tailieunhanh - Plastics Engineering 3E Episode 8

Tham khảo tài liệu 'plastics engineering 3e episode 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mechanical Behaviour of Composites 229 Now for equilibrium of forces F1 F2 F3 ơf jỉd2 4 ơf tdx nd2 4 rnd dx dx J d 4 dơf -Tydx Integrating this equation gives f r dị4 I dơf - I Tydx 0 ỉe 4ry if x 7 ------ This is the general equation for the stress in the fibres but there are 3 cases to consider as shown in Fig. Fig. Sbess variations in short fibres 230 Mechanical Behaviour of Composites a Fibre lengths less than lt In this case the peak value of stress occurs at X 0 so from equation 2ry ơ d The average fibre sữess ơf is obtained by dividing the area under the stress fibre length graph by the fibre length. Now from ơf Tyt d ƠC Vf ơ m Vf b Fibre length equal to It In this case the peak sưess is equal to the maximum fibre stress. So at X 0 v 2rv Of ơ max - Average fibre stress ơf 1 2Tyit 2 d It So from c Fibre length greater than It i For ụ X i - it fTt 4ry ơf d ii for - X 0 ơf constant oy max 2Xyit ơf d Mechanical Behaviour of Composites 231 Also as before the average fibre stress may be obtained from _ _ 07 max - t v max 2 r 1 1 Of --------J------------- Kơ max Ự - Yi So from i er X . . _ 7 V ơ max Ự 0 - v Note that in order to get the average fibre stress as close as possible to the maximum fibre stress the fibres need to be considerably longer than the critical length. At the critical length the average fibre stress is only half of the value achieved in continuous fibres. Experiments show that equations such as give satisfactory agreement with the measured values of strength and modulus for polyester sheets reinforced with chopped sưands of glass fibre. Of course these sưengths and modulus values are only about 20-25 of those achieved with continuous fibre reinforcement. This is because with randomly oriented short fibres only a small percentage of the fibres are aligned along the line of action of the applied stress. Also the packing efficiency is low and the generally accepted maximum value for Vf of .

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