Failure criteria for laminated
composites
• Defining “failure” is a matter of purpose.
• Failure may be defined as the first event that
damages the structure or the point of structural
collapse.
• For composite laminates we distinguish between
“first ply failure” when the first ply is damaged
and “ultimate failure” when the laminate fails to
carry the load.
• Ultimate failure requires “progressive failure”
analysis where we reduce the stiffness of failed
plies and redistribute the load.
Failure criteria for isotropic layers
• Failure is yielding for ductile materials and fracture
for brittle materials.
• Every direction has same properties so we prefer to
define the failure based on principal stresses. Why?
• We will deal only with the plane stress condition,
which will simplify the failure criteria. Then principal
stresses are
 
   
2
 1,2 
x
y
2
 

x
y
2
2
   xy

• What about the third principal stress?
Maximum normal stress criterion
• For ductile materials strength is same in
tension and compression so criterion for
safety is
S y  1, 2  S y
• However, criterion is rarely suitable for ductile
materials.
• For brittle materials the ultimate limits are
different in tension and compression
 Suc   1 ,  2  Sut
Maximum strain criterion
• Similar to maximum normal stress criterion
but applied to strain.
• Applicable to brittle materials so tension and
compression are different.
 uc  1 ,  2   ut
What is wrong with the figure?
Maximum shear stress (Tresca)
criterion
• Henri Tresca (1814-1885) French ME
• Material yields when maximum shear stress
reaches the value attained in tensile test.
• Maximum shear stress is one half of the
difference between the maximum and
minimum principal stress.
• In simple tensile test it is one half of the
applied stress. So criterion is
 12 
Sy
2
or  1   2  S y and  1  S y and  2  S y
Distortional Energy (von Mises)
criterion
• Richard Edler von Mises (1883 Lviv, 1953
Boston).
• Distortion energy (shape but not volume
change) controls failure.
• Safe condition
Ud 
1  
1  2
2
2
2













Sy
 1 2   2 3  3 1 

6E
3E
• For plane stress reduces to
 12   1 2   22  S y2
Comparison between criteria
• Largest differences when principal strains have
opposite signs
Maximum difference between Tresca and
von Mises
• Define stresses as 𝜎1 , 𝜎2 = 𝜎, 𝛼𝜎 . For what 𝛼
do we get the maximum ratio between the two
predictions of critical value of 𝜎? Can assume
|𝛼| ≤1. Why?
1. Positive 𝛼. Tresca gives 𝜎 = 𝑆𝑦 . Von Mises leads
to 𝜎 2 (1 − 𝛼 + 𝛼 2 ) = 𝑆𝑦2 . Maximum for 𝛼=0.5,
𝜎 = 𝑆𝑦
0.75 = 1.155𝑆𝑦
2. Negative 𝛼. Tresca leads to 𝜎 1 − 𝛼 = 𝑆𝑦 . Von
Mises still same equation. Maximum ratio for
𝛼=-1. 𝜎𝑇𝑟𝑒𝑠𝑐𝑎 = 0.5𝑆𝑦 , 𝜎𝑉𝑀 = 𝑆𝑦
• Check!
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