A comparison of two frameworks for kinematic hardening in hyperelasto-plasticity

In this work we compare two frameworks for thermodynamically consistent hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming. The second, formulated by Wallin et al. (2003), has been used to model large shear strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this paper we show that these frameworks can result in equivalent models for certain choices of free energies. Furthermore, it is shown that the choices of free energy found in the literature only result in minor differences. These differences are discussed theoretically and investigated numerically

On the Prediction of Anisotropy Evolution in Polycrystalline Multiphase Materials

In this contribution a multiscale modeling (MSM) framework is used to model the behavior of a multi-phase polycrystalline material. The use of MSM is motivated by the interest in how mechanisms occuring at different length scales contribute to the macroscopic behavior

On the Prediction of Macroscopic Yield Surfaces of a Pearlitic Steel using Multiscale Modeling

On the microscale, pearlite consists of hard and brittle cementite lamellae embedded in a ductile ferrite matrix. The cementite lamellae are arranged in colonies within which the lamella orientation is ideally constant. This composite-like constitution, on the microscale, makes pearlitic steels ideally suited for multiscale modeling. In this contribution a three-scale multiscale modeling setup is used to describe the mechanical behav- ior of a pearlitic steel. The macroscale represents the engineering scale on which a typical structural component would be analyzed. The mesoscale comprises colonies, with varying orientations (both mor- phological and crystallographic), thereby enabling the interactions between colonies to be taken into account. On the microscale a model representing the lamellar structure of pearlite is used. This model accounts for the behavior of the constituents but also the interactions between them. A cornerstone in this contribution is the formulation of a macroscopic, energy based, yield criterion based on homogenized quantities (cf. e.g. [1, 2, 3]). With such a criterion macroscopic yield surfaces can be predicted. The impact of altering the prolongation condition on the resulting yield surface is studied. Furthermore, the effect of adding a pre-loading before carrying out the yield surface prediction is investigated. Regarding the topic of how to identify the correct values of the parameters in a multiscale model several possibilities exists. This topic will be discussed briefly

Macroscale modelling of 3D-woven composites: Elasto-plasticity and progressive damage

There is a growing need across multiple industries for lightweight materials with improved material performance and reduced manufacturing costs. Composites with 3D-woven reinforcement could help fill this need. Their use however, requires the development of computationally efficient and industrially applicable material models to predict their non-linear behaviour. This work proposes a macroscale elasto-plasticity and damage model to capture the experimentally observed inelastic strains and stiffness reductions. The model is general, thermodynamically consistent and allows for various non-linear phenomena to be added and calibrated in a modular fashion depending on loading direction. Further it allows for a simplified parameter identification routine in which the damage and hardening laws are identified directly from experimental curves without the need for complex calibration routines. In order to demonstrate the applicability of the proposed macroscale model, focus is given to predicting the material response of a 3D glass fibre reinforced epoxy material system. The damage and hardening parameters are identified based on uniaxial tensile and in-plane shear experimental curves with unloading cycles. The model performance is validated against an off-axis tensile test with unloading cycles and shows good agreement to the experimental result

A fully coupled chemo-mechanical cohesive zone model for oxygen embrittlement of nickel-based superalloys

For nickel-based superalloys subjected to high temperatures and oxygen-rich environments, mechanical loading in combination with oxygen diffusion along grain boundaries leads to an acceleration of crack propagation. To account for these phenomena, a fully coupled thermodynamically consistent chemo-mechanical modeling framework for stress-assisted oxygen embrittlement of grain boundaries in polycrystals is proposed. We formulate an extended cohesive zone model where the grain boundary strength is reduced by the presence of oxygen and the oxygen diffusion is enhanced by tensile mechanical loading. We show that the model can qualitatively predict experimental results such as: reduction of ultimate tensile strength and accelerated crack growth due to dwell time combined with mechanical loading and saturation of crack growth rates for increasing environmental oxygen pressure levels. In addition, numerical simulation results of intergranular crack growth are shown for a 2D polycrystalline structure. An emphasis is put on the difference in cracking behavior after dwelling with or without mechanical loading

Computationally efficient simulation methodology for railway repair welding: cyclic plasticity, phase transformations and multi-phase homogenization

The in-situ railway repair welding process consists of multiple weld passes, which makes it significantly different from other rail welding processes. In this study, finite element simulations of repair welding are performed to predict the resulting microstructure and residual stresses. To accurately simulate the material behaviour, the modelling includes phase transformation kinetics, cyclic hardening plasticity, transformation induced plasticity, and multi-phase homogenization. More specifically, four different homogenization methods are investigated: isostrain, isostress, self-consistent and linear mixture rule. The performance of the material modelling is demonstrated by simulating multiple weld passes using a classical three-bar welding experiment. Based on the results, the self-consistent method and linear mixture rule are used in a 3D full-scale railhead repair weld simulation, in which the former generates a more realistic mechanical response. The immense computational cost associated with 3D full-scale, full-detail multi-pass welding simulations is addressed by exploring different model reduction schemes. From this study, a 2D generalized plane strain model, extended with out-of-plane axial and bending stiffness, is found to replicate the full-scale model at a mere fraction of the computational cost. Finally, the longitudinal residual stress distribution obtained from the reduced model is shown to correlate well with experimental measurements

A COMPARISON OF TWO FRAMEWORKS FOR KINEMATIC HARDENING IN HYPERELASTO-PLASTICITY

In this work we compare two frameworks for thermodynamically consistent hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming. The second, formulated by Wallin et al. (2003), has been used to model large shear strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this paper we show that these frameworks can result in equivalent models for certain choices of free energies. Furthermore, it is shown that the choices of free energy found in the literature only result in minor differences. These differences are discussed theoretically and investigated numerically

Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials

Anisotropic 1-site and 2-site self-consistent models are developed to describe the elastic-viscoplastic behavior of polycrystalline materials deformed to finite strains on the basis of rate-dependent crystallographic slip and a generalized Hill-Hutchinson self-consistent approach. The choice of rate-dependent constitutive law at single crystal level implemented in the models is discussed through fitting experimental data and calibrating viscous parameters. It is found that drag-stress type Norton law works well for the 1-site elastic-viscoplastic self-consistent (EVPSC) model while threshold stress type Norton law is suitable for the 2-site EVPSC model to assure that the viscoplastic inter-granular interaction is realistic. Both models have been verified by thoroughly fitting experimental data in literatures. For the 1-site EVPSC model, selected experimental data covers both macroscopic and microscopic mechanical responses of steels during deformation with a large range of strain rate from the quasi-static (10−4s−1) to the dynamic (~104s−1). For the 2-site EVPSC model, in situ neutron diffraction data of nickel-based superalloys with various microstructures was fitted. Both models generally fit the experimental data well. A comparison between the EVPSC and elastic-plastic self-consistent (EPSC) models on the prediction of lattice strains has also been made for both the 1-site and 2-site cases, which verifies the predictability on lattice strains of the newly developed EVPSC models. A validation of the homogenization approach for the EVPSC modeling has been performed, which confirms that the proposed EVPSC models are applicable for cubic structure materials with finite deformations. Our formulation of EVPSC modeling developed in this work shines a spotlight on the way of developing a multi-functional self-consistent model to predict both macroscopic and microscopic deformation behaviors of various polycrystalline materials under different loading rates of 10−4s−1~104s−1

Application of a semianalytical strain assessment and multiaxial fatigue analysis to compare rolling contact fatigue in twin-disk and full-scale wheel/rail contact conditions

A semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami\u27s approach. The model is used to compare conditions under small-scale twin-disk experiments to full-scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small-scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full-scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions