Exploring computational techniques for simulating residual stresses for thin wall multi-joint hexagon configurations for a laser directed energy deposition process

Laser cladding is a directed energy deposition process and can lead to high residual stresses, which can compromise the quality of the specimen. As a result, it is crucial to accurately predict and investigate the residual stress distribution in cladded parts and understand the formation mechanisms. In this study, a thermo-mechanical metallurgical simulation model of the laser cladding process was developed for three different deposition sequences for a thin wall hexagon with inner junctions to investigate the formation of residual stress and distortion. The study was performed for single and multilayer scenarios. Two types of computational techniques, the detailed transient approach and the imposed thermal cycle approach, were performed and comparisons conducted. Consistent results were observed when comparing the resultant stress patterns for the single layer; subsequently, the imposed thermal cycle method was applied for the five-layer models. A preheat scenario is explored. This reduced the computational cost significantly, but the stress patterns were not similar. This indicates that building up worn regions at the top of a thin-walled component, such as a roll die, needs to be investigated further as unique issues have been highlighted. The differences between the implemented computational techniques are described as well as the advantages and disadvantages of each. Knowledge obtained from these case studies provides a foundation for efficient and rapid optimization of laser cladding processes, with the aim of minimizing residual stress in both simple and complex laser cladding structures.


Introduction
Directed energy deposition (DED) is one of the most important additive manufacturing (AM) processes for fabricating, repairing, and modifying geometrically complex metallic components, and could significantly reduce product designto-market times [1,2]. The parts built by a DED technique such as laser cladding are exposed to repeated heating and cooling cycles during manufacturing. Residual stress forms during these rapid heating and cooling cycles [3].
Residual stress in additively manufactured metallic parts is a disadvantageous factor that hinders its wide application. Cracking and distortion will occur when the thermal stress is too high. As the sizes of a manufactured part increases, the part becomes subject to greater distortion and stress. Especially for thin-wall parts, the final geometry is often significantly different from the original design [4,5]. Therefore, residual stress and distortion characteristics must be investigated, and control mitigation strategies proposed.
The highly coupled thermo-mechanical behavior of the materials, microstructure evolution, and fluid flow inside molten pools makes it difficult to predict residual stresses accurately [6]. Finite element analysis (FEA) is increasingly used to predict the thermo-mechanical behavior of the laser cladded parts including thermal stresses and distortion. Li et al. [7] developed an FE model for predicting the thermal 1 3 cycle and residual stresses of an inclined thin wall. Some researchers have studied the thermal cycle and residual stress of a circular part [8][9][10]. This literature focuses on modeling and prediction; however, few of them are concerned with optimization strategies in regard to simulation techniques or path planning.
The tool path strategy and its effects on residual stress has been studied by some researchers. K. Ren et al. [11] developed an approach to integrate machine learning methods and FE models to evaluate infill toolpath in the multi-layer (twenty layers) deposition process of a cube to minimize localized heat accumulation during the deposition process. Zhao et al. [12] established an FE model of a ten-layer wall and realized that the deposition direction strongly impacts the resulting stress and strain. Deposition in a reciprocating direction performed better than deposition in the same direction for their study. Somashekara et al. [13] developed an FE model of parts with three different deposition paths (raster, a spiral-in and spiral-out) for wire arc additive manufacturing. The raster patterns had the least residual stress. Wu et al. [14] investigated the residual stress in a cubic rectangle made by printing of titanium and nickel alloys using wire arc additive manufacturing and concluded that the residual stresses in the short deposition raster pattern were smaller than those in the long deposition raster and spiral-in pattern. The finite element method was used by Sun et al. [15] to investigate the temperature field and stress field of cuboids deposited by five different patterns: zig-zag, raster, alternate-line, in-out spiral, out-in spiral, and an S-pattern. The S-pattern had the lowest residual stress. Markus et al. [16] studied the variation of deposition path results in different temperature gradient fields in components. They investigated the meander pattern, the spiral pattern, and the newly developed S pattern and concluded that the S pattern leads to a more homogeneous temperature distribution, showing beneficial effects on the microstructure, porosity, and residual stress formation. However, Mirazimzadeh et al. showed that there is coupling between the tool path and the part geometry; consequently, a solution for one configuration cannot be assumed to be transferrable to another configuration [17].
