1. Introduction
Direct Energy Deposition (DED) is increasingly being used for one-off and low-volume part production. Markets include Spare Parts On-Demand, parts requiring geometric optimisation, and prototyping (Reference Alzahmi, Shamayleh and StefancichAlzahmi et al., 2025; Reference Bandyopadhyay and TraxelBandyopadhyay & Traxel, 2018). DED can also provide energy and resource benefits, particularly if the part has a complex geometry where many subtractive manufacturing operations would be required.
The near-net shape capability is also attractive as it minimises the number of post-processing steps and operations required to create and ship a part. The machines are often fully autonomous with little supervision required as in-process monitoring can be deployed automatically warn and/or stop the process if required. The process is flexible and can be deployed in standard warehouse infrastructure.
The localised heat and energy produced during deposition introduces residual stress and the relative thermal histories can lead to none-uniform residual stress distributions. The residual stress introduced by the processes can limit optimised geometries in achieving their estimated strength characteristics.
Residual stress can be released through post-processing techniques. The ‘ping-back’ phenomena, where a part distorts after being releases from the print bed, is as example of an often undesirable behaviour that the residual stress introduced by the AM process can produce (Figure 1). Heat cycling the component can aid in relaxing the residual stress albeit at the cost of an additional manufacturing process.
Being able to design AM components with consideration of the residual stress could enable designs that mitigate the need for additional manufacturing process thereby removing further processing costs and time as well as possibly using residual stresses to improve the performance characteristics of a component. This currently requires numerical modelling of the thermo-mechanics coupled with geometry activation to simulate the AM process and predict a component’s residual stress distribution. These models are computationally intensive often requiring High-Performance Computing (HPC) levels of compute to be able to model the process accurately.
The gap identified in this research is the development of design heuristics and ‘general rules of thumb’ that can support designers in deciding how they should go about additive manufacturing a component with consideration of the residual stress it is likely to introduce. An area that remains largely unexplored (Reference Qin, Qu, Ding, Song, Gao, Wang and LiaoQinet al., 2023; Reference Zhou, Shen, Lin, Liu and ShengZhou et al., 2022). Heuristics could be in the form of the general behaviours and patterns in how different infill pattern designs, toolpath path, laser power and the toggling of common features within AM slicing tools, such as the inclusion of shells, brims, and rafts, can contribute to the residual stress distribution of the part. These heuristics do not need to be well-defined numerical degrees of accuracy but could include general behaviours and likely vectors of changes such as greatly increasing or decreasing residual stress across a component or in specific areas of a component. This paper’s contribution therein lies in the Design for Additive Manufacturing conference where it reports the findings from a numerical study into the residual stress distribution of a component produced with the commonly found shell feature activated and deactivated.
‘Ping-back’ phenomena caused by the residual stress introduced by an AM process being released as the part is removed from the print bed (Reference Takezawa, Chen and ToTakezawa et al., 2021)
The paper continues with a Related Work (Section 2) that summaries the work to date in understanding residual stresses in additive manufactured parts and the methods used to model them. It then continues with a description of the numerical experiment used to model a DED process where two toolpaths (shell activated and deactivated) to produce the solid wall of 20mm x 60mm x 20mm in size were modelled (Section 3). The results are then presented and discussed in Sections 4 and 6, respectively. The paper then concludes with the key findings and how they can support designers in designing for AM (Section 7).
2. Related work
The Related Work section provides an overview of the field’s understanding of residual stress in Additive Manufacturing (AM) components and how residual stress is being modelled. These summaries set the scene and rationale for the study presented in this paper.
2.1. Residual stress in AM parts
The act of depositing molten or sintering material exposes material to concentrated heat and energy resulting in shock thermal cycling that can lead to the development of residual stress. This is compounded further by subsequent passes of the print-head as it builds the layers that further thermally cycles the material. The process often results in non-uniform distributions of residual stress within the component.
The geometry can also have a considerable effect on the resulting residual stress. Thin membrane structures generate tensile residual stresses due to faster cooling that induce steep temperature gradients (Reference Mercelis and KruthMercelis & Kruth, 2006). In contrast, thick membrane structures create compressive residual stresses as the outer layers cool and contract while the core remains hot (Reference Yadroitsev, Krakhmalev and YadroitsavaYadroitsev et al., 2015).
The resulting residual stress can lead to issues such as part deformation, dimensional inaccuracy and decreased structural integrity (Reference Zaeh and BrannerZaeh & Branner, 2010). Reference Bartlett and LiBartlett and Li (2019) highlights three types of residual stress within additive manufactured components (Figure 2). Type I macro-stresses remaining after plastic bending, Type II intergranular stresses caused by preferred slip orientation misalignment and Type III lattice stresses from substitutional atoms or vacancies. Residual stresses contribute to components that do not meet the potential performance estimated by Finite Element Analysis (FEA) that use the property charts of the feedstock material.
