PLA melt strength at thermoforming-relevant temperatures is intrinsically constrained by the linear chain topology characteristic of commercial extrusion-grade poly(lactic acid). Across the thermoforming temperature range of 90 to 120°C, unmodified PLA resins with weight-average molecular weight (Mw) between 100,000 and 180,000 g/mol and polydispersity index (PDI) of 1.8 to 2.5 generate Rheotens melt strength values of only 3 to 8 cN at 190°C when measured according to ISO 16790:2021. By comparison, polypropylene homopolymer of equivalent melt flow rate exhibits 12 to 20 cN under identical pull-off conditions, while branched polycarbonate routinely exceeds 25 cN. The theological deficiency of linear PLA stems from its low entanglement density, rapid reptation-driven chain relaxation above the glass transition temperature (Tg 55 to 60°C), and minimal strain-hardening response during uniaxial extension. At processing melt temperatures of 185 to 210°C, the terminal carboxyl and hydroxyl groups of PLA are highly susceptible to hydrolytic chain scission when residual moisture exceeds 250 ppm; technical bulletins from NatureWorks LLC for Ingeo 2500HP extrusion thermoforming grade specify pre-drying to below 250 ppm moisture content and caution that melt residence times exceeding 10 minutes above 200°C generate lactide monomer concentrations sufficient to plasticize the sheet and reduce extensional viscosity. The consequence for thermoformed tray production is a narrowing of the effective processing window to approximately ±5°C around the optimal melt temperature when using unmodified resin, a constraint that becomes more severe as regrind content increases beyond 30 wt% due to the cumulative molecular weight reduction from multiple heat histories. Sheet extrusion lines for PLA thermoforming stock typically incorporate a single-screw extruder with screw diameter of 65 to 90 mm, L/D ratio of 30:1 to 36:1, and a barrier-type screw geometry optimized for polyester processing with a compression ratio of 2.5:1 to 3.5:1. A gear pump positioned between the extruder exit and the flat die is essential for damping pressure pulsations that would otherwise propagate as draw resonance precursors in the air gap; melt pressure fluctuations at the die entrance must be maintained below ±1.0 percent of setpoint for sheet thickness uniformity of ±5 percent. Chill roll temperatures between 20 and 40°C arrest crystallization and produce amorphous sheet with haze below 2 percent suitable for high-clarity tray and lid applications, whereas chill roll temperatures of 60 to 80°C induce spherulitic crystallization that increases sheet opacity but improves dimensional stability during elevated-temperature transport and warehouse storage in non-climate-controlled facilities.
The melt strength deficit is most directly quantified through extensional viscosity measurements using a dual-bore capillary rheometer equipped with an opposing-orifice die configuration, where linear PLA demonstrates a Trouton ratio approaching 3 without strain hardening, while branched or chain-extended variants exhibit Trouton ratios of 5 to 12 within the Hencky strain range of 1.5 to 2.5. The practical operational boundary for linear PLA in cast sheet production is a maximum draw ratio—defined as the dimensionless quotient of chill roll velocity to die exit velocity—of approximately 4:1; attempts to operate at draw ratios exceeding 4.5:1 on a conventional chill roll line produce thickness oscillations that render the sheet unsuitable for downstream thermoforming. The thermoforming of PLA sheet into trays for food packaging, modified atmosphere packaging (MAP), and medical device blister applications requires a delicate balance between sufficient sheet stiffness at forming temperature to resist sag during indexing and adequate melt extensibility to fill mold contours without web rupture. Unmodified linear PLA grades exhibit pronounced draw resonance instability at stretch ratios exceeding 4.5:1 when processed on cast film lines equipped with polished chill rolls maintained below the cold crystallization onset temperature. Sheet producers targeting thermoforming stock therefore typically operate at draw ratios of 2.5 to 3.5 for linear PLA, sacrificing throughput capacity to maintain stable extrusion, whereas chain-extended formulations enable draw ratios of 5 to 8 without instability. This throughput differential of 60 to 120 percent on identical equipment represents the primary economic incentive for adopting chain-extended PLA in high-volume tray manufacturing operations where annual output exceeds 2,000 metric tons per line.
