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:

1 = f Vf + m Vm

Failure of the composite depends on whether the fibre or the matrix reaches its failure strain first.

Failure in longitudinal tension

ffT1 V

Failure in longitudinal compression

• Failure is difficult to model, as it may be associated with different modes of failure, including fibre buckling and matrix shear.

• Composite strength depends not only on fibre properties, but also on the ability of the matrix to support the fibres.

• Measurement of compressive strength is particularly difficult - results depend heavily on method and specimen geometry.

Failure in longitudinal compression

Shear failure mode

Microbuckling

f

mfffC1 E

EV1V2

Failure in transverse tension

High stress/strain concentrations occur around fibre, leading to interface failure. Individual microcracks eventually coalesce...

Failure in transverse compression

May be due to one or more of:

• compressive failure/crushing of matrix

• compressive failure/crushing of fibre

• matrix shear

• fibre/matrix debonding

Failure by in-plane shear

Due to stress concentration at fibre-matrix interface:

Five numbers are needed to characterise the strength of a composite lamina:

1T* longitudinal tensile strength

1C* longitudinal compressive strength

2T* transverse tensile strength

2C* transverse compressive strength

* in-plane shear strength‘1’ and ‘2’ denote the principal material directions; * indicates a failure value of stress.

Typical composite strengths (MPa)

UD CFRP UD GRP woven GRP SiC/Al

1T* 2280 1080 367 1462

1C* 1440 620 549 2990

2T* 57 39 367 86

2C* 228 128 549 285

* 71 89 97 113

The use of Failure Criteria

• It is clear that the mode of failure and hence the apparent strength of a lamina depends on the direction of the applied load, as well as the properties of the material.

• Failure criteria seek to predict the apparent strength of a composite and its failure mode in terms of the basic strength data for the lamina.

• It is usually necessary to calculate the stresses in the material axes (1-2) before criteria can be applied.

Maximum stress failure criterion

Failure will occur when any one of the stress components in the principal material axes (1, 2, 12) exceeds the corresponding strength in that direction.

*1212

2*

2

2*

22

1*

1

1*

11

)0(

)0(

)0(

)0(

C

T

C

T

Formally, failure occurs if:

Maximum stress failure criterion

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...

Maximum stress failure envelope

1

2

2T*

1T*

2C*

1C*

Orientation dependence of strength

The maximum stress criterion can be used to show how apparent strength and failure mode depend on orientation:

2

1

12

x

cossin

sin

cos

12

22

21

x

x

x

Orientation dependence of strength

At failure, the applied stress (x) must be large enough for one of the principal stresses (1, 2 or 12) to have reached its failure value.

Observed failure will occur when the minimum such stress is applied:

cossin

sin

cos

min*12

2*2

2*1

*x

Orientation dependence of strength

Off-axis tensile strength (E-glass/epoxy)

0

250

500

750

1000

1250

1500

0 10 20 30 40 50 60 70 80 90

reinforcement angle

stre

ng

th (

MP

a)

long tension

in-plane shear

trans tension

2*1 cos

2*2 sin

cossin*12

Daniel & Ishai (1994)

Maximum stress failure criterion

• Indicates likely failure mode.

• Requires separate comparison of resolved stresses with failure stresses.

• Allows for no interaction in situations of non-uniaxial stresses.

Maximum strain failure criterion

Failure occurs when at least one of the strain components (in the principal material axes) exceeds the ultimate strain.

*1212

2*

2

2*

22

1*

1

1*

11

)0(

)0(

)0(

)0(

C

T

C

T

Maximum strain failure criterion

The criterion allows for interaction of stresses through Poisson’s effect.

For a lamina subjected to stresses 1, 2, 12, the failure criterion is:

*1212

2*

2

2*

21212

1*

1

1*

12121

0,

0,

0,

0,

C

T

C

T

Maximum strain failure envelope

For biaxial stresses (12 = 0), the failure envelope is a parallelogram:

1

2

Maximum strain failure envelope

In the positive quadrant, the maximum stress criterion is more conservative than maximum strain.

1

2

The longitudinal tensile stress 1 produces a compressive strain 2. This allows a higher value of 2 before the failure strain is reached.

max strain

max stress

Tsai-Hill Failure Criterion

• This is one example of many criteria which attempt to take account of interactions in a multi-axial stress state.

• Based on von Mises yield criterion, ‘failure’ occurs if:

12

*12

12

2

*2

22*

1

21

2

*1

1

Tsai-Hill Failure Criterion• A single calculation is required to determine failure.• The appropriate failure stress is used, depending on

whether is +ve or -ve.• The mode of failure is not given (although inspect the

size of each term).• A stress reserve factor (R) can be calculated by setting

2

2

*12

12

2

*2

22*

1

21

2

*1

1 1

R

Orientation dependence of strength

The Tsai-Hill criterion can be used to show how apparent strength depends on orientation:

2

1

12

x

cossin

sin

cos

12

22

21

x

x

x

UD E-glass/epoxy Orientation dependence of strength

0

200

400

600

800

1000

1200

0 10 20 30 40 50 60 70 80 90

angle (o)

app

aren

t st

ren

gth

(M

Pa)

long tension

trans tension

shear

Tsai-Hill

Tsai-Hill Failure Envelope

• For all ‘quadratic’ failure criteria, the biaxial envelope is elliptical.

• The size of the ellipse depends on the value of the shear stress:

1

2

12 = 0

12 > 0

Comparison of failure theories

• Different theories are reasonably close under positive stresses.

• Big differences occur when compressive stresses are present.

A conservative approach is to consider all available theories: