CHAPTER 6: MECHANICAL PROPERTIES

CHAPTER 6: MECHANICAL PROPERTIES ISSUES TO ADDRESS... • Stress and strain: What are they and why are they used instead of load and deformation? • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? • Toughness and ductility: What are they and how do we measure them? 1

Chapter 6: Mechanical Properties of Metals6.1 Introduction • Why Study the Mechanical Properties of Metals ? • It is important for engineers to understand • How the various mechanical properties are measured, and • What these properties represent • The role of structural engineers is to determine stresses and stress distributions within members that are subjected to well-defined loads • By experimental testing • Theoretical and mathematical stress analysis. • Design structures/components using predetermined materials such that unacceptable levels of deformation and/or failure will not occur.

6.2 Concepts of Stress and Strain • Static load changes relatively slowly with time • Applied uniformly over a cross-section or surface of a member. • Tension • Compression • Shear • Torsion

6.2 Concepts of Stress and Strain (Contd.) • TENSION TEST • Most common mechanical stress-strain test • Used to ascertain several mechanical properties that are important in design • A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of the specimen. • A standard specimen is shown in Figure 6-2.

6.2 Concepts of Stress and Strain (Contd.) • The specimen is mounted by its ends into the holding grips of the testing apparatus (Figure 6-3). • Tensile testing machine • To elongate the specimen at a constant rate • To continuously and simultaneously measure the instantaneous load and the resulting extension • Load using load cell • Extension using extensometer • Takes few minutes and is destructive.

6.2 Concepts of Stress and Strain (Contd.) • Engineering Stress (s) = Instantaneous applied load (F) / Original Area (Ao) • Unit: MPa, GPa, psi • Engineering strain (e) • li = instantaneous length • lo = original length • COMPRESSION TESTS • Similar to tensile test, compressive load • Sign convention, compressive force is taken negative  stress negative • Since lo > li , negative strain

6.2 Concepts of Stress and Strain (Contd.) • SHEAR AND TORSIONAL TESTS • Shear stress : t = F / Ao • F: Load or force imposed parallel to the upper and lower faces • Ao: shear or parallel area • Shear strain (g) is defined as the tangent of the strain angle q.

6.2 Concepts of Stress and Strain (Contd.) • GEOMETRIC CONSIDERATIONS OF THE STRESS STATE • Stress is a function of orientations of the planes

ELASTIC DEFORMATION 1. Initial 2. Small load 3. Unload Elastic means reversible! 2

ELASTIC DEFORMATION6.3 Stress-Strain Behavior • Elastic deformation: • Non-permanent, completely reversible, conservative • Follow same loading and unloading path • Linear elastic deformation • Hooke’s Law • Modulus of elasticity or Young’s Modulus  stiffness or a material’s resistance to elastic deformation

6.3 Stress-Strain Behavior (Contd.)

Nonlinear Elastic Behavior • Gray cast iron, concrete, many polymers • Not possible to determine a modulus of elasticity • Eithertangent or secant modulus is normally used.

6.3 Stress-Strain Behavior (Contd.) • On an atomic scale, macroscopic elastic strain is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds.  E is a measure of the resistance to separation of adjacent atoms • Modulus is proportional to the slope of the interatomic force-separation curve (Fig 2.8a) at equilibrium spacing

6.3 Stress-Strain Behavior (Contd.) • With increasing temperature, the modulus of elasticity diminishes • Shear stress and strain are proportional to each other: • Shear modulus or modulus of rigidity ( Table 6.1)

6.4 Anelasticity • Up to this point, it is assumed that • Elastic deformation is time-independent • An applied stress produces an instantaneous elastic strain • Strain remains constant over the period of time the stress is maintained • Upon release of the load, strain is totally recovered (immediately returns to zero) • In most engineering materials, there will also exist a time-dependent elastic strain component , i.e. • elastic deformation will continue after stress application • Upon load release some finite time is required for complete recovery • Loading and unloading path are different • Anelasticity : time-dependent elastic behavior • For metals, the anelastic component is normally small and neglected. • For some polymers, it is significant and known as viscoelastic behavior (Sec. 16.7)

6.5 Elastic Properties of Materials • Poisson’s ratio • E = 2G(1 + n) • Example 6.1 • Example 6.2

PLASTIC DEFORMATION • For most metals, elastic deformation persists only to strains of about 0.005 • Plastic deformation • Stress not proportional to strain (Hooke’s law cease to be valid) • Permanent • Nonrecoverable • Non-conservative • Transition from elastic to plastic deformation • Gradual for most metals • Some curvature results at the onset of plastic deformation

