Stiffness vs Tensile Strength in Foam Sandwich Construction?

When building a composite layup for a hull, is the fabric tensile/compressive strength or the stiffness typically the limiting factor?

I'd imagine stiffer is always better, but I'd also assume there is a point of diminishing returns.

I've been looking at the properties of Kevlar, S Glass, E Glass, Basalt Fiber, & Carbon Fiber, and it seems that the properties of S-Glass are really optimal in everything except its high density, with cost in mind.

Example:
https://i.imgur.com/J6Wh1zf.png

Logically, the increased density doesn't seem like it is that big of a downside, as the more dense fabric will have a lower cross sectional area for the equivalent strength than the weaker less dense carbon fiber, so long as the specific strength is equivalent. Because of that lower cross-sectional area, the resulting layup of S Glass should have less epoxy per cubic cm than the equivalent carbon fiber, resulting in a bit less weight.

This leads me to believe that the primary benefit of carbon fiber lies in the stiffness rather than its strength / weight density, which leads me to my original postulation that stiffness is the typical limiting factor?

 

The foam is more likely to be the limiting factor. From all the materials, it is the one with less strength. If the interface between the foam and the skin fails, it is irrelevant what the tensile/compressive strength of the skins is.

 

If we are talking about a sandwich type compound, with a foam core, and with both skins sufficiently balanced, the tension / compression in the core is irrelevant so the core should not be decisive in this regard. Another thing is that the union, the interface, between the core and the skins does not support the shear stresses, but that would not be the fault of the core.

 

So would you typically add layers on a hull for tensile/compressive strength or for stiffness with fiberglass?

 

I believe you are confusing different properties.

A boat hull is designed to achieve certain attributes.

For example, if you take a very thin core and add tons of glass to each side; you have essentially underutilized the attributes of the core.

If, on the other hand, you use a super thick core and apply very light skins, you have overutilized the core and the skins may be insufficient.

What must be done is a balance, where you achieve meeting the demands of the hull with sufficient core and glass combined.

The stiffness is more closely related to thickness. I will try to find a relevant thread on the cube rule. The real expert is rxcomposite. A few others can also generate a layup well I'm sure. Not me.

 

Also, you keep referring to 'limiting factor'.

i.e. 'stiffness is the limiting factor'

This is an error. The limiting factor in sandwich construction is weight!

The reason for sandwich construction is to reduce the weight of the core and skin to the lightest practical combination that will work for the design.

Erase weight as a concern and the skins can be any thickness, as can the foam.

 

Not quite sure if I follow, but tensile strength is already "per volume" (force per area). So I think E-Glass with 2.5 GPa has to be twice as thick as Carbon medium fibers with 5.1 GPa tensile strength. So for the same tensile strength it would use twice as much epoxy and fibers would weight 2 x 2.6/1.8 = 2.8 times as much.

I believe somewhat mitigated by more elongation of glass before break so more "give" and more thickness is good for local impact resistance.

This does makes me wonder if there are fabrics with mixed thicker and thinner fibers for more compactification and less resin use.

 

Why would specific strength be equivalent? Are you assuming laminate thickness is a constant independent of fiber properties?

 

Add layers to increase stiffness, Stiffness can be thought of as a function of the product of Young's modulus and the thickness raised to the third power.

Making it thicker is the quick and dirty way to gain stiffness because you increase the moment of inertia. As the formula states, you can also substitute the fibers with a "stiffer" property (higher modulus like carbon fiber).

Increasing thickness raises also the distance of the outermost fibers to the neutral axis thus reducing the stress on the surface. Thus you can use a lower "strength" fiber on the outermost layer.

 

Your analysis is correct except that don't confuse "per volume" with "per unit area". Strength is a unit of measure "force per unit area" such as Newton(s) per mm square.

To define it as load bearing, if you can suspend a hundred kg of something with 1 mm square section (X mm long) of carbon fiber, you will need 2 mm square section to suspend a two hundred kilogram. Strength remains the same.

If you chose a weaker "string" like abaca rope, you will need 2mm square section just to suspend a hundred kg, 4 mm square to suspend two hundred kilogram. (Just an example but not reflecting the real strength of the materials mentioned)

Note that we did not include volume or density of material. To define it as such, we would call it "specific strength"

 

Actually, don't confuse the need for strength for the need for stiffness. They are two different properties to design for.
Think of a spectra rope and a steel beam of the same sectional area. The rope is very strong, but only in tension, and only under cyclic loading; it cannot support a compressive end load and greatly deflects under sideload with no pre-load. The steel beam cannot support as much tension load as the spectra but can do it effectively forever, can support almost as much in compression, and has significantly less deflection under a side force.
Stiffness is the important criteria to to ensure that the structure holds shape under loads, strength is what is actually carries the loads. I have designed and built very flexible but strong structures knowing that they were going to have to take the load at maximum flexure. And like I have designed and built very lightweight but stiff structures because that was what was needed for that particular load case. What really should happen is that strength should be just sufficient to fail just after the maximum allowed deflection is reached...the zen of structures.

