Elastocaloric cooling, which exploits superelastic transitions of shape memory alloys to pump heat, has recently emerged as a frontrunner in alternative cooling technologies. Despite its intrinsic high efficiency, elastocaloric materials exhibit hysteresis associated with input work, a common attribute of caloric cooling materials. In this study, the authors created a Ni-Ti-based elastocaloric material by additive manufacturing nanocomposite materials using a laser directed-energy- deposition system. The material exhibited exceptional stability and unusual operational efficiency derived from the unique and intricate nanocomposite structures made by additive manufacturing. This demonstration shows the potential for using additive manufacturing to optimize caloric cooling by providing a highly desirable topology flexibility into materials components that serve as both refrigerants and heat exchangers.

An elastoplastic phase-field model is used to investigate the deformation mechanisms of yttria stabilized tetragonal zirconia in presence of defects. A remarkable tension-compression asymmetry is detected. A higher strength and a lower degree of transformation are observed in compression than in tension. Also, deformation mechanism is asymmetric depending on the crystal orientation. For some cases (other cases), phase transformation is absent in tension (in compression), while both transformation and plasticity are present in compression (in tension). Such tension-compression asymmetry is attributed to activation of different monoclinic variants with different Eigen strain tensors in tension versus compression. Results also reveal a higher degree of transformation and plasticity with lower onset stresses as the void size increases. Elliptic voids exhibit a directional effect with a maximum stress intensity factor of 5.6 MPa m1/2 when the long semi-axis is diagonally oriented with respect to the loading direction, and this prediction is comparable to experiments.

The non-transforming intermetallic Ni3Ti phase generated in NiTi matrix by additive manufacturing was previously reported to create elastocaloric composites with a great coefficient of performance (COP) between 11 and 22 [Hou et al., Science 366 (6469) (2019) 1116–1121]. In this work, we use a fully thermomechanical coupled phase-field model to design microarchitectures considering the effects of all the possible non-transforming intermetallics (Ni4Ti3, Ni3Ti, and Ti2Ni) in NiTi. Our simulations show possibilities of increasing the COP by guiding the type, shape and volume fraction of intermetallics, which are controllable by processing parameters. With 50% intermetallic fraction arranged in strips of 500 nm width perpendicular to the loading direction, the Ti2Ni intermetallic induces higher COP (67.13) than Ni3Ti (16.18) and Ni4Ti3 (14.29), all surpassing that of the bulk NiTi without intermetallics (12.92). Additionally, the COP increases to 79.94 for 65% volume fraction of Ti2Ni and decreases to 56.31 for 35% Ti2Ni content. Even nontrivial designs with 50% of circular or square transforming NiTi domains display high COP of 40.06 and 29.22, respectively. A high COP is achievable by introducing intermetallics having high modulus (for low input energy), thermal conductivity (for temperature change) and heat capacity (for the output energy).

The reversible stress-induced phase transformation in shape memory alloys (SMAs) is a dissipative process during which heat is absorbed or released. The inherent temperature variations inside the material has an elastocaloric effect (eCE) with appealing applications in solid-state cooling technology such as compact and efficient on-board refrigeration system for eletronic devices. In this manuscript, we conduct the first study of eCE of CuAlBe SMAs utilizing phase-field modeling. For an applied stress of 500 MPa, the results for polycrystalline Cu-Al11-2Be (at. %) show a minimum adiabatic unloading temperature change of -10 K over a pseudoelastic window of 40 K. In the absence of plastic deformation, the material demonstrates good reproducibility of the eCE over a few loading-unloading cycles. The presence of plastic deformation is found to cause functional fatigue that deteriorates the cooling capacity; however, the coefficient of performance only decreases from 9.04 to 8.03, which is still a very good value. These results place CuAlBe as a frontrunner SMA for solid-state cooling compared to the expensive NiTi.

Stress-induced martensitic transformation ahead of a crack tip can relax the stress concentration and produce fracture toughness in shape memory alloys (SMAs). In this manuscript, we utilize a non-isothermal phase-field model (PFM) to study the martensitic transformation induced crack tip toughening in CuAlBe SMA. The force-displacement curve, transformation zone and high stress zone in single crystalline samples show high dependency on the grain orientation with respect to the crack alignment. Comparison between isothermal and non-isothermal simulations reveals that the transformation-induced self-heating decreases the toughening capability by increasing the critical transformation stress. Investigating the high stress zones in CuAlBe and the non-transforming CuAl alloy shows that the toughening is obtained by redistributing the stress concentration far from the crack tip, as the high stress zone follows the moving tip of the transformation zone. Increasing the acuity of the crack tip is found to generate more symmetric martensite wings on both side of the crack axis, and a more localized high stress zone. The polycrystal specimen displays higher toughening due to the internal constraints related to the presence of various grains with difference orientations. Depending on the orientation of the grain inclosing the crack tip, the toughening effect can be lower or higher. Coincidence of the crack tip with a triple junction is found to improve the toughening behavior.

