Tiêu chuẩn iso 11443 2014

© ISO 2014 Plastics — Determination of the fluidity of plastics using capillary and slit die rheometers Plastiques — Détermination de la fluidité au moyen de rhéomètres équipés d’une filière capillair[.]

Test device

The test device features a heatable barrel with a bore closed at the bottom end by an interchangeable capillary or slit die Test pressure is applied to the melt inside the barrel using a piston, screw, or gas pressure Suitable examples are illustrated in Figures 1 and 2, with flexibility for other dimensions to be used.

The barrel shall consist of a material resistant to wear and corrosion up to the maximum temperature of the heating system.

Copyright International Organization for Standardization

Provided by IHS under license with ISO Licensee=University of Alberta/5966844001, User=sharabiani, shahramfs

No reproduction or networking permitted without license from IHS

The barrel can have a lateral bore for the insertion of a melt-pressure transducer close to the die entrance.

The permissible deviations in the mean bore diameter throughout the length of the barrel shall be less than ±0,007 mm.

The barrel shall be manufactured using techniques and materials that produce a Vickers hardness preferably of at least 800 HV 30 (see ISO 6507-1 and Note 1) and a surface roughness of less than

R a = 0,25 àm (average arithmetic discrepancy, see ISO 4287).

Nitrided steel is suitable for temperatures up to 400 °C, making it an ideal choice for various applications Materials with hardness values slightly below the specified standards, yet possessing adequate corrosion and abrasion resistance, have been found acceptable for constructing barrels and dies Ensuring proper material selection enhances durability and performance in high-temperature environments.

Increasing the barrel-bore diameter in rheometers allows for more measurements per fill and expands the shear rate range, enhancing testing versatility However, larger bore sizes require greater sample masses and lead to longer times to achieve temperature equilibrium throughout the sample Commercial rheometers typically feature barrel-bore diameters ranging from 6.35 mm to 25 mm, balancing performance and sample requirements.

5.1.3.1 The entire length of the capillary die wall shall be machined to an accuracy of ±0,007 mm for the diameter (D) and ±0,025 mm for the length (L) (see Figure 1).

The capillary shall be manufactured using techniques and materials that produce a Vickers hardness preferably of at least 800 HV 30 (see ISO 6507-1 and Note 1 to 5.1.2) and a surface roughness of less than

R a = 0,25 àm (average arithmetic discrepancy, see ISO 4287).

The capillary opening shall show no visible machining marks nor perceptible eccentricity.

Capillary dies commonly feature diameters ranging from 0.5 mm to 2 mm, with varying lengths to achieve the desired L/D ratios, which are essential for precise flow control For testing filled materials, larger diameters may be necessary to accommodate specific testing requirements.

NOTE 2 Hardened steel, tungsten carbide, stellite, and hardened stainless steel are the most common die materials.

The precision of measuring capillary dimensions depends on both the capillary radius and length, with accurate measurement becoming challenging for diameters smaller than 1.25 mm, where a precision of ±0.007 mm is difficult to achieve Due to the high sensitivity of flow data to capillary dimensions, it is essential to know and report the exact measurements of the capillary and slit die dimensions (thickness, width, and length) This ensures reliable data and consistency in applications requiring precise flow analysis.

1 applied force or constant velocity 7 capillary die

2 thermal insulation 8 die-retaining nut

4 barrel 10 temperature-controlled air chamber

Figure 1 — Typical example of an extrusion rheometer used with a capillary die

1 piston 3 die 5 channel P i = pressure transducers

Figure 2 — Typical example of an extrusion rheometer used with a slit die

To accurately determine the apparent shear rate (γ̇_ap) and apparent shear stress (τ_ap) using a single capillary die, the ratio of the length to diameter (L/D) must be at least 16, with an inlet angle of 180°, unless specified otherwise by the relevant International Standard Only data obtained from capillaries with matching inlet angles (within ±1°), lengths (within ±0.025 mm), and diameters (within ±0.007 mm) should be compared for consistency The inlet angle is defined as shown in Figure 1, ensuring standardized and reliable rheological measurements.

For optimal performance, it is recommended to use a die with a length of either 16 mm or 20 mm, a diameter of 1 mm, and an entry angle of 180° When the standard die size is unsuitable, such as with heavily filled materials, options for die diameters of 0.5 mm, 2 mm, or 4 mm are permitted If using dies with diameters other than 1 mm, the length-to-diameter ratio (L/D) should generally be maintained consistent with that of the 1 mm die, whenever possible.

NOTE 1 Die lengths of 16 mm and 20 mm are most commonly used, the choice often being dependent on, and limited by, the design of the instrument.

NOTE 2 For a given value of the apparent shear rate, the effect of shear heating of the melt is reduced by use of smaller diameter capillary dies.

To accurately determine the true shear rate (γ) and true shear stress (τ), capillary dies with the same diameter (±0.007 mm) and inlet angle (±1°) are required These dies must have at least two different L/D ratios selected from the recommended series, which includes values of 0.25, 1.5, 10, 16, 20, 30, and 40, as referenced in section 8.4.2 It is essential that specific conditions are met during this process to ensure precise and reliable measurements. -**Sponsor**Need help rewriting your article to meet SEO rules and extract key sentences? [Blogify](https://pollinations.ai/redirect-nexad/hLgpruJP) can transform your content effortlessly Blogify's AI-driven platform helps content creators like you convert complex text into SEO-optimized blog posts With Blogify, you can easily generate engaging content and enhance your online visibility, no matter the source format.

The use of only two dies with the same diameter (±0.007 mm) and inlet angle (±1°), where the L/D ratios are between 5 and 16, is permitted under specific test conditions These conditions must ensure that the resulting Bagley plot remains approximately linear, which must be established in advance for each sample class using additional dies (see 8.4) When employing just two dies, their L/D ratios must differ by at least 15 to ensure valid testing parameters.

For accurate shear viscosity measurement corrected for entrance pressure drop effects, it is recommended to use two dies with specific length-to-diameter (L/D) ratios: a short die with an L/D ratio between 0.25 and 1 and a long die with an L/D ratio between 16 and 20, both having a diameter of 1 mm and an entry angle of 180° When a 1 mm diameter die is unsuitable, such as for heavily filled materials, alternative diameters of 0.5 mm, 2 mm, or 4 mm can be used, with the appropriate L/D ratios maintained as specified for the 1 mm diameter die, ensuring consistent measurement accuracy across different sizes.

The correction procedure for entrance pressure drop effects, as outlined in section 8.4, involves extrapolating data to a zero die length rather than assuming that a short die accurately represents the entrance pressure drop This approach ensures more precise adjustments, improving the reliability of pressure drop measurements in extrusion processes Implementing this extrapolation method aligns with best practices for accurate analysis of pressure effects at the die inlet.

The slit die must be precision-machined with an accuracy of ±0.007 mm for thickness, ±0.01 mm for width, and ±0.025 mm for length Additionally, the distance between the centers of the pressure transducers and the exit plane should be measured with an accuracy of ±0.05 mm, ensuring optimal performance and consistency.

The die shall be manufactured using techniques and materials that produce a Vickers hardness preferably of at least 800 HV 30 (see ISO 6507-1 and Note 1 to 5.1.2) and a surface roughness of less than

R a = 0,25 àm (average arithmetic discrepancy, see ISO 4287.)

NOTE For slit die materials, see Note 1 to 5.1.2 and Note 2 to 5.1.3.1.

To determine the apparent shear rate (γ̇ₐₚ) and apparent shear stress (τₐₚ), the slit die should have a thickness-to-width ratio (H/B) of no more than 0.1 and an inlet angle of 180°, unless specified otherwise by the relevant International Standard.

`,`,`,,,`,``,`,,,,,,``,,````,-`-`,,`,,`,`,,` - same inlet angle (±1°), thickness (±0,007 mm), width (±0,01 mm), and length (±0,025 mm) shall be compared.

To accurately determine the true shear rate (γ̇) and shear stress (τ), slit dies compliant with the specifications in sections 5.1.4.1 and 5.1.4.2 can be employed similarly to capillary dies, utilizing the modified Bagley correction method (see 8.4) Alternatively, pressure transducers placed along the slit die channel can measure true shear stress values directly, providing reliable data for rheological analysis.

The piston diameter must be 0.040 mm ± 0.005 mm smaller than the barrel-bore diameter to ensure proper fit and minimal leakage It can be fitted with split or full sealing rings to reduce melt backflow past the piston land, enhancing sealing efficiency The piston hardness should be less than that of the barrel but must meet a minimum of 375 HV 30, according to ISO 6507-1 standards, to ensure durability and optimal performance.

Temperature control

For all temperatures that can be set, the barrel temperature control shall be designed such that, within the range of the capillary die or slit die, as applicable, and the permissible filling height of the barrel, the temperature differences and variations measured at the wall do not exceed those given in Table 2 for the duration of the test.

Table 2 — Maximum allowable temperature differences as a function of distance and as a function of time

Temperature difference from the set temperature as a function of distance a °C

Temperature variation as a function of time a °C

>300 ±2,0 ±1,5 a For all positions within the range of the capillary die or slit die, as applicable, and the permissible filling height of the barrel, for the duration of the test.

The test device shall be designed so that the test temperature can be set in steps of 1 °C or less.

Measurement of temperature and calibration

When using capillary dies, the test temperature should be set to the melt temperature in the barrel near the capillary inlet or, if unavailable, the barrel wall temperature at that point It is recommended to measure the test temperature within 10 mm above the capillary inlet for accurate results (Refer to 5.3.2 for additional guidance.)

When using slit dies, it is essential to measure the die wall temperature and consider it as the test temperature This temperature must closely match the barrel's test temperature within specified distance- and time-related tolerances outlined in Table 2 (Refer to sections 5.3.1.1 and 5.3.2 for additional details.)

The temperature-measuring device tip should be in direct contact with the melt whenever possible If direct contact is not feasible, the tip must contact the barrel or die wall within 1.5 mm of the melt channel Proper placement of the thermometer ensures accurate temperature readings essential for optimal process control.

Thermally conductive fluids can be used in the thermometer well to improve conduction Thermometers, preferably thermocouples or platinum resistance sensors, can be placed as shown in Figure 1 and

The temperature-measuring device used during testing must have an accuracy of within 0.1 °C and be calibrated using a standard thermometer with an error margin of ±0.1 °C It is essential that the device complies with the specified immersion depth for the particular thermometer To ensure accurate calibration, the thermometer's barrel can be filled to the top with a low-viscosity melt, providing reliable temperature readings.

No liquids that can contaminate the die or barrel or influence the ensuing measurements, e.g silicone oil, shall be used as heat transfer media during calibration.

Measurement of pressure and calibration

The test pressure is defined as the pressure drop in the melt, measured between the pressure before the capillary-die or slit-die inlet and at the die exit Ideally, this pressure should be measured using a melt-pressure transducer placed close to the die entrance, with the transducer-to-die face distance maintained at a constant, preferably not exceeding 20 mm If direct transducer measurement is not possible, the test pressure can be determined indirectly by measuring the force exerted on the melt, such as via a piston and load cell setup These methods ensure accurate assessment of melt flow behavior during testing, adhering to standardized procedures for consistency and precision.

Maintaining a constant distance from the die entry face to the pressure transducer is crucial during testing, as variations can affect the accuracy of pressure drop measurements Positioning the pressure transducer at a distance equivalent to the barrel diameter from the die entry face helps minimize fluctuations caused by recirculating flow above the die, leading to more reliable and consistent pressure readings.

