4 Causes of Molded-Part Variation: Material When screening materials for a particular application with specific tolerances, it is important to consider the shrinkage tendencies of the candidate resins Amorphous and semicrystalline resins have unique shrinkage characteristics, and both may be altered by the addition of fillers or reinforcements As discussed in Chs and 5, design elements such as gate location can significantly affect a part’s shrinkage and its differential shrinkage, leading to warping of the finished part The amount of shrinkage in a finished part is primarily controlled by the temperature and pressure used in injection molding to fill the tool cavity volume Due to some compressibility of the resins during the packing phase of processing, the overall shrinkage may be controlled to some degree by the process conditions This chapter examines these effects, presents results, and explains the differences in the behavior of amorphous and semicrystalline resins This chapter also looks at the effects of additives used to modify the performance of each class of polymer resin A method for estimating final part shrinkage is presented that utilizes pressure-volume-temperature (PVT) data generally available from resin suppliers Some examples of PVT curves and data may be found in the data section (Ch 11) of this book 4.1 Amorphous and Semicrystalline Resins Mold design, resin composition (see Appendix B.2 for a list of thermoplastic polymers), and processing conditions all affect the dimensional tolerances that a molder can reasonably expect to achieve during processing Figure 4.1, one of the many types of supplier charts that are readily available, shows dimensions that a molder may expect to hold for a particular resin Another type of tolerance chart that is commonly used is shown in Fig 4.2 This type of chart suggests an acceptable range of tolerances for various types of features in parts molded from a polycarbonate resin Similar charts are available from the Society of Plastics Industries (SPI) for each type of plastic resin SPI also provides a bulletin that outlines the Standards and Practices of Plastics Custom Molders.[53] (A related standard is the German Standard DIN 16901.) These data, along with a well-grounded understanding of shrinkage, are the basis for selecting the optimum resin for a tight tolerance application Figure 4.1 Fine and commercial tolerances for nylon.[9] (Courtesy of DuPont.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 24 Drawing Code Dimension (Inches) Plus or Minus in Thousands of an Inch 10 0.000 A = Diameter (see Note #1) 1.000 2.000 B = Depth (see Note #3) 3.000 C = Height (see Note #3) 4.000 5.000 6.000 Comm ± Fine ± 003 0015 D = Bottom Wall (see Note #3) 003 002 E = Side Wall (see Note #4) 003 002 0.00 to 0.125 002 001 0.125 to 0.250 002 0015 0.250 to 0.500 003 002 0.500 & Over 003 002 0.000 to 0.250 0.250 to 0.500 0.500 to 1.000 002 003 004 002 002 003 1° ½° 0.000 to 3.000 3.000 to 6.000 Internal External 005 007 1B 1A 003 004 2B 2A (T.I.R.) 005 003 6.000–12.000: For each additional inch add (inches) F = Hole Size Diameter (see Note #1) G = Hole Size Depth (see Note #5) Draft Allowance per side (see Note #5) Flatness (see Note #4) Thread Size (Class) Concentricity (see Note #4) Fillets, Ribs, Corners (see Note #6) 015 Surface Finish (see Note #7) Color Stability (see Note #7) 015 Reference Notes These tolerances not include allowance for aging characteristics of material Tolerances based on 1/8" wall section Parting line must be taken into consideration Part design should maintain a wall thickness as nearly constant as possible Complete uniformity in this dimension is impossible to achieve Care must be taken that the ratio of the depth of a cored hole to its diameter does not reach a point that will result in excessive pin damage These values should be increased whenever compatible with desired design and good molding technique Customer-Molder understanding necessary prior to tooling Figure 4.2 Recommended tolerances for a polycarbonate.[10] Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 25 4.1.1 Amorphous Polymers Amorphous polymers with rapid relaxation rates generally produce parts with isotropic shrinkage This isotropic shrinkage is defined as equal shrink in both the flow direction (in-flow) and the direction transverse to flow (cross-flow) Amorphous resins exhibit a broad softening range when heated through their glass transition temperature (Tg) With additional heating above Tg, the polymer viscosity gradually decreases until the desired processing flow is achieved The process of adding energy (heat) to the molecular mass increases the molecular motion, driving the polymer chains to occupy more local volume, and increasing the specific volume of the resin The more energetic (hotter) resin flows more easily, but must be cooled again to Tg for solidification The time required for cooling allows for local molecular relaxations, thereby resulting in the more isotropic shrinkage Examples of amorphous resins with isotropic shrinkage include ABS, polycarbonate, and polystyrene Table 4.1 provides a brief list of flow-direction shrinkage values for typical amorphous resins and demonstrates the effects of incorporated fillers on resultant shrinkage A more complete list appears in the “Data” appendix at the end of this book Shrinkage is generally reported as a dimensionless value or as a percentage The shrink value is determined by measuring the amount of shrinkage along a given dimension, and normalizing it by the length of that dimension Units may also be reported as inches/inch or mm/mm, both units being dimensionless Confusion may result from interpretation of the data when reported as a percent in one table and a dimensionless unit in another Table 4.1 shows both types of units for comparison Processing conditions play an important role in the resultant shrinkage of an amorphous resin Following is a summary of key processing effects: • The hotter a part is on removal from the tool, the longer the post-mold cooling time without the constraint of the cavity This “free shrinkage” is generally higher than shrinkage in a constrained tool because the cold tool surfaces tend to freeze the part in a more constrained volume However, the rapid constrained cooling generally results in higher residual stresses in the finished part Annealing a fastquenched amorphous part by heating it to near its Tg will result in some stress relief, but may actually increase the final shrinkage of the part • Increasing a part’s wall thickness will increase its cooling time and also increase the time for shrinkage Thicker wall sections also exhibit greater temperature differentials between the rapidly frozen skin and the slower cooling core at the center of the cavity thickness This condition will result in residual stresses through the part thickness When the part wall thickness exceeds recommended dimensions, the cooling stresses can result in void formation at the core as the cooling melt near the walls causes the core to develop sufficiently high isotropic tensile stresses that fracture the melt • Injection hold time must be sufficiently long to allow for gate freeze When the Table 4.1 Flow Direction Shrinkage Values for Various Amorphous Polymers Linear Mold Shrinkage % Shrinkage ABS 0.003–0.008 0.3–0.8 PPE 0.004–0.008 0.4–0.8 Polycarbonate (unfilled) 0.005–0.007 0.5–0.7 PC (10% glass fiber) 0.002–0.005 0.2–0.5 PC (30% glass fiber) 0.001–0.002 0.1–0.2 Polystyrene 0.004–0.007 0.4–0.7 © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 26 hold time is too short, material can leak from the cavity prior to solidification, thereby decreasing hold pressure and increasing shrinkage The optimum hold time can be readily determined by weighing a series of parts formed using increasing hold times Starting with a short hold time, the part weight will continue to increase proportionally to increasing hold time When the part weight stabilizes, the gate is properly frozen prior to the release of injection hold pressure • Hold pressure is used to compress the melt in the tool during solidification A constant hold pressure is used to maintain a constant volume of resin in the tool cavity As this resin cools, the specific volume decreases at constant pressure, and additional melt may be squeezed into the tool prior to gate freeze The additional melt volume added prior to gate freeze will decrease the overall shrinkage of the final molded part However, excess hold pressure will overpack that cavity and make part ejection difficult To prevent overpacking, good practice demands a switch from injection pressure to hold pressure slightly before the cavity is completely filled • Increasing the melt temperature will result in a hotter melt in the cavity when the gate freezes This hotter melt will increase the overall cooling time and have the same result on shrinkage as described in the discussion