Vat Photopolymerization Processes PDF

4 Vat Photopolymerization Processes Abstract Photopolymerization processes make use of liquid, radiation-curable resins, or photopolymers, as their primary materials. Most photopolymers react to radiation in the ultraviolet (UV) range of wavelengths, but some visible light systems are used as well. Upon irradiation, these materials undergo a chemical reaction to become solid. This reaction is called photopolymerization, and is typically complex, involving many chemical participants. Photopolymers were developed in the late 1960s and soon became widely applied in several commercial areas, most notably the coating and printing industry. Many of the glossy coatings on paper and cardboard, for example, are photopolymers. Additionally, photo-curable resins are used in dentistry, such as for sealing the top surfaces of teeth to fill in deep grooves and prevent cavities. In these applications, coatings are cured by radiation that blankets the resin without the need for patterning either the material or the radiation. This changed with the introduction of stereolithography, the first vat photopolymerization process. 4.1 Introduction Photopolymerization processes make use of liquid, radiation-curable resins, or photopolymers, as their primary materials. Most photopolymers react to radiation in the ultraviolet (UV) range of wavelengths, but some visible light systems are used as well. Upon irradiation, these materials undergo a chemical reaction to become solid. This reaction is called photopolymerization, and is typically complex, involving many chemical participants. Photopolymers were developed in the late 1960s and soon became widely applied in several commercial areas, most notably the coating and printing industry. Many of the glossy coatings on paper and cardboard, for example, are photopolymers. Additionally, photo-curable resins are used in dentistry, such as # Springer Science+Business Media New York 2015 I. Gibson et al., Additive Manufacturing Technologies, DOI 10.1007/978-1-4939-2113-3_4 63 64 4 Vat Photopolymerization Processes for sealing the top surfaces of teeth to fill in deep grooves and prevent cavities. In these applications, coatings are cured by radiation that blankets the resin without the need for patterning either the material or the radiation. This changed with the introduction of stereolithography. In the mid-1980s, Charles (Chuck) Hull was experimenting with UV-curable materials by exposing them to a scanning laser, similar to the system found in laser printers. He discovered that solid polymer patterns could be produced. By curing one layer over a previous layer, he could fabricate a solid 3D part. This was the beginning of stereolithography (SL) technology. The company 3D Systems was created shortly thereafter to market SL machines as “rapid prototyping” machines to the product development industry. Since then, a wide variety of SL-related processes and technologies has been developed. The term “vat photopolymerization” is a general term that encompasses SL and these related processes. SL will be used to refer specifically to macroscale, laser scan vat photopolymerization; otherwise, the term vat polymerization will be used and will be abbreviated as VP. Various types of radiation may be used to cure commercial photopolymers, including gamma rays, X-rays, electron beams, UV, and in some cases visible light. In VP systems, UV and visible light radiation are used most commonly. In the microelectronics industry, photomask materials are often photopolymers and are typically irradiated using far UV and electron beams. In contrast, the field of dentistry uses visible light predominantly. Two primary configurations were developed for photopolymerization processes in a vat, plus one additional configuration that has seen some research interest. Although photopolymers are also used in some ink-jet printing processes, this method of line-wise processing is not covered in this chapter, as the basic processing steps are more similar to the printing processes covered in Chap. 7. The configurations discussed in this chapter include: • Vector scan, or point-wise, approaches typical of commercial SL machines • Mask projection, or layer-wise, approaches, that irradiate entire layers at one time, and • Two-photon approaches that are essentially high-resolution point-by-point approaches These three configurations are shown schematically in Fig. 4.1. Note that in the vector scan and two-photon approaches, scanning laser beams are needed, while the mask projection approach utilizes a large radiation beam that is patterned by another device, in this case a Digital Micromirror Device™ (DMD). In the two-photon case, photopolymerization occurs at the intersection of two scanning laser beams, although other configurations use a single laser and different photoinitiator chemistries. Another distinction is the need to recoat, or apply a new layer of resin, in the vector scan and mask projection approaches, while in the two-photon approach, the part is fabricated below the resin surface, making 4.2 Vat Photopolymerization Materials 65 a Scanning Galvanometers Laser Optics Platform Vat schematic of vector scan SL La Lase r c r se b DMD Laser or Lamp Optics Platform Vat Schematic of mask projection approach to SL. Vat Two-photon approach Fig. 4.1 Schematic diagrams of three approaches to photopolymerization processes recoating unnecessary. Approaches that avoid recoating are faster and less complicated. In this chapter, we first introduce photopolymer materials, then present the vector scan SL machines, technologies, and processes. Mask projection approaches are presented and contrasted with the vector scan approach. Additional configurations, along with their applications, are presented at the end of the chapter. Advantages, disadvantages, and uniquenesses of each approach and technology are highlighted. 4.2 Vat Photopolymerization Materials Some background of UV photopolymers will be presented in this section that is common to all configurations of photopolymerization processes. Two subsections on reaction rates and characterization methods conclude this section. Much of this material is from the Jacobs book [1] and from a Master’s thesis from the early 2000s [2]. 