Plastic stress-strain behaviour of metals Energy of mechanical ldeformation Hardness testing Design/safety factors

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1 Mechanical Properties of Materials 2 Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka Plastic stress-strain 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 Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 02 1

2 Stress elastic P For most metals, elastic deformation persists only to strains of about Deformation beyond this point (P in the figure) causes plastic yielding or, permanent deformation. Strain Hooke s law is no longer valid Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 03 The yield stress, σ y, is a measure of resistance to plastic deformation of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 permanent deformation. In most ferrous materials, the elastic-plastic transition is welldefined and occurs abruptly. Some steels show two distinct yield points. At the upper yield point, plastic deformation is initiated, with an actual decrease in strength. Continued deformation fluctuates slightly at some constant stress value, termed the lower yield point. The yield strength is then taken as the average stress at the lower yield point. Do you find any change in the nonferrous curve? ferrous materials nonferrous materials 2

3 σ P Stress strain Strain For most nonferrous metals, the elastic to plastic transition is a gradual one, where no well-defined yield point is available. In such cases, an offset strength, or proof strength, σ P, is calculated. The offset is chosen for a stress that causes a permanent strain of 0.1, 0.2 or 0.5 per cent. Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 05 σ y ceramics >> σ y metals >> σ y polymers 3

4 After yielding, plastic deformation becomes more and more difficult. The stress necessary to continue deformation rises with increasing strain, and the curve tends to be flatten out. This is called strain hardening. With deformation, the number of dislocations inside the material is increased, which hinder further dislocation movement, and the material becomes stronger. At point M, the stress becomes the maximum and is known as the ultimate tensile strength (UTS) or simply the tensile strength (TS) of the material. TS stress M Tensile strength maximum stress (~ MPa) strain Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials MME131 2 P 07/ 19-7 If a material is deformed plastically σ y2 and the stress is then released, the strain material ends up with a net, unload hardening permanent strain. σ y1 Stress reapply load permanent strain elastic strain recovery Strain 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 strain or work hardening of material. The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery. Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 08 4

5 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 strain fracture strength Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials MME131 2 P 09/ 19-9 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 MME 291, Lec 10: Mechanical properties of materials 2 P 10 5

6 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 MME 291, Lec 10: Mechanical properties of materials MME131 2 P 11 / A Comparison Materials E, GPa YS, MPa UTS, MPa %EL Steel (1020, annealed) Steel (4140, annealed) Al alloy (2024, annealed) Cast iron (grey G3000) Silicon nitirde (sintered) < 0.2 Alumina (polycrystalline, 99.9%) < 0.2 SiO 2 glass < 0.2 Linear addition thermoplastics a Linear condensation thermoplastics b Thermosetting polymers c Elastomer d 2 10 x 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 6

7 The mechanical properties of metals vary with prior thermal and mechanical treatment, impurity levels, etc. This variability is related to the behavior of dislocations in the material. Elastic moduli are relatively insensitive to these effects. The yield strength, tensile strength, modulus of elasticity and ductility decrease with increasing temperature. Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 13 Area under the σ-ε curve gives: energy volume energy volume stress energy of deformation strain Work, W L i L0 F.dL L i = instantaneous length U W 1 L i L, V = AL i F.dL L0 = σ dε L0 Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 14 7

8 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 0 σ 2 2 pl U elastic = σ dε = = 2E Modulus of resilience σ y 2 2E σ dσ E U r = σ y 2 2E Toughness the ability to absorb energy up to fracture the total area under the strain-stress curve up to fracture for a material to be tough, it must display both strength and ductility Stres ss 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 8

9 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 MME 291, Lec 10: Mechanical properties of materials 2 P 17 Moh s Hardness Scale A qualitative and somewhat arbitrary hardness system that measures the ability of one material to scratch another that is softer. 1, Talk softest ; 10, Diamond hardest gradations are uneven (e.g., 10 is not twice as hard as 5) Extensively used to determine the hardness of minerals. The unknown mineral, which hardness is to be determined, is scratched with another mineral of known hardness. If the mineral can be scratched by the known mineral, then the hardness of the mineral will be less than that of the known mineral. Moh s Scale 1. Talc 2. Gypsum 3. Calcite 4. Feldspar 5. Apatite 6. Orthoclase 7. Quartz 8. Topaz 9. Corundum 10. Diamond Two German Captains Fired An Old Queen To Cruel Death Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 18 9

10 Quantitative Hardness Tests A small indenter is forced into the surface of a material to be tested, under controlled conditions of load and rate of application. The depth or size of resulting indentation is measured and converted into a hardness number. The softer the material, the larger and deeper the indentation and the lower the hardness number Measured hardness is only relative (not absolute), and care should be taken when comparing values determined by different techniques. Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 19 Quantitative Hardness Testing Methods Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 20 10

11 Correlation Between Hardness and Tensile Strength Both hardness and tensile strength are indicative of metal s resistance to plastic deformation. Consequently they are proportional to each other. But the proportionality constant is different for different materials. For most steels, TS (MPa) = 3.45 x HB TS (psi) = 500 x HB MME131 / Rashid, DMME, BUET MME 291, Lec 10: Mechanical properties of materials 2 P 21 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 MME 291, Lec 10: Mechanical properties of materials 2 P 22 11

12 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 MME 291, Lec 10: Mechanical properties of materials 2 P 23 Next Class Dislocation Motion and Yielding in Crystals 12