above on part temperature at ejection Post-mold shrinkage is both time and temperature dependent Accurate post-mold shrinkage should be measured at least twenty-four hours after part ejection During this time, stress relaxation in the freshly formed part can lead to additional changes in the part dimensions Increasing the temperature will decrease the time to stabilize shrinkage Post-mold shrinkage can account for up to one percent of the part’s final dimensions 4.1.2 Semicrystalline Materials Articles molded from semicrystalline plastic resins generally display anisotropic shrinkage, meaning Ch 4: Causes of Molded-Part Variation: Material that there will be a different amount of shrinkage in the flow direction and the transverse flow direction As opposed to amorphous polymers, semicrystalline polymers exhibit a sharp melting transition (Tm) associated with melting the crystals themselves Below Tm , the polymer is a rubbery solid, while above T m the polymer’s crystal structure is dissolved and the polymer flows readily Common examples of semicrystalline polymers include polypropylene, polyethylene, nylon, and acetal Polymer crystallization involves the local ordering of short lengths of adjacent chains that, once nucleated, grow through drawing on the available polymer chains in the local melt This process may involve chain folding as molecules are reeled from the melt onto a growing crystal face On cooling, nucleation takes place throughout the melt, and the crystal structure grows radially from each nucleation point during primary crystallization The resulting structure is spherical around the nucleation point and is referred to as a spherulite Within the spherulite are layers of crystalline lamellae separated by non-crystallized (amorphous) regions Secondary crystallization is the process of incorporating additional available molecular segments onto the established crystals This slower secondary crystallization is responsible for additional shrinkage in molded parts heated above their glass transition temperature Crystallization can be viewed as both a kinetic and thermodynamic process Kinetically, the degree of undercooling (melt temperature minus crystallization temperature) drives both the nucleation and crystallization processes Thermodynamically, the crystal is a lowenergy state that forms through exothermic collapse of the energetic melt into a stable solid regular lattice (the crystal lattice characteristic of each semicrystalline resin) The addition of a nucleating agent will decrease the degree of undercooling necessary to initiate crystallization as well as produce a solid consisting of smaller spherulites The absolute degree of crystallinity is dependent on the rate of crystallization and the cooling rate In injection molding, many semicrystalline polymers not achieve their full potential crystallization because of rapid quenching of the melt in a cold tool Because of the close packing of chains in a crystal lattice, the density of the semicrystalline solid will be proportional to the degree of crystallinity Mechanically, a semicrystalline polymer exhibits an increased stiffness because the crystals themselves act to physically lock the polymer structure together Also, because crystallization is a volume-reduction process, a crys- © Plastics Design Library 27 tallized polymer will exhibit higher shrinkage than would be predicted without crystallization A slow rate of crystallization or a low degree of total crystallinity has the effect of reducing shrinkage and thereby reducing warpage in semicrystalline polymers By contrast, nucleated resin grades result in higher amounts of shrinkage, and proportionally higher degrees of warp This is true for copolymers as well as the homopolymers discussed so far Molecular weight can also influence the degree of shrinkage Higher molecular-weight resins exhibit a higher viscosity on filling, and a higher pressure drop in the tool cavity during filling Higher packing pressure must be used to compensate for the cavity pressure drop or else the lower pressure melt will result in higher shrinkage in the final part Branched polymers crystallize differently from linear polymers The presence of side chains on the molecular backbone inhibits the ability of a molecule to fit into a developing crystal structure The longer the side chains, the lower the resulting crystallinity Highly branched polymers also have a higher degree of chain entanglements that may also inhibit rapid crystallization For example, polyethylene may be produced by different processes that each result in a different degree of branching High-density polyethylene (HDPE) is produced with a low degree of branching and crystallizes easily The degree of crystallinity for HDPE can range from 60% to 80% crystal structure with as- sociated densities of 0.940 to 0.965 g/cc By contrast, the more branched medium-density polyethylene (MDPE) attains only about 50% crystallinity at a density of 0.930 g/cc Table 4.2 provides shrinkage values of various semicrystalline polymers The mold shrinkage values listed are those found on most typical property data sheets and are generated using test specimens of 1/8inch thickness The reported values are measured in the fill or in-flow direction Shrinkage also depends on processing factors and tool design As shown in Fig 4.3,[11] a series of polyethylene grades increases shrinkage as the wall section increases The melt remains hot for a longer time in thick wall sections, thereby increasing the time for kinetically driven crystallization For very thin wall sections, premature gate freeze can diminish the effect of hold pressure, resulting in additional shrinkage In addition, design factors such as the number of gates and their locations can change the filling dynamics of a part and result in different amounts of shrinkage To determine shrinkage accurately, complex computerized models are used that strive to take into effect the local pressures and cooling kinetics of a polymer melt during solidification Table 4.3 shows some of the shrinkage changes that one can expect in polyethylene from part and process changes Table 4.2 Shrinkage Values of Various Semicrystalline Polymers Shrinkage % Shrinkage Unfilled polypropylene (PP) 0.010–0.025 1.0–2.5 40% talc filled PP 0.008–0.015 0.8–1.5 40% CaCO2 filled PP 0.007–0.014 0.7–1.4 HDPE 0.015–0.040 1.5–4.0 Polyamide (Nylon 6) 0.005–0.015 0.5–1.5 Polyamide (Nylon 6,6) 0.008–0.015 0.8–1.5 Nylon with 30% glass fiber 0.003–0.005 0.3–0.5 Acetal 0.020–0.025 2.0–2.5 © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 28 Figure 4.3 Differences in shrinkage based on section thickness for a variety of polyethylene injection-molding resins.[11] (Courtesy of Hoechst Celanese.) Table 4.3 Polyethylene Shrinkage Changes from Part and Process Changes Increase Maximum Shrinkage Change Demolding temperature 20°C to 60°C +0.4% Wall thickness mm to mm +0.5% Hold-pressure time at a wall up to 20 sec, thickness of mm to mm -0.5% Injection-pressure hold in front of the screw tip + 600 bar to 1400 bar pressure at a wall thickness of mm to mm -0.5% 220°C to 280°C +0.3% Parameter Melt temperature (very dependent on wall thickness) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 29 4.2 Effects of Fillers, Reinforcements, Pigments, Time, and Stress A common misunderstanding is that the shrinkage values listed on data sheets are a direct indication of potential part warpage A more reliable indication of warp would be the differential shrinkage obtained by subtracting the shrinkage in the flow direction from that in the transverse direction, as illustrated in Fig 4.4 [7] This is equally valid for semicrystalline and amorphous resins, but greater attention to differential shrinkage is required with semicrystalline plastics Fillers also influence the shrinkage by offsetting some volume of polymer with a low-shrinking filler particle The shrinkage of resins containing isotropic fillers, such as glass beads or powders, will be more isotropic than resins containing high-aspect-ratio fillers like fibers or platelets This results from orientation of the fillers in the flow path during filling, and the restricted shrink along the long axis of the filler particles Fibers are known to create excessive warp as the restricted shrink in the flow direction is compensated by an increased shrink of the polymer in the transverse direction 4.2.1 Effects of Fillers and Fibers Although the topic of thermoplastic shrinkage and warpage is extremely complex, a number of general characteristics can be established For example, while the molecular chains of both amorphous and semicrystalline resins pack together differently upon cooling, the molecules in semicrystalline resins pack to- Figure 4.4 Differential shrinkage equals transverse shrinkage minus flow shrinkage [7] (Courtesy of GE Plastics.) © Plastics Design Library gether more tightly, resulting in higher shrinkage for