Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Chapter 9, Problem 46QTP
A rectangular cantilever beam, 100 mm high, 20 mm wide, and 1 m long, is subjected to a concentrated load of 50 kg at its end. (a) Consider a polymer reinforced with high modulus carbon fibers, with a fiber volume ratio of x = 10%. What is the maximum deflection of the beam if the matrix material is polyester? (b) Obtain the deflection of the beam if aluminum or steel was used, for the same beam dimensions. (c) What fiber volume ratio is needed to produce the same deflection as the aluminum or steel beams? (d) Determine the weight of the beams considered in parts (b) and (c), and compare them.
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Students have asked these similar questions
For a glass/epoxy lamina with a 70% fiber volume fraction using the properties in the tables
provided below
(a) Find the ultimate tensile strength.
(b) Find the minimum and critical fiber volume fractions related to (a).
(c) Find the compressive strength when the matrix undergoes extension mode and when the
matrix undergoes shear mode, which one controls the compressive failure?
Property
Axial modulus
Transverse modulus
Axial Poisson's ratio
Transverse Poisson's ratio
Shear modulus
Axial tensile strength
Axial compressive strength
Transverse tensile strength
Transverse compressive strength
Shear strength
Epoxy Glass Units
3.4 85 GPa
3.4
85
GPa
0.3 0.20
0.3
0.20
1.308 35.42 GPa
72
1550 MPa
102
1550 MPa
72
1550 MPa
102
1550 MPa
34 35 MPa
Glass fibres provide longitudinal reinforcement for a nylon material subject to tensile load. The fibre diameter is 20 μm and the volume fraction is 0.45. (Take Young’s modulus of glass fibres as 70 000 MPa and nylon as 2800 MPa)(i)Calculate the Young’s modulus of composite(ii)Determine the tensile strength in the glass fibre if the tensile strength of the composites and matrix is 14 MPa and 11.8 MPa, respectively
What is the tensile strength of a composite fibre when its diameter is 20 microns and its
critical fibre length is 30 microns? The strength between the fibre and matrix is 150 MPa.
Chapter 9 Solutions
Manufacturing Engineering & Technology
Ch. 9 - Distinguish between composites and metal alloys.Ch. 9 - Describe the functions of the matrix and the...Ch. 9 - Name the reinforcing fibers generally used to make...Ch. 9 - What is the range in length and diameter of...Ch. 9 - List the important factors that determine the...Ch. 9 - Comment on the advantages and limitations of...Ch. 9 - What are the most commonly used matrix materials?...Ch. 9 - Describe the advantages of hybrid composites over...Ch. 9 - What material properties are improved by the...Ch. 9 - Describe the purpose of the matrix material.
Ch. 9 - What are the most common types of glass fibers?Ch. 9 - Explain the difference between a carbon fiber and...Ch. 9 - How can a graphite fiber be made electrically and...Ch. 9 - What is a whisker? What is the difference between...Ch. 9 - Describe the composition of boron fibers. Why are...Ch. 9 - Give a succinct definition of fiber, yarn, and...Ch. 9 - How do you think the use of straw mixed with clay...Ch. 9 - What products have you personally seen that are...Ch. 9 - Describe applications that are not well suited for...Ch. 9 - Is there a difference between a composite material...Ch. 9 - Identify metals and alloys that have strengths...Ch. 9 - What limitations or disadvantages do composite...Ch. 9 - Give examples of composite materials other than...Ch. 9 - Explain why the behavior of the materials depicted...Ch. 9 - Explain why fibers are so capable of supporting a...Ch. 9 - Do metal-matrix composites have any advantages...Ch. 9 - Give reasons for the development of ceramic-matrix...Ch. 9 - Explain how you would go about determining the...Ch. 9 - How would you go about trying to determine the...Ch. 9 - Glass fibers are said to be much stronger than...Ch. 9 - Describe situations in which a glass could be used...Ch. 9 - When the American Plains states were settled, no...Ch. 9 - By incorporating small amounts of a blowing agent,...Ch. 9 - Referring to Fig. 9.2c, would there be an...Ch. 9 - Calculate the average increase in the properties...Ch. 9 - In Example 9.1, what would be the percentage of...Ch. 9 - Calculate the percent increase in the mechanical...Ch. 9 - Calculate the stress in the fibers and in the...Ch. 9 - Repeat the calculations in Example 9.1 if (a)...Ch. 9 - Refer to the properties listed in Table 7.1. If...Ch. 9 - Plot the elastic modulus and strength of an...Ch. 9 - For the data in Example 9.1, what should be the...Ch. 9 - It is desired to obtain a composite material with...Ch. 9 - A rectangular cantilever beam, 100 mm high, 20 mm...Ch. 9 - What applications for composite materials can you...Ch. 9 - Using the information given in this chapter,...Ch. 9 - Would a composite material with a strong and stiff...Ch. 9 - Make a list of products for which the use of...Ch. 9 - Inspect Fig. 9.1 and explain what other components...Ch. 9 - Name applications in which both specific strength...Ch. 9 - What applications for composite materials can you...Ch. 9 - As with other materials, the mechanical properties...Ch. 9 - Developments are taking place in techniques for...Ch. 9 - As described in this chapter, reinforced plastics...Ch. 9 - Comment on your observations on the design of the...Ch. 9 - Make a survey of various sports equipment and...Ch. 9 - Several material combinations and structures were...Ch. 9 - It is possible to make fibers or whiskers with a...Ch. 9 - Describe how you can produce some simple composite...Ch. 9 - Gel spinning is a specialized process used in...Ch. 9 - Figure P9.65 shows a section of a...