We propose an elasto-plastic phase-field model (PFM) to conduct the first microscopic computational study of shape memory effect (SME), pseudoelasticity, stress assisted two-way memory effect (SATWME), and thermomechanical training of CuAlBe shape memory alloy (SMA). This non-isothermal PFM model considers the effects of temperature dependent properties, latent heat, grain boundaries, and asymmetric transformation and plasticity. PFM simulations demonstrate the capacity of our model to capture the thermomechanical and purely mechanical shape recovery in the SMA. When considering transforming grain boundaries, grain refinement generates a higher transformation stress, a steeper transformation hardening, and smaller hysteresis loops for both SME and pseudoelasticity. The results also point out slightly higher transformation stress when geometrical grain boundaries are used. The simulations of SATWME highlight an augmentation of the residual martensite as the hold stress increases, which is consistent with experimental observations. This is the first PFM that can mimic the thermal training within several SATWME cycles, showing an asymptotic increase of plastic strain and the related retained transformation strain until the fourth cycle, and their stabilization thereafter. The activation of plasticity occurs always after initiation of phase transformation. Although plasticity results in more stress relaxation, it deteriorates the shape recovery for both SME and pseudoelasticity by hindering the reverse transformation. Comparison between tension and compression demonstrates the capacity of this PFM to account for, for the first time, the nonsymmetrical transformation and plastic responses of SMAs.

We propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.

Using architected cellular iron-based shape memory alloys (AC Fe-SMAs) can help compensate the relatively higher density of the base material compared to NiTi-based and Cu-based shape memory alloys, while providing good shape recovery, lower production cost, and greater energy dissipation. This article is dedicated to the development of an effective and pressure-dependent constitutive model that predicts the thermomechanical response of AC Fe-SMAs. We first simulate the behavior of the cellular material using the dense model that was previously developed by the authors, along with different unit cells (UCs) subject to periodic boundary. The shape memory effect is simulated by compressing the UCs by 2% of their height, followed by mechanical unloading, and heating above the austenite finish temperature. The results highlight stress concentration, maximum phase transformation, and maximum plastic deformation at the geometry discontinuities or strands necks. Post-processing the ABAQUS ODB files with Python scripts shows that the bending-dominated unit cell with the highest maximum local values of state variables exhibits the lowest volume-averaged outputs. Comparison of the unit cell to cubic multi-cell structures points out an asymptotic vanishing of the effects of the free boundaries as the number of cells in the multi-cell structure increases. The results of the unit cells are used to calibrate the parameters of the pressure-dependent effective model. The ratios of the inelastic hydrostatic strains to the equivalent total inelastic strains indicate higher pressure effects in the bending-dominated cellular lattice than in the stretch-dominated structures. The force-displacement and dissipated energy-temperature curves of the cellular beam and its equivalent bulk structure obtained by simulations of 4-point bending tests are found to be close enough that the effective model can be considered as an efficient design tool for architected cellular iron-based shape memory alloy structures.

Elastocaloric cooling, a solid-state cooling technology, exploits the latent heat released and absorbed by stress-induced phase transformations. Hysteresis associated with transformation, however, is detrimental to efficient energy conversion and functional durability. We have created thermodynamically efficient, low-hysteresis elastocaloric cooling materials by means of additive manufacturing of nickel-titanium. The use of a localized molten environment and near-eutectic mixing of elemental powders has led to the formation of nanocomposite microstructures composed of a nickel-rich intermetallic compound interspersed among a binary alloy matrix. The microstructure allowed extremely small hysteresis in quasi-linear stress-strain behaviors-enhancing the materials efficiency by a factor of four to seven-and repeatable elastocaloric performance over 1 million cycles. Implementing additive manufacturing to elastocaloric cooling materials enables distinct microstructure control of high-performance metallic refrigerants with long fatigue life.

The article focuses on the numerical simulation of the thermomechanical behavior of steel T-stubs connected by iron-based shape memory alloys bolts. The three-dimensional macroscopic model used in this work was previously developed by the authors considering different thermomechanical properties between austenite and martensite, and coupling between phase transformation and plasticity. The model is implemented in a UMAT code using an implicit time-discrete integration scheme that follows a "multisurface plasticity"-like approach. The numerical results show that the shape memory effect can be used to preload the bolt if the initial length of its shank is less than the total thickness of the flanges. For an initial shank length of 21.38 mm and a total flange thickness of 21.4 mm, the shape memory effect produced average contact forces of 101 N between the bolt head and the flange, and 37 N between the two flanges. The resulting average contact pressures were 210 and 25 MPa, respectively. The average bolt force after preload was approximately 22.6 kN. Subsequent application of 2 mm normal displacements at the top and bottom faces of the upper and lower webs induced local plastic deformation around the flange holes and phase transformation in the bolt. The reversibility of martensitic transformation and the confinement of the plastic deformation in a limited zone around the holes allowed nearly complete shape recovery by heating. The obtained results highlight the advantage of using low-cost iron-based shape memory alloys as alternatives to steel bolts for connecting T-stubs.

