Testing of Polymers: Mechanical, Electrical, Thermal, Optical and Melt Flow

This chapter answers Section XE5.8 of XE5 Polymer Science and Engineering, one of the nine optional sections of the Engineering Sciences (XE) paper, any two of which a candidate chooses in the exam. The syllabus text is: “Mechanical-static and dynamic, tensile, flexural, compressive, abrasion, endurance, fatigue, hardness, tear, resilience, impact, toughness; Conductivity-thermal and electrical, dielectric constant, dissipation factor, power factor, electric resistance, surface resistivity, volume resistivity, swelling, ageing resistance, environmental stress cracking resistance, limiting oxygen index; Heat deflection temperature – Vicat softening temperature, ductile to brittle transition, glass transition temperature, coefficient of thermal expansion, shrinkage, flammability, … Optical Properties - Refractive Index, Luminous Transmittance and Haze, Melt flow index.” It teaches what each test measures, its definition and units, and how the results are used. The numericals are flexural stress, volume resistivity, limiting oxygen index and melt flow index.

1. Static mechanical tests: tensile, flexural, compressive, toughness

In the tensile test (ASTM D638, ISO 527) a dumbbell specimen is pulled at constant crosshead speed. Engineering stress σ = F/A₀ (MPa) and strain ε = ΔL/L₀ are plotted. The curve gives modulus (initial slope), yield stress, tensile strength (maximum stress) and elongation at break. Polymers are viscoelastic, so the numbers depend on the testing speed and temperature: a faster pull or lower temperature raises modulus and strength and lowers elongation, and a ductile polymer can turn brittle. Toughness is the energy absorbed to break per unit volume, the area under the stress–strain curve (J/m³ = Pa·(m/m)); a strong but brittle polymer has high strength and low toughness.

The flexural test (ASTM D790, ISO 178) loads a rectangular bar as a beam on two supports, usually at the centre (three-point bending). For span L, width b, thickness d and central load F, the maximum (outer-fibre) flexural stress is σ_f = 3FL / (2bd²). It suits rigid, brittle materials that are hard to grip, and the flexural modulus is found from the load–deflection slope. The compressive test (ASTM D695) crushes a block or cylinder between plates; compressive strength is the maximum load per original area, and for ductile polymers a yield rather than a fracture is recorded. Compressive strength of brittle polymers exceeds their tensile strength.

⚠️ Worked example: flexural stress
A bar 10 mm wide and 4 mm thick on a 80 mm span breaks at a central load of 100 N. σ_f = 3 × 100 × 80 / (2 × 10 × 4²) = 24 000 / 320 = 75 MPa. Use consistent units (N and mm give MPa). Using the thickness instead of its square, or the span as 40 mm, are the usual slips.

2. Dynamic, fatigue, hardness, tear, resilience, impact and abrasion

Dynamic mechanical analysis (DMA) applies a small sinusoidal strain and reports the storage modulus E′ (elastic, stored energy), the loss modulus E″ (viscous, dissipated energy) and tan δ = E″/E′; a peak of tan δ or a fall of E′ marks the glass transition, and tan δ measures damping. Fatigue is failure under repeated cyclic stress: the S–N curve plots stress amplitude against cycles to failure, and the endurance limit is the stress below which the material survives a very large number of cycles; many polymers show no sharp limit, and heating from hysteresis can itself cause failure. Rubber flex-fatigue is tested by repeated flexing until cracks grow (De Mattia type tests).

Hardness is resistance to indentation. The Shore durometer reads a spring-loaded indentor depth on a 0 to 100 scale: Shore A (blunt truncated-cone indentor) for flexible rubbers and soft plastics, Shore D (sharper cone) for harder plastics. IRHD (International Rubber Hardness Degrees) measures a small ball indentation in rubber on a similar 0 to 100 scale. Tear strength is the force needed to propagate a cut, divided by specimen thickness (N/mm or kN/m), using trouser, angle or crescent specimens. Rebound resilience is the percentage of the energy returned when a pendulum or ball strikes and rebounds from rubber; a high-hysteresis rubber has low resilience and a high tan δ. Abrasion resistance is measured as volume loss (DIN abrasion, in mm³) or weight loss per cycle (Taber) against an abrasive.

