A non-linear extension of the additivity rule

Réti, Tamás; Felde, Imre

doi:10.1016/s0927-0256(99)00035-x

Cited by 31 publications

(11 citation statements)

References 30 publications

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“…All these conditions are in general not met. Particular applications, alternatives to the additivity rule and discussions on its validity can be found in Kuban et al (1986); Lusk and Jou (1997); Reti and Felde (1999); Todinov (1998); Zhu et al (1997). Grong and Shercliff (2002) show, when modelling welding, that the results were sufficient accurate applying the additivity principle for calculation of microstructure state variables.…”

Section: Transforming Isothermal Model To Varying Temperaturementioning

confidence: 99%

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: Transforming Isothermal Model To Varying Temperaturementioning

confidence: 99%

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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“…To overcome this problem, optimisation method is employed to calculate k based on the rule of additivity, with k being assumed to be a Gaussian dependence with temperature as suggested by equation (5) 23 and n obtained using the Rios method…”

Section: Calculation Of K Using Optimisation Methodsmentioning

confidence: 99%

Conversion between non-isothermal and isothermal transformation kinetics of γ to α for C–Mn and Nb microalloyed steels

Jia¹,

Liu²,

Yuan³

et al. 2007

Materials Science and Technology

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In the present paper, austenite c to ferrite a transformation kinetics of steels at different cooling rates has been measured by thermal dilatation. The relationship between lnln[1/(12X)] and ln(|C R |) (C R : cooling rate) was plotted using the data at early stage of cooling, which well fitted a linear relationship for the calculation of exponential values of n in the Johnson-Mehl-AvramiKolmogorov (JMAK) equation for isothermal kinetics using the method developed by Rios. The values of k in the JMAK equation obtained with the Rios method, however, have led to big discrepancies when the isothermal equations were used to predict the transformation kinetics during cooling. By assuming a Gaussian function of temperature, k was calculated using an optimisation method based on the rule of additivity. The isothermal transformation model was used to predict the transformation kinetics during cooling, showing good agreement with the measured data. It has been proved that even though the rule of additivity has to be relaxed to take into account the effects of cooling rates, precise conversion between non-isothermal and isothermal kinetics can still be realised.

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“…Following Eq. [21,24] Both the growth rate and the nucleation rate contribute to the rate of a transformation, [25] i.e., [3] where d f n /dt and d f g /dt are the pearlitic transformation rates from nucleation and from growth, respectively. [1] can be mathematically derived.…”

Section: Theoretical Analysis Of Additivity Rulementioning

confidence: 99%

On the application of the additivity rule in pearlitic transformation in low alloy steels

Hsu

Chang

2003

Metall Mater Trans A

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A non-linear extension of the additivity rule

Cited by 31 publications

References 30 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

Conversion between non-isothermal and isothermal transformation kinetics of γ to α for C–Mn and Nb microalloyed steels

On the application of the additivity rule in pearlitic transformation in low alloy steels

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