EFFECTS OF MAGNETIC FIELD ON THE SHAPE MEMORY BEHAVIOR OF SINGLE AND POLYCRYSTALLINE MAGNETIC SHAPE MEMORY ALLOYS

Magnetic Shape Memory Alloys (MSMAs) have the unique ability to change their shape within a magnetic field, or in the presence of stress and a change in temperature. MSMAs have been widely investigated in the past decade due to their ability to demonstrate large magnetic field induced strain and higher frequency response than conventional shape memory alloys (SMAs). NiMn-based alloys are the workhorse of metamagnetic shape memory alloys since they are able to exhibit magnetic field induced phase transformation. In these alloys, martensite and austenite phases have different magnetization behavior, such as the parent phase can be ferromagnetic and martensite phase can be weakly magnetic. The magnetization difference between the transforming phases creates Zeeman energy, which is the main source for magnetic field induced phase transformation, is unlimited with applied field and orientation independent. Thus, metamagnetic shape memory alloys can be employed in polycrystalline form and provide higher actuation stress than conventional MSMAs. High actuation stress levels and frequencies in metamagnetic shape memory alloys are promising for magnetic actuation applications. Effects of heat treatments and cooling rates on the transformation temperatures, magnetization response and shape memory behavior under compressive stress were explored in Ni45Mn36.5Co5In13.5 [100] oriented single crystalline alloys to obtain high transformation temperatures, large magnetization difference, and low hysteresis behavior. It was found that transformation temperatures increase with higher heat treatment temperatures and decrease drastically at lower cooling rates. Temperature hysteresis decreased with increasing heat treatment temperatures. It was revealed that transformation temperatures, hysteresis, and magnetization response can be tailored by heat treatments via modifying interatomic order. Magnetic and mechanical results of NiMn-based metamagnetic alloys in single and polycrystalline forms as functions of composition, stress, temperature and magnetic field (up to 9 Tesla) were revealed through thermal-cycling under stress and magnetic field; stress-cycling as functions of temperature and magnetic field; and magnetic-field-cycling under stress at several temperatures experiments. Single crystalline samples of NiMnCoIn showed recoverable strain of 1.5 % due to magnetic field induced reversible phase transformation under constant stress and strain of 3.7 % by magnetic field induced recovery after variant reorientation of martensite. The magnetic field effect on the superelasticity and shape memory effects were also explored in selected orientations of [100], [110] and [111]. Fe-based ferromagnetic shape memory alloys have received considerable attention due to their better workability, strength, and lower cost compared with commercial NiTi based SMAs. The shape memory properties of a ferrous single crystalline alloy, FeNiCoAlNb, were investigated along the [100] orientation by thermal cycling under constant stress and superelasticity tests in both tension and compression. Aging was used to form nano-size precipitates to demonstrate shape memory behavior and tailor the shape memory properties. It was found that after proper heat treatments, [001] oriented FeNiCoAlNb showed a compressive strain of 15%, low temperature dependent superelastic behavior, high compression-tension asymmetry, and high compressive strength (~3GPa). The orientation dependence of the mechanical properties of FeNiCoAlNb single crystals were investigated along the [100], [110], [012] and [113] orientations. In addition, martensite phase showed higher magnetization than austenite phase as opposed to NiMn-based metamagnetic shape memory alloys. This magnetization difference is promising because it can allow magnetic field induced forward transformation. Ferrous alloys have great potential for high strength, temperature independent, and large scale actuator applications

Septic B spline collocation method for the numerical solution of the modified equal width wave equation

Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable

Petrov Galerkin finite element method for solving the MRLW equation

In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L2, L∞ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigate

Subdomain finite element method with quartic B-splines for the modified equal width wave equation

In this paper, a numerical solution of the modified equal width wave (MEW) equation, has been obtained by a numerical technique based on Subdomain finite element method with quartic Bsplines. Test problems including the motion of a single solitary wave and interaction of two solitary waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable

A numerical solution of the MEW equaiton using sextic B splines

In this article, a numerical solution of the modified equal width wave (MEW) equation, based on subdomain method using sextic B-spline is used to simulate the motion of single solitary wave and interaction of two solitary waves. The three invariants of the motion are calculated to determine the conservation properties of the system. L2 and L∞ error norms are used to measure differences between the analytical and numerical solutions. The obtained results are compared with some published numerical solutions. A linear stability analysis of the scheme is also investigate

Petrov galerkin method with cubic B splines for solving the MEW equation

In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin method in which the element shape functions are cubic B-splines and the weight functions quadratic B-splines . The motion of a single solitarywave and interaction of two solitarywaves are studied. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and L2 , L¥ error norms. The obtained results show that the present method is a remarkably successful numerical technique for solving the modified equal width wave(MEW) equation. A linear stability analysis of the scheme shows that it is unconditionally stable

Numerical solution of the modified equal width wave equation

Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws L2 and L∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated

A numerical solution of the modified regularized long wave (MRLW) equation using quartic B-splines

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the proposed method are tested by calculating the numerical conserved laws and error norms L₂ and L∞. The obtained results show that the method is an effective numerical scheme to solve the MRLW equation. In addition, a linear stability analysis of the scheme is found to be unconditionally stable.Publisher's Versio

Approximation of the KdVB equation by the quintic B-spline differential quadrature method

In this paper, the Korteweg-de Vries-Burgers’ (KdVB) equation is solved numerically by a new differential quadrature method based on quintic B-spline functions. The weighting coefficients are obtained by semi-explicit algorithm including an algebraic system with fiveband coefficient matrix. The L2 and L∞ error norms and lowest three invariants 1 2 I ,I and 3 I have computed to compare with some earlier studies. Stability analysis of the method is also given. The obtained numerical results show that the present method performs better than the most of the methods available in the literatur

Two different methods for numerical solution of the modified burgers’ equation

A numerical solution of the modified Burgers’ equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing \u1d43f����2 and \u1d43f����∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM