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DNV-OS-C501 Composite Components
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Sec.6
C. Fibre failure
Sec.6
C 100 General
Sec.6 C
101 Fibre failure is defined here as the failure of a ply by fracture
of fibres. The fibre strength or strain to failure is based on test
results from plies or laminates as described in section 4. Ply failures
are measured as rupture of the ply in fibre direction.
Sec.6 C
102 The maximum strain criterion should be used to check fibre
failures.
Sec.6 C
103 Other design criteria may be used if it can be shown that they
are equal or conservative compared to the maximum strain criterion
given here. See for example C300.
Sec.6 C
104 Fibre failure should be checked at the ply level, not at the laminate
level.
Sec.6 C
105 If laminates have a lay-up with fibre orientation seen through
the entire thickness that are more than 45o apart, matrix cracking or
deformation due to in plane ply shear stresses may cause rupture
of the laminate. In this case matrix cracking due to ply shear should
also be checked to avoid fracture, burst or leakage (see also D500 and C300), unless it can be
shown that matrix cracks or deformations can be tolerated by the
laminate under the relevant loading conditions.Guidance note:
A pipe made of ±55 laminate with a liner can tolerate
matrix cracks and shear deformations, as long as the pipe sees only
internal pressure. If the pipe must carry axial loads or bending moments
in addition to the pressure, fibres would want to reorient themselves
to a different angle, a complicated condition. This is only avoided
as long as the shear properties of the pipe are intact.
A pipe made of a 0/90 laminate can tolerate matrix
cracks and shear deformations under internal pressure and axial
loads. This pipe would have problems with axial torsion, since the
stresses due to torsion have to be carried by the matrix.---e-n-d---o-f---G-u-i-d-a-n-c-e---n-o-t-e---
Sec.6 C
106 Regardless of the analysis method used, these laminates should
always be analysed with non-degraded in-plane shear moduli G12.
Sec.6 C
107 If laminates have a lay-up with fibre orientation seen through
the entire thickness that are more than 70o apart, matrix cracking or
deformation due to in plane ply shear stresses or stresses transverse
to the fibres may cause rupture of the laminate. In this case matrix
cracking due to all possible stress components should also be checked
to avoid fracture, burst or leakage (see also D100 to
D300), unless it can be shown that matrix cracks or deformations
can be tolerated in by the laminate under the relevant loading conditions.Guidance note:
This condition is typical for UD laminates where all fibres
run parallel in one direction throughout the thickness of the laminate. Great
care should be taken when using such laminates due to their low
properties in all other directions than the fibre direction.---e-n-d---o-f---G-u-i-d-a-n-c-e---n-o-t-e---
Sec.6 C
108 Regardless of the analysis method used, these laminates should
always be analysed with non-degraded matrix dominated elastic constants,
i.e., E2 , G12 , n12 .Sec.6
C 200 Fibre failure at the ply level
Sec.6 C
201 For single loads, the maximum strain design criterion is given
as:
where:
| enk | Characteristic value of the local response of the structure
(strain) in the fibre direction n |
| Characteristic value of the axial strain to fibre failure |
| gF | Partial load effect factor |
| gSd, | Partial load-model factor |
| gM | Partial resistance factor |
| gRd, | Partial resistance-model factor, given in 202 (below). |
Sec.6 C
202 The selection of the resistance model factor gRd depends on the choice of structural
analysis method:| — | if a linear analysis with non-degraded
properties is chosen according to Section
9 B400, then gRd = gA, as described in section 9
C203 |
| — | in all other cases gRd = 1.0. |
Sec.6 C
203 The maximum strain criterion shall be checked in all n directions parallel to the fibres,
and for tensile and compressive strains.
Sec.6 C
204
kfibre is
the time dependent characteristic strength of the ply in fibre direction.
It shall be determined according to section 4C. One value for one
fibre and weave type.
