11/2/2018 7:58 PM. Chapter 6. Mechanical Properties of Metals. Mohammad Suliman Abuhaiba, Ph.D., PE

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1 1 Chapter 6 Mechanical Properties of Metals

2 2 Assignment 7, 13, 18, 23, 30, 40, 45, 50, 54 4 th Exam Tuesday 22/11/2018

3 3 WHY STUDY Mechanical Properties of Metals? How various mechanical properties are measured? What these properties represent? Design structures/components using predetermined materials

4 4 CONCEPTS OF STRESS AND STRAIN Stress = Load / Area Strain = deformation of component / original length A stress may be direct (axial, bending normal), transverse shear, or torsional Stress cannot be measured directly, but deformation can be.

5 5 CONCEPTS OF STRESS AND STRAIN F A 0 L L 0 tension compression

6 6 CONCEPTS OF STRESS AND STRAIN Shear Torsion

7 7 CONCEPTS OF STRESS AND STRAIN Standard Tensile Test Specimen

8 8 CONCEPTS OF STRESS AND STRAIN Standard Tensile Test Specimen Measures resistance of a material to a static or slowly applied force Very small Strain rates: 10-4 to 10-2 mm/mm. s Used to determine mechanical properties of materials: Strength & Ductility Tensile toughness Elastic modulus Strain hardening

9 9 CONCEPTS OF STRESS AND STRAIN Typical Universal Testing Machine

10 10 Elasticity vs. Plasticity Elastic behavior 0 when 0 Reversible deformation: no permanent shape change after load is removed Plastic behavior 0 when 0 Some strain remains after load has been removed

11 Load, P (kn) 11 Load vs. Elongation Curve Total Elongation Uniform Deformation Elastic Deformation Maximum Load, P max Load, P f Elongation, L (mm)

12 Engineering Stress, S=P/Ao 12 Engineering Stress Strain Curve Elongation Sy = 0.2% offset yield stress E (Ultimate) E S u Proportional Limit Engineering Strain, e = L/Lo)

13 13 STRESS STRAIN BEHAVIOR Linear elastic behavior: Hooke s law E

14 14 Modulus of Elasticity & Interatomic Potential Energy between atoms depends on their separation Minimum energy zero net force F d(energy) d(separation) Applying tension or compression raises energy of material tension compression

15 15 Modulus of Elasticity & Interatomic Potential d df A d dl L dr r d E d E d d r A df dr

16 16 Modulus of Elasticity & Interatomic Potential high modulus Force vs interatomic separation for weakly & strongly bonded atoms low modulus Modulus of elasticity df / dr High modulus strong bonding (high curvature of interatomic potential near r o )

17 17 Mechanical Properties of Metals - Elastic Behavior

18 18 Elastic Modulus: Temperature Dependence E gradually as T

19 19 Example 6.1 A piece of copper originally 305 mm long is pulled in tension with a stress of 276 MPa. If the deformation is entirely elastic, what will be the resultant elongation?

20 20 Elastic Properties of Materials Poisson s ratio Elastic dimensional change will occur transverse to applied uniaxial load: v x z y z E = 2G(1 + v)

21 21 Example 6.2 A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10 mm. Determine the magnitude of the load required to produce a mm change in diameter if the deformation is entirely elastic.

22 22 Tensile Properties Yield strength: stress that will result in a specified residual strain 0.2% yield strength 0.002=0.2%) Plastic behavior: some strain remains after removal of load

23 23 Tensile Properties Tensile Strength Mohammad Suliman Abuhaiba, Ph.D., PE

24 24 Example 6.3 From tensile stress strain behavior for the brass specimen shown, determine the following: a. Modulus of elasticity b. Yield strength at a strain offset of c. Max load that can be sustained by a cylindrical specimen having an original diameter of 12.8 mm d. Change in length of a specimen originally 250 mm long that is subjected to a tensile stress of 345 MPa

25 25 Example 6.3

26 26 Tensile Properties Ductility Brittle vs. ductile Two measures of ductility: lf l0 % EL 100 l0 A0 A f % RA 100 A0

27 27 Tensile Properties Ductility Table 6.2: Typical Mechanical Properties of Several Metals and Alloys in an Annealed State

28 28 Tensile Properties Effect of Temperature

29 29 Tensile Properties Modulus of Resilience Measure of a material s capacity to absorb mechanical energy elastically Area under stress-strain curve - units of energy per unit volume Ur y 0 d U r 1 2 y y y 2E 2

30 30 Tensile Properties Modulus of Toughness A measure of energy absorbed during fracture Area under stress-strain curve U T ut %EL U T y ut 2 %EL

31 31 TRUE STRESS AND STRAIN Engineering stress and strain: based on initial dimensions F A 0 L l 0 l l 0 l 0 True stress & strain: based on instantaneous dimensions T F A i T ln l i l 0

32 32 TRUE STRESS AND STRAIN Start of necking σ T = σ 1 + ε ε T = ln(1 + ε) A = πr 2

33 33 Example 6.4 A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile-tested to fracture & found to have an engineering fracture strength of 460 MPa. If its crosssectional diameter at fracture is 10.7 mm, determine: a. Ductility in terms of % reduction in area b. True stress at fracture

34 34 Example 6.5 Compute the strain-hardening exponent n for an alloy in which a true stress of 415 MPa produces a true strain of 0.10; assume a value of 1035 MPa for K.

35 35 Elastic Recovery After Plastic Deformation Plastic behavior: some strain remains after removal of load

36 36 Hardness - Brinell Test Hardness = resistance to permanent indentation Carbide balls are usually recommended for Brinell hardness numbers greater than 500. Impressions in annealed metals generally have a rounded profile.

37 Hardness 37 Table 6.5: Hardness Testing Techniques

38 38 Hardness - Rockwell

39 Hardness 39

40 Hardness 40

41 41 Hardness - Rockwell Test Measures depth of penetration instead of diameter of indentation. Indenter is pressed onto surface, 1 st with a minor load & then with a major load. Difference in depths of penetration is a measure of hardness of material.

42 42 Rockwill C Figure 6.18 Hardness Conversion Knoop Rockwel B Brinnel

43 43 Hardness Correlation between Hardness and Tensile Strength Hardness of a CW metal is about 3 times its yield stress; Y For annealed metals; it is about 5 times Y

44 44 Hardness Correlation between Hardness & Tensile Strength For steels UTS (MPa) = 3.5HB UTS (psi) = 500HB HB is in kg/mm 2, as measured for a load of 3000 kg

45 45 Example 6.6 The following tensile strengths were measured for 4 specimens of same steel alloy: a. Compute average tensile strength b. Determine standard deviation

46 46 Design Example 6.1 A tensile-testing apparatus is to be constructed that must withstand a max load of 220,000 N. The design calls for two cylindrical support posts, each of which is to support half of max load. Plain-carbon (1045) steel ground & polished shafting rounds are to be used; min yield & tensile strengths of this alloy are 310 MPa & 565 MPa, respectively. Specify a suitable diameter for these support posts.