Three type residual stress classification: type I macro-stresses remaining after plastic bending, type II intergranular stresses caused by preferred slip orientation misalignment and type III lattice stresses from substitutional atoms or vacancies (Reference Bartlett and LiBartlett & Li, 2019)
The field has started to look at optimising toolpaths to provide desired residual stress distributions. Reference Zhou, Shen, Lin, Liu and ShengZhou et al. (2022) used a genetic algorithm to propose toolpaths that were than numerically modelled with the results feeding back into the generation of additional toolpaths. The approach was able to generate toolpaths that reduced residual stresses by 87% compared to standard toolpathing. However, this came at a considerable computational cost due to the heavy dependence on thermal-mechanical simulations to provide the residual stress predictions for each candidate path. Reference Qin, Qu, Ding, Song, Gao, Wang and LiaoQin et al. (2023) used adaptive toolpath generation that coupled a heat transfer model with the toolpath generation algorithm. The objective was to complete the toolpath while minimising the heat gradients – a primary factor in residual stress development. They achieved a 46% reduction in the predicted residual stress of a component as well reducing the computational overhead by only considering the thermal modelling of the process.
Combined, the related work shows that geometric features and toolpaths can considerably effect the residual stress distribution of a component. Optimisations can be achieved albeit at a high-computational cost and this may be a limiting factor for some designers wishing to consider residual stress within their component design. Therefore guidance and design heuristics regarding how the features present in AM toolpathing software (e.g., brims, rafts, shells, infill design, speeds and powers) is required to support their design decision-making. Heuristics that can be identified through numerical modelling of these parameters and their effects on the AM process.
2.2. Modelling the additive manufacturing process
The non-linear multi-physics nature of residual stress development in AM requires high-fidelity material models and computationally intensive simulation to accurately capture the physical phenomena (Reference Chen and YanChen & Yan, 2020). Meshes with element sizes range from millimetre to micrometre are required to study Type I, II, or III residual stress formation (Reference Dong, Liang, Chen, Hinnebusch, Zhou and ToDong et al., 2021; Reference Hu, Grilli and YanHu et al., 2023). And step sizes (time increments) rarely go above 0.5 secs and are often lower to ensure convergence.
Reference Prince, Munday, Yushu, Nezdyur and GuddatiPrince et al. (2024) and Reference Takezawa, Yoon, Jeong, Kobashi and KitamuraTakezawa et al. (2014) have modelled the process using combined optimization of stiffness and heat conduction models while Reference Allaire and JakabčinAllaire and Jakabčin (2018) and Reference Wang and SigmundWang and Sigmund (2023) have taken a linear thermoelastic approach. Thermo-mechanical Finite Element (FE) simulations featuring element activation and elimination (Reference Grilli, Hu, Yushu, Chen and YanGrilli et al., 2022; Reference Nagaraj and MaiaruNagaraj & Maiaru, 2023) and realistic heat source modelling (Reference Robinson, Ashton, Fox, Jones and SutcliffeRobinson et al., 2018) are also methods that have been successfully deployed to model the AM process.
Validation has been achieved through comparisons with empirical studies deploying synchrotron-based X-ray diffraction (Reference Hu, Grilli, Wang, Yang and YanHu et al., 2022; Reference Yang, Clare and JinYang et al., 2024, Reference Yang, Speidel, Clare, Bennett and Jin2025), neutron diffraction (Reference Coules, Probert, Azuma, Truman, Seow, Pirling and CabezaCoules et al., 2023; Reference Lee, Feldhausen, Fancher, Nandwana, Babu, Simunovic and LoveLee et al., 2024), hole drilling and contour methods (Reference Robinson, Ashton, Fox, Jones and SutcliffeRobinson et al., 2018) to evaluate the residual stresses in real-world components.
AM simulations can often run slower than the real-time operation and require High-Performance Computing (HPC) levels of compute power to resolve in a reasonable time-frame. While they may take longer than simply building and testing the artifact, they provide unprecedented levels of details into residual stress that could not be attained through empirical examination as the residual stress for all nodes can be captured and its evolution recorded.
