The Application Research Of Nonlocal Friction Model And Strain Gradient Theory In Superplastic Forming

In mental superplastic forming processing, the Coulomb friction model applied on each point of the contact surface is local, which means the friction stress at one point in a certain range of contact surface is only affected by normal stress at the same point. However, real metal surfaces are not smooth, and the contact surface is actually contacts between rough surfaces. In this case, the friction stress of a certain point is not only related to the normal stress of this point, but is affected by the other points' normal stress in a neighborhood of the point. This is called the nonlocal friction effect. Therefore, it is necessary to use nonlocal friction model as a replacement of Coulomb's friction model to analyse the nonlocal friction effect caused by the asperity structure on the contact surface on micro-level. The nonlocal friction model proposed by Oden et al. has been widely used. In addition, all kinds of nonlocal constitutive theories have been established to explain the size effect and to solve the industrial problems at the micron and submicron scales. The simplest version of nonlocal constitutive theories may be suggested by Mühlhaus and Aifantis. The theory introduces the second-order gradients of the effective plastic strain into the constitutive equation for the flow stress, while leaving all other features of classical plasticity unaltered. This theory has been widely used. The major work of this dissertation is to investigate a series of problems with the above mentioned theory.The main content of the research paper is:The nonlocal friction model is applied as a replacement of Coulomb's friction model to study the distribution of pressure on the contact surface in the superplastic forging process of disks. A formula to caculate the pressure in the forging process with nonlocal friction model is obtained. What's more, the differences between the influences on the distribution of pressure on the contact surface caused by nonlocal friction model and Coulomb's friction model under different conditions is also studied. The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of cylindrical body through a cone-shaped die. Perturbation theory is used to get approximate solution.The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of wide strip through a tapered die. Perturbation theory is used to get approximate solution.Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated using the strain gradient plasticity theory.The size effects of free bulging process are investigated using the strain gradient theory and the theoretical results are compared with the available experimental data.All the research findings show that although using nonlocal friction model in replacement of Coulomb's friction model to analyse the friction in the superplastic forming process has made the problem more complex, the findings of the analysis is more accurate and true. The application of nonlocal friction model is helpful for us to gain a deeper understanding of the friction mechanism in the metal superplastic forming process. It is helpful for us to explore the value of the nonlocal friction model and extending the application range of it. In addition, the strain gradient theory is adopted to explain the size effect of superplastic free bulging. It can serve as good theoretical bases for the application and development of the minor forming and processing technology. It can provide a promising future for the improvement and innovation of plastic processing technology.