Finite element–based numerical modeling framework for additive manufacturing process
2019; Wiley; Volume: 1; Issue: 1 Linguagem: Inglês
10.1002/mdp2.28
ISSN2577-6576
AutoresFarshid Hajializadeh, Ayhan Ince,
Tópico(s)Manufacturing Process and Optimization
ResumoMaterial Design & Processing CommunicationsVolume 1, Issue 1 e28 SPECIAL ISSUE ARTICLEFree Access Finite element–based numerical modeling framework for additive manufacturing process Farshid Hajializadeh, Farshid Hajializadeh Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, CanadaSearch for more papers by this authorAyhan Ince, Corresponding Author Ayhan Ince ayhan.ince@concordia.ca orcid.org/0000-0002-2892-8551 Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada Correspondence Ayhan Ince, Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada. Email: ayhan.ince@concordia.caSearch for more papers by this author Farshid Hajializadeh, Farshid Hajializadeh Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, CanadaSearch for more papers by this authorAyhan Ince, Corresponding Author Ayhan Ince ayhan.ince@concordia.ca orcid.org/0000-0002-2892-8551 Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada Correspondence Ayhan Ince, Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada. Email: ayhan.ince@concordia.caSearch for more papers by this author First published: 10 January 2019 https://doi.org/10.1002/mdp2.28Citations: 12AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Additive manufacturing (AM) process has extensively been used to fabricate metal parts for large variety of applications. Residual stresses are inevitable in the AM process since material experiences heating and cooling cycles. Implementing finite element (FE) analysis tool to predict residual stress distributions could be of great importance in many applications. Developing an FE-based modeling framework to accurately simulate residual stresses in a reasonably reduced computational time is highly needed. The FE-based modeling approach presented here to simulate direct metal deposition (DMD) of AISI 304 L aims to significantly reduce computation cost by implementing an adaptive mesh coarsening algorithm integrated with the FE method. Simulations were performed by the proposed approach, and the results were found in good agreement with conventional fine mesh configuration. The proposed modeling framework offers a potential solution to substantially reduce the computational time for simulating the AM process. 1 INTRODUCTION The additive manufacturing (AM) process refers to repeated addition of material onto an existing substrate which has already been deposited or existed as the base. This method has been used for fabricating and forming net and near net shape components for different industries such as aerospace, biomedical, and automobile applications. The AM process normally includes the heating, melting, and solidification cycles of a material in the form of a feeding wire or powder using an electron or laser beam which provides high density energy to melt the material in a fraction of time. Basically, the AM processes resemble the multi-pass welding methods that were extensively studied and reported in the literature to join metallic parts, and they also have inherited most of their features.1-3 Commercial finite element-based packages were developed by different companies in order to simulate welding processes and study different parameters that have significant impact on the geometrical distortions of the weld joints.4 Cyclic heating and cooling of material may impose significant distortions that eventually results in formation of residual stresses in the AM parts; as it is seen in the welding process of metallic alloys.5, 6 The temperature history evaluation during the deposition of material is a very complex phenomenon and directly affects the whole modeling procedure.7, 8 A number of researchers have focused on the thermal source modeling and its effects on the temperature distribution around the scanning line.8-10 As it has been widely reported in the literature, the tensile residual stresses have detrimental effects on the fatigue performance of a structural component. A component produced using welding and the AM process are regarded to have degraded fatigue performance compared with parts produced by conventional manufacturing methods such as machining and forging. Furthermore, the formation of residual stresses deteriorates the corrosion resistance of the material in corrosive environment. Therefore, it is crucial to evaluate the extent of the residual stresses induced inside of an additively manufactured component.11 The AM process involves a very large number of parameters that have significant impact on the properties of the manufactured part related to the material properties, boundary conditions, and geometry complexities of the component as well as the deposition features.10, 11 Implementing experimental procedures to determine impact of every variable on the distortion and residual stress distribution inside the built medium appears to be very expensive and also requires enormous time and effort. Therefore, numerical analysis methods such as a finite element (FE) method offer a very suitable alternative in order to measure and quantify the effect of process parameters. In the recent decades, different strategies and procedure have been introduced to investigate the thermomechanical phenomena during welding and AM processes.12-18 Generally, the FE analysis of a thermomechanical process includes thermal analysis and introduces the temperature history to the mechanical, ie, structural analysis as the thermal load which is known as weakly coupled or uncoupled method. In this approach, the mechanical response has no impact on the thermal behavior or response of the material. On the other hand, the FE analysis of a thermomechanical process can also be accomplished by implementing fully coupled approach, which takes into account all the effects of the structural response on the thermal properties' variations. The latter is considered to be more accurate representation of the AM