Tensioning Webs : Web Mechanics
- What tension will break or deform a web?
- What are stress and strain?
- The Poisson's ratio?
- What is the right tension?
- What is the right tension for a laminated product?
- What are typical tensions by product?
- What is elasticity? Viscoelasticity?
- What is web modulus?
When a web will break or deform is a material property. In all materials, breaking and deforming will occur in response to not just force, but force exerted over a given cross-sectional area. In tensioning a web, the cross-sectional area is the width times the thickness.
A web is a beam. In buying wood boards, a 2 x 4 will have more strength than a 1 x 2 and less strength than a 4 x 4 or 2 x 8. Also, a pine 2 x 4 will be stronger than a 2 x 4 of balsa wood, but weaker than a 2 x 4 made of oak or maple.
The same is true with webs. Material, thickness, and width will all contribute to a web's strength and resistance to breaking or deforming (a.k.a. yielding). A 1-inch wide web will break easier than a 10-inch wide web. A 2-mil thick web will be harder to break or yield than a 0.5-mil thick web. A steel web will be harder to break than a polyethylene web. (Harder to break = higher critical tensile break stress.)
A tensile-elongation test is the best way to find your web's break or yield point. A tensile-elongation tester pulls on a strip of web precisely measuring the elongation distance and force. Converting the load vs. length change data to find the initial slope of stress and strain plot defines the web's Young's modulus.
If this is true, why can I easily break aluminum foil but struggle with the box of cling wrap? The difference is your ability to concentrate an applied force over a small area. With the aluminum foil, you can easily skew the sheet, load everything on an edge and initiate a tear. With the cling wrap, as you skew the sheet, the heavily loaded side will elongate, taking a high portion of the load you have exerted, but the stresses will still be distributed across a large area, not just the cling wrap's edge. To tear the cling wrap, you need help with concentrating the stress, so the cling wrap box includes a serrated blade to focus your load over the small blade tips, creating the critical tear stress.
What are stress and strain?
Definition: Stress is a force over an area (units are lbs/in2 or psi, N/m2 or Pa)
Stress and pressure have the same units. Tensile stress tends to elongate something. Compressive stress (a.k.a. pressure) tends to shorten something.
Definition: Strain is a shape change, usually described as a fraction or percent change calculated from dividing the change in a dimension by its original, unstressed dimension.
When you tension a web, it gets longer in the machine direction. If you stretch a 10-inch sample to 10.1 inches, you have strained it 1 percent.
What is the Poisson's ratio?
When you tension a web, you change its length, but you may not make a significant change its density or volume (volume = length x width x thickness). If the length increases, but the volume doesn't change significantly, then the web must shrink in another direction (and it does). A tensioned web will deform and see a decrease in width and thickness.
When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. Poisson's ratio (ν), named after Siméon-Denis Poisson, is a measure of this tendency. Poisson's ratio is the ratio of the strain normal or perpendicular to the applied load divided by the strain in the direction of the applied load. In web tensioning, we often ignore the small thickness change from tensioning, but the width change can be significant. In many webs, the Poisson's ratio is around 0.3.
Example: Web tension may stretch thin polyethylene or polypropylene films to 1 percent in their machine direction. This tension will also create a width change or necking of 0.3 percent. If the web is 50-inches wide, this would reduce the width by 0.15 inches or 150 mils.
What is the right tension?
As a starting point or rule of thumb, I recommend a web tension that is 10 to 20 percent of the web's break or yield stress. This 10:1 to 5:1 safety factor may seem high, but it is needed. The tension set point is the average tension in the web, but web tension will vary across the web width, over the length of a tension zone, and over time. Crossweb tension can easily vary by 2:1 or more across the web's width due to web bagginess or roller misalignment. Tension variations over time from 10% are fairly normal and can vary as much as 50 or 100 percent during acceleration or within tension zones.
If you blindfold me and make me pick a web tension I'll pick 1 PLI (1 lbf per inch of width or 175 N/m). I would say 90 percent of webs are run between 0.3 and 3.0 PLI and 95 percent of webs are run between 0.1 and 10 PLI. (1 PLI = 17.8 kgf/m = 175 N/m)
Here is a list of typical tensions for various web products.
Regarding the rules on PLI per mil (shown below), thicker products may not need to have a tension proportional to their thickness. For example, 0.5 to 3-mil thick PET will do fine at the 0.5-1.0 PLI per mil tension guideline, but as PET thickness goes up to 5 or 10 mils, the web itself has significant stiffness. Without the need for tension-induced stiffness, you may find that 2-3 PLI will be enough for these thicker webs.
(1 lbf/in/mil = 1000 psi = 6.9 MPa)
In choosing the tension for a laminate, I recommend adding together the recommended tension for the individual layers. I tend to ignore most coating, especially a soft adhesive coating that does not provide any significant stiffness to a laminate. Other coated layers, like a thick cured epoxy layer may have significant stiffness and should be accounted for.
What is elastic? Visco-elastic?
Definition: Elasticity is the property of returning to an initial form after deformation.
Rubber is the classic example of an elastic material. You push on it, it deforms; you let go, it recovers. An elastic material responds to load almost immediately (the load travels through the material at the speed of sound). The amount of deformation is proportional to the load and independent of time.
Definition: Viscosity is the property of having a resistance to flow.
Molasses is the classic viscous material. When a force is applied to a viscous material, it will flow. The longer the load is on the viscous material, the more it will flow. When the force is removed, they will stop flowing, and the material won't recover.
Definition: Viscoelasticity is the property of having both viscous and elastic properties.
When a viscoelastic (V-E) material is loaded, it will respond with a mixture of viscous and elastic behavior. Upon loading, a V-E material will immediately stretch (elastic behavior) and begin to flow (viscous behavior). When the load is removed from a V-E material, it will recover, some immediately (elastic behavior) and some will recover more over time (viscous behavior). Vinyl electrical tape is a classic and easily observed V-E material.
Try this test yourself: Pull out a 2-3 foot length of electrical tape. Hang a 1-2 lb weight on it. Note the initial elongation and that the tape will continue to elongate. Take the weight off. Note the initial recovery and ongoing recovery.
Congratulations, you've just completed your first creep test.
Tension elongation testing is commonly used to find a material's break tension and break elongation. However, the same test will also measure a material's modulus of elasticity or Young's modulus.
Definition: Modulus is the initial slope of the stress-strain curve. Modulus is the ratio of the applied stress to the change in shape of an elastic body (also known as elastic or Young's modulus ).
Modulus will have units of force per area, such at psi or MPa.
Steel 30,000 kpsi
(1kpsi = 6.9 MPa)
Every material has a limit to the load or stretch that can be applied elastically.
Materials like steel and aluminum will require high stresses (load over area) to get even the smallest elongation, but will yield at relatively low strains, if you can apply the stress to get them there.
Once you've reached a web's elastic limit, it will no longer fully recover when unloaded. In web handling, the goal is almost always to handle the web below the elastic limit and avoid any permanent damage to the web.