Hybrid processes are being developing where machining operations are interlaced with deposition operations, as the lack of precision with DED processes [18] indicates that they should be used to fabricate near net shapes. An issue which is problematic for DED and hybrid processes is distortion. Additional stock can be added to address surface roughness and geometric uncertainties, but distortion is a deviation of the part from its actual shape. The temperature gradients during the built process affect these inaccuracies and need to be studied. The toolpath pattern has significant influence on the local thermal condition, which is one of the main factors leading to residual stress build-up and distortion of the printed structures. The previous studies focused on prediction of residual stress in simple and straightforward geometrical parts. They rarely have more complex geometrical features or a thin-walled configuration with junction structures, which have significant importance for practical industrial applications as DED processes lend themselves to large, thin walled parts.
The use of numerical models enables cost-effective prediction of thermal effects, avoiding the time and cost of experiments, and data can be extracted from the complete model. There are two perspectives being studied in this research for analyzing and solving the laser cladding process simulations. In the first approach, a detailed and often partial solution of some of the effects of the laser cladding process, consisting of the molten pool size and shape, heat affected zone and in general the metallurgical and mechanical modifications in the cladded joint is investigated [19,20]. A detailed description of the solution including distribution of temperatures, hardness, the metallurgical phases, stresses, and deformations is the result of this type of analysis.
Andrzej et al. [21] found an effective technique to predict residual stress for metal large scale additive manufactured components and validated their results using the neutron diffraction method. They investigated the effects of time increment magnitudes for the transient-based modeling technique in terms of accuracy and model efficiency for the large-scale Metal Big Area Additive Manufacturing (MBAAM) process simulations. It was found that a coarse time increment of 20 s effectively captured the overall part distortion, but the model was not able to predict the residual stresses accurately. They determined a combination of fine and coarse time increments that offers an optimal computational efficiency and accuracy for residual stress prediction.
The transient models implemented in the above-mentioned literature are not an effective approach to simulate large-scale manufacturing processes. Due to the transient nature of the analysis, the simulation running time is relatively high. Consequently, intelligent approaches should be used to reduce modeling complexity without compromising the accuracy of the results.
The second approach is the application of numerical analysis for a large and complex part. However, due to the complexity of the problem, simplifications should be applied, which to some extent decrease the accuracy of the calculations and results [20,[22][23][24]. Although this is a disadvantage, it allows conducting analyses that in the first approach are impractical to perform [20]. Min Zhu et al. [24] investigate the influence of welding sequence on evolution of residual stress in bimetallic clad plate butt-welded joint using the imposed thermal cycle method. They concluded that the longitudinal residual stress evolution is greatly influenced by the welding sequence. Different welding sequences do not affect the peak value of the surface residual stress on the flyer plate for bimetallic clad plate joints. Wang et al. [25] studied the residual stress formation in multi-layer welding T-joints using the imposed thermal cycle method and validated their findings with experimental measurements using X-ray diffraction method. Although many researchers have studied various FEA approaches for a variety of materials, there are limited residual stress studies on more complex geometries with a system of joints and junctions that are typical for functional components, as highlighted in Table 1, a summary of the literature related to this research.
The long-term goal of this research is to develop optimal process planning strategies to ensure that the built geometry meets the requirements while minimizing the residual stresses. For this research, there are two specific objectives. The first objective is to determine the influence of the deposition sequence on the resulting residual stresses for a representative thin-walled component. Multijoint, multi-layer scenarios were explored. The second objective is to develop computational techniques to reduce the computation time without a loss of content.
A complex, thin-walled hexagon with designed symmetry was utilized. This shape, shown in Fig. 1, has two different three joint junctions, and a four joint junction, and corners with acute angles. The different thermal and residual patterns illustrate the intricate heating and cooling patterns related to thin walled components with systems of joints.

