Composite Strength and Failure Criteria . Micromechanics of failure in a unidirectional ply. In the fibre direction (‘1’), we assume equal strain in fibre and matrix. The applied stress is shared: s 1 = s f V f + s m V m.
In the fibre direction (‘1’), we assume equal strain in fibre and matrix. The applied stress is shared:
s1 = sf Vf + sm Vm
Failure of the composite depends on whether the fibre or the matrix reaches its failure strain first.
Shear failure mode
High stress/strain concentrations occur around fibre, leading to interface failure. Individual microcracks eventually coalesce...
Due to stress concentration at fibre-matrix interface:
s1T* longitudinal tensile strength
s1C* longitudinal compressive strength
s2T* transverse tensile strength
s2C* transverse compressive strength
t12* in-plane shear strength
‘1’ and ‘2’ denote the principal material directions; * indicates a failure value of stress.
UD CFRP UD GRP woven GRP SiC/Al
s1T* 2280 1080 367 1462
s1C* 1440 620 549 2990
s2T* 57 39 367 86
s2C* 228 128 549 285
t12* 71 89 97 113
Failure will occur when any one of the stress components in the principal material axes (s1, s2, t12) exceeds the corresponding strength in that direction.
Formally, failure occurs if:
All stresses are independent. If the lamina experiences biaxial stresses, the failure envelope is a rectangle - the existence of stresses in one direction doesn’t make the lamina weaker when stresses are added in the other...
The maximum stress criterion can be used to show how apparent strength and failure mode depend on orientation:
At failure, the applied stress (sx) must be large enough for one of the principal stresses (s1, s2 or t12) to have reached its failure value.
Observed failure will occur when the minimum such stress is applied:
Failure occurs when at least one of the strain components (in the principal material axes) exceeds the ultimate strain.
The criterion allows for interaction of stresses through Poisson’s effect.
For a lamina subjected to stresses s1, s2, t12, the failure criterion is:
For biaxial stresses (t12 = 0), the failure envelope is a parallelogram:
In the positive quadrant, the maximum stress criterion is more conservative than maximum strain.
The longitudinal tensile stress s1 produces a compressive strain e2. This allows a higher value of s2 before the failure strain is reached.
The Tsai-Hill criterion can be used to show how apparent strength depends on orientation:
t12 = 0
t12 > 0
A conservative approach is to consider all available theories: