摘要
The fractal dimension（FD） of surfaces has been widely used to characterize the properties of materials.However,most of the previous researches were concentrated on the correlation between the FD of surfaces and mechanical properties of materials,such as impact energy and fracture toughness,etc.The aim of this paper is to characterize the spheroidization grade and strength of 15CrMo steel through determination of FD of cementite phase on the basis of two-dimension microstructural image.Two methods,namely slit-island method（SIM） and box-counting method（BCM）,are used to determine the value of FD.It is found that the FD value evaluated by using BCM is generally higher than that evaluated by SIM.This phenomenon may be due to the difference in the principles used in different methods.Whether SIM or BCM is used,the spheroidization grade in 15CrMo steel linearly increases with decreasing the value of FD.The relationship between the FD value,D,and spheroidization grade,Sg,can be approximately expressed as D≌-0.11Sg＋A,where A is a constant value which is depended on the evaluation method.Both the ultimate strength and the yielding strength of 15CrMo steel increase with increasing FD of cementite phase.There may be a common relationship between the FD of cementite phase and strength of 15CrMo steel.When the FD of cementite phase in 15CrMo steel is determined,the strength of this steel can be evaluated.The present paper can provide a novel method to evaluate the strength and spheroidization grade of carbon steel through determination of fractal dimension（FD） of cementite phase.
The fractal dimension（FD） of surfaces has been widely used to characterize the properties of materials.However,most of the previous researches were concentrated on the correlation between the FD of surfaces and mechanical properties of materials,such as impact energy and fracture toughness,etc.The aim of this paper is to characterize the spheroidization grade and strength of 15CrMo steel through determination of FD of cementite phase on the basis of two-dimension microstructural image.Two methods,namely slit-island method（SIM） and box-counting method（BCM）,are used to determine the value of FD.It is found that the FD value evaluated by using BCM is generally higher than that evaluated by SIM.This phenomenon may be due to the difference in the principles used in different methods.Whether SIM or BCM is used,the spheroidization grade in 15CrMo steel linearly increases with decreasing the value of FD.The relationship between the FD value,D,and spheroidization grade,Sg,can be approximately expressed as D≌-0.11Sg＋A,where A is a constant value which is depended on the evaluation method.Both the ultimate strength and the yielding strength of 15CrMo steel increase with increasing FD of cementite phase.There may be a common relationship between the FD of cementite phase and strength of 15CrMo steel.When the FD of cementite phase in 15CrMo steel is determined,the strength of this steel can be evaluated.The present paper can provide a novel method to evaluate the strength and spheroidization grade of carbon steel through determination of fractal dimension（FD） of cementite phase.
基金
supported by National Natural Science Foundations ofChina (Grant Nos. 50835003,50805047,10972078)
National Hi-tech Research and Development Program of China (863 Program,Grant No.2009AA04Z421)
