Introduction to Materials Science and Engineering Chapter 6: Mechanical Properties of Metals Textbook: Chapter 8

Content Introduction Stress and Strain Elastic Deformation Plastic Deformation Toughness and Hardness Summary

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 does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and Ductility: What are they and how do we measure them?

Technological Significance: Aircraft, such as the one shown here, makes use of aluminum alloys and carbon-fiber reinforced composites. (Courtesy of Getty Images.) The materials used in sports equipment must be lightweight, stiff, tough, and impact resistant. (Courtesy of Getty Images.)

History of Strength Test: (a) (b) (c) (a) Tensile Test of Wire by Leonardo da Vinci (b) Galileo’s Illustration of Bending Test (c) Galileo’s Illustration of Tensile Test

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.

Content Introduction Stress and Strain Elastic Deformation Plastic Deformation Toughness and Hardness Summary

Tensile Test: Measures the resistance of a material to a static or slowly applied force. As the force is applied the metal deforms (elongated). • Typical tensile specimen

Engineering Stress: (Force divided by the original area A0) • Tensile stress, σ: • Shear stress, τ: Stress has units: N/m2 or lb/in2

Engineering Strain: • Tensile Strain (e): • Lateral strain: • Shear Strain (g): Strain is always dimensionless.

Schematic Illustration of Different Stress State

Schematic Representation of Normal and Tensile Stresses

Content Introduction Stress and Strain Elastic Deformation Plastic Deformation Toughness and Hardness Summary

Linear Elastic Properties: • Modulus of Elasticity, E: (also known as Young's modulus) • Hooke's Law: • Poisson's Ratio, ν: Metals: ν ~ 0.33 Ceramics: ~0.25 Polymers: ~0.40 Units: E: [GPa] or [psi] n: Dimensionless

Elastic Properties: Schematic stress-strain diagram showing linear elastic deformation for loading and unloading cycles. Schematic stress-strain diagram showing nonlinear elastic deformation, and how secant and tangent moduli are determined.

Properties from Bonding : E Elastic (Young’s) Modulus, E (Y) E ~ Curvature at ro (The Bottom of The Well) E is larger if Eo is larger

Force versus Interatomic Separation:

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)

Other Elastic Properties: • Elastic Shear Modulus, G: Simple torsion test • Elastic Bulk Modulus, K: Pressure test: Initial vol =Vo. Vol change = DV • Special Relations for Isotropic Materials:

Bulk Modulus

Elastic Modulus

Content Introduction Stress and Strain Elastic Deformation Plastic Deformation Toughness and Hardness Summary

Stress at which noticeable plastic deformation has occurred. Yield Strength, σy Stress at which noticeable plastic deformation has occurred.

Yield Strength Comparison:

Tensile Strength, TS: • Maximum Possible Engineering Stress in Tension. Adapted from Fig. 6.11, Callister 6e. • Metals: Occurs when noticeable necking starts. • Ceramics: Occurs when crack propagation starts. • Polymers: Occurs when polymer backbones are aligned and about to break.

Plastic Deformation Necking starts to form Cup and cone failure

Tensile Test: 1. Modulus of Elasticity, E 2. Yield Strength, Y.S. 3. Tensile Strength, T.S. 4. Ductility, 100 x  failure 5. Toughness

Tensile Strength Comparison Room Temp. Values Based on data in Table B4, Callister 6e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers.

True Stress and True Strain True Stress : σt True Strain : εt If no volume change occurs during deformation, namely,

Comparison of Engineering and True Stress-Strain Curves

Comparison of Engineering and True Stress-Strain Curves

Temperature Effect

Testing of Ceramics - Four Point Bend Test

Bend Test Flexile Strength (Modulus of Rupture) Flexile Modulus

Testing of Polymers Polyester Nylon66 Semicrystalline Thermoplastic Spherulite Polyester Nylon66

Plastic Deformation of Polymers

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.

Content Introduction Stress and Strain Elastic Deformation Plastic Deformation Toughness and Hardness Summary

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

Hardness A measure of a material’s resistance Test to plastic deformation. Test - A hard indenter is pressed into the specimen. Standard load applied. Magnitude of indentation is measured: Area of Indentation, or Depth of Indentation.

Hardness Resistance to Permanently Indenting the Surface A Measure of a Material’s Resistance to Localized Plastic Deformation Large hardness means: Better Resistance to Plastic Deformation or Cracking in Compression Better Wear Properties Indentation/indentor; Mohs scale, BHN, etc.

Rockwell Hardness Test Rockwell Hardness Tester

Hardness Measurement

) Hardness • An Increase in σy due to Plastic Deformation. • Curve Fit to the Stress-Strain Response: Hardening Exponent: ) n n= 0.15 (Some Steels) σ = C ε T T to n= 0.5 (Some Copper) True Stress (F/A) True Strain: ln(l/l0)

Hardness Measurement

Hardness vs. Tensile Properties

Design or Safety Factors • Design uncertainties mean we do not push the limit. • Factor of Safety, N Often N is between 1.2 and 4 • Ex: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 1045 plain s y =310MPa TS=565MPa F = 220,000N d L o carbon steel: 5

Strength vs. Density

Summary • Stress and Strain: These are size-independent measures of load and displacement, respectively. • Elastic Behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic Behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches σy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure.