1. Introduction

Additive manufacturing is a 3D manufacturing process able to produce prototypes directly from a CAD file. Powder bed fusion (PBF) processes were, among others, the first commercialized AM processes. Nowadays, the most important powder bed fusion process is selective

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

Since the attention of this chapter is mainly focused on SLM, the only full melting mechanism will be considered in detail. Full melting is indeed the mechanism most commonly associated with PBF processing of engineering metal alloys. In SLM, the entire region of material subjected to the heat source is melted to a depth exceeding the layer thickness. The thermal energy of subsequent scans of a laser is typically sufficient to remelt a portion of the previously solidified material. As a consequence, this type of melting is very effective at creating well-

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Use of optimum process parameters is extremely important for producing satisfactory parts using PBF processes. Among them, special attention must be paid to the scanning strategy, viz. the movements applied by the laser on the powder surface. The path followed by the laser greatly influences the surface heat distribution, as it is responsible for highly localized temperature peaks. Scanning often occurs in two modes, contour and fill mode, as shown in

In contour mode, the outline of the part cross-section is scanned. This is typically done for surface finishing reasons around the perimeter. The rest of the cross-section is then scanned using a raster technique, whereby one axis is incrementally moved across the part being formed and the other axis is continuously swept back and forth. The contour can be scanned

bonded, high-density structures.

Figure 2. An example of scanning strategy: fill mode and contour mode.

Figure 2.

Figure 1. Schematic drawing of SLM process.

laser melting (SLM). Its basic method of operation is schematically shown in Figure 1 and, generally, all other powder bed fusion processes follow the same basic approach.

The process fuses thin layers (typically 30÷60 μm thick) of metallic powder, which has been spread across the build area using a powder depositor and a leveler (wiper). The building area is enclosed in a chamber filled with inert gas to minimize oxidation and degradation of the powdered material. The base plate is heated in order to maintain the powder and the fabricated component at high temperature. Sometimes, infrared heaters are placed above the build platform to increase the temperature around the part being formed. The temperature within the chamber must be controlled to minimize the laser power requirements of the process (when preheating, less laser energy is required for fusion) and to prevent warping of the part due to non-uniform thermal expansion (curling).

Once the layer has been deposited and adjusted by the wiper, a laser beam is directed onto the powder bed and is moved using galvanometers in such a way that it thermally fuses the material to form the slice cross-section. Surrounding powder remains loose and serves as a support for subsequent layer deposition. After completing a layer, the build platform (base plate) is lowered and a new layer is laid. The beam scans the subsequent slice cross-section and the process repeats until the complete part is built. A cool-down period is typically required to allow the parts to uniformly achieve an adequately low temperature to be handled and exposed to ambient atmosphere. Finally, the parts are removed from the powder bed, loose powder is cleaned off the parts, and further finishing operations, if necessary, are performed.

Since the introduction of PBF, each new technology developer has introduced competing terminology to describe the mechanism by which fusion occurs, with variants of sintering and melting being the most popular. However, the use of a single word to describe the powder fusion mechanism is problematic as multiple mechanisms are possible. There are four different fusion mechanisms that are present in PBF processes. These include solid-state sintering, chemically-induced binding, liquid-phase sintering, and full melting [1, 2].

Since the attention of this chapter is mainly focused on SLM, the only full melting mechanism will be considered in detail. Full melting is indeed the mechanism most commonly associated with PBF processing of engineering metal alloys. In SLM, the entire region of material subjected to the heat source is melted to a depth exceeding the layer thickness. The thermal energy of subsequent scans of a laser is typically sufficient to remelt a portion of the previously solidified material. As a consequence, this type of melting is very effective at creating wellbonded, high-density structures.

Use of optimum process parameters is extremely important for producing satisfactory parts using PBF processes. Among them, special attention must be paid to the scanning strategy, viz. the movements applied by the laser on the powder surface. The path followed by the laser greatly influences the surface heat distribution, as it is responsible for highly localized temperature peaks. Scanning often occurs in two modes, contour and fill mode, as shown in Figure 2.

