Computationally Efficient Models of High Pressure Rolling for Wire Arc Additively Manufactured Components  
[PERSON]  
Welding Engineering and Laser Processing Centre, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 0 AL, UK; [EMAIL_ADDRESS] (V.G. ); [EMAIL_ADDRESS] (J.D. ); [EMAIL_ADDRESS] (S.W.) Yongle Sun  
During WAAM deposition the concentrated heating by the electric arc causes local material expansion. The material with low yield strength at elevated temperature deforms in compression during heating due to the constraint imposed by the surrounding material. After the arc heat source passes, the deformed material cools down and tends to shrink [17]. The heating-cooling cycle results in thermal stresses and plastic strains (PSs) in the deposited layers and the substrate (usually restrained by clamps, fixtures, etc.). After the deposition, residual stress (RS) arises in the built part, which can lead to distortion after removal of the external restraint [3; 18; 19]. RS is usually detrimental to performance, since it can adversely affect fatigue life, increase probability of brittle fracture and reduce corrosion resistance [20; 21; 22; 23]. High pressure rolling was found effective in reducing RS and distortion in WAAM built components [3; 4; 24], since it induces tensile PS in the built part and substrate, which compensates for the compressive PS caused by the thermal deposition cycle. The rolling can be implemented in different ways. For instance, inter-pass rolling after WAAM deposition of each layer was demonstrated as effective in reducing RS and distortion [3; 4]; rolling every four deposited layers and rolling solely on the last layer of a WAAM built component were found effective as well [3]. Effective rolling should commence when the WAAM component is cooled to ambient temperature (below 50 \({}^{\circ}\)C), because in situ rolling (i.e., roller follows welding torch) has a negligible effect on distortion [3]. Experiments showed that an increase in rolling load is beneficial for the mitigation of RS and distortion [3; 4]. Regarding the effect of roller geometry, the use of a slotted roller instead of a flat or profiled roller (i.e., roller with a groove) can significantly improve the efficacy of rolling, since the lateral restraint of the slotted roller promotes larger longitudinal deformation in the rolled material [3]. High pressure rolling has been successfully applied to WAAM deposited walls [3; 4] and intersections [25; 26], using materials such as mild steel [3] and titanium alloy [4; 24; 25]. The rolling also can improve fatigue life and mechanical properties [27; 28], refine microstructure [3; 24; 25; 26; 29] and reduce porosity [6; 30]. However, detailed mechanisms of the reduction in RS and distortion during high pressure rolling of WAAM built components are not well understood. The finite element method (FEM) is widely used in simulations of rolling [31; 32], which can reduce experimental effort, time and cost. However, current FEM simulations of rolling in WAAM are highly inefficient, especially for large components. For instance, high performance computing (HPC) facility was required to simulate rolling in a 456 mm long part, and the computational time was up to 92 h [33]. When multi-layer rolling is used in WAAM [3; 4], the computational demands are further exacerbated, and the simulation of rolling for a typical 20-layer WAAM part could take weeks. This makes multi-layer rolling simulation impractical. Therefore, efficient modelling techniques are needed to reduce computational time while still ensuring accuracy. In current literature only two publications were found to address rolling simulation for WAAM built components [34; 35]. For similar problems, the modelling research relevant to WAAM rolling includes the simulations of burnishing [36; 37; 38; 39], deep rolling processes [40; 41; 42; 43], hot and cold manufacture rolling processes [44; 45], and rolling for reducing RS in quenched block [46] and weld seams [33; 47].