Thermal stress and local crystallization parameters in single-crystal rods of Ni-Mn-Ga ferromagnetic shape memory alloys

https://doi.org/10.1016/j.jcrysgro.2020.125485Get rights and content

Highlights

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    Growth into a nonlinear temperature profile causes thermal stress and creep strain.

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    Macroscopic creep strains do not influence the misorientation between dendrite groups.

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    Residual stresses are comparable with or even higher than the twinning stress.

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    Residual stresses can already lead to shape change of a Ni-Mn-Ga rod.

Abstract

Ni-Mn-Ga single crystal material shows a strong magnetic shape memory (MSM) effect with reversible strains above 6%. Single crystal rods of up to 40 mm diameter are produced in Bridgman type processes. For actuator applications small sticks are cut out of the rods. The magneto-mechanical performance of these sticks depends among other parameters on their alignment with the crystal lattice. Thus, each inhomogeneity of lattice orientation within the rod reduces the achievable yield.

The lattice orientation within the single crystal rods usually differs slightly between bottom and top region, and it shows local scattering due to misorientations between the growing dendrites. In the present study the macroscopic thermal stresses induced during the crystallization process are simulated. It is found that these stresses do not affect the crystal orientation. However, they may lead to shape changes of the single crystal rod.

Introduction

Single crystals of Ni-Mn-Ga magnetic shape memory (MSM) alloys are today the most promising bulk materials for magnetic field induced actuation applications, where fast switching, long lifetime, and strains in the order of 11% are desired [1]. Actuation devices typically use rectangular MSM sticks aligned with the crystallographic c-axis parallel to the magnetic field. They are cut out of single-crystal rods, which are produced at ETO MAGNETIC GmbH in a Bridgman type process with diameters of up to 40 mm [2], Fig. 1. Using appropriate grain selection techniques the alignment of the rod axis near the 〈1 0 0〉 lattice direction can be achieved. The alloy solidifies with a dendritic structure, which partly shows a mosaic-like distribution of dendrite orientations. Adjacent dendrite groups can grow tilted against each other, separated by low-angle grain boundaries. This should be avoided because it decreases the accuracy of the crystallographic alignment of the sticks cut along the desired orientation. This in turn affects the resulting magneto-mechanical properties. Moreover, low-angle grain boundaries may be locations of crack initiation during the magneto-mechanical cycling of the stick.

The MAREGA-project aims at the reduction of specific Ga usage. One aspect is the improvement of material quality to increase actuator efficiencies. Within this project, the present study focuses on the thermal stress in the Ni-Mn-Ga crystals during the growth process and on the residual stress after cooling.

Section snippets

Structure analysis

Ni2MnGa close to stoichiometric composition solidifies slightly above 1100 °C as partially disordered B2′ structure and changes at about 700–800 °C to the ordered L21 structure. At lower temperatures (<200 °C) L21 transforms into tetragonal (NM or 10 M modulated) or orthorhombic (14 M modulated) martensite [3]. The material in this study exhibits the 10 M structure and shows fine plate structure of the martensite variants aligned with the original cubic lattice [4]. Fig. 2 shows the fine

Material data

The thermal material properties of the Ni-Mn-Ga alloy were reported in a previous paper [5]. The expansion coefficient of 2 * 10−5/°C was determined between 200 °C and 1000 °C. The elastic coefficients of the L21 lattice were reported in [6] for room temperature (c11 = 140 GPa, c12 = 129 GPa, c44 = 104 GPa) and up to 120 °C. To consider the reduction of elastic stiffness with temperature these data were assumed to reduce to 70% at Tsolidus, to 7% at fraction solid 0.9 and to 0.007% at Tliquidus

Simulation model

Thermal simulations of Bridgman processes have already been performed in various studies, e.g. for Ni-base superalloys [7], [8]. The simulation of stress and deformation in growing crystals requires coupled thermal and mechanical simulation, which has for instance been applied in the field of silicon casting processes, e.g. [9], [10].

For the Bridgman furnace at ETO MAGNETIC GmbH a simulation model including casting part, ceramic mold and all furnace components was created using Siemens software

Results

During the thermal simulation various crystallization parameters are monitored to describe the local crystallization conditions: the gradient at the liquidus position Gliq, the solidification velocity v, the ratio Gliq/v indicating the morphology of the growing structure [14], the solidification time, and the curvature of the solidification front. Examples of their dependence on the height position within the rod are given in Fig. 5 for different process variants designated as process A and

Discussion

The main origin for the development of stresses within the crystal is the nonlinearity of the temperature field in axial and horizontal direction as well as the stress-free growth condition at the melt-crystal interface into the nonlinear profile.

A linear temperature profile, i.e. a constant temperature gradient along the crystal rod would not cause any thermal stress, as far as the material data do not depend on temperature. As soon as the gradient differs between neighboring regions the

Conclusions

Ni-Mn-Ga material produced by a Bridgman type process shows similar dendrite orientation structure as it was reported several times for Ni-base superalloys. The macroscopic thermal stress due to the nonlinear temperature field and the stress evolving due to the crystal growth into this profile have been simulated as well as the remaining residual stress after cooling to room temperature. The levels of stress and deformation increase with the gradient at the liquidus position and with the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The support by the German Bundesministerium für Bildung und Forschung (BMBF) (grant 03XP0042) within the project “MAREGA” is gratefully acknowledged. Siemens PLM has supported the project by providing STAR-CCM+ licenses (partner program no.: 60068580).

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