Parametric numerical simulations of TRIP and its interaction with classical plasticity in martensitic transformation

In previous works we have experimentally demonstrated that a plastic predeformation of the austenitic phase has a significant role on the development of TRIP during the subsequent ferritic transformation (bainitic or martensitic). Such an observation is not predicted by current models, even the most sophisticated “industrial” analytical model existing in literature. By “industrial” we mean a model easy to use in FE code for structural analysis with a reasonable number of easily identifiable parameters.The objective of this paper is to contribute to a better comprehension of the mechanisms leading to the observed discrepancies between experiment and modelling. For that purpose, a FE micromechanical approach originally proposed in [Ganghoffer, J.F., Simonsson, K., 1998. A micromechanical model of the martensitic transformation, Mech. Mater. 27, 125–144] has been used and extended. The effect of different “numerical” parameters related to the simulation of martensitic transformation in 16MND5 steel has been evaluated. This has allowed to determine configurations of modelling that provide correct qualitative and quantitative results as compared to predeformation experimental tests.     

Strain gradient plasticity analysis of transformation induced plasticity in multiphase steels

“To what extent do plastic strain gradients affect the strengthening resulting from the transformation of small metastable inclusions into hard inclusions within a plastically deforming matrix?” is the central question addressed here. Though general in the approach, the focus is on the behavior of TRIP-assisted multiphase steels. A two-dimensional embedded cell model of a simplified microstructure composed of a single metastable austenitic inclusion surrounded by a soft ferritic matrix is considered. The cell is inserted in a large homogenized medium. The transformation of a fraction of the austenite into a hard martensite plate is simulated, accounting for a transformation strain, and leading to complex elastic and plastic accommodation. The size of a transforming plate in real multiphase steels is typically between 0.1 and 2 μm, a range of size in which plastic strain gradient effects are expected to play a major role. The single parameter version of the Fleck–Hutchinson strain gradient plasticity theory is used to describe the plasticity in the austenite, ferrite and martensite phases. The higher order boundary conditions imposed on the plastic flow have a large impact on the predicted strengthening. Using realistic values of the intrinsic length parameter setting the scale at which the gradients effects have an influence leads to a noticeable increase of the strengthening on top of the increase due to the transformation of a volume fraction of the retained austenite. The geometrical parameters such as the volume fraction of retained austenite and of the transforming zone also bring significant strengthening. Strain gradient effects also significantly affect the stress state inside the martensite plate during and after transformation with a potential impact on the damage resistance of these steels.     

A new view on transformation induced plasticity (TRIP)

The phenomenon of transformation induced plasticity (TRIP) in steel is reinvestigated both experimentally and theoretically. The irreversible length change (TRIP strain) consists not only of a plastic contribution (“Greenwood–Johnson” effect) but also of a contribution due to the length change caused by the transformation shear component of the martensitic variants (orientation effect or “Magee” effect). This orientation effect, which is fully accepted for shape memory alloys, is explained for steels. Micromechanical investigations help to quantify the orientation effect. Finally a proposal for a modified constitutive law for elastic plastic phase changing materials is presented.     

A phenomenological description of shape memory alloy transformation induced plasticity

Transformation induced plasticity is defined as the plastic flow arising from solid state phase transformation processes involving volume and/or shape changes without overlapping the yield surface. This phenomenon occurs in shape memory alloys (SMAs) having significant influence over their macroscopic thermomechanical behavior. This contribution presents a macroscopic three-dimensional constitutive model to describe the thermomechanical behavior of SMAs including classical and transformation induced plasticity. Comparisons between numerical and experimental results attest the model capability to capture plastic phenomena. Both uniaxial and multiaxial simulations are carried out.     

Macro modelling and homogenization for transformation induced plasticity of a low-alloy steel

Metal forming processes are important technologies for the production of engineering structures. In order to optimize the resulting material properties, it becomes necessary to simulate the entire forming process by taking into account physical effects such as phase transformations. In this work, we concentrate on the phase change from austenite to martensite and present a macroscopic material model, which combines the effect of classical plasticity with the effect of transformation induced plasticity (TRIP). An extensive experimental database for a low-alloy steel is used for parameter identification, thus taking into account the effects of uniaxial compressive and tensile stress on the kinetics of phase transformation at different temperatures. For temperatures below the martensite start temperature with simultaneous stresses above the yield limit, it is difficult to obtain experimental data. Consequently, a numerical homogenization technique is employed for this case. In a further part of this paper, an effective integration scheme is provided, which is implemented into a commercial finite element program. In a finite element simulation, the austenite to martensite phase transformation in a shaft subjected to thermal loading is investigated.     