Under Non-Isothermal Sheet Casting Conditions, Draw Resonance Instability Manifests as a Self-Sustaining Periodic Oscillation
Draw resonance in linear PLA sheet casting initiates when the draw ratio exceeds a critical threshold determined by the interplay of extensional viscosity, thermal sensitivity, and viscoelastic relaxation time. For linear PLA with an Mw of 140,000 g/mol, the critical draw ratio (Drc) at a melt temperature of 190°C is approximately 4.2 to 4.8 under isothermal laboratory conditions, but this value decreases to 3.5 to 4.0 when non-isothermal effects are incorporated through an Arrhenius-type temperature dependence of extensional viscosity with activation energy of 15 to 25 kJ/mol. The onset criterion is characterized by a dimensionless Deborah number exceeding 0.05, where the relaxation time of the polymer melt (λ) measured by small-amplitude oscillatory shear using a rotational rheometer with 25 mm parallel plate geometry and 1 mm gap per ISO 6721-10:2015 is compared to the residence time in the air gap between die exit and chill roll contact. Linear PLA at 190°C exhibits a relaxation time of 0.02 to 0.05 seconds, yielding Deborah numbers in the unstable regime when air gaps exceed 15 mm at typical cast film line speeds of 8 to 20 m/min. The stability criterion established through linear perturbation analysis for Newtonian fluids provides a theoretical upper bound: draw resonance is predicted when the draw ratio exceeds approximately 20.2 under isothermal conditions, but this critical value is dramatically reduced for shear-thinning, strain-softening, and thermally sensitive polymers. For PLA, the combination of shear-thinning behavior with power-law index n = 0.4 to 0.7 at shear rates of 1 to 100 s⁻¹ and pronounced thermal sensitivity reduces the experimentally observed critical draw ratio to the 4 to 6 range. The periodic thickness oscillation frequency in PLA sheet casting typically falls within 0.5 to 3 Hz, corresponding to the viscoelastic relaxation spectrum of the polymer rather than to die lip gap or chill roll eccentricity, which can be distinguished through time-series analysis of online thickness gauge data. When draw resonance initiates, the thickness variation amplitude can exceed 25 percent of the target sheet thickness, rendering the stock unsuitable for thermoforming operations that require gauge uniformity within ±5 percent for consistent plug-assist force application and uniform wall thickness in the molded tray. The influence of die lip gap on draw resonance onset is particularly significant in the sheet thickness range of 0.3 to 1.2 mm where die lip gaps of 0.5 to 1.5 mm are typical; smaller initial gaps shift the instability to lower draw ratios because the extension rate in the air gap increases at constant take-up velocity. Extension rates in the air gap range from 0.5 to 15 s⁻¹ for commercial sheet production, and PLA exhibits onset of extension thickening only when Hencky strain exceeds 1.5 to 2.0, which corresponds to draw ratios of 4.5 to 7.4 in the absence of stress relaxation. The critical operational implication is that thermoforming-grade PLA sheet must be produced at draw ratios below the resonance threshold while maintaining sufficient molecular orientation to resist sag during subsequent reheat operations; significant molecular orientation imparted during sheet casting increases shrinkage upon reheating, which must be compensated for by pre-shrinking the sheet or by using higher forming temperatures to permit stress relaxation prior to plug contact.
In twin-screw compounding operations targeting thermoforming grade PLA, chain extension chemistry employing epoxy-functionalized oligomers represents the most commercially adopted route to melt strength enhancement. The reaction mechanism involves nucleophilic attack of PLA terminal carboxyl groups at 190 to 240°C on epoxide rings, forming β-hydroxy ester linkages that covalently couple two or more PLA chains; kinetic studies indicate that the reaction reaches 80 to 90 percent conversion within 2 to 4 minutes at 210°C under melt mixing conditions in a co-rotating twin-screw extruder with screw diameter of 27 to 40 mm, outer-to-inner diameter ratio (D₀/Dᵢ) of 1.55, L/D ratio of 40:1, and specific torque of 11 to 13 Nm/cm³. The stoichiometric requirement for effective chain extension is approximately 1 epoxy equivalent per 1 carboxyl equivalent, which translates to 0.3 to 0.8 wt percent for PLA resins with acid numbers of 5 to 10 mg KOH/g. Overfeeding of chain extender beyond 1.0 wt percent produces gel formation and localized crosslinking that manifests as fisheye defects in the extruded sheet with diameters of 0.1 to 0.5 mm, requiring melt filtration with mesh screens of 80 to 120 (177 to 125 µm aperture) upstream of the flat die. The branching reaction, as distinct from linear chain extension, requires epoxy-functionalized oligomers with functionality greater than 2 per molecule. BASF Joncryl ADR 4368-C has an epoxy equivalent weight of approximately 285 g/eq and a functionality of 9 to 12 epoxy groups per molecule, enabling star-shaped and comb-shaped architectures when grafting occurs at multiple PLA chain termini. The resulting branched PLA exhibits a strain-hardening onset at Hencky