M425 Midterm 2010.pdf - Manufacturing of composites MECH...

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1 Manufacturing of composites MECH 425/MECH 6521 Solution Mid term exam - October 15-2010 Closed book- 2 hours Student name:____________________________ Student ID:______________________ Question 1: (5 marks) The table below gives some of the properties of glass fibers, carbon fibers and epoxy matrix. (Values in the table can be used for all problems in this exam). Diameter (µm) Strength (MPa) Strain limit (%) Density (g/cm3) S glass fibers 10 4544 4 Carbon fibers 7 3280 1.4 Epoxy 1.2 The fibers are bent to a radius of curvature of 5 mm. Determine whether the glass fibers or the carbon fibers will break. 2.5 1.8 3 3 Question 2: (5 marks) The following figure shows the axial stress and shear stress acting on an S glass fiber in a matrix environment. If the shear strength between the matrix and fiber is 20.5 Mpa, determine the minimum fiber length such that failure will occur in the fiber, rather than slipping at the interface.
2 ) 2 / )( 2 )( ( ) )( ( 2 L r r π τ π σ = τ σ 2 d L = m x Pa x m x Pa x L 5 6 6 Question 3: ( 5 marks) Assuming that the fibers in matrix in a glass fiber composite follow the square array as shown in the figure below. For a volume fraction of 68%, determine the amount of interface area in a unidirectional composite with thickness of 2 mm, length = 20 cm, width = 5 cm.
3 Interface area in a unit cell = L d π Volume fraction: cell f V d L V 4 2 π = or f cell V d L V 4 2 π = Number of unit cells in the given composite: cell V V n = Total amount of interface area A interface : d V V d L V L d V L d V V L d n f f cell 4 4 2 = = = π π π π 2 6 3 5 int 44 . 5 ) 10 10 ) 10 2 )( 68 . 0 )( 4 ( m m x m x A rface = =

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