semicrystalline materials In addition, the shrinkage of parts molded from any filled resin is governed by the type and level of fillers and reinforcements added to the plastic as discussed in this section Powders, flakes, and fibers are generally incorporated into plastic resins to selectively modify mechanical properties of the original resin For example, high modulus fillers are added to increase the stiffness and creep-resistance of a polymeric system for applications requiring a high-modulus material A secondary effect of using such filler systems is that the composite of filler and resin will have a different shrinkage from the parent resin Use of fiber reinforcements will also produce differential shrinkage between the molding axes of the part, resulting in warpage Most fillers and reinforcements are inorganic and have relatively low coefficients of thermal expansion When an injection-molded composite is cooled during processing, the fillers and reinforcements tend to shrink significantly less than the polymeric matrix to which they are added Particulate and flake fillers both tend to reduce the overall shrinkage when added to amorphous or semicrystalline polymers The reduction in shrink is approximately proportional to their concentration Powders, beads, and flakes are geometrically more uniform than fiber fillers The addition of lowaspect ratio fillers (e.g., powders, beads, or flakes) does not create problems with anisotropic shrinkage With these fillers, the shrinkage in all directions is reduced proportionally to the filler content Particulate fillers have the ability to reduce shrinkage in all directions and also improve dimensional control Particulate fillers are approximately the same size in all directions and, therefore, not become oriented in a flow field, yet by taking up space they reduce shrinkage Fibers are geometrically defined by their aspect ratio, determined as the ratio of the fiber length to its diameter Inorganic fibers, produced from materials such as glass or graphite, are commonly used as reinforcing agents in polymers When chemically coupled to the resin matrix, fibers offer a number of advantages in terms of end-use performance, however their use can also create several processing-related problems For example, compared to particulate- or flakefilled polymers, the differential shrinkage between the in-flow and cross-flow directions of fiber-reinforced polymers can be significantly different, as shown in Fig 4.5.[6] This anisotropic shrinkage can make it more difficult to determine the appropriate cavity dimensions unless the anisotropic shrinkage behavior is properly understood and taken into account in tool design Dif- Ch 4: Causes of Molded-Part Variation: Material 30 ferential shrinkage can also lead to warpage in a molded plastic part Anisotropic shrinkage of fiber-reinforced polymers can be attributed to the fact that the fibers become oriented in the flow-shear field during injection molding Unlike polymer molecules that can orient and relax during filling and cooling, fibers have no tendency to reorient in the cooling melt Flow-induced fiber orientation is maintained during polymer cooling Both shear and elongational flow will influence the orientation of fiber reinforcements Processing variables such as fill rate, cavity thickness, melt viscosity, and gating scheme are all significant factors affecting fiber orientation As a result, flow-related design decisions, such as gate location, are more critical when molding with fiberreinforced polymers Anisotropic shrinkage can result from molecular orientation and relaxation during filling and cooling an unreinforced resin These resins tend to orient in the flow direction during part filling, and will relax during cooling This relaxation of orientation tends to produce more shrinkage in the flow direction than the crossflow direction For reinforced resins, the trend is reversed: fibers that become oriented in the flow direction during filling are frozen into that orientation during cooling Because the fiber shrinks less than the resin, shrinkage is reduced in the flow direction Because volume of the part must be conserved during cooling, the polymer will tend to shrink even more in the crossflow direction Cross-flow shrinkage for a fiber-reinforced resin can exceed the cross-flow shrink of the base polymer Figure 4.6 shows micrographs of sections taken through a glass-fiber–filled polypropylene molding.[2] The upper view shows the section parallel to the flow direction Near the part surface (at the top and bottom of the micrograph) a skin layer is found where the fibers are frozen into a random pattern This skin layer is formed from melt that fountains from the core of the molding and freezes immediately on contact with the tool surface Just inside the skin layer is a region of highly-oriented fibers This layer forms as fibers are oriented along the edges of the flowing melt front because of the shear profile established by the advancing melt front This oriented layer is seen to extend toward the center of the part, with more random orientation resulting at further distances from the wall Finally, in the center of the part is a randomized area of fiber orientation In the core of the part, the melt being pushed forward develops a flattened profile and fibers within this region not orient without a well-developed shear flow Figure 4.5 The mold shrinkage for 30%-glass-fiber reinforced PBT varies with direction (in-flow vs cross-flow) and with part thickness.[6] (Reproduced by permission of Hanser-Gardner.) Figure 4.6 Glass-filled polypropylene sections parallel and perpendicular to the flow.[2] (Reprinted by permission of Oxford Science Publications.) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 31 The lower micrograph shows a section of the same part taken perpendicular to the direction of flow In this section, fibers are found to show little orientation as the view in the flow direction exposes the fibers in cross section, consistent with their alignment in the flow direction At the core of the part, there is a tendency for fibers to be aligned across the flow direction, which is the width direction of the part In this micrograph, no fiber alignment is seen through the thickness of the part These two perpendicular sections of an injectionmolded part give a good representation of the complexity of fiber orientation found in any injectionmolded composite Figure 4.7 shows the mold shrinkage behavior of a glass-fiber–reinforced semicrystalline polymer such as acetal.[6] For the semicrystalline polymer, unfilled, (glass-fiber content = 0), both the flow and cross-flow shrinkage are relatively high (e.g., 1.5% to 2.0%), with the in-flow shrinkage somewhat higher As the fiber content increases, the in-flow–direction shrinkage drops dramatically, while the cross-flow–direction shrinkage drops only slightly The large difference between these behaviors is of primary importance The difference between in-flow and cross-flow molded part shrinkage increases as the fiber content increases While the differential shrinkage between the in-flow and cross-flow directions is found for all fiberreinforced polymers, it tends to be more pronounced in semicrystalline polymer composites because of the excess shrinkage in the resin itself during crystallization Designers should always consider the differential shrinkage and the resulting potential for warpage when fiber-reinforced polymers are used If part flatness is of primary importance, the designer may be forced to select a composite with a lower fiber concentration to minimize differential shrinkage In addition, the designer must balance the differential shrinkage, caused by the addition of fibers, against the stiffening effects the same fibers impart to the composite Higher modulus fibers, such as carbon, may actually counteract the effects of warp caused by differential shrinkage in some designs As discussed in Ch 3, wall thickness plays an important role in part shrinkage This is especially true for semicrystalline polymers where thicker walls lead to longer cooling times With the increased cooling time, the crystalline microstructure becomes more developed and the polymer reaches a higher degree of crystallinity Because crystallization reduces volume within the polymer, longer cooling times found in thicker sections have higher shrinkage This same effect is found in both in-flow and cross-flow directions (Fig 4.5) Regrind or recycled fiber-reinforced polymers will exhibit different mold-shrinkage characteristics than those of the virgin resin The process of regrinding molded parts for remolding produces a distribution of shorter fibers than were present in the first-generation polymer composite The shorter fibers produce a different orientation distribution in the molded part, and create different shrinkage characteristics compared to the first generation material Figure 4.7 Warpage can occur as a result of anisotropic shrinkage in a relatively simple part like this glass-fiber reinforced acetal disc The differential shrinkage tends to cause the part to warp (cup/diameter) like a round potato chip [6] (Reproduced by permission of Hanser-Gardner.