process. However, implementing the fully coupled approach increases the computational time and cost considerably by about four to five times which is not considered as beneficial in the numerical modeling approach.12 A simplified method known as the inherent strain method was proposed by Ueda19 in order to evaluate the residual stresses and distortions in the welded joints in a short period of time compared with conventional FE analysis. The aforementioned method was also implemented in simulating the powder-bed fusion applications.20 The drawback of the aforementioned method is that it cannot take into account the effect of different laser scanning paths and geometrical effects since the inherent strain is constant across the whole volume.21 Bugattin and Semeraro22 reported that even though employing the inherent strain method demonstrated very high potential in evaluating the residual stresses and distortions of a specific geometry in AM processes, the calibration strategy fails to predict the distortion and consequently the residual stress of different geometries. In spite of the material-built process similarity with multi-pass welding, the AM process requires additional considerations unlike multi-pass welding. In welding, it is usually assumed that the material already exists ahead of the heat source. However, in the AM process modeling, the material is added in every increment simultaneously with motion of the heat source which is known as the element activation procedure. The element activation mostly includes three main methods: quiet element, inactive element, and hybrid activation methods. More details on these approaches could be found in Denlinger et al.13 In the present study, the hybrid element activation method is adopted to deal with deposition of the material in every single increment for different layers since it inheres advantageous of the other approaches. The main drawback of implementing the FE analysis in modeling the AM processes is its high computational cost and time. In order to get accurate results, the mesh used for thermal and mechanical analysis has to be fine enough that could capture the high temperature gradients and consequently high stress gradients during deposition. Therefore, an adaptive mesh-based modeling framework is introduced in the present study to reduce computational time while obtaining accurate results in the ABAQUS software package. The adaptive meshing procedure is represented, and the results are compared with the conventional FE analysis. 2 MODELING APPROACH FOR SIMULATING ADDITIVE MANUFACTURING PROCESS The FE analysis approach to simulate direct metal deposition (DMD) of AISI 304 L is briefly reviewed and the material properties and procedure of the proposed modeling approach is presented. The FE analysis of the AM process should provide accurate simulation results in order to capture high stress gradients with a minimum possible run time. The adaptive mesh-based modeling procedure is accomplished based on a layer-by-layer mesh coarsening concept. The material is added on the substrate with a very fine mesh, then in the next steps, mesh of the deposited layer is coarsened to lower the number of elements (or degrees of freedoms) of the entire model. Afterwards, results obtained from previous fine meshed layer(s) is systematically imposed to the new model upon which a deposition of the new layer to be built. 2.1 Thermal analysis The modeling framework developed here begins with a thermal analysis of the deposited layer using a fine mesh in ABAQUS/STANDARD. Temperature-dependent thermal properties are introduced into the model to realistically simulate the heat transfer process using UMATHT subroutine. The hybrid element activation approach was implemented in UMATHT subroutine which limits the heat flow induced by the heat source to only those elements that are in contact/passed by with the heat source by putting the heat conductivity of the material to zero. The thermal properties of the AISI 304 L were given in Table 1. Table 1. Thermal and mechanical properties15 of AISI 304 L Temperature, °C Specific Heat, J·kg·°C Conductivity, J·m·°C Thermal Expansion, ×10−5/°C Yield Stress, MPa Young Modulus, GPa 20 462 14.6 1.70 319 198.5 100 496 15.1 1.74 279 193 200 512 16.1 1.80 238 185 300 525 17.9 1.86 217 176 400 540 18.0 1.91 198 167 600 577 20.8 1.96 177 159 800 604 23.9 2.02 112 151 1200 676 32.2 2.07 32 60 1300 692 33.7 2.11 19 20 1480 700 120 2.16 8 10 Goldak double-ellipsoid heat source model was also implemented using DFLUX subroutine to apply the body heat flux into the depositing material16 as shown in Equation 1: (1)where P is the source power; η is the efficiency; a, b, and c are the dimensions of the ellipsoid; x, y, and z are coordinate system variables of the heat source center; vx is the traverse speed of the heat source in x-direction, and t is time. The thermal boundary conditions were assumed to have an accumulative coefficient of 10 W·m2·K, based on the simulations performed in the literature.16 The energy loss due to the radiation heat transfer was ignored for the analysis. 2.2 Mechanical (structural) analysis The thermal history of the nodes obtained from the heat transfer analysis is applied to the mechanical analysis to evaluate the residual stress distribution after each built layer. The temperature-dependent material properties for AISI 304 L are given in Table 1. The UMAT subroutine was developed to account for the element activation and introduce the temperature-dependent material definition. The scaling factor of KE = 10−12 was considered to scale down the Young modulus for inactive elements. Furthermore, the Von Mises isotropic plasticity was considered in the subroutine UMAT and UHARD. A constant Poisson ratio of 0.3 and material density of 7800 (kg/m3) were considered for analysis. 