Sec.6 C
205 For N combined loads, with combination j being the worst combination
(see section 3 K200) the maximum strain design criterion is given
by:
where,
| eink | Characteristic value of the local response of the structure
(strain) in the fibre direction - n - due to load - i - |
| Characteristic value of the axial strain to fibre failure |
| giF | Partial load effect factor for load - i - |
| Yi | Combination factor for load - i - |
| gjF , | Partial load effect and resistance factors for load - j - |
| gM | Partial resistance factor |
| gRd | Partial resistance-model factor, given in 202 |
Sec.6 C
206 The partial resistance factor gM shall be the largest value for
all load strength combinations - j -.Guidance note:
In the equation above, it is important to see that the partial
resistance factor gjM , corresponding to the load
j alone, is used as the common partial resistance factor.---e-n-d---o-f---G-u-i-d-a-n-c-e---n-o-t-e---
Sec.6
C 300 Fibre failure check using a modified
Tsai-Wu criterion
Sec.6 C
301 In many cases the maximum fibre strain criterion is not available
in commercial software packages. As an alternative the Tsai-Wu criterion
may be used with modified input parameters as described here. This
approach was developed by FiReCo AS.
Sec.6 C
302 If C105 is relevant, this criterion may be used to check simultaneously
for fibre failure and laminate failure due to high shear in the
plies.
Sec.6 C
303 The Tsai-Wu criterion is described in 3-D as:
in 2-D:
with
R = g F · g Sd · g m · g Rd
where,
| n | the co-ordinate system is the ply co-ordinate system, where
n refers to the directions 1, 2, 3, 12, 13 and 23 |
| sn | characteristic value of the local load effect of the structure
(stress) in the direction n |
| characteristic tensile strength in the direction n |
| characteristic compressive strength in the direction n |
| characteristic shear strength in the direction nk |
| gF | partial load effect factor |
| gSd, | partial load-model factor |
| gM | partial resistance factor |
| gRd | partial resistance-model factor, for values see 303. |
Sec.6 C
304 The interaction parameters
,
,
should be determined experimentally
for each material. In that case gRd = 1.0.
Alternatively values between 0 and -0.5 may be chosen as a default,
in that case gRd = 1.15.
Sec.6 C
305 Since Tsai-Wu criterion is here only used to check for fracture
of the laminate (see C105) and
small matrix cracks are acceptable, strength properties should be
taken as described below. Characteristic strengths as described
in section 4 B 400 should always
be used.
| tensile ply strength in fibre direction, as defined in section
4. |
| compressive ply strength in fibre direction, as defined in
section 4. |
| modified inplane tensile ply strength transverse to the fibres. |
| modified inplane compressive ply strength transverse to the
fibres. |
| tensile through thickness ply strength in fibre direction,
as defined in section 4. |
| compressive through thickness ply strength in fibre direction,
as defined in section 4. |
| inplane shear strength, as defined in section 4. |
| through thickness shear strength , as defined in section 4. |
| through thickness shear strength, as defined in section 4. |
Sec.6 C
306 If tensile and compressive fibre strength differ by more than
60% it should be checked that the individual design criteria,
i.e. fibre failure in C200 and
matrix cracking in D200 or D300,
do not give lower allowable stresses than this criterion.
Sec.6 C
307 The characteristic strength
for each of the stress components snk and the corresponding coefficients
of variation COVn are
defined as specified in Section 4 A600.
Sec.6 C
308 The combined COVcomb of
the characteristic strength
is
defined according to one of the following alternatives. The second
alternative is conservative with respect to the first.
or
COVcomb = maxn (COVn )
where,
| n | the co-ordinate system is the ply co-ordinate system, where
n refers to the directions 11, 22, 33, 12, 13 and 23 |
| COVn | COV for stress component - n - |
| COVcomb | COV for the combined stress components |
Sec.6 C
309 When two or more loads are combined, each stress component snk in direction n can be the
result of several combined loads. In that case each stress component snkj,
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
COVcomb. = maxn (COVn )
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.---e-n-d---o-f---G-u-i-d-a-n-c-e---n-o-t-e---
Sec.6 C
310 The choice of the partial safety factors shall be based on the
most conservative partial safety factors obtained when treating
each stress component snkj , which is the local load effect
of the structure in direction n due to load j, as a single load.
