Mechanical Properties of Materials

Mechanical Properties

Learning Objectives

• Identify various mechanical properties.
• Understand how mechanical properties are measured.
• Comprehend what these properties represent.
• Design structures/components using predetermined materials to avoid unacceptable deformation and/or failure.

Overview

• Engineers must understand how mechanical properties are measured and what they represent.
• They design structures/components with materials that prevent unacceptable deformation or failure.
• Materials in service are subjected to forces or loads (e.g., aluminum alloy in airplane wings, steel in automobile axles).
• It's essential to know material characteristics to design members that resist excessive deformation and fracture.
• Mechanical behavior reflects the relationship between a material's response or deformation and applied load or force.
• This lesson primarily covers mechanical behavior of metals; polymers and ceramics are treated separately due to their mechanical dissimilarity.
• It discusses stress-strain behavior of metals, related mechanical properties, and other important mechanical characteristics.

Types of Loads

• Three principal ways a load may be applied:
  1. Tension
  2. Compression
  3. Shear
• In engineering, many loads are torsional rather than pure shear.

Elastic Deformation

• Elastic deformation is reversible.
• Small load $F$ causes bonds to stretch.
• Upon unloading, the material returns to its initial state.
• Deformation where stress and strain are proportional is called elastic deformation.
• The slope of the linear segment corresponds to the modulus of elasticity $E$, representing stiffness or resistance to elastic deformation.
• Elastic deformation is nonpermanent; the material returns to its original shape when the load is released.
• For most metallic materials, elastic deformation persists only to strains of about 0.005.
• Beyond this point, stress is no longer proportional to strain, and permanent (plastic) deformation occurs.
• The transition from elastic to plastic deformation is gradual for most metals, with curvature at the onset of plastic deformation increasing with rising stress.

Plastic Deformation

• Plastic deformation is permanent.
• From an atomic perspective, plastic deformation involves breaking bonds with original atom neighbors and reforming bonds with new neighbors as atoms or molecules move relative to each other.
• Upon stress removal, atoms do not return to their original positions.
• The mechanism differs for crystalline and amorphous materials.

Stress

• Stress units: $N/m^2$ or $lbf/in^2$
• Tensile stress $\sigma$: $\sigma = \frac{F<em>t}{A</em>o}$, where $A_o$ is the original area before loading.
• Shear stress $\tau$: $\tau = \frac{F<em>s}{A</em>o}$

Common States of Stress

• Simple tension (e.g., cable): $\sigma = \frac{F}{A_o}$
• Torsion (a form of shear, e.g., drive shaft): $\tau = \frac{M}{A_c R}$
• Simple compression (compressive structure member): $\sigma = \frac{F}{A_o}$ ($\sigma$ < 0 here)

Strain

• Tensile strain: $\epsilon<em>L = \frac{dL}{L</em>o}$
• Lateral strain: $\epsilon = \frac{-d}{w_o/2}$
• Shear strain: $\gamma = tan \theta$
• Strain is dimensionless.

Stress-Strain Testing

• Typical tensile test involves a testing machine, specimen, and extensometer.
• A typical tensile specimen includes a gauge length.

Tension Tests

• Used to ascertain various mechanical properties of materials important in design.
• A specimen is deformed, usually to fracture, with a gradually increasing tensile load applied uniaxially along its long axis.
• The "dogbone" specimen configuration ensures deformation is confined to the narrow center region with a uniform cross-section, reducing fracture likelihood at the ends.

Linear Elastic Properties

• Modulus of Elasticity, $E$ (Young's modulus):
• Hooke's Law: $\sigma = E \epsilon$

Poisson's Ratio

• $\nu = -\frac{\epsilon<em>L}{\epsilon</em>l}$
• Units: $E$ - [GPa] or [psi], $\nu$ - dimensionless
• $\nu$ > 0.50: density increases (not physically possible)
• $\nu$ < 0.50: density decreases (voids form)
• Metals: $\nu \approx 0.33$
• Ceramics: $\nu \approx 0.25$
• Polymers: $\nu \approx 0.40$

Young’s Moduli Comparison

• Comparison of Young's Moduli (E(GPa)) for various materials:
  • Metals, Alloys, Graphite, Ceramics, Semicond, Polymers, Composites/ fibers.

Plastic (Permanent) Deformation

• Simple tension test showing elastic and plastic regions.
• Elastic + Plastic at larger stress.
• Permanent (plastic) deformation after load is removed.

Proportional Limit and Yield Strength

• A structure or component that has plastically deformed may not function as intended.
• It is desirable to know the stress level at which plastic deformation begins (yielding).
• Proportional limit: the point of yielding, determined as the initial departure from linearity of the stress-strain curve (point P).
• Yield strength, $\sigma_y$: the stress corresponding to the intersection of a line (offset by a specific strain, e.g., 0.002), and the stress-strain curve in the plastic region.
• For materials with a nonlinear elastic region, yield strength is defined as the stress required to produce a specific amount of strain (e.g., 0.005).

