Blade materials, testing methods and structural design - Wind Power Generation and Wind Turbine Design - page 445

The criterion for tensile failure perpendicular to the fi ber direction is ( s T > 0):

s
s +

T

≥ 1

( 4 )

Tu

and the criterion for compression failure perpendicular to the fi ber direction
( s T < 0) is:

s
s −

T

≥ 1

( 5 )

Tu

while the criterion for shear failure is

t ≥ t

LTu . ( 6 ) LT

More advanced failure criteria account for the multiaxial stress state that is usu-
ally present in laminated composites. A popular criterion is the so-called Tsai-Hill
criterion, which is a generalization of an orthotropic yield criterion form metallic
materials. It can be written as (assuming s L > 0 and s T > 0):

2 2 2

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞

s s s s t

t

( 7)

L L T T LT

− + + ≥ 1

⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟

⎜ ⎟

+ + + +

s s s s ⎝ ⎠

⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

LTu

Lu Lu Lu Tu

s + and s + if

If s L < 0,

s − should be used instead of s − should be replace

Lu Tu

Lu Tu

s T < 0.
The Tsai-Hill criterion provides a single function for the prediction of failure,
but it does not give any prediction of the failure mode . Other criteria are, like the
simple maximum stress criteria described above, are split after various failure
mode. One such example is the Hashin criteria [60], which is split into two criteria,
which enables the distinction between failure that involves fi ber failure (fracture in
a plan perpendicular to the fi ber direction) and matrix failure (failure along planes
parallel to the fi ber direction). The criterion for fi ber failure is ( s L > 0):

2 2

⎛ ⎞ ⎛ ⎞

s t

t

L LT

+ ≥ 1

( 8)

⎜ ⎟

⎜ ⎟

s +

⎝ ⎠

⎝ ⎠ LTu

Lu

and the criterion for fi ber failure under axial compression ( s L < 0) is:

s
s −

L

≥ 1

( 9)

Lu

Tensile failure in the matrix is predicted from ( s T > 0):

2 2

⎛ ⎞ ⎛ ⎞

s t

t

T LT

+ ≥ 1.

( 10 )

⎜ ⎟

⎜ ⎟

s +

⎝ ⎠

⎝ ⎠ LTu

Tu

Similar criteria are developed by Puck and Schürmann [61].