66 4.2.1 4 Vat Photopolymerization Processes UV-Curable Photopolymers As mentioned, photopolymers were developed in the late 1960s. In addition to the applications mentioned in Sect. 4.1, they are used as photoresists in the microelectronics industry. This application has had a major impact on the development of epoxy-based photopolymers. Photoresists are essentially one-layer SL, but with critical requirements on accuracy and feature resolution. Various types of radiation may be used to cure commercial photopolymers, including gamma rays, X-rays, electron beams, UV, and in some cases visible light, although UV and electron beam are the most prevalent. In AM, many of these radiation sources have been utilized in research, however only UV and visible light systems are utilized in commercial systems. In SL systems, for example, UV radiation is used exclusively although, in principle, other types could be used. In the SLA-250 from 3D Systems, a helium–cadmium (HeCd) laser is used with a wavelength of 325 nm. In contrast, the solid-state lasers used in the other SL models are Nd-YVO4. In mask projection DMD-based systems, UV and visible light radiation are used. Thermoplastic polymers that are typically injection molded have a linear or branched molecular structure that allows them to melt and solidify repeatedly. In contrast, VP photopolymers are cross-linked and, as a result, do not melt and exhibit much less creep and stress relaxation. Figure 4.2 shows the three polymer structures mentioned [3]. The first US patents describing SL resins were published in 1989 and 1990 [4, 5]. These resins were prepared from acrylates, which had high reactivity but typically produced weak parts due to the inaccuracy caused by shrinkage and curling. The acrylate-based resins typically could only be cured to 46 % completion when the image was transferred through the laser [6]. When a fresh coating was put on the exposed layer, some radiation went through the new coating and initiated new photochemical reactions in the layer that was already partially cured. This layer was less susceptible to oxygen inhibition after it had been coated. The additional cross-linking on this layer caused extra shrinkage, which increased stresses in the layer, and caused curling that was observed either during or after the part fabrication process [7]. The first patents that prepared an epoxide composition for SL resins appeared in 1988 [8, 9] (Japanese). The epoxy resins produced more accurate, harder, and stronger parts than the acrylate resins. While the polymerization of acrylate compositions leads to 5–20 % shrinkage, the ring-opening polymerization of epoxy compositions only leads to a shrinkage of 1–2 % [10]. This low level of shrinkage associated with epoxy chemistry contributes to excellent adhesion and reduced tendency for flexible substrates to curl during cure. Furthermore, the polymerization of the epoxy-based resins is not inhibited by atmospheric oxygen. This enables low-photoinitiator concentrations, giving lower residual odor than acrylic formulations [11]. However, the epoxy resins have disadvantages of slow photospeed and brittleness of the cured parts. The addition of some acrylate to epoxy resins is required to 4.2 Vat Photopolymerization Materials Fig. 4.2 Schematics of polymer types 67 a linear b branched c cross-linked rapidly build part strength so that they will have enough integrity to be handled without distortion during fabrication. The acrylates are also useful to reduce the brittleness of the epoxy parts [7]. Another disadvantage of epoxy resins is their sensitivity to humidity, which can inhibit polymerization [11]. As a result, most SL resins commercially available today are epoxides with some acrylate content. It is necessary to have both materials present in the same formulation to combine the advantages of both curing types. The improvement in accuracy resulting from the use of hybrid resins has given SL a tremendous boost. 4.2.2 Overview of Photopolymer Chemistry VP photopolymers are composed of several types of ingredients: photoinitiators, reactive diluents, flexibilizers, stabilizers, and liquid monomers. Broadly speaking, when UV radiation impinges on VP resin, the photoinitiators undergo a chemical transformation and become “reactive” with the liquid monomers. A “reactive” photoinitiator reacts with a monomer molecule to start a polymer chain. Subsequent reactions occur to build polymer chains and then to cross-link—creation of strong covalent bonds between polymer chains. Polymerization is the term used to describe the process of linking small molecules (monomers) into larger molecules (polymers) composed of many monomer units [1]. Two main types of photopolymer chemistry are commercially evident: 68 4 Vat Photopolymerization Processes • Free-radical photopolymerization—acrylate • Cationic photopolymerization—epoxy and vinylether The molecular structures of these types of photopolymers are shown in Fig. 4.5. Symbols C and H denote carbon and hydrogen atoms, respectively, while R denotes a molecular group which typically consists of one or more vinyl groups. A vinyl group is a molecular structure with a carbon–carbon double bond. It is these vinyl groups in the R structures that enable photopolymers to become cross-linked. Free-radical photopolymerization was the first type that was commercially developed. Such SL resins were acrylates. Acrylates form long polymer chains once the photoinitiator becomes “reactive,” building the molecule linearly by adding monomer segments. Cross-linking typically happens after the polymer chains grow enough so that they become close to one another. Acrylate photopolymers exhibit high photospeed (react quickly when exposed to UV radiation), but have a number of disadvantages including significant shrinkage and a tendency to warp and curl. As a result, they are rarely used now without epoxy or other photopolymer elements. The most common cationic photopolymers are epoxies, although vinylethers are also commercially available. Epoxy monomers have rings, as shown in Fig. 4.3. When reacted, these rings open, resulting in sites for other chemical bonds. Ringopening is known to impart minimal volume change on reaction, because the number and types of chemical bonds are essentially identical before and after reaction [12]. As a result, epoxy SL resins typically have much smaller shrinkages and much less tendency to warp and curl. Almost all commercially available SL resins have significant amounts of epoxies. Polymerization of VP monomers is an exothermic reaction, with heats of reaction around 85 kJ/mol for an example acrylate monomer. Despite high heats of reaction, a catalyst is necessary to initiate the reaction. As described earlier, a photoinitiator acts as the catalyst. Schematically, the free radical-initiated polymerization process can be illustrated as shown in Fig. 4.4 [1]. On average, for every two photons (from the laser), one radical will be produced. That radical can easily lead to the polymerization of over 1,000 monomers, as shown in the intermediate steps of the process, called propagation. In general, longer polymer molecules are preferred, yielding higher molecular weights. This indicates a more complete reaction. In Fig. 4.4, the P–I term indicates a photoinitiator, the I● symbol is a free radical, and M in a monomer. Polymerization terminates from one of three causes, recombination, disproportionation, or occlusion. Recombination occurs when two polymer chains merge by joining two radicals. Disproportionation involves essentially the cancelation of one radical by another, without joining. Occlusion occurs when free radicals become “trapped” within a solidified polymer, meaning that reaction sites remain available, but are prevented from reacting with other monomers or polymers by the limited mobility within the polymer network. These occluded sites will most certainly react eventually, but not with another polymer chain or monomer. Instead, they will react 4.2 Vat Photopolymerization Materials 69 a Fig. 4.3 Molecular structure of VP monomers H H O C C C H O Acrylate R b O H H C C R H Epoxy c H H C C O H R Vinylether P-I -I• (free radical formation) I• +M I-M• I-M• I-M-M-M-M...-M• (propagation) (initiation) I-M-M-M-M...