Additive manufacturing represents a powerful tool for the fabrication of parts with complex shapes by the deposition and the consolidation of materials as opposed to subtractive manufacturing methodology. Selective laser sintering (SLS), one of the most popular powder bed fusion (PBF) technologies for thermoplastic part production, has demonstrated extensive applications in various industrial sectors. The process involves the deposition of homogeneous powder layers and employs a laser source to selectively melt a powder bed according to a CAD model. Due to its layer-by-layer nature, voids and pores are inevitably introduced in the fabricated thermoplastic parts. Porosity represents one of the major limitations of this technology being one of the main causes of the variation of the mechanical properties. With the intention of providing support for reducing the porosity and thus increasing the quality and performance of the final product, in this paper, a brief review was carried out focusing on the SLS process parameters and their interaction with the porosity of the product. In addition, an in-depth look was given to the mechanisms of formation and consolidation of pores within parts made of polymeric material.
Due to the ability to rapidly manufacture materials into complex shapes and the great number of benefits concerning conventional technologies including low time-to-market, enhanced customization, reduction of material consumption and wastage, and large freedom in design, additive manufacturing (AM), or three-dimensional printing (3D printing) , ,  has received in the last three decades an increasing interest in a variety of areas of society such as medicine (biomedical  and dentistry [5, 6]), construction and architecture [7, 8], ergonomic , food  art , textile and fashion , jewelry , education , sporting good , toy , and it is presently used for various applications in the engineering industry, for example in electronics , metamaterials , industrial components , automotive , energy , oil and gas , maritime construction , and aerospace . Many efforts have also been made in recent years to compensate for the lack of specific standards, a key point to be taken into account among the obstacles to the wider adoption of AM .
As defined by the American Society for Testing and Material International Standard , AM is the “process of joining materials to make parts from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing and formative manufacturing methodologies”. The materials can be formed into complex shapes, ranging from metals to ceramics, polymers, natural materials, or living cells and tissues . Moreover, this technology could be successfully employed for composite fabrication , , .
Among these, powder bed fusion (PBF)  is one of the earliest and most versatile and popular AM processes, being well-suited for a great variety of materials. In PBF, a heat source is required to fuse the powder to form material for realizing a 3D product. Depending on the heat source used, different types of fusion techniques can be distinguished, laser fusion (L) , electron beam fusion (EB) , and thermal fusion generally by infrared light (IrL) . However, the laser fusion type can also be subdivided into selective laser sintering (SLS) , and selective laser melting (SLM) .
SLS and IrL processes are suitable for making plastic parts, SLM is for metal, and electron beam melting (EBM) can be used for plastic as well as for metals. The SLM and the IrL are also known as direct metal laser sintering (DMLS) and high speed sintering (HSS).
PBF processes are of great interest across many industries as a means of direct manufacturing because they are characterized by high efficiency and provide high-accuracy parts at low cost. This technique allows the fabrication of a 3D part by an overlay of 2D powder layers with a beam or a lamp that selectively fuses the powdered material following a specific path described by the 3D model of the final part, e.g., the CAD model.
Comprehensive reviews and books were published about the fabrication methods based on Powder Bed Fusion processes , , , , , . For a detailed report on quantitative research direction indices on laser powder bed fusion production of polymers, updated to the last 10 years, refer to the accurate report by Kusoglu et al. .
As in many other manufacturing processes, porosity is a phenomenon inevitably present in components made using AM. The presence of internal pores is usually found in any additively manufactured parts, whatever the material or process used. The quantity, shape, and distribution of pores, and the propensity to their formation depend strongly upon the type of process and on the processing conditions used to produce the part. It is well known that porosity influences in a dramatic way the quality and reliability of the manufactured materials and, therefore, it deserves special attention.
A large number of papers have been written on the characterization of 3D products involving the determination of the pore size distribution as well as the total pore volume or porosity and the pore shape and the interconnectivity , , , .
Among the PBF family, SLS is one of the most widely used additive manufacturing technologies, as it offers an efficient technique for fabricating thermoplastic parts, which makes it highly popular for modeling, prototyping, and production applications. From 1987, more than 15,000 Scopus indexed articles reported among the “keywords” at least one of the PBF techniques (Figure 2), and more than 25 % of them concern SLS, i.e., polymer powder feedstocks.
Although the interest has increasingly shifted to both SLM and EBM processes (with the SLM predominating) since the early 2000s, attention to the SLS has not diminished but is still very relevant, a sign that there are still many issues to be understood.
Among the approximately 4000 articles that cited the SLS process, almost 15 % exhibit the occurrence of the word “porosity” thus confirming the importance of the topic and justifying the need for further studies. In fact, due to its layer-by-layer nature, the printed part produced by this technology exhibits pores or defects that represent one of the main causes of the dispersion of the mechanical properties (e.g., tensile strength, tensile modulus, strain at break, and fatigue limit). To reduce the influence of porosity on the quality and performance of the final product, it is crucial to well understand the mechanisms that lead to its formation and to identify the role played by the process parameters. In this paper, a brief review is presented starting with a background on the porosity, on the 3D printing process, and discussing physical phenomena involved during the fabrication process. Moreover, the main process parameters have been identified as well as their interaction with the porosity. In addition, an in-depth look was given to clarify the consolidation processes of additive manufacturing that give rise to the formation of pores within parts made with polymeric materials.