PLASTIC DEFORMATION (METALS) 1. Initial 2. Small load 3. Unload Plastic means permanent! 3

PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: 14

Plastic deformation (Contd.) • From as atomic perspective • Plastic deformation corresponds to the breaking of bonds with original atom neighbors • Reforming bonds with new neighbors • Large number of atoms and molecules move relative to one another • Upon removal of stress, they do not return to their original position • Mechanism of plastic deformation: • Crystalline Solids: • accomplished by a process called slip • Involves the motion of dislocations (Sec 7.2) • Non-crystalline solids (as well liquids) • Occurs by a viscous flow mechanism (Sec 13.9)

YIELD STRENGTH, sy • Stress at which noticeableplastic deformation has occurred. when ep = 0.002 15

6.6 Tensile Properties • YIELDING and YIELD STRESS Typical stress strain behavior (Figure) • Proportional Limit (P) • Yielding • Yield strength In most cases, the position of yield point may not be determined precisely. • Established convention: a straight line is constructed parallel to the elastic portion at some specified strain offset, usually 0.002 (0.2%) Fig. 6.10a  corresponding intersection point gives yield strength.

6.6 Tensile Properties (Contd.) • Some steels and other materials exhibit the behavior as shown in Fig 6.10b • The yield strength is taken as the average stress that is associate with the lower yield point. • Magnitude of yield strength is a measure of its resistance to plastic deformation • Range from 35 MPa to 1400 MPa • 35 MPa for low-strength aluminum • 1400 MPa for high-strength steel

6.6 Tensile Properties (Contd.) • TENSILE STRENGTH • Tensile strength TS (MPa or psi) is the stress at the maximum on the engineering stress-strain curve • All deformation up to this point is uniform. • Onset of necking at this stress at some point  all subsequent deformation at this neck. • Range: 50 - 3000 MPa 50 MPa for aluminum 3000 MPa for high strength steel

DUCTILITY, %EL • Plastic tensile strain at failure: Adapted from Fig. 6.13, Callister 6e. • Another ductility measure: • Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. 19

Effect of Temperature • As with modulus of elasticity (E), the magnitudes of both yield and tensile strengths decline with increasing temperature • Ductility usually increases with temperature • Figure shown stress-strain behavior of iron

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) • Associated property • Area under the engineering stress-strain curve • Strain energy per unit volume required to stress from an unloaded state to yielding • Mathematically,

TOUGHNESS • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. 20

TOUGHNESS • A measure of the ability of a material to absorb energy up to fracture. • Specimen geometry and the manner of load application are important in toughness determination: • Notch toughness: dynamic (high strain rate) loading, specimen with notch (or point of stress concentration) (Sec 8.6) • Fracture toughness: property indicative of a materials resistance to fracture when crack is present (Sec 8.5) • For static (low strain rate) condition, modulus of toughness is equal to the total area under the stress-strain curve (up to fracture ): For Ductile Material : For Brittle Material:

6.7 True Stress and Strain • Engineering stress-strain curve beyond maximum point (M) seems to indicate that the material is becoming weaker. • Not true, rather it becomes stronger. • Since cross-sectional area is decreasing at the neck  reduces load bearing capacity of the material • True stress: Actual or current or instantaneous force divided by the instantaneous cross-sectional area. • True Strain: Change in length per unit instantaneous length

6.7 True Stress and Strain (Contd.) • Relation between two definitions • Above equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, area and gauge length. Schematic comparison in Figure 6.16 • Corrected takes into account complex stress state with in neck region.

6.7 True Stress and Strain (Contd.) • For some metals and alloys, the true stress-strain curve is approximated as • Parameter n • strain-hardening exponent • A value less than unity • Slope on log-log plot • Parameter K • Known as strength coefficient • True stress at unit true strain

6.8 Elastic Recovery During Plastic Deformation • Upon release of load, some fraction of total strain is recovered as elastic strain • During unloading, straight path parallel to elastic loading • Reloading • Yielding at new yield strength

Solve Examples in Class • 6.3 • 6.4 • 6.5 • 6.6 • Design Example 6.1

CHAPTER 6: MECHANICAL PROPERTIES