-M-I (termination) Fig. 4.4 Free-radical polymerization process with oxygen or another reactive species that diffuses into the occluded region. This may be a cause of aging or other changes in mechanical properties of cured parts, which should be a topic of future research. Cationic photopolymerization shares the same broad structure as free-radical polymerization, where a photoinitiator generates a cation as a result of laser energy, the cation reacts with a monomer, propagation occurs to generate a polymer, and a termination process completes the reaction. A typical catalyst for a cationic polymerization is a Lewis Acid, such as BF3 [13]. Initially, cationic photopolymerization received little attention, but that has changed during the 1990s due to advances in the microelectronics industry, as well as interest in SL technology. We 70 4 Vat Photopolymerization Processes will not investigate the specifics of cationic reactions here, but will note that the ring-opening reaction mechanism of epoxy monomers is similar to radical propagation in acrylates. 4.2.3 Resin Formulations and Reaction Mechanisms Basic raw materials such as polyols, epoxides, (meth) acrylic acids and their esters, and diisocyanates are used to produce the monomers and oligomers used for radiation curing. Most of the monomers are multifunctional monomers (MFM) or polyol polyacrylates which give a cross-linking polymerization. The main chemical families of oligomers are polyester acrylate (PEA), epoxy acrylates (EA), urethane acrylates (UA), amino acrylates (used as photoaccelerator in the photoinitiator system), and cycloaliphatic epoxies [11]. Resin suppliers create ready-to-use formulations by mixing the oligomers and monomers with a photoinitiator, as well as other materials to affect reaction rates and part properties. In practice, photosensitizers are often used in combination with the photoinitiator to shift the absorption towards longer wavelengths. In addition, supporting materials may be mixed with the initiator to achieve improved solubility in the formulation. Furthermore, mixtures of different types of photoinitiators may also be employed for a given application. Thus, photoinitiating systems are, in practice, often highly elaborate mixtures of various compounds which provide optimum performance for specific applications [10]. Other additives facilitate the application process and achieve products of good properties. A reactive diluent, for example, is usually added to adjust the viscosity of the mixtures to an acceptable level for application [14]; it also participates in the polymerization reaction. 4.2.3.1 Photoinitiator System The role of the photoinitiator is to convert the physical energy of the incident light into chemical energy in the form of reactive intermediates. The photoinitiator must exhibit a strong absorption at the laser emission wavelength, and undergo a fast photolysis to generate the initiating species with a great quantum yield [15]. The reactive intermediates are either radicals capable of adding to vinylic or acrylic double bonds, thereby initiating radical polymerization, or reactive cationic species which can initiate polymerization reactions among epoxy molecules [10]. The free-radical polymerization process was outlined in Fig. 4.4, with the formation of free radicals as the first step. In the typical case in VP, radical photoinitiator systems include compounds that undergo unimolecular bond cleavage upon irradiation. This class includes aromatic carbonyl compounds that are known to undergo a homolytic C–C bond scission upon UV exposure [16]. The benzoyl radical is the major initiating species, while the other fragment may, in some cases, also contribute to the initiation. The most efficient photoinitiators include benzoin ether derivatives, benzyl ketals, hydroxyalkylphenones, α-amino 4.2 Vat Photopolymerization Materials 71 ketones, and acylphosphine oxides [16, 17]. The Irgacure family of radical photoinitiators from Ciba Specialty Chemicals is commonly used in VP. While photoinitiated free-radical polymerizations have been investigated for more than 60 years, the corresponding photoinduced cationic polymerizations have received much less attention. The main reason for the slow development in this area was the lack of suitable photoinitiators capable of efficiently inducing cationic polymerization [18]. Beginning in 1965, with the earliest work on diazonium salt initiators, this situation has markedly changed. The discovery in the 1970s of onium salts or organometallic compounds with excellent photoresponse and high efficiency has initiated the very rapid and promising development of cationic photopolymerization, and made possible the concurrent radical and cationic reaction in hybrid systems [19]. Excellent reviews have been published in this field [10, 18, 20–23]. The most important cationic photoinitiators are the onium salts, particularly the triarylsulfonium and diaryliodonium salts. Examples of the cationic photoinitiator are triaryl sulfonium hexafluorophosphate solutions in propylene carbonate such as Degacure KI 85 (Degussa), SP-55 (Asahi Denka), Sarcat KI-85 (Sartomer), and 53,113-8 (Aldrich), or mixtures of sulfonium salts such as SR-1010 (Sartomer, currently unavailable), UVI 6976 (B-V), and UVI 6992 (B-VI) (Dow). Initiation of cationic polymerization takes place from not only the primary products of the photolysis of triarylsulfonium salts but also from secondary products of the reaction of those reactive species with solvents, monomers, or even other photolysis species. Probably the most ubiquitous species present is the protonic acid derived from the anion of the original salt. Undoubtedly, the largest portion of the initiating activity in cationic polymerization by photolysis of triarylsulfonium salts is due to protonic acids [18]. 4.2.3.2 Monomer Formulations The monomer formulations presented here are from a set of patents from the mid- to late-1990s. Both di-functional and higher functionality monomers are used typically in VP resins. Poly(meth)acrylates may be tri-, pentafunctional monomeric or oligomeric aliphatic, cycloaliphatic or aromatic (meth)acrylates, or polyfunctional urethane (meth)acrylates [24–27]. One specific compound in the Huntsman SL-7510 resin includes the dipentaerythritol monohydroxy penta(meth)acrylates [26], such as Dipentaerythritol Pentaacrylate (SR-399, Sartomer). The cationically curable epoxy resins may have an aliphatic, aromatic, cycloaliphatic, araliphatic, or heterocyclic structure; they on average possess more than one epoxide group (oxirane ring) in the molecule and comprise epoxide groups as side groups, or those groups form part of an alicyclic or heterocyclic ring system. Examples of epoxy resins of this type are also given by these patents such as polyglycidyl esters or ethers, poly(N or S-glycidyl) compounds, and epoxide compounds in which the epoxide groups form part of an alicyclic or heterocyclic ring system. One specific composition includes at least 50 % by weight of a cycloaliphatic diepoxide [26] such as bis(2,3-epoxycyclopentyl) ether (formula A-I), 3,4-epoxycyclohexyl-methyl 3,4-epoxycyclohexanecarboxylate (A-II), 72 4 Vat Photopolymerization Processes dicyclopentadiene diepoxide (A-III), and bis-(3,4-epoxycyclohexylmethyl) adipate (A-IV). Additional insight into compositions can be gained by investigating the patent literature further. 