The objective of this work is to provide experimental validation of the graph theory approach for predicting the thermal history in additively manufactured parts that was recently published in the ASME transactions. In the present paper the graph theory approach is validated with insitu infrared thermography data in the context of the laser powder bed fusion (LPBF) additive manufacturing process. We realize this objective through the following three tasks. First, two types of test parts (stainless steel) are made in two corresponding build cycles on a Renishaw AM250 LPBF machine. The intent of both builds is to influence the thermal history of the part by changing the cooling time between melting of successive layers, called interlayer cooling time. Second, layerwise thermal images of the top surface of the part are acquired using an insitu a priori calibrated infrared camera. Third, the thermal imaging data obtained during the two builds were used to validate the graph theorypredicted surface temperature trends. Furthermore, the surface temperature trends predicted using graph theory are compared with results from finite element analysis. As an example, for one the builds, the graph theory approach accurately predicted the surface temperature trends to within 6% mean absolute percentage error, and approximately 14 Kelvin root mean squared error of the experimental data. Moreover, using the graph theory approach the temperature trends were predicted in less than 26 minutes which is well within the actual build time of 171 minutes.
more » « less NSFPAR ID:
 10219742
 Date Published:
 Journal Name:
 ASME Manufacturing Science and Engineering Conference
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract The objective of this work is to provide experimental validation of the graph theory approach for predicting the thermal history in additively manufactured parts that was recently published in these transactions. In the present paper the graph theory approach is validated with insitu infrared thermography data in the context of the laser powder bed fusion (LPBF) additive manufacturing process. We realize this objective through the following three tasks. First, two types of test parts (stainless steel) are made in two corresponding build cycles on a Renishaw AM250 LPBF machine. The intent of both builds is to influence the thermal history of the part by changing the cooling time between melting of successive layers, called interlayer cooling time. Second, layerwise thermal images of the top surface of the part are acquired using an insitu a priori calibrated infrared camera. Third, the thermal imaging data obtained during the two builds were used to validate the graph theorypredicted surface temperature trends. Furthermore, the surface temperature trends predicted using graph theory are compared with results from finite element analysis. As an example, for one the builds, the graph theory approach accurately predicted the surface temperature trends to within 6% mean absolute percentage error, and approximately 14 Kelvin root mean squared error of the experimental data. Moreover, using the graph theory approach the temperature trends were predicted in less than 26 minutes which is well within the actual build time of 171 minutes.more » « less

null (Ed.)Despite its potential to overcome the design and processing barriers of traditional subtractive and formative manufacturing techniques, the use of laser powder bed fusion (LPBF) metal additive manufacturing is currently limited due to its tendency to create flaws. A multitude of LPBFrelated flaws, such as partlevel deformation, cracking, and porosity are linked to the spatiotemporal temperature distribution in the part during the process. The temperature distribution, also called the thermal history, is a function of several factors encompassing material properties, part geometry and orientation, processing parameters, placement of supports, among others. These broad range of factors are difficult and expensive to optimize through empirical testing alone. Consequently, fast and accurate models to predict the thermal history are valuable for mitigating flaw formation in LPBFprocessed parts. In our prior works, we developed a graph theorybased approach for predicting the temperature distribution in LPBF parts. This meshfree approach was compared with both nonproprietary and commercial finite element packages, and the thermal history predictions were experimentally validated with in situ infrared thermal imaging data. It was found that the graph theoryderived thermal history predictions converged within 30–50% of the time of nonproprietary finite element analysis for a similar level of prediction error. However, these prior efforts were based on small prismatic and cylindershaped LPBF parts. In this paper, our objective was to scale the graph theory approach to predict the thermal history of large volume, complex geometry LPBF parts. To realize this objective, we developed and applied three computational strategies to predict the thermal history of a stainless steel (SAE 316L) impeller having outside diameter 155 mm and vertical height 35 mm (700 layers). The impeller was processed on a Renishaw AM250 LPBF system and required 16 h to complete. During the process, insitu layerbylayer steady state surface temperature measurements for the impeller were obtained using a calibrated longwave infrared thermal camera. As an example of the outcome, on implementing one of the three strategies reported in this work, which did not reduce or simplify the part geometry, the thermal history of the impeller was predicted with approximate mean absolute error of 6% (standard deviation 0.8%) and root mean square error 23 K (standard deviation 3.7 K). Moreover, the thermal history was simulated within 40 min using desktop computing, which is considerably less than the 16 h required to build the impeller part. Furthermore, the graph theory thermal history predictions were compared with a proprietary LPBF thermal modeling software and nonproprietary finite element simulation. For a similar level of root mean square error (28 K), the graph theory approach converged in 17 min, vs. 4.5 h for nonproprietary finite element analysis.more » « less