Impact tests measure the energy absorbed by a notched bar struck by a swinging pendulum. In Izod (ASTM D256) the bar is clamped vertically as a cantilever and struck above the notch; the result is energy per unit notch width (J/m). In Charpy (ISO 179) the bar lies horizontally on two supports and is struck at the centre, opposite the notch; the result is often energy per unit cross-section at the notch (kJ/m²). The notch concentrates stress, so a notch-sensitive polymer (polystyrene, PVC) shows a far lower notched than unnotched value, whereas a tough polymer does not break.

3. Electrical and thermal conduction properties

The dielectric constant (relative permittivity) is ε_r = C/C₀, the capacitance of a capacitor with the polymer between the electrodes divided by that with vacuum (or air). Non-polar polymers such as polyethylene (about 2.3) and PTFE (about 2.1) have low values; polar polymers such as PVC have higher ones. Under an alternating field a polymer stores part of the energy and dissipates part as heat. With loss angle δ (the angle by which the current falls short of exactly 90° ahead of the voltage), the dissipation factor is tan δ = ε″/ε′. The power factor is cos θ = sin δ, where θ is the phase angle between voltage and current; for the small losses of good insulators, power factor ≈ dissipation factor. A low tan δ is needed for high-frequency insulation, and a high tan δ lets polar plastics be heated by dielectric (radio-frequency) welding.

Electrical resistance R of a specimen between electrodes depends on its geometry, so standard tests report resistivities. Volume resistivity is ρ_v = R_v × A / t (A electrode area, t thickness; Ω·m or Ω·cm), the resistance of a unit cube through the bulk. Surface resistivity is the resistance between two parallel electrodes of length P (perimeter) a distance g apart along the surface, ρ_s = R_s × P/g, with unit ohm (Ω per square). Insulating polymers have very high values; antistatic grades are reduced by conductive fillers or additives, and a high surface resistivity lets static charge accumulate. Moisture and contamination lower surface resistivity far more than volume resistivity.

Thermal conductivity k (W/m·K) is the heat flow per unit area per unit temperature gradient, measured by a guarded hot plate or heat-flow meter; unfilled polymers are poor conductors (about 0.1 to 0.5 W/m·K), which makes them good insulators and slows cooling in moulding. Fillers such as metal or carbon raise it.

🧠 Worked example: volume resistivity
A 1.5 mm thick sheet gives R_v = 3.0 × 10¹² Ω with an effective electrode area of 25 cm². ρ_v = R_v A / t = 3.0 × 10¹² × 25 cm² / 0.15 cm = 5.0 × 10¹⁴ Ω·cm = 5.0 × 10¹² Ω·m. Converting Ω·cm to Ω·m divides by 100.

4. Thermal tests: HDT, Vicat, brittleness, Tg, expansion and shrinkage

Heat deflection temperature (HDT, ASTM D648, ISO 75) is the temperature at which a bar loaded in three-point bending under a fixed outer-fibre stress (commonly 0.455 or 1.82 MPa) deflects by a specified amount while heated at a constant rate (in the ASTM method 2 °C/min and 0.25 mm deflection). Vicat softening temperature (ASTM D1525, ISO 306) is the temperature at which a flat-ended needle of 1 mm² cross-section, under a load of 10 N (method A) or 50 N (method B), penetrates 1 mm into the specimen while heated at 50 or 120 °C/h. Both are comparative index temperatures, not true transitions or safe service limits: HDT depends on the stress used, and amorphous polymers reach HDT near Tg whereas semicrystalline ones lie between Tg and Tm and are raised greatly by glass-fibre filling.

The ductile-to-brittle transition is the temperature range below which the failure mode in impact changes from ductile (yielding, high energy) to brittle (low energy); it is found by impact tests across temperature, and the brittleness temperature is where half the specimens fail under a standard impact. The glass transition temperature Tg is found from a step in the heat capacity (DSC), a peak of tan δ or fall of E′ (DMA), or a change of slope of the expansion curve (TMA). The coefficient of linear thermal expansion is α = ΔL / (L₀ ΔT) (K⁻¹, often in ppm/K); for polymers it is several times that of metals, and a jump in α marks Tg. Mould shrinkage is (mould dimension − part dimension) / mould dimension × 100%, measured after conditioning; semicrystalline polymers shrink more than amorphous ones because crystallisation raises the density, and fillers and orientation make shrinkage anisotropic.