When conducting testing involving extrusion into a channel or vessel pressurized above atmospheric levels, it is essential to measure the pressure at the die exit This should be done using a pressure transducer positioned immediately below the die exit for accurate readings Proper pressure measurement ensures reliable test results and optimal process control.

The force- or pressure-measuring devices shall be operated in the range between 1 % and 95 % of their nominal capacity.

5.4.2 Pressure drop along the length of the slit die

When using slit dies, the pressure profile along the length of the die shall be measured by flush-mounted melt-pressure transducers positioned along the die wall.

When using slit dies without melt-pressure transducers, the combined pressure losses at the entrance and exit can be accurately accounted for by applying the Bagley correction specifically modified for slit dies, as detailed in section 8.4.3.

External hydraulic test equipment is essential for calibrating melt-pressure transducers to ensure accurate measurements Load cells must be calibrated according to the manufacturer's specifications, maintaining a maximum permissible error of 1% of the full-scale value and 5% of the absolute value For optimal accuracy, the calibration of melt-pressure transducers should be conducted at the test temperature Proper calibration ensures reliable performance and compliance with industry standards.

Measurement of the volume flow rate of the sample

The volume flow rate shall be determined either from the feed rate of the piston or by weighing the mass of the sample extruded during a measured period of time.

When performing weighing, it is essential to convert the measurement to the volume flow rate using the melt's density at the current test temperature Hydrostatic pressure effects on density are to be disregarded to ensure accurate conversion This method ensures precise volume flow rate calculations based on mass measurements under standardized conditions.

The volume flow rate shall be determined to within 1 %.

For accurate and comparable test data, it is recommended to set apparent shear rates and flow rates accordingly, enabling the determination of true shear rates specified in ISO 11403-2 through interpolation Apparent shear rates should be spaced evenly on a logarithmic scale, with at least two data points per decade to ensure reliable and consistent results.

The maximum permissible error in determining the volume flow rate through the piston feed rate can only be achieved if the leakage between the piston and barrel remains sufficiently low According to experience, maintaining a clearance of no more than 0.045 mm between the piston and barrel helps ensure accurate measurements and minimizes leakage, thereby conforming to specified error limits.

A representative sample must be carefully selected from the test material to ensure accurate testing The number of determinations per barrel filling varies based on the molding material and should be mutually agreed upon by all parties involved Additionally, the temperature during test sample preparation should be lower than the temperature during the subsequent testing process to ensure reliable results.

Cleaning the test device

Before taking each measurement, thoroughly inspect the barrel, transducer bores (if applicable), piston, and capillary or slit die to ensure they are free of any adherent foreign matter Conduct a visual examination to verify cleanliness, which is essential for accurate and reliable measurement results Proper cleaning and inspection of these components help maintain measurement precision and prevent contamination-related inaccuracies.

If solvents are used for cleaning, ensure that no contamination of the barrel, piston, and capillary or slit die has occurred that might influence the test result.

For effective cleaning, circular brushes made of copper/zinc alloy (brass) and linen cloths are recommended, though caution is advised as copper-based materials may accelerate polymer degradation in polyethylene and polypropylene tests Alternatively, gentle burning out can be used for cleaning, and applying graphite on threads can aid in unlocking after testing, ensuring thorough maintenance without compromising material integrity.

Warning: The selected operating conditions may cause partial decomposition of the test material or release hazardous volatile substances Users of this International Standard must be aware of these potential risks, take appropriate measures to prevent or minimize them, and ensure proper protective equipment is in place.

Selection of test temperatures

For accurate comparison or modeling, it is recommended to obtain data at three different temperatures following ISO 11403-2 standards One of these temperatures should ideally match the temperature specified in the relevant material designation or standards like ISO 1133-1 and ISO 1133-2 for melt flow rate testing The other two temperatures should be spaced approximately 20°C apart, and can be either higher or lower than the melt flow rate test temperature, or one of each Depending on the specific grade of material and intended application, alternative temperature values may be used to optimize data relevance.

NOTE 1 From an analysis of CAMPUS databases, the average interval in temperature used to measure shear viscosity ranged from 10 °C to 30 °C and was dependent on the material grade.

Table 3 presents typical test temperatures for various materials, primarily for informational purposes However, the most relevant data are usually obtained at the processing temperatures, ensuring that test conditions closely mimic real-world conditions Additionally, shear stresses and shear rates applied during testing are designed to replicate those encountered during actual material processing, providing more accurate and applicable results.

Acrylonitrile-butadiene-styrene (ABS) 200 to 280

Polyethylene and ethylene copolymers and terpolymers 150 to 250

Polystyrene and styrene copolymers 180 to 280

Ethylene-vinyl alcohol copolymer 190 to 230

Preparation of samples

To ensure optimal melt fluidity, implement pretreatment or conditioning procedures based on International Standards or relevant material standards, especially when factors like residual monomer content, gas inclusions, and moisture influence the process.

NOTE Examples of materials that can require special preparation regimes include poly(ethylene terephthalate), poly(butylene terephthalate), and polycarbonate.

Allow the assembled apparatus to reach thermal equilibrium at the test temperature before applying the final torque on the die (where applicable), then start charging (see Warning in 7.1).

To minimize air inclusions, introduce the sample into the barrel in small, separate quantities, with each layer compacted using a piston Fill the barrel until it is approximately 12.5 mm from the top to ensure proper compaction Complete the charging process within 2 minutes to maintain sample integrity and achieve consistent results.

Preheating

Begin by charging the barrel and immediately starting the preheat timer Extrude a small amount of material at a constant pressure or apply a steady volume flow rate until a positive load or pressure is established, then halt the extrusion or flow Continue the preheating process for at least 5 minutes to ensure thermal equilibrium within the barrel, verifying that key measurements remain stable within ±5% or by confirming the sample temperature matches the specified test temperature within the allowed tolerance After preheating, extrude a small quantity of the test material, pause for 1 minute, then proceed with the measurement to ensure accurate test results.

Determination of the maximum permissible test duration

To ensure accuracy and detect potential degradation or other processes affecting measurements, perform a repeat measurement on the same barrel charge under identical conditions at the end of the test Compare the initial and final measurement results; significant differences indicate possible degradation or measurement interference This process helps maintain the integrity of test results and verifies that no process has compromised the data throughout the testing period.

For each sample and test temperature, determine the maximum permissible test duration by conducting tests with various preheating times This duration corresponds to the period from the end of barrel charging during which the measured parameter—such as volume flow rate or test pressure—remains within ±5% of its initial value under constant test conditions.

If it is not possible to determine the required test pressure or volume flow rate within the maximum allowable test duration, perform measurements incrementally by multiple barrel fillings using the same sample.

For unstable materials, it is recommended to conduct tests using a decreasing speed profile to minimize measurement variations caused by material changes Additionally, the degree of sample compaction significantly impacts its stability, affecting test accuracy and reliability.

Determination of test pressure at constant volume flow rate: Method 2

If the test pressure necessary to maintain a given volume flow rate is to be determined (see also 5.4.1 and 7.8), use either of the following methods (see Table 1):

Determination of volume flow rate at constant test pressure: Method 1

If, as an alternative to 7.6, the volume flow rate for a given test pressure drop is required (see also 7.8), use either of the following methods (see Table 1):

Waiting periods during measurement

At each measurement, wait until the test pressure (method A2 or B2) or the volume flow rate (method A1 or B1) has become constant (e.g to ±3 %) over a given time period (e.g 15 s).

NOTE 1 With a single barrel filling, it is generally possible to determine several pairs of values for volume flow rate and test pressure.

NOTE 2 It is recommended that selected measurements are repeated to check the repeatability.

Measurement of extrudate swelling

Measure the degree of extrudate swelling either at the test temperature during the extrusion process, or after cooling of the extruded strand to room temperature.

The diameter of the extrudate depends on several factors, including flow rate, test temperature, and the time since extrusion Cooling method, extrudate length, capillary die dimensions (length, diameter, entry geometry), and barrel diameter also significantly influence extrudate size Accurate and consistent measurement techniques are crucial, as results are highly sensitive to testing conditions To ensure reliable comparisons, all testing parameters must be identical across measurements.

The procedures outlined assess the degree of extrudate swelling, providing valuable insights into the extrusion process While these methods are specifically designed for capillary dies, they can also be applied by analogy to slit dies, offering versatility in measuring extrudate behavior Alternative techniques may be employed depending on specific requirements, but the described procedures serve as a reliable standard for evaluating swelling during extrusion.

The diameter of the extruded strand is measured with a micrometer In order to minimize the effects of gravity, use the following procedure:

— remove any extrudate attached to the capillary die by cutting it off as close as possible to the die;

— extrude a length of extrudate not longer than 5 cm and cut off the length of extrudate, marking the end that was extruded first;

— when cutting off the length of extrudate, hold it with tweezers and subsequently allow it to cool, suspended in air, to room temperature;

— measure the diameter of the strand as close as possible to the marked end (outside the area deformed by cutting and marking).

7.9.3 Measurement at the test temperature

Use a photographic or optical method that involves no mechanical contact with the extruded strand In order to minimize the effect of gravity, use the following procedure:

— remove any extrudate attached to the capillary die by cutting it off as close as possible to the die;

— extrude a length of extrudate not longer than 5 cm;

— measure the diameter of the extruded strand at a fixed point below the die outlet by photographic or optical techniques.

To accurately measure extrudate swelling while minimizing cooling of the extruded strand, it is recommended to extrude the strand into a temperature-controlled air chamber, as illustrated schematically in Figure 1 This approach helps maintain the strand's temperature, ensuring precise measurement of its swelling behavior Using a controlled environment reduces inconsistent cooling effects, leading to more reliable experimental results in extrusion processes.

Volume flow rate

Calculate the volume flow rate Q, in cubic millimetres per second, by means of one of the following formulae:

A is the piston cross-sectional area, in square millimetres; v is the velocity of the piston, in millimetres per second;

 m is the mass flow rate of the sample, in grams per second; ρ is the density of the sample at the test temperature, in grams per cubic millimetre.

Apparent shear rate

Calculate the apparent shear rate γ ap , in reciprocal seconds, at the die wall, using the formula given in 8.2.2 or 8.2.3, as applicable.

D is the diameter of the capillary die bore, in millimetres;

Q is the volume flow rate, in cubic millimetres per second (see 8.1).

In Newtonian fluids, Formula (3) accurately provides the true shear rate (γ) at the capillary wall However, since most plastics melts do not exhibit Newtonian behavior, the calculated shear rate using this formula is referred to as the apparent shear rate (γ ap) To obtain the true shear rate from the apparent value, a correction procedure is necessary, as detailed in section 8.5.1.

B is the width of the die, in millimetres;

H is the thickness of the die, in millimetres;

Q is the volume flow rate, in cubic millimetres per second (see 8.1).

Formula (4) is accurate only for very small thickness-to-width ratios (H/B), specifically when H/B is less than 0.1 When this condition is met, using Formula (4) overestimates the apparent shear rate (γ̇ₐₚ) by less than 3% A comprehensive analysis of the approximation's validity and a correction method are provided in Annex A.

Apparent shear stress

Calculate the apparent shear stress τ ap , in pascals, at the die wall, using the formula given in 8.3.2 or 8.3.3, as applicable.

8.3.2 Method A: Capillary dies τ ap = pD

4 (5) where p is the test pressure, in pascals;

L is the length of the die, in millimetres;

D is the diameter of the die, in millimetres.

8.3.3 Method B: Slit dies τ ap ( H B HB + ) × p L

2 (6) where p is the test pressure above the die inlet, in pascals;

L is the length of the die, in millimetres;

B is the width of the die, in millimetres;

H is the thickness of the die, in millimetres.