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 32 4.2.2 Minimizing the Effects of Fiber Reinforcements Introducing non-fibrous reinforcements into a composite may diminish differential shrinkage, but fiber reinforcements tend to reduce mold shrinkage even more In addition, the mold shrinkage of fiber-reinforced thermoplastics may be lower in the direction of material flow than in the cross-flow direction, causing differential mold shrinkage and warpage A number of techniques can minimize the potential for warpage in parts molded from fiber-reinforced polymers One of the more common is to use a polymer composite containing both fiber and flake reinforcements Flake-type reinforcements, like other particulate fillers, have a lower aspect ratio than long fibers Hybrid composite materials, incorporating both fiber and flake reinforcements, have mold shrinkage values that tend to be more isotropic than conventional fiber-reinforced polymers These hybrid composite resins offer the mechanical performance of a fiber-reinforced composite, with a more isotropic shrinkage These hybrid composites are widely used in applications requiring tighter tolerances on the finished parts (see Fig 4.8).[6] For example, mixtures of mica flakes with appropriate coupling agents and glass-fiber reinforcements can give consistently equal shrinkage in the in-flow and cross-flow directions during molding This reinforcement technique results in both lower warpage and shrinkage in the final molded part Studies on filler shape have shown that fibrous reinforcements of non-circular cross sections can be useful in controlling warpage in fiber-reinforced polymers One study[6] has shown a 30–40% reduction in warp for semicrystalline polymers reinforced with glass fibers having a bi-lobe cross section (a fiber with some plate-like character) versus circular fibers of a smaller cross sectional area This warp reduction was achieved while maintaining a mechanical performance similar to the traditional fiber composite Figure 4.9 shows the difference in in-flow versus cross-flow shrinkage for 30%-glass–reinforced polypropylene.[6] Differences in shrinkage between composites reinforced with bead, flake, and fiber fillers are due to differences in aspect ratio among the fillers Glass beads little other than occupy volume in the composite; they reduce the shrinkage in all directions equally Flake-type reinforcements have a length and width that is significantly greater than their thickness, so they impede shrinkage parallel to the plane of the flake more than perpendicular to the plane of the flake In a flow field, flake-like reinforcements will tend to align parallel to the cavity wall When frozen in this orientation, flake reinforcements reduce shrinkage in the plane of the wall section, and increase shrinkage in the wall thickness direction A test mold design that would typically be used for estimating mold shrinkage is also shown in Fig 4.9 Note how a fan gate is used to promote a uniform flow pattern into the part It is important to establish a uniform flow field down the length of the part in order Figure 4.8 An example of hybrid composite materials that include both flake and fibrous materials for reinforcement.[6] Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 35 crease in shrinkage The pigments usually promote shrinkage by acting as a nucleating agent The use of pigments tends to increase the crossflow shrinkage in semicrystalline materials For example, polypropylene typically shrinks about 10% more in the in-flow direction than in the cross-flow direction Some blue and red pigments can cause the crossflow shrink to increase to 40% more than the in-flow direction Especially notable are the following organic pigments: phthalocyanine blue, quinacridone violet, and indanthrone blue Inorganic pigments such as ultramarines, manganese violet, and carbazole violet cause the same type of shrinkage change to a lesser degree.[13] The presence of foreign bodies like pigment particles or regrind particles can effect the crystallization and, therefore, the mold shrinkage Figure 4.10 shows the effect of different pigments on Delrin® 500.[14] The results shown here were obtained using standard bars The values are not necessarily valid for all part configurations; however, the effect on the test bars compared to the natural material can indicate a trend in other molded parts Seemingly minor variations and irregularities affect filling patterns, temperature, and shrinkage In Ch 5, it is shown that seemingly balanced runner systems can cause variations in temperature and filling patterns in multiple cavity molds Minor variations in the temperature of one half of the mold with respect to the other half encourage a flow shift away from the center of the part toward the warmer half of the mold because a thicker skin forms on the cooler side of the flow path Assuming an absolutely flat cavity, this flow shift results in an area of greater shrinkage that is slightly removed from the center or theoretically neutral axis of the part The offcenter shrinkage creates a bending moment that tries to make the part concave toward the warmer side This bending moment may be resisted by the stiffness of the part until long after it is molded or until it is exposed to elevated temperature If the moment is small enough, it may not be noticed or ever cause problems; nevertheless, it is there The temperature variations can be caused by uneven distribution of water lines or variations in coolant flow rates, temperature, or patterns When ribs are present, the flow is divided and the side branch is normally filled with cooler material while the warmer material tends to divert slightly toward the rib or branch This tendency to move the warmer flow toward the rib leads to off-center cooling, as above, as well as the shrinkage normally associated with inside corners of molded parts that is discussed in the Mold Design chapter (Ch 5) In most cases, if temperatures are relatively uniform, these variations will not significantly affect the end result Most mold-filling analyses operate on the assumption of symmetry Asymmetric analysis is more time consuming and costly and should normally be used when there is significant temperature differential across the mold or where there are numerous large ribs on one side of the part Even under these conditions, there may not be enough shrink/ warp to significantly affect the function of the molded part Figure 4.10 The effect of selected pigments on mold shrinkage of Delrin® 500 in a 2-mm thick part In some cases, different formulations of the same color are shown.[14] (Courtesy of DuPont.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 36 4.2.4 The Effects of Time and Stress on Dimensional Stability Creep is the tendency of a material to change over time when loaded with stresses well below the yield stress In the case of plastics, the rate of dimensional change (the creep rate) is determined by the stress level and the temperature at which the part is held under stress At increasing times, the part under load will deform in response to the applied load At very low loads and short times (and also at lower temperatures), polymers behave elastically, returning to their original shape when the stress is removed However, under higher stresses, polymers begin to show viscoelastic behavior This behavior is characterized by a plastic deformation of the part that is not reversible when the stress is removed Creep is generally considered to be this nonreversible aspect of dimensional change in a plastic part The plastic-part designer must consider long-term exposure to assembly stresses or external stresses in any new design If the designer overlooks the effect of creep, over time the part shape can change beyond expected tolerances, or even fail through creep rupture Figure 4.11 shows the creep behavior of two semicrystalline polymers (nylon and acetal) compared to two amorphous polymers (ABS and polycarbonate).[15] Note that the primary creep rates (at short time) are nearly the same for all of these polymers Primary creep is the result of readily available molecular motions within the polymer In the solid state, these motions are generally believed to be related to the stretching or straightening of molecules between entanglements or crystal lamellae Amorphous polymers tend to creep through molecular de-tangling, rearrangements, and slipping at the molecular scale However, the molecular structure of semicrystalline polymers is more restricted by the crystal structure Beyond primary creep, semicrystalline polymers tend to reduce their rate of creep as the available molecular relaxation mechanisms are depleted Creep charts are generally presented as a change in dimension versus time Creep curves are normally shown on semilog plots with elapsed time plotted on log scales because the deformations are important at both short and long times In this presentation format, amorphous polymers, with constant rates of creep, appear to show an acceleration of deformation with time The apparent constant creep rate exhibited by the semicrystalline polymers is actually a slowing of the rate of deformation with time Figure 4.11 Percent creep of various materials at a stress level of 8–9 MPa at 31°C Note that time is plotted on a log scale.