4.2.3.3 Interpenetrating Polymer Network Formation As described earlier, acrylates polymerize radically, while epoxides cationically polymerize to form their respective polymer networks. In the presence of each other during the curing process, an interpenetrating polymer network (IPN) is finally obtained [28, 29]. An IPN can be defined as a combination of two polymers in network form, at least one of which is synthesized and/or cross-linked in the immediate presence of the other [30]. It is therefore a special class of polymer blends in which both polymers generally are in network form [30–32], and which is originally generated by the concurrent reactions instead of by a simple mechanical mixing process. In addition, it is a polymer blend rather than a copolymer that is generated from the hybrid curing [33], which indicates that acrylate and epoxy monomers undergo independent polymerization instead of copolymerization. However, in special cases, copolymerization can occur, thus leading to a chemical bonding of the two networks [34]. It is likely that in typical SL resins, the acrylate and epoxide react independently. Interestingly, however, these two monomers definitely affect each other physically during the curing process. The reaction of acrylate will enhance the photospeed and reduce the energy requirement of the epoxy reaction. Also, the presence of acrylate monomer may decrease the inhibitory effect of humidity on the epoxy polymerization. On the other hand, the epoxy monomer acts as a plasticizer during the early polymerization of the acrylate monomer where the acrylate forms a network while the epoxy is still at liquid stage [31]. This plasticizing effect, by increasing molecular mobility, favors the chain propagation reaction [35]. As a result, the acrylate polymerizes more extensively in the presence of epoxy than in the neat acrylate monomer. Furthermore, the reduced sensitivity of acrylate to oxygen in the hybrid system than in the neat composition may be due to the simultaneous polymerization of the epoxide which makes the viscosity rise, thus slowing down the diffusion of atmospheric oxygen into the coating [31]. In addition, it has been shown [31] that the acrylate/epoxide hybrid system requires a shorter exposure to be cured than either of the two monomers taken separately. It might be due to the plasticizing effect of epoxy monomer and the contribution of acrylate monomer to the photospeed of the epoxy polymerization. The two monomers benefit from each other by a synergistic effect. It should be noted that if the concentration of the radical photoinitiator was decreased so that the two polymer networks were generated simultaneously, the plasticizing effect of the epoxy monomer would become less pronounced. As a result, it would be more difficult to achieve complete polymerization of the acrylate monomer and thus require longer exposure time. Although the acrylate/epoxy hybrid system proceeds via a heterogeneous mechanism, the resultant product (IPN) seems to be a uniphase component [36]. The 4.3 Reaction Rates 73 properties appear to be extended rather than compromised [31, 34]. The optimal properties of IPNs for specific applications can be obtained by selecting two appropriate components and adjusting their proportions [34]. For example, increasing the acrylate content increases the cure speed but decreases the adhesion characteristics, while increasing the epoxy content reduces the shrinkage of curing and improves the adhesion, but decreases the cure speed [36]. 4.3 Reaction Rates As is evident, the photopolymerization reaction in VP resins is very complex. To date, no one has published an analytical photopolymerization model that describes reaction results and reaction rates. However, qualitative understanding of reaction rates is straightforward for simple formulations. Broadly speaking, reaction rates for photopolymers are controlled by concentrations of photoinitiators [I] and monomers [M]. The rate of polymerization is the rate of monomer consumption, which can be shown as [3]: Rp ¼ d ½M=dt α ½M ðk½I Þ1=2 ð4:1Þ where k ¼ constant that is a function of radical generation efficiency, rate of radical initiation, and rate of radical termination. Hence, the polymerization rate is proportional to the concentration of monomer, but is only proportional to the square root of initiator concentration. Using similar reasoning, it can be shown that the average molecular weight of polymers is the ratio of the rate of propagation and the rate of initiation. This average weight is called the kinetic average chain length, vo, and is given in (4.2): vo ¼ Rp =Ri α ½M=½I1=2 ð4:2Þ where Ri is the rate of initiation of macromonomers. Equations (4.1) and (4.2) have important consequences for the VP process. The higher the rate of polymerization, the faster parts can be built. Since VP resins are predominantly composed of monomers, the monomer concentration cannot be changed much. Hence, the only other direct method for controlling the polymerization rate and the kinetic average chain length is through the concentration of initiator. However, (4.1) and (4.2) indicate a trade-off between these characteristics. Doubling the initiator concentration only increases the polymerization rate by a factor of 1.4, but reduces the molecular weight of resulting polymers by the same amount. Strictly speaking, this analysis is more appropriate for acrylate resins, since epoxies continue to react after laser exposure, so (4.2) does not apply well for epoxies. However, reaction of epoxies is still limited, so it can be concluded that a trade-off does exist between polymerization rate and molecular weight for epoxy resins. 74 4.4 4 Vat Photopolymerization Processes Laser Scan Vat Photopolymerization Laser scan VP creates solid parts by selectively solidifying a liquid photopolymer resin using an UV laser. As with many other AM processes, the physical parts are manufactured by fabricating cross-sectional contours, or slices, one on top of another. These slices are created by tracing 2D contours of a CAD model in a vat of photopolymer resin with a laser. The part being built rests on a platform that is dipped into the vat of resin, as shown schematically in Fig. 4.1a. After each slice is created, the platform is lowered, the surface of the vat is recoated, then the laser starts to trace the next slice of the CAD model, building the prototype from the bottom up. A more complete description of the SL process may be found in [12]. The creation of the part requires a number of key steps: input data, part preparation, layer preparation, and finally laser scanning of the two-dimensional cross-sectional slices. The input data consist of an STL file created from a CAD file or reverse engineering data. Part preparation is the phase at which the operator specifies support structures, to hold each cross section in place while the part builds, and provides values for machine parameters. These parameters control how the prototype is fabricated in the VP machine. Layer preparation is the phase in which the STL model is divided into a series of slices, as defined by the part preparation phase, and translated by software algorithms into a machine language. This information is then used to drive the SL machine and fabricate the prototype. The laser scanning of the part is the phase that actually solidifies each slice in the VP machine. After building the part, the part must be cleaned, post-cured, and finished. During the cleaning and finishing phase, the VP machine operator may remove support structures. During finishing, the operator may spend considerable time sanding and filing the part to provide the desired surface finishes. 