strain of 0.8 to 1.2, compared to 2.0 to 2.5 for linear PLA, indicating that the molecular architecture modification shifts the rheological response into the regime suitable for stable biaxial stretching during plug-assisted thermoforming. Published data comparing the two chain extension routes from twin-screw extrusion trials indicate that epoxy-functionalized oligomers increase Mw by 30 to 80 percent while maintaining PDI below 3.5, whereas peroxide branching increases Mw by only 10 to 20 percent with PDI values exceeding 4.0 due to radical recombination events. For thermoforming-grade sheet production, the epoxy chain extension route is preferred because it yields narrower molecular weight distribution, which correlates with more uniform biaxial extensional response and reduced variability in plug-assist force requirements across a production shift. The peroxide-initiated branching alternative employs organic peroxides such as 2,5-dimethyl-2,5-di(tert-butylperoxy)hexane (Luperox 101) at 0.1 to 0.3 wt percent to generate macroradicals via hydrogen abstraction from PLA methine carbons, which then undergo combination reactions to produce long-chain branching; this approach achieves melt strength increases of 2 to 3 times the linear baseline but carries the risk of uncontrolled molecular weight degradation at temperatures above the peroxide half-life threshold of 1 minute at 170°C. The branching efficiency depends critically on peroxide concentration and extruder temperature profile: when the melt temperature exceeds 220°C during peroxide addition, β-scission competes with branching, producing a net decrease in melt strength and eliminating any potential draw resonance suppression benefit. Published data for this specific configuration is limited, and the industrial adoption of peroxide-branched PLA in thermoforming applications remains substantially lower than that of epoxy chain-extended systems due to the narrower dosage tolerance window.
What Processing Window Sustains Stable Sheet Extrusion for PLA Trays?
Four interacting constraints bound the stable processing window for PLA sheet extrusion intended for thermoformed tray production: minimum melt temperature to achieve adequate flow and die filling, maximum melt temperature to limit hydrolytic degradation, minimum chill roll temperature to prevent roll sticking, and maximum chill roll temperature to avoid premature crystallization that interferes with subsequent thermoforming. For linear extrusion-grade PLA, the practical melt temperature window spans 180 to 210°C, with the upper limit dictated by the hydrolysis rate constant at 210°C being approximately 3 times greater than at 180°C as determined by melt viscosity loss measurements over a 30-minute residence time. The flat die design—either a coat hanger manifold or a T-die with adjustable lip gap and restrictor bars—must deliver melt temperature variations of no more than ±2°C across the width to prevent localized draw resonance initiation. Temperature uniformity of ±1°C across the die width is specified for high-clarity tray applications because viscosity variation of 5 to 8 percent per degree Celsius at PLA processing temperatures translates directly into thickness non-uniformity through the die lip. The chill roll press gap and contact wrap angle determine the final sheet gauge and the degree of residual stress frozen into the amorphous sheet; wrap angles of 200 to 260 degrees on the primary chill roll are typical, with secondary and tertiary rolls operated at progressively lower temperatures (15 to 25°C) to complete cooling below Tg before edge trimming and winding. Sheet thickness for thermoforming tray applications ranges from 0.3 mm for shallow deli tray bases to 2.0 mm for deep draw tray applications with depth-to-width ratios of 0.5:1, and thickness tolerance of ±5 percent is required for consistent thermoforming behavior. The use of a gear pump between extruder exit and die entrance is essential for maintaining volumetric output stability of ±0.5 percent, without which the instantaneous draw ratio fluctuates at frequencies of 0.1 to 1 Hz, periodically exceeding the critical draw resonance threshold. Extruder output rates for stable PLA sheet production typically range from 80 to 400 kg/h on production lines with screw diameters of 65 to 120 mm and die widths of 800 to 2,200 mm. At output rates below 20 kg/h per meter of die width, the residence time distribution in the flat die can exceed the thermal degradation half-life at 210°C, producing measurable reductions in sheet melt strength that are spatially non-uniform; conversely, at output rates above 150 kg/h per meter of die width, the shear rates in the die exceed 1,000 s⁻¹ and may initiate shear-induced chain scission for high-Mw PLA grades, reducing molecular weight and compromising the property profile required for tray end-use compliance. Vacuum venting at barrel zones 7 to 8 with applied vacuum of -0.08 to -0.09 MPa is specified on twin-screw lines to strip moisture and lactide monomer from the melt, and the vent port must be positioned downstream of the chain extender addition point when reactive extrusion is employed to prevent loss of volatile epoxide components before they can react with PLA carboxyl termini.