The Related Work has shown that residual stress is an inherent property of the AM process and one that needs to be accounted for by design engineers when designing the geometry and selecting the manufacturing process parameters used to produce the geometry. However, there remains much to be studied regarding the development of residual stress. Understanding the development of residual stress can subsequently lead to the development methods, such as design heuristics and optimisation algorithms, that can assist the designer in accounting for residual stress. The gap in knowledge that was selected in this study was in evaluating the impact of the shell feature, a commonly found feature in AM toolpath software, on the residual stress of a manufactured component.
3. Numerical experiment
A numerical experiment was created to examine the shell features contribution to residual stress development in a Direct Energy Depositioned (DED) part. Numerical simulation was selected as it is the only viable method to examine the distribution of Residual Stress throughout the part. Techniques, such as synchrotron-based X-ray diffraction, can provide residual values for the surface of the component which each measurement typically taking tens of minutes to make resulting a in a labour-intensive process. The following section details the definition of the part, toolpath selection and generation, numerical model development and deployment, and post-processing analysis.
A 30mm x 60mm x 15mm component on a 70mm x 100mm x 10mm baseplate (not to scale)
The part was a wall of 30mm x 60mm x 15mm that was printed on a 70mm x 100mm x 10mm baseplate. Toolpaths were generated using Python and featured a linear infill in the direction of the 60mm length and a linear infill with two shells in the direction of the 60mm length. Figure 4 shows the toolpath for each case. The shells feature deposits material around the perimeter before preceding to deposit the linear infill. Two shells were selected as much software typically the default to that setting.
Print patterns
The model used was a sequentially coupled thermal-mechanical Finite Element model using the commercially available Abaqus software. The model featured two elements sets – one for the base plate and one for the potential manufacturing domain. Elements in the manufacturing domain start in an inactive state. They are subsequently activated as the model simulates the material deposition. A 0.9mm DC3D8 and C3D8 cell mesh was created for the entire domain (baseplate and part) for the thermal and mechanical analysis, respectively. Cells in the manufacturing domain that were known not to feature in the printed part were removed prior to running the simulation. The mesh featured as total of XX nodes and YY elements.
The model used parameters derived from the Abaqus “Sequential thermomechanical analysis of a directed energy deposition build” model. The model featured two steps:
-
1. PRINTING
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2. COOLING
The PRINTING step used element activation with the custom Python script providing an Abaqus event series to simulate the toolpath. The element activation field was defined as Equation (1):
$${q_{activation}} = H\left( {1 - {{{\left| {x - {x_L}\left( t \right)} \right|}}\over{{{a_x}}}}} \right)H\left( {1 - {{{\left| {y - {y_L}\left( t \right)} \right|}}\over{{{a_y}}}}} \right)H\left( {1 - {{{\left| {z - {z_L}\left( t \right)} \right|}}\over{{{a_z}}}}} \right)$$
Where
$$\left( {{x_L}\left( t \right),{y_L}\left( t \right),{z_L}\left( t \right)} \right)$$
are co-ordinate of the heat source in the reference system of an individual track and
$${a_x},\;{a_y}$$
and
$${a_z}$$
are the bead dimensions.
PRINTING used a 0.5s timestep, a 2kW laser power when depositing material, initials conditions of 26°C ambient temperature, and film and radiate boundaries across the entire of 18E-3 and 0.28, respectively. The laser was modelled using a Goldak profile with a laser spot radius of 4mm and penetration depth of 1.1mm. Inconel625 was selected as the feedstock and the material for the baseplate. The temperature dependent material properties are detailed in Table 1 and are from Reference Denlinger and MichalerisDenlinger and Michaleris (2016) and Reference Denlinger, Heigel, Michaleris and PalmerDenlinger et al. (2015). These were selected as they were available in the Abaqus additive manufacturing tutorial documentation that has been validated against real-world experiments. Thus, it provided confidence that the residual stress distribution developed would be representative of the real-world.
COOLING turned the laser off and left the part to cool on the baseplate. The step incremented in 10s intervals for 100s. The thermal model was run first with nodal temperatures (NT) being captured for each increment. The resulting thermal history was then imported into the static analysis model that then repeated the steps and iterations to produce the residual stress distribution – captured in S. The static analysis featured adaptive time-stepping with a maximum timestep of 0.5s in line with the Heat Transfer model. The adaptive timestepping allowed the simulation time when required to ensure convergence of the static behaviour. The simulations were run on the University of Bristol’s BluePebble Heterogenous High-Performance computer with each simulation requesting 16-CPU cores and access to a 40GB Nvidia A100 GPU. A Python script was used to interface with the Python interpreter bundled with the Abaqus software to extract the residual stress distributions from the.odb files. The.dat files were parsed to provide summary information on the simulation runtime.
