The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary an...The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.展开更多
This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-proces...This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.展开更多
This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
The current efforts in production of low-alloyed steels are aimed at achieving high ultimate and yield strengths,while maintaining sufficient elongation and good weldability in these materials.Among advanced heat trea...The current efforts in production of low-alloyed steels are aimed at achieving high ultimate and yield strengths,while maintaining sufficient elongation and good weldability in these materials.Among advanced heat treatment processes capable of reaching this goal,there is also the Q-P process (Quenching and Partitioning).The process consists in rapid quenching of the material between the M s and M f temperatures in order to prevent full martensitic transformation.The immediately following heating leads to tempering of the martensite and to diffusion of excess carbon from martensite to retained austenite.This increases the stability of the latter.The aim of the Q-P process is to produce very fine martensite microstructure with retained austenite between martensite plates.The experimental programme was carried out on a high-strength low-alloyed steel containing 0.2% carbon and a higher amount of silicon about 1.5%.Higher silicon content in the microstructure contributes to stabilization of retained austenite by suppressing formation of carbides.This grade of steel is an advantageous material thanks to its low amount of alloying elements.This group of low-alloyed steels,if heat treated or thermomechanically treated in a suitable manner,offers a favourable combination of strength,elongation and toughness.The paper is aimed at possibility of the Q-P process optimization with the use of quenching dilatometer.The experimental material is CMnSiMo steel.Conventional process optimization consists of standard samples treatment in laboratory furnaces and baths.This procedure can be time consuming with higher requirements on the experimental material.Therefore,it was proposed that the Q-P process optimization can be done with the use of quenching dilatometer and in this way the development of new procedures can be accelerated.Q-P processes were conducted in the standard way and with the aid of a dilatometer.Comparison of the obtained results provided by the standard procedure and by the procedure using the quenching dilatometer showed very similar results.On the basis of the obtained results,it can be concluded that the quenching dilatometer can be a powerful tool in Q-P processes optimization.展开更多
Cold forming of high strength materials is accompanied by an undesirable spring-back effect and therefore the automotive industry prefers to produce components from high strength steels by hot stamping.Hot deformation...Cold forming of high strength materials is accompanied by an undesirable spring-back effect and therefore the automotive industry prefers to produce components from high strength steels by hot stamping.Hot deformation and cooling in a die are applied to obtain shaped components with martensitic microstructure and high yield strength and ultimate tensile strength.This article presents new applications of this forming technology by incorporating another innovative heat treatment by the Q-P process,which improves both strength and ductility of obtained structures at the same time.Ultimate strengths over 2000 MPa with ductility above 10% can be achieved by this processing.To test microstructure development,thin sheet was hot formed and a corresponding FEM simulation was created.This processing was applied to low alloyed AHS steel with 0.42% of carbon and with an alloying strategy based on Mn,Si and Cr.Martensitic microstructure with retained austenite was obtained by this processing with a strength of around 2000 MPa and ductility of 10%.展开更多
Based upon the composition of C-Si-Mn,four types of transformation induced plasticity（ TRIP） steels with different contents of Si and M n were designed,which are subjected to quenching and partitioning（ Q＆P）proce...Based upon the composition of C-Si-Mn,four types of transformation induced plasticity（ TRIP） steels with different contents of Si and M n were designed,which are subjected to quenching and partitioning（ Q＆P）processes with variable austenitizing temperatures. The as-treated steels exhibits good combination of high strength and substantial elongation. In particular,with austenitizing at 820 ℃,0. 18C-1. 8Si-2. 2M n（ %） steel and0. 18C-1. 8Si-2. 5M n（ %） steel possessed high elongation（ more than 20%） with the tensile strength over 1000 M Pa. The microstructures of the as-treated steels were obtained by scanning electron microscope,the volume fraction and carbon content of retained austenite has been quantified by X-ray diffraction. The designed Q＆P processed steels contained a multiphase microstructure including ferrite,lath martensite,and retained austenite. The volume fraction and carbon content of those steels were higher,which was treated by Q＆P processes with austenitizing at 820 ℃. Due to the TRIP effect during the deformation process,retained austenite gives better stability as well as effectively improves the formability of steels with slightly decreasing the strength,contributing to overall better performance.展开更多
文摘The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.
