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INTRODUCTION

TO obtain the required mechanical properties, solutionizing and quenching of heat-treatable aluminum alloys (AA) are the key steps. After solutionizing and perfect quenching, a supersaturated solid solution is desired so that during aging elements in solid solution aggregate into fine hardening precipitates and thus increase yield strength. Fast quenching is necessary to avoid any coarse precipitation that would reduce the mechanical properties after heat treatment. However, fast quenching causes also residual stresses (RS) in the part because of its inhomogeneous temperature distribution. In general, it can be said, the thicker the part the more pronounced this effect. As a result, these RS lead to distortions in thick products during machining at final temper,[1] and even in quenched plates, where RS is reduced by a factor ~10 after stress relief.[2] This applies also to large hot-forged parts of AA2618 that

NICOLAS CHOBAUT, Scientist, and JEAN-MARIE DREZET, Senior Scientist, are with the Ecole Polytechnique Fe´de´rale de Lausanne, Laboratoire de Simulation des Mate´riaux, Station 12, 1015 Lausanne, Switzerland. Contact email: jean-marie.drezet@epfl.ch DENIS CARRON, Associate Professor, is with the Univ. Bretagne Sud, FRE CNRS 3744, IRDL, 56100 Lorient, France. PETER SAELZLE, Engineer, is with ABB Turbo Systems Ltd, Bruggerstrasse 71a, 5400 Baden, Switzerland. Manuscript submitted April 7, 2016. Article published online August 29, 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A

are heat treated and then machined to produce impellers. In Al-Cu-Mg-based alloys, two types of precipitation may take place during quenching and affect the formation of internal stresses. A first precipitation occurs at intermediate temperature (688 K to 573 K (415 C to 300 C)[3]) for low cooling rates. The large precipitates are undesirable since they do not harden the material significantly while reducing the amount of elements in solid solution. A second precipitation occurs at lower temperature (below 573 K to 523 K (300 C to 250 C)[4]) even for high cooling rates. The resulting effect of these two types of precipitation is an increase of the yield strength and thus of the residual stresses at the surface of large quenched components.[5] For the prediction of RS after quenching, it is thus important to characterize the mechanical properties during cooling by considering possible precipitation. Bibliographical reviews of the finite element (FE) methods applied to the simulation of quenching are given by Mackerle[6] and by Robinson et al.[7] The general approach to take into account precipitation is to use yield strength and strain-hardening models where the flow stress depends on the precipitation state.[8–10] Such models require an extensive mechanical characterization of the influence of precipitation on flow stress.[11] Alternatively, Reich and Kessler[12] used their own model with four hardening parameters dependent on the cooling rates and quenching finish temperatures but without viscous effects. Instead, a simpler approach t