Practical DOE-Based Approach for Predicting Impact of Stress and Deformation in SLM Overhanging Features During Product Design

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Introduction
One of the major challenges with implementing additive manufacturing (AM) technologies lies within production management [1]; the processes are not well understood by either product designers or production managers, which limits their usefulness and applicability in practice.Many of these processes exist but managers are often reluctant to adopt them for fear of unknown complications or problems.Additive technologies have much to offer the production world beyond prototyping, with new possibilities in mass customization, design freedom, simplified supply chains, and elimination of specialized tooling [2].A first step in this direction would be to equip engineering designers and production engineers with an appropriate tool to examine and judge the value of a manufacturing process within the scope of their work, a tool that can be applied easily and consistently across working groups and that has a universal meaning to stakeholders.The present study presents such a tool: a simple and powerful design tool to examine very complex problems relating to the successful and efficient application of AM technologies using a design-of-experiments approach [3].
One of the most useful of the AM processes is the selective laser melting (SLM) process, a variation of the powder bed fusion family of AM processes, typically used to create full-density metal parts.There are many advantages to employing SLM, including fine detail resolution, good surface finish, customizability of the mechanical properties, and ability to handle materials that traditionally have low manufacturability, such as nickel and titanium alloys [2,4].Figure 1 shows the basic mechanics of the SLM process [5].
Figure 1: SLM process schematic [5] However, the SLM process has a serious inherent problem: the process is extremely sensitive to the process control and input parameters; if the process is not very carefully controlled, the heat cycling of the fusing laser can introduce severe residual stresses into the material.These residual stresses can initiate part deformation, cracking, and delamination; these stresses can cause significant reduction of fatigue life or, in extreme cases, part selfdestruction during or immediately after printing [6,7].The most common way to deal with this problem, in practice, is to attach every feature to the build plate using solid and bulky support structures and perform stress relieving operations on the entire part before cutting it from the plate using an electric discharge machine or bandsaw [8].This is a practical solution for simple parts, but the problem becomes far more complex when dealing with the stresses in overhanging features.A number of fixes have been devised to deal with these residual stresses without special post-processing operations or cumbersome, wasteful support structures; some of them attempt to directly control the process parameters while some are efforts to work around the process constraints; a comprensive discussion of these methods can be found in [3,5] and will not be reproduced here.While some of these solutions have been quite successful in particular cases, what is sorely needed is a general design-for-manufacturability (DFM) theory for SLM [9].When designing parts that will be manufactured using any AM process (and especially so in very sensitive processes such as SLM), it is important to incorporate DFM principles whenever possible.DFM provides tools both for mitigating potential manufacturing problems from the inherent weaknesses of a process and for providing insight into extra design benefits that may be available when using a particular process [5,9,10,11].

Motivation and Approach
Part of the design of any experiment is the specification of a technique, usually in the form of an analysis of raw data taken during experimental runs.However, SLM is extremely difficult to experiment with in-situ, due to the fact that the chamber must remain oxygen-free and strictly undisturbed to work correctly [4].Even with the use of thermal cameras, it is next to impossible to capture reliable data that is not subject to interpretation on the instantaneous stresses and deformations as they form in the part during printing.It is a simple matter to study the damage and deformation after the part is complete, but that does not give the instantaneous inprocess perspective needed to understand SLM from the DFM perspective.Improvements are being made in this area [12] but a practical real-time solution is not widely available.Therefore, in order to capture a snapshot of the process in action in the most practical way without manufacturing thousands of dollars worth of test parts, thermo-mechanical Finite Element Analysis (FEA) model was built to simulate the SLM process in action at a particular point in time during the printing process.The energy input for the model is the laser power and the outputs range from thermal to stress and deformation results.FEA is a common method for studying AM processes in-run [6,13].

Heat Transfer Model Development
The FEA model was generated using the SolidEdge ST6 FEMAP FEA tool.The required inputs for an FEA model are the loads, the initial conditions, and the boundary conditions.The loading for the present experiment was the laser input.The proper initial conditions were calculated using a simple thermal model based on the first principles of heat transfer, as seen in Figure 2. Boundary conditions were applied to the model to simulating the effects of the powder support or a support structure.Powder-only support was modeled as a pressure equal to the force of gravity, where the overhang was free to move up, but not down into the powder bed.The support material was simulated using full fixed constraints on the bottom surface of the overhang.The study by Patterson et al. [3] uses a similar thermal model to simulate heat transfer in overhangs; setup of this theoretical model and its equations can be found by consulting Sections 3-4 of that work.

Model Validation
Once the FEA model was set up, an in-depth verification and validation study was completed.A series of test scenarios were created, borrowing geometry, process settings, and results from published studies [6,13,14,15,16], from which the geometries, boundary conditions, inputs, and final outcomes were known.In most cases the results from the FEA model were similar to the studies but some adjustments to the values of the boundary conditions (such as initial temperatures) were prompted by a few of the runs.Once these adjustments were made, the results from the model and the test studies were very similar, so the FEA model was considered to be valid.

