Week 4 MECHANICAL PROPERTIES AND TESTS

1. Week 4MECHANICAL PROPERTIES AND TESTS Materials Science

2. Stress • Stress is a measure of the intensity of the internal forces acting within a deformable body. • Mathematically, it is a measure of the average force per unit area of a surface within a the body on which internal forces act • The SI unit for stress is Pascal (symbol Pa), which is equivalent to one Newton (force) per square meter (unit area). • Three types of stresses -> Tensile; Compressive; Shear

3. Mechanism of Stress (Tensile)

4. Strain • Strain is deformation of a physical body under the action of applied forces • It is the geometrical measure of deformation representing the relative displacement between particles in the material body • Strain is a dimensionless quantity • Strain accounts for elongation, shortening, or volume changes, or angular distortion • Normal stress causes normal strain (tensile or compressive) • Shear strain is defined as the change in angle between two originally orthogonal material lines

5. Types of Strains tensile load produces an elongation and positive linear strain. compressive load produces contraction and a negative linear strain. torsional deformation

6. Tensile Test and Stress-strain relationship

7. Tensile Test • Used for determining UTS, yield strength, %age elongation, and Young’s Modulus of Elasticity • The ends of a test piece are fixed into grips. The specimen is elongated by the moving crosshead; load cell and extensometer measure, respectively, the magnitude of the applied load and the elongation

8. Stress-Strain Relationship

9. Important Terms (Stress-Strain Rel.) • Elastic Limit -> Maximum amount of stress up to which the deformation is absolutely temporary • Proportionality Limit -> Maximum stress up to which the relationship between stress & strain is linear. • Hooke’s Law -> Within elastic limit, the strain produced in a body is directly proportional to the stress applied. σ = E ε

10. Important Terms (Stress-Strain Rel.) • Young’s Modulus of elasticity -> the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds • Elasticity -> the tendency of a body to return to its original shape after it has been stretched or compressed • Yield Point -> the stress at which a material begins to deform plastically

11. Important Terms (Stress-Strain Rel.) • Plasticity-> the deformation of a material undergoing non-reversible changes of shape in response to applied forces • Ultimate Strength -> It is the maxima of the stress-strain curve. It is the point at which necking will start. • Necking -> A mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material

12. Important Terms (Stress-Strain Rel.) • Fracture Point -> The stress calculated immediately before the fracture. • Ductility -> The amount of strain a material can endure before failure. • Ductility is measured by percentage elongation or area reduction

13. Important Terms (Stress-Strain Rel.) • A knowledge of ductilityis important for two reasons: • It indicates to a designer the degree to which a structure will deform plastically before fracture. • It specifies the degree of allowable deformation during fabrication

14. Engineering stress– strain behavior for Iron at three temperatures

15. Resilience • Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered • Modulus of Resilience (Ur) is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.

16. Resilience • Assuming a linear elastic region • For SI units, this is joules per cubic meter (J/m3, equivalent to Pa) • Thus, resilient materials are those having high yield strengths and low moduli of elasticity; such alloys would be used in spring applications

17. Shear and Torsional Tests Shear Stress: • The shear strain γ is defined as the tangent of the strain angle θ • Torsion is a variation of pure shear, wherein a structural member is twisted in the manner of the figure • Torsional stress -> The shear stress on a transverse cross section resulting from a twisting action • Torsional forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end

18. ANELASTICITY • In most engineering materials, there also exists a time-dependent elastic strain component. • This time-dependent elastic behavior is known as anelasticity • For metals the anelastic component is normally small and is often neglected • For some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior

19. EXAMPLE PROBLEM 6.1 • A piece of copper originally 305mm (12 in.) long is pulled in tension with a stress of 276MPa (40,000psi). If the deformation is entirely elastic, what will be the resultant elongation? • Magnitude of E for copper from Table 6.1 is 110GPa

20. Poisson’s Ratio • Poisson’s ratio is defined as the ratio of the lateral and axial strains • Theoretically, Poisson’s ratio for isotropic materials should be 1/4; furthermore, the maximum value for ν is 0.50 • For isotropic materials, shear and elastic moduli are related

21. EXAMPLE PROBLEM 6.2 • A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10mm. Determine the magnitude of the load required to produce a 0.0025mm change in diameter if the deformation is entirely elastic. For the strain in the x direction:

22. EXAMPLE PROBLEM 6.2

23. True Stress and Strain • The decline in the stress necessary to continue deformation past the point M, indicates that the metal is becoming weaker. • Material is increasing in strength. • True stress σTis defined as the load F divided by the instantaneous cross-sectional area Ai over which deformation is occurring • True strain ЄTis defined as:

24. True Stress and Strain • If no volume change occurs during deformation—that is, if Aili= A0l0 • Then true and engineering stress and strain are related according to • The equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, cross-sectional area, and gauge length measurements