In contour mode, the outline of the part cross-section is scanned. This is typically done for surface finishing reasons around the perimeter. The rest of the cross-section is then scanned using a raster technique, whereby one axis is incrementally moved across the part being formed and the other axis is continuously swept back and forth. The contour can be scanned

Figure 2. An example of scanning strategy: fill mode and contour mode.

laser melting (SLM). Its basic method of operation is schematically shown in Figure 1 and,

The process fuses thin layers (typically 30÷60 μm thick) of metallic powder, which has been spread across the build area using a powder depositor and a leveler (wiper). The building area is enclosed in a chamber filled with inert gas to minimize oxidation and degradation of the powdered material. The base plate is heated in order to maintain the powder and the fabricated component at high temperature. Sometimes, infrared heaters are placed above the build platform to increase the temperature around the part being formed. The temperature within the chamber must be controlled to minimize the laser power requirements of the process (when preheating, less laser energy is required for fusion) and to prevent warping of the part

Once the layer has been deposited and adjusted by the wiper, a laser beam is directed onto the powder bed and is moved using galvanometers in such a way that it thermally fuses the material to form the slice cross-section. Surrounding powder remains loose and serves as a support for subsequent layer deposition. After completing a layer, the build platform (base plate) is lowered and a new layer is laid. The beam scans the subsequent slice cross-section and the process repeats until the complete part is built. A cool-down period is typically required to allow the parts to uniformly achieve an adequately low temperature to be handled and exposed to ambient atmosphere. Finally, the parts are removed from the powder bed, loose powder is cleaned off the parts, and further finishing operations, if necessary, are performed. Since the introduction of PBF, each new technology developer has introduced competing terminology to describe the mechanism by which fusion occurs, with variants of sintering and melting being the most popular. However, the use of a single word to describe the powder fusion mechanism is problematic as multiple mechanisms are possible. There are four different fusion mechanisms that are present in PBF processes. These include solid-state sintering,

chemically-induced binding, liquid-phase sintering, and full melting [1, 2].

generally, all other powder bed fusion processes follow the same basic approach.

due to non-uniform thermal expansion (curling).

Figure 1. Schematic drawing of SLM process.

124 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

either before or after the cross-section, depending on the surface characteristics of the part being done. Multiple scanning strategies are available for the fill section as shown in Figure 3.

behavior of the molten pool is one of the most critical factors influencing the reliability of the part, as it affects geometrical accuracy, material properties, and residual stresses. In addition, the heat exchange between laser and powder is a very complex process that involves a lot of variables. Despite direct measurements of the thermal field are available, this is not enough to fully understand the molten pool behavior. Finite element analysis (FEA) is a powerful tool to gather

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The first studies about numerical simulation applied to PBF were developed during the 1990s of the last century. In 1998, Williams and Deckard [4] were the first that setup a framework for the numerical analysis applied to PBF. The numerical model was able to study the effects of process parameters on the selective laser sintering (SLS). Afterward, Shiomi and Yoshidome proposed a model where melting and solidifying process could be studied, using FE analysis [5]. In this chapter, the behavior of a molten pool due to a single laser spot is considered. The laser works in pulse mode and the melted part of the powder are assumed to change into a sphere that increases the dimensions after each pulsed irradiation. Fisher and Romano [6] investigated the variation in sintering process using pulse and continuous heat source. They noticed that during continuous wave interaction, the grains are homogeneously heated (the authors use an analogy to distinguish between different heating: they say that with homogeneously heating, the grains are cooked), while during pulsed laser interaction, the heating is no longer homogeneous (the grains are roasted). As mentioned before, the interaction of laser radiation with powder bed is a very complex mechanism greatly responsible for the mechanical characteristics of the final product. Gusarov et al. made a great effort in developing a numerical model that is able to simulate the heat transfer between laser and powder [7, 8]. It is worth mentioning that all the new models developed for the SLM simulation always refer to the models that have just been developed for the welding process [9] inasmuch SLM can be considered as a series of micro welding processes. Among all the numerical frameworks proposed in the literature, it seems that the most powerful tool for the process simulation is the finite element method. The first example of 3D finite element analysis is the paper of Contuzzi and Campanelli [10]. The aim of this study is to evaluate the temperature evolution in a 3D part being formed with SLM process. The molten liquid phase is considered by introducing the specific latent heat while the thermal properties are kept constant, aiming to reduce the computational cost of the analysis. The model proposed by Kolossov and Boillat [11] instead, allows for the nonlinear behavior of thermal conductivity and specific heat due to the temperature change and phase transformation. Introducing nonlinear behavior for the material increases the reliability of the simulation. However, the measurements of the thermal properties are greatly affected by uncertainty. The thermal properties can be directly measured [12–14] or calculated with thermal models [15]. A more precise thermal conductivity of the powder bed, named effective thermal conductivity, can be calculated using the relation proposed by Dai and Shaw [16]. Their model encompasses the effect of temperature- and porosity-dependent thermal conduction and radiation as well as the temperature-dependent natural convection. Not only material properties but also heat source definitions greatly affect the numerical results. Hashemzadeh and Chen [17] collected a variety of heat distributions that can be used to model the heat exchange. Articles [11] and [18] are an example where the heat source can be

