Mechanical Behavior of Composite Materials

Abstract

This closing chapter presents the qualitative and quantitative aspects of the mechanical behavior of composites. A classification chart of composite materials is first presented followed by a discussion on the various types of composites with particular reference to fibrous composites. The physical and mechanical properties of carbon fiber reinforced polymer (CFRP) composites are tabulated with emphasis on their applications in aerospace industry. Mechanical behavior of fibrous composites are discussed involving engineering analyses for unidirectional continuous fiber composite under longitudinal loading as well as under transverse loading. Additionally, Poisson’s ratio and shear modulus calculations for composites are included. Finally, the mechanical behavior of particulate composites are mathematically modeled and the relevant problems are solved. This chapter contains 15 worked examples (solved problems), 7 diagrams, 19 mathematical models/formulae, 8 exercise problems, and 3 MCQs with answers.

Questions and Problems

• 15.1. Draw the classification chart of composite materials.

• 15.2. What are the roles of matrix material and reinforcing material in a composite?

• 15.3. Draw diagrams showing various composites based on reinforcing material structures.

• 15.4. Draw diagrams showing various fibrous composites.

• 15.5. Why are CFRP composites extensively used in aerospace structures?

• 15.6. Differentiate between iso-strain condition and iso-stress condition with the aid of diagrams.

• 15.7. Derive Eq. 15.6.

• 15.8. The Young’s modulus of aluminum alloys is 70 GPa and the density is 2.73 g/cm³. Compute and compare the specific moduli of aluminum alloys and CFRP.

• 15.9. The tensile strength of a glass fiber is 3400 MPa, and its diameter is 13 μm. The adhesive bond strength of epoxy is 22 MPa. Calculate the critical fiber length to produce the composite.

• 15.10. A GFRP composite has 45% by volume of unidirectional continuous glass fibers with a Young’s modulus of 70 GPa and a tensile strength of 3480 MPa; and an epoxy matrix with a modulus of 2.4 GPa and a tensile strength of 54 MPa. A tensile stress of 70 MPa is applied in the longitudinal direction over an area of 280 mm² of the composite. Calculate the (a) Young’s modulus of the composite under longitudinal loading, (b) force carried by the fibers and by the matrix, (c) stresses for each of the fibers phase and the matrix, (d) strains for each of the fibers phase and the matrix, (e) tensile strength of the composite under longitudinal loading, and (f) Young’s modulus the composite under transverse loading.

• 15.11. A fibrous composite contains 60% by volume of fibers with a Poisson’s ratio of 0.26. The Poisson’s ratio of the matrix is 0.41. The modulus of elasticity of the composite measured in direction 1 is 32 GPa, and that measured in direction 2 is 4.2 GPa. Calculate the Poisson’s ratio of the composite measured in 1–2 plane.

• 15.12. By using the data in Problem 15.10, calculate the in-plane shear modulus for each of the fibers and the matrix phases. The Poisson’s ratios of the fiber is 0.22 and that of matrix is 0.44.

• 15.13. A fibrous composite has 57% by volume of unidirectional continuous fibers with a shear modulus of 92 GPa. and a matrix with a shear modulus of 1.5 GPa. The Poisson’s ratios of the fibers and the matrix are 0.20 and 0.36, respectively. Calculate the modulus of elasticity of the composite under longitudinal loading.

• 15.14. An epoxy-matrix composite contains 40 wt.% glass beads with a particle size of 0.05 mm. The tensile strength of the matrix is 107 MPa. Calculate the: (a) inter-particle spacing, and (b) tensile strength of the composite. Take the constant S = 1.5 × 10⁻³ MPa∙m.

• 15.15. The Young’s modulus of nylon-6 nano-composite is 2.5 GPa. The composite contains silica particles with a volume fraction of 0.30 and with a particle size of 90 nm. Calculate the Young’s modulus of the polymer matrix in the composite.

• 15.16. (MCQs). Encircle the correct answers for each of the following questions. (a) Which of the following materials possesses the highest specific modulus? (i) GFRP, (ii) CFRP, (iii) steel, (iv) aluminum (b) What should be the critical fiber length-to-diameter ratio for a fibrous composite? (i) 100–150, (ii) 20–110, (iii) 10–80, (iv) 30–140 (c) Which type of composite corresponds to concrete? (i) particulate, (ii) fibrous, (iii) laminate, (iv) none