3.1 Mechanical Properties of Materials

Strength Properties

Tensile and Fatigue Strength

When you load a material, it first deforms elastically (it springs back), then plastically (it stays deformed), and eventually fractures. The stress levels at which these transitions happen define a material's strength.

• Yield strength is the stress at which a material begins to permanently (plastically) deform. Because the transition from elastic to plastic isn't always sharp, the 0.2% offset method is commonly used: you draw a line parallel to the elastic region, offset by 0.2% strain, and where it intersects the stress-strain curve is your yield strength.
• Ultimate tensile strength (UTS) is the maximum stress a material can withstand. On the engineering stress-strain curve, it's the highest point. Beyond UTS, the material begins to neck and will eventually fracture.
• Fatigue strength measures how well a material holds up under repeated cyclic loading, which is critical for components like shafts, springs, and connecting rods. Ferrous alloys (steels, cast irons) exhibit an endurance limit, a stress level below which the material can theoretically survive an infinite number of cycles without failure. Most non-ferrous alloys (aluminum, copper) do not have a true endurance limit; their fatigue strength is instead reported at a specific cycle count, typically $10^7$ or $10^8$ cycles.

Hardness and Toughness

• Hardness quantifies a material's resistance to localized plastic deformation, such as indentation or scratching.
  • Measured using scales like Rockwell, Brinell, Vickers, and Knoop, each suited to different materials and applications
  • Correlates with wear resistance and can give a rough estimate of tensile strength (for steels, $UTS \approx 3.45 \times HB$, where $HB$ is Brinell hardness in MPa)
• Toughness is a material's ability to absorb energy before fracturing. It's represented by the total area under the stress-strain curve.
  • A material can be strong or ductile and still not be tough. Toughness requires a combination of both: reasonable strength and reasonable ductility.
  • High toughness is especially important where impact loading or low temperatures could promote brittle fracture. The Charpy impact test is a common way to measure notch toughness under dynamic loading.

Elastic Properties

Stress and Strain

These two quantities are the foundation of all mechanical property analysis. Stress describes the internal forces in a material; strain describes how much it deforms.

• Stress ($\sigma$) is force per unit area: $\sigma = F/A$
  • Units: pascals (Pa) or, more practically, megapascals (MPa)
  • Types include normal stress (tensile or compressive, acting perpendicular to a surface) and shear stress (acting parallel to a surface)
• Strain ($\epsilon$) is the deformation response to an applied stress: $\epsilon = \Delta L / L_0$
  • It's a dimensionless ratio (change in length divided by original length)
  • Elastic strain is fully recoverable when the load is removed. Plastic strain is permanent.

Elastic Modulus and Poisson's Ratio

• Elastic modulus (Young's modulus, $E$) relates stress and strain in the linear elastic region: $E = \sigma / \epsilon$
  • It's a direct measure of stiffness, meaning how much a material resists elastic deformation. A higher modulus means the material deflects less under load.
  • Typical values: steel $\approx 200$ GPa, aluminum $\approx 70$ GPa, common polymers $\approx 1{-}4$ GPa, elastomers $\approx 0.01{-}0.1$ GPa
• Poisson's ratio ($\nu$) is the negative ratio of transverse strain to axial strain: $\nu = -\epsilon_{transverse} / \epsilon_{axial}$
  • When you pull a bar in tension, it gets longer axially but thinner laterally. Poisson's ratio captures that lateral contraction.
  • Most engineering materials fall between $\nu = 0.25$ and $\nu = 0.35$. Rubber approaches $\nu = 0.5$ (nearly incompressible), while cork is close to $\nu = 0$ (which is why it works so well as a bottle stopper).

Deformation Properties

Ductility and Creep Resistance

• Ductility is a material's ability to undergo significant plastic deformation before fracturing.
  • Quantified by percent elongation ($\%EL = \frac{L_f - L_0}{L_0} \times 100$) or percent reduction in area ($\%RA = \frac{A_0 - A_f}{A_0} \times 100$)
  • Ductile materials (most metals at room temperature) exhibit necking and large strains before failure. Brittle materials (ceramics, glasses) fracture with little to no plastic deformation. As a rough benchmark, materials with $\%EL < 5\%$ are generally considered brittle.
  • Ductility matters for design because ductile materials give visible warning before failure (they deform noticeably), while brittle materials fail suddenly.
• Creep resistance is a material's ability to resist slow, time-dependent deformation under a constant load.
  • Creep becomes significant at elevated temperatures, generally above about $0.4 \, T_m$ (where $T_m$ is the absolute melting temperature). For steel, that's roughly 450°C; for aluminum alloys, it can be as low as 150°C.
  • Creep strain depends on applied stress, temperature, and time. The three stages of creep are: primary (decreasing rate), secondary/steady-state (constant rate, used for design life predictions), and tertiary (accelerating rate leading to rupture).
  • Materials with strong interatomic bonding and high melting points, such as nickel-based superalloys and ceramics, offer superior creep resistance. This is why jet engine turbine blades use nickel superalloys rather than steel.