34 J.-B. Le Cam et al. – PLC band kinematics is highly repeatable from one heat source jump to another: the same shape of PLC bands and the same angles of the formed cross are observed. – As thermoelasticity leads to low heat absorption compared to the heat produced by PLC bands, these maps can be assumed to give mechanical dissipation field. This assumption is classically used to neglect the effect of thermoelastic coupling [16, 21]. Therefore, heat source maps can be considered as mechanical dissipation maps. Further analyses on the PLC band kinematics have been carried out and four steps have been identified. They are precisely presented and detailed in [24]. 5.6 Conclusion This paper provides the first study on spatio-temporal distribution of heat produced by PLC bands formed under equibiaxial tensile loading. Equibiaxial tensile testing has been carried out at an ambient temperature with an Al-Mg alloy. The temperature field was measured during the test and corresponding heat sources were reconstructed by means of the bidimensional formulation of the heat diffusion equation. The heat source map enables us to visualize spatio-temporal gradients in the calorific response of the material and to investigate the kinematics of PLC bands induced by equibiaxial tensile loading, which forms dissipative waves. At the specimen centre, the heat source exhibits jumps that fit well with jumps in the equivalent deformation rate and the temperature. The results are a promising alternative of inquiry into the effects of complex loading conditions as those encountered during sheet metal forming processes on occurrence and kinematics of PLC bands. Additionally, the present study provides additional data for the development and validation of PLC band kinematic models. Funding Information This work has received the financial support of the AIS Scientific Grant from Rennes Métropole (2012), the Mission of Resources and Skills Technology (MRCT) Grant from the French National Center for Scientific Research (2012), the Interdisciplinary Mission (MI) Grant from the French National Center for Scientific Research (2013). References 1. Van Den Beukel, A.: Theory of the effect of dynamic strain aging on mechanical properties. Phys. Status Solidi. 30, 197 (1975) 2. Kubin, L.P., Estrin, Y.: Acta Metall. 33, 397 (1985) 3. Estrin, Y., Kubin, L.P., Aifantis, E.C.: Introductory remarks to the viewpoint set on propagative plastic instabilities. Scr. Metall. Mater. 29(9), 1147–1150 (1993) 4. Jiang, H., Zhang, Q., Chen, X., Chen, Z., Jiang, Z., Wu, X., Fan, J.: Three types of Portevin-Le Chatelier effects: experiment and modelling. Acta Mater. 55(7), 2219–2228 (2007) 5. Lebedkina, T.A., Lebyodkin, M.A.: Effect of deformation geometry on the intermittent plastic flow associated with the Portevin-Le Chatelier effect. Acta Mater. 56(19), 5567–5574 (2008) 6. Coër, J., Manach, P.Y., Laurent, H., Oliveira, M.C., Menezes, L.F.: Piobert-Lüders plateau and Portevin-Le Chatelier effect in an al-mg alloy in simple shear. Mech. Res. Commun. 48, 1–7 (2013) 7. Balik, J., Lukac, P.: Portevin-Le Chatelier instabilities in Al-3 Mg conditioned by strain rate and strain. Acta Metall. Mater. 41(5), 1447–1454 (1993) 8. Fujita, H., Tabata, T.: The effect of grain size and deformation sub-structure on mechanical properties of polycrystalline aluminum. Acta Metall. 21(4), 355–365 (1973) 9. Korbel, A., Dybiec, H.: The problem of the negative strain-rate sensitivity of metals under the Portevin-Le Chatelier deformation conditions. Acta Metall. 29(1), 89–93 (1981) 10. Thomas, A.T.: The tensile deformation behaviour of an aluminium-magnesium alloy. Acta Metall. 14(10), 1363–1374 (1966) 11. Li, M., Lege, D.J.: Serrated flow and surface markings in aluminum alloys. J. Eng. Mater. Technol. 120, 48–56 (1998) 12. Coër, J., Bernard, C., Laurent, H., Andrade-Campos, A., Thuillier, S.: The effect of temperature on anisotropy properties of an aluminium alloy. Exp. Mech. 51(7), 1185–1195 (2010) 13. Hu, Q., Zhang, Q., Cao, P., Fu, S.: Thermal analyses and simulations of the type a and type b Portevin-Le Chatelier effects in an al-mg alloy. Acta Mater. 60(4), 1647–1657 (2012) 14. Ait-Amokhtar, H., Fressengeas, C., Boudrahem, S.: The dynamics of Portevin-Le Chatelier bands in an al-mg alloy from infrared thermography. Mater. Sci. Eng. A. 488, 540–546 (2008) 15. Bernard, C., Coër, J., Laurent, H., Chauvelon, P., Manach, P.Y.: Relationship between local strain jumps and temperature bursts due to the Portevin-Le Chatelier effect in an al-mg alloy. Exp. Mech. 53(6), 1025–1032 (2013) 16. Chrysochoos, A., Louche, H.: Thermal and dissipative effects accompanying luders band propagation. Mat. Sci. Eng. A Struct. 307, 15–22 (2001)
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