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- A unidirectional fiber reinforced composite contains Kevlar 49 fibres and epoxy resin. the fibers are to carry 88% of a load applied in the longitudinal direction. determine the volume fraction of fibers that will be required ( two decimal places, e.g. 0.31).( elastic modulus of Kevlar 49 is 129GPA, and elastic modulus of epoxy 4.6 GPaarrow_forwardQuestion 2 = 219,48 M//a = 247,3785 Pa 2.1 Consider a polymer reinforced with Spectra 1000 fibers, with a fiber volume ratio of x = 15 %. For a cross sectional area of 130 mm² and a load of 250 kg, calculate the stress in the fibers and in the matrix if the matrix material is polycarbonate. 2.2 Why are fibres capable of supporting a large portion of the tensile load in composite materials?arrow_forwardA composite with a minimum elastic modulus of 50 GPa is to be created by mixing uniaxial epoxy with metal fibre. Calculate the minimum Elastic modulus of the metal fibre given the following data for the epoxy matrix: Elastic modulus of the epoxy matrix is 5 GPa • Volume fraction of the epoxy matrix is 0.6 A- в I U S x2 xarrow_forward
- A tensile load of 120N is applied to an aluminum boron composite with 1mm^2 cross sectional area.the volume of parallel fibers is 20%.what is the stress in the fibers when the load Axis is (a)parallel to the fibers (b)perpendicular to the fibersarrow_forwardA continuous and aligned glass fiber-reinforced composite with modulus of elasticity of 55 GPa. The volume fiber fraction is 40 and the modulus of elasticity of the fiber is 75 GPa. Calculate the volume fraction of epoxy matrix if you know the modulus of elasticity of the modulus of elasticity of the matrix is 2.5 GPa and then determine the strain that is sustained by each phase under applied stress of 27 Mpa. (assume that the cross-section area is 150 mm2)arrow_forwardIt is desired to produce an aligned and continuous fiber-reinforced epoxy composite having a maximum of 50% fibers. A minimum longitudinal modulus of elasticity of 55 GPa and a minimum tensile strength of 1200 MPa are required. E-glass and carbon (PAN standard modulus) fibers are the possible candidates to select. In addition, assume the stress levels on the epoxy matrix at fiber failure are 70 MPa for E-glass fiber and 30MPa for carbon fiber, respectively. Which fiber meets the design requirement? Use the properties given in the Table below to evaluate your selection. Materials Epoxy matrix E-glass Carbon Modulus of Elasticity (GPa) 3.1 72.5 230 Tensile Strength (MPa) 69 3450 4000arrow_forward
- helparrow_forwardCalculate the composite elastic modulus for polyester reinforced with 60% volume fraction of carbon fibers under isostrain longitudinal conditions. Modulus of elasticity of polyester is 2900 MPa and for carbon fiber is 175,000 MPa.arrow_forwardFor a continuous and aligned fiber-reinforced composite, the modulus of elasticity in the transverse direction is 4.91 GPa. If the volume fraction of fibers is 0.3 and the modulus of elasticity of matrix phase is 3.78 GPa, determine the modulus of elasticity of composite in longitudinal direction.arrow_forward
- Calculate the density of a composite made with 35% Kevlar-49 fibers in an epoxy resin (ρ = 1.1 kg/m3, E = 2.5 GPa). For Kevlar-49, Ef = 131 GPa; density = 1440 kg/m3arrow_forwardA composite sample of carbon reinforced epoxy has dimensions of 12 in x 12 in x 0.25 in and mass of 1.8 lb. The carbon fibers have a modulus of elasticity of 50(106) lb/in² and a density of 0.069 lb/in³. The epoxy matrix has modulus of elasticity of 0.61(106) lb/in² and a density of 0.042 lb/in³. What is the volume fraction of (a) the carbon fibers and (b) the epoxy matrix in the sample? Assume there are no voids in the sample. What is the predicted value for the modulus of elasticity (c) in the longitudinal direction and (d) the perpendicular to the carbon fibers?arrow_forward(b) A continuous and aligned fiber-reinforced composite is to be produced using 45 vol% of aramid fibers and 55 vol% of polycarbonate matrix. Mechanical properties of these two materials that are given in Table Q5(b): Table Q5(b): Mechanical properties of fiber and matrix Modulus of Elasticity (GPa) Tensile Strength (MPa) Aramid Fiber 131 3600 Polycarbonate 2.4 65 If the stress on the polycarbonate matrix is 35 MPa, when the aramid fibers fail, then compute the followings: (i) the longitudinal tensile strength (ii) the longitudinal modulus of elasticityarrow_forward
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