Strength of composites Flashcards
What is shear lag theory?
The concept that there is a non-uniform stress distribution in members adjacent to a connection. This occurs next to a fibre break in a composite, where the stress in concentrated in one element (the matrix) at one end and then the stress is redistributed to be in both elements (matrix and fibre) at the other end.
How is the stress redistributed in the shear lag region near a fibre break?
The fibre pulls through the composite, resisted by the matrix shear strength, or a frictional stress. This is what causes the load transfer onto the fibre
What method can be used to calculate the length of the shear lag region?
Using a force balance on a differential element of fibre, and integrating with the boundary conditions that when stress is fully redistributed there is no relative strain between the fibre and the matrix, and at the other end of the shear lag zone the fibre stress is 0.
What is the consequence of the length of the shear lag zone with regards to further breaks in the fibre and adjacent fibres?
As the length is needed to build the fibre stresses to the original value, we can expect further fibre breaks to occur MORE than this distance away from the original break. Adjacent fibres will have an excess stress over this length so will tend to break less than this distance from the original fibre break.
What is the equation for strain concentration, relating the strains in the matrix and the composite?
F = em^+ / eT^+
What are the 4 mechanisms for failure in axial compression?
Fibre crushing, Plastic micro-buckling, Elastic micro-buckling, longitudinal cracking
What is ply blocking and why is it done and does it have an effect on composite performance?
It is the process of grouping plies of the same orientation together. it is done for manufacturing reasons and to inhibit some failure modes. It does affect the properties however this can be ignored for a first approximation
What tends to be the common source of interlaminar failure?
Complex geometry such as ply drops (when you desire a varied thickness), notch/holes, bond joints, bolted joints.
What are the 3 modes of crack growth?
Mode I: Opening
Mode II: In-plane shear
Mode III: Out-of-plane shear
What is the equation for the stress intensity factor for mode I (opening)?
K = Yσ(πa)^0.5 (databook)
What is the equation for the stress intensity factor for mode II (in-plane shear)?
Same as for mode 1 (databook) but instead of σ, substitute τ (tau-shear stress)
What is splitting in terms of crack growth, and why is it common in composites?
When the crack grows through the matrix along the fibre direction, and it is common as the toughness for cracks running along the fibres is much lower than for cracks running transverse for the fibre direction.
How to derive an equation for the compressive strength in plastic micro buckling:
Plastic microbucking occurs when there is an initial fibre realignment, and rotation/buckling occurs when the shear stress equals the shear yield stress. By use of mohr’s circle, putting the x intercepts at 0 and at the compressive strength SL^-, you can find an expression for the shear stress in terms of the misalignment angle. (remember, moving around mohrs circle has twice the angle as in reality)
Why might a fibre not break on the crack line when cracking in a direction transvers to the fibre direction?
Even though the fibre stress is at a maximum at the crack line, fibre strength variations along its length mean that fibres may break above or below the crack.
What is the most common direction for cracks to grow in composites?
Cracks tend to grow along the fibres as toughness here is much lower, causing splitting cracks
