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DNV-OS-C501 Composite Components

Sec.6: Failure Mechanisms & Design Criteria

D: Matrix cracking

Sec.6
D. Matrix cracking

Sec.6
D 100   General

Guidance note:
Matrix cracking is a simple concept at first sight but quite involved in details.

Some laminates have already matrix cracks after manufacturing. These cracks can be introduced by thermal stresses or by shrinkage of the matrix during cure.

Laminates without matrix cracks have an initial ply stress when the first cracks start to form.

Once cracks are formed they start to propagate at higher ply stresses and additional cracks are formed.

Crack formation will eventually lead to a change in stiffness. This point is usually referred to as the matrix crack point or first ply failure etc., because this is what can easily be measured.

Eventually laminates show crack saturation and no further cracks form when loaded more. The change of modulus has been related to matrix crack density in some publications.

See A102 and A103 for relevance of matrix cracking for a particular application.

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Sec.6
D 200   Matrix failure based on simple stress criterion

where,

n	direction of the dominating stress
snk	characteristic value of the local load effect of the structure (stress) in the direction n
	characteristic value of the stress components to matrix cracking in direction n
gF	partial load effect factor
gSd	partial load-model factor
gM	partial resistance factor
gRd	partial resistance-model factor, gRd = 1.0

The co-ordinate system is the ply co-ordinate system.

Guidance note:
The stress to matrix cracking is in general direction-dependent. This is due to the presence of fibres that concentrate the stresses, such that the matrix stress to failure in the direction parallel to the fibres is in generally larger than in the perpendicular direction.

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max_i

The co-ordinate system is the ply co-ordinate system, where i and n refer to the directions 22, 33, 12, 13 and 23.

Sec.6 D
203   When the combination between the stress components in several directions shall be taken into consideration, the design criterion for matrix cracking is given by:

where,

n	the co-ordinate system is the ply co-ordinate system, where n refers to the directions 22, 33, 12, 13 and 23
snk	characteristic value of the local load effect of the structure (stress) in the direction n
	characteristic value of the stress components to matrix cracking in direction n
gF	partial load effect factor
gSd,	partial load-model factor
gM	partial resistance factor
gRd	partial resistance-model factor, gRd = 1.15.

Guidance note:
A resistance-model factor g_Rd = 1.15 should be used with this design rule. The model factor shall ensure a conservative result with respect to the simplifications made regarding the treatment of combined loads.

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Guidance note:
This design criterion is often not available in finite element codes or other commercial software. The Tsai-Wu criterion can be used instead to check for matrix cracking, if the following modifications are made to the strength parameters:

-	the ply strengths in fibre direction may be chosen to be much (1000 times) higher than the actual values
-	the interaction parameter f12=0 shall be set to 0.

It is, however, recommended to use the Puck criterion to predict matrix cracking, see D300).

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or

COV_comb = max_n (COV_n )

where:

n	the co-ordinate system is the ply co-ordinate system, where n refers to the directions 22, 33, 12, 13 and 23
COVn	COV for stress component n
COVcomb	COV for the combined stress components.

Sec.6 D
206   When two or more loads are combined, each stress component s_nk in direction n can be the result of several combined loads. In that case each stress component s_nk^j, which is the local load effect of the structure in direction n due to load j, shall be considered separately as an individual stress component to determine the COV.

or

COV_comb. = max_n (COV_n )

Guidance note:
This approach is conservative compared to the approach of Tukstra's rule as used for the fibre design criteria. This approach has been chosen for simplification. In the case of fibre failure, only the strains parallel to the fibre directions have to be considered, whereas for matrix cracking all stress directions may interact.

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Sec.6
D 300   Matrix failure based on Puck's criterion

In addition, the stress component s_II in fibre direction is needed.

s_II = g _f · g _Sd · g _M · _Rd s₁

Failure is evaluated based on the stress state s_n, t_nt, t_nl for all angles q between - 90 and + 90 degrees. The design criterion is:

if s_n (q) £ 0

for all q with -90 £ q £ 90,

if s_n (q) < 0

for all q with -90 £ q £ 90,

where,

s1, s2, s3, s12, s13, s23	characteristic values of the local load effect of the structure (stress) in the co-ordinates of the ply.
gF	partial load effect factor (see 307)
gSd,	partial load-model factor (from structural analysis see section 9)
gM	partial resistance factor (see 307)
gRd	partial resistance-model factor (see 308)
Fik	strength factors (see 303).

Sec.6 D
303   The strength factors F_ik are functions of the ply strength

 parameters ^matrix , ^matrix, ^shear, ^fibre , ^fibre , and shape parameters of the failure surface. The factors are defined as:

	, if and
	, if
	,
	,
	,

with,

A_t = A_c = 1.6

where the shape parameters should be determined experimentally.
If they are not available the following default values shall be used:

= ^matrix , ^matrix, ^shear.

Sec.6 D
304   The characteristic strength for each of the stress

 components ^matrix , ^matrix, ^shear and the corresponding coefficients of variation COV_n are defined as specified in section 4 A600. The combined COV_comb is defined as:

COV_comb = max_n (COV_n )

or

COV_comb. = max_n (COV_n )

Guidance note:
This approach is conservative compared to the approach of Tukstra's rule as used for the fibre design criteria. This approach has been chosen for simplification. In the case of fibre failure, only the strains parallel to the fibre directions have to be considered, whereas for matrix cracking all stress directions may interact.

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Sec.6
D 400   Obtaining orientation of the failure surface

Guidance note:
Matrix cracks with an orientation of 30^o to 60^o occur mainly when the ply is exposed to high inplane shear stresses or compressive stresses normal to the fibre direction.

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Sec.6
D 500   Matrix cracking caused only by shear

where,

s12	characteristic value of the local load effect of the structure (stress) in the inplane shear direction 12
	characteristic value of the stress components to matrix cracking in the inplane shear direction 12
gF	partial load effect factor
gSd	partial load-model factor
gM	partial resistance factor
gRd	partial resistance-model factor, gRd = 1.0

The co-ordinate system is the ply co-ordinate system.

Sec.6
D 600   Matrix failure checked by component testing