Failure Criteria for Isotropic Materials(1)

8/11/2019 Failure Criteria for Isotropic Materials(1)

1/8

Failure criteria for laminated

composites

Defining failure is a matter of purpose.

Failure may be defined as the first event thatdamages the structure or the point of structuralcollapse.

For composite laminates we distinguish betweenfirst ply failure when the first ply is damagedand ultimate failure when the laminate fails tocarry the load.

Ultimate failure requires progressive failureanalysis where we reduce the stiffness of failedplies and redistribute the load.


2/8

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

What about the third principal stress?

2

21,2

2 2x y x y

xy


3/8

Maximum normal stress criterion

For ductile materials strength is same in

tension and compression so criterion for

safety is

However, criterion is rarely suitable for ductile

materials.

For brittle materials the ultimate limits are

different in tension and compression

1 2,y yS S

1 2,uc ut S S


4/8

Maximum strain criterion

Similar to maximum normal stress criterion

but applied to strain.

Applicable to brittle materials so tension and

compression are different.

1 2,uc ut

What is wrong with the figure?


5/8

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 1 2 1 2 or and and

2

y

y y y

SS S S


6/8

Distortional Energy (von Mises)

criterion

Richard Edler von Mises (1883 Lviv, 1953

Boston).

Distortion energy (shape but not volume

change) controls failure.

Safe condition

For plane stress reduces to

2 2 2 2

1 2 2 3 3 1

1 1

6 3d yU S

E E

2 2 2

1 1 2 2 yS


7/8

Comparison between criteria

Largest differences when principal strains have

opposite signs


8/8

Maximum difference between Tresca and

von Mises

Define stresses as , 2 = , . For what do we get the maximum ratio between the twopredictions of critical value of ? Can assume|| 1. Why?

1. Positive . Tresca gives = . Von Mises leadsto 2(1 + 2) =

2. Maximum for =0.5, = 0.75 = 1.155

2. Negative . Tresca leads to 1 = . Von

Mises still same equation. Maximum ratio for=-1. = 0.5 , = 3

Check!

Failure Criteria for Isotropic Materials(1)

Documents

Transcript of Failure Criteria for Isotropic Materials(1)