The paper presents results of finite element analysis of architectured iron-based shape memory alloy (SMA) samples consisting of bulk SMA and void combined to different proportions and according to different geometric patterns. The finite element simulation uses a constitutive model for iron-based SMAs that was recently developed by the authors in order to account for the behavior of the bulk material. The simulation of the architectured SMA is then carried out using a unit cell method to simplify calculations and reduce computation time. For each unit cell, periodic boundary conditions are assumed and enforced. The validity of this assumption is demonstrated by comparing the average behavior of one unit cell to that of a considerably larger sample comprising multiple such cells. The averaging procedure used is implemented numerically, by calculating volume averages of mechanical fields such as stress and strain over each finite element model considered as a combination of mesh elements.

The paper presents a 3D macroscopic constitutive model for Iron-based shape memory alloys (Fe-SMAs) that uses different thermomechanical properties for austenite and martensite, and considers nonlinear coupling effects between phase transformation and plasticity. The constitutive equations are derived from a potential comprising the Voigt mixture of the free energies of the two phases adapted from the ZM model, and a new interaction energy term. The loading conditions for phase transformation and plastic deformation are obtained by requiring the governing thermodynamic forces to derive from an appropriate dissipation potential, in which a quadratic plasticity-dependent term has been introduced to account for its suppressive effect on forward transformation. The model is implemented in ABAQUS through a user defined material subroutine (UMAT), validated against experimental data taken from the literature, and used to simulate partial unloading and investigate the influences of interaction parameters. Finite element analysis of a precracked compact tension sample is then carried out under both plane stress and plane strain (nonproportional stress fields with strong gradients). The results show highly heterogeneous stress distribution in the specimen. The inelastic strain singularity at the crack front is a consequence of pure phase transformation at low temperature, pure plasticity at high temperature, and a mix of both at intermediate temperatures. During unloading, the crack front accommodates the compression of the surrounding material by undergoing cyclic phase transformation and/or reversed plasticity, which, in turn, induces partial crack closure. If the mechanical loading cycle is operated at low temperature then heating leads to complete crack closure due to martensite -> austenite transformation, while if it is operated at elevated temperature, heating leads to further but not complete crack closure as a result of the thermal induced plasticity. (C) 2017 Elsevier Ltd. All rights reserved.

Low-cost iron-based shape memory alloys (SMAs) have great potential for applications in large engineering parts. Their main drawback relates to their higher density compared to Nitinol and Cu-based SMAs, and can be compensated by using porous Fe-SMAs or by lightening the structures through the introduction of engineered cavities. In this manuscript, we simulate the thermomechanical response of a tapered Fe-Mn-Si beam with web openings using a 3D phenomenological model that was previously developed by the authors. The model is implemented in ABAQUS through a user defined material subroutine (UMAT). The results obtained by applying a pressure of 1 MPa and fixing both vertical ending faces show that, at room temperature, the smart beam can recover completely its initial shape. In contrast, a steel beam with the same geometry subjected to identical boundary conditions is found to fail at a much lower load. Even if the deformation of the SMA beam is dominated by plastic deformation as the loading temperature increases, its perfect shape memory effect at room temperature can be used to renovate architectural heritage or to design new smart structures.

The paper presents a new constitutive model for iron-based shape memory alloys (Fe-SMAs) adapted from the ZM model initially proposed for Nitinol by Zaki and Moumni [JMPS2007]. The model introduces nonlinear hardening terms to account for interactions between the grains, martensite variants and slip systems that may exist within a volume element of the material. The expressions used for the hardening terms are similar to those in (Khalil et al. [JIMSS2012]). The equations of the model are derived from the expression of a Helmholtz free energy potential, with complementary loading conditions obtained within the framework of generalized standard materials with internal constraints. A detailed derivation of the implicit algorithm used for the integration of the model is provided and used for numerical simulations that are shown to agree with experimental data.

Constitutive models for shape memory alloys have seen significant development in the last decades. They have evolved from uniaxial, mostly empirical, relations to full-fledged mathematical descriptions accounting for many of the effects observed in these materials with an ever-higher degree of detail. The models available today are constructed using various approaches ranging from micromechanics with or without scale transition, to statistical physics and particle dynamics, to methods of classical plasticity, to energy approaches coupled with thermodynamic and conservation principles. They have finally matured to the extent where they can be utilized in reasonably accurate numerical analysis of potentially complex shape memory alloy devices subjected to non-trivial thermomechanical loading. This paper aims at providing an up-to-date review of key constitutive models for shape memory alloys, with an attempt to track their evolution from their inception to their most recent versions. The models are categorized in terms of the approach they use in describing the behavior of shape memory alloys.

The pre-existing inner stresses in composite materials should be determined in order to avoid structural failure. Such stresses are accumulated during the manufacturing process. Thus, they are called “process-induced residual stress”. In this paper, the process-induced residual stresses in glass/epoxy composites were predicted by using micro-mechanical model in ABAQUS. Moreover, the effect of parameters such as the fiber volume fraction, cooling rate, and nature of the matrix were investigated. The viscoelastic nature of the epoxy was implemented in a UMAT code by using FORTRAN. The results showed that higher fiber volume fraction induces higher residual stress. However, the increase of the cooling rate slightly changes the residual stress values. Moreover, using elastic solution of the epoxy overestimated the residual stress.