[15] (Courtesy of DuPont.) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 37 4.3 Shrinkage Predictions: Using Pressure-Volume-Temperature (PVT) Relationships This section introduces a method for estimating shrinkage of injection-molded parts The pressurevolume-temperature (PVT) diagram is introduced and explained for different classes of polymers This method represents current thinking about the responses of polymer solids and melts during melt-processing, and is dependent on obtaining the PVT diagram, or a series of constants that can reproduce the PVT behavior, from the material supplier or a standard data source To better understand PVT behavior, it is necessary to first understand the concept of thermal expansion and contraction Material producers supply thermal expansion behavior as a property on a standard data sheet, listed as coefficient of thermal expansion (CTE) As a material is heated, energy input into the material causes the molecules to move at increasing rates and occupy larger volumes within the mass This expansion of volume on heating is shown graphically in Fig 4.12 for a solid amorphous polymer This figure shows not one but two curves overlaid that are nearly identical The two curves represent data collected in both the direction of flow and across the direction of flow For this unfilled amorphous polymer, the rate of thermal expansion is equivalent in all directions Presented in this manner, as thermal strain versus temperature, the slope of the curve is the CTE, describing how the solid polymer expands on heating Because of experimental limitations, CTE data are only collected for the solid-phase polymer Semicrystalline polymers exhibit a different thermal response than amorphous polymers As shown in Fig 4.13, the semicrystalline polymer exhibits two distinct slopes of expansion rate in the solid state A change in CTE shows that there is a thermal transition in the polymer The polymer shown has a thermal transition at about 85°C This is the primary thermal transition for the amorphous phase of this blend The primary amorphous transition of any polymer is known as its glass transition temperature, Tg While Tg is not a sharp transition, extrapolation of the data from below and above T g will show an intersection that is generally accepted as being Tg These two slopes represent the expansion rates below and above Tg The amorphous polymer shown earlier is only characterized below Tg, because it begins to soften and flow when heated above Tg By contrast, the semicrystalline polymer contains sufficient crystallinity to maintain structural continuity above Tg While the amorphous content in this polymer exhibits a Tg, the crystal structure allows characterization up to nearly the temperature where the crystals melt 4.3.1 PVT System Properties Thermal expansion, PVT relationships, and thermal properties are characteristic properties of a polymer These properties are the same for any molded part Figure 4.12 Thermal expansion of a Lexan® 121, an unfilled polycarbonate, showing equivalent expansion in both in-flow and cross-flow directions (Courtesy of GE Plastics.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 38 Figure 4.13 Glass transition temperature, Tg, in Noryl® GTX, a semicrystalline polymer, is evidenced through a slope change (Courtesy of GE Plastics.) made from the polymer Shrinkage and warpage are not properties of the material being molded They are instead “system properties,” or properties that depend on the processing history that the polymer has seen during molding The shrinkage and warpage will depend on the material properties (PVT, thermal properties, etc.), the part geometry (wall thickness, gate location, mold constraints, etc.), and the molding conditions (temperature, pressures, flow rates, etc.) Because of this complexity, it is necessary to understand the material, design, and processing variables that together result in a given amount of shrinkage, as well as the degree and direction of warpage A simplified PVT diagram for an amorphous polymer is shown in Fig 4.14 For the sake of simplicity, this plot presents a single pressure only The diagram gives very similar information to the CTE plot shown earlier (Fig 4.12), but covers a wider temperature range than the CTE plot The PVT diagram shows the expansion behavior of the polymer from room temperature to the highest temperature under which the polymer would typically be melt processed For this amorphous polycarbonate material, T g, is clearly seen as the temperature where the polymer goes from a solid to a melt The rate of expansion per temperature increment is much smaller in the solid state than in the melt state On cooling from the melt, the polymer will contract at a faster rate above Tg (in the melt) and the rate of thermal contraction will be slowed as the polymer goes through Tg and cools to a solid Ch 4: Causes of Molded-Part Variation: Material The second important difference between CTE and PVT diagrams is that the PVT diagram represents volume expansion on heating, whereas the CTE diagram shows only linear expansion The “volume” that is read from a PVT diagram is always normalized by the mass of the material under evaluation Thus, a “specific volume” is always reported rather than just a volume It is important to understand the difference between volume, specific volume, and density Volume is simply the space occupied by a given mass (amount) of material As the amount of material increases, so does its volume Two materials cannot be compared on a common basis using volume alone Specific volume is a way of normalizing the volume description of the material By dividing a volume by its weight, a normalized volume is determined Materials can be easily compared using their specific volumes, similar to comparison shopping for hamburger based on cost per pound rather than just cost Density is a normalized measure also Density is the name given to “specific weight.” Density is the weight of a material, normalized by the volume it occupies One can use density to determine which of a group of materials is the heaviest As density increases, materials are found to be heavier Specific volume is the inverse of density, so it becomes a measure of the “lightness” of a material Specific volume increases as a material is heated, implying that the material is becoming lighter, or less dense on heating © Plastics Design Library 39 Figure 4.14 Thermal expansion of an unfilled, amorphous polycarbonate through both the solid and melt temperature ranges (Courtesy of GE Plastics.) The next important feature of the PVT diagram is its display of the compressibility of a polymer as it is pressurized Figure 4.15 is a complete PVT diagram for a typical amorphous polymer As pressure is increased, both the solid and melt phases are seen to compress to smaller specific volumes This plot represents the compressibility of polycarbonate over a range of pressures from MPa to 200 MPa (~29,000 psi) All plastic processing methods involve the application of both temperature and pressure The polymer will respond to increasing temperature by increasing its volume, and will respond to increasing pressure by decreasing its volume Just as the melt phase is more sensitive to temperature than the solid phase (as seen by the more rapid thermal expansion), the polymer melt is more compressible than the solid polymer (as seen by the higher sensitivity of the melt to changing volume with a given application of pressure) Figure 4.15 PVT diagram of an unfilled amorphous polycarbonate showing the compressibility of the solid and melt phases (Courtesy of GE Plastics.