Internal stresses in dislocation subgrain structures R. Sedl a cek * , W. Blum Institut f  ur Werkstowissenschaften, Lehrstuhl I, Universit at Erlangen-N urnberg, Martensstrasse 5, D-91058 Erlangen, Germany Abstract Long-range internal stresses in dislocation subgrain structures are proposed to be a consequence of a plastic in- compatibility caused by dislocations bowing between subgrain boundaries which act as obstacles to dislocation glide. Assuming elliptically bowed dislocations on two slip systems, a plane strain model of the incompatible plastic defor- mation is formulated. The internal stresses are computed using a numerical method based on Fast Fourier Transform (FFT). Considerable internal stresses arise especially in subgrain structures with subgrain boundaries inclined with respect to glide planes. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Internal stress; Subgrain structure; Plastic incompatibility; Dislocation 1. Introduction The composite model of plastic deformation has been quite successful in dealing with the het- erogeneity of the dislocation structure in plastic deformed crystalline materials which is associated with internal stresses. The model has been exten- sively applied to cyclic deformation localized in persistent slip bands [1], monotonic deformation in the case of work hardening where cellular dislo- cation structures are formed [1] and to high tem- perature deformation and creep with steady state subgrain structures [2]. In the latter case the model oers the possibility to distinguish between two processes, namely de- formation in the hard regions near subgrain boundaries leading to recovery of the dislocation structure and deformation in the soft subgrain interior responsible for most of the glide [3]. As the kinetics of deformation in the two regions are dierent, it is easy to explain the dierence in ki- netics of steady state deformation and deforma- tion at constant dislocation structure [4]. An important feature of the model is the existence of stress concentrations in the hard regions coupled to internal back stresses in the subgrain interior. The stress concentrations allow the hard region to be deformed in spite of the high local dislocation density. The back stresses explain why the creep rate decreases in a test at constant stress in the primary range when the subgrain structure is formed. The long-range stresses stem from the hetero- geneous dislocation structure. Mughrabi has pre- sented a convincing explanation of the sources of internal stresses in cell structures [1]. They are caused by a plastic incompatibility between the soft and the hard regions which is accommodated by interface dislocations. Unfortunately this pic- ture cannot be extended to high temperature sub- grain structures where the plastic deformation combined with lattice rotation is compatible. In Computational Materials Science 13 (1998) 148±153 * Corresponding author. Tel.: +49 9131 8527486; fax: +49 9131 8527504; e-mail: sedlacek@ww.uni-erlangen.de. 0927-0256/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 9 8 ) 0 0 0 5 5 - X