metals at finite strains: theory, experiment and computation (Lee, E. H., Mallet, R. L., eds.) pp. 65-102. The Division of Applied Mech., Stanford Univ., Stanford, CA, and Dept. Mech. Eng. Aeronautical Eng. and Mech., R.P.I., Troy 1982. |
| [15] | Bammann, D. J.: An internal variable model of viscoplasticity. Int. J. Eng. Sci.22, 1041-1053 (1984). · Zbl 0553.73034 · doi:10.1016/0020-7225(84)90105-8 |
| [16] | Swift, W.: Length changes in metals under torsional overstrain. Engineering163, 253-257 (1947). |
| [17] | Bailey, J. A., Haas, S. L., Nawab, K. C.: Anisotropy in plastic torsion. J. Basic Engrg.94, 231-237 (1972). · doi:10.1115/1.3425374 |
| [18] | Hart, E. W., Chang, Y. W.: Material rotation effects in tension-torsion testings. In: Metal deformation testing (Wagoner, R. H., ed.) pp. 253-263. The Metall. Society AIME 1982. |
| [19] | Montheillet, F., Cohen, M., Jonas, J. J.: Axial stresses and texture development during the torsion testing of Al, Cu, and ?-Fe. Acta Metall.22, 2077-2089 (1984). |
| [20] | Zbib, H. M., Aifantis, E. C.: The concept of relative spin and its implications to large deformation theories. Part II: plasticity with back stress. MM Report No. 13, MEEM MTU, Houghton, Michigan 1987. · Zbl 0667.73032 |
| [21] | Atluri, S. N.: On constitutive relations at finite strain: hypo-elasticity and elastoplasticity with isotropic or kinematic hardening. Computer Methods Appl. Mech. Eng.43, 137-171 (1984). · Zbl 0571.73001 · doi:10.1016/0045-7825(84)90002-1 |
| [22] | White, C., Anand, L.: private communication. |
| [23] | Zbib, H. M., Aifantis, E. C.: Constitutive equations for large material rotations. In: Constitutive laws for engineering materials. Theory and Applications. Volume II (Desai, C.S., Krempl, E., Kiousis, P. D., Kundu, T., eds.), pp. 1411-1418. Elsevier 1987. |
| [24] | Aifantis, E. C.: The physics of plastic deformation. Int. J. Plasticity3, 211-247 (1987). · Zbl 0616.73106 · doi:10.1016/0749-6419(87)90021-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