4.5 Photopolymerization Process Modeling Background on SL materials and energy sources enables us to investigate the curing process of photopolymers in SL machines. We will begin with an investigation into the fundamental interactions of laser energy with photopolymer resins. Through the application of the Beer–Lambert law, the theoretical relationship between resin characteristics and exposure can be developed, which can be used to specify laser scan speeds. This understanding can then be applied to investigate mechanical properties of cured resins. From here, we will briefly investigate the ranges of size scales and time scales of relevance to the SL process. Much of this section is adapted from [1]. Nomenclature Cd ¼ cure depth ¼ depth of resin cure as a result of laser irradiation [mm] Dp ¼ depth of penetration of laser into a resin until a reduction in irradiance of 1/e is reached ¼ key resin characteristic [mm] 4.5 Photopolymerization Process Modeling 75 E ¼ exposure, possibly as a function of spatial coordinates [energy/unit area] [mJ/mm2] Ec ¼ critical exposure ¼ exposure at which resin solidification starts to occur [mJ/mm2] Emax ¼ peak exposure of laser shining on the resin surface (center of laser spot) [mJ/mm2] H(x, y, z) ¼ irradiance (radiant power per unit area) at an arbitrary point in the resin ¼ time derivative of E(x, y, z).[W/mm2] PL ¼ output power of laser [W] Vs ¼ scan speed of laser [mm/s] W0 ¼ radius of laser beam focused on the resin surface [mm] 4.5.1 Irradiance and Exposure As a laser beam is scanned across the resin surface, it cures a line of resin to a depth that depends on many factors. However, it is also important to consider the width of the cured line as well as its profile. The shape of the cured line depends on resin characteristics, laser energy characteristics, and the scan speed. We will investigate the relationships among all of these factors in this subsection. The first concept of interest here is irradiance, the radiant power of the laser per unit area, H(x, y, z). As the laser scans a line, the radiant power is distributed over a finite area (beam spots are not infinitesimal). Figure 4.5 shows a laser scanning a line along the x-axis at a speed Vs [1]. Consider the z-axis oriented perpendicular to the resin surface and into the resin, and consider the origin such that the point of interest, p0 , has an x coordinate of 0. The irradiance at any point x, y, z in the resin is related to the irradiance at the surface, assuming that the resin absorbs radiation according to the Beer–Lambert Law. The general form of the irradiance equation for a Gaussian laser beam is given here as (4.3). Hðx; y; zÞ ¼ H ðx; y; 0Þez=Dp ð4:3Þ From this relationship, we can understand the meaning of the penetration depth, Dp. Setting z ¼ Dp, we get that the irradiance at a depth Dp is about 37 % (e1 ¼ 0.36788) of the irradiance at the resin surface. Thus, Dp is the depth into the resin at which the irradiance is 37 % of the irradiance at the surface. Furthermore, since we are assuming the Beer–Lambert Law holds, Dp is only a function of the resin. Without loss of generality, we will assume that the laser scans along the x-axis from the origin to point b. Then, the irradiance at coordinate x along the scan line is given by 76 4 Vat Photopolymerization Processes Fig. 4.5 Scan line of Gaussian laser Wo Vs x r p’ y p H ðx; y; 0Þ ¼ H ðx; yÞ ¼ H 0 e2x 2 =W 20 2y2 =W 20 e z ð4:4Þ where H0 ¼ H(0,0) when x ¼ 0, and W0 is the 1/e2 Gaussian half-width of the beam spot. Note that when x ¼ W0, H(x,0) ¼ H0e2 ¼ 0.13534H0. The maximum irradiance, H0, occurs at the center of the beam spot (x ¼ 0). H0 can be determined by integrating the irradiance function over the area covered by the beam at any particular point in time. Changing from Cartesian to polar coordinates, the integral can be set equal to the laser power, PL, as shown in (4.5). Z PL ¼ r¼1 H ðr; 0Þ dA ð4:5Þ r¼0 When solved, Ho turns out to be a simple function of laser power and beam halfwidth, as in (4.6). H0 ¼ 2PL πW 20 ð4:6Þ As a result, the irradiance at any point x, y between x ¼ 0 and x ¼ b is given by: H ðx; yÞ ¼ 2pL 2x2 =W 20 2y2 =W 20 e e πW 20 ð4:7Þ However, we are interested in exposure at an arbitrary point, p, not irradiance, since exposure controls the extent of resin cure. Exposure is the energy per unit area; when exposure at a point in the resin vat exceeds a critical value, called Ec, we assume that resin cures. Exposure can be determined at point p by appropriately integrating (4.7) along the scan line, from time 0 to time tb, when the laser reaches point b. 4.5 Photopolymerization Process Modeling Z Eðy; 0Þ ¼ 77 t¼tb H ½xðtÞ, 0dt ð4:8Þ t¼0 It is far more convenient to integrate over distance than over time. If we assume a constant laser scan velocity, then it is easy to substitute t for x, as in (4.9). Eðy; 0Þ ¼ Z 2PL 2y2 =W 20 e πV s W 20 x¼b e2x 2 =W 20 dx ð4:9Þ x¼0 The exponential term is difficult to integrate directly, so we will change the variable of integration. Define a variable of integration, v, as v2 2x2 W 20 Then, take the square root of both sides, take the derivative, and rearrange to give W0 dx ¼ pﬃﬃﬃdv 2 Due to the change of variables, it is also necessary to convert the integration pﬃﬃﬃ limit to b ¼ 2=W 0 xe : Several steps in the derivation will be skipped. After integration, the exposure received at a point x, y between x ¼ (0, b) can be computed as: 2 2y2 PL Eðy; 0Þ ¼ pﬃﬃﬃ e W0 ½erf ðbÞ 2πW 0 V s ð4:10Þ where erf(x) is the error function evaluated at x. erf(x) is close to 1 for negative values of x, is close to 1 for positive values of x, and rapidly transitions from 1 to 1 for values of x close to 0. This behavior localizes the exposure within a narrow range around the scan vector. This makes sense since the laser beam is small and we expect that the energy received from the laser drops off quickly outside of its radius. Equation (4.10) is not quite as easy to apply as a form of the exposure equation that results from assuming an infinitely long scan vector. If we make this assumption, then (4.10) becomes 2PL 2y2 =W 20 Eðy; 0Þ ¼ e πV s W 20 and after integration, exposure is given by Z x¼1 x¼1 e2x 2 =W 20 dx 78 4 Vat Photopolymerization Processes rﬃﬃﬃ 2 PL 2y2 =W 20 Eðy; 0Þ ¼ e πW0 Vs ð4:11Þ Combining this with (4.3) yields the fundamental general exposure equation: rﬃﬃﬃ 2 PL 2y2 =W 20 z=Dp Eðx; y; zÞ ¼ e e πW 0Vs 4.5.2 ð4:12Þ Laser–Resin Interaction In this subsection, we will utilize the irradiance and exposure relationships to determine the shape of a scanned vector line and its width. As we will see, the cross-sectional shape of a cured line becomes a parabola. Starting with (4.12), the locus of points in the resin that is just at its gel point, where E ¼ Ec, is denoted by y* and z*. Equation (4.12) can be rearranged, with y*, z*, and Ec substituted to give (4.13). 