The Constitutive Relations Of Shape Memory Alloys And Its Composites

The concept of intelligent materials came into being in the late 1980's. Shape memory Alloys(SMAs) smart composites have been one of the most absorbable things in the diversity of intelligent materials. The constitutive relations of shape memory alloys and its composites have been a crucial issue for application of the shape memory alloys smart composites. Two constitutive relations were constructed along two different direction, and the constitutive relations of composites reinforced by long shape memory alloys fibers were formed by using the phenomenological model of shape memory alloys, the work can be useful for smart composites design. The main works are as follows:In the phenomenological model of Tanaka's, the volume fraction of transformation products is exponential to stresses and temperature, and the four characteristic transformation temperatures are linear to the stress, so when the shape memory alloys which morphology is full twinned martensite, was stretched, the model of Tanaka's can not reflect the reorientation of the martensite. The author constructed his own phenomenological model by using Tanaka's exponential model of transformation products, but Brinson's relations of transformation temperatures and stresses were adopted, different recoverable strains expressions were determined according to the applied load, meanwhile, the process which twinned martensite detwinned can be assumed as transformation, so the new model can reflect the reorientation of martensite, and it can be expanded to three dimensional easily by using the concept of equivalent stress. The model is simple because only one dynamic equation of martensite is adopted. The theoretical predictions of the model consist well with experiment.The constitutive model of composites reinforced by long SMAs fiber was constructed by using the framework of Dvorak's elastoplastic fibrous composites theory. In the model, the elastoplastic matrix was considered, and the definite expressions of five subdivisions can be obtained from the continuous constraint of interface between the matrix and the fibers The macroscopic properties can be determined by the model, and it is useful for intelligent composites design.Usually the long SMAs fiber reinforced aluminum matrix composite is madeby the method of casting with high pressure, or pressure with high temperature and agglomeration of powder, the internal stresses in the fibers and matrix of composites must be studied under the variation of temperature for the research does influence macroscopic properties of the composites. The micromechanical model of long SMAs fibrous composites was constructed by using the phenomenological model of SMAs, the residual stresses in the fibers and matrix were calculated by using the micromechanical model. The research is useful for manufacture of intelligent composites.A multivariant model was produced by using the principle of thermodynamics in the phases of martensitic transformation and its reverse transformation. The interactions among different grains were calculated by Eshelby-Kroner method, the plastic strain can be introduced at the fact that the dislocations can be reproduced and merged in the phases of martensitic transformation and its reverse transformation, the plastic strain can be considered as a internal variable of dissipation, it should be noted that the plastic strain is only a part of expressions of energy dissipation and complementary free energy, so when the transformation and its reverse cannot occur the plastic strain cannot change. As an example, we selected an ideal SMAs with two completely self-accommodated martensite variants, the results of the calculations can be simulated well with the phenomena of shape memory effect and transformation pseudoelasticity.