in [1], which only provides default equations for the in- plane modulus.


It is now necessary to make some pretty sweeping assumptions in order to produce usable results


from


equation (5). This is acceptable, since these results will be subsequently compared with experimental results. The assumptions made are:


 Subscript t (denoting tension) may be understood to mean tension or compression, whichever is the most onerous


 Vf = Vt (this means the size of flexural and tensile coupons are possible)


 t2/t1 = 8 (test coupons are assumed to be made up of at least 8 plies)


Equation (5) now reduces to: 


ply  in plane  16( 1)} 1/ (6)


Where ply is the apparent strain to be used in a stack analysis and in-plane is the smaller of the tensile and compressive strain obtained from UTS/E or UCS/E as published in Annex C of [1].


At this stage, the analysis and experimental scope is limited to 0-90 continuous fibres in E-glass, carbon and aramid. All E-glass CSM/WR mixes are least onerously handled using equation 2a using the flexural strength formula already provided in Annex C [1].


Double-


bias/quad-axial plies involve angle plies which are starting to stretch the validity of the simple laminate stack method outlined in Annex H [1]. Over the range of suitable fibre content by mass, the minimum in-plane failure strain for 0/90 cloths is about 1.1% (E-glass), 0.6% (carbon), 0.5% (aramid). Equation (6) lacks only the  term. These were obtained from solving:


   


f {2( 1) } t


21/ (7)


where the flexural to compressive stress ratio was taken from published [1, 4] and private data. The  factors were found to be E-glass – 16, carbon 7, aramid 9. Using these results with equation (6), the thin-ply failure strain was found to be as given in Table 1.


Fibre


E-glass Carbon Aramid


Apparent ply failure strain 1.6% 1.2% 0.9%


Table 1: Apparent failure strains from simplistic analysis


Table 2 shows the comparison between the failure moment per unit width using the two methods currently


similar – no other assumption is


in [1] for a range of fibre contents representing a total of 6000 gsm of CSM and/or WR in polyester resin, i.e. (Eqn (2b) with UFS and Eqn(1) with the minimum of the two in-plane strength. The final column corresponds to the use of equation (1) with the modified apparent ply failure strain, calculated as follows: total glass mass of 6000 gsm of glass, 50% fibre. t = 7.34mm. E = 14000 Mpa (from [1].


MFPF = 14000 x 7.343/12 x 0.016 / 3.67 = 2013 Nmm/mm


Fibre


content 0.45


0.50 0.55 0.60


Failure bending moment (Nmm/mm)


Eqn (2b) Eqn (1) with Eqn(1) with with UFS min(UCS/UTS) 2486 2090 1786 1546


1662 1321 1066 870


1.6% strain 2307 2013 1756 1530


Table 2: Comparison of failure moments


Table 2 shows that the use of the apparent failure strain of 1.6% for glass does give tolerably close agreement between the two alternative procedures (laminate stack equation (1) v flexural strength, equation (2b)). This is encouraging


foregoing derivation. The current procedure from Annex H [1] gives much lower values.


that the two different methods employed in ISO 12215-5 should be eventually brought into alignment. This is in no sense a criticism of [1] which in common with most classification society rules and guides, require a period of re-evaluation following harmonisation.


although by no means proof of the It is surely desirable


Unfortunately,


standard developers do not enjoy the luxury of producing a ‘tentative rule’ as has been done in the past by a number of leading class societies.


As a further check before embarking on empirical verification, one class society [9] appears to use an apparent strain of 1.7% (all fibres in polyester), 2.5% (glass and aramid in epoxy) and 1.25% for carbon in epoxy. Quite why the failure strain should be resin- dependent to this extent or


indeed much higher interpretation has been checked out for


carbon and polyester than carbon and epoxy is unclear given that normal practice is to ensure that failure strains of the resin exceed that of the fibres by a good margin. This


using the


software available from the society. However, there may still be some misinterpretation on the part of the author and taking lower-bound values of 1.25% for carbon and 1.7% for glass would certainly broadly agree with the above figures of 1.2% and 1.6%. Some caution is needed here as the factor of safety employed in [9] are significantly higher than those used in [1], although this may be more to do with load assumptions rather than material properties.


The author appreciates that a number of gross


simplifications have been made in the analyses thus far. Apologies are tended to any reliability theory experts.


B-34 © 2008: Royal Institution of Naval Architects


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