Which test measures what
TestMeasuresUnit
TensileStrength, modulus, elongation at breakMPa, GPa, %
Izod / CharpyNotched impact energyJ/m or kJ/m²
HDT / VicatIndex temperature for load deflection or 1 mm penetration°C
Shore A / D, IRHDIndentation hardness0 to 100
Dielectric constant, tan δCharge storage; lossdimensionless
Surface / volume resistivityResistance per square; bulk resistance of a unit cubeΩ; Ω·m

5. Swelling, ageing, ESCR, flammability and optical tests

Swelling tests immerse a specimen (usually crosslinked rubber) in a liquid and report the % gain in mass or volume, or the equilibrium swelling ratio Q = swollen volume / dry volume. Swelling is limited by crosslinks, so higher crosslink density gives less swelling (the Flory–Rehner relation), and a solvent of similar solubility parameter swells most. Ageing resistance is tested by exposing specimens to heat (oven ageing), ozone, light or weather and reporting the % retention of a property such as tensile strength or elongation; heat ageing is accelerated on the assumption of Arrhenius behaviour. Environmental stress cracking is brittle cracking of a stressed polymer in contact with a liquid that does not dissolve it; in the bent-strip test (ASTM D1693) notched polyethylene strips are bent and immersed in a surfactant and the time for half of them to crack is recorded. ESCR is higher for higher molecular weight and lower crystallinity, which give more tie molecules.

Flammability. The limiting oxygen index (LOI) is the minimum concentration of oxygen, as volume % of an O₂/N₂ mixture, that just supports flaming combustion of a vertically held specimen: LOI = 100 × [O₂] / ([O₂] + [N₂]). Air has about 21% oxygen, so a polymer with LOI clearly above 21 does not keep burning in air after the ignition source is removed, and a lower LOI means more flammable (polyethylene about 17 to 18, rigid PVC about 45, PTFE about 95). The UL 94 tests classify plastics as HB (slow horizontal burning) or V-0, V-1, V-2 in the vertical test, V-0 being the best (self-extinguishing within 10 s of each flame application without flaming drips that ignite cotton).

Optical properties. The refractive index n = c/v = sin i / sin r is measured with an Abbe refractometer (PMMA about 1.49, polystyrene about 1.59). Luminous transmittance is the percentage of incident luminous flux that passes through the specimen. Haze is the percentage of the transmitted light that is scattered by more than 2.5° from the incident beam (ASTM D1003); it makes a clear object look cloudy. Transmittance and haze are independent: a frosted glazing can have high transmittance and high haze, and crystalline spherulites or filler particles whose refractive index differs from that of the matrix raise haze.

🧠 Worked example: LOI
A specimen just burns when the flows are 2.8 L/min of O₂ and 7.7 L/min of N₂. LOI = 100 × 2.8 / (2.8 + 7.7) = 100 × 2.8 / 10.5 = 26.7%. Flows of gases at the same temperature and pressure are proportional to volumes, so flow fractions equal volume fractions. Using the O₂/N₂ ratio (36%) instead of the fraction is the usual slip.

6. Melt flow index

The melt flow index (MFI, melt flow rate, ASTM D1238, ISO 1133) is the mass of polymer in grams extruded in 10 minutes through a standard die (2.095 mm diameter, 8 mm long) by a piston carrying a specified dead load at a specified temperature; the unit is g/10 min. The conditions must always be quoted, for example 190 °C / 2.16 kg for polyethylene and 230 °C / 2.16 kg for polypropylene. A melt volume rate (MVR, cm³/10 min) uses the volume instead, and melt density = MFR / MVR. Since the extrudate is cut at intervals and weighed, MFI = 600 × (mass of cut in g) / (cut interval in s).