2y2 =W 20 þz=DP e rﬃﬃﬃ 2 PL ¼ π W 0 V s Ec ð4:13Þ Taking natural logarithms of both sides yields "rﬃﬃﬃ # y2 z 2 PL ¼ ln 2 2þ π W 0 V s Ec W 0 Dp ð4:14Þ This is the equation of a parabolic cylinder in y* and z*, which can be seen more clearly in the following form, ay2 þ bz ¼ c ð4:15Þ where a, b, and c are constants, immediately derivable from (4.14). Figure 4.6 illustrates the parabolic shape of a cured scan line. To determine the maximum depth of cure, we can solve (4.14) for z* and set y* ¼ 0, since the maximum cure depth will occur along the center of the scan vector. Cure depth, Cd, is given by "rﬃﬃﬃ # 2 PL Cd ¼ DP ln π W 0 V s Ec ð4:16Þ As is probably intuitive, the width of a cured line of resin is the maximum at the resin surface; i.e., ymax occurs at z ¼ 0. To determine line width, we start with the line shape function (4.14). Setting z ¼ 0 and letting line width, Lw, equal 2ymax, the line width can be found: 4.5 Photopolymerization Process Modeling 79 Fig. 4.6 Cured line showing parabolic shape, cure depth, and line width Lw X Y Cd Z LW ¼ W 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2Cd =Dp ð4:17Þ As a result, two important aspects become clear. First, line width is proportional to the beam spot size. Second, if a greater cure depth is desired, line width must increase, all else remaining the same. This becomes very important when performing line width compensation during process planning. The final concept to be presented in this subsection is fundamental to commercial SL. It is the working curve, which relates exposure to cure depth, and includes the two key resin constants, Dp and Ec. At the resin surface and in the center of the scan line: Eð0; 0Þ Emax rﬃﬃﬃ 2 PL ¼ πW0 Vs ð4:18Þ which is most of the expression within the logarithm term in (4.16). Substituting (4.18) into (4.16) yields the working curve equation: Cd ¼ DP ln Emax Ec ð4:19Þ In summary, a laser of power PL scans across the resin surface at some speed Vs solidifying resin to a depth Cd, the cure depth, assuming that the total energy incident along the scan vector exceeds a critical value called the critical exposure, Ec. If the laser scans too quickly, no polymerization reaction takes place; i.e., exposure E is less than Ec. Ec is assumed to be a characteristic quantity of a particular resin. An example working curve is shown in Fig. 4.7, where measured cure depths at a given exposure are indicated by “*.” The working curve equation, (4.19), has several major properties [1]: 80 4 Vat Photopolymerization Processes Cure Depth vs. Exposure 25 20 Cure Depth (mils) 15 Dp 10 5 0 Ec –5 –10 100 101 102 Exposure 103 (mJ/cm2) Fig. 4.7 Resin “working curve” of cure depth vs. exposure 1. The cure depth is proportional to the natural logarithm of the maximum exposure on the centerline of a scanned laser beam. 2. A semilog plot of Cd vs. Emax should be a straight line. This plot is known as the working curve for a given resin. 3. The slope of the working curve is precisely Dp at the laser wavelength being used to generate the working curve. 4. The x-axis intercept of the working curve is Ec, the critical exposure of the resin at that wavelength. Theoretically, the cure depth is 0 at Ec, but this does indicate the gel point of the resin. 5. Since Dp and Ec are purely resin parameters, the slope and intercept of the working curve are independent of laser power. In practice, various Emax values can be generated easily by varying the laser scan speed, as indicated by (4.19). 4.5.3 Photospeed Photospeed is typically used as an intuitive approximation of SL photosensitivity. But it is useful in that it relates to the speed at which the laser can be scanned across the polymer surface to give a specified cure depth. The faster the laser can be scanned to give a desired cure depth, the higher the photospeed. Photospeed is a 4.5 Photopolymerization Process Modeling 81 characteristic of the resin and does not depend upon the specifics of the laser or optics subsystems. In particular, photospeed is indicated by the resin constants Ec and Dp, where higher levels of Dp and lower values of Ec indicate higher photospeed. To determine scan velocity for a desired cure depth, it is straightforward to solve (4.16) for Vs. Recall that at the maximum cure depth, the exposure received equals the cure threshold, Ec. Scan velocity is given by (4.20). rﬃﬃﬃ 2 PL Cd =DP Vs ¼ e π W 0 Ec ð4:20Þ This discussion can be related back to the working curve. Both Ec and Dp must be determined experimentally. 3D Systems has developed a procedure called the WINDOWPANE procedure for finding Ec and Dp values [41]. The cure depth, Cd, can be measured directly from specimens built on an SL machine that are one layer thickness in depth. The WINDOWPANE procedure uses a specific part shape, but the principle is simply to build a part with different amounts of laser exposure in different places in the part. By measuring the part thickness, Cd, and correlating that with the exposure values, a “working curve” can easily be plotted. Note that (4.19) is log-linear. Hence, Cd is plotted linearly vs. the logarithm of exposure to generate a working curve. So how is exposure varied? Exposure is varied by simply using different scan velocities in different regions of the WINDOWPANE part. The different scan velocities will result in different cure depths. In practice, (4.20) is very useful since we want to directly control cure depth, and want to determine how fast to scan the laser to give that cure depth. Of course, for the WINDOWPANE experiment, it is more useful to use (4.16) or (4.19). 4.5.4 Time Scales It is interesting to investigate the time scales at which SL operates. On the short end of the time scale, the time it takes for a photon of laser light to traverse a photopolymer layer is about a picosecond (10–12 s). Photon absorption by the photoinitiator and the generation of free radicals or cations occur at about the same time frame. A measure of photopolymer reaction speed is the kinetic reaction rates, tk, which are typically several microseconds. The time it takes for the laser to scan past a particular point on the resin surface is related to the size of the laser beam. We will call this time the characteristic exposure time, te. Values of te are typically 50–2,000 μs, depending on the scan speed (500–5,000 mm/s). Laser exposure continues long after the onset of polymerization. Continued exposure generates more free radicals or cations and, presumably, generates these at points deeper in the photopolymer. During and after the laser beam traverses the point of interest, cross-linking occurs in the photopolymer. 82 4 Vat Photopolymerization Processes The onset of measurable shrinkage, ts,o, lags exposure by several orders of magnitude. This appears to be due to the rate of cross-linking, but for the epoxybased resins, may have more complicated characteristics. Time at corresponding completion of shrinkage is denoted ts,c. For the acrylate-based resins of the early 1990s, times for the onset and completion of shrinkage were typically 0.4–1 and 4– 10 s, respectively. Recall that epoxies can take hours or days to polymerize. Since shrinkage lags exposure, this is clearly a phenomenon that complicates the VP process. Shrinkage leads directly to accuracy problems, including deviation from nominal dimensions, warpage, and curl. The final time dimension is that of scan time for a layer, denoted td, which typically spans 10–300 s. The time scales can be summarized as tt tk te ts, o < ts, c td ð4:21Þ As a result, characteristic times for the VP process span about 14 orders of magnitude. 