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NUMERICAL PROBLEMS (15 points each) 21. A hybrid composite material is made up of 20% HS carbon fibers (ρ = 1800 kg/m3) by weight and 30% E-glass fibers (ρ = 2540 kg/m3 ) by weight in an epoxy matrix. If the density of the epoxy is 1300 kg/m3, calculate the density of the composite. 22. A plastic beam of rectangular cross-section is subjected to a steady bending moment of 1 Nm and simultaneously to an alternating bending moment of 0.75 Nm. a) Calculate the necessary beam thickness, d, (b = 2d) so as to avoid fatigue failure (the factor of safety is to be 2.5). The fatigue limit for the material in reversed bending is 25 MN/m2 and the creep rupture strength at the equivalent time may be taken as 35 MN/m2. b) Calculate also the beam thickness if the fatigue strength reduction factor is to be taken as 2. 23. A series of impact tests on PVC specimens with a range of crack depths gave the following 4 5 results: Crack length (mm): 1 2 3 Fracture Energy (mJ): 200 124 93 74 62 If the sample section is 10 mm x 10 mm and the support width is 40 mm, calculate the fracture toughness of the PVC. The modulus of the PVC is 2 GN/m2. 24. An aircraft component is fabricated from a polymer that has a plane strain fracture toughness of 60 MPa.m1/2. It has been determined that fracture results at a stress of 450 MPa when the maximum (or critical) internal crack length is 6.0 mm. For this same component and material, will fracture occur at a stress level of 390 MPa when the maximum internal crack length is 9.0 mm? Why or why not? Some useful information b = 2d wf wc a C B P Gc δ δ 2 2 = P P

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