A modified model on solute alloying element effect in Al–Mg alloys: Mechanical properties and dislocation density evolutions S.S. Firouzabadi, M. Kazeminezhad ⇑ Department of Materials Science and Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran article info Article history: Received 23 July 2011 Accepted 31 October 2011 Available online 9 November 2011 Keywords: A. Non-ferrous metals and alloys E. Mechanical F. Plastic behavior abstract A modified dislocation based model is introduced to explain the flow stress of Al–Mg alloys at different temperatures and strain rates considering solute alloying element concentration. The solute effect on flow stress is studied on the basis of storage and annihilation of dislocation. It is studied that how the increase of solute content can postpone the dislocation annihilation and how this can affect the storage phenomenon. It is found that the increasing of solute concentration can postpone the beginning of dis- location annihilation through deformation and also increase the critical strain that plateau occurs in plot of annihilation of dislocation versus shear strain. Thus, the plateau level gets higher value and a better strength improvement occurs. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction It is well known that the addition of solute atoms influences the stacking-fault energy and thus the strength, the recovery and the recrystallization characteristics of aluminum [1]. Plastic deforma- tion in low stacking fault energy (SFE) FCC alloys occurs by disloca- tion glide and twinning. However, for high SFE aluminum alloys, plastic deformation occurs mainly by slip [2]. Dislocations in such alloys are pinned through interactions with the solute atoms like Mg and therefore higher stresses are required for dislocation movement through a solute field. Strengthening is typically di- vided into two categories: strong pinning, in which individual sol- utes are sufficient to pin the dislocation at the solute position; and weak pinning, in which the dislocation is pinned by a favorable col- lective configuration of solutes in a region of the material [3]. For FCC materials such as Al–Mg alloys, dislocations move by bowing out from pinning points and the bowing is restricted by the dislo- cation line tension. As the dislocation attempts to move or bow out in regions where it is not pinned, the remaining pinned dislocation segments experience additional forces, resulting from the disloca- tion curvature, which drive the unpinning dislocation. Thus, the amount of strengthening achieved by solutes is a function of solute concentration, the fundamental strength and spatial range of the solute–dislocation interactions, the dislocation line tension and the spatial configuration of solutes [3]. Since the hardening and softening mechanisms are both significantly influenced by many factors such as strain, strain-rate, and forming temperature [4], it is of great importance to provide a microstructural based model to predict the flow stress of Al–Mg alloys at different temperatures and strain rates considering alloy concentration. Many researches have been carried out on the microstructural modeling of mechan- ical properties but there are still some deficiencies in these models that must be resolved. For instance, Lin et al. used the Johnson– Cook (JC) constitutive model which is a most widely known as a forming temperature, strain and strain-rate-dependent phenome- nological flow stress model, and is successfully used for a variety of materials with different ranges of deformation temperature and strain-rate [4]. But in this model, there is no proper term to de- scribe the solute atom effect in the flow stress. Bazzaz et al. [5] and Enikeev et al. [6], also studied a three-dimensional version of the dislocation-density-based strain hardening model to describe all stages of hardening but similarly, there is no solute effect consid- eration through the flow behavior prediction. Sellars and Zhu [7] reported that the flow stress in plastic deformation of Al–Mg alloys is mainly determined by mobile dislocations. But the solute effect of Mg atoms on the dislocation pinning has not been considered. Moreover, there are some researches carried out by Nes et al. and Marthinsen et al. [8–11] in which the effect of solute atoms on the mobility of dislocations is considered by a constant term but the dependency of solute effect on temperature and strain rate has not been directly attended. These classical analyses have char- acterized the basic pinning/line tension competition for the strong and weak pinning limits, and shown the proportionality of strengthening to c 1/2 and c 2/3 , respectively, where c is the solute concentration [12]. Nes and Marthinsen [9] suggest an equation for describing the stress as a function of temperature and strain rate that considers the effect of alloying element by a power law term expressed by: s /ðc e Þ ð1Þ 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2011.10.057 ⇑ Corresponding author. Tel.: +98 21 66165227; fax: +98 21 66005717. E-mail address: mkazemi@sharif.edu (M. Kazeminezhad). Materials and Design 36 (2012) 804–808 Contents lists available at SciVerse ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes