Curl from Compression

Often rigid barrier coatings are applied to a polymer substrate that is heated by the deposition process. The thermal expansion coefficient of the coating is often much less than that of the substrate so it becomes compressed by the shrinkage of the substrate. This produces a curl in the film for which the radius R can be easily measured. If the coating is further annealed (as is often the case with, say, ITO) there is a further compression from the annealing process, so the curl is stronger and the radius is smaller.

This compression can be helpful if the substrate ever gets into tension - rigid barrier films are strong in compression but easily cracked under tension. In the Fragmentation test the compression gives an apparent improvement in the COS - Crack Onset Strain. The Fragmentation app allows you to enter a compression strain to adjust for this fact.

The compressive stress, σ, in a coating can be readily calculated from knowledge of the moduli of the coating and substrate E_c, E_s, their thicknesses h_c and h_s and the Poisson ratio of the substrate ν_s, here assumed to be 0.3.

`σ = (E_sh_s^2)/(6R(1-v_s)h_c )[1+h_c /h_s(4E_c /E_s-1)]`

The compressive strain γ is calculated as `γ = σ(1-ν_c)/E_c`, again with the Poisson ratio assumed to be 0.3. The L input is for those who don't have a Radius measurement but instead have a displacement δ over a sample length L. After entering the value for L, change R till you get the measured value of δ and the strain is calculated correctly. `R = L^2/(2δ)`.
Warning: include(apps\curl.php): Failed to open stream: No such file or directory in /var/www/vhosts/stevenabbott.co.uk/httpdocs/practical-adhesion/curl.php on line 24

Warning: include(): Failed opening 'apps\curl.php' for inclusion (include_path='.:/opt/plesk/php/8.0/share/pear') in /var/www/vhosts/stevenabbott.co.uk/httpdocs/practical-adhesion/curl.php on line 24

It sounds easy to "measure the curl". In fact it can be complicated. The first problem is that some substrates are pre-curled so the radius, R should be calculated from the radii before and after via 1/R=1/R_after-1/R_before, where for an originally flat film R_before is infinite so that R=R_after. Unfortunately different parts of a film (especially PET) show different curls so some careful experimentation is required before deciding, for example, only to take samples from the centre of a roll which tends to have less curl. Measuring the radius is also not always trivial. Some use some sort of image analysis from a video image, others create templates of known radius with which to compare the actual sample which, if long enough, can be placed on its edge for the comparisons.

The analysis here and its application to the "correction" to the calculations in the Fragmentation app is described by Y. Leterrier¹ and his group at the Ecole Polytechnique Fédérale de Lausanne and helpful discussions are warmly acknowledged. Extra input from Dr Charles Bishop is also warmly acknowledged.