Energy conversion in shape memory alloy heat engine - Part II: Simulation

In this paper, a theoretical model proposed in Part I (Zhu et al., 2001a) is used to simulate the behavior of a twin crank NiTi SMA spring based heat engine, which has been experimentally studied by Iwanaga et al. (1988). The simulation results are compared favorably with the measurements. It is found that (1) output torque and heat efficiency decrease as rotation speed increase; (2) both output torque and output power increase with the increase of hot water temperature; (3) at high rotation speed, higher water temperature improves the heat efficiency. On the contrary, at low rotation speed, lower water temperature is more efficient; (4) the effects of initial spring length may not be monotonic as reported. According to the simulation, output torque, output power and heat efficiency increase with the decrease of spring length only in the low rotation speed case. At high rotation speed, the result might be on the contrary.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Depth dependence of nanohardness in a CuAlNi single crystal shape memory alloy

Instrumented nanoindentation was employed to study the depth dependence of nanohardness in a CuAlNi single crystal shape memory alloy that exhibits shape memory effect (SME). A Berkovich indenter and a cube comer indenter were used in this study, and the

A Discussion on Modeling Shape Memory Alloy Embedded in A Composite Laminate as Axial Force and Elastic Foundation

In this paper, the possible error sources of the composite natural frequencies due to modeling the shape memory alloy (SMA) wire as an axial force or an elastic foundation and anisotropy are discussed. The great benefit of modeling the SMA wire as an axial force and an elastic foundation is that the complex constitutive relation of SMA can be avoided. But as the SMA wire and graphite-epoxy are rigidly bonded together, such constraint causes the re-distribution of the stress in the composite. This, together with anisotropy, which also reduces the structural stiffness can cause the relatively large error between the experimental data and theoretical results.

Energy Conversion in Shape Memory Alloy Heat Engine Part I: Theory

Shape Memory Alloy (SMA) can be easily deformed to a new shape by applying a small external load at low temperature, and then recovers its original configuration upon heating. This unique shape memory phenomenon has inspired many novel designs. SMA based heat engine is one among them. SMA heat engine is an environment-friendly alternative to extract mechanical energy from low-grade energies, for instance, warm wastewater, geothermal energy, solar thermal energy, etc. The aim of this paper is to present an applicable theoretical model for simulation of SMA-based heat engines. First, a micro-mechanical constitutive model is derived for SMAs. The volume fractions of austenite and martensite variants are chosen as internal variables to describe the evolution of microstructure in SMA upon phase transition. Subsequently, the energy equation is derived based on the first thermodynamic law and the previous SMA model. From Fourier’s law of heat conduction and Newton’s law of cooling, both differential and integral forms of energy conversion equation are obtained.

A Thermodynamic Constitutive Model for Stress Induced Phase Transformation in Shape Memory Alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading). (C) 2002 Elsevier Science Ltd. All rights reserved.

Measurement of Microscopic Deformation in a Cualni Single Crystal Alloy by Nanoindentation with a Heating Stage

Thermally induced recovery of nanoindents in a CUAINi single crystal shape memory alloy was studied by nanoindentation in conjunction with a heating stage. Nanoindents formed by a Berkovich indenter at room temperature were heated to 40, 70 and 100 degrees C. Partial recovery was observed for the nanoindents. The recovery ratio depended on the heating temperature. Indentation of CuAlNi can induce inelastic deformation via dislocation motion and a stress-induced matensitic transformation. The percentages of dislocation-induced plastic strain would affect the thermal deformation of CuAlNi, because the induced dislocations could stabilize stress-induced martensite plates even when the temperature above austenite finish temperature, A(f). When the applied indentation load is low (less than 10,000 mu N), the shape recovery strain is predominant, compared with the dislocation-induced plastic strain. Therefore, the degree of indent recovery in the depth direction, delta(D), is high (about 0.7-0.8 at 100 degrees C).

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Shape memory effect of poly(L-lactide)-based polyurethanes with different hard segments

A series of biodegradable polylactide-based polyurethanes (PLAUs) were synthesized using PLA diol (M-n = 3200) as soft segment, 4,4 '-diphenylmethane diisocyanate (MDI), 2,4-toluene diisocyanate (TDI), and isophorone diisocyanate (IPDI) as hard segment, and 1,4-butanediol as chain extender. The structures and properties of these PLAUs were studied using infrared spectroscopy, differential scanning calorimetry, tensile testing, and thermomechanical analysis. Among them, the MDI-based PLAU has the highest T-g, maximum tensile strength, and restoration force, the TDI-based PLAU has the lowest T-g, and the IPDI-based PLAU has the highest tensile modulus and elongation at break. They are all amorphous. The shape recovery of the three PLAUs is almost complete in a tensile elongation of 150% or a twofold compression. They can keep their temporary shape easily at room temperature (20 degrees C). More importantly, they can deform and recover at a temperature below their T-g values. Therefore, by selecting the appropriate hard segment and adjusting the ratio of hard to soft segments, they can meet different practical demands for shape memory medical devices.