Experimental Design: Factors
Five factors or main effects were chosen for study after an extensive literature review [3,5] to understand the experimental designs used in previous studies.The stated goal of the experiment is to provide a simple and easy-to-use model for design engineers and production managers and this outlook was essential in choosing which factors to examine.Many others could have been chosen, including layer thickness, but the five that appear to best represent the parameters set or evaluated by designers and managers were examined.The choice will be made by both engineers and management; the approach outlined in this paper facilitates this well, as it allows analysis of any important variables relative to each other and is not dependent on specific input variables.The variables and their levels for this study were (summary in Table 1): 1. Laser power: Modeled as a constant heat flux input into the FEA model on a square element equal in area to the laser spot.2. Laser spot diameter: Modeled as an element on the surface of the material, which the idea range of areas taken from the review completed for the factors (as discussed previously) 3. Laser scan speed: The heat flux is the load on the model, so the rate of input must be known 4. Thickness of the overhanging feature: The material thickness strongly affects the thermal gradient and the mechanical behavior of the material during processing 5. Support Structure: Support materials can often cause problems during design and processing and require extra resources to remove.

Experimental Design: Material Choice
It was decided to set up the experiment for two runs, each modeling the use of a different material.Run 1 was set up to use TI-6V-4Al and run 2 was set up to run 316L stainless steel, two commonly used materials in SLM.It was decided to keep the materials separate and not include them as an extra factor in the experimental design; this allowed the final results of the experiment to be more easily validated by being compared with the theory and with single-material published studies on SLM.In SLM, the material properties cannot be assumed to follow the standard material datasheets, due to the heat cycling and strain hardening experienced by the material; for the present study, a survey of SLM-related characterization studies [6,16,17,18,19,20,21,22,23,24,25] was conducted to collect experimentallyverified properties.The results are shown in Table 2; the shown properties are averages and were used as inputs into the FEA model.It should be noted that appropriate settings were pre-selected within the FEA software to account for heat of fusion and the gradients in material properties as the material is heated.

Experimental Design: Responses
Responses were chosen after group discussions about important part design parameters: 1.The in-process Von Mises stress near the laser melt spot but still in a non-molten area 2. The Von Mises stress 5mm away from the pool into the recently scanned area in order to read how the heat gradient affects the stress throughout the overhang 3. The Z-direction deformation of the material immediately surrounding the melt pool in order to deduce if enough stress was produced to plastically deform the part and introduce stresses 4. The Z-direction deformation at the furthest overhanging point on the feature from the melt pool in order to best understand the influence of any support material

Experimental Model
See Figures 2 and 3 for details of the geometry under study.The timedependent nature of the responses is converted to non-time-dependent by using the aforementioned FEA model to measure all of the responses at the same point in time in the printing.While this does not give a simulation of the SLM process as a function of time, it does allow all of the input factors and their interactions to be studied relative to the instantaneous responses and to each other; this allows the impact of each factor and each interaction on the responses to be captured, accomplishing the goals of this study.The most important assumption for this type of model is that the heat transfer and the material physics behave approximately the same in each layer of the part regardless of geometry, with the caveat that enough solid material exists beneath the layer in progress to effectively transfer the heat like a fin; this has been experimentally determined to be a minimum of 0.5-0.9mm[6,15] or approximately 10-15 layers.

Level of Significance
For the present study, a model adequacy level of significance of = 0.05 was chosen to be used to verify the ANOVA [26].A much more subjective decision is the selection of the level of significance for the ANOVA data, as this choice is based on the circumstances and goals of the experiment.The main purpose of the present study is to develop an engineering design tool, so it is imperative that the experiment provides the widest possible view of the process to designers.Therefore, it is vital to reduce the possibility of committing Type II errors; the probability of avoiding Type II errors is known as a power of the experiment.Increasing the power also increases the probability of making a Type I error (false acceptance of an insignificant factor), but this was judged acceptable for this experiment; any falsely accepted insignificant factors will remain insignificant and will not influence the outcome of the process, as the missing of a significant factor would in a major way.Therefore to reduce the possibility of false rejections to the lowest feasible level, it was decided to use a level of significance of = 0.25 for the ANOVA tests.

Experimental Runs
Following the basic set of assumptions and approximations for such an SLM model (as described in [3]), the numerical experiments to run.Loading the CAD model into the FEA software and applying the initial and boundary conditions were the first steps for each run.The experiment was run a total of 32 times each for the Ti-6Al-4V and 316L stainless steel materials, with the four responses gleaned for each run, for a total output of 256 data points.The planning, setup, execution, and data collection required approximately 80 hours to complete and were conducted over a period of three weeks.Two screenshots of the experiment during the execution phase in one of the runs are shown in Figure 4.The raw values of the responses from the experiment are shown in Figure 5.

