Strength · how to calculate and test it

Plastic core strength: pressure, creep and temperature

ROLL Lab · updated 24 October 2026 · sources at the bottom of the page

The pressure the roll puts on the core

Every wrap wound under tension squeezes the ones below. The core collects the sum: an almost uniform radial pressure that, in the literature, ranges from about 5 bar to over 100 bar. It depends on the type and thickness of the material, winding tension, lay-on roller, number of wraps, environment and time.

The simplest elastic model gives an upper bound: P ≈ σ × ln(R/r), where σ is the tension stress in the wound material, R the roll radius and r the outside radius of the core. In reality the wraps are not rigid and the pressure grows less; with stretch films, shrinkage after winding also matters a lot. According to data published by a core manufacturer, with cast film core failure usually happens within 72 hours, with blown film between 7 and 14 days: the pressure keeps building after winding while the film settles.

Plastic and cardboard under load: two different curves

Crushed between two plates, the two cores tell different stories:

• Cardboard: the force rises, reaches a peak and collapses when the plies give way. ISO 11093-9 measures exactly that peak, on a 100 mm specimen, at 50–65 mm/min.
• Plastic: the force rises continuously, with no clear peak. The core goes oval and keeps carrying load. That is why the force is measured at a given deflection: 3% of the diameter, as in ISO 9969 for the ring stiffness of thermoplastic pipes, at 2 mm/min up to Ø 100 and 5 mm/min up to Ø 200.

Fiaptech technical documentation (a company with corporate ties to ROLL) uses exactly this criterion. At the same size it reports a 3% strength for plastic cores of 1.01 to 1.58 times that of cardboard, and a maximum load of 2.22 to 3.5 times. Two caveats: paper and plastic are tested at different speeds, so the comparison is indicative; and these are tests lasting a few minutes, which do not show creep.

The two wall checks

1. Material crushing (Lamé)

A thick-walled tube under external pressure has its maximum stress at the inner surface. The pressure that takes the stress to the material’s limit is approximately:

p = σ_all × (r_o² − r_i²) ÷ (2 × r_o²)

where r_o and r_i are the outside and inside radii and σ_all is the allowable stress of the polymer, reduced for time and temperature.

2. Wall buckling

A thin ring under external pressure can collapse by buckling long before it yields. The critical pressure of a long tube is approximately:

p_cr = 2 × E ÷ (1 − ν²) × (t ÷ D_m)³

where E is the polymer modulus, ν Poisson’s ratio, t the wall and D_m the mean diameter. The cube explains two practical facts: doubling the wall multiplies the critical pressure by eight; doubling the diameter for the same wall divides it by eight. That is why a 6" core needs much thicker walls than a 3" core.

This formula is directly linked to the ISO 9969 test. The ring stiffness S measured by the standard equals E × t³ ÷ (12 × D_m³). It follows that p_cr ≈ 24 × S ÷ (1 − ν²): a ring stiffness of 100 kN/m² corresponds to a short-term critical pressure of about 28 bar (ROLL Lab analysis).

The calculation is below. For the full version, with the formulas explained, open the minimum wall estimate with creep.

Orders of magnitude

The table applies the two checks with stated assumptions. It is a ROLL Lab exercise to show orders of magnitude, not test data.

Assumptions: 23 °C; moduli 3,000 (PVC), 1,500 (PP), 1,000 MPa (HDPE); limit stresses 50, 32, 25 MPa; long-term factor 0.65 for PVC and 0.45 for PP and HDPE; free ring, no shaft, no safety factor. Lower of the two checks. In the heat the values drop further. A safety factor of 1.5–2 on the estimated roll pressure is prudent.

Two readings. First: at 3", a well-sized plastic core carries the typical pressures of films. Second: at 6", buckling dominates and PP and HDPE need thick walls; PVC, being stiffer, starts with an advantage.

Creep: strength that wears away over time

Under constant load a plastic keeps deforming. The structured-wall thermoplastic pipe standards give a reference: EN 13476-2 requires a creep ratio, measured to EN ISO 9967 and extrapolated to two years, of up to 2.5 for PVC-U and up to 4 for PP and PE. This means that at two years the effective stiffness of PP can be a quarter of the value measured in the short test.

For a roll that stays in storage for weeks the drop is smaller, but it is enough to close the bore of a marginal core. That is why our calculations use a long-term factor, and we recommend measuring the bore after 1, 7 and 14 days in a real trial.

Temperature

With heat, the modulus and the allowable stress fall, and creep speeds up. Fiaptech documentation reports that at 50 °C the strength of a virgin PVC core drops by about 20% compared with 25 °C, and that of a recycled PVC core by about 30%. PVC has its glass transition around 80 °C; PP and HDPE, being semi-crystalline, lose stiffness more gradually but start from lower values. A check at 23 °C is not enough for rolls that travel in containers or sit in summer warehouses.

How a plastic core is tested

To compare cardboard and plastic on equal terms, both cores should be tested at the same speed and temperature. No standard requires this today: a good reason to ask the supplier how the data sheet numbers were obtained.

Signs of failure

• the roll will not come off the shaft after storage;
• the bore measured after some days has dropped by more than a few tenths;
• the core is oval where the roll was resting;
• long cores are bent after the summer.

The most common causes are an insufficient wall, underestimated temperature and storage without plugs or cradles. Core plugs and end walls.

Frequently asked questions

Further reading

Sources

1. ISO 9969:2007, Thermoplastics pipes — Determination of ring stiffness
2. EN 13476-2 and EN ISO 9967, creep ratio of thermoplastic pipes (PVC-U ≤ 2.5; PP and PE ≤ 4 at 2 years)
3. ISO 11093-9, flat crush resistance of paper cores
4. D. Van Hove, “Radial approach for the design of cores in film applications” (pressure 5–100+ bar; failure times; CCTI T-158)
5. Fiaptech technical documentation, Smart Book “Which core?” and “What about radial resistance?” (a company with corporate ties to ROLL)
6. Classical formulas for thick-walled tubes (Lamé) and buckling of a ring under external pressure
7. ROLL Lab analysis (orders-of-magnitude table, link between ring stiffness and critical pressure)