Shear stresses calculated using Formulae (5) and (6) are apparent quantities since the pressure drop along the die is less than the test pressure p, which includes pressure losses at the die entrance, within the die, and at the exit To obtain true shear stresses, it is essential to apply appropriate corrections to either the test pressure p or the die length L, as detailed in section 8.4.

True shear stress

The true shear stress can be accurately determined using the Bagley correction method [3], as detailed in sections 8.4.2 or 8.4.3, depending on the specific application Alternatively, when slit dies equipped with pressure transducers (methods B1 and B2) are used, shear stress can be directly measured, as explained in section 8.4.4 These methods ensure precise assessment of shear stress in polymer processing.

If nonlinear Bagley or slit-die pressure-drop versus distance plots are observed, this must be clearly stated in the test report In these cases, using shorter dies is recommended unless otherwise agreed upon, with any alternative procedures explicitly detailed in the report for transparency.

When measuring the shear viscosity of plastics with capillary-die or slit-die extrusion rheometers, it is important to consider factors such as viscous dissipation and the pressure dependence of viscosity, as these can influence the accuracy of the results Nonlinear viscosity plots may occur due to these effects, potentially impacting data interpretation and reliability Proper understanding and control of these variables are essential for obtaining precise rheological measurements.

8.4.2 Bagley correction for capillary dies (method A)

To determine the total entrance and exit pressure losses, follow a systematic procedure For Method A1, utilize at least two capillary dies with identical inlet angles and diameters but varying L/D ratios, ensuring that (L/D)1 < (L/D)2 Measure the apparent shear rate for each die to accurately assess the pressure drops associated with entrance and exit losses This approach helps in analyzing how different L/D ratios influence pressure losses in capillary extrusion processes.

The article discusses measuring the apparent shear rate (γ̇ₐₚ) at the die wall as a function of the test pressure (p), highlighting the importance of consistent die geometry For Method A2, it is recommended to use multiple capillary dies with identical inlet angles and diameters but different L/D ratios (where L/D₁ < L/D₂) to measure how test pressure varies with apparent shear rate Data collected from these experiments should be plotted as test pressure versus L/D at various shear rates, resulting in Bagley lines with slopes four times the true shear stress, aiding in accurate characterization of die flow behavior.

When using long capillary dies, deviations from a straight line may occur due to pressure effects on melt viscosity or viscous dissipation To ensure accurate measurements, it is recommended to use shorter capillary dies unless otherwise agreed upon In cases of alternative procedures, the chosen method must be clearly specified in the test report, adhering to standard testing protocols.

The Bagley correction can be efficiently performed using specialized computer software, eliminating the need for traditional data-plotting methods However, generating graphic printouts of the Bagley plots remains valuable, as it allows operators to verify the accuracy of the correction assumptions Specifically, assessing whether the Bagley lines are straight on the plot helps ensure the validity of the corrections applied to measured data.

Extrapolate the Bagley line for each apparent shear rate (γ̇_ap) down to zero pressure to determine the die entrance and exit pressure losses The ordinate value, p_c, represents the combined pressure losses at the die entrance and exit corresponding to the specified apparent shear rate This method helps to accurately assess flow behavior and pressure contributions within the extrusion process.

Figure 3 — Application of the Bagley correction method [3] — Plot of the apparent shear rate γ ap versus the test pressure p for different values of L/D

NOTE The melt pressure p is plotted as a function of L/D for dies of the same diameter for different values of the apparent shear rate γ ap

Figure 4 — Schematic Bagley plot for capillary dies

Calculate the true shear stress τ for the apparent shear rate γ ap of interest using either Formula (7) or Formula (8): τ = −( p p D c ) L

4 (7) where p is the test pressure, in pascals; p c is the pressure correction, in pascals;

D is the diameter of the capillary die, in millimetres;

L is the length of the capillary die, in millimetres.

The die diameter (D) remains constant, making the abscissa distances (L/D)c indicative of die-length corrections To accurately determine the true shear stress (τ) for the apparent shear rate (γ̇ap), Formula (8) can be used as an alternative to Formula (7) This formula accounts for die-length corrections through the dimensionless term (L/D)c, ensuring precise shear stress calculations in extrusion processes.

8.4.3 Bagley correction for slit dies (method B)

To determine the total pressure losses in the entrance and exit sections, start by employing method B1 with multiple slit dies sharing identical inlet angles, widths, and thicknesses but varying in length, with L₁ < L₂ Measure the apparent shear rate across these die configurations to accurately assess the pressure loss contributions Utilizing at least two different slit die lengths ensures a reliable calculation of the pressure drop, essential for optimizing die performance and process efficiency.

In the experimental procedure, the test pressure p is measured as a function of the apparent shear rate γ̇_ap at the die wall For method B2, at least two slit dies with identical inlet angles, widths, and thicknesses but different lengths (L1 and L2, with L1 < L2) are used to obtain data by measuring p against γ̇_ap The collected data is then plotted as p versus (L(H + B))/HB for various shear rates, with the resulting Bagley lines exhibiting a slope twice that of the true shear stress, enabling accurate characterization of the material's flow behavior.

NOTE The test pressure p is plotted as a function of L ( H + B )/ HB for dies of the same width B and thickness H for a single value of the apparent shear rate γ ap

Figure 5 — Schematic Bagley plot for slit dies

When using long slit dies, if deviations from a straight line occur due to pressure effects on melt viscosity or viscous-dissipation, it is advisable to perform measurements with shorter slit dies If a different procedure is agreed upon, it must be specified in the test report, referencing the relevant notes (see Notes to 8.4.1 and 8.4.2).

Extrapolate the Bagley line to zero pressure for each apparent shear rate γ̇ₐₚ, with the ordinate distance p_c representing the total pressure loss at the die entrance and exit This approach helps in accurately determining the die's pressure profile by assessing how pressure losses vary with shear rate Understanding the relationship between shear rate and pressure loss is essential for optimizing extrusion processes and ensuring quality production Analyzing the Bagley line extrapolation provides valuable insights into die design and performance in polymer processing.

