Simulation of Shape Memory Effect and Superelasticity in Shape Memory Alloys Using Dissipation Potential Model
Inner hysteresis loop at 500C
The main objective of this study is to introduce a self expanding 'dissipationless band' to model inner hysteresis loops of shape memory alloys (SMAs). Dissipation that occurs when the material undergoes phase transformation is critical to the modeling of hysteretic behavior. Using a dissipationless virtual response of the material, a logical framework for the onset transformation under reversal of cycles is simulated. It is identified that this dissipationless band occurs due to the difference between the starting states of forward and reverse transformation. Width of dissipationless band varies for inner hysteresis with loading history.
The construction of the generalized driving force for the transformation along with the rate of dissipation function is formulated. Simulated hysteresis loops for different kinds of partial and complete loading cycles at different thermo-mechanical conditions. The constitutive model is implemented within the finite-element software ABAQUS using a user defined material subroutine (UMAT) and USERMAT using ANSYS. An implicit algorithm has been developed to analyse varies applications.
M.Kishore Kumar, S.M. Sivakumar and C.Lakshmana Rao
A Micromechanical Model for Ferroelectric Materials Considering Boundary Effects
(a) Electric field Vs Strain and (b) Electric field Vs Electric displacement
Ferroelectric materials are outstanding candidates for mass applications calling for short response times, high precision positioning and considerable actuation forces in systems of possibly complex shape. The increasing economic importance of these materials has brought about the need for an improved knowledge of them under variety of loading conditions. Hence there is a strong necessity to model the behavior of this class of materials accurately enough to be used in both sensor and actuator applications.
In view of this a micromechanical model for ferroelectric materials derived from thermodynamics principles is proposed. It is assumed that the reduction in the energy of different states act as driving force and when it exceeds a critical value domain switch occurs. The proposed model considers all six domain variants of the tetragonal state and evolution of each of them in terms volume fraction is pursued during loading. Resistance to evolution of new domains is taken into account in this model in a phenomenological way and it is assumed to be increasing with volume fraction. The proposed model could predict the non linear hysteresis behavior of single crystal barium titanate and polycrystal PZT under electrical, mechanical and combined loading conditions.
K. Jayabal, A. Arockiarajan and S M. Sivakumar
Studies on Structural Health Monitoring using Smart Materials
Structural Health Monitoring (SHM) is a system with which a non-intrusive, active damage evaluation mechanism is attached to each structural component to continuously monitor the integrity of the structure or damage signatures. A comprehensive review of the literature is made on SHM and damage evaluation of aerospace structures. Three dimensional finite element model of Honeycomb sandwich cantilever plate is made and validated with the experimental and theoretical results. Fig.1 shows the three dimensional finite element model of sandwich plate.
Fig.2 shows the load vs deflection for experimental as well as theoretical and 2D models. Fig.3 & 4 shows the deformed pattern of the 3D and 2D models respectively. The 3D model will be used for the simulation of damaged sandwich panel and its response evaluation.
K.R.Pradeep, S.M.Sivakumar, K.Balasubramanium and B.Nageswara Rao
On Smeared And Micromechanical Approaches To Modeling Martensitic Transformations In SMA
Sequential Laminate Tree and Subloop Simulations on Homogenized Polycrystals
The purpose of this work is three fold. One is to have a detailed look at the clear links that exist between the formulations arising out of a "smeared" natural state approach and a micro-mechanical approach. This provides an understanding of the role of different terms that take part in the "driving force" expression in each of these approaches. The other is to numerically implement a proposed micro-mechanical approach with simplification to small deformations. And, thirdly to simulate the behavior of polycrystalline SMA by simple homogenization bounds, to throw some light on the assumptions made in the macroscopic models on the hysteretic behavior.
The results for a typical example of Cu-Al-Ni crystal show some unique behavior that needs further validation from tests. For certain loading cases, there is a shift from one preferred martensite plate to another before full transformation is complete. This implies that there is an abrupt switch in the shape and orientation of the martensite plate under certain proportional loading conditions. This is the first time such an observation is made in the numerical simulation results related to martensitic transformation for simple proportional loading cases. It remains to be seen if this is in fact is the case in the experimental observations. This could depend on actual factors like the threshold driving force that can resist such a shift in the natural state.
The results on hysteresis simulations on homogenized polycrystalline SMA show that there is no concrete dissipationless zone though are bounded by the complete transformation curves. These simulations provide critical pointers to modeling dissipative behavior of the material under partial cycles of loading at the macroscopic phenomenological level.
V.S.R. Guthikonda, M. Kranthi Kiran, S.M. Sivakumar, A.R. Srinivasa
Design And Testing of a PVDF Hydrophone
PVDF Hydrophone Device and Experimental Setup
This work focuses on the development a methodology of design for a circular flexural plate PVDF hydrophone taking into consideration the various design parameters such as acoustical parameters, structural requirement and electromechanical properties of the PVDF. Little attention has been paid in the past on a systematic design of a hydrophone considering the various design parameters. Sensitivity and static pressure capability curves obtained in this work will help the designer in selecting an appropriate design for a given application with specific design constraints. Since the support conditions affect the sensitivity drastically, two bounding conditions, namely, the simply supported and the clamped boundary conditions were considered for the design.
