State equation for shape-memory alloys. Aplication to Cu-Zn-Al

We deal with the hysteretic behavior of partial cycles in the two¿phase region associated with the martensitic transformation of shape¿memory alloys. We consider the problem from a thermodynamic point of view and adopt a local equilibrium formalism, based on the idea of thermoelastic balance, from which a formal writing follows a state equation for the material in terms of its temperature T, external applied stress ¿, and transformed volume fraction x. To describe the striking memory properties exhibited by partial transformation cycles, state variables (x,¿,T) corresponding to the current state of the system have to be supplemented with variables (x,¿,T) corresponding to points where the transformation control parameter (¿¿ and/or T) had reached a maximum or a minimum in the previous thermodynamic history of the system. We restrict our study to simple partial cycles resulting from a single maximum or minimum of the control parameter. Several common features displayed by such partial cycles and repeatedly observed in experiments lead to a set of analytic restrictions, listed explicitly in the paper, to be verified by the dissipative term of the state equation, responsible for hysteresis. Finally, using calorimetric data of thermally induced partial cycles through the martensitic transformation in a Cu¿Zn¿Al alloy, we have fitted a given functional form of the dissipative term consistent with the analytic restrictions mentioned above.

Atomic Ordering and Martensitic Transitions in Cu-Zn-Al Shape Memory Alloys

We present results from both, calorimetric and dilatometric studies of the isothermal ordering process taking place in a Cu-Zn-Al shape memory alloy after quenches from Tq temperatures ranging from 350 K to 1200 K. The dissipated energy and the length variations of the system are obtained during the process. The change of these quantities in the whole process have been compared with the difference [MATH] between Ms, measured after the relaxation and Ms measured just after the quench. We obtain that these three quantities present, as a function of Tq, the same qualitative behaviour. These changes are then associated with changes of the L21 ordering after the quench in the system. The relaxational process does not follow a single exponential decay. Instead, a continuous slowing down is observed. A relaxation time [MATH] has been defined to characterize the relaxation rate. We show that [MATH] depends on both the annealing and the quenching (Tq [MATH] 800 K) temperatures through an Arrhenius law.

Hysteresis in a system driven by either generalized force or displacement variables: martensitic phase transition in single-crystalline Cu-Zn-Al

We report on experiments aimed at comparing the hysteretic response of a Cu-Zn-Al single crystal undergoing a martensitic transition under strain-driven and stress-driven conditions. Strain-driven experiments were performed using a conventional tensile machine while a special device was designed to perform stress-driven experiments. Significant differences in the hysteresis loops were found. The strain-driven curves show reentrant behavior yield point which is not observed in the stress-driven case. The dissipated energy in the stress-driven curves is larger than in the strain-driven ones. Results from recently proposed models qualitatively agree with experiments.

Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal

Stress-strain trajectories associated with pseudoelastic behavior of a Cu¿19.4 Zn¿13.1 Al (at.%) single crystal at room temperature have been determined experimentally. For a constant cross-head speed the trajectories and the associated hysteresis behavior are perfectly reproducible; the trajectories exhibit memory properties, dependent only on the values of return points, where transformation direction is reverted. An adapted version of the Preisach model for hysteresis has been implemented to predict the observed trajectories, using a set of experimental first¿order reversal curves as input data. Explicit formulas have been derived giving all trajectories in terms of this data set, with no adjustable parameters. Comparison between experimental and calculated trajectories shows a much better agreement for descending than for ascending paths, an indication of a dissymmetry between the dissipation mechanisms operative in forward and reverse directions of martensitic transformation.

Laüe back-reflection method for crystallographic orientation of a martensitic Cu-Zn-Al single crystal of the monoclinic system

A martensitic single crystal Cu-23.95Zn-3.62(wt.%)Al alloy was obtained melting pure Cu, Zn and Al using Bridgman's method. The martensitic phase (monoclinic) can present up to 24 variants, and orienting the surface according to a certain plane is a very hard task. The single crystal was submitted to 8 tons of tension (stress) along the longitudinal direction to reduce the number of variants and facilitate the surface orientation according to the desired plane. This single crystal was oriented using the Laüe back-reflection method to give surfaces with the following oriented crystallographic planes: (010), (120) and (130). It was observed that the tension stress was applied along the [010] direction.

Hysteresis in a system driven by either generalized force or displacement variables: martensitic phase transition in single-crystalline Cu-Zn-Al

We report on experiments aimed at comparing the hysteretic response of a Cu-Zn-Al single crystal undergoing a martensitic transition under strain-driven and stress-driven conditions. Strain-driven experiments were performed using a conventional tensile machine while a special device was designed to perform stress-driven experiments. Significant differences in the hysteresis loops were found. The strain-driven curves show reentrant behavior yield point which is not observed in the stress-driven case. The dissipated energy in the stress-driven curves is larger than in the strain-driven ones. Results from recently proposed models qualitatively agree with experiments.

Laüe back-reflection method for crystallographic orientation of a martensitic Cu-Zn-Al single crystal of the monoclinic system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo eletroquímico de uma liga de Cu-Zn-Al, monofásico de fase'beta' poli e monocristalina com orientação (100)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Síntese de hidróxidos duplos lamelares do sistema Cu, Zn, Al-CO3: propriedades morfológicas, estruturais e comportamento térmico

Hidrotalcitas são argilas aniônicas, também conhecidas como Hidróxidos Duplos Lamelares (HDLs) e possuem estrutura semelhante ao mineral brucita. Os HDLs do sistema Cu, Zn, Al-CO₃ foram sintetizados em condições que favorecem a formação de cristais pequenos e de elevada área superficial. A caracterização foi feita por difração de raios X, análise termogravimétrica, espectroscopia na região do infravermelho e microscopia eletrônica de varredura. A síntese foi feita pelo método de coprecipitação em pH variável, utilizando sulfatos de cobre e zinco, soluções de alumínio e solução de hidróxido sódio. Os difratogramas de raios X mostram que os compostos sintetizados possuem alta cristalinidade; a intensidade e a largura dos picos comprovam que os materiais se apresentam bem organizados e com empilhamento das lamelas. Os espectros de infravermelho apresentaram bandas associadas ao ânion carbonato presente na região interlamelar dos HDLs.

Local Electrochemical Investigation of Single Grains of Polycrystalline Cu-16%Zn-8%Al Alloy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the electrochemical behavior of Cu-16%Zn-6.5%Al alloy containing the β'-phase (martensite) in borate buffer

In this work, the electrochemical behavior of Cu-16(wt.%)Zn-6.5(wt.%)Al alloy containing the β'-phase (martensite) was studied in borate buffer solution (pH 8.4) by means of open-circuit potential (EOC), electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV). The alloy EOC was -0.29 V vs. Hg/HgO/OH-, similar to that of pure copper in this medium, indicating that the processes which occur on the alloy surface are mainly governed by copper. EIS response was related to the dielectric and transmission properties of the complex oxide layer. The CVs showed peaks concerning the redox reactions for copper and zinc. These peaks were assigned to the formation and reduction of copper and zinc species. Furthermore, they showed that the copper oxidation was suppressed by the presence of zinc and aluminum in the alloy composition. The copper and zinc oxidation to form complex oxide layers and the reduction of the different metallic oxides generated in the anodic potential scan suggest that a solid state reaction could determine the metallic oxide formation. © 2013 Elsevier Ltd. All rights reserved.