2 Porosity and its measurement
For a complete overview of the state of the art of nomenclature related to porosity and for a brief illustration of the measurement methods most used in the field of additive manufacturing, reference can be made to the review produced by the authors . Below the basic concepts necessary for a better continuation of the reading of this paper are recalled, starting with the terms “Porosity” and “Pore”. Porosity, which is often used to indicate the porous nature of solid material, may be defined as:
where V is the apparent volume of the sample and is the pores’ volume. Pores, on the other hand, may be described as either apertures, channels, or cavities within a solid body or as space (i.e. interstices or voids) between solid particles in a bed, compact or aggregate.
Pores can be classified according to their capability to intercept an external fluid but, also in function of their sizes and shapes and, sometimes, according to their origin. With regard to the capability to intercept an external fluid, pores in a solid can be distinguished into accessible (or open) pores and closed pores. Consequently, the pore volume Vp value that is employed in eq. (1) could be that of the open pores or that of the closed pores or the volume of both types of pores, leading to the “open porosity”, the “closed porosity”, or the “total porosity” values, respectively.
Another possible classification of pores is based on pore geometry. Pores are classified according to the following geometrical shapes: cylinders, prisms, cavities and windows, slits, or spheres. In many cases, as in parts produced with AM technologies, the presence of irregular pores, with shapes often not attributable to that listed above, is detectable. Due to that, for 2D analysis, circularity, and aspect ratio are used to represent pore shape while, for 3D analysis, pore morphology is usually represented by sphericity and aspect ratio.
Considering the pores classification based on their size, generally, the dimension involved in grouping pores is the smallest one, which is typically indicated as pore width. Based on this consideration, IUPAC  classified pores into three-dimensional categories: micropores (i.e., the pore width is smaller than 2 nm), mesopores (i.e., the pore width ranges between 2 and 50 nm), and macropores (i.e., the pore width is greater than 50 nm). However, the description of porosity as a function only of the average one-dimensional pore width is not exhaustive. Due to that, pore size classification for 2D analysis is also based on ferret diameter or pore area while for 3D analysis pore volume or the projected area on various plane are considered. Examples of irregular pores are found in part produced by AM either for metallic  or plastic materials . Consequently, it would be better to use the average three-dimensional geometry of the pore and the pore size distribution (PSD) of the void space, the pore density, and the spatial arrangement of the population of pores for porosity characterization.
Finally, two different types of pores can be distinguished depending on their origin: “intrinsic pores” that are formed unintentionally during the fabrication process (these pores could be avoided or minimized because of the negative effects on mechanical properties and for improving the consistency of built parts); “extrinsic pores” that are intentionally introduced for a particular purpose, such as pores for engineering applications (filtration and purification, plastic injection molds, and heat exchangers/heat pipes), and others [45, 46].
In this paper, only the unintentional intrinsic pores will be examined.
Several methods for the characterization of porous solids have been proposed over time. A general introduction of these methods and some recommendations for their selection and appraisal are reported in [47, 48], with regards to the characterization of micropores and mesopores, while a more detailed and still valid updated list of the methods for the characterization of porous materials having pore widths in the macropore range is reported and discussed in . A critical review of the most used methods for porosity characterization in AM is reported in . For other methodologies see Espinal  and Yadroitsev et al. .
3 Selective laser sintering (SLS)
3.1 Process and physical phenomena involved
Ideated at the University of Texas in 1986 , the laser sintering process, also referred to as selective laser sintering (SLS®), a copyrighted acronym, has become today an important and popular AM process. Due to its high accuracy and productivity, even for the fabrication of complex parts, and the possibility to guarantee satisfying mechanical properties of the fabricated objects, it is regarded as one of the most promising additive manufacturing techniques for industrial applications.
Although the SLS technologies could be adapted to process a large variety of materials and combinations of multiple materials, the thermoplastic polymers (both, amorphous and semi-crystalline), thanks to their lower processing temperature and consequent demand for low-power lasers, were the first and still are today the most widely applied material in SLS.
The consolidation of thermoplastic polymers, during the SLS process, involves mechanisms that are very complex and yet not well known. It is worth noting that, despite the name given to the method, the binding mechanisms occurring in selective laser sintering of thermoplastic polymers involve different chemical and physical processes and one of the main important ones is the diffusion phenomenon . This mechanism allows the growth of different connections between adjacent particles. Moreover, the increase of chamber temperature promotes this mechanism thus allowing acceleration of the sintering process for both the liquid-phase and the solid-state sintering strategies. Overall, the mechanism of consolidation characterizing the semicrystalline polymers can be considered as partial or full melting while, as regarding the amorphous polymers, it could be deemed as a liquid phase sintering process without fusions . Nevertheless, the SLS has been used in many papers when referring to polymer coalescence, and it is now well-accepted in the literature. It must point out that, if we exclude some papers dating back to the early 2000s, the acronym SLS has been and is currently used exclusively for polymers processing, to be distinguished, therefore, from the acronym SLM (selective laser melting) reserved for metals.
The SLS 3D printers are very simple. The common commercial SLS machines mainly consist of the following components (see Figure 3): a chamber for powder dispensing including a powder supply, a build platform, a blade or a rotating roller, an overflow tank, and some IR irradiation lamps and/or resistance heaters; a CO2 infrared laser and a laser scanner unit that generates the prescribed horizontal contour according to a digitally programmed design; a computer that controls all the process parameters.
In the pre-heating step, the powder bed is heated just below the softening temperature to minimize the required laser energy and to minimize the part distortion during cooling. The predefined temperature, called bed temperature (Tb), is maintained during the entire build process.
In the building step, the following sub-steps are repeated for each layer. Firstly, the building platform is lowered by a value equal to layer thickness, and powder particles are spread on it using a roller or recoating blade. Then a laser beam scans the powder layer to melt the exposed powder according to the prescribed geometry. After the exposition to the laser beam, the powder particles coalescence begins. This phenomenon occurs at temperatures that result be higher than the material melting temperature. After that, the part is gradually cooled to the Tb value to ensure solidification, i.e., adjacent particles are bonded. The powder deposition is generally carried out under an inert atmosphere (e.g., argon and nitrogen) to avoid any environmental contamination of powders during the process.
In the cooling step, the heat source is off and the powder bed cools gradually to the part extraction temperature.
It is necessary to highlight that behind the apparent simplicity of the machine, there is a very complex multiphysical process that involves numerous parameters and interactions between them. A comprehensive and accurate description of the main mechanisms that occur during the SLS process, e.g., laser beam-powder interaction, powder spreading and melting, coalescence, solidification, and crystallization phenomena, is reported in .
3.2 SLS process parameters and their effects on the porosity of the manufactured part
The SLS process parameters can be grouped into four categories : powder, laser, temperature, and scan-related parameters. The most relevant ones, for each category, are collected in Table 1. It should be noted that many of these parameters are strongly interdependent and mutually interacting and, since they directly affect the macroscopic characteristics of the printed parts, a proper setting is required to obtain high quality by an SLS process.
|SLS process parameters|
|Powder based||Laser based||Temperature based||Scan based|
|Particle shape, size, number, and spatial distribution||Laser power||Powder bed temperature||Scan speed|
|Powder flowability||Spot size||Powder feeder temperature||Hatching distance|
|Recoating speed, layer thickness, and powder density||Pulse duration||Temperature distribution||Scanning pattern|
|Material properties||Pulse frequency|
As in any other PBF process, the powder is also the main element in the SLS process. Choosing the most suitable powder is crucial since its properties affect both processing capacity, e.g., deposition and consolidation, and the final characteristics of the part, e.g., the surface roughness, the resolution of details, and, inevitably, also the porosity [56, 57]. Furthermore, powder characteristics are decisive for the subsequent assignment of the values of all the other parameters involved in the process, both intrinsic and extrinsic , , .
In the next sections, the properties of the powder and the process parameters that have a predominant impact on the formation of porosity in a part manufactured by SLS will be discussed. In particular, the following will be examined: the effects of powder rheology; the influence of the temperature of the powder bed and the link between this latter and the thermal properties of the final parts; the influence of the thickness of the layer and the link between it and the optical properties of the powder; the influence of the rheological properties of the final parts; the influence of the energy density used for the consolidation and its relationship with the laser and scan-related parameters.
3.3 Effects of the rheological properties
The flowability of the powder  plays a key role in the SLS process as an inappropriate distribution of the powder causes the unsuccessful formation of homogeneous and even layers leading to porous and weak SLS parts . Therefore, particular attention was paid to the ability of the powders to flow , , , , , , , which was found to be influenced by different factors [58, 63]. The parameters that influence the powder flowability and their role in the SLS process are discussed by Lupone et al. .
Environmental conditions (temperature and moisture) and external factors such as gas/air ratio, storage duration, mechanical motion (vibrations), or interactions with additives and the mechanical forces during processing can play a critical role. The behavior of a powder is also influenced by some properties of the particles themselves. The size and the particle size distribution are important, but not only: shape, surface characteristics (smooth, rough, and jagged), density, cohesion, elasticity, plasticity, electrostatic charge, and others. All of these properties must often be evaluated in terms of distribution rather than as single variables.
Friction, mechanical blocks, cohesion forces between particles, and liquid bridging oppose flowability, gravitational forces, on the other hand, favor it. To a certain extent, the flowability can also be improved and adjusted by means of additives, but the flow agent, typically 1 μm or less particle size, should be added in minimal quantity to not compromise the mechanical properties.
Generally, the flowability of powders is determined from the bulk and tapped density of the powder by the so-called Hausner ratio HR (HR = bulk density/tapped density) . If HR < 1.25 the powder has a free-flowing powder behavior (high flowability), while HR > 1.4 characterize powder with poor flowability that might lead to the formation of agglomerates and cause problems when spread into layers, resulting in an inhomogeneous distribution and surface defects .
Appropriate particle size and morphology are required to achieve high flowability. Unfortunately, there are no powdered polymeric materials with suitable characteristics to be used directly in the SLS process. The majority of them must be converted to an appropriate particle size before processing them. The methods for producing polymer powders can be broadly classified into three categories: mechanical, solution-based, and melt-based methods . Different particle forms can be obtained from the different powder generation processes (see Figure 4). Spherical particles with good flowability are usually obtained from melt-based or solution-based (direct polymerization) processes. Potato-shaped particles with good flowability are typically obtained from a precipitation process (solution-based). The particles obtained from a mechanical-based process (cryogenic or wet grinding) are characterized by an irregular shape and poor flowability. Due to that, they are inadequate in the majority of cases and fail for LS processing. The poorer powder flowability generates a poor part bed surface in the LS machine and a reduced powder density as well.
According to Goodridge et al.  and Wang et al.  for the fabrication of macro-sized parts, the powder particle size that seems to be optimal to be employed for the SLS is, generally, in the range between 45 μm and 90 μm (although different ranges have been suggested, 10–150 μm in , 20–80 μm in , and 75–100 μm in ). On the other hand, when small parts with good surface quality and high detail resolution need to be fabricated, small particles must be used. Particles larger than 90 μm can also be used to obtain parts with good mechanical characteristics with the compromise of having more rough surfaces and higher internal porosity and could find use in applications where a smooth surface is not required .