25. Assignment • (a) Completely describe “Compression Test”. (b) How is it different from Tensile test? (c) What are the effects of Friction and Workpiece’s height-to-diameter ratio on the test? (d) Derive relationship between true stress/strain and engineering stress/strain for compression test (also show by stress-strain curve) • Only hand-written assignments

26. EXAMPLE PROBLEM 6.4 • A cylindrical specimen of steel having an original diameter of 12.8mm is tensile tested to fracture and found to have an engineering fracture strength σf of 460MPa. If its cross-sectional diameter at fracture is 10.7mm, determine: (a) The ductility in terms of percent reduction in area (b) The true stress at fracture Ductility is computed as

27. EXAMPLE PROBLEM 6.4 True stress is defined by Equation where the area is taken as the fracture area Af However, the load at fracture must first be computed from the fracture strength as And the true stress is calculated as

28. Elastic Recovery after Plastic Deformation • Upon release of the load during the course of a stress–strain test, some fraction of the total deformation is recovered as elastic strain • During the unloading cycle, the curve traces a near straight-line path from the point of unloading (point D), and its slope is virtually parallel to the initial elastic portion of the curve • The magnitude of this elastic strain, which is regained during unloading, corresponds to the strain recovery

29. Hardness • Hardness is the property of material by virtue of which it resists against surface indentation and scratches. • Macroscopic hardness is generally characterized by strong intermolecular bonds • Hardness is dependent upon strength and ductility • Common examples of hard matter are diamond, ceramics, concrete, certain metals, and superhard materials (PcBN, PcD, etc)

30. Hardness Tests (BRINELL HARDNESS TEST) • Used for testing metals and nonmetals of low to medium hardness • The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece • A hardened steel (or cemented carbide) ball of 10mm diameter is pressed into the surface of a specimen using load of 500, 1500, or 3000 kg.

31. BRINELL HARDNESS TEST where: P = applied force (kgf) D = diameter of indenter (mm) d = diameter of indentation (mm) • The resulting BHN has units of kg/mm2, but the units are usually omitted in expressing the numbers

32. Rockwell Hardness Test • Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a preload • A cone shaped indenter or small diameter ball (D = 1.6 or 3.2mm) is pressed into a specimen using a minor load of 10kg • Then, a major load of 150kg is applied • The additional penetration distance d is converted to a Rockwell hardness reading by the testing machine.

33. Rockwell Hardness Test

34. Vickers Hardness Test • Uses a pyramid shaped indenter made of diamond. • It is based on the principle that impressions made by this indenter are geometrically similar regardless of load. • The basic principle, as with all common measures of hardness, is to observe the questioned material's ability to resist plastic deformation from a standard source. • Accordingly, loads of various sizes are applied, depending on the hardness of the material to be measured

35. Vickers Hardness Test Where: F = applied load (kg) D = Diagonal of the impression made the indenter (mm) The hardness number is determined by the load over the surface area of the indentation and not the area normal to the force

36. Knoop Hardness Test • It is a microhardness test - a test for mechanical hardness used particularly for very brittle materials or thin sheets • A pyramidal diamond point is pressed into the polished surface of the test material with a known force, for a specified dwell time, and the resulting indentation is measured using a microscope • Length-to-width ratio of the pyramid is 7:1

37. Knoop Hardness Test (contd…) • The indenter shape facilitates reading the impressions at lighter loads • HK = Knoop hardness value; F = load (kg); D = long diagonal of the impression (mm)

38. Hardness of Metals and Ceramics

39. Hardness of Polymers

40. TOUGHNESS • It is a property of material by virtue of which it resists against impact loads. • Toughness is the resistance to fracture of a material when stressed • Mathematically, it is defined as the amount of energy per volume that a material can absorb before rupturing • Toughness can be determined by measuring the area (i.e., by taking the integral) underneath the stress-strain curve

41. Toughness (contd…) • Toughness = Where • ε is strain • εf is the strain upon failure • σ is stress The Area covered under stress strain curve is called toughness

42. Toughness (contd…) • Toughness is measured in units of joules per cubic meter (J/m3) in the SI system • Toughness and Strength -> A material may be strong and tough if it ruptures under high forces, exhibiting high strains • Brittle materials may be strong but with limited strain values, so that they are not tough • Generally, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupture

43. Effect of Temperature on Properties • Generally speaking, materials are lower in strength and higher in ductility, at elevated temperatures

44. Hot Hardness • A property used to characterize strength and hardness at elevated temperatures is Hot Hardness • It is the ability of a material to retain its hardness at elevated temperatures

45. Numerical Problems • Problems 6.3 to 6.9; • 6.14 to 6.23; • 6.25 to 6.33; • 6.46 to 6.48