Sec.6 C
311 The partial safety factors gF and gM shall be chosen as described
in section 8 with COVs equal to COVcomb,
as described in 308 and 309.Sec.6
C 400 Special considerations for fibre
failure under inplane compressive loads
Sec.6 C
401 The orientation of matrix cracks shall be checked if the compressive
strength of a laminate is important (D400).
Sec.6 C
402 If matrix cracks with an orientation of 30o-60o relative to
the plane of the laminate may be present, the compressive strain
to fibre failure used in the design criteria of this section shall
be obtained from measurements on laminates with the presence of
matrix cracks with an orientation between 30o and 60o. Alternatively, the compressive
strain to failure may be reduced by 50%, or a component
test shall be carried out (C500).Sec.6
C 500 Fibre failure checked by component
testing
Sec.6 C
501 Refer to section on component testing (section 10)Sec.6
C 600 Fracture mechanics approach
Sec.6 C
601 The fibre design criteria described above can always be used.
However, in the presence of stress concentrations that reach infinity
a fracture mechanics approach may be applied.
Sec.6 C
602 Stress concentration can be caused by the following factors:| — | cut-outs |
| — | discontinuous linear and smooth geometry (including rough
edges) |
| — | joints which include bolted joints, bonded joints, and
other mechanical joints |
| — | mismatch of elastic properties between two adjacent
components or materials |
| — | voids and damage due to material fabrication. |
Sec.6 C
603 Unidirectional laminates should never be used in the presence
of infinite stress concentrations, because matrix cracks and delaminations
can propagate from that point through the structure with nearly
no resistance.
Sec.6 C
604 In the presence of infinite stress concentrations matrix cracking
and delamination will occur. If that is not acceptable on a local
level, the design shall be changed to remove the stress concentration.
Sec.6 C
605 The suggested design criterion is the point stress criterion:
Failure occurs when the stress or strain at a distance d0 away from the tip of the stress
concentration point is equal to or greater than the strength of
the un-notched material, see Figure 3. This means the design
criteria described above shall be applied at a distance d0 away from the stress concentration point.
Fig. 3 Point Stress Criterion.
Sec.6 C
606 The distance d0 has
to be determined experimentally for the laminate in question.
Sec.6 C
607 The stress field ahead of the stress concentration point may
be calculated by analytical or FE methods.
Guidance note:
For an infinite orthotropic plate, with a circular hole, subjected
to a uniform stress, sx¥, applied parallel
to the x-axis at infinity, the normal stress, sx, along the y-axis ahead of
the hole, see figure 4 below, can be expressed as:
where
Fig. 4 Infinite plate with a circular hole
For an infinite orthotropic plate, with a crack, subjected
to a uniform stress, sx¥ , applied parallel
to the x-axis at infinity, the normal stress, sx, along the y-axis ahead of
the crack tip, see the Figure 5, can be expressed as:
Fig. 5 Infinite plate with sharp crack
The equations above are valid for infinite plates. For finite
plates, it is necessary to add a Finite Width Correction (FWC) factor. There
are several analysis methods, including finite element methods,
to determine the FWC factor.
---e-n-d---o-f---G-u-i-d-a-n-c-e---n-o-t-e---
Sec.6 C
608 If certain damage is expected to be present in the structure
at various points that can cause stress concentrations, the structure
shall be analysed by modelling the presence of this damage. The
damage shall be placed into the structure in a representative and
conservative way.
Sec.6 C
609 As an alternative to analysing the structure with various points
of damage the structure can be analysed with a reduced strength
that represents the damage. All strength values used in the design
criteria shall be based on measurements from damaged laminates (see section 4 A700).
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