Moreover, the particle size distribution (PSD) of the powder is a parameter of fundamental importance. In fact, in many cases, the knowledge of the average size of the powder is not enough but it is necessary to know if large or small particles are present. A high percentage of large particles, as just mentioned, harms the surface quality and the resolution of the details of the final part but also leads to the possibility of the formation of a streak-free powder surface in the powder bed. On the other side, if the fraction of fine particles is too high, there is a negative effect on the flowability and free-flowing behavior of the powders  with the consequent lack of homogeneous deposition of the powder layers. In addition, fine particles may also ‘‘evaporate off’’, strongly contributing to the formation of pores. Finally, as observed by Goodridge et al. , under identical conditions, small particles melt at a faster rate with respect to the larger ones, so powders containing very small particle sizes can undergo secondary sintering conditions, thus compromising the accuracy of the part.
For these reasons, it is very important to know if the distribution curve is more or less extensive, symmetric, or asymmetric and if there is an uni-, bi-, or higher-modal distribution . Sometimes multimodal powders, i.e., those containing a high range of particle sizes, can provide the right compromise, with smaller particles filling the spaces between larger particles, to increase density while maintaining an adequate powder flow.
Typically, during 3D printing with the SLS technology, each powder layer is spread through a roller/blade that gives the possibility to obtain a layer with a specific thickness with no external pressure application.
The size, shape, and surface characteristics have a decisive influence on the powder behavior during this step of the SLS process. If the powder particles are not substantially round and the surface is very jagged and rough, a homogeneous formation of the powder bed during the powder application can be severely affected, and the LS process can be disturbed massively.
Finally, different studies have been carried out to understand which of the two recoating systems is better , , , . However, it is not possible to completely clarify this point since layer quality is also strictly dependent on different factors, e.g., powder dynamics. Overall, it could be assessed that the interaction mechanisms that exist between the powder particles and the spreader as well as the modification of the morphology of the powder bed in function of the recoated movement are not still clear and, due to that, these factors should be investigated.
3.4 Effects of the thermal properties
During the SLS process, polymer powders are heated to elevated temperatures changing their state from a solid or glassy material at room temperature to a softer material and then ultimately to a viscous flowing melt [80, 81]. The temperatures at which these transitions occur depend on the chemical structure of the polymer and they can be evaluated by a differential scanning calorimetry (DSC) analysis. The process of coalescence of polymer powders is a viscous sintering process described by the Frenkel model . In this model, both the viscosity and the surface tension play a key role but, while the viscosity can significantly vary with temperature, the surface tension did not appreciably vary with it and is in function of the polymer type and lies within a narrow range of values. Therefore, the sintering process is mainly influenced by the viscosity that represents an indicator of the capability of the melted polymer to flow. In particular, with an increase in the polymer viscosity, the fluidity decreases thus resulting in a more difficult coalescence between particles .
Amorphous polymers usually have higher molecular weights and then higher melt viscosity than semi-crystalline polymers . When these materials are heated their melt viscosity decreases, but, normally, their viscous flow (and thus the sintering rate) remain lower than semi-crystalline polymers. As a result, amorphous materials tend to exhibit higher levels of porosity and thus lower strength than the traditionally processed counterparts . The semi-crystalline polymers, on the other hand, can reach a near-full density and thus have mechanical properties similar to molded specimens.
Typically, the amorphous and the semi-crystalline polymers show different behaviors. Both types exhibit a glass transition temperature Tg, i.e., a temperature above which they gradually soften, but only semi-crystalline materials have a defined melting point.
A typical DSC curve for a semi-crystalline polymer is illustrated in Figure 5. The melting process occurs over a temperature range rather than at a discrete temperature and can be identified with the initial melting temperature Tmi. When the melted polymers are cooled, the crystallization process also occurs over a temperature range and can be identified with the initial crystallization temperature Tci. In practice, due to the hysteresis between melting and crystallization, it is possible to identify an optimal processing window between the two transitions, commonly known as stable sintering  or supercooling window . For successful processing, this window should be wide enough to guarantee good material processability without any distortion into the final parts, i.e., powder particles should not melt before laser exposure as well as they should not crystallize ahead of the process end .
To rapidly achieve fluidity, without the need for excess energy, polymer powders generally need to be heated whilst in the powder bed. The bed is preheated by the heating system (Figure 3). Operating with a high bed temperature, the laser power is reduced, and the thermal gradient between the sintered and supporting powder and the thermal expansion of the powder caused by the laser minimizes, thus mitigating the non-uniform shrinkage of sintered parts, especially at the part contours. However, the bed temperature must not exceed the softening temperature of the polymer; otherwise, the powders will stick and not flow freely.
On the other hand, the temperature of the powder bed must not be too low to avoid the curling of the corners and edges of the sintered layer which can produce distortions or deformations of the finished piece or, in the worst cases, block the covering mechanism.
Generally, due to their broad softening range, the processing of amorphous polymers only requires that the pre-heating temperature is set above the glass transition temperature. Conversely, for semi-crystalline polymers, it is required that this temperature is inside the sintering window. Depending on the production method employed, intrinsic property changes can be induced, such as a shift of the melting or crystallization point .
3.5 Effects of the optical properties
Due to their chemical nature and granular state, the polymer powders can be considered semitransparent materials and when a laser beam hits their surface three effects can occur in principle: reflection, absorption, and transmission [55, 58]. Only part of the incident rays is diffused out of the powder bed, the other rays are transmitted or absorbed inside the powder bed through the phenomenon known as multiple scattering .
The influence of multiple scattering on the reflection, absorption, and transmission behavior of powdered material was studied by Osmanlic et al.  and Xin et al.  for polymeric powders. It was found that the polymer absorption capability influences the amount of laser radiation that is transmitted or absorbed by each particle. However, to increase the absorption, additives can also be blended with the SLS powder .
Absorption as well as the transmission of the laser energy in the direction perpendicular to the powder bed, i.e., along the depth, is highly relevant in a sintering process. These factors have a strong influence on the effective dimensions of the melt pool that is dependent on the laser beam penetration beam as well as by the conversion of the optical energy into heat energy.
To reduce the formation of pores or defects between the layers and, therefore, to induce adequate adhesion with already sintered layers to avoid delamination phenomena when the part produced is in service, the transmission should be such as to address a sufficient portion of the radiation energy in the deeper regions of the powder bed.
The laser penetration depth, and then the capability of the polymer to transmit the radiation into the powder bed, assumes, in this context, a very important role as it can lead to the choice of layer thickness. Experimental studies carried out on different polymers (TrueForm TM , PA12, and PEEK ) have shown that a 150 μm-thick layer guarantees the dissipation of a great amount of laser energy.
In case of poor absorption and transmission capability, an increase in the laser energy power can compensate to some extent for the effect. However, an increase in the laser power must be limited to not destroy the polymer with too high energy.
The thickness of the layers employed during part fabrication influences the productivity of the LS process as the thicker the layer, the less time it takes to build a part. However, thick layers can harm the surface roughness and dimensional accuracy of the part, and thus a balance is needed according to the requirements of the application [81, 91].
3.6 Effects of laser and scan-based parameters
The SLS process requires a high-intensity and collimated beam of energy to melt, along a selected pattern, the grains on the surface of the powder bed. Lasers are ideal candidates for this task, as long as the laser energy is compatible with the material transformation mechanisms, as they provide a beam that can be moved very quickly in a controlled manner with the use of directional mirrors (scanning system) . The radiation must carry a thermal energy amount sufficient to melt the powders in a controlled way without generating excessive heat accumulations, so that, when the laser energy is removed, the molten material slowly solidifies again and cools down to bed temperature ensuring the bonding between adjacent particles . The CO2 lasers with a wavelength of 10.6 μm are well suited for the sintering of polymer powders, as polymers show high absorption at far infrared or long wavelengths. Since they are made up of aliphatic compounds, the polymers have, in most cases, some group vibrations in the ‘fingerprint’ infrared region, sufficient to absorb significant portions of 10.6 μm CO2-laser radiation [55, 93, 94]. The long wavelength of the mid-infrared source excites the resonant vibrational modes of larger segments of the polymer molecule implying the generation of heat energy. Generally, the commercialized SLS machines are equipped with continuous-wave CO2 laser sources with a maximum power rating between 50 and 200 W.
During the SLS process, the laser is dynamically scanned on the powder surface along several predefined laser tracks  (Figure 6). Due to the preheating of the powder bed, only a small portion of residual energy needed to melt the powder particles is introduced in this phase of the process.
The interaction between the powder bend and the laser beam results in the formation of a melt pool with properties strongly depending on the adopted process settings such as the laser spot, laser power, laser scanning speed, hatch spacing, and the thickness of the layer.
To evaluate the effects of the process parameters on the quality of the finished part (for example, surface roughness and mechanical properties) and the porosity , several authors [38, 44, 48, 81, 97, 98] found it convenient to refer to a unique parameter, the energy density (ED) provided by the laser to the powder bed. Also known as Andrew’s number , ED is a measure of the amount of energy supplied to the particles per unit area of the powder bed surface. It can be calculated by the following equation:
where P represents the laser power (in W), s is the laser scan spacing (the distance between the middle points of two consecutive laser tracks) (in mm), and v is the scan speed of the laser beam over the powder surface (in mm/s). The supplied energy density ED is then given in J/mm2.
It must be observed that Eq. (2) can give equal ED values for different combinations of values of the parameters involved, with sintering results that do not necessarily remain the same. For example [100, 101], higher scanning speeds lead to higher porosity and lower mechanical properties of the produced parts, because, to keep the ED value constant, it is necessary to increase the laser power. Unfortunately, too high laser power values could damage the material and, for that, it would be better to work with lower scanning speeds and lower laser powers. However, this condition could make the process uneconomical due to the reduction in production speed.
Alternatively, different definitions can be adopted, leading to the formulation of a volumetric energy density (J/m3) which also includes the layer thickness [93, 100, 102] in the denominator of Eq. (2). It should be noted, however, that the energy density values obtained with this modified formula may not adequately describe what happens. In fact, very often it happens that, to obtain good adhesion between the layers, the depth of penetration of the laser beam is greater than the thickness of the powder layer, as well as, it could happen (for many reasons, for example, when the powder layer is very thick), that the laser beam does not reach the bottom of the layer.
Another parameter that strongly influences the 3D printed part properties and quality is the so-called overlay ratio, defined as the ratio between the laser beam diameter and the scan spacing. In fact, it has been shown to play a fundamental role in the properties of printed components and was recently included in the definition of surface energy density .
A useful parameter relating process conditions to the physic of powder melting, the energy–melt ratio, was introduced by Starr . This parameter could be calculated as the ratio between the volume energy density and the energy requested for obtaining the complete melting of a unit volume of a layer of powder. The energy–melt ratio can be obtained starting from the powder temperature and properties (e.g., specific heat, pecking density melting temperature, and heat of fusion), and can be used to predict the effect of a change in bed temperature or a material change.
3.7 Other processing parameters
In addition to the parameters discussed above, there are many other factors influencing the properties of laser-sintered parts and, even if they do not seem to be directly related to the formation of porosity, for the sake of completeness, they are briefly recalled below. A more thorough discussion can be found in the work of Goodridge et al. .