Research methodology
A thermo-mechanical model has been developed and calibrated using experimental data for single bead and multibead scenarios [26]. The material for this research was P420 stainless steel deposited onto a 1018 low carbon steel substrate. The base plate is 15 cm × 17 cm. One-layer and five-layer case studies were explored (Fig. 2). For the onelayer scenarios, three different deposition sequences were explored using the transient approach (Fig. 3). The deposition path with the minimum residual stress in the critical areas was selected for subsequent analyses. Then, the imposed thermal cycle approach, which reduced the computational time considerably, was applied to this selected path. The results were compared with the transient technique and compared well. The imposed thermal cycle technique was employed to investigate the five-layer model. A preheat scenario was explored to determine whether introducing a higher initial state temperature for a partial bead set would also reduce the computational time.
A summary of the research methodology is shown in Fig. 4.

Development of the thermo-mechanical model
The mechanical boundary conditions were applied to the bottom surface of the substrate during the calculation to avoid rigid body motion. It is assumed that the substrate is located on a table in an unclamped condition. The details of the applied boundary conditions are shown by the arrows in Fig. 5. The geometry was meshed using eight nodded brick elements. After performing the mesh sensitivity analysis, the average element size in the bead regions and closer to the heat source is 0.5 × 0.5 × 0.5 mm. A relatively coarse mesh is assigned in the remaining part. The total numbers of elements for the one-layer hexagon and the five-layer hexagon are 15,363 and 30,788 respectively. Figure 6 shows the temperature-dependent material properties of the AISI 1018 substrate and P420 stainless steel beads. The simulations for all patterns were conducted under the same process parameters and efficiency.
During the laser cladding process, three different heat transfer phenomena occur, which are conduction, convection, and radiation. Figure 7 shows the heat input from the laser and the heat loss due to convection and radiation as well as conduction into the substrate. A 600 s delay is considered for the cooling stage to ensure that the model cools down to room temperature (20 °C) naturally.

Thermomechanical simulations
For the DED process, the thermal history strongly influences the mechanical behavior. A 3D coupled thermal metallurgical mechanical FE model using commercial software SYSWELD (version 16) was developed for this investigation. First, a 3D transient thermal analysis is used to calculate the temperature field. Secondly, the temperature results were used as the initial loading of a 3D quasi-static incremental analysis model to solve the stress problem [27].

Transient approach: moving heat source
When using the transient technique, calculations are made for each subsequent time step, which is automatically calculated depending on the mesh density of the model. In this type of analysis, the mathematical model of the heat source follows the path that determines the deposition trajectory. In this case, the parameters used to describe the heat source model are the laser cladding process parameters, such as the velocity, material feed rate, and the thermal efficiency of the process. A conical model with a Gaussian distribution is for the heat source ( Fig. 8). where Q 0 is the maximum value of the volumetric heat flux density, r e and r i are upper and lower of cone diameter; z e and z i are cone length parameters; x, y, and z are nodes coordinates.
Equation (1) is the volumetric heat flow density into material with respect to nodes' coordinates. Equation (2) supplements Eq. 3 by defining the radius change in the depth direction [20]. This method of defining the heat source model and performing numerical analyses needs calibration of the heat source. During this stage of the simulation, inaccurate calibration of the heat source model leads to errors and incorrect results. Figure 9 shows an example of the heat source model calibration procedure. The process parameters and the material models used in this research are selected based on a calibrated model using the experimental data [26].
The analysis using the transient technique is divided into three parts: preparation of the material base, the thermal and related metallurgical changes, and the mechanical characteristics calculations such as the residual and Von Mises stresses and displacement distributions [20].
For this research, the heat source parameters were set as following: energy per unit length, 110 J/mm; welding speed, 8 mm/s; arc heat efficiency, 0.9; length, width, and depth of conical heat source model, 4, 3, and 2 mm. The element birth and death technique along with moving heat source was used. In this technique, all the elements of the entire model are created at the beginning. All the deposited elements are initially deactivated and then gradually activated following the movement of the heat source [28,29]. This complex solution comes at the cost of an extended calculation time. This is the primary reason that there are other calculation techniques used when calculating large and complex structures. However, such a large amount of  data, including distribution of temperatures, hardness, the metallurgical phases, stresses, and deformations, make it an ideal solution to analyze the local effects of laser cladding process (Fig. 10).

Imposed thermal cycle
As already mentioned, the "transient" technique is practically impossible to use during calculations of numerical large and complex components as an analysis tool due to the amount of data generated and the computational cost. In these cases, the imposed thermal cycle technique is used [19,30]. In a way, this is an extension of the "transient" technique, which involves applying a proper thermal cycle to the group of elements within a bead section simultaneously. Based on the resultant temperature profile, the average thermal cycle for the nodes on the molten zone is calculated. As a standard procedure, the thermal cycle is prepared based on a simple model "transient" analysis. The cycle is then applied successively to all elements of the bead. The difference between the transient approach with the moving heat source and the imposed thermal cycle approach is that in transient approach, the numbers of time steps or calculation cards are equal to the number

Thermal analysis
In the SYSWELD solver, the calculation of the temperature fields is based on the Fourier differential formula. It is necessary to obtain the temperature dependence of the heat conductivity coefficient, specific heat capacity, and density [29].
T(K) is the temperature, t(s) is the time, x, y, and z (m) are the nodes coordinates, m 2 s −1 is the thermal diffusivity coefficient, W.m −1 K −1 is the heat conductivity coefficient, c J.Kg −1 K −1 is the specific heat, and kg.m −3 is the mass density [29].
The heat convection equation with respect to coupled thermal metallurgical analysis is presented by the Eq. 4. P is the the phase proportion, ij is the phase index, Q is the heat source, L ij (T) is the latent heat of i → j , and A ij is the proportion of phase i transformed to j in time unit [29].

0.2.4 Mechanical analysis
The mechanical model is the second step of the current analysis. The previous thermal histories are utilized in this step of the analysis as the thermal loading for the stress evolution at the end of the analysis which is left in the build part as residual stress. In the mechanical analysis, the same finite element mesh was employed as in the thermal analysis. According to Hooke's law, the stress tensor is related to elastic strain [31]: Fig. 9 Example of calibration of heat source parameters by comparing the analyzed shape and size of the melt pool and heat affected zone with a real macrograph of the laser bead [26] Fig. 10 The imposed thermal cycle averaged from the thermal cycle of nodes in the molten pool where D is the elastic stiffness matrix determined by Young's modulus (E) and Poisson's ratio (v). The total strain increment can be composed of the following components [32]: where e , p , and t are the elastic, plastic, and thermal strain, respectively. v is the volumetric strain induced by the phase transformation. The thermal strain Δ t is calculated as [31]: where ΔT is the temperature increment, and shows the temperature dependent coefficient of thermal expansion.
The elastic strain increment component Δ e ij can be described by the stress component ij [31].
where ij is the Kronecker delta. Plastic strain is caused by yield and strain hardening, ij is the deviating stress, and kk is the hydrostatic pressure. In this model, isotropic hardening is assumed at the plastic zone, and the plastic strain increment according to the normality rule can be calculated as [31]: where n is the flow direction, and I is a unit matrix. p and q are the two directions that are perpendicular to each other. εp and εq can be calculated by the equations [18,20,21,33].
In the above equations, Hα is a set of hardening parameters, and p, q, and Hα are defined by the following equations [31,34,35]: where Hβ is the hardening modulus with G and K being the shear and bulk modulus.

Geometric analysis methodology comparing simulation results
To quantitatively compare the residual and Von Mises stress results, a structured methodology for directly comparing the observed residual stress patterns developed by Urbanic et al. [36] is utilized. This is extended where images from the results models are converted into topology and "raster" data via image analysis and geometry creation tools using Rhino® CAD tools and the Grasshopper® visual programming language and VBA. Each stress color coded range in the legend is classified into a z height. A point cloud data set is generated for the desired level of granularity to provide positional residual stress data in a geometric format, as shown in Fig. 11. From this point set, quantitative comparisons were performed using Excel. , Δ q, p, q, H )   Fig. 11 a The Von Mises stresses for the Hex1 configuration with x,y points, and b the topology point set, where the z height for each (x, y) point is associated with a stress level

