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.     

New investigations on transformation induced plasticity and its interaction with classical plasticity

In this paper, transformation induced plasticity (TRIP) in anisothermal single as well as double transformations (austenite → bainite and austenite → bainite + Martensite) in 16MND5 steel is experimentally analyzed. Several investigations have been performed related mainly on: (a) the evaluation of the physical mechanism responsible of the TRIP in bainitic transformation; (b) the kinetics of TRIP and its specificity in a double transformation; (c) the consequence when the load is applied during only a part of phase transformation; (d) the interaction between TRIP and classical plasticity and so on. The results seem indicate that Greenwood and Johnson mechanism is dominant compared to Magee mechanism. The interaction between classical plasticity and TRIP is clearly demonstrated and it seems that the strain hardening state of the parent phase plays an important role in the TRIP progress. Due to such interaction, TRIP appears even in the absence of external applied load; the behavior depends strongly on the transformation under consideration (bainitic or martensitic). From a modeling point of view, it is shown that Leblond’s model that is the only one “industrial” model which enables qualitatively to account for such interactions, fails to predict the observed phenomena especially in martensitic transformation.     

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.     

Analysis of size effects associated to the transformation strain in TRIP steels with strain gradient plasticity

The size dependent strengthening resulting from the transformation strain in Transformation Induced Plasticity (TRIP) steels is investigated using a two-dimensional embedded cell model of a simplified microstructure composed of small cylindrical metastable austenitic inclusions within a ferritic matrix. Earlier studies have shown that within the framework of classical plasticity or of the single length parameter Fleck–Hutchinson strain gradient plasticity theory, the transformation strain has no significant impact on the overall strengthening. The strengthening is essentially coming from the composite effect with a marked inclusion size effect resulting from the appearance during deformation of new boundaries constraining the plastic flow. The three parameters version of the Fleck–Hutchinson strain gradient plasticity theory is used here in order to better capture the effect of the plastic strain gradients resulting from the transformation strain. The three parameters theory incorporates separately the rotational and extensional gradients in the formulation, which leads to a significant influence of the shear component of the transformation strain, not captured by the single-parameter theory. When the size of the austenitic inclusions decreases, the overall strengthening increases due to a combined size dependent effect of the transformation strain and of the evolving composite structure. A parametric study is proposed and discussed in the light of experimental evidences giving indications on the optimization of the microstructure of TRIP-assisted multi-phase steels.     

Experimental analysis of the correlation between martensitic transformation plasticity and the austenitic grain size in steels

This work investigates the effect of the Austenite Grain Size (AGS) on the thermo-mechanical behavior of 35NiCrMo16 steel during the martensitic transformation under complex loading. Particularly in view of some thermal cycles, we analyzed the evolution of the austenite grain size under different austenitizing conditions. Using the same temperature-holding time parameters, we performed a series of experiments to assess the Transformation-Induced Plasticity (TRIP) under uniaxial (tension or torsion) and biaxial (tension + torsion) loading. The results suggest that the uniaxial torsion loading case, Transformation-Induced Plasticity does not depend on the prior Austenite Grain Size (AGS) whereas, in the uniaxial tension loading case, it is a “slightly” increasing function of the AGS.     

Computational simulation of the dependence of the austenitic grain size on the deformation behavior of TRIP steels

Due to the strain-induced martensitic transformation which occurs during plastic deformation, a transformation-induced plasticity (TRIP) phenomenon is generated. With the TRIP phenomenon, the TRIP steel possesses favorable mechanical properties such as high strength, ductility and toughness, and is frequently employed as a structural material. In the past, several researchers clarified experimentally that the strain-induced martensitic transformation and the deformation behavior of TRIP steel depend upon the austenitic grain size. In order to obtain the expected mechanical properties of TRIP steel through control of the austenitic grain size, prediction and control of the material characteristics in the deformation processes is essential. Here, the new strain-induced martensitic transformation kinetics model and constitutive equation of TRIP steels are proposed by considering the dependence of the austenitic grain size. Then, the deformation behavior of a type 304 austenitic stainless steel cylinder is simulated under different environmental temperatures with the various austenitic grain sizes by the finite-element method along with newly-proposed constitutive equations. Finally, the validity of proposed constitutive equations and the possibility of the improvement of the mechanical properties through control of the austenitic grain size are discussed.     

