An anisotropic elastic-plastic constitutive model for single and polycrystalline metals. II—Experiments and predictions concerning thin-walled tubular OFHC copper

Predictions based on an anisotropic elastic-plastic constitutive model proposed in the first part of this paper are compared with the experimental stress and strain data on OHFC copper under first torsion to about 13% and partial unloading, and then tension-torsion to about 10% along eight different loading paths. This paper also describes the deformation and stress of the thin-walled tubular specimen under finite deformation, the numerical implementation of the model, and the detailed procedure for determining the material parameters in the model. Finally, the model is extended to a general representation of the multiple directors, and the elastic-viscoplastic extension of the constitutive model is considered.

A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.

An anisotropic elastic-plastic constitutive model for single and polycrystalline metals .1. Theoretical developments

An anisotropic elastic-plastic constitutive model for single and polycrystalline metals is proposed. The anisotropic hardening of single crystals, at first, is discussed with the viewpoint of yield surface and a new formulation of it is proposed. Then, a model for the anisotropic hardening of polycrystals is suggested by increasing the number of slip systems and incorporating the interaction of all slip systems. The interaction of grains through grain boundaries is shown to be similar to, and incorporated into, the interaction of slip systems in grains. The numerical predictions and their comparisons with experiments will follow in Part II of this paper.

Constitutive model for localized Lüders-like stress-induced martensitic transformation and super-elastic behaviors of laser-welded NiTi wires

The application of the shape memory alloy NiTi in micro-electro-mechanical-systems (MEMSs) is extensive nowadays. In MEMS, complex while precise motion control is always vital. This makes the degradation of the functional properties of NiTi during cycling loading such as the appearance of residual strain become a serious problem to study, in particular for laser micro-welded NiTi in real applications. Although many experimental efforts have been put to study the mechanical properties of laser welded NiTi, surprisingly, up to the best of our understanding, there has not been attempts to quantitatively model the laser-welded NiTi under mechanical cycling in spite of the accurate prediction required in applications and the large number of constitutive models to quantify the thermo-mechanical behavior of shape memory alloys. As the first attempt to fill the gap, we employ a recent constitutive model, which describes the localized SIMT in NiTi under cyclic deformation; with suitable modifications to model the mechanical behavior of the laser welded NiTi under cyclic tension. The simulation of the model on a range of tensile cyclic deformation is consistent with the results of a series of experiments. From this, we conclude that the plastic deformation localized in the welded regions (WZ and HAZs) of the NiTi weldment can explain most of the extra amount of residual strain appearing in welded NiTi compared to the bare one. Meanwhile, contrary to common belief, we find that the ability of the weldment to memorize its transformation history, sometimes known as ‘return point memory’, still remains unchanged basically though the effective working limit of this ability reduces to within 6% deformation.

1-D constitutive model for evolution of stress-induced R-phase and localized Lüders-like stress-induced martensitic transformation of super-elastic NiTi wires

NiTi alloys have been widely used in the applications for micro-electro-mechanical-systems (MEMS), which often involve some precise and complex motion control. However, when using the NiTi alloys in MEMS application, the main problem to be considered is the degradation of functional property during cycling loading. This also stresses the importance of accurate prediction of the functional behavior of NiTi alloys. In the last two decades, a large number of constitutive models have been proposed to achieve the task. A portion of them focused on the deformation behavior of NiTi alloys under cyclic loading, which is a practical and non-negligible situation. Despite of the scale of modeling studies of the field in NiTi alloys, two experimental observations under uniaxial tension loading have not received proper attentions. First, a deviation from linearity well before the stress-induced martensitic transformation (SIMT) has not been modeled. Recent experiments confirmed that it is caused by the formation of stress-induced R phase. Second, the influence of the well-known localized Lüders-like SIMT on the macroscopic behavior of NiTi alloys, in particular the residual strain during cyclic loading, has not been addressed. In response, we develop a 1-D phenomenological constitutive model for NiTi alloys with two novel features: the formation of stress-induced R phase and the explicit modeling of the localized Lüders-like SIMT. The derived constitutive relations are simple and at the same time sufficient to describe the behavior of NiTi alloys. The accumulation of residual strain caused by R phase under different loading schemes is accurately described by the proposed model. Also, the residual strain caused by irreversible SIMT at different maximum loading strain under cyclic tension loading in individual samples can be explained by and fitted into a single equation in the proposed model. These results show that the proposed model successfully captures the behavior of R phase and the essence of localized SIMT.