Theoretical and numerical investigations on confined plasticity in micropillars

Multiscale dislocation dynamic simulations are systematically carried out to reveal the dislocation mechanism controlling the confined plasticity in coated micropillar. It is found that the operation of single arm source (SAS) controls the plasticity in coated micropillar and a modified operation stress equation of SAS is built based on the simulation results. The back stress induced by the coating contributes most to the operation stress and is found to linearly depend on the ‘trapped dislocation’ density. This linear relation is verified by comparing with the solution of the current higher-order crystal plasticity theory and is used to determine the material parameters in the continuum back stress model. Furthermore, based on the linear back stress model and considering the stochastic distribution of SAS, a theoretical model is established to predict the upper and lower bound of stress–strain curve in the coated micropillars, which agrees well with that obtained in the dislocation dynamic simulation.     

聚心火焰与激波相互作用的数值研究

基于带化学反应的2维轴对称Euler方程,利用带有monotonized centered(MC)限制器的波传播算法,在两端敞开的圆桶中对惰性介质的聚心激波和氢气-空气混合物的聚心火焰与激波的相互作用进行了数值模拟。数值结果表明,在惰性介质中激波在轴心的每次汇聚均可成长为马赫干,马赫干的追赶使激波得到一定程度的增强,但整体还呈下降趋势。在氢气-空气混合物中,燃烧诱导的激波,由于与火焰的反复作用,使激波在轴心处产生马赫干的频率和强度皆高于惰性介质中的情形。同时,火焰在与激波的相互作用过程中发生失稳变形,使其形状呈扁平头部的蘑菇云。     

Evolution of a laser-generated shock wave in iron and its interaction with martensitic transformation and twinning

Effects of shock waves (generated by a nanosecond laser pulse in plates of Armco-iron) on structural changes are analysed. Localisation of processes of martensitic transformation and twinning – for various values of laser pulse duration – is studied both experimentally and numerically. A proposed model accounts for interaction of shock wave propagation and structure changes. Realisation of martensitic transformation and twin formation influences wave front modification. A stress amplitude decrease with increasing distance from a microcrater determines, together with the pulse duration, a character of spatial localisation of structural changes. Numerical results are compared with experimental data and serve as a basis for additional interpretation of phenomena. Received 9 August 1994 / Accepted 30 June 1997     

Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite

A new crystal plasticity model incorporating the mechanically induced martensitic transformation in metastable austenitic steel has been formulated and implemented into the finite element analysis. The kinetics of martensite transformation is modeled by taking into consideration of a nucleation-controlled phenomenon, where each potential martensitic variant based on Kurdjumov–Sachs (KS) relationship has different nucleation probability as a function of the interaction energy between externally applied stress and lattice deformation. Therefore, the transformed volume fractions are determined following selective variants given by the crystallographic orientation of austenitic matrix and applied stress in the frame of the crystal plasticity finite element. The developed finite element program is capable of considering the effect of volume change by the Bain deformation and the lattice-invariant shear during the martensitic transformation by effectively modifying the evolution of plastic deformation gradient of the conventional rate-dependent crystal plasticity finite element. The validation of the proposed model has been carried out by comparing with the experimentally measured data under simple loading conditions. Good agreements with the measurements for the stress–strain responses, transformed martensitic volume fractions and the influence of strain rate on the deformation behavior will enable the model to be promising for the future applications to the real forming process of the TRIP aided steel.     

Nonlocal plasticity effects on interaction of different size voids

A nonlocal elastic–plastic material model is used to show that the rate of void growth is significantly reduced when the voids are small enough to be comparable with a characteristic material length. For a very small void in the material between much larger voids the competition between an increased growth rate due to the stress concentrations around the larger voids and a reduced growth rate due to the nonlocal effects is studied. The analyses are based on an axisymmetric unit cell model with special boundary conditions, which allow for a relatively simple investigation of a full three dimensional array of spherical voids. It is shown that the high growth rate of very small voids predicted by conventional plasticity theory is not realistic when the effect of a characteristic length, dependent on the dislocation structure, is accounted for.     

