Practical Design Limits

1.0 Introduction

Here is an attractive fact:  E-glass fibers are approximately 70 times stronger than steel (on a strength / weight basis). [1] [2]  Imagine a building material so astoundingly strong.  We could build yachts at a fraction of their current weight!  That is the promise behind composite materials.  So if they offer such massive improvements, why don’t we have composite materials everywhere?  Two reasons:  they do not deliver on the promised strength; and designing with composites gets a lot more complicated.  Today we explain some of the practical design limits behind composite materials.

1.1 Terminology

These are all terms for different types of materials and techniques within the field of composites.  Each of these materials have slightly different properties, and an engineer should consider the relative merits of each.  But for today, I want to lump them all together under the heading of composites.  They all follow the same rulebook.

  • FRP: Fiber Reinforced Plastic
  • CSM: Chop Strand Matt
  • Fiberglass
  • Carbon fiber
  • Aramid / Kevlar
  • Polyster / Vinylester
  • Epoxy
  • Fiber
  • Resin

2.0 Variable Strength

Composites will never deliver on their initial promise of outstanding strength, for a variety of reasons.  That first number I quoted about the strength of E-glass, that was just the fiber, under ideal circumstances.  First, the fiber strength drops rapidly with any slight misalignment between the load direction and the fiber.  Second, the fiber alone is useless.

All composites are a mixture of a strong fiber and a pathetically weak resin. (Figure 2‑1)  The resin holds the fibers together.  But the resin also weakens the composite.  For the final laminate, we need to balance the resin and the fiber.

Figure 2‑1:  Diagram Showing Typical Composite Laminate [3]

Table 2‑1 shows a comparison of relative strengths between the fiber, resin, and steel for a reference point.  The strength of the final composite laminate lies somewhere between the two extremes of the fiber and resin.  And it all depends on the ratio of fiber to resin in the final laminate.

Table 2‑1:  Relative Strength of Fiberglass Components

Component Material Tensile Strength Percentage of Steel
Fiber E-Glass Fibers [1] 3450 MPa 230%
Resin /Matrix Epoxy 8551-7 [1] 99.2 MPa 66%
  Mild Steel 150 MPa 100%

 

This laminate ratio is why manufacturing quality becomes so critical for composite materials.  The manufacturer controls that fiber/resin ratio during assembly, with wild swings in strength.  It all depends on achieving a consistent ratio of resin and fiber.

1.1 Composites Testing

Regulatory agencies and class societies anticipate this variation in material quality.  When setting standard values, they expect the worst quality manufacturing.  Table 2‑2 compares actual tested values to the standard design values assumed by ABS and DNV-GL.  The standard can be less than half of actual tested values, because the regulators need to account for the worst manufacturing quality out there. 

Table 2‑2:  Comparison of Design Values for E-Glass

Material

Tested Tensile Strength

Design Limit

Tested E-glass [4],

Unidirectional Fiber (55% VF)

Average:  743 MPa

Lowest Result:  689 MPa

689 MPa

ABS Standard Value

 

357 MPa

DNV-GL Standard Value

 

225 MPa

This is why for critical structures, I advise manufacturers to get their layups tested.  (Figure 2‑2)  If you think you can do better than the worst manufacturer out there, make sure you get credit for it. If you can prove that you create higher quality, that will allow you to design a lighter boat, with better performance.

But be careful about the samples you send in.  Make sure they are your best quality, because your limiting design value will not be the average of results from those tests.  The class societies require that we use the worst of the test results.  (DNV-GL uses a statistical representation rather than the worst single test result.)  Unless you are careful, material testing may do more harm than good.

Figure 2‑2:  Material Testing Rig [4]

The other consideration is the type of test.  A standard testing lab will probably recommend that you send multiple samples of the actual laminate layup from different points on your hull (bottom section, side, deck, etc.)  This derives from a DNV-GL procedure for as-built testing [5], meant to confirm that you maintained build quality throughout the entire hull.  But for the designer, those tests do not include any useful samples.  The designer wants results from a single ply in the laminate.  The single ply tests allow the designer to combine different plies when designing your structure.  I recommend the following tests when trying to supply designer values:

  1. 0-90 fabric test (tensile and compressive)
  2. Unidirectional fiber test (tensile and compressive)
  3. [Optional] +45/-45 fabric test (tensile and compressive)
    1. We can derive the properties of this fabric from the results of the 0-90 test. But the math theory never matches reality with 100% accuracy. 

Thankfully, most ship structures are not this critical.  But if you do want to convert your company quality into a competitive advantage, make sure you do it carefully.

3.0 Structure and Material Design

Composites behave differently from normal metals.  Direction matters.  Composites fall into the class of orthotropic materials, which means they display different strength limits depending on the direction of stresses. (Figure 3‑1)  If you pull in the direction of the fiber strands, a composite is much stronger than its other directions.  We even see different limits for tension vs compressive stresses.  Now, when we need to check against strength limits, we have four separate numbers to check for each laminate.

Stress Distribution of Fibers in Composite Mat

Figure 3‑1:  Stress Distribution of Fibers in Composite Mat [6]

That presents a design problem, because the stresses in ship structures rarely act in a single direction.  We could easily encounter a scenario where the composite works great along the fiber direction, but a small side force breaks the hull.  When designing with composites, we need to consider both the magnitude and orientation of the stresses.

