Orientation dependence of plastic deformation in nickel-based single crystal superalloys: Discrete–continuous model simulations A. Vattre ´ a , B. Devincre b, * , A. Roos a a DMSM, ONERA, 29 Avenue de la Division Leclerc, BP 72, 92322 Cha ˆtillon Cedex, France b LEM, CNRS-ONERA, 29 Avenue de la Division Leclerc, BP 72, 92322 Cha ˆtillon Cedex, France Received 2 September 2009; received in revised form 20 November 2009; accepted 21 November 2009 Available online 21 December 2009 Abstract The anisotropic mechanical response of single-crystal nickel-based superalloys is simulated. At 1123 K, two uniaxial tensile loading cases are simulated: one along [0 0 1] and another along [1 1 1]. Resulting stress–strain curves, stress distributions, interfacial dislocation structures are analysed. In accordance with experiments, the simulations show an anisotropic yield strength. The applied strain is accom- modated by dislocations propagating through matrix channels on octahedral slip systems. The net result appears as slip bands along the cubic directions, even though no cubic slip systems are activated. In the [0 0 1] case, the plastic flow is distributed more or less evenly among the three matrix channels, whereas in the [1 1 1] case it is mainly concentrated in one single channel. Typical zig–zag configurations are observed. The elementary mechanisms controlling their formation are explained. Cross-slip does not play any role there. The hard- ening anisotropy between both loading cases is related to strong differences between the interfacial dislocation microstructures. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel alloys; High-temperature deformation; Plastic deformation; Dislocation dynamics; Work-hardening modelling 1. Introduction Single crystals of nickel-based superalloys are specifically developed for high-temperature applications [1,2]. These materials are used for turbine blades in aircraft engines and in power plants. Their particular microstructure consists of ordered c 0 Ni 3 Al precipitates with a L1 2 structure, coherently set in the c-matrix, a face-centred cubic (fcc) nickel-based solid solution. Nickel-based superalloys derive much of their excel- lent mechanical properties at high temperature from the c 0 precipitates. They have a roughly cuboidal shape and are reg- ularly distributed, with faces parallel to the {1 0 0} planes and with narrow c-matrix channels between them. The dimensions of precipitates and channels are in the sub-micrometer range. The trend in nickel-based superalloy development has been towards increasing their volume fraction up to values provid- ing an optimum of mechanical properties: the first generation, such as Waspalloy, contains about 25 vol.%, whereas more recently developed alloys contain up to 70 vol.%. In uniaxial tension or compression tests, the yield strength depends strongly on loading direction and temper- ature [3–10]. For instance, at 1273 K and at low tensile stress, plasticity is mainly concentrated within the channels on 1 2 h110if111g planes [11,12]. The precipitates are not plastically deformed, because of the anomalous yield behaviour of the Ni 3 Al phase, whose flow stress increases from room temperature up to a peak value at about 1243 K [13]. Also, in the h001i loading cases (i.e. for crys- tals with one of the h001i axes oriented along the loading direction), the 0.2% yield stress and the strain hardening are considerably higher than for other orientations. Under- standing such plastic behaviour is essential because the crystallographic alignment during blade solidification can deviate from the strongest h001i orientation, and blades can be subjected locally to complex stress states. The question has been raised whether cube slip occurs in crystals oriented away from the h001i directions [6,7,9]. In 1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.11.037 * Corresponding author. Tel.: +33 1 46 734155. E-mail address: benoit.devincre@onera.fr (B. Devincre). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 58 (2010) 1938–1951