Edit to correct a spellcheck tpyo ensure/unsure

 

Thanks for the info guys.

I think I have a better understanding of the differences between Tensile & Deflection loading and the benefits of carbon fiber; however, I think I still could use some help on the limiting factor.

By this, I mean that say you require x layers of S glass or E glass for your hull to be sufficient, assuming a suitable core thickness. @fallguy

Do you continue adding layers until you have a Specific Modulus of >Y, or instead do you continue adding layers until you have a Specific Tensile Strength of > Z.
Or, if both of the above is the case, for a typical hull structure, do you typically achieve a suitable Modulus or a suitable Tensile strength first? (Assume E Glass)

For the other discussion on higher density & epoxy, take for example two hypothetical fibers:
* Fiber A has a density of 2 g/cm^3, a tensile strength of 2 GPa, and an elastic modulus of 100 GPa.
* Fiber B has a density of 4 g/cm^3, a tensile strength of 4 GPa, and an elastic modulus of 200 GPa.

As both Fibers A and B have an identical specific modulus and specific tensile strength, my theory is that fiber B would be superior in all cases, due to a lower degree of resin required as the fiber B composite only has to be half as thick as the fiber A composite, therefore making the resulting composite lighter. I'm not sure if the resulting increase in width of fiber A would in any way make up for the increase in resin use by increased elastic modulus, though this might be dependent on if thickness matters for the hull.

This falls somewhat in line with the point brought up by @rxcomposite about fibers further from the center requiring less strength than internal fibers, though I'd expect they'd also need a negligibly higher degree of elongation. This seems like it would only help in tension though, not in compression. In compression, wouldn't the outermost layers have take the highest amount of compression? This is assuming compression strength is important in boat hull composites. I've read that it may not be?

@Dejay , I think you are correct on E Glass vs Carbon Fiber, but take for example S2 Glass vs Carbon Fiber (Large). The specific strength of each is relatively close, but S-2 Glass is much more dense. In order to have a required tensile strength of say 10 GPa, you'll need a carbon fiber laminate approximately 33% thicker than that of the S2 Glass. While the carbon fiber would still be approximately 7% lighter, even at that greater thickness, the additional epoxy mass requirement for that 33% additional thickness is likely much higher than 7%. This would imply that S2 Glass is superior to Carbon Fiber on a thinness, strength, and weight basis, so long as the stiffness of the S2 glass is sufficient for your use case.

 

You need to include the core in the calculation to find out where the failure will occur. Once you find the failure mode, the limiting factor (or material) will be evident. For example, if you are calculating the failure by impact like hitting the corner of a dock, the skins may deflect within their elastic limit and recover. However, the core may be crushed and fail. It could also happen that the core will be within its elastic limit, but the skin will fracture. Ideally, but unrealistically, both would fail at the same point, which is the holy grail of light structures.

 

Ok, there are a lot of structural concepts tied up in here that selection of fiber strength and modulus have little to no effect on. I can't tell from your posts so far, but have you had a college level structures courses? Because this is going to get fairly messy fairly quickly.
So, trying to address them in a logical sequence...
1) Absolute axial tension and compression is distributed throughout the layup. In elastic theory, each individual component supports a portion of the load in proportion of it's deflection and modulus. This means in tension the un-stretchable fibers support most of the load; in compression it is the resin and the core.
2) Realistically, in boat shapes, there is rarely any pure axial forces. The shape of the hull gives some out of axis geometry, both in tension and compression. This load is distributed through the layup in accordance with the relative deflection of the sectional modulus, tension on the outside of the deflection and compression on the inside. Note also this is for the complete hull, and the individual panels that comprise the hull (i.e. there is a SM for a transverse section of the whole hull and a layup specific SM through that individual panel.)
3) Boat hulls in particular, and structures in general, are simultaneously subjected to multiple load cases. In vessels these are 1) Primary Loads. This the total longitudinal bending moment forces from hydrodynamic and hydrostatic forces. The loads are primarily carried through the shell. 2) Secondary loading. This is the transverse loads generated by the primary loads. They are normally carried by the transverse frames and bulkheads. What this does is to break the shell panels up into to short lengths that will resist buckling. 3) Tertiary loading. This the the actual hydrodynamic and hydrostatic load normal to the skin. The skin has to support this load without deflecting or shearing.
Let us look at a curved composite panel low in the hull with the vessel hogging. The primary load is axial compression (inner compression, outer compression), but the curvature of the panel adds a bending component (inner compression, outer tension) that is restrained by the secondary end fixation (inner tension, outer compression, negative shear) due to the tertiary hydrostatic load (inner tension, outer compression, positive shear). The designed layup needs to meet this condition as well as the exact opposite sagging condition, as well as internal attachment loads, foundations, and damage criteria. In some cases, compression and shear may drive layup criteria, not fiber strength.

 

Stiffness is the quality in short supply with GRP, have a look at a fishing rod, which works a treat if there is no sudden transition to the inflexible, like bending a fishing rod jammed into a stiff steel pipe, it will snap like a carrot at the junction. Boats have hard points like that, and the solution is to build heavier, for greater stiffness, or use cored laminates.