Experiments were conducted to assess the performance of the hydrophones constructed using the proposed design methodology. Experimental results of testing the hydrophones both in air and underwater are presented. Results obtained show superiority of the hydrophones constructed using the proposed design methodology. In addition, theoretical calculations made on the designed hydrophone correlate well with the experimental observations. This demonstrates that the proposed methodology can be directly used for the design of a hydrophone given the design considerations.
R. Vigel Raj, C. Lakshmana Rao, S.M. Sivakumar and C. Padmanabhan
Constitutive Modelling Of Pseudoelastic and Shape Memory Effect Hysteresis of SMA - A Plasticity Approach
Total Strain Vs Stress
This project deals with the design of a smart air dam and development of suitable inner hysteresis model for Shape Memory alloy. To use the Shape Memory Alloy (SMA) wires in actuator applications, it is important to characterize their partial loading and unloading hysteretic behavior. In this work, we have modelled the inner hysteretic PE and SME behavior of SMA based on plasticity principles. In martensitic transformation, austenite undergoes transformation to form different variants of martensite under thermo-mechanical loading. The proposed model considered two variant of martensite and also incorporated the interaction between austenite and martensite grain boundaries.
Interaction between austeniteaustenite grains and martensite-martensite grains are neglected. The constitutive equations are derived by taking recourse to the principles of thermodynamics and assuming a form for the Gibbs potential. Loading criteria, yield function, flow rule, hardening rule and consistency conditions are systematically formulated and solutions of constitutive equations are obtained using a simple elastic predictor - plastic corrector algorithm. Kinematic hardening rule with non-linear, non-symmetric hardening parameter is used for both loading and unloading. Linear evolution law has been employed to calculate the martensite fraction. Used developed model for design of air dam. When an automobile moves at high speed, air circulation in the radiator compartment is inadequate. To increase the air supply, air dam is introduced in the front end of the automobile below the bumper. Aero-dynamic effects should be considered while optimizing the shape of the air dam.
N.Ashok kumar, S.M. Sivakumar and C.Lakshmana Rao
Domain Switching Criteria & Switch Toughening of Ferroelectrics
Comparison of various energy criteria for 180 switching in PZT 5H and Geometry of switching zones for 0 ° , 45 ° and 90 ° orientations of polarizations in mono-crystals
Domains, which exist in ferroelectric ceramics, on the application of external loads, such as electric fields and stress, undergo reorientation known as domain switching. This domain switching results in nonlinear behavior of ferroelectric ceramics. A domain switching criterion applicable to a generalized electromechanical loading is proposed based on an instability condition of the current domain state determined by a critical value of the input energy calculated with respect to the state of switch-worthiness. The criterion highlights the importance of the loading sequence in response evaluation. The model is able to capture the essential features and trends of experimental results found in literature.
In ferroelectrics under electromechanical loading, the intensified stress and electric field in the vicinity of crack-tip lead to domain switching. The switched domains induce incompatible strain near the crack and consequently change the fracture toughness of the material. A model of stress assisted 90o polarization switching, using a suitable domain switching criteria, to quantify the toughening process is proposed. The results are used to verify experimentally observed fracture toughness anisotropy viz. the material is tougher for a crack parallel to the poling direction but less tough for a crack perpendicular to it. The importance and physical significance of the orthotropic rescaling parameter is studied along with its effect on geometry of switching zone and toughness increment.
Non Uniform Heat Generation In Elastic Rod And Piezoelectric Bar With Hysteretic Damping Under Steady State Vibration.
(a) Electric field Vs Strain and (b) Electric field Vs Electric displacement
Heat is generated and vibrational energy is dissipated when damped structures are excited. The resulting increase in temperature of the structure causes a change in its material properties. Therefore, there is a change in the response of the structure to the excitation. In certain applications, the associated increase in temperature is moderate but affects the performance of resonant vibrators and linear analysis is expected to provide insight. The internal loss is modelled as hysteretic damping. In this work, analytical expressions of frequency and amplitude at which the maximum dissipated power are derived for a lumped mass-spring and a long, thin, viscoelastic rod with hysteretic damping. It is seen from the linear analysis that heat generation is spatially non-uniform, Fig. 1 and will affect the temperature distribution. The effect of loss factor on the dissipated power and its frequency shift are also studied.
Heat generated due to vibration of damped structures is of interest because it is one of the reasons for the failure of piezoelectric ceramic transducers. In this work, from generalised solution of a piezoelectric slab, for power dissipation, a one dimensional equation is deduced and numerically computed, length expander; ends stress free-free condition under electrical excitation. The non uniform temperature distribution was measured using IR camera and shown in Fig.2.
D Thomas, M S Sivakumar and D D Ebenezer