A Melt Strength Threshold of 8 cN at 190°C Defines the Viability Boundary
When the Rheotens value at 190°C drops below 8 cN, thermoformed tray production encounters a characteristic failure sequence that propagates from the bottom corner geometry through the entire forming cycle. Below this threshold, the sheet undergoes progressive thinning in the plug-assisted draw region, leading to premature failure at the tray bottom corners where the local wall thickness may decrease to 0.08 mm or less for a starting sheet thickness of 0.5 mm. The failure manifests in production as a characteristic pattern of localized whitening followed by puncture during the forming step, with the whitening resulting from microvoid formation and craze propagation in the strained PLA at Hencky strains exceeding 1.5. Processing interventions to compensate for low melt strength include reducing the plug-assist travel distance, increasing sheet temperature by 5 to 15°C, decreasing the plug speed below 500 mm/s, and increasing the time delay between sheet heating and forming. However, these adjustments have diminishing returns: increasing sheet temperature above 110°C begins to overlap with the cold crystallization region, producing hazy trays with uncontrolled shrinkage, while plug speeds below 300 mm/s produce excessive cycle time penalty when tray output must exceed 20 cycles per minute for economic viability. Equipment configurations for production of trays from chain-extended PLA typically specify a plug-assisted thermoforming machine with a clamping force of 50 to 300 kN depending on tray dimensions, a two-zone infrared heating system with ceramic elements operating at 400 to 600°C and emissivity of 0.85 to 0.92, and a temperature-controlled plug constructed from syntactic foam with polytetrafluoroethylene coating or from polyamide-imide. The plug temperature is maintained at 80 to 100°C to prevent premature sheet quenching at the contact interface while remaining below the PLA cold crystallization onset. Published production data from thermoforming trials indicate that chain-extended PLA sheet with a melt strength of 18 to 25 cN at 190°C can be successfully formed into trays with depth-to-diameter ratios of up to 1:1 using plug-assisted forming, whereas linear PLA with melt strength below 8 cN is restricted to shallow blister geometries with depth-to-diameter ratios below 0.4:1. The melt strength threshold is not arbitrary; it correlates with the minimum extensional viscosity required to resist necking propagation during the biaxial stretching phase of plug-assisted forming, where the local extension rate at the plug edge can reach 10 to 50 s⁻¹ and the sheet must maintain structural integrity while being stretched from an initial thickness of 0.5 to 2.0 mm to a final wall thickness of 0.15 to 0.6 mm across the tray sidewall.
Nucleation and Crystallization Kinetics in Plug-Assist Thermoforming
The crystallization behavior of PLA during the thermoforming cycle determines whether the final tray retains the dimensional stability necessary for hot-fill applications or undergoes distortion during cooling and storage. PLA is a slowly crystallizing polymer with a maximum crystallization rate at 105 to 110°C, approximately halfway between Tg (55 to 60°C) and Tm (145 to 155°C). The half-time for isothermal crystallization (t₁/₂) at 110°C for unmodified PLA is 2 to 5 minutes, which is longer than typical thermoforming cycle times of 10 to 30 seconds. This kinetic sluggishness means that thermoformed PLA trays remain predominantly amorphous immediately after forming, with crystallinity levels of 5 to 15 percent achievable only when mold temperatures are maintained at 80 to 110°C and the formed part is held under contact pressure for 5 to 15 seconds. The addition of nucleating agents such as talc at 1 to 5 wt percent, calcium carbonate at 3 to 8 wt percent, or proprietary amide-based nucleators at 0.5 to 2 wt percent reduces the crystallization half-time to 30 to 90 seconds at 110°C and enables crystallinity levels of 20 to 35 percent in the molded tray. Crystallinity directly influences tray heat distortion temperature: amorphous PLA trays soften at approximately 55°C, whereas trays with 25 to 35 percent crystallinity retain dimensional stability up to 90 to 100°C. For hot-fill tray applications requiring filling temperatures of 80 to 90°C, the crystallinity specification becomes mandatory, and the thermoforming equipment must include a temperature-controlled mold with oil heating capability in the range of 90 to 120°C, which is not required for amorphous tray production. The