MME 291: Lecture 10 Mechanical Properties of Materials 2 Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka Today s Topics Plastic stress- behaviour of metals Energy of mechanical ldeformation Hardness testing Design/safety factors Reference: 1. WD Callister, Jr. Materials Science and Engineering An Introduction, 5 th Ed., Ch. 6, pp.124-145. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 02
Stress-Strain Behaviour in the Plastic Region Stress elastic P For most metals, elastic deformation persists only to s of about 0.005. Deformation beyond this elastic limit (P in the figure) plastic causes yielding or, permanent deformation. Strain Hooke s law is no longer valid Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 03 Yielding and Yield Strength The yield stress, σ y, is a measure of resistance to plastic deformation of material. It is the maximum stress that a material can withstand before starting gpermanent deformation. In most ferrous materials, the elastic-plastic transition is well-defined and occurs abruptly. stress ferrous materials nonferrous materials σ P stress For most nonferrous metals, the elastic to plastic transition is a gradual one, where no well-defined d yield point is available. 0.002 In such cases, an offset strength, or proof strength, σ P, is calculated. The offset is chosen for a stress that causes a permanent of 0.1, 0.2 or 0.5 per cent.
Comparison of Yield Strengths σ y ceramics >> σ y metals >> σ y polymers Loading Beyond Yield Point Beyond yield point, the curve is flattened out and, after the ultimate tensile stress (point M), the curve goes downward. So it appears that t the strength th of material is decreased, i.e., the material is getting weaker. TS stress s M Tensile strength maximum stress (~50-3000 MPa) This is not the case; as a matter of fact, strength of the material increases continuously. The plastic deformation becomes more and more difficult. The stress necessary to continue deformation rises with increasing. This is called hardening. With deformation, the number of dislocations inside the material is increased, which hinder further dislocation movement, and the material becomes stronger. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 MME131 P 06 / 19-7
True Stress and True Strain Engineering stress (or simply, stress, σ) is calculated by dividing the instantaneous load with the original area of the sample. True stress, σ T, on the other hand is calculated by dividing the instantaneous load with actual area. In a similar manner, engineering and true are calculated. M In the stress- diagram, true stress continues to rise to the point of fracture, in contrast to the engineering stress, which goes downward. Relation between true and engineering stress and : σ T = σ (1+ε) ε T = ln (1+ε) Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 MME131 P 07/ 19-11 Elastic Recovery After Plastic Deformation σ y2 σ y1 Stress unload reapply load permanent elastic recovery hardening Strain If a material is deformed plastically and the stress is then released, the material ends up with a net, permanent. If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point. This is due to or work hardening of material. The amount of elastic that it will take before reaching the yield point is called elastic recovery. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 08
Formation of Necking during Plastic Deformation Beyond the point M, necking occurs at the sample and stress decreases to eventual fracture. During necking, pores and other defects start to form or propagate, accumulate, and multiply, and reduce the effective cross-section of the material. When the cross-section can hold the applied load no more, fracture or material takes place. st tress necking fracture strength Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 MME131 P 09 / 19-9 Ductility of Materials Ductility is the measure of deformation at fracture of materials during tension Small %EL Material is brittle, if %EL < 5% Usually measured as either Elongation at failure (%E) or, Reduction in area (%RA): Larger %EL Materials is ductile, if %EL > 5% %EL = %RA = L L 0 x 100 A A 0 x 100 %EL and %RA are often comparable. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 10
