Effect Of Shear Strain On The Deflection Of A Clamped Magnetostrictive Film-substrate System

In recent years, rare earth giant magnetostrictive materials are attracting muchattention of theorists and experimentalists because of its excellent characteristics-largestrain, high magneto-mechanical coupling coefficient, short response time, large exertedforce, wide frequencyband and non-contact driving. Especially, the cantilever systemcomposed of magnetostrictive thin film and non-magnetic substrate which are simple toprepare are widely used in microsensors and microactuators. Using this as a measure ofthe deformation of the static structure displacement sensor and applying static force ofactuators, the most important is to build the right model to design and optimization.As considering the influence of shear, the bending deflection with arbitraryfilm-substrate thickness ratio is solved exactly by employing the principle ofthree-parameter and four-parameter Gibbs free energy minimization in the paper. At thesame time, the exact solution for the bending problem of a free-end point loadedfilm-substrate cantilever is obtained by using the basic mechanical equilibrium equation.The longitudinal curvature is assumed to constant, and a function of aspect width tolength(w/l) is taken into transverse. The coordinate system is set up in a neutral plane inthe three-parameter method. Considering the shear energy of substrate, a more accuratemodel for the thin film is obtained with a constant value p in regard to w/l introduced.Resetting the constant p top1, the shear energy of film is in addtion to get theanalytical expressions. But they are nonliner equations and too complicated to be appliedto the further discussion. So the four-parameter Gibbs free energy minimization is takeninto account. In the case, the coordinate system is set up at the interface and a set ofstandard liner equations are received. By means of Carmer’s rule, a new bendingdeflection formulation of thick film is presented. Meanwhile, the bending problem of afree-end point loaded film-substrate cantilever is also solved. Furthermore, the optimal condition for actuator application is presented and some theoretical problems are clarified.The results show that, the prediction is more efficient for l value going from0.1w to10w. In general, the greater the film-to-substrate thickness ratio, the higher the ability oftaking load, namely the larger the actuator force when the thickness of substrate is keptconstant. when the total thickness of the cantilever is kept constant, however, the actuatorforce will experience a maximum and this maximum value of actuator force will decreasewith the increasing film-to-substrate stiffness ratio.Meanwhile, the optimal thickness ratiocorresponding to this maximum actuator force also decreases with the increasing stiffnessratio. Whether for the cases of fixed substrate or fixed total thickness, the influence ofpoisson’s ratio of two cantilever components on the actuator force is remarkable, andshould not be neglected.