The Quantitative Analysis Of Superplastic Tensile Deformation

In 1912, superplastic phenomenon firstly was reported, and from that time on, over ninety years have passed. During the period, scientists in many countries widely researched superplasticity that involves metallography, metallurgy, mechanical property, manufacturing technology and so on, and obtained many significant results. It was promoting superplastic research to one important branch of advanced material science. Superplastic forming technology in aviation, spaceflight, building, vehicle, electron and so on is applied more and more.However, my tutor, Prof. Song Yuquan insisted on that the existing results of superplastic research mostly focused on the micro-physics and deformation mechanism of superplastic forming, and those are valuable to discover and develop new materials. Perhaps, since the forming force is very low and plasticity is very good in superplastic state, the mechanical nature of superplastic forming was ignored. And so, little study is related on mechanical law of superplastic forming.Now, with hard, brittle, high-temperature resistant advanced materials becoming more important to modern manufacturing, the investigation of these materials that involve ceramic and intermetallic compound becomes a very urgent mission in material and processing fields. To complete the mission, the scientists should build up the connection between the macroscopical mechanical parameters and the microscopic physical mechanisms, and understand the effects of internal conditions that involve composition of materials, crystal structure and metallographic phase, and external conditions that involve stress state, strain path and so on. Only the macro-micro connection and integration of internal and external conditions do promote the rapid development of superplastic research. The precondition of this work is understanding the macro-mechanical law of superplastic deformation. With the development of superplastic precise forming technology, regular instruction and universal explanation from mechanical theory are required for solving a series of questions in manufacture. The knowledge of superplastic optimal forming law is the key of transition from theory to practice and to large-scale manufacture. It has been one important part of superplastic study that the investigation to superplastic forming technology and the corresponding deformation mechanics. However, The plastic mechanics evolved from elastic mechanics and semi-viscosity theory based on viscosity theory have not been able to explain a series of phenomena in superplastic mechanics and solve the problems related to superplastic processing. This would restrict the application and development of superplastic forming technology. Accordingly, Establishing superplastic mechanics on the base of tests becomes very urgent. In addition, Prof.Song put forward a notion that the investigation of superplastic deformation should take strain path in account due to strong sensitivity to structure during superplastic and plastic deformation.Following the instruction from Prof. Song, and based on his idea, I has completed superplastic tensile tests and their theoretic analysis, and established the quantitative mechanical analysis theory of superplastic tensile deformation. In the dissertation, I firstly reviewed the existing investigations of constitutive relation, measurement of material parameters, tensile instability and fracture of superplastic tensile deformation, and pointed out their shortages. Then, I mainly completed the next work, which includes:1. The theory and measurement of material parameters1) Based on the state equation in which stress is the function of strain and strain-rate, the tensile differential constitutive equation is established, and according to the elemental theory for plastic mechanics, the mechanical meanings of strain-rate sensitivity index (m value) and strain hardening index (n value) are defined, and their constraint equation is built up. By combining test variables l, v and P, three typical deformation paths are respectively defined as three cases that test variables l, v and P are respectively constants. And correspondingly, the formulae for measuring ml , mv , and mP are theoretically deduced, and their precise methods with numerical simulation are presented. In a similar way, by combining variablesε& , v and P, three typical deformation paths are respectively defined as three cases that variablesε& , v and P are respectively constants. And correspondingly, the formulae for measuring nε& , nv , and n P are theoretically deduced, and their precise methods with numerical simulation are presented.2) Based on the state equation in which stress is the function of strain, strain-rate and time, the tensile differential constitutive equation is established, and according to the elemental theory for plastic mechanics, the mechanical meanings of stress relaxation index (τvalue) is defined. Only during stress relaxation test, time t could be separated from strainεand strain rateε& , and so stress relaxation test is the basis method for measuringτvalue. The formulae for measuringτvalue are theoretically deduced, and its simple method and precise method with numerical simulation are presented.3) With three superplastic materials, the uniaxial tensile tests under constant strain rate, constant velocity and constant load, and the stress relaxation test are operated. And the precise results of material parameters are obtained by the presented methods.The conclusion is obtained as follows: (1) Material parameters m and n values are not constants but variables. The results proves that mεvalues are dependent on strain rateε& , and their dependences onε& vary with different strainsε. similarly, nε& values are dependent on strainε, and their dependences on strainεvary with different strain rateε&; (2) Under different deformation paths, the dependence of m value onε& are different, and using different formulae, the m values under the same deformation path are also different. During the measurement of the m and n value, the deformation path should be given, and, the corresponding formula must be used for obtaining correct value; (3) It is proved theoretically and experimentally that mv < ml < mP, and further, that 0 < ml< 1, mv is likely to be negative and mP is likely to be greater than 1 are as results of that the strain hardening effect is mingled into the strain rate hardening effect; (4) It is proved the stress relaxation effect diminishes with strain increasing according to the experimental results.2. The establishment of constitutive