*2.1. Theory of Bonding*

The thin film theory prevails as the primary explanation for bimetal bonding in high pressure cold rolling. Like rolling, extrusion is also a high-pressure process in which the theory is viable as other mechanisms that explain bonding are unlikely to occur. Other such bonding mechanisms are diffusion, overcoming energy barrier, and joint recrystallization [52]. A brief summary of the theory is as follows:


In ARB applications, the brittle surfaces are prepared by light scratch brushing using stainless brushes, and the high pressure is provided by rolls. For example, nickel plated Cu/Al [53], Mg/Nb [13], Al/Ni [54], and Al/Al [55] sheets were produced using this technique. In this work, high pressure is provided by a die, a mandrel, and a punch mounted in a hydraulic press. The theory and extrusion process are depicted schematically in Figure 1. In stage 1, as indicated by the bubble numbers, the two metal tubes are under compression due to the punch (not shown), and an initial air gap is present at the metalmetal interface. This surface must be as clean as possible, free of any contamination, and prepared such that a thin brittle surface exists. As the material is forced into the extrusion ledge in stage 2, the air gap is significantly reduced, the metal-to-metal interface is formed, and plastic strain occurs within the metals. Due to the high strain levels, cracks form within the thin brittle surfaces, and virgin material of each metal extrudes through the cracks, interact, and bond. Entering stage 3 completes the extrusion process by providing the final desired shape: a reduced outer diameter and maintained inner diameter of a new tube size. Some areas may not bond, and voids may become present. Further processing, by repeating the process shown in Figure 2, will continue to thin and stretch the interfaces such that voids, and trapped oxides will be thinned and blended into the metallic structure where their influence on material behavior is minimized [13].

**Figure 1.** Axis-symmetric cross section of extrusion process and the three stages of bonding using AEB. The metal initially experiences compression (stage 1) before entering the extrusion zone (stage 2), where severe plastic deformation occurs, and exits in the final desired shape (stage 3).

**Figure 2.** (**a**) The manufacturing process flow map for achieving ultrafine-laminated structures in metallic tubes via AEB. (**b**) Graphical visual of the nominal layer thickness within the tube wall when a bimetal is processed multiple times using AEB. When processing using AEB, the wall thickness is maintained while individual layers exponentially decrease. Note that processing steps, such as cleaning and expansion, will impact layer thicknesses and overall wall thickness such that each individual layer is not expected to be exactly the same.