2.3 Adaptive mesh-based modeling framework Adaptive mesh coarsening technique during the analysis of the already deposited layers is not supported in the ABAQUS software package. Indeed, there are available options for mesh refinement in ABAQUS such as adaptive meshing and ALE method.14 However, these techniques cannot be applied to the thermomechanical analysis, especially, when the weakly coupled approach is adopted. The ABAQUS has also developed a useful tool called solution mapping that can only be used for mesh refinement manually when the present mesh is incapable of handling high distortions. However, the solution mapping cannot be applied to AM process simulations due to the continuous addition of material to the built part.14 Therefore, a modeling framework in Python script was developed to implement the proposed adaptive mesh coarsening in the AM processes. The mesh coarsening modeling approach is performed in a layer-by-layer, as the AM process itself. After mechanical analysis for a particular layer, eg, the first layer is completed, the developed Python code is run to map the results of the fine mesh to the coarser mesh. The mapping process begins with extrapolating the solution results to the nodal point of the fine mesh. Then, based on spatial locations of nodes of coarse mesh, the results are interpolated to the nodes of the coarse mesh. Afterwards, the values for stress and strain tensor are interpolated to the integration point of elements in the coarse mesh configuration using a linear shape function. Afterwards, the field values, eg, stress components, are imported as predefined field variables for those coarsened layers, then, the new layer deposition begins. Based on the temperature or stress gradients, the coarsening technique can be adjusted to be performed in certain intervals. If the temperature during the deposition is so high that could melt the deposited layers, the coarsening better begins from the third layer or even fourth layer deposition keeping the top deposited layers with fine mesh to be able to handle the high temperature or stress gradients. A schematic representation for implementing adaptive mesh coarsening technique in the present study is illustrated in Figure 1. Figure 1Open in figure viewerPowerPoint A, Schematic representation of analysis sequences and B, sequence of finite element approach for adaptive mesh-based modeling 3 RESULTS AND DISCUSSION An 18-layer L-shape part made from AISI 304 L was built using both the conventional and adaptive mesh-based models in order to assess the capability and accuracy of the proposed approach. Both models were generated with the same thermal and mechanical features and also the same process parameters. Each L-shape layer with length of equally 12 (mm) and thickness and width of 1 (mm) was built using laser power of 250 (W), beam radius of 0.5 (mm), and traverse speed of 11.25 (mm/s). All the layers were built considering a cooling time approximately equal to deposition time of each layer. The adaptive meshing is used in four steps to coarsen the fine mesh (five elements in thickness) to coarse mesh (three elements in thickness) of each layer. Eight-node linear heat transfer and structural brick element were used for thermal and structural analysis, respectively. The bottom layer is fixed to act as a substrate for the model. Figures 2 and 3 represent S11 (or σxx) and S22 (or σyy) contour for the coarsened and fine meshes, respectively. The numbers 1, 2, and 3 correspond to X, Y, and Z directions in the global coordinate system, respectively. The adaptive meshing on areas with consistent stress distribution demonstrates reasonable performance shown in Figures 2 and 3. The stress pattern remains almost the same for those areas, and the stress values are also found to be very close to the fine mesh ones. On the other hand, very local stresses with high stress gradients do not show mapping capability since the new coarse mesh is incapable of capturing very localized stress gradients. The S11 is almost near zero (−58 to 58 MPa) for both approaches in the middle of the wall. However, stress distribution in the stacking direction (S22) illustrates high compressive values which could be important in fatigue performance of the AM processed parts. Figure 2Open in figure viewerPowerPoint S11 contour of A, coarsened and B, fine mesh of modeling 18-layer AISI 304 L Figure 3Open in figure viewerPowerPoint S22 contour of A, coarsened and B, fine mesh of modeling 18-layer AISI 304 L Another important factor that justifies using the adaptive meshing in modeling of AM process is the computation run time for the FE model. Analysis were performed by a Core i7 desktop PC with 16 GB RAM. Table 2 represents the significant difference in the computation run time of the fine uniform mesh and adaptive mesh. It shows that the analysis time to achieve an 18-layer build with the fine uniform mesh is almost three times the time required for adaptive mesh approach. It should be noted that adaptive meshing run time converges to a specific value after several pairs of layers. This could be beneficial especially when dealing with the simulation of a very large component. The total mapping time of approximately 2 hours is added upon the computational time for the coarsening approach. Table 2. Comparison of run time between fine mesh and adaptive mesh. Layer No. 1-3 4-6 7-9 10-12 13-15 16-18 Total Coarsening approach Run time, h 1:50 2:35 3:20 3:50 4:15 4:20 20:10 + 2:00 (mapping time) Layer No. 1-18 Fine mesh Run time, h 58:30 58:30 4 CONCLUSION In this study, a new modeling framework for implementing coarsening approach in simulation of the AM processes was presented. The simulation results showed that the adaptive mesh coarsening approach is capable of capturing very important aspects of the AM parts regarding the formation and distribution of compressive and tensile stresses in the body of the component. Furthermore, the results showed significant improvement of the computation time in comparison to the conventional FE analysis. CONFLICT OF INTEREST Farshid Hajializadeh and Ayhan Ince declare that they have no conflict of interest. REFERENCES 1Chiumenti M, Cervera M, Salmi A, Agelet de Saracibar C, Dialami N, Matsui K. Finite element modeling of multi-pass welding and shaped metal deposition processes. 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