Biodegradable polyurethane based on random copolymer of L-lactide and epsilon-caprolactone and its shape-memory property

A series of biodegradable polyurethanes (PUs) are synthesized from the copolymer diols prepared from L-lactide and epsilon-caprolactone (CL), 2,4-toluene diisocyanate, and 1,4-butanediol. Their thermal and mechanical properties are characterized via FTIR, DSC, and tensile tests. Their T(g)s are in the range of 28-53 degrees C. They have high modulus, tensile strength, and elongation ratio at break. With increasing CL content, the PU changes from semicrystalline to completely amorphous. Thermal mechanical analysis is used to determine their shape-memory property. When they are deformed and fixed at proper temperatures, their shape-recovery is almost complete for a tensile elongation of 150% or a compression of 2-folds. By changing the content of CL and the hard-to-soft ratio, their T(g)s and their shape-recovery temperature can be adjusted. Therefore, they may find wide applications.

Shape-memory and biocompatibility properties of segmented polyurethanes based on poly(L-lactide)

A series of segmented poly (L-lactide)-polyurethanes (PLA-PU) were synthesized by a two-step method, with oligo-poly(L-lactide) (PLA) as the soft segments and the reaction product of 2,4-toluene diisocyanate(TDI) and ethylene glycol(EG) as the hard segments. The shape memory properties of PLA-PUs were examined. The processed PLA-PUs could recover almost 100% to their original shape within 10 degrees C from the lowest recovery temperature. In the recovery process, the PLA-PUs showed a maximum contracting stress of shape change in the range of 1.5-4 MPa depending on the PLA segmental length and the hard-segmental content and higher than that of poly (e-caprolactone polyurethane) (PCL-PU). Besides, the influence of deforming and fixing temperatures on shape memory properties of PLA-PU was studied in detail. They could affect not only the recovery temperature but also the maximum contracting stress. The experiments of cell incubation were used to evaluate the biocompatibility of PLA-PU. The results show that the biocompatibility of PLA-PU is comparable to that of the pure PLA. This kind of polyurethane can be used as implanted medical devices with a shape memory property.

The influence of hard-segments on two-phase structure and shape memory properties of PCL-based segmented polyurethanes

Poly(epsilon-caprolactone)-based segmented polyurethanes (PCLUs) were prepared from poly(epsilon-caprolactone) diol, diisocyanates (DI), and 1,4-butanediol. The DIs used were 4,4'-diphenylmethane diisocyanate (MDI), 2,4-toluenediisocyanate (TDI), iso-phorone diisocyanate (IPDI), and hexamethylene diisocyanate (HDI). Differential scanning calorimetry, small-angle X-ray scattering, and dynamic mechanical analysis were employed to characterize the two-phase structures of all PCLUs. It was found that HDI- and MDI-based PCLUs had higher degree of microphase separation than did IPDI- and TDI-based PCLUs, which was primarily due to the crystallization of HDI- and MDI-based hard-segments. As a result, the HDI-based PCLU exhibited the highest recovery force up to 6 MPa and slowest stress relaxation with increasing temperature. Besides, it was found that the partial damage in hard-segment domains during the sample deformation was responsible for the incomplete shape-recovery of PCLUs after the first deformation, but the damage did not develop during the subsequent deformation.

Polylactide-based polyurethane and its shape-memory behavior

A series of polylactide polyurethanes (PLAUs) were synthesized from poly(L-lactide) diols, hexamethylene diisocyanate (HDI), and 1,4-butanediol (BDO). Their thermal and mechanical properties and shape-memory behavior were studied by infrared spectroscopy (IR), differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXID), tensile testing, and thermal mechanical analysis (TMA). The T(g)s of these polymers were in the range of 33-53 degrees C, and influenced by the Mn of the PLA diol and the ratio of the soft-segment to the hard-segment. These materials can restore their shapes almost completely after 150% elongation or twofold compression. By changing the M-n of the PLA diol and the ratio of the hard-to-soft-segment, their Ts and shape-recovery temperatures can be adjusted to the neighborhood of the body temperature. Therefore, these PLAUs are expected to find practical medical applications.