Cyber-physical flexible wing for aeroelastic investigations of stall and classical flutter

The fluid–structure interactions of a finite aspect ratio, cantilevered, flexible wing were investigated using a cyber-physical system to virtually augment the torsional dynamics of the wing. Cyber-physical systems (CPS), which have recently been pursued by a small number of research groups, have proven to be a very useful mechanism to interrogate the fluid–structure interaction parameter space. The premise of a CPS is to use dynamic feedback control to make a system behave according to desired equations of motion. Systems are composed of embedded hardware and software coupled with real-time computing to give the user the flexibility to quickly explore a range of structural parameters. With the advancement of modern control theory, robotics and embedded systems, CPSs integrate both simulation and physical properties into a smart structure which can be used to push the boundaries of research investigations.The CPS in this work allows for the investigation of dynamic aeroelastic instabilities of a three-dimensional, flexible, rectangular planform wing. Two dynamic instability regimes are observed: first, stall flutter, in which the torsional or pitch mode is excited through the dynamic stall process, and second, coupled (or classical) flutter, in which the pitch mode couples with the bending mode. By varying the torsional stiffness and therefore the frequency of torsional versus bending oscillations of the wing, both of these regimes can be attained at the same aerodynamic conditions using the CPS.     

Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei

The experimental work of Taleb and Petit-Grostabussiat [Taleb, L., Petit-Grostabussiat, S., 2002. Elastoplasticity and phase transformations in ferrous alloys: some discrepancies between experiments and modeling. J. Phys. IV 12 (11), 187–194; Taleb, L., Petit, S., 2006. New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity 22 (1), 110–130] has shown evidence that the evolution of TRansformation Induced Plasticity (TRIP) in a low carbon steel (16MND5) could be significantly influenced by the loading history of the parent phase, for a martensitic as well as a bainitic transformation. Furthermore, estimates from the Leblond model – one of the few micromechanical models currently found in different Finite Element (FE) softwares – have appeared to be in disagreement with experiments in these cases where the parent phase has been strain hardened. This has motivated the development of alternative approaches based on FE computations. This paper presents our first investigations about simulations of diffusive transformations with FE in an idealized case: the parent and the product phase are considered as two homogeneous materials with given elastoplastic properties and density; the transformation takes place at the same instant at predefined elements constituting the nuclei; then it progresses at a uniform rate by changing the material properties of the layer of elements surrounding the nuclei. In the basic configuration of modelling, the volume of discretization stands for a unit cell of a periodic cellular array, with a single central nucleus. In a more complex configuration, which is introduced shortly here and to be presented in details in the paper under preparation [Barbe, F., Quey, R., Taleb, L., Souza de Cursi, E., 2006. Numerical modelling of the plasticity induced during diffusive transformation. Case of a random instantaneous array of nuclei, in preparation], the volume of computation contains few to several nuclei at random locations. For both configurations, results in terms of effective (mean) TRIP as a function of the volume fraction of product phase are in correct quantitative and qualitative agreement with experimental results.     

Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

Some investigations on shock wave induced phase transitions

This paper briefly presents the activities of our laboratory in the area of phase transition studies under shock waves. Both experimental and theoretical studies are carried out. For experimental investigations, a single stage gas gun and associated diagnostic techniques have been set up. For interpretation of shock wave data, theoretical methods based on density functional formalism and molecular dynamics techniques are employed. Some examples from our work are presented.     

Numerical modeling of vortex/shock wave interaction and its transformation by localized energy deposition

Three-dimensional unsteady Euler simulations are presented for the interaction of a streamwise vortex with an oblique shock of angle β = 23.3° at Mach 3 and 5. The flowfield features are analyzed for weak, moderate and strong interaction regimes. The details of the free recirculation zone at conditions of subsonic and supersonic flow on the vortex axis are considered. The vortex breakdown under conditions of a subsonic vortex core is characterized by a continuous growth and gradual degeneration of the region, unlike the supersonic core condition wherein a steady recirculation zone is achieved. The possibility of using a localized steady and pulsed periodic energy deposition on the vortex axis for stimulating the breakdown is demonstrated for various interaction regimes. It is shown that the formation of a subsonic wake downstream of an energy source lying on the vortex axis contributes to a more significant growth of the dimensions of the recirculation zone compared to the case when the vortex core remains supersonic. The possibility of achieving the effects similar to the steady case is demonstrated by the effect of a pulsed periodic energy source on the flow under consideration for corresponding equivalence parameters.      

Mathematical modelling of transformation plasticity in steels II: Coupling with strain hardening phenomena

The models for the plastic behaviour of steels during phase transformations proposed in Part I and in a previous paper ( et al. [1986b]) for the case of ideal-plastic phases are extended to include strain-hardening effects (isotropic or kinematic hardening). An expression for the transformation plastic strain rate is obtained by modifying the treatment of Part I in a suitable manner. The classical plastic strain rate is also studied in a similar way. Complementary evolution equations for the hardening parameters are finally given, taking into account the possible “recovery” of strain hardening during transformations (i.e., the fact that the newly formed phase can “forget,” partially or totally, the previous hardening).