On the evaluation of large homogeneous plastic strains

A simple technique is proposed for the evaluation of large strain increments such as those that occur in some metal-forming processes or in orthogonal metal cutting. This method depends on the use of the usual equations for the transformation of strain in two dimensions modified to include a correction due to the change in the orientation of the element during straining. This correction has been calculated for various values of strain and of initial angular orientation of the strained element, and it is shown that the average value of the element orientation, during straining, used in the equations for the transformation of “natural” strain gives excellent results.     

TiNi形状记忆合金变形特性实验研究

给出了一种ＴｉＮｉ形状记忆合金（多晶）的单轴拉压、循环拉伸加卸载、形状记忆效果、恢复力、相变塑性变形及拉压。扭转比例、非比例加卸载的实验结果，实验结果显示，其变形特性非常不同于普通的弹塑性材料：如Ｂａｕｓｃｈｉｎｇｅｒ效果提前，甚至于会出现于卸载阶段；低温下的残余变形会在加热后消失；恒载下冷却时产生相当大的塑性变形（相变塑性变形）且在加热时消失等等。多轴加载实验结果表明，比例加载时该材料的加载屈服面及卸载屈服面都基本满足Ｍｉｓｅｓ准则，但非比例加载时则不然。     

A multi-mechanism model for cutting simulations combining visco-plastic asymmetry and phase transformation

We develop a multi-mechanism model for strainrate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformations, which are important phenomena in steel production processes. To this end the well-known Johnson–Cook model is extended by the concept of weighting functions, and it is combined with a model of transformation-induced plasticity (TRIP) based on Leblond’s approach. The bulk model is formulated within a thermodynamic framework at large strains, and it will be specialized and applied to cutting processes in steel production. In this prototype situation we have: Transformation of the martensitic initial state into austenite, then retransformation of martensite. For incorporation of visco-plastic asymmetry two variations of the classical Johnson–Cook model are presented: In “Model A” we introduce a rate dependent flow factor with a rate independent yield function. In “Model B” we introduce a rate independent flow factor with a rate dependent yield function. In the examples parameters are identified for the material DIN 100Cr6, and we illustrate the characteristic effects of our multimechanism model, such as strain softening due to temperature, rate dependence and temperature dependence as well as the SD-effect. A finite-element simulation illustrates the different mechanisms for a cutting process.     

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress–strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For “hard” orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for “soft” orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation.     

Couplings between plasticity and martensitic phase transformation: overall behavior of polycrystalline TRIP steels

Several couplings between plasticity and martensitic phase transformation are at the origin of remarkable properties of ductility and toughness in the case of TRIP steels. A micromechanical model is developed to predict the conditions of nucleation and growth of a martensitic microdomain inside an inhomogeneous plastic strain field. More explicit relations are developed in the case of a simple shear test where a heterogeneous plastic strain field leads to a significant decrease of the critical stress for martensitic transformation. The obtained results are combined with a kinetics and kinematics studies to derive the constitutive equation of an austenitic single crystal from which the overall behavior of a polycrystalline steel is deduced using the self-consistent scale transition method. Comparison with experimental data shows a good agreement.     

Size,geometry and nonuniformity effects of surface-nanocrystalline aluminum in nanoindentation test

In the present research, the mechanical behavior of the surface-nanocrystalline aluminum (SNCA) is investigated through nanoindentation experiment and theoretical modeling. Firstly, through microscopical observation and measurement for the SNCA material, a microstructure cell model is developed. Secondly, based on the microstructure cell model and the strain gradient plasticity theory, and based on introducing a parameter accounting for the grain size nonuniformity effect, the discrete features of the hardness–depth relations of the SNCA material are described. The “U-type” feature of the hardness–depth experimental curves is modeled and simulated. Thirdly, in the SNCA material the mechanical property of the grain boundary, i.e., the strength of plastic zone penetrating the grain boundary is characterized by introducing a criterion parameter, the critical effective plastic strain. The “waterfall-type” feature of the hardness–depth curves is modeled and simulated. It is worth pointing out that, in the present study, the length scale parameter in the strain gradient plasticity theory is taken as a universal material parameter instead of a simulation parameter, and it is determined through applying the strain gradient plasticity theory to the modeling of the corresponding single crystal aluminum.     

Transformation-induced plasticity in ferrous alloys

We study the mechanical behavior of a class of multiphase carbon steels where metastable austenite at room temperature is found in grains dispersed in a ferrite-based matrix. During mechanical loading, the austenite undergoes a displacive phase change and transforms into martensite. This transformation is accommodated by plastic deformations in the surrounding matrix. Experimental results show that the presence of austenite typically enhances the ductility and strength of the steel. We use a recently developed model (Turteltaub and Suiker, 2005) to analyze in detail the contribution of the martensitic transformation to the overall stress-strain response of a specimen containing a single island of austenite embedded in a ferrite-based matrix. Results show that the performance of the material depends strongly on the lattice orientation of the austenite with respect to the loading direction. More importantly, we identify cases in which the presence of austenite can in fact be detrimental in terms of strength, which is relevant information in order to improve the behavior of this class of steels.     

