===>>GO TO THE STORE<<=== п»їModelling of strain-induced martensite formation in advanced medium-Mn automotive sheet steel.
The modelling of strain-induced martensite formation is simulated in advanced medium-Mn steel. The fraction of retained austenite (8%) embedded in the bainitic matrix is transforming into the strain-induced martensite during progressive static tensile tests. The originally elaborated technique and algorithms (using C++ language) are presented. The finite element method and LS-DYNA (LSTC Company, USA) have been deployed. The calculations of the stress-induced martensite start temperature were performed to characterize the austenite stability. The structural investigations using the SEM and EBSD have been conducted. The comparison of the experimental and numerical results has been made in terms of mechanical austenite stability.
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1 Introduction.
Automotive industry is continuously developing and gradually implementing new materials used for the structural components. Despite the growing trend of using materials such as polymers, composites, aluminium or magnesium alloys, steels are still the main construction material used in automobile production. Medium manganese steels belonging to the newest, third-generation advanced high-strength steels (AHSS) are of particular interest of automotive industry due to their superior strength–ductility product (UTSxTEl = 20,000−30,000 MPa%) [1,2,3]. Due to beneficial mechanical properties of this type of steels, the reduction in car’s body-in-white weight is possible while maintaining high crash performance. The development of lightweight materials and technologies is crucial for the reduction in the amount of emissions emitted to the environment during production and vehicle life cycle [4, 5].
The microstructure of cold-rolled and intercritically annealed medium-Mn steels contains an ultrafine mixture of ferrite and austenite [1, 3], whereas the thermomechanically processed steel sheets of higher thickness (used for underbody elements) comprise a mixture of ferrite, bainite, martensite and some fraction of retained austenite (RA) [6]. This microstructural constituent controls the strain hardening behaviour and ductility of steels due to its gradual transformation into martensite during plastic deformation. This provides the transformation-induced plasticity (TRIP) effect related to the simultaneous strength and plasticity increase due to delaying necking during tensile deformation [2, 6]. RA may transform into martensite during sheet forming operations such as stamping, and bending, allowing the production of complex geometry elements [7, 8]. Moreover, the strain-induced martensitic transformation (SIMT) of RA may occur during vehicle crash events absorbing some part of kinetic energy, and as a result, enhanced crashworthiness can be obtained [9, 10]. The effectiveness of SIMT is closely related to the amount, morphology and stability of RA [11, 12]. The retained austenite present in steels showing the TRIP effect can be in a form of blocky grains or thin laths (films). For different morphological types of RA, the mechanism of martensitic transformation is different, which results in differences in mechanical properties of steel products. Experimental results obtained by Shen et al. [11] and Jimenez-Melero et al. [12] show that RA in the form of thin films is characterized by higher mechanical stability than in a form of blocky grains. Moreover, the small grains/laths of RA are more resistant against SIMT than the large ones. The tendency of retained austenite to SIMT is also dependent on its chemical composition. The RA is characterized by a carbon concentration gradient and resulting change in micromechanical behaviour inside its grains during straining [13, 14].
The optimization of the SIMT mechanism is crucial for obtaining high mechanical properties of medium-Mn steels [15, 16]. Estimation of the stability of retained austenite is possible through thermodynamic modelling, which is based on the calculated critical driving force for martensitic transformation of RA with a defined chemical composition. This approach allows to determine the martensite start \(\hbox _>\) temperature of RA [17, 18]. Several reports concerning the application of representative volume element (RVE) modelling method [19,20,21] or digital material representation (DMR) approach [22,23,24] to monitor the microstructure evolution of dual phase (DP) and TRIP-aided steels with a microstructure composed on ferrite, bainite and retained austenite are available in the literature. This type of steels belongs to the first-generation AHSS. The numerical modelling and numerical simulations of SIMT belong to particularly difficult and complex tasks [25, 26]. Over the years the finite element method (FEM) has been developed but so far it is challenging to follow the changes in material properties during the numerical simulation process using commercial computer systems. These computer systems are usually dedicated for solving mechanical problems in macroscale such as designing light constructions as well as heavy duty machinery, in civil engineering, spacecrafts, etc. [27, 28]. Thus, applying such software for modelling the SIMT is rather cumbersome and unadjusted yet. However, special procedures can applied to overcome these difficulties using for example C++ language.
