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The Shear-Lag Model...

Make that overlap length as long as possible…the longer the better I always say…we don’t want the bonded joint to fail…says the confident designer with an unfettered surety…hmmm...well, not quite.

Longer is not necessarily better in this case. So, for those of you interested in approximating the performance of an adhesively bonded joint “quickly” while adhering to a few basic engineering principles that will establish optimal joint parameters, then perhaps you may want to take a look at one of the simplest closed-form methods available. In 1938, the Volkersen’s Method, also known as the “shear-lag model”, was first used for mechanical joints with fasteners. Invariably, this method was used to assess failure in adhesively bonded lap joints. Of course, the method is not without some underlying assumptions which limit its use, but I will be address those later.

Volkersen shear-lag shear stress bonded joint adhesive

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What are your Strengths…”Specific” that is?

When your being interviewed for a job be prepared to answer a classic interview question regarding your strengths. This is an invitation to talk about your skills…perhaps its analytical thinking; or, maybe organization…wait-just-a-minute, ahh...wrong topic! The strength I am referring to matters when one is considering the strength of a material. So, do you know, or did you ever consider “Specific Strength” when deciding what material to use in a design? No…well, you should have! You may have a good design; but, is it the best design…. If not, consider adding Specific Strength to your decision matrix before making that all too critical material choice.

Specific Strength Calculate Breaking Length

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The Free Edge Effect

The free edge effect is an inter-galactic phenomenon found on the outer reaches of the cosmos that leads to a parallel…well…no, not exactly. What I’m referring to is a region within a laminate that produces a fully three-dimensional stress field at the free edge, then decays quite rapidly to a two-dimensional stress field as the distance from the free edge increases. The three-dimensional stress field is responsible for delamination at a free edge, and is commonly referred to as inter-laminar stresses. A composite analysis is typically confined to classical lamination theory. Unfortunately, this assumes that all out-of-plane stresses are zero, making the determination of transverse stresses impossible. Consequently, this assumption is not valid when one is interested in calculating out-of-plane stresses in regions near or at a free edge.

stress Poisson notch inter-laminar free edge cutout

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Got Shear Lock?

Funny…I was at the barber the other day and he kept complaining about his shears locking up…pesky scissors keep jamming on me he said! Well…obviously this is nothing but banal witticism, because that’s surely not what this article is about. I draw your attention to an experience I had regarding a fabric drapeability study that I performed inorder to evaluate fabric compliance over non-developable tool geometry…huh…bear with me. First the basics, when draping a composite fabric (or tape) over a tool, particularly a tool with compound curvatures, it is incumbent upon the designer to check for wrinkling and/or bridging in the fabric; especially near a radius or doubly curved surfaces. Fabric distortions of this type are clearly undesirable, and often yield poor laminate performance in terms of stiffness and lower than expected margins.

shear-lock fabric draping

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Did you check for Pull-through?

Not surprisingly over my career…I’ve seen it once and I continue to see it again and again and again…a failure to check a fastened joint for pull-through. What is seemingly a simple stress check is often overlooked. This tip provides a quick method to check for pull-through failure anytime...but hopefully you check during the preliminary phase of the design before a failure or a messy redesign is required. A check that readily ascertains whether a composite joint is thick enough, or possesses the minimum inter-laminar shear strength needed to prevent a pull-through failure is discussed in this article.

pull-through protruding fastener failure

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Quasi-Isotropy | Wait...what is that?

### Quasi-Isotropy…wait…what is that?

What is it you ask…well, this is one of my favorite meals. A large quasi-isotropy with a side of fries and coke. LOL…but of course is isn’t…actually, this is a laminate that when constructed correctly emulates a metallic material that follows the isotropic relationship defined as: E_{x}= E_{y} = E_{θ. }Quantitatively this can be described using a *general **rule **for a **quasi-isotropic** layup. Simply **apply the following equation** that defines the angle between the plies for a symmetric laminate having an identical number of plies at each orientation**:*

**Equation: π/n → n≥3**

stiffness quasi matrix laminate isotropy composite

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Is your Laminate Special?

### Is your laminate special?

I would like to think that all my laminates are special…and I’m sure that, well, all of your laminates are special too. Hmmm…this is starting to sound like an intervention! Well, not quite…what I’m actually referring to is a type of layup that excludes the use of angle plies, greatly simplifying an upfront analysis and allowing for the use of a closed-form solution (you mean no FEA!). You’re kidding right! No…in fact I’m not…I’m referring to laminate construct commonly referred to as Specially Orthotropic.

theory plate orthotropic deflection analysis

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Are you Balanced or Unbalanced?

So how do we know that we have an unbalanced laminate in the first place? Moreover, if you end up with an unbalanced layup, what are the implications? Good questions to have answers to before signing-off on that laminate design.

Firstly, a perfunctory definition is in order regarding a balanced laminate. A designer will need to ensure that for every -α ply there is a +α ply (with the same material and thickness) somewhere within stacking sequence irrespective of location. Examples of balanced laminates are: [0/30/-30/0] or [45/-45/0/0]. An unbalanced laminate is: [0/30/30/0]...notice that the negative 30-degree ply is no longer present. Now maybe you desire an unbalanced laminate or maybe it’s simply unavoidable but in a majority of design cases this layup scheme should be avoided at all costs. Why? Well, perhaps you have already surmised, this layup scheme has adverse implications, one of them significant…the often dreaded and undesirable in-plane extension-shear coupling.

unbalanced shear plate laminate extension coupling balanced

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Flatwise Tension in a Curved Plate

### Composites…It’s not just a 2D world…got Flatwise Tension?

Too often I hear both analysts and designers toss around the term quasi-isotropy…a mythical monster to some, an in-plane idealization to simplify a 3D problem for others. I for one am guilty…because I appreciate the fact that you can take a complex 3D composite problem and knock it down a dimension...in this case, the out-of-plane direction.

tension stress radius plate flatwise failure curved