# Accumulative Roll Bonding--A Review
## 5 Computational Studies  
The ARB process involves many variables, such as, material, rolling & post rolling treatment each having a considerable influence on the final product. Hence, it is desirable to have a computational framework to simulate and understand the ARB process in order to obtain optimized process parameters, to avoid trial and error experimental setups. To date, the efforts on the ARBed materials have mostly been devoted to experimental investigations and few computational studies have been reported in this regard [139; 140; 141; 142; 143]. [PERSON] and [PERSON] [144], first correlate computational studies to ARB process parameters with the aim to quantify the strains in each component as well as to estimate the equivalent strain during a rolling process using finite element (FE) analysis. They used an FE method considering stress-strain relationships depending on strain rate and friction between rolls and sheet. The rolling condition of the ARB was verified through the embedded-pin method employed in their FE analysis. Using ABAQUS/Explicit, the exact magnitude of the total strains in each component and the equivalent strain during rolling were shown. According to Figure 23a, they showed that a considerably large equivalent strain, almost five times higher than that at the center, appears upon the surface. The equivalent strain at the surface of ARBed AA1100 without lubricant correspond to equivalent strain of five ARB cycles of lubricated samples. These quantitative strain analyses would be useful for analyzing the microstructural evolution of ARBed materials [145; 146]. [PERSON] et al. [147] applied a FE analysis to investigate the induced plastic strain during the ARB processing of AZ31 sheets using ABAQUS/Explicit as shown in Figure 23b; the effects of temperature and friction (between roller/sheet or sheet/sheet) on the through thickness deformation distributions were discussed. According to their results, the equivalent plastic strain increases when the friction coefficient is increased. As the temperature arises, the equivalent plastic strain diminishes. For AZ31 under this condition, they found that the temperature of 300 \({}^{\circ}\)C and friction coefficient of 0.35  
Figure 22: Up, (**a**) S-N curves of CG and UFG steels. (**b**) Number of cycles to failure plotted against stress amplitude normalized by hardness [138]; bottom, FCGR curves of the two steels at the same ratio between stress amplitude and hardness. (**c**) Crack length versus the number of cycles. (**d**) Crack growth rate versus crack length [138]. compromised ARB processing parameters to achieve the highest homogeneous strain distribution accompanied by no significant grain growth. Similar FE investigations on the affecting parameters on deformation behavior during roll bonding were also carried out by [PERSON] et al. [148] and [PERSON] et al. [149]. As it is relatively difficult to directly measure the plastic strain and stress distributions at the interface of the laminated composites in a hot-rolling process, [PERSON] et al. [150] used a FE analysis (Deform 2D software program) to characterize the bonding behavior of the laminated composites. [PERSON] et al. [151] used a FE simulation to investigate the interface bonding quality of bimetallic foils produced by a combination of ARB and asymmetric rolling techniques. LS-DYNA software was employed to simulate the deformation of the bimetallic foils at various experimental conditions wherein a particular attention was placed on the interfacial bonding between AA1050 and AA6061 layers. The equivalent strain at the interface of the AA1050 and AA6061 layers was checked to reach a maximum value at a roll speed ratio of \(\sim\)1.2-1.3, corresponding to a high-quality interfacial bonding. [PERSON] et al. [152] proposed a framework for multiple pass rolling using ABAQUS explicit poly-crystal texture model for studying visco-plastic self-consistent response to demonstrate the capabilities of this framework to predict the response of ARBed AA5754 alloy.