In a present study, the FEM method and thermodynamic calculations were used to predict the tendency of RA to SIMT during progressive tensile deformation. In the presented approach, the austenite properties have been adjusted to reflect in more detail the real situation. The gradient of carbon content inside austenite grains was taken into account during simulations. Hence, it was possible to analyse the micromechanical evolution inside individual grains with the focus on the SIMT details and corresponding stress–strain evolution as a function of increasing strain. The presented approach was not applied yet for advanced medium-Mn steels. Therefore, the study aims to complete this research gap combining modelling and experimental approaches.
2 Experimental.
2.1 Material and processing route.
The investigated material with the chemical composition of Fe-0.17C-3.3Mn-1.7Al-0.22Si-0.23Mo (wt.%) was melted using a vacuum induction furnace under Ar atmosphere. After homogenization at \(1200 ^\hbox \) for 2 h, ingots were hot-forged (in a temperature range of \(1200 ^\hbox \) – \(900 ^\hbox \) ) and air-cooled to room temperature. Afterwards, the ingots were hot-rolled in 4 passes to obtain the sheet samples with a thickness of 9 mm. Then, final thermomechanical rolling in 3 passes with a decreasing temperature range from \(1050^\hbox \) to \(850^\hbox \) was applied. The final sheet thickness was 4.5 mm. Following the hot rolling, the investigated steel sheet was directly cooled to the isothermal holding temperature of \(400^\hbox \) at the bainitic transformation range and held at this temperature for 300 s followed by air cooling. The detailed information about processing routes of investigated steel can be found in [29, 30].
2.2 Microstructure modelling.
The micromechanical model of the microstructure was prepared based on the EBSD image of the sample after hot rolling (Fig. 1). This approach allows to preserving the complex geometry of individual RA grains. The microstructure at the initial state (after hot rolling) was composed of bainite matrix and some fraction of retained austenite ( \(\sim \) 8%) located between bainite laths. The blocky RA and lathy RA can be distinguished in the image, which are embedded in the bainitic (B) matrix. In order to monitor the strain-induced martensite formation, simulations of the deformation during interrupted static tensile test was carried out using FEM method and LS-DYNA software. The simulations were interrupted at defined strain values of: 0.02, 0.04, 0.06, 0.08 and 0.1. (The 0.1 strain corresponds to uniform elongation.) The strain-induced martensitic transformation (SIMT) also occurs after necking in the post-uniform elongation range (up to rupture). However, the most important from the industrial point of view is to monitor the mechanism of martensitic transformation in the uniform strain range. The gradual progress of SIMT in this deformation range ensures the high tensile strength and uniform elongation of formed sheet elements. The metal forming processes such as bending and stamping are conducted at the strain level corresponding to the uniform elongation range.
EBSD map of investigated steel in the initial state (after hot rolling) used for micromechanical modelling showing bainitic matrix (B) marked in red colour and retained austenite (RA) marked in green colour.
2.3 Description of the numerical model.
The special procedure has been developed in order to simulate the SIMT using the C language. The steps were as follows:
\(\bullet \) conversion of bitmaps obtained from EBSD method into grey scale images and next into finite elements, nodes and material groups, \(\bullet \) during the conversion the following restrictions have been imposed: \(\bullet \) grains should be located inside the modelled region, \(\bullet \) grains cannot be located at the boundary region of the modelled sample, \(\bullet \) grains can touch the boundary regions but cannot cross them either be located beyond them, \(\bullet \) grains can be in contact but cannot overlap one another.
The way of changing the mechanical properties during numerical simulations was as below:
\(\bullet \) input of all necessary data including the material properties especially for austenite and bainite structural constituents, \(\bullet \) starting the main simulation, which contains four steps (four individual subsimulations), \(\bullet \) if the pseudotime equals one-fifth of the total time of simulation (corresponding to 0.02 strain) then the simulation process is stopped and the following action takes place: \(\bullet \) recording of the actual state of stress, strain and displacement, \(\bullet \) after the above action, the change of mechanical properties occurs in the original file, where the task is already defined, \(\bullet \) the earlier recorded state of stress, strain and displacement is treated as initial data in this particular step, \(\bullet \) starting the subsequent subsimulation,
The numerical simulations have been conducted using the finite element method and LS-DYNA software. On the basis of experimental images obtained by EBSD maps, the individual phases have been approximately mapped by appropriate modelling using finite element method. The microscale model has been developed in order to simulate the transformation of the retained austenite into martensite. The level of complexity relies on elaboration of many stages connected with the formation of the martensitic phase. In this particular case, as many as four different meshes of the same model have been generated. The corresponding calculations of state of stress and strain in the microstructure according to predetermined conditions of deformation and progress of SIMT have been performed. Conceptually, this can be taken to mean that each of the four modelling systems representing the successive stages of martensitic development and corresponding to them the individual meshes has been finally transformed into one highly complex finite element model.