Purpose The purpose of this paper is to develop, apply and validate a meshfree graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach In this study, the authors develop a novel meshfree graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti6Al4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications This study uses data from fixed thermocouples when printing thinwall DED parts. In the future, the authors will incorporate infrared thermal camera data from large parts. Practical implications The DED process is particularly valuable for nearnet shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation. Originality/value This paper presents a new meshfree computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.more » « less

The goal of this work is to predict the effect of part geometry and process parameters on the instantaneous spatiotemporal distribution of temperature, also called the thermal field or temperature history, in metal parts as they are being built layerbylayer using additive manufacturing (AM) processes. In pursuit of this goal, the objective of this work is to develop and verify a graph theorybased approach for predicting the temperature distribution in metal AM parts. This objective is consequential to overcome the current poor process consistency and part quality in AM. One of the main reasons for poor part quality in metal AM processes is ascribed to the nature of temperature distribution in the part. For instance, steep thermal gradients created in the part during printing leads to defects, such as warping and thermal stressinduced cracking. Existing nonproprietary approaches to predict the temperature distribution in AM parts predominantly use meshbased finite element analyses that are computationally tortuous—the simulation of a few layers typically requires several hours, if not days. Hence, to alleviate these challenges in metal AM processes, there is a need for efficient computational models to predict the temperature distribution, and thereby guide part design and selection of process parameters instead of expensive empirical testing. Compared with finite element analyses techniques, the proposed meshfree graph theorybased approach facilitates prediction of the temperature distribution within a few minutes on a desktop computer. To explore these assertions, we conducted the following two studies: (1) comparing the heat diffusion trends predicted using the graph theory approach with finite element analysis, and analytical heat transfer calculations based on Green’s functions for an elementary cuboid geometry which is subjected to an impulse heat input in a certain part of its volume and (2) simulating the laser powder bed fusion metal AM of threepart geometries with (a) Goldak’s moving heat source finite element method, (b) the proposed graph theory approach, and (c) further comparing the thermal trends predicted from the last two approaches with a commercial solution. From the first study, we report that the thermal trends approximated by the graph theory approach are found to be accurate within 5% of the Green’s functionsbased analytical solution (in terms of the symmetric mean absolute percentage error). Results from the second study show that the thermal trends predicted for the AM parts using graph theory approach agree with finite element analyses, and the computational time for predicting the temperature distribution was significantly reduced with graph theory. For instance, for one of the AM part geometries studied, the temperature trends were predicted in less than 18 min within 10% error using the graph theory approach compared with over 180 min with finite element analyses. Although this paper is restricted to theoretical development and verification of the graph theory approach, our forthcoming research will focus on experimental validation through inprocess thermal measurements.more » « less

Abstract The goal of this work is to predict the effect of part geometry and process parameters on the instantaneous spatial distribution of heat, called the heat flux or thermal history, in metal parts as they are being built layerbylayer using additive manufacturing (AM) processes. In pursuit of this goal, the objective of this work is to develop and verify a graph theorybased approach for predicting the heat flux in metal AM parts. This objective is consequential to overcome the current poor process consistency and part quality in AM. One of the main reasons for poor part quality in metal AM processes is ascribed to the heat flux in the part. For instance, constrained heat flux because of illconsidered part design leads to defects, such as warping and thermal stressinduced cracking. Existing nonproprietary approaches to predict the heat flux in AM at the partlevel predominantly use meshbased finite element analyses that are computationally tortuous — the simulation of a few layers typically requires several hours, if not days. Hence, to alleviate these challenges in metal AM processes, there is a need for efficient computational thermal models to predict the heat flux, and thereby guide part design and selection of process parameters instead of expensive empirical testing. Compared to finite element analysis techniques, the proposed meshfree graph theorybased approach facilitates layerbylayer simulation of the heat flux within a few minutes on a desktop computer. To explore these assertions we conducted the following two studies: (1) comparing the heat diffusion trends predicted using the graph theory approach, with finite element analysis and analytical heat transfer calculations based on Green’s functions for an elementary cuboid geometry which is subjected to an impulse heat input in a certain part of its volume, and (2) simulating the layerbylayer deposition of three part geometries in a laser powder bed fusion metal AM process with: (a) Goldak’s moving heat source finite element method, (b) the proposed graph theory approach, and (c) further comparing the heat flux predictions from the last two approaches with a commercial solution. From the first study we report that the heat flux trend approximated by the graph theory approach is found to be accurate within 5% of the Green’s functionsbased analytical solution (in terms of the symmetric mean absolute percentage error). Results from the second study show that the heat flux trends predicted for the AM parts using graph theory approach agrees with finite element analysis with error less than 15%. More pertinently, the computational time for predicting the heat flux was significantly reduced with graph theory, for instance, in one of the AM case studies the time taken to predict the heat flux in a part was less than 3 minutes using the graph theory approach compared to over 3 hours with finite element analysis. While this paper is restricted to theoretical development and verification of the graph theory approach for heat flux prediction, our forthcoming research will focus on experimental validation through inprocess sensorbased heat flux measurements.