ABSTRACT
A general ECAP setup is shown in Fig. 5.1. A workpiece is pressed through a die that contains two equal cross-section channels joining at an angle j with an out angle j. The shear deformation behavior has been investigated by various methods including strain analysis based on the slip line theory or geometric considerations [39-43], and stress analysis based on the upper bound theory [44]. The effective strain for one pass through the channel can be calculated as follows [40]: 1= 2cot + + cosec + 2 2 2 23 j j j (5.1)
Figure 5.1 Schematic of an ECAP setup with back pressure.When a die with a sharp outer corner j = 0 is used, the von Mises equivalent strain is [39] 1= 2cot 23 (5.2)In such an analysis, the ideal situations are assumed that there is no friction with the die walls, the entire cross section of the workpiece undergoes uniform shear deformation as it is pressed through the intersection zone of the two channels, and the material is quasi-perfect plastic that can fill the die completely no matter what the die corner shape is. However, these are normally not the case in reality, and finite element analysis (FEA) is often used, taking into consideration of the real material properties and boundary conditions, to investigate the constitutive behavior during deformation [45-47] and effects of die geometry and processing variations [46, 48]. The method has provided better guidance to theoretical models and process designs, especially by simulating die filling and strain distributions in the deformed volume during ECAP.As an alternative, a back pressure is sometimes applied in the exit channel, as shown in Fig. 5.1, to prevent cracking during low temperature processing or for materials with lower ductility. It is especially useful for consolidation of powder samples [25].