The most relevant ones are the following: (i) layer scanning strategy; (ii) beam spot size; (iii) the delay time; (iv) the skywriting; (v) part accuracy; (vi) powder aging and reuse; (vii) temperature distributions, and (viii) build orientation.
The strategy employed to scan layers (fill/contour and scan count) can affect the strength and the dimensional inaccuracies of the part. The optimal strategy is dependent on the material and the geometry. For example, the double scanning of the contour is a very commonly used strategy for thin-walled structures . Moreover, multiple scanning is useful for those materials characterized by small processing windows .
The beam spot size can affect the density and strength of laser-sintered parts. It was noted that, for polycarbonate, an increase in spot size can produce parts with increased densities and strengths . This variation in function of changes in the laser beam spot size was attributed to the different distribution of irradiation intensity contained within the laser spot. An increase in the spot size exposes a greater area to more uniform, less intense laser irradiation. Unfortunately, the physical diameter of the laser beams on current commercial machines (normally 0.5–0.7 mm) cannot be changed. However, there is a curing zone around the physical diameter that can be influenced by optimizing several factors such as building temperature, laser power, layer thickness, and others.
The delay time is the time between the instant in which the scanning of a layer ends and the instant in which a fresh layer of powder is brought over the build area before the next layer can be scanned. The value of this parameter is dependent on the other system parameters, i.e., it is typically required that the bed temperature reaches a specific value before the deposition of a new layer . This parameter can determine the occurrence of delamination of the layers or curling of the parts .
The skywriting involves an extra energy supply that can be imparted at the beginning and end of the line of the scanned powder, and this could be exploited when a dense outer shell layer must be combined with a more porous interior, e.g., drug delivery devices . This strategy is commonly employed for prototyping since the quality of the outer surface is requested to be higher than those of the inner volume.
The part accuracy is a significant concern for AM, especially when semi-crystalline polymers are used, as the degree of shrinkage in laser-sintered parts is unlikely to maintain dimensional accuracy, even in cases where the compensation ploys are used. The degree of shrinkage depends on the material employed for part fabrication, the part geometry, and some process parameters such as the building temperature, the cooling rate, or the laser power. Overall, by increasing the temperature variation during part printing, the shrinkage increases .
The reusing of the powder not melted during printing is recommended to reduce cost and waste. However, the aged powder could exhibit properties different from the virgin one thus affecting the properties of the final parts. In fact, it is well known that polymers exhibit some changes in their structures after exposure to high temperatures . Actually, it is not possible to employ 100 % of reused powder for part fabrication. An excess of recycled powder leads to a decrease in parts quality, e.g., shrinkage and roughness .
The uneven temperature distributions in the build chamber of the sintered powder change both the intrinsic polymer properties and the particle size distribution of the powder. Moreover, when that occurs, it leads to inconsistencies in the mechanical properties of parts that result to be dependent on where they are built in the powder bed [63, 109].
Finally, according to their build orientation, the finished parts can have anisotropic characteristics that affect their mechanical properties. This effect is well documented in different works [97, 110], , . Typically, parts built along the z-axis are characterized by the lowest mechanical properties  and this occurrence should be taken into account during the 3D printing parts design.
4 Genesis and morphology of porosity in SLS part
The enormous progress achieved by commercial SLS 3D printers, in recent years, has certainly made it possible to overcome some initial performance limitations (for example, the uniform temperature distribution in the building area) , but these improvements are still not sufficient if the goal is to achieve the high-quality standards currently required by an AM process, especially if the aim is to obtain physical and mechanical properties of the parts produced comparable to those obtained through traditional production processes. Improving the quality of production requires a better understanding of the physical phenomena involved during the 3D printing, e.g., the powder spreading, the laser beam-powder bed interaction, the polymer melting, the coalescence of molten powder and its densification, the gas diffusion, the crystallization, and the shrinkage of the polymer. Unfortunately, such relationships are difficult to establish due to their complexity.
Much effort is still needed to clarify the interaction between the physical phenomena involved during the sintering process and to understand how they can affect the mechanical and physical properties of the materials produced. For example, in recent decades, the study of the porosity of materials produced through AM and the mechanisms that influence its formation has aroused great interest. Despite the many studies done, the relationships between the various mechanisms that influence the formation of porosity have not yet been fully identified. However, the harmful effects of the presence of pores in the material on its mechanical characteristics are well known (yield strength, toughness, anisotropy, etc.) .
Unfortunately, the incomplete knowledge of the origin of the porosities affecting the polymeric parts produced by SLS is the cause, even today, of the lack of porosity control.
The degree of porosity of the parts sintered by SLS is linked to the consolidation mechanisms of the powders and, therefore, as will be shown shortly, to the nature of the polymeric material used.
However, numerous parameters can modulate the development of these mechanisms such as, for example, the entity of the thermal gradient both in the plane and out of the plane and its temporal variation, the density of the powder bath, the size distribution of the particles composing the powder as well as the temperature of the powder bed.
During the process, the energy radiated by the laser beam is focused on the scanned region of the powder bed and is transformed into heat. Heating can produce temperatures so high to change the structure of the thermoplastic material from a hard structure to a softer one and then turn it into a viscous flowing melt, giving life to the formation of a melt pool [55, 83, 115, 116] (Figure 6). The way and the temperatures at which those transitions occur are depending on the kind of polymers [53, 63].
The semi-crystalline polymers have a glass transition temperature quite distinct from the melting temperature. They do not gradually soften as the temperature rises but remain hard until a certain amount of heat is absorbed and then rapidly transformed into a viscous liquid.