more information about the process [3].

Since high thermal gradients result in large residual stresses, a great effort must be made to well define the movement of the heat source on the surface. The choice of the path is not unique and it must be done trying to find the most suitable one depending on the cross-section characteristics. Moreover, the scan strategy rotates at each subsequent layer as it is explained in Figure 4.

The rotation helps to balance the temperature of the working area. Despite the rotation, the path increment in horizontal direction remains constant and opposite to the gas flux. Consequently, the working area is kept clean because the melting slags drop far from the loose powder. The user can set the rotation angle. The angle used in this study has been suggested by the machine manufacturer and it is equal to 67, so the rotation scheme repeats every 180 layers.

Nowadays, SLM specifically permits to manufacture highly customized products that are almost ready to use rather than mere prototypes. An object with very complex shape, which is almost impossible to produce with traditional technologies, can be easily created saving cost and time. Despite the benefit, these manufacturing processes are very problematic to control because of the high number of involved parameters. The numerical simulation helps to reduce the number of experimental trial-and-error tests necessary to optimize the process, minimizing the time and cost of manufacture of the final product while maintaining its quality unmodified. The thermal

Figure 3. The four different scanning strategies: meander, stripes, chess, and contour.

Figure 4. The meander path rotation and the oriented path progress.

behavior of the molten pool is one of the most critical factors influencing the reliability of the part, as it affects geometrical accuracy, material properties, and residual stresses. In addition, the heat exchange between laser and powder is a very complex process that involves a lot of variables. Despite direct measurements of the thermal field are available, this is not enough to fully understand the molten pool behavior. Finite element analysis (FEA) is a powerful tool to gather more information about the process [3].

either before or after the cross-section, depending on the surface characteristics of the part being done. Multiple scanning strategies are available for the fill section as shown in Figure 3. Since high thermal gradients result in large residual stresses, a great effort must be made to well define the movement of the heat source on the surface. The choice of the path is not unique and it must be done trying to find the most suitable one depending on the cross-section characteristics. Moreover, the scan strategy rotates at each subsequent layer as it is explained in

126 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

The rotation helps to balance the temperature of the working area. Despite the rotation, the path increment in horizontal direction remains constant and opposite to the gas flux. Consequently, the working area is kept clean because the melting slags drop far from the loose powder. The user can set the rotation angle. The angle used in this study has been suggested by the machine

Nowadays, SLM specifically permits to manufacture highly customized products that are almost ready to use rather than mere prototypes. An object with very complex shape, which is almost impossible to produce with traditional technologies, can be easily created saving cost and time. Despite the benefit, these manufacturing processes are very problematic to control because of the high number of involved parameters. The numerical simulation helps to reduce the number of experimental trial-and-error tests necessary to optimize the process, minimizing the time and cost of manufacture of the final product while maintaining its quality unmodified. The thermal

manufacturer and it is equal to 67, so the rotation scheme repeats every 180 layers.

