Micromechanics and Modelling of Adaptive Shape Memory Composites

The present work investigates the micromechanics approaches to model the thermomechanical behaviours of shape memory alloy composites. The research is primarily focussed on modelling the pseudoelastic and shape memory behaviours of smart composites, which are inherent in multifunctional materials like shape memory alloys and polymers. In the study, non- adaptive and adaptive matrix materials are used to address the adaptive fibre non-adaptive matrix, and adaptive fibre adaptive matrix concepts, respectively. Nickel-Titanium shape memory alloy wire is used as an adaptive shape memory fibre. Similarly, epoxy matrix that does not exhibit shape memory behaviours is considered as non-adaptive, while matrix possessing such behaviours has been employed as an adaptive matrix. The importance of the present research is to develop the modelling procedures for shape memory composites useful in high performance applications. The first and the foremost requirements are to propose the constitutive relations, which should be simpler in computation and at the same time address the fundamental mechanics of constituent materials. Therefore, simple analytical approaches are streamlined and the exis

Micromechanics and Modelling of High Performance Adaptive Shape Memory Composites with Multifunctional Materials

The present work investigates the micromechanics approaches to model the thermomechanical behaviours of shape memory alloy composites. The research is primarily focussed on modelling the pseudoelastic and shape memory behaviours of smart composites, which are inherent in multifunctional materials like shape memory alloys and polymers. In the study, non- adaptive and adaptive matrix materials are used to address the adaptive fibernon-adaptive matrix, and adaptive fiber- adaptive matrix concepts, respectively. Nickel- Titanium shape memory alloy wire is used as an adaptive shape memory fiber. Similarly, epoxy matrix that does not exhibit shape memory behaviours is considered as non-adaptive, while matrix possessing such behaviours has been employed as an adaptive matrix. The importance of the present research is to develop the modelling procedures for shape memory composites useful in high performance applications. The first and the foremost requirements are to propose the constitutive relations, which should be simpler in computation and at the same time address the fundamental mechanics of constituent materials. Therefore, simple analytical approaches are streamlined and the existing shortcomings are overcome by proposing the suitable modifications. The significant contributions include the derivation of consistent forms of the phase transformation, and hygro-thermal inelastic composite relations, addressing the effect of moisture in matrix on the composite behaviour, the derivation of interface stress model to compute the interfacial axial and shear stress distributions, shape memory fiber and shape memory polymer composite model development, proposing the thermomechanical actuation cycle for the composite, and the study on the high performance multifunctional laminate behaviours. The methodology adopted includes the application of micromechanics approaches such as the method of mixture, method of inclusion, and the method of cells. Method of mixture and method of inclusion is derived using zeroth order displacement field, while the method of cells is based on the first order displacement field. Emphasis has been placed on the evaluation of effective elastic properties as well as the composite behaviours. The pseudoelastic behaviour of non-adaptive composite is analysed first. In addition, the fibermatrix interface effects are introduced to investigate the stress distribution in the nonadaptive composite based on the equilibrium equations of elasticity. Next, both pseudoelastic as well as the shape memory effects of adaptive composite with phase changes in fiber and matrix is studied using the method of mixture and method of inclusion. The effective properties and thermo-mechanical behaviour of adaptive shape memory composite laminate are also examined by adopting a two step homogenization scheme. In the first step, the effective properties of each layer are determined using method of mixtures and method of cells with iso-strain conditions. In the second step, the effective properties evaluation has been extended to the laminate through a thin plate theory assumption with transverse shear deformations. The possible elastic couplings are discussed. Extensive results are presented by using the constitutive relations with the proposed modifications and derivations. The thermo-elastic and hygro-thermo-elastic nature of multifunctional composite are computed. A comparison is also made with the strain energy approach for a simple uniaxial loading. The variation in the composite stiffness and the stresses are studied for different fiber volume fractions, fiber modulus, and fiber cross sections. The modifications in the modeling approaches are highlighted with analytical case studies involving hysteretic stress–strain behaviors. Further, the interfacial axial and shear stress distributions in the composite due to the phase transformations in the fiber in view of the applied boundary conditions on the matrix, is computed. Furthermore, adaptive fiber adaptive matrix composite model development is presented for the first time in this research work. The highlight of the study is the proposed thermomechanical cycle, which has been adopted for the actuation of the adaptive shape memory composite. Due to the multifunctional nature of adaptive materials, the effect of change in stiffness of the constituent phases on the overall stiffness of the composite is examined primarily. The variations in force and moment resultants are simulated for different laminate configurations with respect to fiber orientations and stacking sequences. The present work also takes into account the effects of phase transformations and the resulting change in the fiber-matrix modulus. Major conclusions can be drawn from the present research work. As compared to the passive composites (without smart materials), the active composites with adaptive fibers and nonadaptive matrix are able to carry large stress with high energy absorption capability due to the associated hysteresis. As such, it is observed that the effect of moisture in the matrix will also influence the high performance behaviours of composites. The results of the interface effects also suggest that a considerable shear stress is developed within the matrix accommodating the shape memory fiber. The shear stress increases more rapidly as the fiber radius is increased. Also, it is evident that the interface effect of shape memory composites is influenced by the fiber stiffness as compared to the geometric parameters. The modeling approach is further successfully validated extensively for different geometric and volumetric parameters under various loading conditions. Additionally, it has been brought out that adaptive composites with adaptive fiber and matrix are able to sustain large elastic deformations. Subsequently, it is noticed that the proposed modeling procedure for adaptive composites is able to reproduce consistently the overall composite response by taking into consideration not only the phase transformations, variable modulus and transformation stresses in the fiber but also the variable modulus, the evolution of stored strain and thermal strain in the adaptive matrix. Furthermore, the results prove that adaptive composite laminates can be developed, which provides shape controllability via tunable laminate stiffnesses, leading to have optimal structural response. Moreover, the work presents the necessary framework for a reliable and efficient analysis of high performance adaptive composites for practical structure and applications. Finally, the work concludes that efficient adaptive laminate development for high performance composite applications, exhibiting large shape adjustments, high stresses and increased stiffnesses, are feasible by incorporating shape memory fiber and shape memory polymer matrix as multifunctional materials