trade-off between crystallinity and clarity is unavoidable: crystalline PLA exhibits haze exceeding 30 percent, while amorphous PLA sheet and trays maintain haze below 3 percent for sheet thicknesses up to 0.8 mm when measured according to ASTM D1003-21. In applications where transparency is specified, such as fresh produce tray lids and bakery containers, the amorphous route is selected, and the resulting tray must be used at temperatures below 50°C to avoid dimensional distortion; published data for the long-term creep response of amorphous PLA trays at 45 to 50°C under stacking loads of 0.5 to 2.0 kPa indicates progressive deformation exceeding 5 percent over 24 hours, which limits warehouse storage in warm climates without climate-controlled logistics. The interaction between chain extension and crystallization must also be considered: branched and chain-extended PLA grades typically crystallize at 20 to 40 percent slower rates than their linear counterparts at equivalent molecular weight because the branching points impede lamellar folding and spherulitic growth, which extends the metastable amorphous window during thermoforming but also requires longer mold residence times or higher mold temperatures to achieve equivalent crystallinity in the final tray, representing a measurable cycle time penalty of 2 to 5 seconds per cycle that must be weighed against the throughput benefit of stable sheet extrusion at higher draw ratios.
Table 1: Comparative Melt Strength and Draw Resonance Parameters Across PLA Formulation Classes
| Parameter | Linear PLA (Ingeo 2003D) | Linear PLA (Luminy LX175) | Chain-Extended PLA (0.5 wt% Joncryl ADR 4368) | Branched PLA (Peroxide-Modified) |
|---|
| MFR (g/10 min, 210°C/2.16 kg, ISO 1133-1:2022) | 5 to 7 | 4 to 6 | 1 to 3 | 2 to 5 |
| Mw (g/mol) | 135,000 to 155,000 | 140,000 to 160,000 | 200,000 to 260,000 | 180,000 to 220,000 |
| PDI (Mw/Mn) | 1.8 to 2.2 | 1.9 to 2.3 | 2.5 to 3.2 | 3.5 to 4.5 |
| Melt strength (cN at 190°C, ISO 16790:2021) | 3 to 6 | 4 to 8 | 18 to 35 | 10 to 18 |
| Strain-hardening onset (Hencky strain) | 2.0 to 2.5 | 2.0 to 2.5 | 0.8 to 1.2 | 1.0 to 1.5 |
| Trouton ratio at Hencky strain 2.0 | 3.0 to 3.5 | 3.2 to 3.8 | 6 to 12 | 4.5 to 7 |
| Critical draw ratio (isothermal, 190°C) | 4.2 to 4.8 | 4.0 to 4.6 | 7.5 to 10.5 | 5.5 to 7.0 |
| Maximum sustainable draw ratio (production) | 2.5 to 3.5 | 2.5 to 3.5 | 5 to 8 | 4 to 6 |
| Throughput potential (relative, %) | 100 (reference) | 95 to 105 | 160 to 220 | 130 to 180 |
The degradation of melt strength during multiple thermomechanical cycles in extrusion, regrind reprocessing, and thermoforming represents a critical batch-to-batch variability source on production lines processing more than 30 wt percent regrind. Each pass through a single-screw extruder at 190 to 210°C reduces the Mw of linear PLA by 8 to 15 percent under properly dried conditions and by 15 to 25 percent if the regrind flake has absorbed moisture above 500 ppm from ambient storage, where the equilibrium moisture uptake of PLA at 23°C and 50 percent relative humidity is approximately 0.3 to 0.5 wt percent. The negative impact on melt strength is disproportionately larger than the molecular weight reduction would suggest because the lower-molecular-weight tail produced by chain scission acts as a plasticizer, reducing the extensional viscosity at the critical Hencky strain range where draw resonance initiates. Production lines that rely on regrind incorporation at 50 wt percent without compensating chain extender dosage demonstrate progressive deterioration of sheet gauge uniformity over an 8-hour shift, with the coefficient of variation for sheet thickness increasing from 1.5 to 4.0 percent as the effective melt strength declines from 8 to 4 cN. The corrective action involves either reducing regrind content below 20 wt percent, implementing real-time melt viscosity monitoring via in-line rheometer at the extruder exit, or adding a chain extender masterbatch at a dosage adjusted in proportion to the measured melt pressure and die temperature. The in-line rheometer, typically a slit die arrangement with pressure transducers spaced 50 to 100 mm apart, provides a continuous apparent shear viscosity reading that correlates with extensional behavior through the Cox-Merz rule at the Gordon-Schowalter limit for PLA melts below 1,000 s⁻¹; operators have used a minimum apparent shear viscosity threshold of 400 to 600 Pa·s at 100 s⁻¹ and 190°C as a proxy for adequate melt strength in production environments where Rheotens testing frequency is insufficient for real-time control.