Material properties used for Inconel625
4. Results
Table 2 summarises the simulation runs for the shell and no shell cases. The heat transfer models ran consistently across the two cases with a small difference in the number of increments in the PRINTING step owing to the different print paths. The static analysis took a similar amount of time as the heat transfer models with a slight increase in steps where it would have had to decrease the time-step in order to achieve convergence. The values demonstrate the computational intensity required to resolve and understand residual stress within AM components. The consistency in the runtimes and steps taken to resolve each case provides confidence that the simulations ran successfully for both cases.
Simulation statistics
The resulting.odb files were 1.7GB and 0.2GB for the heat transfer and static analysis respectively with the heat transfer being larger as the entire thermal history was required for the static analysis. The static analysis only saved the stress values at the beginning and end of each step. The static analysis would have otherwise reached terabytes if all increments were saved. This, further reinforces the computational complexity in model and investigating residuals stresses in additively manufacturing. And particularly so for the simulation of large scale components.
Table 3 reports the summation of the Von Mises stress within the component after PRINTING and COOLING. It shows there is little difference in the sum total of von mises stress of the component with the shell feature activated or deactivated as it is within the 1-2% across all the steps. Table 3 does show a marked 40% increase in the stress as the component is left to cool by its own.
Figure 5 show the histograms for the Von Mises stresses recorded on the elements representing the component at the end of each step in the process. Figure 5a exhibits a peak in stress at approx. 400 with a range of cells reporting stress between 100-300. Slight differences can be observed in the distribution that can be attributed to the activation of the shell feature. Figure 5b shows a drop in the density of cells reporting 100-300 and an increase in cells reporting approximately 420. In both cases, it appears that the cooling has shifted the cells that were originally reporting 100-300 to sit within the 400-500 range. One could liken this to the component “tightening up”. So, while there are differences between the residual stress at the end of PRINTING, this is lost by the time the component is left to cool naturally.
Von Mises stress distribution through the component at the end of the simulation steps
Figure 6 show the distribution of the stress for one of the layers within the component athe the end of the PRINTING and COOLING steps. Both the shell and no_shell components follow a similar trend with the perimeter of the geometry, particularly the top and bottom, featuring cells with the highest stresses after PRINTING (Figures 6a and 6b). We observe the opposite after COOLING with the cells within both models exhibited the larger stresses (Figures 6c and 6d).
Spatial stress distributions for s middle layer (7mm) of the component
5. Discussion
The results from the study reveal the shell feature does impact the generation of residual stress during PRINTING stage. The argument for this would be the shell preventing the linear infill from expanding as it is printed after the shell. This resistance would prevent the relaxation of the stress.
However, this stress does not remain post COOLING where the stress within the components converge to similar distribution. This suggests that the post-processing cooling regime applied to a component post-print has a greater and more significant effect on the the residual stresses within the component. The stress within the component increased by 43% and 39%, respectively. The slight difference could be attributed to the fact that shell wall may help reduce the degree of contraction within the component thereby reducing the overall increase in stress by the 4% observed in the modelling.
The analysis of the spatial distribution of stress across the two steps further affirms the COOLING’s leading contribution of stress within the part where there was a clear inversion with the perimeter dominating the stress durinng printing and the internal cells dominating the stress after cooling.
The study has shown that the residual stresses is different across the manufacturing phases and both toolpath and cooling strategy have a part to play in controlling the development of residual stress. More studies are required that evaluate many more toolpaths across many more geometries so that some general design heuristics can be generated to feature alongside manufacturing process optimisation strategies (Reference Qin, Qu, Ding, Song, Gao, Wang and LiaoQin et al., 2023; Reference Zhou, Shen, Lin, Liu and ShengZhou et al., 2022).
The study has also highlighted the considerable time it takes to run numerical residual stress studies and methods of speeding up the simulation could further aid residual stress investigation. Increasing simulation speeds could also enable them to be introduced into design optimisation loops and enable studies and large additive manufactured parts.
6. Conclusion
This paper has investigated the impact of the shells feature on the residual stress distribution of a Direct Energy Deposition Additive Manufactured part. The results showed that the shells did increase the residual stress during the print phase with the shells preventing the linear infill from relaxing. However, the cooling regime post-manufacture largely mitigated this effect and the final parts were within 2% of one another. If reducing residual stress was a priority then it is advised that turning the shell feature would provide a marginal gain although designers can largely not worry about using the shell feature when it comes to the stress in a DED manufacturing component.
Acknowledgement
The work has been undertaken as part of a UKRI’s Innovation Launchpad Researcher-in-Residence Booster (EP/W037009/1) and Digital Design Network+ (UKRI394) awards.
Open access