Ductility of Materials A knowledge on ductility of materials is important: it indicates to a designer the degree to which the structure will deform plastically before fracture. it specifies the degree of allowable deformation during fabrication operations. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 MME131 P 11/ 19-11 Mechanical Properties of Materials A Comparison Materials E, GPa YS, MPa UTS, MPa %EL Steel (1020, annealed) 207 295 395 36.5 Steel (4140, annealed) 207 417 655 25.7 Al alloy (2024, annealed) 72.4 75 185 20 Cast iron (grey G3000) 90-113 207 -- Silicon nitirde (sintered) 304 414-650 < 0.2 Alumina (polycrystalline, 99.9%) 380 282-551 < 0.2 SiO 2 glass 73 104 < 0.2 Linear addition thermoplastics a 0.04-0.60 9.73 8.72 2-1200 Linear condensation thermoplastics b 0.25-0.60 55-83 63-94 15-150 Thermosetting polymers c 0.5-1.6 26-90 1.5-6.0 Elastomer d 2 10 x10-3 6.9-24.1 350-2000 a) e.g., polyethylene, polyvinyl chloride polypropylene, Teflon b) e.g., nylon 6.6, polycarbonate c) e.g., phenolics, thermosetting polyesters, epoxies d) e.g., silicone
Variables Affecting Mechanical Properties The mechanical properties of metals vary with prior thermal and mechanical treatment, impurity levels, etc. This variability is related to the bh behavior of fdil dislocations in the material. As little plastic deformation takes place during the elastic zone, elastic modulus is relatively insensitive to these effects. The yield strength, tensile strength, modulus of elasticity and ductility decrease with increasing temperature. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 13 Energy of Mechanical Deformation Area under the σ-ε curve gives: energy volume stress energy of deformation Energy/Work, W L i L 0 F.dL L i = instantaneous length energy volume U W 1 L i L, V = AL i F.dL L0 = σ dε L0 Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 14
Energy of Mechanical Deformation Modulus of Resilience Total work of elastic deformation is a measure of resilience. Given: σ = Eε, dσ = Edε ( E E(σ) in the elastic region ) Resilient materials have high yield strengths and low moduli of elasticity. Suitable to use in spring applications. ε pl ε pl 0 U elastic = σ dε = 0 σ 2 pl σ 2 y = 2E 2E Modulus of resilience σ dσ E U r = σ y 2 2E Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 15 Energy of Mechanical Deformation Toughness the ability to absorb energy up to fracture the total area under the -stress curve up to fracture for a material to be tough, it must display both strength and ductility Stress Low toughness (ceramics) Strain High toughness (metals, PMCs) Low toughness (unreinforced polymers) Units: Energy / volume, e.g. J/m 3 For dynamic loading conditions, notch / impact toughness is measured by an impact test For brittle materials, fracture toughness is used, which indicates material s resistance to fracture when a crack is present Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 16
Hardness The most popular mechanical testing methods: 1. simple and inexpensive 2. nondustructive testing 3. estimation of other mechanical properties (eg.,ts) from hardness data A measure of material s resistance to localized plastic deformation by indentation or scratching. The further into the material the indenter sinks, or the more the material is scratched by another material, the softer is the material and lower its yield strength. The high hardness means : better resistance to plastic deformation or cracking in compression better wear properties Values depends on method of testing; different testing methods different scales and values Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 17 Hardness Quantitative Hardness Testing Methods Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 18
Correlation Between Hardness and Tensile Strength Both hardness and tensile strength are indicative i of metal s resistance to plastic deformation. Consequently they are proportional to each other. The proportionality constant is different for different materials. For most steels, TS (MPa) = 3.45 x HB TS (psi) = 500 x HB Hardness MME131 / 20-12 Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 19 Design Stress and Safety Factor For structural applications, the yield stress is usually a more important property than the tensile strength, since once the yield point is passed, the structure has deformed beyond recovery. Design stress: σ d = N σ c σ c = maximum anticipated stress N is the design factor > 1 (usually 1.2 4) Safe or working stress: σ w = σ y /N where N is factor of safety > 1. Want to make sure that σ d < σ y Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 20
Design Stress and Safety Factor Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod when a load of 220 kn is applied. Use a factor of safety of 5. Materials data: σ y = 310 MPa, σ TS = 565 MPa. Rashid, DMME, BUET, 2011 MME 291, Lec 10: Mechanical properties of materials 2 P 21 Next Class MME 291: Lecture 11 Dislocation Motion and Yielding in Crystals