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 40 The material property, Tg , is found to be a function of both temperature and pressure, as shown in Fig 4.16 The glass transition temperature, Tg , is the temperature where the polymer chains have enough energy to slip easily past their neighboring chains At temperatures well above T g, the polymer has sufficient mobility to flow under processing stresses When the pressure is increased, more thermal energy is required to get the chains moving; hence, a higher Tg is found at higher pressures When a polymer melt is cooled under pressure, this effect becomes significant: the polymer melt will solidify at a higher temperature than it would if being cooled at a lower pressure The line representing the pressure effect on Tg is generally called the freeze line on the PVT diagram because it represents the line where the polymer will freeze on cooling PVT data look different for a semicrystalline polymer In a semicrystalline polymer, there are two transitions: a glass transition, Tg , associated with the amorphous content within the polymer, and a melt transition, T m, associated with melting the crystal structure within the polymer Figure 4.17 shows how the volume expansion associated with melting is much more significant than the expansion associated with Tg The melt transition temperature, T m, is also a function of pressure Notice the behavior of Valox® 310 at 240°C In Fig 4.17, the top curve shows that at the lowest pressure, MPa, the polymer has melted It is above the melt transition line and is found to be highly expanded, typical of a polymer melt However, if the pressure is increased on this melt, and the temperature remains constant at 240°C, the polymer is found to recrystallize as can be seen by following down the line at 240°C This polymer is seen to be able to crystallize at a higher temperature than that found on a data sheet only through the application of pressure In a real molding process, where the melt is being held under a packing pressure, the polymer is capable of crystallization at a higher temperature than would be expected Data Modeling Being able to model the complex behavior found in PVT relationships greatly simplifies both the presentation and the use of the data A suitable model for the simple two-phase behavior of amorphous polymers is the Double Domain Tait Equation, commonly viewed in practice as having an acceptable fitting capability This model is generally hard-wired into CAE packages used to model polymer behavior during melt processing The Tait Equation is given below for reference From this simple equation and a set of constants, any volume of a polymer can be determined by knowing only the temperature and pressure of the system While it looks complicated at first glance, this form of the Tait Equation simply is a prediction of specific volume, v(T, p), as a function of temperature and pressure The three conditional terms, v(T), B(T), and v(T, p), change form based on whether the selected temperature is above or below the freeze line That is why we call this a “double domain equation.” It is not necessary to know this equation exactly It is important only to know that it is coded into all moldfilling software Plastics suppliers have generated the necessary databases of PVT constants to describe many commercial materials Figure 4.16 PVT diagram showing the pressure dependence of the T g for an amorphous polycarbonate (Courtesy of GE Plastics.) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 41 Figure 4.17 A typical PVT diagram for a semicrystalline polymer showing the pressure dependence of both Tg and Tm (Courtesy of GE Plastics.) p + vt (T , p) v (T , p) = v (T ) 1 − C ln1 + B(T ) b1m + b2 mT if T > Tt v0 (T ) = b1s + b2 s T if T < Tt b exp( −b4m T ) B(T ) = 3m b3s exp( −b4 s T ) T ≡ T − b5 if T > Tt if T < Tt Tt ( p ) = b5 + b6 p if T > Tt 0 v(T , p) = b7 exp(b8 T − b9 p) if T < Tt Constants b1m through b4m describe the pressure and temperature dependence of the melt; b1s through b4s are constants describing the pressure and temperature dependence of the solid (glass); b5 is Tg ; b6 is the pressure dependence of Tg ; b7 through b9 are particular to semicrystalline polymers and describe the shape of the melting transition as a function of pressure and temperature These constants are unique to each plastic formulation Some representative values may be found in the data section (Ch 11) of this book C is a “universal constant.” Generally, a value of 0.0894 gives good results according to Sam Miller.[58] A plot of the PVT data for Valox 310 is shown in Fig 4.18 This plot shows the simplified curves associated with using fitted data rather than raw data © Plastics Design Library This PVT diagram represents the behavior of Valox 310 being heated slowly from the solid state at room temperature to the highest temperatures generally used in melt processing One limitation of commercial PVT test equipment is that it cannot be used to collect data at fast heating or cooling rates This limitation must be overcome through creative modeling of the “real” behavior of semicrystalline polymers under more realistic processing conditions that represent the fast cooling rates in tooling Crystallization is the process of solidification upon cooling in semicrystalline polymers At a temperature below the T m, but well above the Tg, a cooling semicrystalline polymer will begin to develop crystal structure The polymer is considered “solidified” when its temperature is below the crystallization temperature Both crystal nucleation and the rate of crystallization are kinetic processes The temperature where nucleation begins and crystallization takes place is a function of the cooling rate seen by the polymer melt The faster the cooling, the lower will be the temperature where crystallization begins High cooling rates are not possible in commercial PVT equipment, but differential scanning calorimetery (DSC) experiments can provide crystallization temperatures at high cooling rates Figure 4.19 shows crystallization temperatures as a function of cooling rate for a semicrystalline polymer.[16] Extrapolation of this data can provide crystallization temperatures at the cooling rates found in injection molding processes Ch 4: Causes of Molded-Part Variation: Material 42 Figure 4.20 shows how crystallization temperature is modeled on the PVT diagram As seen in this figure, the Tm , measured during heating, and the crystallization temperature, Tc, measured during fast cooling, are significantly different By studying the cooling kinetics of each semicrystalline polymer system, it is possible to establish the T c as a function of cooling rate Using specially developed algorithms, material suppliers can supply the Tait constants for any semicrystalline product, at the cooling rate that is in effect for any given tool and part geometry The degree of crystallinity will also affect the specific volume of a cooling semicrystalline polymer As the degree of crystallinity increases, the specific volume will decrease This is because of the additional densification due to the growing crystal structure in the polymer Experimenters get around this problem by always characterizing PVT on injection-molded parts The degree of crystallinity in the initial samples will be approximately the same as that found in a part of 1/8-inch wall thickness processed using standard molding conditions The difference between Tm and Tc is known as undercooling The faster the cooling rate, the larger will be the undercooling Studies have shown that the pressure sensitivity of T c is the same as the pressure sensitivity of T m Therefore in predicting Tc( p), the slope of T m( p) is used with confidence During shrinkage estimates, accuracy is greatly improved for semicrystalline polymers when using Tc( p) as the “solidification line” instead of using Tm( p) Figure 4.18 Model representation of the PVT curve for a semicrystalline polymer (Courtesy of GE Plastics.) Figure 4.19 Typical crystallization temperature data from DSC cooling scans for semicrystalline resins and their extrapolation to higher cooling rates.[16] (Courtesy of SPE.) Ch 4: Causes of Molded-Part Variation: Material Figure 4.20 The shift shows T c and Tm for a semicrystalline polymer being cooled at 500°C/min (Courtesy of GE Plastics.) © Plastics Design Library 43 4.3.2 Predicting Mold Shrinkage In an injection-molding process, the hot melt is transferred from the injection barrel through a sprue, runner, and gate into the mold cavity As the molten plastic fills the cavity, pressure from the melt can be detected in the tool using pressure sensors If pressure sensors are placed near the gate, in the center of a part, and near the end of flow, three distinct traces of pressure versus time are found Figure 4.21 shows how pressure varies with time at these three locations Notice how location 1, nearest the gate, shows the first spike in pressure, followed by a response at position 2, and finally at position The size of the pressure plateau also varies with location The highest pressures are found near the gate and the lowest pressure is found at the end of flow These pressure histories are the key to understanding packing, melt densification, and ultimately shrinkage in the finished molded part Figure 4.22 is a “model” description of the pressure at location 2, the center of the part It is conveniently divided into four distinct segments, each corresponding to a phase of the molding process The first block in the figure represents the pressure building during injection of the melt