Figure 3. The four different scanning strategies: meander, stripes, chess, and contour.

Figure 4. The meander path rotation and the oriented path progress.

Figure 4.

The first studies about numerical simulation applied to PBF were developed during the 1990s of the last century. In 1998, Williams and Deckard [4] were the first that setup a framework for the numerical analysis applied to PBF. The numerical model was able to study the effects of process parameters on the selective laser sintering (SLS). Afterward, Shiomi and Yoshidome proposed a model where melting and solidifying process could be studied, using FE analysis [5]. In this chapter, the behavior of a molten pool due to a single laser spot is considered. The laser works in pulse mode and the melted part of the powder are assumed to change into a sphere that increases the dimensions after each pulsed irradiation. Fisher and Romano [6] investigated the variation in sintering process using pulse and continuous heat source. They noticed that during continuous wave interaction, the grains are homogeneously heated (the authors use an analogy to distinguish between different heating: they say that with homogeneously heating, the grains are cooked), while during pulsed laser interaction, the heating is no longer homogeneous (the grains are roasted). As mentioned before, the interaction of laser radiation with powder bed is a very complex mechanism greatly responsible for the mechanical characteristics of the final product. Gusarov et al. made a great effort in developing a numerical model that is able to simulate the heat transfer between laser and powder [7, 8]. It is worth mentioning that all the new models developed for the SLM simulation always refer to the models that have just been developed for the welding process [9] inasmuch SLM can be considered as a series of micro welding processes. Among all the numerical frameworks proposed in the literature, it seems that the most powerful tool for the process simulation is the finite element method. The first example of 3D finite element analysis is the paper of Contuzzi and Campanelli [10]. The aim of this study is to evaluate the temperature evolution in a 3D part being formed with SLM process. The molten liquid phase is considered by introducing the specific latent heat while the thermal properties are kept constant, aiming to reduce the computational cost of the analysis. The model proposed by Kolossov and Boillat [11] instead, allows for the nonlinear behavior of thermal conductivity and specific heat due to the temperature change and phase transformation. Introducing nonlinear behavior for the material increases the reliability of the simulation. However, the measurements of the thermal properties are greatly affected by uncertainty. The thermal properties can be directly measured [12–14] or calculated with thermal models [15]. A more precise thermal conductivity of the powder bed, named effective thermal conductivity, can be calculated using the relation proposed by Dai and Shaw [16]. Their model encompasses the effect of temperature- and porosity-dependent thermal conduction and radiation as well as the temperature-dependent natural convection. Not only material properties but also heat source definitions greatly affect the numerical results. Hashemzadeh and Chen [17] collected a variety of heat distributions that can be used to model the heat exchange. Articles [11] and [18] are an example where the heat source can be easily modeled as a 2D flux applied on the powder surface, neglecting the effect of the laser penetration into the powder. Li and Wang [19] explained how a 3D heat flux can be modeled in order to improve the numerical results related to the molten pool depth. Despite the great accuracy of all the previous models, results coming from the numerical simulations are slightly different from the experimental evidence. This is due to the high complexity of the physics involved in SLM and indeed to a large number of simplifications needed to simulate the process. Hu and Kovacevic [18] tried to reduce the mismatch between numerical and experimental data with a calibration procedure that adjusts the process parameters in order to fit the molten pool dimension retrieved from the simulation with the experimental measurements. It can be noticed from the previous papers that the discretization of the domain is always kept constant so that all the analysis must be applied to microscopic scale in order to keep the computational time low. Patil, Pal et al. [20, 21] explained how the dynamic mesh refinement can be applied to reduce the computational cost needed to solve such problems (like SLM), where different levels of mesh density are required to capture the localized phenomena.

parameters needed for the simulation are collected. Then, the laser path is simulated using MatLab®. This permits the definition of each point of heat application. Their spatial coordinates are imported into ANSYS® to apply the thermal load into the FE model. The performances of the simulation are improved through a tight interaction between MatLab® and ANSYS®. The main analysis environment is ruled by MatLab® and ANSYS®, which is launched in batch mode only when it is needed. Moreover, a dynamic mesh refinement is applied to the model to reduce the computational cost of the simulation. Finally, a calibration