Table 2: Regulatory and Test Method Compliance Matrix for PLA Thermoformed Trays
| Designation | Scope | Parameter Assessed | Typical Acceptance Criterion |
|---|
| US FDA FCN 178 | Food contact (polylactic acid) | Migration limits, residual lactide | Residual lactide < 0.5 wt% |
| EU Regulation 10/2011 Annex I | Plastic materials in food contact | Overall migration | < 10 mg/dm² |
| EN 13432:2000 / ASTM D6400-21 | Compostability | Biodegradation, disintegration | > 90% biodegradation in 180 days |
| REACH (EC) 1907/2006 | Chemical registration | SVHC content | < 0.1 wt% per SVHC |
| RoHS 2011/65/EU | Hazardous substances | Cd, Pb, Hg, Cr(VI), PBB, PBDE | Pb < 1,000 ppm; Cd < 100 ppm |
| ISO 16790:2021 | Rheotens method | Melt strength, drawability | > 8 cN at 190°C (deep trays) |
| ISO 1133-1:2022 | Melt volume-flow rate | Flow stability | 1 to 8 g/10 min at 210°C/2.16 kg |
| ASTM D638-14 / ISO 527-2:2012 | Tensile properties | Tensile strength, elongation at break | 40 to 65 MPa; 3 to 8% elongation |
| ASTM D1003-21 | Haze and luminous transmittance | Optical clarity | Haze < 3% (amorphous, 0.8 mm) |
| ASTM D1922 / ISO 6383-2 | Tear resistance | Elmendorf tear strength | 5 to 15 N/mm |
| ASTM D3985 / ISO 15105-2 | Oxygen transmission rate | Barrier performance | 20 to 45 cm³/(m²·day·atm) at 23°C, 0% RH |
| ASTM F1249 / ISO 15106-2 | Water vapor transmission rate | Moisture barrier | 8 to 15 g/(m²·day) at 38°C, 90% RH |
The operational boundary conditions for chain-extended PLA sheet extrusion on a production-scale line with a 90 mm single-screw extruder (L/D = 32:1, barrier screw) and a 1,400 mm flat die include the following equipment-specific parameters: die lip gap set at 0.8 to 1.2 mm for 0.5 mm target sheet thickness; melt temperature at die exit maintained at 195 to 205°C with a maximum deviation of ±1.5°C across the die width; gear pump inlet pressure of 8 to 12 MPa and outlet pressure of 10 to 15 MPa; primary chill roll temperature 25 to 30°C with a surface roughness of 0.05 to 0.10 µm Ra to achieve sheet haze below 2 percent; secondary chill roll temperature 15 to 20°C; air gap 10 to 18 mm; draw ratio 3.0 to 4.5 for linear PLA and 5.0 to 7.5 for chain-extended PLA; and winder tension 50 to 80 N/m of sheet width. Under these conditions, production lines with annualized output of 1,500 to 3,000 metric tons per year demonstrate stable sheet extrusion with thickness coefficient of variation of 1.5 to 3.5 percent when using chain-extended PLA, compared to 4 to 8 percent for linear PLA at equivalent throughput. The draw resonance suppression benefit of chain extension is not solely attributable to increased zero-shear viscosity but rather to the onset of extensional strain hardening at lower Hencky strain values, which damps the thickness perturbation growth rate by providing increasing local resistance as thinner sections experience higher extension rates. This self-stabilizing mechanism is absent in linear PLA, where the extensional viscosity remains constant or decreases slightly with Hencky strain (strain softening), permitting thickness perturbations to amplify monotonically until the sheet ruptures or the amplitude saturates through non-linear effects at amplitudes that remain commercially unacceptable for thermoforming stock.
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