4.6 Vector Scan VP Machines At present (2014), 3D Systems is the predominant manufacturer of laser scanning VP machines in the world, although several other companies in Japan and elsewhere in Asia also market VP machines. Fockele & Schwarze in Germany produces a micro-VP technology, although they only sell design and manufacturing services. Several Japanese companies produce or produced machines, including Denken Engineering, CMET (Mitsubishi), Sony, Meiko Corp., Mitsui Zosen, and Teijin Seiki (license from Dupont). Formlabs is a start-up company, funded in part by a Kickstarter campaign, markets a small, high-resolution SL machine. A schematic of a typical VP machine was illustrated in Fig. 4.1a, which shows the main subsystems, including the laser and optics, the platform and elevator, the vat and resin-handling subsystem, and the recoater. The machine subsystem hierarchy is given in Fig. 4.8. Note that the five main subsystems are: recoating system, platform system, vat system, laser and optics system, and control system. Typically, recoating is done using a shallow dip and recoater blade sweeping. Recoating issues are discussed in [37]. The process can be described as follows: • After a layer has been cured, the platform dips down by a layer thickness. • The recoater blade slides over the whole build depositing a new layer of resin and smoothing the surface of the vat. A common recoater blade type is the zephyr blade, which is a hollow blade that is filled with resin. A vacuum system pulls resin into the blade from the vat. As the blade translates over the vat to perform recoating, resin is deposited in regions where the previous part cross section was built. When the blade encounters a region in the vat without resin, the resin falls into this region since its weight is stronger 4.6 Vector Scan VP Machines 83 SL Machine Recoating System Blade Platform System Elevator Resin Delivery Vat System Beam Generation Vat Drive System Laser & Optics System Resin Level Adjustment Control System Environment Control Lenses Temperature Sensors Beam Control Process Control Beam Sensors Scanning Fig. 4.8 Subsystems for SL technology than the vacuum force. Blade alignment is critical to avoid “blade crashes,” when the blade hits the part being built and often delaminates the previous layer. The blade gap (distance between the bottom of the blade and the resin surface) and speed are important variables under user control. The platform system consists of a build platform that supports the part being built and an elevator that lowers and raises the platform. The elevator is driven by a lead-screw. The vat system is simply the vat that holds the resin, combined with a level adjustment device, and usually an automated refill capability. The optics system includes a laser, focusing and adjustment optics, and two galvanometers that scan the laser beam across the surface of the vat. Modern VP machines have solid-state lasers that have more stable characteristics than their predecessors, various gas lasers. SL machines from 3D Systems have Nd-YVO4 lasers that output radiation at about 1,062 nm wavelength (near infrared). Additional optical devices triple the frequency to 354 nm, in the UV range. These lasers have relatively low power, in the range of 0.1–1 W, compared with lasers used in other AM and material processing applications. The control system consists of three main subsystems. First, a process controller controls the sequence of machine operations. Typically, this involves executing the sequence of operations that are described in the build file that was prepared for a specific part or set of parts. Commands are sent to the various subsystems to actuate the recoating blade, to adjust resin level or changing the vat height, or to activate the beam controller. Sensors are used to detect resin height and to detect forces on the recoater blade to detect blade crashes. Second, the beam controller converts operation descriptions into actions that adjust beam spot size, focus depth, and scan speed, with some sensors providing feedback. Third, the environment controller adjusts resin vat temperature and, depending on machine model, adjusts environment temperature and humidity. Two of the main advantages of VP technology over other AM technologies are part accuracy and surface finish, in combination with moderate mechanical properties. These characteristics led to the widespread usage of VP parts as form, 84 4 Vat Photopolymerization Processes fit, and, to a lesser extent, functional prototypes. Typical dimensional accuracies for VP machines are often quoted as a ratio of an error per unit length. For example, accuracy of an SLA-250 is typically quoted as 0.002 in./in. [38]. Modern VP machines are somewhat more accurate. Surface finish of SL parts ranges from submicron Ra for upfacing surfaces to over 100 μm Ra for surfaces at slanted angles [39]. The current commercial VP product line from 3D Systems consists of two families of models: the SLA Viper Si2, and the iPro SLA Centers (iPro 9000XL, iPro 9000, and iPro 8000). Some of these machines are summarized in Table 4.1 [40]. Both the Viper Si2 and the iPro models have dual laser spot size capabilities. In the Viper Si2, a “high-resolution” mode is available that provides a spot size of about 80 μm in diameter, useful for building small parts with fine features. In the iPro machines, in contrast, the machine automatically switches between the “normal” beam of 0.13 mm diameter for borders and fills and the “wide” beam of 0.76 mm diameter for hatch vectors (filling in large areas). The wide beam enables much faster builds. The iPro line replaces other machines, including the popular SLA-3500, SLA-5000, and SLA-7000 machines, as well as the SLA Viper Pro. Additionally, the SLA-250 was a very popular model that was discontinued in 2001 with the introduction of the Viper Si2 model. 4.7 Scan Patterns 4.7.1 Layer-Based Build Phenomena and Errors Several phenomena should be noted since they are common to all radiation and layer-based AM processes. The most obvious phenomenon is discretization, e.g., a stack of layers causes “stair steps” on slanted or curved surfaces. So, the layer-wise nature of most AM processes causes edges of layers to be visible. Conventionally, commercial AM processes build parts in a “material safe” mode, meaning that the stair steps are on the outside of the CAD part surfaces. Technicians can sand or finish parts; the material they remove is outside of the desired part geometry. Other discretization examples are the set of laser scans or the pixels of a DMD. In most processes, individual laser scans or pixels are not visible on part surfaces, but in other processes such as material extrusion, the individual filaments can be noticeable. As a laser scans a cross section, or a lamp illuminates a layer, the material solidifies and, as a result, shrinks. When resins photopolymerize, they shrink since the volume occupied by monomer molecules is larger than that of reacted polymer. Similarly, after powder melts, it cools and freezes, which reduces the volume of the material. When the current layer is processed, its shrinkage pulls on the previous layers, causing stresses to build up in the part. Typically, those stresses remain and are called residual stresses. Also, those stresses can cause part edges to curl upwards. Other warpage or part deformations