Tsai-Hill Failure Criterion
Failure Criterion
The Tsai-Hill failure criterion applies to composite shells.
This criterion considers the distortion energy portion of the total
strain energy that is stored due to loading. The distortion energy is
the portion of strain energy that causes shape change. The other portion
is the dilatation energy that causes volume change (area change in the
case of 2D) due to loading.
The figure illustrates the difference between dilatation and distortion
when a 2D model is loaded.
For a 2D lamina, which is the case for composite shells, each lamina
is assumed to be in a state of plane stress with s3 =0,
t13 =0, t23 =0. The failure index is computed as follows:
The program reports the factor of safety (FOS)
as 1 / (F.I.). So, the FOS should be greater than 1 for laminates to be
safe.
where:
X1 is the tensile strength in material
direction 1
X2 is the tensile strength in material
direction 2
S12
is the shear strength
Click principal material directions
for a definition of material directions 1 and 2.
Further,
X1
= X1T if s1 > 0
X1
= X1C if s1 < 0
X2
= X2T if s1
> 0
X2
= X2C if s1 < 0
Superscripts T
and C denote tensile and compressive
strengths respectively.
NOTE: The Tsai-Hill
criterion considers the interaction between different stress components.
Hence, it is an interactive failure theory.
Limitation
The Tsai-Hill failure criterion cannot predict different failure modes
including fiber failure, matrix failure, and fiber-matrix interface failure.
Related Topics
Performing factor of safety check
Guidelines
for Selecting a Failure Criterion
Composite
Failure Criteria