Case Study: The Maker Movement
3.9 Summary
Eight important mechanical properties of solid materials were discussed in this chapter. The differences between duc- tile and brittle materials were presented. It was found that, at fracture, ductile materials exhibit considerable plastic defor- mation, whereas brittle materials exhibit little or no yielding before failure.
Four major classes of solid material were described: met- als, ceramics and glasses, polymers and elastomers, and com- posites. The members of each class have common features, such as similar chemical makeup and atomic structure, simi- lar processing routes, and similar applications.
A stress-strain diagram was presented for each class of solid material because they differ significantly. The stress- strain diagrams for metals are essentially the same for com- pression and tension. This feature is not true for polymers or ceramics. Results of transverse bending tests for ceramics were found to be similar to tensile test results for metals.
A number of solid material properties used in choos- ing the correct material for a particular application were pre- sented: mass density, modulus of elasticity, hardness, Pois- son’s ratio, shear modulus, strength, resilience, toughness, thermal conductivity, linear thermal expansion coefficient, specific heat capacity, and Archard wear constant. These pa- rameters were presented for a large selection of materials.
Two-parameter materials charts were also presented.
Stiffness versus weight, strength versus weight, stiffness ver- sus strength, and wear constant versus limiting pressure for the various classes of material can give a better idea of the best material for a particular machine element.
An introduction to manufacturing processes and their ef- fects on materials was also presented, with the most common approaches presented for each class of material. These in- clude casting, bulk and sheet forming for metals, many types of molding for polymers, and casting and molding operations for ceramics. Each material can be machined to some extent as well.
The Case Study described the emerging Maker Move- ment, wherein designers can produce their desired products in a CAD program and have them manufactured directly on a 3D printer. A large number of applications and materials have been used by the Maker Movement.
Key Words
anisotropic material having different properties in all direc- tions at a point in a solid
Archard wear constant wear property of a material
Brinell hardness a hardness measure that results from a Brinell test, where a steel or tungsten carbide ball is im- pressed onto a material.
brittle material material that fractures at strain below 5%
ceramics compounds of metallic and nonmetallic elements composite materials combinations of two or more materials,
usually consisting of fiber and thermosetting polymer density mass per unit volume
ductile material material that can sustain elongation greater than 5% before fracture
ductility degree of plastic deformation sustained at fracture elastic limit stress above which material acquires perma-
nent deformation
elastomers polymers with intermediate amount of cross- linking
fracture stress stress at time of fracture or rupture
glasses compounds of metallic and nonmetallic elements with no crystal structure
hardness resistance to surface penetration
homogeneous material having properties not a function of position in a solid
isotropic material having the same properties in all direc- tions at a point in a solid
Knoop hardness a hardness measure that results from a Knoop test, also known as a microhardness test metals combinations of metallic elements
modulus of elasticity proportionality constant between stress and strain
modulus of rupture stress at rupture from bending test, used to determine strength of ceramics
necking decreasing cross-sectional area that occurs after ul- timate stress is reached and before fracture
orthotropic material having different properties in three mu- tually perpendicular directions at a point in a solid and having three mutually perpendicular planes of material symmetry
Poisson’s ratio absolute value of ratio of transverse to axial strain
polymers compounds of carbon and other elements forming long-chain molecules
proportional limit stress above which stress is no longer lin- early proportional to strain
resilience capacity of material to release absorbed energy
Rockwell hardness a hardness measure that results from a Rockwell test, where the penetration of a cone or ball into a material is measured
rule of mixtures linear interpolation between densities of al- loy concentration
specific heat capacity ratio of heat stored per mass to change in temperature of material
strain hardening increase in hardness and strength of duc- tile material as it is plastically deformed
thermal conductivity ability of material to transmit heat thermal expansion coefficient ratio of elongation in mate-
rial to temperature rise
thermoplastics polymers without cross-links
thermosets polymers with highly cross-linked structure toughness ability to absorb energy up to fracture
ultimate strength maximum stress achieved in stress-strain diagram
Vickers hardness a hardness measure that results from a Vickers test, where a diamond pyramid is impressed onto a material
yield strength stress level defined by intersection of refer- ence line (with slope equal to initial material elastic modulus and x-intercept of 0.2%) and material stress- strain curve
yielding onset of plastic deformation Young’s modulus (see modulus of elasticity)
Summary of Equations
Material Properties:
Percent elongation:%EL=
lfr−lo
lo
×100%
Elastic modulus:E= σavg
avg
Poisson’s ratio:ν=−Transverse strain Axial strain Shear modulus:G= E
2(1 +ν) Modulus of resilience:Ur= Sy2
2E Heat capacity:Q=Cpma(∆T) Composite Materials:
Elastic modulus:Ec=Em(1−vf) +Efvf
Load sharing: Pf
Pm = Efvf
Emvm
Hardness:
Brinell hardness: HB= 2P (πD) D
−√
D2−d2 Su= 3.5HB
Vickers hardness: HV=1.854P L2
Knoop hardness: HK= 14.2P L2
Rockwell hardness: HRA= 100−500t, HRB= 130−500t, etc.
Archard Wear Law:v=k1W L 3H
Recommended Readings
Ashby, M.F. (2010)Materials Selection in Mechanical Design, 4th ed., Butterworth-Heinemann.
ASM Metals Handbook, 8th ed. (2009) American Society for Metals.
Brandt, D.A., and Warner, J.C. (2009)Metallurgy Fundamen- tals: Ferrous and Nonferrous, 5th ed. Goodheart-Wilcox.
Budinski, K., and Budinski, M. (2009)Engineering Materials, Properties and Selection, 9th ed., Prentice-Hall.
Callister, W.D., and Rethwisch, D.G. (2011) Fundamentals of Materials Science and Engineering: An Integrated Approach, 4th ed. Wiley.
Farag, M.M. (2007) Selection of Materials and Manufacturing Processes for Engineering Materials, 2nd ed. Prentice-Hall.
Flinn, R. A., and Trojan, P. K. (1986)Engineering Materials and Their Applications, Houghton Mifflin.
Kalpakjian, S., and Schmid, S.R. (2010)Manufacturing Engi- neering and Technology. 6th ed., Pearson.
Raman, A. (2006) Materials Selection and Applications in Me- chanical Engineering, Industrial Press.
Schey, J.A. (2000)Introduction to Manufacturing Processes, 3rd ed., McGraw-Hill.
References
Ashby, M.J. (2010)Materials Selection in Mechanical Design, 4th ed., Butterworth-Heinemann.
Kalpakjian, S., and Schmid, S.R. (2010)Manufacturing Engi- neering and Technology, 6th. ed., Pearson.
Schey, J.A. (2000)Introduction to Manufacturing Processes, 3rd ed., McGraw-Hill.
Questions
3.1 Define the terms ductile and brittle.
3.2 What are the three basic classifications of solids?
3.3 What is the difference between a thermoset and a ther- moplastic?
3.4 What is a composite material?
3.5 Define proportional limit. How is this different from elastic limit? How are these different from the yield strength?
3.6 How is the yield strength defined?
3.7 What is strain hardening?
3.8 What is the glass transition temperature for polymers?
Does this behavior occur with other materials? Explain.
3.9 What is the elastic modulus of a material?
3.10 What are the advantageous properties of glass?
3.11 What is hardness?
3.12 What is ductility, and how is it measured?
3.13 What is the difference between thermal expansion and specific heat?
3.14 What is casting? What materials can be cast?
3.15 Give three examples of bulk metal forming operations.
Quantitative Problems 85 3.16 What is PM?
3.17 What is sintering?
3.18 What is a thermoplastic? A thermoset?
3.19 What are the main manufacturing processes applicable to ceramics?
3.20 Why are the molds for producing PM parts larger than the desired shape?
Qualitative Problems
3.21 What are the primary functions of the reinforcement in a fiber reinforced polymer? What are the primary func- tions of the matrix?
3.22 Explain why ceramics and cast metals are much stronger in compression than in tension.
3.23 Without using the words stress orstrain, define elastic modulus.
3.24 Sketch typical stress-strain diagrams for metals, ceram- ics, and polymers.
3.25 What is the main difference between resilience and toughness? What is the main similarity between re- silience and toughness?
3.26 Describe the events that occur when a specimen un- dergoes a tension test. Sketch a plausible stress-strain curve, and identify all significant regions and points be- tween them. Assume that loading continues up to frac- ture.
3.27 Which hardness tests and scales would you use for very thin strips of metal, such as aluminum foil? Explain.
3.28 List the factors that you would consider in selecting a hardness test. Explain your answer.
3.29 A statistical sampling of Rockwell C hardness tests is conducted on a material, and it is determined that the material is defective because of insufficient hardness.
The supplier claims that the tests are flawed because the diamond-cone indenter was probably dull. Is this a valid claim? Explain.
3.30 In a Brinell hardness test, the resulting impression is found to be an ellipse. Give possible explanations for this result.
3.31 Which of the properties described in this chapter are im- portant for (a) pots and pans, (b) gears, (c) clothing, (d) paper clips, (e) music wire, (f) beverage cans? Explain your answers.
3.32 Identify products that cannot be made of steel, and ex- plain why this is so. (For example, electrical contacts commonly are made of gold or copper because their softness results in low contact resistance, while for steel the contact resistance would be very high.)
3.33 What characteristics make polymers advantageous for applications such as gears? What characteristics are drawbacks for such applications?
3.34 Review Fig. 3.25 and list reasons why the connecting rod is manufactured in multiple steps, instead of one cavity with one press stroke.
3.35 Review Fig. 3.26b and list potential applications for ex- truded products.
Quantitative Problems
3.36 The design specification for a metal requires a minimum hardness of 80 HRA. If a Rockwell test is performed and the depth of penetration is 60µm, is the material accept- able?Ans.No.
3.37 It can be shown that thermal distortion in precision de- vices is low for high values of thermal conductivity di- vided by thermal expansion coefficient. Rank the ma- terials in Table 3.1 according to their suitability to resist thermal distortion.
3.38 If a material has a target hardness of 300 HB, what is the expected indentation diameter? Assume the applied load is 3000 kg.Ans.d= 2.95mm.
3.39 For a material that follows a power law curve for stress- strain behavior, that is, σ = Kn, where K is the strength coefficient andnis the strain hardening expo- nent, find the strain at which necking occurs.Ans.=n.
3.40 A 2-m-long polycarbonate tensile rod has a cross- sectional diameter of 150 mm. It is used to lift a tank weighing 45 tons (45,000 kg) from a 1.8-m-deep ditch onto a road. The vertical motion of the crane’s arc is lim- ited to 4.2 m. Will it be possible to lift the tank onto the road?Ans.Yes.
3.41 Materials are normally classified according to their properties, processing routes, and applications. Give ex- amples of common metal alloys that do not show some of the typical metal features in their applications.
3.42 Equation (B.56) in Appendix B gives the relationship be- tween stresses and strains in isotropic materials. For a polyurethane rubber, the elastic modulus at 100% elon- gation is 7 MPa. When the rubber is exposed to a hy- drostatic pressure of 10 MPa, the volume shrinks 0.5%.
Calculate Poisson’s ratio for the rubber.Ans.ν= 0.499.
3.43 A fiber-reinforced plastic has fiber-matrix bond strength τf = 15MPa and fiber ultimate strengthSu = 1GPa.
The fiber length is constant for all fibers at l = 1.25 mm. The fiber diameterd = 30µm. Find whether the fiber strength or the fiber-matrix bond will determine the strength of the composite.Ans.The fiber determines the composite strength.
3.44 Using the same material as in Problem 3.43 but with fiber lengthl= 0.75mm, calculate if it is possible to in- crease the fiber stress toSu= 1GPa by making the fiber rectangular instead of circular, maintaining the same cross-sectional area for each fiber, and if so, give the cross-section dimensions.Ans.ht= 8.22µm,wt= 86.0 µm.
3.45 A copper bar is stressed to its ultimate strength, Su = 150 MPa. The cross-sectional area of the bar before stressing is 120 mm2, and the area at the deformed cross section where the bar starts to break at the ultimate strength is 70 mm2. How large a force is needed to reach the ultimate strength?Ans.18 kN.
3.46 AISI 440C stainless steel has ultimate strengthSu= 807 MPa and fracture strength Sfr = 750MPa. At the ul- timate strength the cross-sectional area of a tension bar made of AISI 440C is 80% of its undeformed value. At the fracture point the minimum cross-sectional area has shrunk to 70%. Calculate the real stresses at the point of ultimate strength and at fracture. Ans. At fracture, σ= 1071MPa; at ultimate strength,σ= 1009MPa.
3.47 According to Sketcha, a beam is supported at point A and at either B or C. At C the silicon nitride tensile rod is lifting the beam end with forceP =Sfrt, whereAcis the cross-sectional area of the rod. Find the distance A- B such that the silicon nitride rod would be crushed if it took up a compressive force at B instead of a tensile force at C. Note that the strength in compression is fif- teen times larger than the strength in tension for silicon nitride. Also, find the reaction forces at A for the two load cases.Ans.l0= 151l,Ay= 1207 P.
P P’
x mag
l l’
B C
A Compressive
rod Tensile
rod
Sketcha, for Problem 3.47
3.48 Polymers have different properties depending on the re- lationship between the local temperature and the poly- mer’s glass transition temperature Tg. The rubber in a bicycle tire has Tg = −12◦C. Could this rubber be used in tires for an Antarctic expedition at temperatures down to−70◦C?Ans.No.
3.49 What is the modulus of resilience of a highly cold- worked steel with a hardness of 300 HB? Of a highly cold-worked aluminum with a hardness of 120 HB?Ans.
Urs= 1.957MPa.
3.50 Given an aluminum bronze with 25 wt% aluminum and 75 wt% copper, find the density of the aluminum bronze.
Ans.ρbronze= 7382kg/m3
3.51 The glass-fiber-reinforced plastic in Example 3.6 (Sec- tion 3.5.2) is used in an application where the bend- ing deformations, caused by the applied static load, will crack the plastic by overstressing the fibers. Will a carbon-fiber-reinforced plastic also crack if it has the same elastic properties as the glass-fiber-reinforced plas- tic?Ans.Yes.
3.52 In Problem 3.51, carbon fibers were used to reinforce a polymer matrix. The concentration of fibers was de- creased in Example 3.6 (Section 3.5.2) to give the same elastic properties for the carbon-fiber-reinforced poly- mer as for the glass-fiber-reinforced polymer. If instead, the fiber concentration were kept constant at 10% when the glass fibers were changed to carbon fibers, how much smaller would the deformation be for the same load, and would the fibers be overstressed? The mate- rial properties are the same as in Example 3.6.
3.53 A bent beam, shown in Sketchb, is loaded with force P = 125,000N. The beam has a square cross sectiona2. The length of a sidea = 30mm. The lengthl1 = 50 mm andl2 = 100mm. The yield strengthSy = 350 MPa (medium-carbon steel). Find whether the stresses in tension and shear are below the allowable stresses.
Neglect bending.
P l1
l2
a a
Sketchb, for Problem 3.53
3.54 A steel cube has side lengthl= 0.1m, modulus of elas- ticity E = 206GPa, and Poisson’s ratio ν = 0.3. A stressσ is applied to one direction on the cube. Find the compressive stresses needed on the four remaining cube faces to give the same elongation that results from σ.Ans.σc=−1.67σ.
3.55 For the stressed steel cube in Problem 3.54, calculate the volume ratio (vt/vc) whenσ= 500MPa. Ans. vt/vc = 1.0042.
3.56 A tough material, such as soft stainless steel, has yield strength Sy = 200MPa, ultimate strength Su = 500 MPa, and 200% elongation. Find the ratio of the mate- rial toughness to the resilience at fracture (thehyperstatic resilience), assuming that the stress-strain curve consists of two straight lines according to Sketchc.Ans.Tough- ness/resilience=1080.
0.002 2.00
Normal stress, σ, MPa
Sy = 200 Su = 500
ε =δ
l Sketchc, for Problem 3.56
3.57 Hooke’s law describes the relationship between uniaxial stress and uniaxial strain. What is the ratio of the strain encountered by the most compliant material mentioned in this chapter compared to the stiffest?Ans.1.125×105.
Design and Projects 87 3.58 According to Archard’s wear equation, the wear depth
is proportional to the sliding distance and the contact pressure. How will the contact pressure be distributed radially for a disk brake if the wear rate is the same for all radii? Ans. Pressure is inversely proportional to ra- dius.
3.59 Given a brake pad for a disk brake on a car, and using Archard’s wear constant, determine how the wear is dis- tributed over the brake pad if the brake pressure is con- stant over the pad. Ans. Wear rate is proportional to radius.
3.60 Derive an expression for the toughness of a material rep- resented by the stress-strain lawσ = K(+ 0.2)nand whose fracture strain is denoted byf.
Design and Projects
3.61 List and explain the desirable mechanical properties for (a) an elevator cable, (b) a paper clip, (c) a leaf spring for a truck, (d) a bracket for a bookshelf, (e) piano wire, (f) a wire coat hanger, (g) the clip for a pen, and (h) a staple.
3.62 List applications where the following properties would be desirable: (a) high density, (b) low density, (c) high stiffness, (d) low stiffness, (e) high thermal conductivity, and (f) low thermal conductivity.
3.63 Give several applications in which both specific strength and specific stiffness are important.
3.64 Conduct a literature search and add the following ma- terials to Table 3.1: cork, concrete, ice, sugar, lithium, chromium, and platinum.
3.65 A recent development in the automotive industry is to use steel alloys with a high manganese content, called TRIP, TWIP, and martensitic steels. Conduct an Internet search and literature review and write a one-page sum- mary of these materials and their mechanical properties.
3.66 Design an actuator to turn on a switch when tempera- ture drops below a certain level. Use two materials with different coefficients of thermal expansion in your de- sign.
3.67 Assume that you are in charge of public relations for a large steel-producing company. Outline all of the at- tractive characteristics of steels that you would like your customers to be informed about.
3.68 Assume that you are in competition with the steel indus- try and are asked to list all of the characteristics of steels that are not attractive. Make a list of these characteristics and explain their relevance to engineering applications.
3.69 Aluminum is being used as a substitute material for steel in automobiles. Describe your concerns, if any, in purchasing an aluminum automobile.
3.70 Add a column to Table 3.1 and add values of electrical conductivity for the materials given.
3.71 Review the technical literature, and produce a figure similar to Fig. 3.24 for investment casting.
3.72 Perform an Internet search, and produce a Powerpoint presentation that summarizes applications of rapid pro- totyping. Whenever possible, indicate the material and machinery used.