Interpretation. MFI is inversely related to melt viscosity at the low shear stress of the test, hence inversely related to molecular weight: for entangled melts the zero-shear viscosity rises roughly as M_w^3.4, so a small rise in molecular weight lowers MFI sharply. Low MFI (long chains, high viscosity, high melt strength) suits blow moulding, film and pipe extrusion; high MFI (short chains, easy flow) suits injection moulding of thin or long flow-path parts. MFI is a single-point, low-shear quality-control number: it does not reveal molecular-weight distribution, and two grades of equal MFI can process differently. The flow rate ratio (MFI at a heavier load, such as 21.6 kg, divided by MFI at 2.16 kg) indicates how shear-thinning, that is how broad the distribution is. Different loads or temperatures give different values, so MFI of different polymers cannot be compared directly.

⚠️ Worked example: MFI from cut-offs
Extrudate cuts taken every 30 s weigh 0.42 g on average at the stated condition. MFI = 0.42 g × (600 s / 30 s) = 8.4 g/10 min. The multiplier is 600/30 = 20, not 10 or 30.

Key takeaways

  • Tensile gives strength, modulus and elongation and depends on speed and temperature; toughness is the area under the stress-strain curve; flexural stress is 3FL/(2bd²).
  • Izod is a vertical notched cantilever (J/m), Charpy a horizontal beam (often kJ/m²); Shore A is for soft rubbers and Shore D for hard plastics; IRHD is for rubber.
  • Dielectric constant is C/C₀, dissipation factor is tan δ, power factor is cos θ = sin δ; volume resistivity is R·A/t and surface resistivity is R·P/g in ohm per square.
  • HDT and Vicat are comparative index temperatures; Tg comes from DSC, DMA or TMA; α = ΔL/(L₀ΔT); shrinkage is relative to the mould size.
  • LOI = 100[O₂]/([O₂]+[N₂]) and a value above 21 means no self-sustained burning in air; ESCR is the time to crack in a stress-and-liquid test; haze is scatter beyond 2.5°.
  • MFI is grams per 10 min at stated load and temperature, falls as molecular weight rises, and is one low-shear point that cannot show the distribution.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. A semicrystalline polymer is tensile tested at the same temperature at a crosshead speed ten times higher than before. The usual result is

    1. lower modulus and lower yield stress, with greater elongation at break, as the chains flow more easily
    2. higher modulus and yield stress, with lower elongation at break, because of viscoelastic response
    3. unchanged properties, since stress depends only on the applied force and the area
    4. lower modulus but higher yield stress, since polymers soften when loaded quickly
    Show answer

    Answer: B — higher modulus and yield stress, with lower elongation at break, because of viscoelastic response

    Polymers are viscoelastic: chains have less time to rearrange at higher strain rate, so the material behaves stiffer, stronger and less extensible. Metals at room temperature show a much smaller rate effect, and fast loading does not soften polymers.

  2. In the Izod impact test the specimen is

    1. a flat disc that is dropped onto a hard surface from a fixed height
    2. a horizontal beam lying on two supports and struck at its centre opposite the notch
    3. a notched bar clamped as a vertical cantilever and struck above the notch
    4. an unnotched dumbbell specimen that is pulled slowly until failure occurs
    Show answer

    Answer: C — a notched bar clamped as a vertical cantilever and struck above the notch

    Izod uses a notched cantilever struck above the notch. The horizontal beam struck opposite the notch is Charpy; a slow pull is a tensile test; a dropped disc is a falling-weight type test.

  3. Shore A and Shore D durometers differ in that

    1. Shore A uses a blunt indentor for soft rubbers; Shore D a sharper one for hard plastics
    2. Shore A measures the abrasion loss of rubber, while Shore D measures tear strength
    3. Shore A is meant for rigid plastics only and Shore D for soft rubbers only
    4. Shore A reads energy in joules and Shore D reads force in newtons
    Show answer

    Answer: A — Shore A uses a blunt indentor for soft rubbers; Shore D a sharper one for hard plastics

    Both read indentation depth on a 0 to 100 scale; type A (blunt indentor) is for soft materials and type D (sharper) for hard ones. Neither measures abrasion or tear, and neither reads in joules or newtons.