Yield Strength

• Stress at which noticeable plastic deformation has occurred.
• When $\epsilon<em>p = 0.002$, $\sigma</em>y$ = yield strength.
• Note: for a 2-inch sample, $\epsilon = 0.002 = \frac{\Delta z}{z}$, therefore $\Delta z = 0.004$ in.

Yield Strength Comparison

• Comparison of Yield Strength ($\sigma_y$) in MPa for various materials.
  • Metals, Alloys, Composites/fibers, Polymers, Graphite/Ceramics/Semicond.
  • Includes various treatments such as annealed (a), hot rolled (hr), aged (ag), cold drawn (cd), cold worked (cw), quenched & tempered (qt).

Tensile Strength

• Tensile strength TS (MPa or psi): the stress at the maximum on the engineering stress-strain curve.
• This corresponds to the maximum stress sustained by a structure in tension; if this stress is applied and maintained, fracture will result.

Tensile Strength, TS

• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are aligned and about to break.
• Maximum stress on the engineering stress-strain curve.

Tensile Strength Comparison

• Comparison of Tensile Strength (TS) in MPa for various materials.
  • Graphite/ Ceramics/ Semicond, Metals/ Alloys, Composites/ fibers, Polymers.

Ductility

• A measure of the degree of plastic deformation sustained at fracture.
• A material experiencing very little or no plastic deformation upon fracture is termed brittle.

Ductility Measures

• Plastic tensile strain at failure.
• Calculation:
  • $\%EL = \frac{L<em>f - L</em>o}{L_o} \times 100$
  • $\%RA = \frac{A<em>o - A</em>f}{A_o} \times 100$

Toughness

• Energy to break a unit volume of material.
• Approximate by the area under the stress-strain curve.
• It is a measure of the ability of a material to absorb energy up to fracture.

Toughness Examples

• Brittle fracture: elastic energy only.
• Ductile fracture: elastic + plastic energy.

Resilience

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

Resilience, Ur

• Ability of a material to store energy, best stored in the elastic region.
• If assuming a linear stress-strain curve: $U<em>r = \int</em>0^{\epsilon<em>y} \sigma d\epsilon = \frac{1}{2} \sigma</em>y \epsilon_y$

Elastic Strain Recovery

• Upon release of the load during a stress-strain test, some fraction of the total deformation is recovered.
• During the unloading cycle, the curve traces a near straight-line path.
• Slope = modulus of elasticity, elastic strain = strain recovery.

Hardness

• Resistance to permanently indenting the surface.
• Large hardness indicates:
  • Resistance to plastic deformation or cracking in compression.
  • Better wear properties.

Hardness Tests

• Performed more frequently than any other mechanical test for several reasons:
  1. Simple and inexpensive (no special specimen preparation, inexpensive apparatus).
  2. Nondestructive (specimen is neither fractured nor excessively deformed; small indentation).
  3. Other mechanical properties (e.g., tensile strength) may be estimated from hardness data.

Hardness Measurement

• Rockwell:
  • No major sample damage.
  • Each scale runs to 130 but is only useful in the range of 20-100.
  • Minor load: 10 kg
  • Major load: 60 (A), 100 (B) & 150 (C) kg
  • A = diamond, B = 1/16 in. ball, C = diamond
• HB = Brinell Hardness
  • TS (psia) = 500 x HB
  • TS (MPa) = 3.45 x HB

Hardness Testing Techniques

• Comparison of different Hardness Testing Techniques. Ex: Brinell, Vickers, Knoop and Rockwell, including indenter type, formula for hardness number, shape of indentation, load.

Design or Safety Factors

• Uncertainties exist in characterizing the magnitude of applied loads and their associated stress levels.
• Load calculations are often approximate.
• Design allowances protect against unanticipated failure.
• One approach involves establishing a design stress or safe stress for the application.

Factor of Safety

• Design uncertainties mean we do not push the limit.
• Factor of safety, N: $N = \frac{\sigma<em>y}{\sigma</em>{working}}$
• Often N is between 1.2 and 4.
• Example: Calculate a diameter, d, to ensure that yield does not occur in a 1045 carbon steel rod with a factor of safety of 5.
  • 1045 plain carbon steel: $\sigma_y = 310$ MPa, TS = 565 MPa, F = 220,000 N
  • $N = \frac{\sigma<em>y}{\sigma</em>{working}} = \frac{\sigma_y}{\frac{F}{\pi d^2/4}}$
  • $d = 0.067$ m = 6.7 cm

Reference

• W.D. Callister, Jr., and D.G. Rethwisch, Materials Science and Engineering: An Introduction (7th Edition), John Wiley & Sons, Inc., 2007, ISBN-13: 978-0-471-73696-7