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MECHENG 743 City MECHANICAL ENGINEERING
创建日期：2024-04-13 15:49:57
标签： MECHENG 743
City MECHANICAL ENGINEERING

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MECHENG 743

Campus: City MECHANICAL ENGINEERING Composite Materials 

(Time Allowed: THREE hours) NOTE: Attempt any FIVE questions. All questions carry equal marks. The marks allocated to parts of questions are indicated. A list of formulae is given in the APPENDICES BOOKLET. MECHENG 743 Page 2 of 7 1. (a) (i) Define the state of plane stress. (ii) What are the conditions that allow the assumption of a plane stress state? (4 marks) (b) Cylindrical fibres in an idealised unidirectional, continuous fibre-reinforced composite material may be packed either in a square or a hexagonal pattern. Both cross-sectional arrangements are shown in Figure 1. S S d S d S Figure 1 (i) Determine the fibre volume fraction of the composite material in each case as a function of the fibre-to-fibre spacing between the centres of the fibres, S and the fibre diameter, d. (ii) If cylindrical carbon fibres of 10 µm diameter are packed in epoxy in both of the arrangements shown in Figure 1 and the fibre volume fraction of the composite is 0.5, calculate the fibre-to-fibre spacing between the centres of the fibres in each case. (8 marks) MECHENG 743 Page 3 of 7 (c) A unidirectional, continuous fibre-reinforced composite lamina is subjected to the stresses shown in Figure 2. σ11 σ22 τ12 Figure 2 (i) Derive the compliance coefficients in the material coordinate system for the lamina as functions of the engineering constants. (ii) The composite lamina shown in Figure 2 has the following compliance coefficients in the material coordinate system: S11 = 4.15x10-12 Pa-1; S12 = S21 = -1.25x10-12 Pa-1; S22 = 41.5x10-12 Pa-1; S66 = 96.7x10-12 Pa-1 Find the engineering constants of the lamina. (8 marks) 2. (a) (i) Describe briefly the meaning of the term “prepreg material”. (ii) Why are prepregs typically used in the production of high-performance composites? (4 marks) (b) Two unidirectional, continuous fibre-reinforced composite materials consist of the same matrix but different fibres; both composite materials have a fibre volume fraction of 0.5. In the first case, Ef /Em = 50 and in the second case, Ef /Em = 25. (i) In each case, find the ratio of the tensile modulus parallel to the fibres to the tensile modulus perpendicular to the fibres. (ii) Compare the calculated ratios and briefly discuss your conclusions. (8 marks) (c) (i) A short fibre-reinforced composite, consisting of completely aligned fibres is loaded in a direction parallel to the fibres. Show that the tensile strength of the composite in the direction of the fibres is given by when the length of the fibres, l, is greater than the fibre critical length, lc. (1 ) 2 v vcc fu f m m l l σ σ σ ′= − + MECHENG 743 Page 4 of 7 (ii) A carbon fibre-polycarbonate composite consists of completely aligned, short fibres of diameter 7 µm; the volume fraction of the fibres in the composite is 0.4. The tensile strength of the fibres, shear strength of the fibre- matrix interface, and the stress in the matrix at the failure strain of the fibres are 2.5 GPa, 12.5 MPa and 30 MPa, respectively. Calculate the critical fibre length. For the specific case in which the length of the fibres in the composite is ten times the critical fibre length, estimate the tensile strength of the composite in the direction of the fibres. (8 marks) 3. A composite laminate, constructed from identical continuous fibre-reinforced laminae made of E-glass fibres and epoxy, has the stacking sequence: [45º/-45º/45º/-45º/0º/0º/-45º/45º/-45º/45º]. Each lamina, of 0.125 mm thickness, has the following engineering constants: E11 = 40 GPa; E22 = 9.8 GPa; G12 = 2.8 GPa; ν12 = 0.3. (a) Find the elements of the extensional stiffness matrix. (10 marks) (b) Calculate the in-plane Young’s moduli of the laminate in the X and Y directions of the global co-ordinate system. (10 marks) 4. The stress state in the critical lamina of a component made from a composite laminate has been calculated to be: σ1 = 550 MPa, σ2 = -175 MPa, τ12 = 0. The strengths of all laminae in the laminate are equal and are as follows: �1= 1000 MPa, �1 = 600 MPa, �2= 75 MPa, �2= 200 MPa, ̂12= 73 MPa. (a) Calculate the factor of safety against failure using the maximum stress failure criterion. (2 marks) (b) Calculate the factor of safety against failure using the Tsai-Hill failure criterion. (3 marks) (c) Calculate the factor of safety against failure using the Tsai-Wu failure criterion. (5 marks) (d) Sketch the approximate failure loci in the σ1-σ2 plane using both the maximum stress and the Tsai-Hill failure criteria. Indicate where the actual state of stress for the critical lamina is on the diagram. (4 marks) MECHENG 743 Page 5 of 7 (e) Show on the σ1-σ2 failure loci (that you have drawn for part (d)) where the stress state would be if the stresses in the lamina increased by 30%, and identify the resulting failure mode. Clearly differentiate it from the original stress state on the loci. (4 marks) (f) Illustrate with a sketch four different modes of failure initiation for a unidirectional composite under uniaxial tension. (2 marks) 5. A four point bending test is to be undertaken to determine the shear strength of a polymeric foam (SAN foam). A sandwich beam 60 mm wide is constructed for this purpose with facesheets made from a bi-axial E-glass/epoxy composite. 

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