Calculate the true shear stress τ for the apparent shear rate γ ap of interest using either Formula (9) or Formula (10): τ = ( HB + ) × ( − )

H is the thickness of the slit die, in millimetres;

B is the width of the slit die, in millimetres; p is the test pressure, in pascals; p c is the pressure correction, in pascals;

L is the length of the slit die, in millimetres.

Since the die dimensions H and B are constant, the abscissa distances Lc, which are calculated as (H + B) / (HB), serve as die-length corrections Therefore, instead of using Formula (9), the true shear stress τ corresponding to the apparent shear rate γ̇ap can be determined using Formula (10): τ = 2 (L / (L + p c )) × (H B / HB).

(10) where L c (H + B)/HB is the die-length correction (dimensionless).

8.4.4 Direct determination using slit dies (method B)

To determine the true shear stress (τ) at the die wall, measure the longitudinal pressure gradient (dp/dL) using pressure transducers positioned along the slit die Calculate shear stress using the formula: τ = 2(H B HB +) × (dp/dL), where dp/dL is expressed in pascals per millimeter This method ensures accurate assessment of shear forces within the die, essential for optimizing extrusion processes.

B is the width of the slit die, in millimetres;

H is the thickness of the slit die, in millimetres.

True shear rate

To accurately determine the true shear rate (γ̇) at the capillary-die or slit-die wall, apply the Weissenberg-Rabinowitsch correction method to convert the apparent shear rate Use Formula (12) for method A (refer to section 8.5.2) and Formula (13) for method B (refer to section 8.5.3), ensuring precise rheological analysis of polymer melts and enhance flow characterizations.

The slope of the curve, represented as γ̇_ap = f(τ) in log-log scale, is a critical parameter in shear rate correction It is important to note that the method used to determine this slope—either through fitting a specific function to the log(γ̇_ap) versus log(τ) data or by employing an alternative approach—can introduce significant errors in the corrected true shear rate and, consequently, the true shear viscosity These errors are especially prominent when the curve's slope is large or when the chosen fit does not accurately represent the data, such as at the highest and lowest shear rate points.

3 2 (13) where d dlog log γ  ap τ is as defined in 8.5.2.

Viscosity

Calculate the viscosity as the ratio of the shear stress to the shear rate.

If the ratio is not based solely on true shear stress and shear rate, it will produce one of several apparent viscosities These apparent viscosities are labeled and identified using subscripts, as specified in sections 3.8 to 3.10, ensuring clear differentiation for accurate rheological analysis.

Determination of extrudate swelling

Calculate the extrudate swell ratio at room temperature S a and the percent swell at room temperature s a , using Formulae (14) and (15):

D a is the extrudate diameter, in millimetres, measured at room temperature;

D is the capillary-die diameter, in millimetres, measured at room temperature.

8.7.2 Measurement at the test temperature

Calculate the swell ratio at the test temperature S T and the percent swell at the test temperature s T , using Formulae (16) and (17):

D m is the extrudate diameter, in millimetres, measured at the test temperature;

D T is the capillary-die diameter, in millimetres, measured at the test temperature.

For slit dies, these calculations should utilize the extrudate's thickness or width instead of diameter, and the die's thickness or width in place of the die diameter within Formulas (14) to (17) It is important to consider that swelling may vary between the width and thickness directions, so measurements should ideally be taken in both orientations to ensure accurate assessment.

Two interlaboratory test programmes have been carried out The first interlaboratory test programme was completed in 1990, involving seven laboratories and two materials (PP and PVC).

In the first interlaboratory comparison, two types of apparatus and two measurement procedures were used:

— a rheometer measuring the extrusion pressure at the capillary inlet (four laboratories) and a rheometer measuring the force applied to the piston (two laboratories);

— the shear rates applied during the tests were imposed successively in decreasing order of magnitude (two laboratories) or increasing order (four laboratories).

Repeatability was evaluated by two laboratories, showing significant improvement when pressure is measured at the capillary inlet rather than from piston force The study found that measurement accuracy decreases at low shear rates (100 s−1) When using long dies (L/D > 20), the influence of capillary inlet geometry becomes negligible if the inlet angle is ≥90°, ensuring more consistent flow measurements.

The reproducibility of the viscosity measurement method was evaluated across seven laboratories at different temperatures: PVC at 180 °C and 190 °C, and PP at 210 °C and 240 °C Results showed that reproducibility was less reliable at low shear rates (100 s⁻¹), which had variations of ±10% Factors influencing reproducibility include shear rate and temperature conditions during testing.

— the order in which the various shear rates are examined during a single test;

The sensitivity of pressure and force sensors varies depending on shear rate conditions Measurements at high pressures and high shear rates often lack the same precision as those at low pressures and low shear rates when using the same sensor Therefore, selecting sensors optimized for specific pressure ranges is essential for obtaining accurate and reliable results across different operational conditions.

— the method used to determine the shear stress: measurement of pressure at the capillary inlet is preferred since it is more accurate.

The effect of the cleanliness of the capillary on the results was not investigated in these tests.

In the second interlaboratory test programme completed in 1996, a total of 20 laboratories participated, evaluating polyethylene (PE) and glass-fibre-filled polypropylene (GFPP) samples The study provided detailed precision data on key measurements such as extrusion pressure, entrance pressure drop, and shear viscosity, with corrections for entrance effects and non-Newtonian velocity profiles, ensuring accuracy and consistency across different testing environments.

`,`,`,,,`,``,`,,,,,,``,,````,-`-`,,`,,`,`,,` - determined Values presented are for 95 % confidence levels, these values having been determined using a factor of 2,8 times the calculated standard deviation values.

NOTE 1 The contraction ratio is defined as the ratio of the barrel diameter to the die diameter.

