Corrigendum to “Physically based modeling, characterization and design of an induction hardening process for a new slurry pipeline steel” [Mater. Des. 182 (2019) 108047]

Javaheri, Vahid; Pohjonen, Aarne; Asperheim, John Inge; Ivanov, Dmitry; Porter, David

doi:10.1016/j.matdes.2019.108366

Cited by 3 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the current study, a cosine function was applied to describe the transition from 1 to 0 as the distance from the nearest fully ferritic gridpoint increases, that is, 𝜙(r) = 1 2 (1 + cos(r𝜋∕ΔL)), where r ≤ ΔL is the shortest distance from the fully ferritic region and ΔL is the length of the transition region between ferrite and austenite. This condition was applied only in the initial definition of the field and the subsequent time evolution was described by solving Equation (2).…”

Section: Phase Front Propagationmentioning

confidence: 99%

“…The capability of simulating the microstructure evolution provides important insight to the phenomena occurring in the industrial processes. [1,2] Splitting the general DOI: 10.1002/adts.202200771 observations into separable phenomena, and providing quantitative description for each phenomena is the basis of the method of natural sciences, which has enabled vast progress in modern science and technology. In addition to explaining separately the phenomena, also the interaction of the different basic phenomena produces new effects, that must be taken into account in the full description of a process.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

Pohjonen

2023

Advcd Theory and Sims

View full text Add to dashboard Cite

A novel mathematical formulation is presented for describing growth of phase in solid-to-solid phase transformations and it is applied for describing austenite to ferrite transformation. The formulation includes the effects of transformation eigenstrains, the local strains, as well as partitioning and diffusion. In the current approach the phase front is modeled as diffuse field, and its propagation is shown to be described by the advection equation, which reduces to the level-set equation when the transformation proceeds only to the interface normal direction. The propagation is considered as thermally activated process in the same way as in chemical reaction kinetics. In addition, connection to the Allen-Cahn equation is made. Numerical tests are conducted to check the mathematical model validity and to compare the current approach to sharp interface partitioning and diffusion model. The model operation is tested in isotropic 2D plane strain condition for austenite to ferrite transformation, where the transformation produces isotropic expansion, and also for austenite to bainite transformation, where the transformation causes invariant plane strain condition. Growth into surrounding isotropic austenite, as well as growth of the phase which has nucleated on a grain boundary are tested for both ferrite and bainite formation.

show abstract

Section: Phase Front Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

Pohjonen

2023

Advcd Theory and Sims

View full text Add to dashboard Cite

show abstract

“…For this reason, it is very important to obtain the capability of modelling the microstructure evolution in detail. Although the mean field models, such as the ones used in [1,2,3,4], are useful in rapid modelling and optimization of the relative quantities related to the microstructure, they lack the capability of including local effects, which can play important role in the microstructure evolution. For example in [2], it was recently observed that in order to understand and to model stabilization of austenite regions in steel processing, it is necessary to consider local carbon enrichment and the effect of local mechanical strains.…”

Section: Introductionmentioning

confidence: 99%

Application of two-grid interpolation to enhance average gradient method for solving partial differential equations

Pohjonen

2024

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Previously presented method of calculating local average gradients for solving partial differential equations (PDEs) is enhanced by using interpolating gridpoints and triangular grids. The interpolating mesh provides finer computational grid, which is then used for solving the PDE. The combined use of the finer interpolating grid together with the original sparser grid is a two-grid method. By comparing the previous application of rectilinear grid for diffusion from initial point concentration to the new triangular two grid method, it was found that the application of triangular two-grid method improves stability of the solution and it provides more rapid convergence to the correct analytical solution.

show abstract

“…Previous experiments and numerical simulations [2] show that also differential cooling rates could be applied to controlledly create desired heterogeneous microstructure to the material. Furthermore, due to its effect on the mechanical properties, the microstructure development during processing [3][4][5][6] needs to be understood in detail in order to control it effectively. The continuous development of accurate mean field models [7,8] also requires input from detailed microstructure formation models [9], where the phase front propagation needs to be explicitly modeled.…”

Section: Introductionmentioning

confidence: 99%

Numerical experiments on the solution of advection equation for moving phase interface: Encountered problems and their solutions

Pohjonen

2023

11th International Conference on Mathematical Modeling in Physical Sciences

View full text Add to dashboard Cite

As a part of the effort of constructing fundamentally physics based numerical model for growth of a phase in solid-to-solid phase transformations, a suitable mathematical description for advancing phase front and its numerical solution are required. The advection equation can be used for simulating the propagating phase front. However, it is well known that simple explicit finite difference solution in this case is unstable. Averaging of the spatial derivative provides useful stabilization for the numerical scheme, but exacerbates numerical dissipation and broadening of the continuous function describing the diffuse phase front. Numerical experiments were made, where these problems were observed. Simple solution procedures were introduced that effectively solved the problems for time scales that were required for the numerical solver to operate in the designed context.

show abstract

Corrigendum to “Physically based modeling, characterization and design of an induction hardening process for a new slurry pipeline steel” [Mater. Des. 182 (2019) 108047]

Cited by 3 publications

References 0 publications

Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations

Application of two-grid interpolation to enhance average gradient method for solving partial differential equations

Numerical experiments on the solution of advection equation for moving phase interface: Encountered problems and their solutions

Contact Info

Product

Resources

About