Stress results
Comparisons of the Von Mises stress distributions and selected junctions are performed for the 3 different deposition path strategies for the one-layer configuration after the parts are cooled to room temperature. The images were transformed into point cloud data results using a 70 × 70 point grid (4900 points) for the analyses (Fig. 12). The Excel conditional formatting is applied to create the color maps. The gradient scale varies from green to yellow to red based on the data values. Therefore, graphs with filtered data (Fig. 12) or the graphs where a difference map are presented also illustrate the fill color range (Fig. 12).
It is quite apparent that the Hex 3 configuration has the greatest amount of "zero to very low stress" islands. There are several large islands in the interior regions for Hex 3 and these "zero to very low stress" islands comprise 13% of the results. For the Hex 1 and Hex 2, the "zero to low stress region" comprise 9 and 10% of the results respectively. Conversely, the "moderately low stress" regions for the Hex 2 are approximately 4% greater than the Hex 3 and Hex 1 configurations, which are almost equivalent (~ 29%). Extracting the "medium to high stress" regions clearly highlights that the top edges and the center cross have higher stress regions for the Hex 1 and Hex 2 configurations, whereas these are medium stress regions for the Hex 3 configuration. The stress ranges are summarized in Fig. 13.
The acute angle 3 point junctions (furthest left and right junctions) have the highest stress regions for all   Fig. 13 The Von Mises stress summary configurations. Interestingly, the high stress patterns are very similar for all configurations for both the left and right joints, which may be due to overlap conditions. This pattern is illustrated in Fig. 14 and graphed in Fig. 15, where the high stress cells are counted and compared using the center line as the reference.
Detailed longitudinal residual stress, xx measurements, and comparisons were performed at specific areas of concern. The curves and maximum stress values are presented for the four joint cross, one acute angle three joint, and one two joint vertex along the lines AB, CD, and EF on top of the bead (Fig. 16). The longitudinal residual stress, xx on the abovementioned lines, has lower values for Hex 3 as depicted in Fig. 17.
The yy residual stress along the line GH has been measured as shown in Fig. 16. The yy compressive stress was slightly lower for the Hex 3 as compared to the other two versions (Fig. 18).
Similarly, the residual stress in the normal direction, zz, was measured and plotted along the line IJ, figure. It can be seen that the Hex 3 has values closer to zero, Fig. 19.
These assessments indicate that the Hex 3 deposition path has better performance as there are lower induced residual stresses. Consequently, the Hex 3 path deposition sequence was selected for the subsequent simulation scenarios. Different techniques on prediction of residual stress, the imposed thermal cycle approach and the transient approach (detailed solution), are investigated.  Fig. 16 The considered paths for investigation of the xx, yy, and zz residual stress comparison in three different path strategies 1 3

The imposed thermal cycle to the transient moving heat source comparisons
The imposed thermal cycle results are compared with transient method for Hex 3. The computational time employing the transient technique is five times of the macro bead technique for the one-layer configuration. While offsetting the transient curve by ± 10%, 82% of the imposed thermal cycle data is within this bounded region. When changing the offset to ± 15%, this increases to 90%. Therefore, it was concluded that the imposed macro simulation strategy is an effective simulation strategy. The xx residual stress was compared along the line KL on the top of the bead after cooling the specimen. The compressive xx residual stress along the line KL for both techniques has a sharp decrease at the start, middle, and end of the bead (Fig. 20). The reason for these inflections is that the laser ignites at the start and extinguishes at the end of the bead; and in the middle, there are reheating effects due to deposition of the vertical middle beads. For the imposed thermal cycle approach,  Fig. 18 The yy stress comparison along line GH The yy residual stress in transient and imposed thermal cycle approach is compared along the line MN on the substrate. In the middle zone on the substrate, the maximum tensile residual stress is observed for both the transient and imposed models (Fig. 21). The transient stress peak value is ~ 60 MPa less than the imposed thermal cycle results.
The zz residual stress is being compared along the line OP starting from the top of bead to the substrate, the normal stress in transient approach changes between 360 MPa and 0 and in the imposed approach, it varies between 210 and 35 MPa (Fig. 22).
When evaluating the induced residual stresses along selected paths, it can be seen that the results generated from the imposed thermal cycle technique compare well to the transient technique. At the cross junction, there is a localized spike, but overall, the observed data and patterns correlate.

5-layer study
As it was shown that the imposed thermal cycle approach is much faster and effectively predicts the mechanical characteristics, the five-layer thin-walled model was developed using the imposed thermal cycle to investigate the residual stress formation. There were two scenarios considered for the multi-layer deposition. The first one was a 5-layer deposition sequence. To investigate the effect of increasing the number of layers on the residual stress formation in the part, the Von Mises stress and the yy residual stress have been compared along the paths AB and GH (cross joint) respectively for the one-layer transient, one-layer imposed thermal cycle, and five-layer deposition scenario (Fig. 23). In Fig. 23a, the Von Mises stress for the 1-layer imposed and transient models showed agreement along the line AB. The tensile Von Mises stress is observed on top of the bead for the one-layer hexagon scenario while the Von Mises stress is close to zero. This shows a reduction of stresses on the top layer after five layers have been deposited. In Fig. 23b, the yy residual stress along the path GH is tensile in the center region (cross joint) of the line GH. The stress changes to compressive due around this region for both the transient and imposed thermal cycle approaches. For the five-layer case, a unique pattern is observed. The stress is close to zero   in the center, and there are generally tensile stresses except at an inflection point at ± 2.5 mm.
For the second scenario, the first three layers were preheated to 100 °C for 20 s and then deposition of the fourth and fifth layer started immediately after the preheat cycle was finished. The comparison of stress results for both scenarios showed that this preheat simulation strategy is not an effective strategy to replace the full five-layer deposition approach. There is a sharp transition of stresses between the last preheated layer and the first deposited layer. Figure 24 shows the Von Mises stress changes along the line QR between the 3rd and 4th layers for both scenarios. As it can be seen, there is 650 MPa difference between the maximum values on the considered path.

Displacement comparison for one layer and five layers: HEX3
The displacement in z direction has been measured along the path KL (shown in Fig. 16), on the surface of the substrate for the HEX 3 build strategy for the one-layer and five-layer scenarios. The displacement for the one-layer case, at the start and end of the path KL, is 40% ~ 0.4 mm, higher for the one-layer case comparing with the five-layer scenario while in the middle of the path KL, the displacement is 7% ~ 0.1 mm more for the one-layer case Fig. 25.

Thermal results
To study the thermal behavior of the different layers, the thermal cycles of the middle nodes on the top of first and fifth layers are considered. Figure 26 shows the nodes being considered and the thermal cycles of each node for the fivelayer deposition scenario. Figure 27 demonstrates the simulated thermal cycles of during and after deposition for the 1st and the 5th layer. As shown in Fig. 28, the peak temperature of the midpoint in the 1st layer decreases during deposition. As the thermal cycle is applied, the 1st peak of the thermal cycle occurs for this node. The dashed line is the melting temperature of P420 stainless steel which is 1500 °C. The second and third peak occurs when middle beads are being deposited and the middle point is thermally affected. The fourth peak occurs when the thermal cycle is applied to the top bead in the second layer. During the deposition of the second layer, the molten pool formed in the middle point of the 2nd layer remelts the middle point of first layer. As it is above the melting point, there is a remelting effect. The midpoint of the 1st layer rises in temperature when the 3rd, 4th, and 5th layer are deposited but do not remelt.
The peak temperature reduction of the first layer middle point, from the 2nd layer to the 5th layer is due to heat dissipation and gradual distance from the imposed thermal cycles in top layers. As a result, this point has experienced multiple post heating effects. The Von Mises stress changes and the zz residual stress along the path UV is shown in Fig. 29a and b respectively with respect to the thermal cycle applied for the one-layer ITC and the 5-layer ITC. The Von Mises stress along the path UV has decreased moving from the first to fifth layer in the 5-layer deposition and is larger than the one layer, Fig. 29a. The zz residual stress oscillates from compressive to tensile by increasing the number of layers in 5-layer case study, Fig. 29b. The cooling cycles are long due to the size of this component.
In 3 + 2 layers scenario as shown in Fig. 30, the first three layers are being preheated for 20 s to 100 °C and immediately the 4th and 5th layers are deposited. As shown in Fig. 31, the third layer is exposed to a great thermal gradient and the temperature of the middle node on top of the 3rd layer increases sharply to above melting temperature while the 4th layer is being deposited. As a result, the sharp transition of stress result between the 3rd and the 4th layer can be due to the sharp temperature changes in the 3rd layer.
The Von Mises stress comparison for the five-layer deposition case and 3 + 2 layers scenario starting from the top through the depth is shown in Fig. 32. There is severe stress difference, 600 MPa, on top of the third layer between two cases.
As a result of this research, cladding for worn thin wall components, such as a roll die, will introduce unique residual stress build ups that will need to be managed for repair activities, and this computational preheat strategy is not a viable approach to reducing computational time.

Summary and conclusion
In this study, a thermo-metallurgical mechanical FE model was established to study the residual stress for a multi-joint  26 The nodes in the middle zone on top of 1st and 5th layers considered for thermal effects study 1 3 component when using the laser cladding based DED AM process. The single and multi-layer thin-walled case studies, with junction structures, were modeled using the SYSWELD software package. The effect of the path strategy on the residual stress for different build strategies was explored, and distinct residual stress patterns were generated. A rigorous assessment of the resulting stress patterns was conducted, and the tool path that provided the least stress (Hex 3) was used for the subsequent analyses. The application of an optimized method to reduce the computational time was proposed and tested. The optimized simulation technique was leveraged to explore the residual stress formation for the multi-layer thin-walled case studies. The major conclusions are as follows: • Investigating different path strategies to determine an optimal deposition approach is an important research question. The three different path strategies for the onelayer thin wall hexagon scenario showed that the Hex 3 deposition path has the least amount of longitudinal, transverse, and normal residual stress and lower overall maximum stresses as compared to the other path strategies. The effect of the tool path cannot be ignored and developing strategies to explore deposition options is an important area of research. • The imposed thermal cycle approach can produce meaningful results with significantly less computational time.
Consequently, it is an appropriate approach to investigate multilayer and more complex components which are difficult or impossible to study when using the transient method. This is critical when considering that the DED process lends itself thin-walled components. • The preheating of the primary layers cannot be a substitute for the deposition modeling approach. The thermal cycles being experienced by each deposited layer during the laser cladding process affects the thermal, metallurgical mechanical characteristics of the deposited layers and cannot be simplified by a preheating process. This virtual experiment highlighted a challenge to be addressed for the repair of thin wall components. • The displacement along the path KL in z direction has been compared for the HEX3, one-layer and five-layer scenario. It has been observed that the z displacement has been decreased by increasing the number of layers and also the displacement is lower in the middle of the path for both one and five layers in comparison with start and end of the path.
Knowledge obtained from these case studies provides a foundation for efficient and rapid optimization of laser cladding processes, with the aim of minimizing residual stress in both simple and complex laser cladding structures. Research to optimize joint designs and interweave heat only passes or machining operations is future work along with considering the tool path direction and sequences.
Author contribution Bita Mohajernia has done the data collection, analysis, and writing. Dr. Jill Urbanic has contributed in writing and data analysis.
Funding This research is funded by the NSERC Discovery Grant.
Data availability Not applicable.
Code availability Not applicable.

Declarations
Ethics approval The authors declare that this is an original work by them and the data used from previously published publications is cited in the paper. No data, text, or theories by others are presented as if they were the authors' own ("plagiarism"). The paper is not currently being considered for publication elsewhere.

Consent to participate Not applicable.
Consent for publication All authors approve the manuscript and give their consent for submission and publication in The International Journal of Advanced Manufacturing Technology.

Conflict of interest
The authors declare no competing interests.