References
- Arai , N. , Matsunaini , A. and Churchill , S. W. 1996 . A review of measurements of heat flux density applicable to the field of combustion . Experimental, Thermal and Fluid Science , 12 : 452 – 460 .
- Austin , J.B. and Ricketts , R..L. 1939 . Kinetics of the decomposition of austenite at constant temperature . Trans. A.I.M.E. , 135 : 396 – 415 .
- Avrami , M. 1940 . Kinetics of phase change. II . J. of chemical physics , 8 : 212 – 224 .
- Bohm , M. , Hunkel , M. , Schmidt , A. and Wollf , M. 2004 . Evaluation of various phase‐transition models for 100cr6 for application in commercial FEM programs . J. de Physique IV , 120 : 581 – 589 .
- Bunting , K. A. and Cornfield , G. 1975 . Toward a general theory of cutting: A relationship between the incident power density and the cut speed . Transactions of the ASME , 116
- Burke , J. 1965 . The kinetics of phase transformation in metals , Pergamon press .
- Christian , J. W. 1965 . The theory of transformations in metals and alloys , Pergamon press .
- Dachkovski , S. Evolution of diffusional phase transformation with varying temperature . Proc. Of 3rd International Conference Computational modeling and simulation of materials . Sicily, Italy. pp. 265 – 272 .
- Dachkovski , S. and M&B;ouml , M. 2004 . Finite thermoplastisity with phase changes based on isomorphisms . Int. J. Plast. , 20 : 323 – 334 .
- Dachkovski , S. and M&B;ouml , M. 2004 . Modeling of elastoplastic materials with phase changes . J. de Physique IV , 120 : 153 – 160 .
- Dachkovski , S. , Böhm , M. , Schmidt , A. and Wolff , M. 2003 . Comparison of several kinetic equations for pearlite transformation inl00cr6 steel , Berichte aus der technomathematik, ZeTeM, University of Bremen .
- Fasano , A. and Primicerio , M. 1996 . An analysis of phase transition models . Europ. J. Appl Math. , 7 : 439 – 451 .
- Friedman , A. and Jiang , L. 1984 . A Stefan‐Signorini problem . J. Differential Equations , 51 : 213 – 231 .
- Hafercamp , H. , Niemeyer , M. , Hoerner , J. , Bosse , J. , Kock , M. and Konemann , F. 1999 . Numerical modelling of thermal plasma cutting . Thermal cutting conference . 1999 , Timisoara.
- Hömberg , D. 1995 . A mathematical model for the phase transitions in eutectoid carbon steel . J. of Appl. Math. , 54 : 31 – 57 .
- Johnson , W. and Mehl , R. 1939 . Reaction kinetics in processes of nucleation and growth . Trans. AIME , 315 : 416 – 441 .
- Kempen , A. T.W , Sommer , F. and Mittemeijer , J. E. 2002 . Determinetion and iterpretation of isothermal and non‐isothermal kinetics; the effective activation energies in terms of nucleation and growth . J. Mat. Sci. , 37 : 1321 – 1332 .
- Kim , M. 2000 . Transient evaporative laser‐cutting with boundary element method . Journal of Applied Mathematical Modelling , 25 : 25 – 39 .
- Matsuyama , K. 1997 . Mathematical modelling of kerf formation phenomena in thermal cutting . Welding in the World , 39 (1) : 28 – 34 .
- Mittemeijer , J. E. 1992 . Review analysis of the kinetics of phase transformations . J. Mat. Sci. , 27 : 3977 – 3987 .
- Mittemeijer , J. E. and Sommer , F. 2002 . Solid state phase transformation kinetics: a modular transformation model . Z. Metallkd. , 93 : 352 – 361 .
- Narimanyan , A. 2006 . Stefan‐Signorini moving boundary problem arisen from thermal plasma cutting: mathematical modelling, analysis and numerical solution , ZeTeM, Faculty of Mathematics, University of Bremen . PhD thesis
- Narimanyan , A. and Muntean , A. 2006 . Mathematical modelling driven by two industrial applications: A moving boundary approach . Mathematical Modelling and Analysis , 11 : 295 – 314 .
- Reti , T. , Horvath , L. and Felde , I. 1997 . A comparative study of methods used for the prediction of nonisothermal austenite decomposition . J. of materials engineering and performance , 6 (4) : 433 – 441 .
- Rosenthal , D. 1941 . Mathematical theory of heat distribution during welding and cutting . Welding Journal , 20 : 220 – 234 .
- Scheil , E. 1935 . Anlaufzeit der austenitumwandlung . Arch. Eisenhuettenwes. , 12 : 565 – 567 .
- Schulz , W. , Kostrykin , V. , Zefferer , H. , Petring , D. and Poprawe , R. 1997 . A free boundary problem related to laser beam fusion cutting: Ode approximaton . Int. J. Heat Mass Transfer , 40 (12) : 2913 – 2928 .
- Shen , Z. , Zhang , S. , Lu , J. and Ni , X. 2001 . Mathematical modelling of laser induced heating and melting in solids . Optics and Laser Technology , 40 (8) : 533 – 537 .
- Sheng , P. S. and Joshi , V. S. 1995 . Analysis of heat‐affected zone formation for laser cutting of stainless steel . J. Material Processing Technology , 53 : 879 – 892 .
- Storti , M. 1995 . Numerical modelling of ablation phenomena as two‐phase Stefan problems . Int. J. Heat Mass Transfer , 38 (15) : 2843 – 2854 .
- Ton , B.An . 1994 . A Stefan‐Signorini problem with set‐valued mappings in domains with intersecting fixed and free boundaries . Bollettino U.M.I. , 7 : 231 – 249 .
- Wever , F. and Krisement , O. 1952 . Anlaufziet der Austenitumwandlung bei verschiedener Art der Abkühlung . Archiv für das Eisenhüttenwesen , 23 : 229 – 237 .