into the tool The pressure builds uniformly as the melt flows into the tool, starting at atmospheric pressure and finishing at the packing pressure Figure 4.21 Pressure traces associated with different locations in an injection-molded plaque Position is near the gate, position is at the center of the plaque, and position is near the end of flow (Courtesy of GE Plastics.) © Plastics Design Library The second block is a constant pressure representing the packing phase in the tool During packing, the part begins to cool, but the packing pressure is maintained from the screw Any loss of material volume due to cooling shrinkage is replaced by additional melt during this phase Note that while the total part volume remains constant during this phase, the specific volume is going down due to part cooling at constant pressure This is followed by a cooling phase In the cooling phase, the part is isolated from the packing pressure because of gate freeze-off In the cooling phase, the part volume is considered constant Both the temperature and the pressure are decreasing during cooling In the final eject phase, the part is released from the tool In this phase, the part is allowed to cool from the eject temperature to room temperature Some shrinkage will occur during the eject phase because of this unconstrained cooling The same four phases are easily located on the PVT diagram shown in Fig 4.23 Line segment A-B represents the constant temperature during injection, as the pressure builds from atmospheric to the packing pressure During packing, the material cools and shrinks along a constant pressure line represented by segment B-C on the PVT diagram When the part reaches the “freeze line,” it is sufficiently solidified to release from the tool During this phase, the volume of the part is constant, and the pressure and temperature both decrease The final phase, segment D-E, represents cooling and shrinking of the part at atmospheric pressure It is important to note that the part shrinkage is the difference between the tool volume and the final part volume On the PVT diagram, the volume change is that associated with free cooling In other words, the real shrinkage is the difference in volume between point D and point E Figure 4.22 A simple model of the stages of an injection molding process This model approximates the behavior away from the gate (Courtesy of GE Plastics.) Ch 4: Causes of Molded-Part Variation: Material 44 Sv = Figure 4.23 PVT diagram showing the injection phases corresponding to the blocks in Fig 4.22 (Courtesy of GE Plastics.) Physically, the four stages can be correlated to the injection process as shown in Fig 4.24 Between A and B, molten polymer flows into the tool at constant temperature, but under increasing pressure From B to C, the part is held at constant pressure When sufficiently packed, the gate freezes off and cooling begins The part cools at constant volume—the volume of the cavity During cooling, the pressure slowly relieves and the temperature drops On opening the cavity, the part is now allowed to shrink without constraint The part shrinks to final dimensions on release from the cavity Volume shrinkage can, therefore, be calculated as the volume change between the mold and cold part, divided by the original mold volume Volume shrinkage, Sv, is represented in equation form as: V mold − Vpart Vmold where VMold is the volume of the mold and VPart is the volume of the molded part after cooling Shrinkage is dependent on the volume of the mold, and the final volume of the part While the mold volume is always constant, the part volume can be changed by the amount of polymer that is packed into the tool during the injection and holding phases of the injection process As shown in Fig 4.25, different packing pressures can create different amounts of shrinkage If the process is such that the part can cool under pressure without premature freeze-off, the shrinkage will be determined by the specific volume when the part is cooled to the “freeze line.” For the material in this example, processed using two different packing pressures, the part is found to have four times higher shrinkage with 50 MPa packing pressure versus what is found at 100 MPa packing pressure The data sheet properties for this resin are quoted for low-pressure molding as seen by the area marked “data sheet shrink range” in the accompanying graph in Fig 4.25 Figure 4.26 presents the result of another study[58] showing shrinkage at three locations along a standard injection-molded plaque From the pressure traces obtained during filling, we can determine the pressure that was in effect during packing at the three locations By processing under a series of packing pressures and measuring the shrinkage at the three locations, we obtain the curves shown in Fig 4.27 Notice that the gate, where the packing pressure was highest, has the lowest shrinkage Conversely, the end of the plaque, where the pressure was lowest, has the highest shrinkage Figure 4.24 The stages of injection molding correlated to the segments of the PVT diagram shown in Fig 4.23 (Courtesy of GE Plastics.) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 45 Figure 4.25 The effect of packing pressure on shrinkage (Courtesy of GE Plastics.) Figure 4.26 Pressure traces at four locations in an injection-molded plaque (Courtesy of GE Plastics.) Figure 4.27 The left graph shows shrinkage vs nozzle-packing pressure for three locations in the plaque The right graph shows a collapsed plot of shrinkage vs maximum mid-cavity pressure (Courtesy of GE Plastics.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 46 A plot of maximum mid-cavity pressure versus shrinkage is shown in Fig 4.27 for the results of this study The curves from all locations are shifted onto a single curve of pressure versus shrinkage The curve is found to be continuous for all locations where data were taken This implies that the peak packing pressure controls the shrinkage at all locations on the plaque It is also clear from the study that there is no single “shrinkage number” associated with a material The processing controls the shrinkage, which varies widely even in a simple part like this flat plaque Based on the complexity of variable pressure throughout a part during molding, the most accurate shrinkage predictions are obtained from computer-aided simulations of the filling, packing, and cooling processes for each part’s geometry Recall that local pressures vary with location in the plaque Analyzing the PVT diagram of Fig 4.28 in light of the pressure traces and cooling times found during the experiment, we see that the shrinkage estimates vary considerably over the length of the plaque: from a low of 0.14% at the gate end of the plaque to a high of 0.40% at the far end of the plaque Differential shrinkage within a single part is the primary source of warpage in an injection-molded part When the gate freezes off prematurely, the part will be under-packed and the shrinkage will be increased In the example shown in Fig 4.29, the gate froze during the packing stage at point C and the part began to cool and shrink in the tool When the part shrinks in the tool due to insufficient packing, the final part at room temperature will be smaller than expected of a well-molded part In the associated PVT diagram, premature freezeoff is seen as a shorter segment B-C When premature freeze-off cuts off the applied pressure from the screw, the part begins to cool and shrink away from the tool, losing pressure The part, in effect, is ejected at a higher temperature than expected In this case, less material gets packed into the part during the packing cycle, and the resulting part appears to shrink excessively In fact, it is not only smaller but also weighs less than a fully packed part In this case, shrinkage would be estimated from the change in specific volume between point D and point F 4.3.3 Predicting Mold Warpage Warp is the result of nonuniform shrinkage in a part For unfilled materials, nonuniform shrinkage is generally the result of temperature differences during cooling for different locations on the same part If one tool surface is hotter than another, the hotter surface cools more slowly In a semicrystalline polymer, the hotter surface will develop a higher degree of crystallinity, and consequently shrink more This surface will be relatively shorter than the surface that is quenched against a colder tool surface The resulting difference in surface dimensions will produce a bending stress in the part, curving it toward the surface with the higher shrinkage Volume Shrinkage SV = Vc1 − VE = 014 Vc SV = Vc − V E = 023 Vc SV = Vc − VE = 040 Vc Figure 4.28 PVT diagram and associated shrinkage calculations for three locations within a single injection-molded plaque The volume shrinkage at various locations is given by Svn where n = position 1, 2, or The specific volume, VCn , is given for points C1-3; VE is the