can occur due to these residual stresses, as well. 4.7 Scan Patterns 85 Table 4.1 Selected SL systems (photos courtesy of 3D Systems, Inc.) iPro 9000XL SLA center Laser type Solid-state frequency tripled Nd:YV04 Wavelength 354.7 nm Power at vat 1,450 mW @ 5,000 h Recoating system Process Zephyr™ Recoater Layer thickness min 0.05 mm (0.002 in) Layer thickness max 0.15 mm (0.006 in) Optical and scanning Beam diameter 0.13 mm (borders) (@ 1/e2) 0.76 (large hatch) Drawing speed Maximum part weight Vat: Max. build envelope, capacity iPro 8000 SLA center Specifications are the same as the iPro 9000XL, except the following Maximum part weight Vat: Max. build envelope, capacity SLA Viper Si2 Laser type Wavelength Power at vat 3.5 m/s (borders) 25 m/s (hatch) 150 kg (330 lb) 650 350 300 (39.1 gal) 650 750 50 (25.1 gal) 650 750 275 (71.9 gal) 650 750 550 (109 gal) 1,500 750 550 75 kg (165 lb) 650 350 300 (39.1 gal) 650 750 50 (25.1 gal) 650 750 275 (71.9 gal) 650 750 550 (109 gal) Solid-State Nd:YV04 354.7 nm 100 mW (continued) 86 4 Vat Photopolymerization Processes Table 4.1 (continued) Recoating System: process Typical Minimum Optical and scanning Beam diameter (@ 1/e2): standard mode High-resolution Part drawing speed Maximum part weight Vat capacity Maximum build envelope High-res. build envelope Zephyr recoater 0.1 mm (0.004 in) app. 0.05 mm (0.002 in) app. 0.25 0.025 mm (0.01 0.001 in) 0.075 0.015 mm (0.003 0.0005 in) 5 mm/s (0.2 in/s) 9.1 kg (20 lb) Volume 250 250 200 mm XYZ (10 10 10 in) 32.2 L (8.5 U.S. gal) 125 125 250 mm (5 5 10 in) The last phenomenon to be discussed is that of print-through errors. In photopolymerization processes, it is necessary to have the current layer cure into the previous layer. In powder bed fusion processes, the current layer needs to melt into the previous layer so that one solid part results, instead of a stack of disconnected solid layers. The extra energy that extends below the current layer results in thicker part sections. This extra thickness is called print-through error in SL and “bonus Z” in laser sintering. Most process planning systems compensate for printthrough by giving users the option of skipping the first few layers of a part, which works well unless important features are contained within those layers. These phenomena will be illustrated in this section through an investigation of scan patterns in SL. 4.7.2 WEAVE Prior to the development of WEAVE, scan patterns were largely an ad hoc development. As a result, post-cure curl distortion was the major accuracy problem. The WEAVE scan pattern became available for use in late 1990 [1]. The development of WEAVE began with the observation that distortion in postcured parts was proportional to the percent of uncured resin after removal from the vat. Another motivating factor was the observation that shrinkage lags exposure and that this time lag must be considered when planning the pattern of laser scans. The key idea in WEAVE development was to separate the curing of the majority of a layer from the adherence of that layer to the previous layer. Additionally, to prevent 4.7 Scan Patterns 87 laser scan lines from interfering with one another while each is shrinking, parallel scans were separated from one another by more than a line width. The WEAVE style consists of two sets of parallel laser scans: • First, parallel to the x-axis, spaced 1 mil (1 mil ¼ 0.001 in. ¼ 0.0254 mm, which historically is a standard unit of measure in SL) apart, with a cure depth of 1 mil less than the layer thickness. • Second, parallel to the y-axis, spaced 1 mil apart, again with a cure depth of 1 mil less than the layer thickness. However, it is important to understand the relationships between cure depth and exposure. On the first pass, a certain cure depth is achieved, Cd1, based on an amount of exposure, Emax1. On the second pass, the same amount of exposure is provided and the cure depth increases to Cd2. A simple relationship can be derived among these quantities, as shown in (4.21). Cd2 ¼ Dp lnð2Emax 1 =Ec Þ ¼ Dp lnð2Þ þ Dp lnðEmax 1 =Ec Þ ð4:21Þ Cd2 ¼ Cd1 þ Dp lnð2Þ ð4:22Þ It is the second pass that provides enough exposure to adhere the current layer to the previous one. The incremental cure depth caused by the second pass is just ln(2)Dp, or about 0.6931Dp. This distance is always greater than 1 mil. As mentioned, a major cause of post-cure distortion was the amount of uncured resin after scanning. The WEAVE build style cures about 99 % of the resin at the vat surface and about 96 % of the resin volume through the layer thickness. Compared with previous build styles, WEAVE provided far superior results in terms of eliminating curl and warpage. Figure 4.9 shows a typical WEAVE pattern, illustrating how WEAVE gets its name. Lw 1 mil hs y Fig. 4.9 WEAVE scan pattern x 88 4 Vat Photopolymerization Processes Even though WEAVE was a tremendous improvement, several flaws were observed with its usage. Corners were distorted on large flat surfaces, one of these corners always exhibited larger distortion, and it was always the same corner. Some microfissures occurred; on a flat plate with a hole, a macrofissure tangent to the hole would appear. It was concluded that significant internal stresses developed within parts during part building, not only post-cure. As a result, improvements to WEAVE were investigated, leading to the development of STAR-WEAVE. 4.7.3 STAR-WEAVE STAR-WEAVE was released in October 1991, roughly 1 year after WEAVE [1]. STAR-WEAVE addressed all of the known deficiencies of WEAVE and worked very well with the resins available at the time. WEAVE’s deficiencies were traced to the consequences of two related phenomena: the presence of shrinkage and the lag of shrinkage relative to exposure. These phenomena led directly to the presence of large internal stresses in parts. STAR-WEAVE gets its name from the three main improvements from WEAVE: 1. Staggered hatch 2. Alternating sequence 3. Retracted hatch Staggered hatch directly addresses the observed microfissures. Consider Fig. 4.10 which shows a cross-sectional view of the hatch vectors from two layers. In Fig. 4.10a, the hatch vectors in WEAVE form vertical “walls” that do not directly touch. In STAR-WEAVE, Fig. 4.10b, the hatch vectors are staggered such that they directly adhere to the layer below. This resulting overlap from one layer to the next eliminated microfissures and eliminated stress concentrations in the regions between vectors. a hs WEAVE b hs STAR-WEAVE Fig. 4.10 Cross-sectional view of WEAVE and STAR-WEAVE patterns 4.7 Scan Patterns 89 Fig. 4.11 WEAVE problem example Upon close inspection, it became clear why the WEAVE scan pattern tended to cause internal stresses, particularly if a part had a large cross section. Consider a thin cross section, as shown in Fig. 4.11. The WEAVE pattern was set up to always proceed in a certain manner. First, the x-axis vectors were drawn left to right, and front to back. Then, the y-axis vectors were drawn front to back and left to right. Consider what happens as the y-axis vectors are drawn and the fact that shrinkage lags exposure. As successive vectors are drawn, previous vectors are shrinking, but these vectors have adhered to the x-axis vectors and to the previous layer. In effect, the successive shrinkage of y-axis ve

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