  4. A polymer film has a dissipation factor tan δ = 0.40 at the test frequency. Its power factor (cos θ, with θ the phase angle between voltage and current) is closest to

    1. 0.37, because power factor = sin δ
    2. 0.92, because power factor is taken as cos δ at the same loss angle
    3. 2.50, because power factor is the reciprocal of the dissipation factor
    4. 0.40, because power factor always equals the dissipation factor exactly
    Show answer

    Answer: A — 0.37, because power factor = sin δ

    Power factor = cos θ = sin δ, and sin δ = tan δ / √(1 + tan²δ) = 0.40 / √1.16 = 0.371. The two factors are equal only when losses are small (tan δ ≲ 0.1); at 0.40 they differ visibly. A power factor cannot exceed 1.

  5. The heat deflection temperature of a polymer reported at 1.82 MPa is usually

    1. higher than the value at 0.455 MPa for the same polymer, since a heavier load helps stiffen it
    2. independent of the load, since it is a fundamental material constant
    3. lower than at 0.455 MPa, since a higher stress gives the set deflection at a lower temperature
    4. always equal to the glass transition temperature measured by DSC
    Show answer

    Answer: C — lower than at 0.455 MPa, since a higher stress gives the set deflection at a lower temperature

    HDT is an index temperature that depends on the stress: the same deflection occurs at a lower temperature when the load is higher. It is not a material constant and equals Tg neither exactly nor in general.

  6. A polymer rod 250 mm long has a linear expansion coefficient of 1.0 × 10⁻⁴ K⁻¹. When it is heated by 40 K and is free to expand, its length increases by about

    1. 0.10 mm
    2. 1.0 mm
    3. 10 mm
    4. 0.25 mm
    Show answer

    Answer: B — 1.0 mm

    ΔL = α L₀ ΔT = 1.0 × 10⁻⁴ × 250 mm × 40 = 1.0 mm. The other values come from a misplaced decimal or from dropping one factor.

  7. Which polymer is least likely to sustain burning in air after the ignition source is removed, based on its limiting oxygen index?

    1. a polymer with LOI of 17%
    2. a polymer with LOI of 19%
    3. a polymer with LOI of 21%
    4. a polymer with LOI of 45%
    Show answer

    Answer: D — a polymer with LOI of 45%

    Air contains about 21% oxygen; a polymer needing 45% oxygen to burn cannot sustain flame in air, whereas LOI of 17% or 19% is below the oxygen level of air, so those burn readily. An LOI of 21% sits at the margin.

  8. Two polyethylene grades are tested at 190 °C and 2.16 kg: grade X has MFI 0.4 g/10 min and grade Y has MFI 22 g/10 min. Which conclusion is best supported?

    1. X has the lower melt viscosity at the test stress, and is the better injection moulding grade
    2. X and Y must have the same molecular weight, only different densities
    3. Y has the higher average molecular weight, since more polymer flows out in 10 min
    4. X has the higher molecular weight and viscosity, and suits blow moulding or film more than Y
    Show answer

    Answer: D — X has the higher molecular weight and viscosity, and suits blow moulding or film more than Y

    MFI is inversely related to viscosity and molecular weight, so low-MFI X has longer chains and higher viscosity and melt strength (blow moulding, film), while high-MFI Y flows easily for injection moulding. MFI alone cannot show density or distribution.

  9. Select ALL correct statements about mechanical tests of polymers.

    1. Toughness in a tensile test is the area under the stress-strain curve
    2. The three-point flexural stress is σ = 3FL/(2bd²)
    3. DMA reports storage modulus, loss modulus and tan δ
    4. Rebound resilience of rubber is the energy absorbed in the impact, as a percentage
    Show answer

    Answer: A — Toughness in a tensile test is the area under the stress-strain curve; B — The three-point flexural stress is σ = 3FL/(2bd²); C — DMA reports storage modulus, loss modulus and tan δ

    Toughness, the flexural stress formula and the DMA outputs are right. Resilience is the percentage of energy returned on rebound, not absorbed.

