טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentDavidi Gal
SubjectPlastic Forming Processes of Composite Materials
DepartmentDepartment of Aerospace Engineering
Supervisors Research Professor E Daniel Weihs
Professor Emeritus David Durban


Abstract

Structures composed of layered metallic-composites offer a solution for the lack of homogenous materials with requirements of special combinations of mechanical and physical properties. There are distinct advantages to multi-layered materials in the nuclear, chemical as well as cryogenic and aeronautical engineering.

In production processes of plastic extrusion or drawing of sheets, cylindrical rods and tubes, the flow of material is pushed through converging dies. Designers, when designing for a specific configuration of forming processes assume that the flow through the dies remain uniformly radial converging. This assumption turns out sometimes to be incorrect, and leads to defects and possible failures that occur in such processes.

In this work an analysis of the radial stress and velocity fields are performed according to the J2 flow theory for a constitutive model of rigid/perfectly plastic materials. The flow fields that are used to simulate the forming processes of sheets and rods are the two-dimensional and axis-symmetric flow pattern, respectively. The significant achievement of this work is the generalization of these two flow patterns that corresponds to Nadai-Hill's (two-dimensional) and Shield's (axis-symmetric) solutions for homogeneous materials and materials with general transverse non-homogeneity. In Addition, a special un-coupled form of the equations is obtained where the task of solving them is reduced to solving a single ODE for the shear stress along the working zone.

The main outcome of this work is the finding of validity limits of the radial flow solutions and the mapping of the "state space" that encompasses all the processes configurations. It is also demonstrated that this result cannot be derived under the assumptions akin to known solutions for multi-layered materials. High sensitivity of the ratio of two adjacent layers material's properties is observed, and its influence on the feasibility of converging radial flow. From the un-coupled equations system, explicit analytical asymptotic solutions are derived by assuming: small die angle, tapered working zones, low friction coefficients and low shear stresses. The importance of these asymptotic solutions is that they facilitate the approximation of the real working tractions, making use of the upper and lower bounds methods, for these flow fields are admissible. A representation is given that compares the estimation of extrusion and drawing stresses using: exact, asymptotic and bounds solutions, to experimental results.