The model of microstructure by means of computer system called LS PrePost has been elaborated, next the boundary conditions have been defined and the material models have been assumed. Then, the appropriate mesh using authors’ computer system elaborated in C language has been produced. Finally, the highly nonlinear physical phenomenon of martensitic phase formation has been solved numerically. The results are presented in the form of colourful contour maps illustrating the distribution of Huber Mises stresses in successive stages during the progressive tensile test.
The initial microstructure was composed of bainite (as a matrix) and islands of retained austenite (RA). The quantitative contribution of austenitic phase in bainitic matrix equals to 8% and the rest 92% is bainite, according to the real EBSD map in Fig. 1. The austenitic grains (islands) have been modelled in the shape of mirror images. The selected geometrical features are given in Table 1, and the dimensions of the modelled sample are given in Table 2. The total number of nodes in the model equals to 13,904, and the total number of plane state of strain elements is 13,650. In each node, there are two degrees of freedom along x and y axis, respectively. The sample has been fixed at the nodes belonging to the left utmost side of the model (Fig. 2). The displacement along x axis has been applied to all nodes belonging to the right utmost edge of the model and has been assumed as linear function of time, which varies from \( = 0 \,\upmu \hbox \) to \( = \Delta \hbox = 0.95\, \upmu \hbox \) , what is presented in detail in Fig. 2.
Table 1 Selected geometrical features of austenitic and bainitic structural constituents.
Table 2 Dimensions of the modelled sample.
The developed model of the SIMT is taking into account the various mechanical stability and yield strength of different areas located inside the RA grains. These areas correspond to the gradient of carbon content inside the individual RA grains. The carbon content is the lowest in the middle part of the grain, while the areas located near grain boundaries are characterized by the highest C content [13]. The higher carbon content means greater stability against SIMT [14, 31]. Therefore, three subareas of austenitic phases were included in the developed model (Table 1), which reflects the gradient of carbon content inside individual RA grains. Areas characterized by different mechanical stability of RA are represented by different colours in Fig. 2.
Boundary conditions, dimensions of the assumed modelled sample, boundary between bainite and randomly generated locations of the austenitic phases.
The modelling technique is intended for materials with composite microstructures, in which several phases have been modelled with different hardening behaviour. The bainitic phase constituted the matrix, in which there are two more phases: austenite which belongs to the softer one and newly generated martensitic phase, which is a hard microstructural constituent. All these phases have been modelled as deformable elastically as well as plastically until reaching the limited strain value corresponding to the uniform elongation of the sample, which has been established during experimental investigation on the level of 0.1 strain.
The material properties of bainitic ferrite, retained austenite and martensite were taken from the literature [32, 33] focused on the estimation of Young’s modulus for different phases: austenite, martensite and bainite in multiphase high-strength TRIP-aided steels based on the experimental results obtained in their previous study [34]. For most low-alloyed steels, the Young’s modulus is lower than that is presented in Table 3. In the present study, the investigated material was high-strength medium-Mn steel, which shows higher mechanical properties than low-alloyed steels. Therefore, the adopted Young’s modulus values for the analysed phases, i.e. austenite, bainite and martensite, are higher [32, 33] than usually occurring in the literature for conventional steels.
Table 3 Material parameters for individual phases which have been assumed similarly like in the literature [32, 33]
The relationship between the true stress–strain curve for bainitic matrix, martensite and austenitic phases of different mechanical stability has been assumed according to the following mathematical formula [32]:
$$\begin \sigma =R_\cdot \left( 1+H\cdot \varepsilon \right) ^, \end $$
All aforementioned individual material phases described by Eq. (1) are additionally shown in Fig. 3.
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