Ⅰ. INTRODUCTIONThe index m value of strain rate sensitivity is an important mechanical factor for evaluating superplasticity. The authors have established the analytically mechanical theories of m value on the basis ...Ⅰ. INTRODUCTIONThe index m value of strain rate sensitivity is an important mechanical factor for evaluating superplasticity. The authors have established the analytically mechanical theories of m value on the basis of many formulae for measuring rn value by means of tension and have given out a unified measuring methodt. m value is affected by stress status because展开更多
In consideration of superplastic deformation being highly sensitive to structure, superplastic bulging constitutive equations with varying m values are given for the first time by solving the differential equation tha...In consideration of superplastic deformation being highly sensitive to structure, superplastic bulging constitutive equations with varying m values are given for the first time by solving the differential equation that defines m values with the function simulation method according to the m-log curve in the biaxial tensile stress state. The constitutive equation established by simulating the m-log curve with negative power functions can not only exhibit the characteristics of varying m values, but also express either by or by . The equation contains three constants,~mm, ~mk and η, and the larger the ~mm and η, the nearer the ~mm/m^k to unity, and the better the material's superplasticity. So superplastic bulging indexes of materials are related with the shape of the m-log curve, which can explain why mere ~mm measured at theuniaxial tension is unable to describe the law of superplastic bulging and express the superplastic bulging indexes of materials singly. Superplastic bulging constitutive equations with varying m values are also given according to the measured m-log curves for two superplastic sheets, ZnAl_(22) and ZnAl_4Cu.展开更多
The functional relations between the constant-height bulging m_h value, constant-pressurebulging m_p value and constant-velocity bulging m_v have been established on the basis of them-value definition of superplastic ...The functional relations between the constant-height bulging m_h value, constant-pressurebulging m_p value and constant-velocity bulging m_v have been established on the basis of them-value definition of superplastic bulging, using equivalent stress, equivalent strain andequivalent strain rate of superplastic bulging as well as the analytical expressions of them-value for free bulging in a few typical loading paths. To non-work hardening, workhardening and work softening materials, the relationships between m_h, m_p and m_v have beenquantitatively analyzed in different stages. The m-values of two typical superplastic sheetmetals, ZnA122 and ZnA14Cu, were measured by means of bi-specimen and theoretical calcula-tions basically agree with experimental results. The abnormal phenomena of why m_v canbe a negative value and why m_h, m_p and m_v are different are clarified theoretically.展开更多
Strain rate sensitivity index m is one of the vital mechanical parameters for deter- mining material superplasticity. In this paper, the existing formulae for measuring m value are reviewed, and it is found that the m...Strain rate sensitivity index m is one of the vital mechanical parameters for deter- mining material superplasticity. In this paper, the existing formulae for measuring m value are reviewed, and it is found that the m values can be classified into three classes: mi under constant length, mv under constant velocity, and mP under con- stant load. The constraint equation of the generalized m value is established ac- cording to the tensile constitutive equation and the basis theory for plastic me- chanics. Based on three typical deformation paths, the m value is redefined. Fur- thermore, from the formula of generalized m value, the formulae for measuring mi, mv and mP are theoretically deduced. The precise methods with numerical simula- tion are presented. The results prove that the m value is a non-constant and its dependence on ε changes with the deformation path. Under different deformation paths, the m values calculated from the same formula are different. Using different formulae, the m values under the same deformation path are also different. There- fore, deformation path and corresponding formula should be given during the measurement of the m value. Moreover, it is explained theoretically and experi- mentally that why the mv value under constant velocity is sometimes negative but the mP value under constant load is sometimes lager than 1. The aim of the analysis and measurement of the m value is to facilitate the study on the relationship be- tween macroscopical mechanical laws and microscopic physical mechanisms during superplastic deformation.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONThe index m value of strain rate sensitivity is an important mechanical factor for evaluating superplasticity. The authors have established the analytically mechanical theories of m value on the basis of many formulae for measuring rn value by means of tension and have given out a unified measuring methodt. m value is affected by stress status because
基金Project supported by the National Natural Science Foundation of China.
文摘In consideration of superplastic deformation being highly sensitive to structure, superplastic bulging constitutive equations with varying m values are given for the first time by solving the differential equation that defines m values with the function simulation method according to the m-log curve in the biaxial tensile stress state. The constitutive equation established by simulating the m-log curve with negative power functions can not only exhibit the characteristics of varying m values, but also express either by or by . The equation contains three constants,~mm, ~mk and η, and the larger the ~mm and η, the nearer the ~mm/m^k to unity, and the better the material's superplasticity. So superplastic bulging indexes of materials are related with the shape of the m-log curve, which can explain why mere ~mm measured at theuniaxial tension is unable to describe the law of superplastic bulging and express the superplastic bulging indexes of materials singly. Superplastic bulging constitutive equations with varying m values are also given according to the measured m-log curves for two superplastic sheets, ZnAl_(22) and ZnAl_4Cu.
基金Project supported by the National Natural Science Foundation of China.
文摘The functional relations between the constant-height bulging m_h value, constant-pressurebulging m_p value and constant-velocity bulging m_v have been established on the basis of them-value definition of superplastic bulging, using equivalent stress, equivalent strain andequivalent strain rate of superplastic bulging as well as the analytical expressions of them-value for free bulging in a few typical loading paths. To non-work hardening, workhardening and work softening materials, the relationships between m_h, m_p and m_v have beenquantitatively analyzed in different stages. The m-values of two typical superplastic sheetmetals, ZnA122 and ZnA14Cu, were measured by means of bi-specimen and theoretical calcula-tions basically agree with experimental results. The abnormal phenomena of why m_v canbe a negative value and why m_h, m_p and m_v are different are clarified theoretically.
基金Supported by the National Natural Science Foundation of China (Grant No. 50375064)"985 Project" of Jilin University of China
文摘Strain rate sensitivity index m is one of the vital mechanical parameters for deter- mining material superplasticity. In this paper, the existing formulae for measuring m value are reviewed, and it is found that the m values can be classified into three classes: mi under constant length, mv under constant velocity, and mP under con- stant load. The constraint equation of the generalized m value is established ac- cording to the tensile constitutive equation and the basis theory for plastic me- chanics. Based on three typical deformation paths, the m value is redefined. Fur- thermore, from the formula of generalized m value, the formulae for measuring mi, mv and mP are theoretically deduced. The precise methods with numerical simula- tion are presented. The results prove that the m value is a non-constant and its dependence on ε changes with the deformation path. Under different deformation paths, the m values calculated from the same formula are different. Using different formulae, the m values under the same deformation path are also different. There- fore, deformation path and corresponding formula should be given during the measurement of the m value. Moreover, it is explained theoretically and experi- mentally that why the mv value under constant velocity is sometimes negative but the mP value under constant load is sometimes lager than 1. The aim of the analysis and measurement of the m value is to facilitate the study on the relationship be- tween macroscopical mechanical laws and microscopic physical mechanisms during superplastic deformation.
