## 2 Materials and Methods  
### Experimentation  
#### 2.1.1 Build Conditions and Input Parameters: Double Back, Interlayer Time and Layer Time  
The build was printed with a six-axis KUKA robot system. A fiber laser of 20.0 kW was used to melt wire and deposit in the LMD-w system. The laser spot diameter and robot travel speed were 7.4 mm and 8.0 mm/s, respectively. The laser was delivered to the work piece through an optical fiber. The material was fed from 1.6 mm Ti-6 Al-4V wire with an Abicor Binzel wire feeder. The printing was performed in a closed argon environment. A single or double beads wall with 46 layers were built for the experiments. A bead width of 11.5 mm and height of 1.6 mm were set for the single bead deposit. The distance between bead centers was 7.6 mm for double beads deposit.  
Figure 1 shows the variation of laser power as a function of time during the build process. The power used to melt the wire and wall fluctuates between layers. A layer deposition time was approximately 78 s, which included two beads melting time (=22 s for each bead), double back time (shown in Figure 2 and 1.25 s for each bead), bead time (=13.3 s between beads), and layer time (=17.5 s at every layer). Interlayer cooling time was applied at every three layers for 110 s. An additional ~10 min of cooling was applied on top of the interlayer cooling time at the 34 th and 40 th layers, to prevent overheating the build. The inset shows the power on and off at each layer.  
Figure 1: Estimation of layer deposition time from the measurement. There is additional cooling time at 34 th and 40 th layers to prevent the build overheating. Inlet shows the power variation at the layer 1–6.  
A characteristic melting strategy used in the experiment and simulation is presented in Figure 2. In the experiment, the beam moved backward by 10 mm for the first layer and then increased the distance by 1 mm per layer, up to 20 th layer. This backward melting with addition of material was designed to recover the declined deposit edge of the wall, i.e., part slumping. The backward melting (i.e., double-back) became a constant of 30 mm from 21 th layer onward. The double-back time continuously increases by roughly 0.125 s up to 20 th layer.  
Six walls were built to investigate the effect of interlayer cooling time and constraint on the part deformation: a single bead (SB), three double beads (DB) with full clamp (bolted at every other hole) and two DB with center clamp conditions (bolted at two center holes). Three interlayer cooling times of 0 (=DB-1), 2 (=DB-2) and 4 (=DB-3) min were tested for the full clamping condition, and the two interlayer cooling times of 4 (=DB-4) and 0 (=DB-5) min were tested for the center clamping condition. The experimental conditions were summarized in Table 1 below. Figure 3 shows the deposited single and double walls with 0-, 2- and 4-min interlayer cooling time.  
Figure 3: Deposited walls fabricated with 0, 2 and 4 min interlayer cooling time.  
Figure 2: A characteristic melting strategy called double-back which is used to recover the declined wall edge. The melting time continuously increases by 0.125 s per layer up to 20 th layer and becomes constant at further layers.