This adds a whole new challenge to the cycle of structural design.  In traditional steel structures, failure checks simplify to algorithms and formulas.  Add all the stresses at each location and you get a single number.  Check that number against the material limit and adjust thickness to stay under the limit.  (I oversimplify; the safety checks require more complicated math.) 

But there is no simple method to sum up all the forces in composites.  No single, reliable number.  Material science gives us multiple failure theories, attempts to create a single number, but we don’t have a single uniform formula.  When designing for composites, we need to consider each direction at each location in the structure.  To be more efficient than metal structures, composite laminates need to change their orientation and adapt to match the stress patterns throughout the hull.  This adds an entirely new level for the engineer.  We now need to design for optimum ship structure and optimum material properties.

4.0 No Reserve Strength

Composites also disappoint in terms of reserve strength.  Did you ever see pictures of a ship’s metal hull dented, but not ruptured?  That was the reserve strength of steel, acting as a final safety measure.  We account for that strength when deciding on appropriate reserve factors for ship structures. 

Figure 4‑1 shows a simplified stress strain curve for metallic materials, like steel.  We design the structures to always keep their stresses within the blue elastic region.  This prevents any permanent deformation of the metal.  No dents.  But if disaster strikes, the steel shows ample reserve strength as it progresses through the green plastic region.  Examine the area under the curve for the blue and green regions.  This area represents the energy that the steel can absorb from some type of impact.  It shows massive amounts of energy within the plastic region.  That explains why steel bends but doesn’t break easily.  It holds untapped reserve strength, for safety.  On the other hand, composites break.

Stress Strain Curve

Figure 4‑1:  Stress Strain Curve [7]

Composites behave much more brittle.  They do not have a significant plastic region.  The composite just stretches until it snaps.  If we designed to the limits of the elastic region, it would eliminate the reserve strength normally seen in steel hulls.  And we want that reserve strength; it provides an additional safety factor against unknown risks. 

To compensate for the lack of plastic behavior, we cut back even further on the allowed limits for a composite.  Table 4‑1 compares the reserve factors required by class societies for steel versus composites.  The reserve factors for composites were almost double those of steel.  This further reduces the advantages of composites.

Table 4‑1:  Required Reserve Factors

Material

Reserve Factor

% of First Failure

Steel – ABS Limits

1.66

60%

Composite – DNV-GL Limits [5]

3.00

33%

Note that these reserve factors are simplifications. 

For full requirements, see individual rules.

5.0 Conclusion

The practical design of composites severely limits their capabilities.  At the beginning, I stated that pure E-glass fibers were theoretically 70x stronger than steel.  But remember the limits from manufacturing quality and requirements for additional reserve factors.  Accounting for those limits, E-glass fibers were only 2.5x stronger than steel (strength/weight comparison).  That still presents a significant advantage, but the extra strength comes with an additional burden.  Composites require far more engineering effort to fully utilize their strength.  And there are several other design considerations that I did not cover in this article.  Many ships cannot justify that extra engineering cost.  And not every ship needs the performance advantage of composites.  But when we understand the practical cost / benefit of composites it helps us identify small, specialized applications that do justify the cost.  Done properly, these materials can be a game changer.  With careful, targeted applications, composites far exceed the capabilities of steel.

https://youtu.be/cxjb9RsQWAw

6.0 References

[1]

E. J. Barbero, Introduction to Composite Materials Design, 2nd Ed., Boca Raton, FL: CRC Press, 2011.

[2]

R. A. F. J R Calvert, An Engineering Data Book, Southampton, UK: Palgrave, 1999.

[3]

W. Author, “Example of a Composite Material,” Wikimedia Commons, 25 Jan 2009. [Online]. Available: https://commons.wikimedia.org/wiki/File:Composite_3d.png. [Accessed 27 Nov 2020].

[4]

M. Gopalakrishnan, S. Muthu, R. Subramanian, R. Santhanakrishnan and L. Karthigeyan, “Tensile Properties Study of E-Glass/Epoxy Laminate and pi/4 Quasi-Isotropic E-glass/Epoxy Laminate,” Polymers & Polymer Composites, vol. 24, no. 6, pp. 429 – 446, 2016.

[5]

DNV-GL, “Materials,” in Rules for Classification: Yachts, Houston, TX, DNV-GL, October 2016, pp. Part 3, Chapter 5, Section 2.

[6]

C. Kothlow, “How Rule of Mixtures is Killing Your Composite Design,” Siemens, 7 May 2020. [Online]. Available: https://blogs.sw.siemens.com/simcenter/how-rule-of-mixtures-is-killing-your-composite-design/. [Accessed 30 Nov 2020].

[7]

M. Manske, “Generic Stress-Strain Graph for a Ductile Material,” Wikimedia Commons, 13 May 2008. [Online]. Available: https://commons.wikimedia.org/wiki/File:Stress-strain1.svg. [Accessed 27 Nov 2020].

[8]

American Bureau of Shipping, “Materials for Hull Construction – Fiber Reinforced Plastic (FRP),” in Guide for Building and Classing Yachts, Houston, TX, American Bureau of Shipping, July 2020, pp. Part 2, Chapter 6, Sect. 1.

[9]

Shenoi, “Composite Mechanics – Introduction,” in Course Notes: Structural Integrity, Southampton, UK, School of Engineering Sciences, University of Southampton, 2008.