NOTE 2 The standard deviations and repeatability and reproducibility limits (95 % confidence values) were determined in accordance with Reference [7].

NOTE 3 See also Annexes A to C.

Table 4 — Precision data for extrusion rheometry

Material Polyethylene Glass-fibre-filled polypropylene

Shear viscosity measurement [corrected for entrance pressure drop and non-Newtonian velocity profile (Weissenberg-Rabinowitsch correction)]

Material Polyethylene Polyethylene Glass-fibre-filled polypropylene

General

The test report must reference the relevant International Standard and any applicable referring standards, include the information specified in clauses 10.2, 10.3, and 10.4 as applicable, and clearly state the date when the test was conducted.

Test conditions

This article describes the test material, including its properties and composition Prior to testing, samples were conditioned through drying and compounding to ensure consistency The testing methodology employed is specified as either A1, A2, B1, or B2, depending on the procedure The rheometer used for measurements is detailed, including its model and barrel diameter (D_b) Key dimensions of the capillary die are provided, such as diameter D, length L, and the L/D ratio, along with the measurement precision Additionally, for slit dies, the thickness (H), width (B), and length (L) are reported, including their measurement accuracy to ensure reliable results.

This article outlines key parameters for extrusion testing, including a detailed description of the capillary-die or slit-die inlet angle profile, and the technique used to measure extrudate swelling It specifies the temperature at which the measurements are conducted, along with the pressure conditions below the die exit when extruding under non-atmospheric pressures, including methods used for pressure measurement and their accuracy Additionally, the article covers sample preheating time, dwell time, and the specific dwell time at which material alterations are observed, if applicable It emphasizes the maximum permissible test duration, outlines the extrusion time, and mandates reporting any deviations from the standard or incidents that may have impacted the test results, ensuring comprehensive documentation for accurate analysis.

Flow characteristics

Report whether the shear rate, the shear stress, and the viscosity are “apparent” or “true” values.

Report the method of viscosity determination if the Bagley or pressure drop versus distance plots are nonlinear.

For plastics which are not wall-adhering, present the results in the form of apparent shear stress plotted as a function of flow rate Q, or vice versa.

The following plots can be included, as necessary:

— log shear stress versus log shear rate, or vice versa;

— log viscosity versus log shear stress or log shear rate;

— log viscosity versus the reciprocal of absolute temperature at constant shear stress or shear rate;

— log viscosity versus temperature in °C at constant shear stress or shear rate;

— log critical shear stress or log critical shear rate for each of the observed effects (see 3.19 and 3.20) versus the reciprocal of absolute temperature;

— log critical shear stress or log critical shear rate for each of the observed effects (see 3.19 and 3.20) versus temperature in °C;

— log volume flow rate versus log shear stress, or vice versa;

— pressure versus distance of pressure transducer from die exit (slit dies);

— log pressure correction versus log shear stress or log shear rate or log volume flow rate;

— swell ratio at room temperature or at the test temperature versus shear rate or volume flow rate;

This article discusses the relationship between percent swell at room temperature or test temperature and shear rate or volume flow rate It also highlights the importance of presenting both apparent and true values of shear rate, shear stress, and viscosity to ensure accurate characterization of the material's flow properties Understanding these parameters is essential for optimizing processing conditions and ensuring material performance.

These can be given for a given series of test conditions, as necessary:

— shear rate, in reciprocal seconds;

— swell ratio at room temperature;

— percent swell at room temperature;

— swell ratio at the test temperature;

— percent swell at the test temperature.

Apparent and/or true values of shear rate, shear stress, and viscosity can also be presented.

Visual examination

When conducting a visual examination of extrudate, it is essential to report any surface changes such as flow breaks or distortions, along with the specific test conditions under which these changes occur Noting these observations helps in assessing extrudate quality and process consistency, ensuring optimal manufacturing performance.

Such changes can correspond to the critical shear stresses In this case, note the values individually in the test report as “visual” critical shear stresses.

In addition, if the material changes colour, report the corresponding dwell time.

Method of correcting for the influence of H / B on the apparent shear rate

Formula (4) from section 8.2.3 is valid only for an infinitely wide slit to determine the apparent shear rate It estimates the shear rate based on a volume flow rate Q over a length B in the die, assuming no flow in the width or thickness directions For finite H/B ratios, Formula (4) remains a good approximation, as demonstrated in Figure A.1, which compares apparent shear rates derived from Formula (4) and the corrected Formula (A.1) (Reference [5]) at identical flow rates.

( ) π (A.1) where n is an odd integer.

Y shear rate ratio γ ap /y ap c

Dividing Formula (4) by Formula (A.1) gives Formula (A.2):

 (A.2) which expresses the ratio of the apparent shear rates as a function of the thickness-to-width ratio H/B.

The summation term in Formula (A.2) is 1,004 4 when H/B ≤ 0,3 Thus the corrected apparent wall shear rate is given (using Formula 4) by

The error introduced by using Formula (4) instead of Formula (A.3) is less than 3 % for thickness-to- width ratios less than 0,1.

B.1 Error due to piston friction

Friction arises from contact between the piston and the barrel, but its impact is typically negligible compared to the pressure drop across the capillary or slit die To ensure this, it is important to conduct a dry run at the test temperature and confirm that the frictional force does not significantly affect the process, thereby validating the assumption of negligible friction.

This precaution can be disregarded if measurements are made at constant velocity, and pressure is measured using a pressure sensor placed in the immediate vicinity of the die inlet.

B.2 Error due to back-flow of material

The clearance between the piston head and barrel can cause some sample to flow back past the piston, resulting in a measured shear rate that is lower than the actual value Typically, this back-flow error is negligible, but it may require correction when the piston operates at low speed under a substantial load To account for this, the material that flows back past the piston is collected and weighed, then compared to the extrudate produced during the same period to determine the percentage of error caused by back-flow.