基金the NNSF of China(10371092,10771185,10471148)the Foundation of Wuhan University
文摘This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金the project GACR 106/09/1968: Development of New Grades of High-Strength Low-Alloyed Steels with Improved Elongation Values
文摘The current efforts in production of low-alloyed steels are aimed at achieving high ultimate and yield strengths,while maintaining sufficient elongation and good weldability in these materials.Among advanced heat treatment processes capable of reaching this goal,there is also the Q-P process (Quenching and Partitioning).The process consists in rapid quenching of the material between the M s and M f temperatures in order to prevent full martensitic transformation.The immediately following heating leads to tempering of the martensite and to diffusion of excess carbon from martensite to retained austenite.This increases the stability of the latter.The aim of the Q-P process is to produce very fine martensite microstructure with retained austenite between martensite plates.The experimental programme was carried out on a high-strength low-alloyed steel containing 0.2% carbon and a higher amount of silicon about 1.5%.Higher silicon content in the microstructure contributes to stabilization of retained austenite by suppressing formation of carbides.This grade of steel is an advantageous material thanks to its low amount of alloying elements.This group of low-alloyed steels,if heat treated or thermomechanically treated in a suitable manner,offers a favourable combination of strength,elongation and toughness.The paper is aimed at possibility of the Q-P process optimization with the use of quenching dilatometer.The experimental material is CMnSiMo steel.Conventional process optimization consists of standard samples treatment in laboratory furnaces and baths.This procedure can be time consuming with higher requirements on the experimental material.Therefore,it was proposed that the Q-P process optimization can be done with the use of quenching dilatometer and in this way the development of new procedures can be accelerated.Q-P processes were conducted in the standard way and with the aid of a dilatometer.Comparison of the obtained results provided by the standard procedure and by the procedure using the quenching dilatometer showed very similar results.On the basis of the obtained results,it can be concluded that the quenching dilatometer can be a powerful tool in Q-P processes optimization.
基金the project 1M06032 Research Centre of Forming Technology
文摘Cold forming of high strength materials is accompanied by an undesirable spring-back effect and therefore the automotive industry prefers to produce components from high strength steels by hot stamping.Hot deformation and cooling in a die are applied to obtain shaped components with martensitic microstructure and high yield strength and ultimate tensile strength.This article presents new applications of this forming technology by incorporating another innovative heat treatment by the Q-P process,which improves both strength and ductility of obtained structures at the same time.Ultimate strengths over 2000 MPa with ductility above 10% can be achieved by this processing.To test microstructure development,thin sheet was hot formed and a corresponding FEM simulation was created.This processing was applied to low alloyed AHS steel with 0.42% of carbon and with an alloying strategy based on Mn,Si and Cr.Martensitic microstructure with retained austenite was obtained by this processing with a strength of around 2000 MPa and ductility of 10%.
文摘Based upon the composition of C-Si-Mn,four types of transformation induced plasticity（ TRIP） steels with different contents of Si and M n were designed,which are subjected to quenching and partitioning（ Q＆P）processes with variable austenitizing temperatures. The as-treated steels exhibits good combination of high strength and substantial elongation. In particular,with austenitizing at 820 ℃,0. 18C-1. 8Si-2. 2M n（ %） steel and0. 18C-1. 8Si-2. 5M n（ %） steel possessed high elongation（ more than 20%） with the tensile strength over 1000 M Pa. The microstructures of the as-treated steels were obtained by scanning electron microscope,the volume fraction and carbon content of retained austenite has been quantified by X-ray diffraction. The designed Q＆P processed steels contained a multiphase microstructure including ferrite,lath martensite,and retained austenite. The volume fraction and carbon content of those steels were higher,which was treated by Q＆P processes with austenitizing at 820 ℃. Due to the TRIP effect during the deformation process,retained austenite gives better stability as well as effectively improves the formability of steels with slightly decreasing the strength,contributing to overall better performance.