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Thermal residual stresses are greatly affected by the temperature distribution. Moreover, the thermal field is greatly affected by laser characteristics and scanning strategies. Therefore, a proper setup of machines parameters is a key issue in reducing thermal residual stresses. Even if different scanning strategies can be adopted, the meandering path only will be considered in the following as it seems to be the most reliable one, ensuring a uniform thermal field and a low machining time. In this configuration, the laser scans the powder with the trajectory shown in Figure 2. The most important process parameters that are related to the different laser scanning

Changing these parameters can lead to different material characteristics, for example, material density, surface roughness, and porosity. All these characteristics are directly responsible for the mechanical properties of the sample. It is important, indeed, to have a powerful tool that is

The SLM machine available for this study is a Renishaw® model AM250. The main characteristic of this machine is the pulsed laser technology. The process parameters used in the simulation are

The most suitable metallic material for surgical implants is Ti-6Al-4 V and the data collected in the subsequent tables always refer to this alloy. Ti-6Al-4 V is a titanium alloy with 6% of

able to predict the thermal field with respect to different laser parameters.

collected in Table 1 and refers to the machine setup.

procedure is proposed to correct the titanium alloy properties.

2. Process parameters

strategies are listed below:

• Path rotation [0÷90]

2.1. Material properties

• Laser power [150÷500 W]

• Hatch distance [50÷105 μm] • Point distance [20÷75 μm]

• Layer thickness [30÷60 μm] • Time exposure [30÷70 μs]

• Powder absorbance [0.3÷0.5]

Despite the strong reduction in computational time due to the dynamic mesh refinement, it is not feasible to simulate the thermal field evolution of an entire object, also for very small components. This is due to the extremely large number of spots that are required to melt the cross-section of a single layer. This problem can be partially solved with an analytical solution of the thermal field [22, 23]. Nevertheless, this solution returns the global temperature of a single layer and it is not possible to distinguish between different heat distributions due to the multiple scanning strategies. Therefore, the simulation presented in this chapter is mainly focused on the study of the thermal evolution of a microscale domain. The FEA domain presented here includes only one layer of powder and its dimensions are chosen to reduce as much as possible the number of elements. A model that is able to simulate the thermal evolution of a complete part, taking also into consideration the effect of the scanning strategy, is still an open challenge.

SLM technology is widely used in different domains of the industry, such as aerospace, automotive, and consumer goods. However, the most important industrial application is the medical and surgical field. In this context, SLM is acting a major transformation of the traditional production techniques, more and more surgical implants are fabricated with PBF technologies. Since the industrial applications of SLM are continuously increasing, numerical simulations of the process become fundamental to predict the mechanical properties of the parts starting from the behavior of the thermal field. ANSYS® and ABAQUS® are an example of general purpose software that is widely used for the FE simulation of SLM process. Moreover, the industries are so interested in the new manufacturing possibilities offered by the SLM, so that numerical simulations were no more confined to academic research but became a powerful tool for the companies willing to develop new commercial products. As a result, specific software has launched onto the marketplace, for example, 3DSIM (based on dynamic adaptive mesh refinement [24]), SIMUFACT (based on the inherent strain theory [25, 26]), and NETFABB.

The framework presented in this chapter involves both ANSYS® and MatLab® to perform the FE analysis of a SLM process on a titanium alloy powder. At the beginning, all the process parameters needed for the simulation are collected. Then, the laser path is simulated using MatLab®. This permits the definition of each point of heat application. Their spatial coordinates are imported into ANSYS® to apply the thermal load into the FE model. The performances of the simulation are improved through a tight interaction between MatLab® and ANSYS®. The main analysis environment is ruled by MatLab® and ANSYS®, which is launched in batch mode only when it is needed. Moreover, a dynamic mesh refinement is applied to the model to reduce the computational cost of the simulation. Finally, a calibration procedure is proposed to correct the titanium alloy properties.
