The flexural strength for single skin is usually obtained from the standard three-point bending test and applies only to a specific laminate. So although equation 2a appears useful in that it directly gives the required panel thickness, this only works in practice for certain types of quasi-homogeneous (through the thickness) layups, such as the commonly used alternate plies of chopped strand mat (CSM) and woven roving (WR). If a designer wishes to investigate the effect of placing stiffer, stronger plies towards the extreme fibres, the laminate stack approach is the only method available without recourse to laboratory tests.
For reasons that will be discussed later, the flexural strength is often significantly greater than the tensile strength or the compressive strength. For example, using the ISO default data in Annex C of [1] for a typical all CSM, mixed CSM/WR laminate or all WR (all with polyester), the flexural strength would be about 1.47 and 1.42 times the tensile and compressive strengths respectively.
Analysis of 84 E-glass (various resins)
laminates [4] indicated a flexural:tensile ratio of 1.64 and flexural:compressive ratio of 1.55 on average.
The failure moment obtained from a laminate stack analysis based on in-plane properties would be governed by the smaller of the tensile or compressive strengths of the plies. A typical quasi-homogeneous lay up consisting of ‘n’ identical plies (e.g. CSM/WR) would need to be about 20% thicker than one analysed using the measured flexural strength according to [2a], since the thickness ratio (laminate stack method compared with flexural strength method) would be
equal to flexural
strength/minimum of tensile or compressive strength. Now, this
does not matter when the two design
procedures are entirely separate and use design method- specific stress factors and/or pressures. Some rules use either the stack or equation 2a. However, the ISO scantling standard admits both methods with the same stress factor of 0.5 and design pressure and hence this discrepancy is at least worthy of further debate.
2. FLEXURAL PROPERTIES V IN-PLANE PROPERTIES
Strength prediction of composites is essentially a reliability calculation. The greater the number of imperfections and the more
uniform is the stress
distribution, so the greater probability of a highly stressed zone coinciding with a zone of weakness and hence the lower the strength.
2.1 PLY THICKNESS EFFECTS
The probability of encountering a flaw is often dependent on the sample size. A flaw in this context might mean a zone of poor resin-fibre bond (it is probably in this area that the resin properties exercise greatest influence), fibre
‘out of
material properties.
alignment’ or spatial variation in the parent This
size’.
is well understood by
designers of wood structures where a distinction is made between properties obtained from small, clear samples and those of ‘structural
‘The structural-sized
specimens contain defects such as knots and distorted grain which result in appreciable loss in strength, though only a slight effect on modulus of elasticity’ [5]. This effect is formally characterized in timber design codes [6]. For solid wood, the strength may be increased from the standard value for a 150mm deep sample by a factor of (150/h)0.2, giving a 25% increase for a 50mm deep sample, where h is consideration.
the depth of the member under
Some investigators [7, 8] have attempted to derive tensile properties from flexural tests by means of a Weibull based reliability analysis.
Their work indicates that
tensile strength depends on coupon thickness, i.e. that ‘thin specimens will have a higher characteristic strength compared with thick specimens’ [8]. The derived relationship from [8] is shown below:
t1 2
t21
t t
1/ (3)
Where, t1 and t2 are the sample thickness and is the Weibull shape parameter (given as 15-25 for glass and carbon unidirectionals respectively).
Now a single ply in a laminate stack may be about 0.4- 1.5mm thick.
tensile or compressive test.
This is too thin to test in isolation in a Taking 8 plies as a more
realistic coupon size*, then the in-plane strength used in a laminate stack analysis ought to be about 8-15% greater than the ‘thick-coupon’ test value.
*The author prefers to test at about 4mm, which is about mid-range of thickness given by various standards.
2.2. EFFECT OF NON-UNIFORM STRESS DISTRIBUTION
A second issue is that in a standard tensile/compressive strength test, all parts of the coupon are equally stressed (see Figure 1 – upper).
only a zone at mid-span, close to
In a three-point bending test, the surfaces
experiences the peak stress, most of the material being stressed to a very low level (see Figure 1 – lower). The chances of this highly-stressed zone coinciding with a zone of weakness are very much less than in the tensile load case. The relationship between flexural (f) and tensile strength (t), based on a Weibull reliability analysis, again from [7, 8] is:
ff tt
2
2( 1)
V V
1/ (4)
B-32
© 2008: Royal Institution of Naval Architects
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