A Material Function of Endochronic Theory and its Application to Test Under Axisymmetrically Cyclic Loading Conditions

Abstract

A material function of endochronic theory is proposed for investigating the plastic behaviors of material. Depending on the material parameters properly chosen, the present model can be classified into four categories, and is appropriate for describing various materials behaving cyclic strain hardening inherently with respect to the deformation history. Experimental verification of the theory was demonstrated using the experimental results of Shiao [1] and Lamba and Sidebottom [2]. The theory is in good agreement with experimental results obtained by Shiao [1] through comparing the stress-strain hysteresis loops of SAE 4340 steel under axisymmetrically cyclic loading condition with various amplitudes. In addition, the present model is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom [2].

A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

“…where β c controls the rate of evolution, and the value at steady state is c > 1, for hardening materials, and c < 1, for softening materials. Yeh (1995) and Lin et al (2007) proposed the following improvements to the scale function…”

“…It is worth noting that for c > s > 1, the initial saturation value c is greater than the saturation value c/s at cyclic stabilization, i.e., the scale function describes the progressive cyclic softening typically observed in particle-binder composites. Figure 2 shows a schematic representation of the scale function proposed by Lin et al (2007). It is evident from the figure that the rate of evolution of the material scale function is controlled by β c , whereas the rate of evolution of the saturation value is controlled by β s .…”

“…The formulation uses Ogden's hyperelastic model (Ogden, 1972a,b) to predict the rubber-like nonlinear elastic response of the polymeric binder, and a hereditary (path-dependent) yield-surface-free endochronic plasticity theory (Valanis, 1970), based on the concept of internal state variables (Horstemeyer & Bammann, 2010), to account for irreversible deformations. A discontinuous isotropic damage model (Kachanov, 1986;Lemaitre et al, 1985) is utilized to model the stress-softening that occurs during unloading, and an endochronic material scale function (Valanis, 1970;Wu & Yip, 1981;Yeh, 1995;Lin et al, 2007) is utilized to model progressive cyclic stress softening and attainment of stable cyclic response. The number of model parameters is a function of the number of active Ogden terms and endochronic branches, and therefore a significant number of parameters may need to be identified.…”