B.3 Error due to melt compressibility

Certain liquids demonstrate high compressibility, which impacts flow behavior during processing Since the shear rate at the die wall is determined based on piston movement speed, variations in hydrostatic pressure lead to errors in shear rate calculation As the liquid's density decreases along the die length, its flow velocity increases, causing shear rates to rise toward the die exit Understanding these effects is crucial for optimizing extrusion processes involving highly compressible fluids.

B.4 Error due to non-zero liquid velocity at the die wall

Flow calculations within the die assume zero velocity at the die wall; however, for high-viscosity polymer melts, slip might occur between the polymer and the die surface, affecting flow behavior and processing outcomes.

Uncertainties in the determination of shear viscosity by capillary extrusion rheometry testing

The combined uncertainty \( u_c(y) \) of the measurand \( y \) can be calculated based on the partial derivatives of the function \( y = f(x_i) \) and the uncertainties \( u(x_i) \) associated with each parameter \( x_i \) Assuming that the individual sources of uncertainty are uncorrelated, the total uncertainty \( u_c(y) \) is obtained by applying the root sum squares method, which involves summing the squares of the partial derivatives weighted by their respective uncertainties and then taking the square root of this sum.

(C.1) where c i is the sensitivity coefficient (partial derivative) associated with the quantity x i ; u(x i ) is the uncertainty in that quantity.

The combined uncertainty u c (y) corresponds to one standard deviation and therefore has an associated confidence level of approximately 68 % Assuming a normal distribution, then an expanded uncertainty

A U value, corresponding to a 95% confidence level, can be calculated by applying a coverage factor of 2, which is twice the combined uncertainty The relative uncertainty is defined as the ratio of the measurement's uncertainty to the actual parameter value, providing a normalized measure of the uncertainty's impact on the result.

To determine the uncertainties, an expression relating the shear viscosity to the measurement parameters shall first be derived From Formulae (3), (7), and (12), 3.7, and the formulae:

4 (C.5) the shear viscosity corrected for entrance pressure drop and non-Newtonian velocity profile (Weissenberg-Rabinowitsch correction) is given by: η =( ) ×    × − ( )

ap γ is the apparent shear rate;

Q is the volume flow rate;

D b is the barrel diameter; v is the piston speed; p is the extrusion pressure; p c is the entrance pressure drop correction;

D is the capillary-die diameter;

L is the capillary-die length.

Thus, using Formulae (C.1), (C.2), and (C.6), it can be shown that the combined uncertainty in the measurement of shear viscosity u c (η) is given by: c b u u D

 (C.7) and the combined uncertainty in the shear rate u c ( ) γ by: u c u D

Relative uncertainty is defined as the ratio of the absolute uncertainty in a measurement to the measured value itself, such as u(D)/D for the parameter D This measure provides a clear understanding of the precision of a measurement, indicating the degree of uncertainty relative to the actual value Understanding and calculating relative uncertainty is essential in scientific and engineering contexts to assess the reliability of measurement data.

The effects of the temperature dependence of viscosity and degradation can be incorporated into

Formula (C.7) as additional terms, thus: c b u u D

The article discusses the relative uncertainties affecting measurements, focusing on two main factors: degradation and temperature dependence The total uncertainty is given by the equation (C.9): + ( ) + ( )f d 2 f θ 2, where f(d) represents the relative uncertainty resulting from material degradation, and f(θ) accounts for the combined effects of temperature-dependent viscosity variations and measurement errors in test temperature Specifically, f(θ) can be expressed as a function of the viscosity, ηu(θ), and temperature variations, highlighting the significance of accurately assessing temperature effects to ensure precise measurements.

Formula (C.9) is essential for accurately estimating the uncertainty in shear viscosity measurements by considering the uncertainties and magnitudes of each contributing term These formulas, (C.7) and (C.9), provide corrected shear viscosity values that account for entrance effects and non-Newtonian velocity profiles, following the Weissenberg-Rabinowitsch method, ensuring more precise and reliable rheological data.

Formula (C.8) describes the true shear rates, while equivalent expressions for apparent shear viscosity and apparent shear rate can be derived by replacing the true shear viscosity η with the apparent shear viscosity ηₐₚ and substituting the true shear rate γ̇ with the apparent shear rate γ̇ₐₚ, effectively setting the terms involving n and u(n) to zero.

An expression for apparent shear viscosity, uncorrected for entrance effects, can be derived by removing the terms u(p_c) and p_c from Formula (C.7), effectively setting both u(p_c) and p_c to zero.

Uncertainty values for various components in shear viscosity measurement have been calculated and detailed in Table C.1, following the tolerance values and assumptions outlined in this International Standard To maintain clarity and simplicity in the uncertainty analysis, measurements were conducted using two types of dies, including a long die, ensuring accurate and reliable shear viscosity results.

20 mm length and a short die of negligible length that is used to determine the entrance pressure drop.

For a comprehensive uncertainty analysis of a specific instrument, it is recommended to use calibration data to accurately determine the actual quantity ranges Assuming normal probability distributions for these ranges is preferable, as it provides a more realistic representation of measurement uncertainty compared to rectangular distributions Incorporating calibration data and suitable probability models enhances the precision and reliability of the uncertainty assessment.

Table C.1 — Uncertainty terms and estimates for shear viscosity measurement

Quantity, symbol, and units Type a Probability distribution b Divisor c Quantity value, x Quantity range d

Pressure measurement p , Pa B R √3 variable ±1 % of range — 0,005 8 f

Gradient of log τ versus log γ ap plot, n A N 1 0,4 0,03 h 0,03 0,075

Tiêu đề	Plastics — Determination of the Fluidity of Plastics Using Capillary and Slit-die Rheometers
Trường học	International Organization for Standardization
Chuyên ngành	Plastics
Thể loại	international standard
Năm xuất bản	2014
Thành phố	Geneva

Định dạng
Số trang	42
Dung lượng	825,92 KB