On the other hand, amorphous polymers do not show a clear transition since they do not have a melting point but only a glass transition temperature. Above such a temperature, their randomly ordered molecular structure softens gradually as the temperature rises.
The consolidation mechanisms of thermoplastic polymers even involve the solid-state diffusion phenomenon . Moreover, other and different consolidation mechanisms are involved depending on whether the polymers are (semi) crystalline or amorphous .
In the first case, a full melting consolidation occurs. This kind of consolidation arises when the powder is heated above its melting temperature. Under these conditions the powder melts and, thanks to its low viscosity, flows between the powder particles. If the heat is enough, the powder layer melts completely and settles on the previous layer. When the molten polymer cools below the melting point, polymeric crystals nucleate and grow, giving rise to recrystallized regions within disordered amorphous regions. Generally, crystallization involves an important shrinkage that may induce geometrical inaccuracies and distortion of the part.
The densities obtained will be close to the full density [53, 58, 63] with very low porosity (Figure 7a), and the mechanical properties will be close to those of the molded polymers  if the process parameters are properly optimized. By way of example, the results of the investigations carried out by Dupin et al.  on two laser sintering semi-crystalline materials (Duraform PA® from 3D Systems and Innov PA 1550® from Exceltec) can be considered. Figure 8a presents 2D sections as observed by X-ray tomography for parts sintered with different energy densities. Striking differences appear in terms of size, morphology, and distribution of the porosity, especially between the two powders. Indeed, the pore size seems to be larger for the Duraform PA samples. In samples sintered with Innov PA, the successive layers are clearly distinguished at the lower energy density level, contrarily to Duraform PA samples. In both case, a great reduction of the closed porosity was observed passing from the lower energy density to the higher energy density (from 5.1 % to 2.8 % and from 10.3 % to 1.8 % for Duraform PA and Innov PA, respectively).
The authors state that the origin of the different morphologies of porosity observed is, probably, due to three factors: the density of the powder bed influenced by the morphology and size of the powder, the coalescence process influenced by the physicochemical parameters of the polymers and the impact of the crystallization temperature during the cooling phase.
A clear picture, obtained by X-ray computed tomography, of the shape, size, and spatial distribution of internal pores of both Duraform PA (3D Systems) and PA2200 (EOS) parts, was reported by Stichel et al. [38, 44] as the results of a round robin initiative including six different SLS machines set with the optimized parameters. Figure 8b show pore shapes and arrangements of samples built with the different machines and different material (with M1 and M4 identifying Duraform PA specimens). The shape, as well as the arrangement, varies depending on the machine used. Some pores possess quite complex, stretched shapes, while others seem to be more round. The stretched pores, which consist obviously of small interconnected pores, seem to be predominantly orientated along the layer direction. Their results showed porosity values between 2.4 % and 3.9 %.
In the second case, a partial melting binding mechanism occurs. This kind of consolidation arises when the powder is heated above the glass transition temperature. At this temperature, amorphous materials are often highly viscous. The viscosity of these materials decreases when heated, but never reaches levels comparable to that of semi-crystalline materials. The flow and sintering rates are lower than those of semicrystalline materials. Usually, there is an incomplete coalescence [53, 58, 63], resulting in the formation of sintered necks between the powder grains (Figure 7b) and, consequently, in a lower degree of consolidation with a lower density and a greater porosity and, then, less strength. However, amorphous polymers do not exhibit such a sudden increase in volumetric shrinkage on cooling as semi-crystalline polymers, which is why they have been mainly used to produce models for lost-wax casting applications.
As an example, in this case, the results of the investigations carried out by Ho et al. [118, 119] on parts made by SLS with polycarbonate (PC) powder can be cited. Some cryogenically fractured cross-sections of the selective laser-sintered PC specimens fabricated at different energy densities are shown in Figure 9. At the lower energy density (Figure 9a), the particles were only slightly fused at the points of contact, and the individual particles can still be identified. Nevertheless, the powder particles changed from the irregular shape shown when they were virgin to a more spherical shape, and their surfaces became smoother after the softening process induced by the laser beam. Also, the pores follow the same behavior.
It was also noted that the spherical voids are arranged in rows. In fact, the voids were originally interlayer spaces that turned into spherical voids under the effect of surface tension of the molten polymer because of a more thorough melting process at high energy density. It was also noted that the voids enlarge for increasing energy density. This was due partly to the trapped gases and partly to the coalescence of the interlayer voids. The latter would reduce the overall surface area and, hence, the surface energy of the voids. However, a great reduction of the porosity is observed, passing from the lower energy density to the higher energy density (going from about 50 % to about 10 %).
The mechanism of the heat transfers through the powder bed  and, more specifically, the thermophysical properties of the powder  on which the heat transmission mainly depends, play an extremely important role, as they determine the spatial and temporal variation of the thermal gradient. The penetration capacity of the thermal gradient, both in-depth and in-plane, is crucial to guarantee a strong consolidation [55, 115].
The appropriate variation of the energy density  and the optimization of the parameters on which it depends (scanning speed, hatching distance, and laser power) allows to modify the amount of porosity, but, unfortunately, does not allow precise control of the percentage of pores and their morphology. The experimental studies confirm a negative correlation of ED with porosity : in general, by increasing the energy density value involved in the process it is possible to obtain parts with higher density since the higher energy density values lead to more effective particles fusion, i.e., more solid manufacturing; by contrast, at lower energies the sintering process is incomplete and parts usually show a porous structure with interconnected voids [97, 123, 124].
However, there is a temperature value beyond which the porosity of the material increases again. Above this temperature value, phenomena of thermal degradation occur in the material which causes changes in the chemical structure of the material  and leads to a local emission of gas with the formation of bubbles and consequently porosity [63, 83, 97].
