Assignment #1 Due Date 22 September 2009; 5PM Group I: Odd questions, Group II : Even questions

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1 Assignment #1 Due Date 22 September 2009; 5PM Group I: Odd questions, Group II : Even questions 1. A burnout test was performed to determine the volume fraction of constituents in a glass-fibre- reinforced epoxy composite. The following observations were made Weight of empty crucible = g Weight of crucible and a small piece of composite = g Weight of crucible and glass after the burnout = g Calculate the weight and volume fractions of glass fibers and epoxy resin. Assume that the densities of the fibers and resin are 2.5 and 1.2 respectively. Calculate the density of the composite using weight fractions and densities of the constituents. If the density was experimentally determined to be 1.86, calculate the void content in the composite. 3.1&2 2. Calculate the ratios of fiber stress to matrix stress and fiber stress to composite stress for unidirectional composites with = 10, 25, 50, and 75%. Assume that the composites are loaded in the fiber direction; =400 GPa and = 3.2 GPa Estimate,, and of glass-epoxy, graphite-epoxy, Kevlar-epoxy, and boron-aluminum composites with = 25,50, and 75%. Constituent properties are Material E (GPa) v Epoxy Glass fibers Graphite fibers Kevlar fibers Boron fibers Aluminum For the purpose of calculations assume all fibers to be isotropic

2 4. A rod consists of a binder and two types of filamentous reinforcement with the following constituent properties Material Density( ) Wt. % E (GPa) (GPa) Binder Fiber A Fiber B (a) What maximum load can this rod carry without rupturing any of the constituents? (Assume cross-sectional area of the rod =10.) (b) What is the maximum load the rod can carry? (c) What constituent will rupture last? (d) Plot the load-elongation curves for the rod to failure in load maintained and elongation maintained tests Two composites are fabricated with glass fibers ( = =50%) and matrices A and B whose stress-strain curves are shown in Fig.1. The glass fibers are elastic up to failure and have an elastic modulus of 70 GPa and ultimate tensile strength of 2.8 GPa. Assuming that the composites are stressed parallel to the unidirectional glass fibers, calculate (a) the composite stress at 1 and 4% strains for each composite and (b) the minimum and critical fiber volume fractions for both composites. (c) Draw the stress-strain diagrams for the two composites. (d) Calculate the longitudinal strengths of the composites. 3.6 & 3.7 Fig 1. : Stress-strain curves of matrices A and B 6. The material of a tension link is changed from an aluminum alloy to a unidirectional graphite-epoxy composite. Calculate the volume fraction of graphite fibers required in the composite to match its longitudinal modulus with that of the aluminum alloy. What is the percentage weight saving in this material replacement? The elastic modulus of epoxy is 3.5 GPa and its density is 2. Estimate the longitudinal strength of the composite by neglecting the load carried by epoxy. Use the properties given below 2

3 Material E (GPa) Strength (GPa) Density ( ) Aluminum alloy Graphite fibers Kevlar fibers & The material of a tension link is changed from an aluminum alloy to a unidirectional Kevlar-epoxy composite. Calculate the volume fraction of Kevlar fibers required in the composite to match its longitudinal modulus with that of the aluminum alloy. What is the percentage weight saving in this material replacement? The elastic modulus of epoxy is 3.5 GPa and its density is 2. Estimate the longitudinal strength of the composite by neglecting the load carried by epoxy. Use the properties given below Material E (GPa) Strength (GPa) Density ( ) 3.10 Aluminum alloy Graphite fibers Kevlar fibers A unidirectional glass-epoxy composite has / =1.5. What minimum volume fraction of carbon fibers should be added to the glass-epoxy composite, without changing the ratio of volume fractions of epoxy resin and glass fibers, to obtain any strengthening? Following are the constituent properties. Material Density (g/ ) E (GPa) (MPa) Epoxy resin Glass fibers Carbon fibers While maintaining the matrix volume fraction at 30%, addition of what volume fraction of carbon fibers will double the longitudinal modulus of a unidirectional glass-epoxy composite? What is the percent reduction in density by this addition of carbon fibers? Also, calculate the longitudinal strengths of the two composites. Take the constituent properties as Material Density (g/ ) E (GPa) (MPa) Epoxy resin Glass fibers Carbon fibers

