Constitutive modeling of cyclic deformation of metals under strain controlled axial extension and cyclic torsion

Abstract

The present work provides a formulation of a constitutive model for metals with the aim to simulate cyclic deformation under axial extension or compression assisted by cyclic torsional (or shearing) straining of specified amplitude and frequency. Such a mode of deformation was recently implemented in technological processes such as extrusion, forging and rolling, cf. Bochniak and Korbel (Eng Trans 47:351-367, 1999, J Mater Process Technol 134:120-134, 2003, Philos Mag 93:1883-1913, 2013, Mater Sci Technol 16:664-674, 2000. The constitutive model accounting for combined hardening (isotropic-kinematic) with both hardening and recovery effects is presented and calibrated for several materials: pure copper, aluminum alloy (2024), and austenitic steel. The experimental data are used to specify model parameters of materials tested, and next the cyclic response for different shear strain amplitudes is predicted and confronted with empirical data. The constitutive model is developed in order to simulate technological processes assisted by cyclic deformation.

Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading

“…Hence, as long as constant stress is applied along the axial direction, the plastic strain in this direction will not be sensitive to the amplitude of the cyclic torsional load, which is clearly seen in the simulation results for axial creep in Figure 7 . Since this is a fundamental restriction, no attempt is made to test other modeling strategies for J2 plasticity, although in the literature, it has been demonstrated that an associated flow rule in combination with a three-surface hardening-recovery model for kinematic hardening could be successfully parameterized to describe the material behavior of thin-walled tubular specimens under monotonic-cyclic loading [ 15 ].…”

“…for asymmetric loading with amplitude ratios different from , the mean stress typically takes a rather high positive or negative values at the beginning of the cyclic experiment, but then it usually relaxes towards zero. The importance of the correct description of kinematic hardening in constitutive models for multiaxial cyclic loading has been demonstrated for investigations on thin-walled tubular specimens under axial tension, and cyclic torsion [ 15 ]. To describe kinematic hardening in general, the empirical kinematic hardening models of Armstrong–Fredrick [ 16 ], Chaboche [ 17 ], and Ohno–Wang [ 18 ] are most widely used.…”

Estimation of cyclic hardening/softening and ratcheting response of materials through an algorithm to optimize parameters in Chaboche's hardening rule

“…Over the years, applications of several constitutive models 33–37 are reported for different materials towards the simulation of various cyclic‐plastic phenomena. Most of the constitutive models in the domain of cyclic‐plasticity are phenomenological in nature; the models are being constantly modified and upgraded to achieve better agreement to experimentally observed response of different materials 9,38–43 . However, the modifications are empirical in nature and generally lead to an increase in the number of model parameters; this aspect makes the calibration procedure complex, as the identification of the model parameters requires a multitude of experimental results for a material.…”

Identification of Chaboche–Lemaitre combined isotropic–kinematic hardening model parameters assisted by the fuzzy logic analysis

“…Under the cyclic loading, elastoplastic materials indicate different mechanical responses associated with the plastic deformation [1,2]. Ratcheting, Bauschinger effect, strain hardening, and the stress relaxation are examples of the hysteresis phenomena associated with the cyclic plasticity [3][4][5][6]. The knowledge about the mechanical behavior of materials under the cyclic loading is essential for civil engineering in the prediction of their fatigue life [7,8].…”