Micromechanics- Composite Strength 2 Flashcards
For a crack tip in an isotropic system, where are the stresses?
They are located at the crack tip in the axial plane.
Run ahead of the crack tip in the transverse plane
What does a transverse crack lead to?
Can cause debonding at the fibre/matrix interface allowing it to circumvent the fibre, leaving it intact. This is crack deflection and is an important toughening mechanism in composites
What is the peak stress in a fibre neighbouring a failed fibre a function of?
The interfacial shear stress or the matrix stress
Graphs of relative stress concentration (transmitted to neighbouring fibre) vs relatively sliding stress of relative far field matrix stress
Δ σ1/σf vs τ/σf: concave curves up from origin
Δ σ1/σf vs σm/σYm (matrix stress over yield stress): starts roughly horizontal at a y-intercept, curves up a bit around 0.5 and then settles to higher horizontal near 1
What influences neighbouring stress?
Higher for higher ratio of fibre/matrix stiffness.
Tends to zero as shear stress tends to zero.
Increased when the distance is less.
Increased with a yielding matrix
What do shear forces present in composites dictate?
That failure will occur on the orthogonal planes
The three pairs of shear forces and how important they are
1- typically great resistance to fibre fracture so forces of the type τ12=τ13 are unlikely to occur.
2- in thin lamina in the 1-2 plane, stresses in the 3 direction do not occur so τ23=τ32 are less important.
3- the remaining τ21=τ31 shear forces are most important (fibres sliding along each other, not across)
See slide 10 for diagrams
Important shear forces τ21 and τ31
Similar to tensile failure, stress concentrations in the matrix cause failure. Local matrix deformation (without cracking) can occur. No simple expression to predict τ21u but empirical observations suggest it is similar to τmu for ff<0.6. Higher ff impose sever restrictions on the matrix
Shear stress concentration factor vs ff
Very flat until after 0.6 where it shoots up to nearly vertical
How does compressive failure work?
Under axial loading in compression, fibres will tend to buckle. Lateral constraints (like matrix and other fibres) require the buckling to occur in phase. Extensive buckling leads to collapse and failure of composite but localised buckling more common. Local buckling leads to kink-bands in fibres where plastic deformation of the matrix is required, leading to plastic micro-buckling.
How does the type of fibre influence compressive failure?
Brittle fibres like carbon fracture when they form kink-bands.
Ductile fibres like Kevlar don’t
Euler buckling stress
The stress at which buckling occurs
σb=(π^2 E/16)(d/L)^2
Where E is YM
L is full fibre length
d is fibre diameter
Means buckling favoured for high aspect ratios (σb decreases)
Compressive strengths of carbon, glass and Kevlar
Carbon and glass have similar tensile and compressive strength.
Kevlar has compressive strength about 20% of its tensile strength. In tension, covalent bonding along polymer backbone controls properties. In compression, van der Waals interactions are dominant but ultimately weaker
Formula for compressive failure stress of a composite
σcu=τ(ym)/Δφ
Where τ sub ym is the shear yield stress of the matrix and Δφ is the average fibre misalignment angle in radians. Data suggest that Δφ is roughly 3°.
Compressive failure stress vs matrix yield stress
When both on log scales is linear graph with positive gradient.