4 Explain why the composite strength decreases even though the strengths of carbon fibers and glass fibers are equal A unidirectional composite shows the following properties in tension: =40GPa = = l0gpa = =O.25 Estimate longitudinal compressive strength of the composite. Assume composite moduli to be equal in tension and compression The coefficient of longitudinal thermal expansion of a unidirectional composite is measured as x /.Estimate the coefficient of thermal expansion of the fibers. Given: =294GPa, = 3.5 GPa, = 54x /, and = 55% The maximum water absorption in a typical epoxy is 6%. What is the maximum amount of water in a graphite-epoxy composite ( =70%)? Assume that graphite fibers do not absorb moisture and the specific gravities of epoxy and composite are 1.2 and 1.6, respectively Longitudinal axis of an orthotropic lamina makes an angle of 45 with the x axis. It is subjected to the following stresses: =20MPa, =0, = 20 MPa (a) Draw a neat sketch of the lamina indicating x, y, L, and T axes. Also show the applied stresses.(b) Calculate stresses along longitudinal and transverse directions. (c) Does the lamina fail under these stresses? Use the maximum work theory to predict failure and take the following strength values for the lamina: =500 MPa = l0mpa =350 MPa =75MPa, =35MPa (d)will your answer change if the direction of applied shear stress is reversed? 5.16a 14. Calculate, E y,,,, and at 30, 45, and 60 for an orthotropic lamina having the following properties: =14 GPa, =3.5 GPa =4.2 GPa = Plot the variation of, E y,,,, and for a lamina with the following properties: =35 GPa =3.5 GPa =4 GPa, = Verify that the elastic constants given in below equation are actually zero for a material that has the plane as a plane of symmetry. 1113,E 2223 E 1123, E 2213, E 1213, E 1223, E 1333, E 2333, 5.1 E 4

5 17. Verify that the elastic constants given in below equation are actually zero for a material that has the plane as a plane of symmetry. E 1233,E 1323 E 1222, E Obtain the stiffness and compliance matrices for a unidirectional lamina that has the following elastic constants: =20GPa, = 2 GPa, = 0.7 GPa = Following are the experimentally observed elastic constants of a boronepoxy composite: =81.7 GPa =9.1GPa, =1.97, = Determine whether the data satisfy the constraints on the elastic constants of an orthotropic material. Comment on the large value of n LT. Will it be an admissible number for the Poisson ratio of an isotropic material? 20. Calculate the Q matrix at 30, 45, and 60 for a lamina whose Q matrix is given by Derive expressions for, and by assuming that is the only nonzero stress acting on the lamina shown in following figure 2. Fig 2 : Generally orthotropic lamina Derive expressions for and by assuming that is the only nonzero stress acting on the lamina shown in above figure A graphite-epoxy lamina shows the followings strength properties: = 1725 MPa =40MPa = 1350 MPa = 275 MPa, = 95 MPa Using the maximum work theory of failure, estimate off-axis shear strength of the lamina for orientations of 30 and

6 24. A tensile specimen of a unidirectional composite with a rectangular cross section of dimensions12.5 mm x 4 mm has the fibers oriented at 45 to a longitudinal edge of the specimen. It is subjected to an axial force of 500 N. (a)calculate normal strains in the axial and perpendicular directions and shear strain on the specimen. Properties of the composite in the L and T directions are given as =14 GPa =3.5 GPa =4.2 GPa =0.4 (b)calculate off-axis modulus. the Poisson ratio, and cross-coupling coefficient for this specimen Longitudinal axis of an orthotropic lamina makes an angle of 30 with the x axis. It is subjected to the following stresses: =20MPa, =0, = 20 MPa (a) Draw a neat sketch of the lamina indicating x, y, L, and T axes. Also show the applied stresses. (b) Calculate stresses along longitudinal and transverse directions. (c) Does the lamina fail under these stresses? Use the maximum work theory to predict failure and take the following strength values for the lamina: =500 MPa = l0mpa, =350 MPa =75MPa, =35MPa, (d)will your answer change if the direction of applied shear stress is reversed? 5.16b 26. Plot the variations of, E y,,,,, and for a balanced lamina with the following properties: = =15GPa, = 2.5 GPa, = = A tensile specimen of a unidirectional composite with a rectangular cross section of dimensions12.5 mm x 4 mm has the fibers oriented at 30 to a longitudinal edge of the specimen. It is subjected to an axial force of 500 N. (a)calculate normal strains in the axial and perpendicular directions and shear strain on the specimen. Properties of the composite in the L and T directions are given as =14 GPa =3.5 GPa =4.2 GPa =0.4 (b)calculate offaxis modulus. the Poisson ratio, and cross-coupling coefficient for this specimen. 5.14b 6