Anisotropic hardening model based on non-associated flow rule and combined nonlinear kinematic hardening for sheet materials

 A material model for more effective analysis of plastic deformation of sheet materials is presented in this paper. The model is capable of considering the following aspects of plastic deformation behavior of sheet materials: the anisotropy in yielding stresses in different directions by using a quadratic yield function (based on Hill’s 1948 model and stress ratios), the anisotropy in work hardening by introducing non-constant flow stress hardening in different directions, the anisotropy in plastic strains in different directions by using a quadratic plastic potential function and non-associated flow rule (based on Hill’s 1948 model and plastic strain ratios, r-values), and finally some of the cyclic hardening phenomena such as Bauschinger’s effect and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening (so-called Armstrong-Frederick-Chaboche model). Basic fundamentals of the plasticity of the model are presented in a general framework. Then, the model adjustment procedure is derived for the plasticity formulations. Also, a generic numerical stress integration procedure is developed based on backward-Euler method (so-called multistage return mapping algorithm). Different aspects of the model are verified for DP600 steel sheet. Results show that the new model is able to predict the sheet material behavior in both anisotropic hardening and cyclic hardening regimes more accurately. By featuring the above-mentioned facts in the presented constitutive model, it is expected that more accurate results can be obtained by implementing this model in computational simulations of sheet material forming processes. For instance, more precise results of springback prediction of the parts formed from highly anisotropic hardened materials or that of determining the forming limit diagrams is highly expected by using the developed material model.

Ratchetting of railhead in the vicinity of the gap of the insulated rail joints

Insulated Rail Joints (IRJs) are designed to electrically isolate two rails in rail tracks to control the signalling system for safer train operations. Unfortunately the gapped section of the IRJs is structurally weak and often fails prematurely especially in heavy haul tracks, which adversely affects service reliability and efficiency. The IRJs suffer from a number of failure modes; the railhead ratchetting at the gap is, however, regarded as the root cause and attended to in this thesis. Ratchetting increases with the increase in wheel loads; in the absence of a life prediction model, effective management of the IRJs for increased wagon wheel loads has become very challenging. Therefore, the main aim of this thesis is to determine method to predict IRJs' service life. The distinct discontinuity of the railhead at the gap makes the Hertzian theory and the rolling contact shakedown map, commonly used in the continuously welded rails, not applicable to examine the metal ratchetting of the IRJs. Finite Element (FE) technique is, therefore, used to explore the railhead metal ratchetting characteristics in this thesis, the boundary conditions of which has been determined from a full scale study of the IRJ specimens under rolling contact of the loaded wheels. A special purpose test set up containing full-scale wagon wheel was used to apply rolling wheel loads on the railhead edges of the test specimens. The state of the rail end face strains was determined using a non-contact digital imaging technique and used for calibrating the FE model. The basic material parameters for this FE model were obtained through independent uniaxial, monotonic tensile tests on specimens cut from the head hardened virgin rails. The monotonic tensile test data have been used to establish a cyclic load simulation model of the railhead steel specimen; the simulated cyclic load test has provided the necessary data for the three decomposed kinematic hardening plastic strain accumulation model of Chaboche. A performance based service life prediction algorithm for the IRJs was established using the plastic strain accumulation obtained from the Chaboche model. The predicted service lives of IRJs using this algorithm have agreed well with the published data. The finite element model has been used to carry out a sensitivity study on the effects of wheel diameter to the railhead metal plasticity. This study revealed that the depth of the plastic zone at the railhead edges is independent of the wheel diameter; however, large wheel diameter is shown to increase the IRJs' service life.

Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading-unloading with different R-ratios

Plastic zones and associated deformations ahead of a fatigue crack are well established nowadays. In-depth plane strain elasto-plastic finite element analysis is conducted in this investigation to understand the nature of cyclic plastic deformation and damage around soft and hard elliptical inclusions. Similar to fatigue crack tip, cyclic/reverse plastic zone and monotonic plastic zone are visible for soft elliptical inclusion. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of remote stress while, the size of monotonic plastic zone depends upon the maximum remote stress. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling. The shape and size of plastic zones also depend upon the orientation of the soft inclusion. Cyclic plastic damage progression in the cyclic plastic zone for soft (MnS) inclusion is significant, while no cyclic plastic zone is visible for hard inclusion (Al2O3).

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.