A nonlinear constitutive model for describing cyclic mechanical responses of composites
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2017, Springer-Verlag Wien. In this study, the macroscopic hysteretic response of BaTiO 3/ Ag composites under uniaxial cyclic mechanical loading was characterized and described by formulating a thermodynamically consistent constitutive model. Cylindrical composite samples with varying silver composition (from 0 to 13vol%) were fabricated by powder metallurgy technique. The stressstrain hysteretic response was characterized at room temperature under uniaxial compressive stress by cyclically loading and unloading samples to different stresses, until 200MPa or failure of the sample. For each loading cycle, the tangent modulus was determined at the initiation of the unloading stage. The tangent modulus showed changes after each cycle with increasing loading magnitude in all samples. Permanent deformations were also observed after each unloading cycle, which were associated with changes in the microstructures of the specimens. In formulating the model to describe the above macroscopic mechanical responses of the composites, we assume that the body has two natural configurations, which are different stress-free configurations associated with the original and newly formed microstructures. The new microstructure is formed when the body is subjected to relatively large stress, leading to reorientation of the dipole moments in the crystalline structures and other possible microstructural changes such as cracking. The Gibbs potential was defined in terms of the stress and the volume fraction of the domain transformation, and the internal state variable and its corresponding driving force for domain transformation (dipole reorientations and microstructural changes) were identified. A Preisach operator was adopted to model the relation between the internal state variable and the driving force. The material parameter calibrations were discussed, and the model predictions of the hysteretic response were compared to the experiment results.