Homogenization and pseudoelastic behavior of composite materials reinforced with shape memory alloy fibers

Pseudoelastic behavior of cylindrical shape memory alloy (SMA) fiber embedded in a polymer matrix is investigated by using micromechanic approaches. A homogenization scheme based on Eshelby's equivalent inclusion method is adopted to derive the expressions for strains in the fiber and matrix in terms of the average strain in the composite. The constitutive laws for the SMA fiber and matrix are also expressed in terms of the average strain in the composite. The expressions for the SMA composite stiffness and the inelastic strains tensors are derived using dilute distribution theory and rule of mixtures approach. The composite stiffness and inelastic strain tensors are used in the generalized Hooke's law to compute the transformation stresses and associated hysteresis of the SMA composite. A comparison is also made with the strain energy approach. The computational results in terms of the composite stiffness and the stresses are presented within different fiber volume fraction, using the proposed methods. Finally, the modifications in the modeling approaches are highlighted with analytical case studies involving hysteretic stress-strain behaviors

Modeling the effective properties and themomechanical behavior or SMA-SMP multifunctional composite lamintes

The research work presents the modeling of effective properties and thermo-mechanical behavior of shape memory fiber (SMF) and shape memory polymer (SMP) composite laminates using micromechanical approaches based on the method of mixtures (MOM) and method of cells (MOC). The fiber is made of a nickel-titanium (Ni-Ti) shape memory alloy (SMA), while the matrix consists of a shape memory thermoset epoxy polymer (SMP). The use of an SMP matrix provides large strain compatibility with the SMA fiber, while being active at high temperatures without losing its elastic properties. Additionally, the SMP matrix is also able to produce similar pseudoelastic and shape memory effects, which are noticed in SMAs. In the analysis, a two step homogenization scheme is followed. In the first step the effective properties of each layer are determined via a micromechanics approach with iso-strain conditions. In the second step the effective properties of the SMF-SMP composite are computed making a thin plate theory assumption, which takes into account the transverse shear deformations. The possible elastic couplings for SMF-SMP laminates are discussed, and the laminate force and moment resultants are computed for various laminate configurations. The analysis takes into account the effects of phase transformations and the resulting change in the fiber-matrix modulus. The results have been compared by considering different fiber volume fractions, temperatures, fiber orientations, and lamina stacking sequences. The results show that adaptive SMA-SMP composites laminates can be developed that provide shape controllability via tunable laminate stiffnesses leading to optimal response. Furthermore, the work presents the necessary framework for a reliable and efficient analysis of SMA-SMP laminates for practical applications. The theory can be directly used in established plate and shell formulations of finite element analysis. Finally, the variations in force and moment resultants with respect to fiber orientations and stacking sequences are presented, which are useful to study the bending and buckling characteristics of active composites for shape control of adaptive structures. The work concludes that efficient adaptive laminate development for high performance composite applications, exhibiting large shape adaptivity, high stresses, and increased stiffness, are feasible as compared to SMA composites without active matrix. POLYM. COMPOS., 32:910-927, 2011. (C) 2011 Society of Plastics Engineer