Results and Analysis
Once the experiment was complete, the data (Figure 5) was checked for severe skewing and outliers and other indications that errors were made in the conduct and collection of the experiment.None were found, so the recorded data was divided into eight groups: one for each response for each material under study.Each of the eight subsets was then checked and subjected to a residual analysis using Minitab to verify the model adequacy and perform a preliminary check for significant factors and interactions.As shown, the model adequacy was immediately established in seven of the eight cases, while a Box-Cox transform was needed to show the adequacy of the model for the eighth case.A more detailed presentation of this technique and the procedure for model adequacy testing can be found in [3,26].Figure 6 shows the results of all eight of the ANOVAs that were conducted during the present study; the factors highlighted were the ones that had a significant influence on the particular response under study.

Discussion and Conclusions
In the present study, five SLM process input factors were studied to determine their influence upon each of four responses and two material cases for a 90-degree overhanging part feature.With the exception of the feature thickness factor, it was known at the beginning of the experiment that the chosen factors were likely to have significant influence on the generic SLM process from reviewed studies [6,15,27,28].The feature thickness was added because it was an obvious design consideration and had not been explored in any of the many studies reviewed by the authors.
The raw output values of the stress and deformation were reasonable and similar to those found in previous studies; four of the responses had equivalent conditions and responses in other studies including material choice, which aided in evaluation of the findings.These are shown in Figure 7.In all shown cases, the red bars indicate the range of values found in indicated previous studies [6,27] and the blue markers show the data taken in the present work.The use of supports in the present experiment has a clear influence, which is most obvious on Runs 17-32 in the comparisons with Kruth et al. [27].Note that the overhang geometry contains severe stress concentrations, so at in the overhang the stress readings will be significantly higher than they would be in a more generic geometry.Therefore, in order to compare the data with the studies in question, the raw values of the data were transformed by dividing them by the stress concentration factor, which was taken to be 2.5, which is an average textbook value for this kind of geometry.This way, the influence of the manufacturing process can be studied separate from the geometric influences and compared to experimental data fairly.This transform explains the difference between the stress data shown in Figure 5 with that in Figure 7.It should be re-stated that the goal of this experiment is not to collect technical or material process data but to provide a new perspective for designers and production managers to judge and evaluate the value of SLM within their production system.The purpose of analyzing technical data here is to provide further validation of the model and its relationship information.In practice, the model would be used to collect decision data primarily, in form of factors, interactions, and their p-values for comparison.
The following discussion addresses the experimental findings from this perspective and not from that of a specialized technical expert.There were five major findings from the present experiment: First was the fact that the feature thickness has a major influence on all of the responses, which had not been tested previously in other studies.The dominantly significant factor for an overhanging feature was its thickness.The second and most surprising of these findings was that the laser power had such a small influence upon the responses, where it only had any type of influence on the stress responses directly around the melt pool.
The third important finding in this study was the influence of the factor interactions.One of the major advantages of using full factorial experiments conduct this type of study is the ability to study the interactions between the factors, as well as the factors themselves.It is very clear from the findings of the present study that there are many significant interactions for each response; historically, this is not often considered in SLM studies, depriving a typical study of an extra dimension of view concerning SLM behavior.Using the ANOVA to determine significance weighed each interaction equally with each factor, demonstrating clearly that some of the interactions between factors can have much influence on the experiment and an interaction can be significant even of its constituents are not significant.The determination of all the important design inputs is important to the creation of a generalized DFM methodology for SLM and it is obvious that the interactions between factors, even insignificant factors, are worthy of much further study; in the present study, there were an average of 1.73 significant interactions per significant factor for Ti-6Al-4V and 3.8 per significant factor for 316L stainless steel.
The fourth major finding from this study was the large influence that specific material properties, particularly the yield and tensile strength, have on the stress and deformation responses from the overhanging feature.for the stainless steel shows a much larger difference between the melt pool stress and the central feature stress than what is seen for the titanium referring to Table 2, this difference in inversely proportional to the differences in yield and tensile strength for the two materials.A similar effect can be observed in the unsupported runs of the deformation responses (Figure 5).This is a very important consideration for designing for SLM, as the final part properties can vary significantly between processes and machines; the best example is the material properties collected in Table 2: in this case, the titanium alloy is actually more ductile on average than the stainless steel, while stainless steel is one of the most ductile engineering materials when bulk-formed.The effect of the material choice on the likelihood of having significant factor interactions is also shown in the results of Table 3: for the titanium alloy, the probability of a main effect being significant is 0.75, while the probability of an interaction being significant is 0.25; for the stainless steel, the probabilities are 0.50 and 0.37.
It is obvious that the information gathered and presented by this model is valuable to design engineers and production managers using or considering the use of SLM; it can be used for many other problems besides the design and production of overhanging features.This information would be very difficult and costly to extract out of a large series of specialized studies and to translate into a form that is useful in a business-industrial setting.Users of this technique will be able to quickly and easily examine or predict the outcomes of the SLM process in a way that is easily communicable with non-specialists.Further development of the method is needed, including comprehensive (and very expensive) experimental verification.

Figure 4 :
Figure 4: Example (L) deformation and (R) stress responses during experiment

Figure 6 :
Figure 6: ANOVA results and interactions

Table 1 :
Factors and levels

Table 2 :
Material properties used in model