equation with variation parameters1) According to phenomenological continuum theory, by strict deduction based on general differential constitutive equation, I establishes the phenomenological constitutive equations with variation parameters that involve nε& (ε) and mε(ε& ). And I re-defines the mechanical meanings of experiential constitutive equations presented by the former investigators, namely, Hollomon equation is the constitutive equation under the deformation path of constant strain rate when nε& is a constant; Backofen equation is the constitutive equation with constant strain when mε& is a constant; And Rossard equation is the constitutive equation when both mε& and nε& are constants.2) By fitting three dimensional surface to the tensile test data, where the fitting function is that stressσis the function of strainεand strain rateε& , the experiential constitutive equations with variation parameters are established. The experiential constitutive equations could describe the mechanical behavior of materials more truly than the phenomenological constitutive equations based on general differential constitutive equation because it is taken into account in the experiential constitutive equations that nε& (ε) is dependent on strain rateε& and mε(ε& ) is dependent on strainε. In addition, based on the experiential constitutive equations, the exact expressions of nε& (ε,ε& ) and mε(ε,ε& ) are deduced, and according to these expressions, it is proved that both mεvalues and nε& values are the functions of strainεand strain rateε& .3. The analysis of superplastic tensile instability1) According to the characters of superplastic tensile flow, the mechanical meanings of load instability, geometry instability, stress instability and fracture instability are defined. Their general instability criterions are obtained by theoretic analysis based on the basis mechanical state equation. In the criterions, the effects of material parameters are independent, which would be favor to the connection between the macroscopical mechanical parameters and the microscopic physical mechanisms. By analyzing load instability, geometry instability and stress instability under typical deformation paths, their criterions are obtained, and the critical strains corresponding to the instabilities are calculated from superplastic tensile tests of materials.2) Based on state equation that stress is the function of strain, strain-rate and temperature, the differential constitutive equation and the variational constitutive equation are established, which involve strain hardening index, strain-rate sensitivity index, temperature sensitivity index presented for the first time and temperature undulation index presented for the first time. And then, based on the general condition of plastic elementary theory, the influences of temperature on superplastic tensile instabilities are respectively analyzed under continuously rising temperature and under the non-uniform temperature along the axes of specimen, and the criterions that involve temperature parameters are obtained corresponding to load instability, geometry instability and stress instability.The conclusion is obtained as follows: (1) The theoretic deductions and experimental results prove the origin of the large strain during superplastic deformation, that is, geometry instability would not happen when load instability occurs, but happens when uniform deformation has lasted after load instability. The appearance of necking would not result in fracture of specimen, and the movement of neckings happens by their propagation and disappearance instead. Thus, the very large semi-stable deformation is re-formed. The stronger stress relaxation effect is, the harder to happen fracture instability is and the less the elongation is; (2) The theoretic analysis explains the tensile elongation under constant velocity is always greater than that under constant strain rate because the propagation and transfer of neckings under constant velocity is easier to happen than those under constant strain rate, and the elongation under constant load is less because necking could not transfer and the semi-stable deformation would not happen in that case. (3) The analysis explains that during superplastic temperature field, constant temperature is not necessary condition of superplasticitiy, however, the slower the temperature rises and the more uniform the temperature is, the more stable deformation is during the deformation.In the dissertation, firstly, the mechanical meanings of material parameters are defined, and the precise methods for measuring the material parameters are presented. According to test data of three materials, the results of material parameters are obtained by the methods. Then, the phenomenological and semi-experiential constitutive equations are respectively established. Finally, the general criterions of tensile instabilities and the special criterions under typical deformation paths are obtained by deduction and analysis, and the influences of material parameters and temperature on tensile instabilities are investigated. Thus, all things in the dissertation are integrated into a theory of quantitative mechanical analysis during superplastic tensile deformation. The investigation and its results are very necessary to the connection between the macroscopical mechanical parameters and the microscopic physical mechanisms, which are significant to discover the origin of superplasticity, and have important references for simplifying superplastic pretreatment and developing new superplastic materials. In addition, the methods and conclusions also are theoretic instruction for superplastic forming process. All analysis in the dissertation is based on the elemental theory in continuum mechanics. The test materials are three different kind of superplastic materials, which involve Zn-5%Al, Al-Zn-Mg-Zr and H62, and the test data are detailed and credible. So, the conclusions deduced from the elemental theory and the results obtained from test data have universal values used for reference. Following the ideas and methods of investigations of deformation in one-dimension stress state in the dissertation, the deformations in two-dimension and three-dimension stress state would be analyzed, and the hard and brittle materials that involve ceramic, intermetallic compound and so on would be investigated. And based on the investigations in the dissertation, the influences of temperature, time and so on would be taken into account in constitutive relationships, which would make the mechanical theory of superplastic deformation more perfect.