Modelling the thermomechanical behaviour of shape memory polymer materials

The increasing applications of smart structures in technology development have led to a wide variety of new high perfdormance materials, especially smart polymers. In the present work, a uniaxial model for shape memory polymer (SMP) is analyzed and a consistent form of the constitutive law is proposed. The coefficient of thermal expansion is expressed using the rule of mixtures approach. In this study, a copmparison is made between thermal strains computed by using the analogous rule of mixtures approach. In this study, a comparison is made between thermal strains computed by using the analogous rule of mixture equation and the empirical relation that has been stated on the basis of experimental findings. The inconsistency in the computation of coefficient of thermal expansion is addressed. Furthermore, the consistent form of the stored strain and thermal strain expressions are also presented using fourth order Runge-kutta method. A noteworthy difference is observed due to change in temperature. Moreover, the difference between the proposed analytical solutions with the empirical relation is brought out. Finally, the consistent form of the constitutive model with modified CTE and strain expressions for the SMP is presented

Hygro-thermo-electric properties of carbon nanotube epoxy nanocomposites with agglomeration effects

In the present study, the effective electric, thermal, and moisture properties of carbon nanotube (CNT) epoxy composites are derived by considering the agglomeration effect of CNT concentrations in the epoxy matrix. In this direction, the Voigt and Reuss homogenization method is adopted in the derivations. It is well known from experiments that the CNT thermal and electrical conductivities and the epoxy hygro-thermal expansion coefficients have significant effects on the behavior of CNT nanocomposites. Moreover, it has been experimentally proved that the agglomeration of CNTs in the matrix with high and low concentrations of the CNTs certainly affects the resistivity and, hence, the thermal expansion properties. Therefore, the effective elastic, thermal, electrical, and moisture properties for the randomly distributed CNTs in the matrix has been derived in terms of the agglomeration volume fractions of CNTs. In the effective relations, a single agglomeration parameter is considered to be active for a given potential. The results of variation in the hygro-electro-thermal properties due to change in CNT volume fraction as well as agglomeration parameters have been presented. The results and observation show that CNT agglomeration has a strong influence on the effective hygro-thermo-electric properties of the nanocomposites

Micro-mechanical behaviors of SMA composite materials under hygro-thermo-elastic strain fields

AbstractAn analytical procedure to evaluate the behavior of shape memory alloy (SMA) composite under hygrothermal environment is presented. The SMA wires are considered as inclusions embedded in a homogeneous matrix medium of the composite. The inhomogeneity associated with the phase transformation and thermal strains in the SMA wire as well as the hygrothermal strain in the matrix is homogenized using Eshelby’s equivalent inclusion method. In the present work, a similar approach adopted for SMA composites by Marfia and Sacco [Marfia, S., Sacco, E., 2005. Micromechanics and homogenisation of SMA-wire-reinforced materials. J. Appl. Mech. 72 (2), 259–268.] is considered in order to validate the response of SMA composite subjected to thermo-elastic strain field. However, in the present approach, certain modifications and new derivations for the inelastic strain tensors is carried out. First, the constitutive laws for the SMA wire and matrix are expressed in terms of the average strain in the composite. The evolutionary equations used to characterize the pseudoelastic (PE) behavior of the SMA wire are redefined in terms of the eigen strains (phase transformation and thermal strains) occurring in the SMA wire, which are then expressed in terms of the average strain in the composite. Further, the SMA composite constitutive law under coupled hygro-thermo-elastic strain fields is proposed. The generic homogenized hygric and thermal inelastic composite tensors required for the proposed hygro-thermo-elastic constitutive law are derived. Finally, the SMA composite lamina is characterized using Eshelby’s equivalent inclusion method. Using the proposed modifications and derivations, the analytical results are validated for the case of thermo-elastic strain fields and the procedure is then extended to evaluate the SMA composite behavior under hygro-thermo-elastic strain fields. The results include the effect of thermo-elastic and hygro-thermo-elastic strains on the transformation stresses and the nature of hysteresis due to hygric and thermo-elastic strains