  10. Select ALL correct statements about electrical testing of polymers.

    1. Dielectric constant is the ratio of capacitance with the polymer to that with vacuum
    2. Surface resistivity is expressed in ohm (per square)
    3. Volume resistivity R·A/t has units of ohm-metre
    4. A high dissipation factor is desirable for a high-frequency insulator
    Show answer

    Answer: A — Dielectric constant is the ratio of capacitance with the polymer to that with vacuum; B — Surface resistivity is expressed in ohm (per square); C — Volume resistivity R·A/t has units of ohm-metre

    The first three are the standard definitions and units. A high dissipation factor means large heat loss, which is undesirable in an insulator.

  11. Select ALL correct statements about thermal tests.

    1. Vicat softening temperature is where a 1 mm² flat needle penetrates 1 mm under a specified load
    2. Tg can be found from a step in heat capacity in DSC
    3. Mould shrinkage is expressed relative to the mould dimension
    4. Semicrystalline polymers normally shrink less than amorphous ones
    Show answer

    Answer: A — Vicat softening temperature is where a 1 mm² flat needle penetrates 1 mm under a specified load; B — Tg can be found from a step in heat capacity in DSC; C — Mould shrinkage is expressed relative to the mould dimension

    Vicat, DSC Tg and the shrinkage definition are right. Crystallisation densifies the polymer, so semicrystalline grades usually shrink more.

  12. Select ALL correct statements about swelling, ESCR, haze and melt flow index.

    1. Higher crosslink density reduces the equilibrium swelling of a rubber in a good solvent
    2. Haze is the percentage of transmitted light scattered by more than 2.5° from the beam
    3. MFI is expressed in grams per 10 minutes at a stated load and temperature
    4. ESCR is usually higher for polyethylene of lower molecular weight
    Show answer

    Answer: A — Higher crosslink density reduces the equilibrium swelling of a rubber in a good solvent; B — Haze is the percentage of transmitted light scattered by more than 2.5° from the beam; C — MFI is expressed in grams per 10 minutes at a stated load and temperature

    Crosslinks limit swelling; haze and MFI are defined as stated. ESCR improves with higher molecular weight, which gives more tie molecules, not lower.

  13. A rectangular polymer bar, 12 mm wide and 3 mm thick, is broken in three-point bending on a 64 mm span at a central load of 180 N. Using σ = 3FL/(2bd²), the flexural stress at break is ____ MPa (integer).

    Numerical answer — type the value.

    Show answer

    Answer: 160

    σ = 3 × 180 × 64 / (2 × 12 × 3²) = 34 560 / 216 = 160 MPa (N and mm give MPa).

  14. A 2.0 mm thick polymer sheet shows a volume resistance of 2.4 × 10¹³ Ω between electrodes of effective area 30 cm². Using ρ_v = R·A/t, the volume resistivity is ____ × 10¹³ Ω·m (one decimal place).

    Numerical answer — type the value.

    Show answer

    Answer: 3.6

    ρ_v = 2.4 × 10¹³ Ω × 30 cm² / 0.20 cm = 3.6 × 10¹⁵ Ω·cm. Dividing by 100 gives 3.6 × 10¹³ Ω·m. Forgetting the unit conversion would give 3.6 × 10¹⁵.

  15. In a limiting oxygen index test the specimen just sustains burning at gas flows of 3.6 L/min oxygen and 10.4 L/min nitrogen, both at the same temperature and pressure. The LOI is ____ % (one decimal place).

    Numerical answer — type the value.

    Show answer

    Answer: 25.7

    LOI = 100 × 3.6 / (3.6 + 10.4) = 100 × 3.6 / 14.0 = 25.7%. Taking the O₂/N₂ ratio (34.6%) is the slip. Since LOI > 21%, it should not burn in air after removal of the flame.

  16. In a melt flow test at the stated standard conditions, extrudate cut-offs taken every 15 s have an average mass of 0.27 g. The melt flow index is ____ g/10 min (one decimal place).

    Numerical answer — type the value.

    Show answer

    Answer: 10.8

    MFI = mass × (600 s / cut interval) = 0.27 g × (600 / 15) = 0.27 × 40 = 10.8 g/10 min.