To produce parts with a good mechanical performance it is essential to ensure the consolidation between adjacent layers as well as within each layer. The incomplete fusion at different areas of the layer-to-layer interfaces results in unsatisfactory densification that leads to the development of voids. Due to that, the parts could be characterized by poor mechanical properties.
To reduce this type of porosity and to obtain stronger mechanical performance, the material should melt completely and, therefore, the depth of the melt pull should be greater than the thickness of the single layer of powder but should not, however, greatly exceed its thickness; otherwise, excessive remelting can occur, which could cause high thermal stresses and even polymer degradation .
Furthermore, it is also essential to ensure the consolidation of adjacent tracks and, then, it is important to evaluate the transversal influence of the laser radiation and the melting width to evaluate the hatch space to be set. Its knowledge can be very useful for efficient preprocessing settings.
The density of laser-sintered parts is known to influence the mechanical properties , with higher-density parts having greater strength. The preheating temperature of the powder bath plays an important role in the density of the parts. Higher densities and better mechanical performance of polyamide parts [93, 123, 124] have been correlated with higher preheat temperatures. It seems that when the latter are kept close to the melting temperature, the cooling rate of the molten phase is slowed down, causing an increase in crystallization.
Denser parts can be obtained by correctly choosing the morphology and particle size of the laser sintering powders. The right choice can improve the packing of the particles with the result of reducing the porosity of the final part . In theory, if the particles are spherical and packed as a cubic closest packed crystal, the density of the powder bed can reach a theoretical maximum value of approximately 74 % of its volume occupied by spherical particles whereas 26 % of the volume is occupied by empty spaces. If the dust has a bimodal distribution with smaller particles that can fill the cavities between the large spheres, theoretically the maximum density can still be increased by a few percentage points.
In practical applications, however, the density rarely reaches values higher than 60 % [58, 127], and very often, the particle size distribution of the powder almost always contains, albeit in limited quantities, particles of small size.
It is necessary to underline that small particles do not always contribute to increasing the density of the powder bed. In fact, if not adequately distributed, they can produce the opposite effects. Furthermore, the induced heating can be such as to lead these small particles to evaporation or disintegration, creating a dusty atmosphere that disturbs the process as it attenuates the laser beam, and shields the heating elements with a negative influence on the consistency and process economy. The fine particles can also compact giving rise to coagulation, which can prevent the homogeneous deposition of the layers, thus preventing a good consolidation of the layer. Finally, possible disintegration or evaporation of these particles can leave voids resulting in increased porosity.
5 Current trends
As discussed in this work, porosity represents one of the main limits of additive manufacturing, and identifying the main mechanisms that contribute to void development during the 3D printing process is a crucial point. This aspect has been deeply investigated and the main mechanisms that occur during parts consolidation have been described and analyzed. However, it would appear that further investigations are needed for establishing useful strategies to avoid porosity formation or, at least, to limit its development economically, e.g., no additional treatment or increase of time to market [128, 129]. In fact, different studies demonstrated that mechanical properties could be affected negatively by unintentional pores . Moreover, it was not deeply investigated the influence of pores morphology on parts fatigue behavior. Finally, the possibility to estimate porosity percentage and pores characteristics starting from the SLS process parameter could be of primary importance. In fact, many efforts have been done in the last years to identify a correlation between processing parameters, porosity, and parts’ mechanical properties [44, 128, 130]. However, a standard procedure that gives the possibility to predict the mechanical properties of 3D printed parts starting from processing parameters is missing. Developing this relationship could improve the reliability of additive manufacturing parts.
On the other hand, different studies have demonstrated that intentional porosity could improve the mechanical performance of 3D printed parts, as observed in different biomaterials [131, 132]. In fact, porosity could play a crucial role in material performances, giving the possibility to obtain lightweight structures with improved performances , , . Typical examples of these structures are bones or nacre shells. However, this aspect needs to be further investigated to develop an effective strategy for porous parts design. The main purpose is to develop reliable modeling approaches that give the possibility to fabricate engineered porosity on different length scales, i.e., hierarchical porosity.
Selective laser sintering is one of the most widely used technologies for the fabrication of polymeric parts by additive manufacturing. Although it may seem like a very simple technique, the physical phenomena involved during the SLS processing of polymers are very complex due to their layer-by-layer nature. This technology exhibits inherent weakness compared to conventional manufacturing technologies, e.g. injection molding or casting. Pores or defects within the SLS printed samples are probably the main cause of the dispersion of the mechanical properties (tensile strength, tensile modulus, strain at break, and fatigue). To reduce the impact of porosity on the quality of a final product and its performance, it is essential to understand its formation mechanisms and the influences that it has on the structure, and, then, to tackle the problem on two fronts, from one side with advancements in the field of materials and the development of new materials and, on the other side, by the improvement of the printing process. In this work, a brief review was carried out focusing on the SLS process parameters and their interaction with the porosity of the product. In addition, an in-depth look was given to the consolidation processes of additive manufacturing that give rise to the formation of pores within parts of material made of polymeric material. Further efforts must be made to identify the strategies to be followed to maximize density and guarantee high-performance components that can be of help to users, such as, for example, the development of simple and rapid procedures capable of allowing the optimization of process parameters and experimental activities for identifying useful relationship relating porosity to the process parameters. Despite the intense research carried out on the different materials that can be processed by SLS, and the numerous papers in the literature reporting data on porosity, to the knowledge of the authors of this paper, to date, no researcher has tried to compare the measured porosity levels. It is believed that a comparison of the numerous data available could be important to increase knowledge in the field.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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