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.     

Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches

In this paper, we derive the mechanical fields (internal stresses, elastic energy) arising from the presence of an inelastic distortion field representing a typical intra-granular “microstructure” as the one observed during the plastification of metallic polycrystals. This “microstructure” is due to the formation of discrete intra-granular plastic slip heterogeneities characterized by at least two internal lengths: the first one is the individual grain size which represents a stochastic parameter inherent to the processing route (prior working, annealing), and, the second one is the spatial distance between active slip lines or slip bands associated with inhomogeneous plastic slip in the interior of grains. These internal lengths can be observed and measured using conventional experimental techniques (EBSD, TEM, AFM). The micro-mechanical modeling of the mechanical fields associated with plastic slip events inside grains is performed with two different assumptions. The first one is based on the well-known Eshelby’s problem of plastic inclusion where only the grain diameter is considered as internal length scale. This classical method considers homogeneous plastic distortion in the grain and leads to a uniform and grain size independent total strain field in the grain. The second method accounts for a non-uniform plastic distortion in the grain characterized by its discrete nature and the two aforementioned internal lengths. Both methods consider grains as spherical inclusions with a given diameter embedded in a homogeneous medium. For the second method, plastic slip is constrained by grain boundaries seen as impenetrable obstacles to dislocations. Thus, plastic strain is embodied by distributions of discrete circular glide loops. After writing the field equations and the free energy of the medium, a micro-mechanical formulation based on the Fourier transform method is developed. It is then found that in contrast with the mean-field approach, the internal stress fields as well as the elastic energy corresponding to different dislocation configurations depend on internal lengths associated to the deformed medium. Different possible configurations associated with intra-granular plastic flow due to circular glide dislocation loops are analyzed. Finally, the results are discussed with respect to the grain size dependence of the flow strength and the Bauschinger effect for plastically deforming polycrystals and perspectives to develop new micro–macro transition schemes accounting for internal length scales are sketched out.     

Modelling of the plastic flow of trip-aided multiphase steel based on an incremental mean-field approach

An incremental mean-field model is developed for the prediction of transformation induced plasticity (TRIP) in multiphase steel. The partitioning of strain between softer and harder constituents is computed based on an elastic-plastic Mori–Tanaka approach that accounts for the progressive transformation of austenite into martensite. The latter transformation is predicted using an energy-balance criterion that is formulated at the level of individual austenite grains. The model has been tested against experimental data. Macroscopic stress-strain curves and rate of martensite formation have been measured on sheet samples subjected to various loading modes: uniaxial tension, simple shear, and (in-plane) uniaxial compression. These experiments were performed at 20 °C and the uniaxial tensile test was repeated at ?30 °C. The mean-field model produces fair predictions of the macroscopic hardening resulting from TRIP on the condition that a sufficient proportion of the load is carried by the very hard martensite inclusions. Such prediction implies that one accounts for the stress heterogeneity across the ferrite-based matrix. At the same time, the model reproduces the elastic lattice strains and the plastic elongation which are measured within the phases by neutron diffraction and by image correlation in a scanning electron microscope, respectively. The model can be used in finite element simulations of forming processes which is illustrated in a study of necking of a cylindrical bar under uniaxial tension.     

Application of photoelasticity to a weld-penetration problem

The need for more information on the “initiation period” in fatigue tests of weld specimens with penetration defects is discussed and the literature which relates the elasticity stress-concentration factor and Irwin's stress-intensity factor is reviewed. A series of photoelasticity tests on two-dimensional plane-stress models of typical penetration defects is described. In particular a method for casting “ready to use” very narrow defects is explained. The results are presented in a graph of stress-concentration factor against defect length. This graph has a “knee” at defect length-to-plate thickness ratios around 0.2. Below the “knee”, the stress-concentration factor changes very little with changes in defect length but, for lengths beyond the knee, i.e., ratios larger than 0.2, the stress concentrations increase linearly with defect length. It is concluded that such a critical defect length should have a strong effect on fatigue life of defective welds and that it may constitute a first approach to the specification of an “acceptable” level of penetration defects for production processes.