specific volume at equilibrium (room temperature and pressure) (Courtesy of GE Plastics.) Ch 4: Causes of Molded-Part Variation: Material © Plastics Design Library 47 Figure 4.29 Premature freeze-off of the gate as shown schematically on the left, and in the PVT diagram at the right (Courtesy of GE Plastics.) Warp also results from filler orientation Fiber fillers in particular are known to restrict shrinkage along the direction of fiber orientation This direction is generally the direction of flow during part filling As shrinkage is restricted along the flow direction, it is increased along the transverse flow direction Again, this differential shrinkage will produce internal stresses in the molded part that are finally manifested as warp as the part cools Figure 4.30 shows a standard warp measurement Comparing the height produced by warpage to the length of the part will result in a warp index The more the part warps, the higher the warp index This measurement is convenient for comparing warpage in parts of a single material molded in the same tool during a processing study to minimize warp Warp is difficult to estimate from the PVT diagram The most accurate predictions of warp come from using computer-aided engineering analyses of the molding process Sl = lmold − l part lmold or SV = Vmold − Vpart Vmold Spherical fillers, such as glass beads or powders, have no effect on differential shrinkage Consequently, these dimensionally uniform fillers have no effect on warpage Spherical fillers will reduce shrinkage, because the volume displaced by the filler shrinks less than the polymer surrounding the filler Because the volume shrinkage is non-directional, the linear shrinkage in each direction is simply one third of the volume shrinkage For this case, the PVT diagram is very useful for estimating shrinkage in all directions Platelet fillers, such as mica, tend to align in the flow direction with their long axes parallel to the part surfaces These fillers restrict shrinkage in the in-flow and cross-flow directions equally; however, parts molded with platelet fillers will exhibit excessive shrinkage in the thickness direction As a rule of thumb, polymers with platelet fillers have three to six times higher shrinkage in the thickness direction versus the planar directions The shrinkage in the in-flow and cross-flow directions is the same, so the volume shrinkage is the w = hpart or w = hpart /d part Figure 4.30 Shrinkage and warpage sketches and formulae Different fillers have different effects on shrinkage and warpage [58] (Courtesy of GE Plastics.) © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material 48 sum of the shrinkage in the thickness plus twice the shrinkage in the in-flow direction Fiber fillers are the most common type of filler for reinforced plastics Fibers are most effective for increasing modulus in the in-flow direction However, fibers aligned in the flow direction tend to restrict shrinkage in that direction Shrinkage in the cross-flow direction is generally about three to six times higher than shrinkage in the in-flow direction Fiber-filled plastics have nearly equivalent shrinkage in the cross-flow and thickness directions The volume shrinkage therefore is the sum of the in-flow direction shrinkage plus twice the cross-flow shrinkage Computer-aided engineering (CAE) analysis software will generally take into account the general rules for differential shrinkage as a function of filler type and filler loading However, shrinkage and warp predictions are not yet an exact science and prototyping is still the best way to estimate exact tool dimensions for high-tolerance parts In summary, an understanding of the PVT diagram is very useful in making estimates of shrinkage in injection-molded parts A good understanding of the processing parameters is required if the estimates are to be accurate Keep in mind that shrinkage is not uniform throughout a part For all critical locations on the part, it is necessary to know the temperature history, the pressure history, and the freeze time during molding These histories are most accurately determined in instrumented tooling, but with a little experience it is possible to make good estimates and determine shrinkage with some degree of accuracy Warp predictions require a good understanding of shrinkage Only by determining the amount of local shrinkage at different locations on a part can an estimate of the amount and direction of warp be made 4.3.4 Accuracy of Shrinkage Predictions The local mold shrinkage in an injection-molded part is the result of many factors Local pressure variations are a primary source of different shrinkage in different locations of a molded part For isotropic amorphous polymers, molded into simple parts, a good estimate of shrinkage is possible using the techniques described in this chapter When filler systems are incorporated into the plastic molding compound, the shrinkage will be a function of the amount of filler, the shape of the filler, and the orientation of the filler at each location in the part Estimating the shrinkage of semi- Ch 4: Causes of Molded-Part Variation: Material crystalline polymers requires the additional use of data relating to the kinetics of crystallization In addition to the material effects, the tooling can also play a role in determining the local shrinkage of a part The shrinkage values found on data sheets for plastic compounds are usually determined by molding and measuring uniform flat plaques The number of gates and their locations have already been discussed in relation to controlling shrinkage In addition, when the part incorporates shapes such as ribbing or walls, the tool can restrict shrinkage during cooling prior to ejection Parts with such features can have 20% to 30% less shrinkage along the restricted directions Gating and mold geometry lead to constraints that must be taken into account during any estimation of shrinkage Similarly, overpacking has a large effect on shrinkage When a part is overpacked, excessive material is forced into a confined space On release from the tool, the overpacked part will have a compensating expansion as well as material shrinkage from cooling The resulting part will be larger than a part with normal packing Overpacking will also increase the friction between the solidifying part and the tool surface For large parts, friction can be enough to restrict shrinkage Injection-compression operations tend to use the machine’s clamp force to pack the part, however, large friction-forces are also associated with this type of molding operation Studies have shown[58] that when the processing conditions are well known, the shrinkage of simple parts, molded from amorphous polymers, can often be predicted to within ±10% of the measured shrinkage values Amorphous resins containing fiber fillers tend to be less predictable: the accuracy of prediction can approach ±30% of the actual molded shrinkage values The shrinkage of unfilled semicrystalline resins can be predicted to about ±20% accuracy when the crystallization temperature is known in addition to the processing temperatures and pressures Filled semicrystalline resins are predictable to about ±30% of the measured part-shrinkage As the part becomes more complex, the accuracy of predicting shrinkage becomes more difficult Toolmakers require accurate shrink predictions for every section of a new tool The practice of undercutting tool steel to leave steel so that it may be removed to bring the part into tolerance is known as cutting a tool “steel safe.” While this practice can minimize the cost of replacing damaged tooling from improper shrinkage determinations, it is costly in that it requires finishing the tool and molding a part to check its dimensions If the © Plastics Design Library 49 part is found to be undersized, the toolmaker then reworks the tool to get to the right-sized part The most accurate process for estimating complex parts is through the use of a computer equipped with engineering software for modeling the packing, cooling, and ejection operations during injection molding The CAE software is built to break the complex part geometry into many small elements Each element is assigned a set of properties that represents the plasticmolding compound and connects to the neighboring elements To model the injection process, the elements are oriented along the flow path, compressed according to the relationships described in the PVT diagram, cooled, and ejected using the rules established by PVT, and then free-cooled to ambient temperature Because the CAE software takes into account each element independently, but connected to its neighbor elements, shrinkage results are more accurately predicted for complex parts This process is described in detail in Ch LEXAN®, VALOX® , and NORYL® are registered trademarks of the General Electric Company © Plastics Design Library Ch 4: Causes of Molded-Part Variation: Material