Mathematical Model Coupling Phase Transformations and Temperature Evolutions in Steels.

Denis, S.; Farı́as, Daniel; Simón, A.

doi:10.2355/isijinternational.32.316

Cited by 131 publications

(70 citation statements)

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“…For each transformation temperature step, it is necessary to know the fraction of phases in equilibrium (by the end of the transformation), the transformation start time, and the N and k coefficients of the JMAK law (or two characteristic times to determine the values). This type of model has been first established for steels (Denis et al 1992;Fernandes et al 1985), and more recently also for titanium alloys Sha and Malinov 2009;Teixeira et al 2007). Kinetics and physical modelling of TTT-diagrams for Ti-6Al-4V based on JMAK theory is used here to model the diffusional phase transformations.…”

Section: Transformation Kinetic Parameters For Diffusional To Phasesmentioning

confidence: 99%

“…One should also bear in mind that experimentally determined data themselves, such as the basic TTTdiagrams, are quite uncertain in that they are highly dependent on exact chemical composition and on phase grain sizes (Callister 2007). The application of the additivity principle is based on the use of a fictitious time (Denis et al 1992;Grong and Shercliff 2002;Malinov et al 2001a). Demonstration of the use of the additivity rule is presented in Figure 27.…”

Section: Transforming Isothermal Model To Varying Temperaturementioning

confidence: 99%

“…Figure 27. Schematic illustration of the principle of additivity rule, showing the approximation of cooling as the sum of short time step-wise isothermal temperature holding, after (Denis et al 1992;Grong and Shercliff 2002;Malinov et al 2001a). …”

Section: Transforming Isothermal Model To Varying Temperaturementioning

confidence: 99%

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A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

Murgau

Pederson

Lindgren

2012

Modelling Simul. Mater. Sci. Eng.

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This thesis is devoted to microstructure modelling of Ti-6Al-4V. The microstructure and the mechanical properties of titanium alloys are highly dependent on the temperature history experienced by the material. The developed microstructure model accounts for thermal driving forces and is applicable for general temperature histories. It has been applied to study wire feed additive manufacturing processes that induce repetitive heating and cooling cycles. The microstructure model adopts internal state variables to represent the microstructure through microstructure constituents' fractions in finite element simulation. This makes it possible to apply the model efficiently for large computational models of general thermomechanical processes. The model is calibrated and validated versus literature data. It is applied to Gas Tungsten Arc Welding -also known as Tungsten Inert Gas welding-wire feed additive manufacturing process. Four quantities are calculated in the model: the volume fraction of phase, consisting of Widmanstätten , grain boundary , and martensite . The phase transformations during cooling are modelled based on diffusional theory described by a Johnson-Mehl-AvramiKolmogorov formulation, except for diffusionless martensite formation where the Koistinen-Marburger equation is used. A parabolic growth rate equation is used for the to transformation upon heating. An added variable, structure size indicator of Widmanstätten , has also been implemented and calibrated. It is written in a simple Arrhenius format. The microstructure model is applied to in finite element simulation of wire feed additive manufacturing. Finally, coupling with a physically based constitutive model enables a comprehensive and predictive model of the properties that evolve during processing.

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Section: Transformation Kinetic Parameters For Diffusional To Phasesmentioning

confidence: 99%

Section: Transforming Isothermal Model To Varying Temperaturementioning

confidence: 99%

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A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

Murgau

Pederson

Lindgren

2012

Modelling Simul. Mater. Sci. Eng.

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“…This phenomenon is mainly influent for the martensitic transformation [22] and has been taken into account in our model through a decrease in the martensite yield stress. In the proposed method- ology, the plastic strain due to martensitic transformation has not been physically modelled.…”

Section: Mechanical Modellingmentioning

confidence: 99%

Residual stresses in surface induction hardening of steels: Comparison between experiment and simulation

Coupard

Palin‐Luc

Bristiel

et al. 2008

Materials Science and Engineering: A

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractDeep induction hardening has been performed on two batches of smooth cylindrical specimens with a hardening depth respectively around 2 mm and 3 mm. The distributions of axial and circumferential residual stresses are analysed for the two specimen batches by X-ray diffraction technique. The radial normal stress field is estimated through the use of the well known Moore and Evans correction. Finally, the experimental residual stresses are compared with those obtained from a multiphysic finite element modelling of the whole induction treatment process, including electromagnetic, thermal, metallurgical and mechanical phenomena. The simulated residual stress field is in good agreement with X-ray analysis especially at depths lower than one-tenth the specimen diameter. At deeper depths, a correction of the experimental X-ray analysis has been done to obtain realistic values.

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“…Reheating Process Based on an isothermal model and on the rule of additivity (the heating cycle is subdivided into small successive isothermal time steps), Denis 7) developed a model for the analysis of the transformation kinetics during continuous cooling or heating.…”

Section: The Calculation Of the Grain Size In A Continuousmentioning

confidence: 99%

The Modeling of the Grain Growth in a Continuous Reheating Process of a Low Carbon Si-Mn Bearing TRIP Steel.

et al. 2000

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Making use of Anelli's idea and an own model for isothermal grain growth, a new model for the grain growth during a continuous reheating process was deduced. This model makes use of the real three dimensional grain diameter instead of the mean linear intercept distance as a measure for the grain size. Two series of experiments have been undertaken: in the first series, the validity of the model for several intermediate temperatures has been investigated, while in the second series, the influence of the heating rate on the validity of the model has been verified. In both cases a quite reasonable matching between the prediction of the model and the experimentally determined three dimensional grain size has been found.

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Mathematical Model Coupling Phase Transformations and Temperature Evolutions in Steels.

Abstract: (Fig. 2). Figure 5 shows the experimental evolutions of car- (Fig. 6).

Cited by 131 publications

References 0 publications

A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

A model for Ti–6Al–4V microstructure evolution for arbitrary temperature changes

Residual stresses in surface induction hardening of steels: Comparison between experiment and simulation

The Modeling of the Grain Growth in a Continuous Reheating Process of a Low Carbon Si-Mn Bearing TRIP Steel.

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