Mechanical & Structural Properties

Strength

Ability of a material to withstand an applied load without failing

Units: Pa

Stress (σ)

Definition: Internal force per unit area acting on a material

Equation: σ = F/A

Units: N/m² or Pa

Strain (ε)

Definition: Amount of deformation relative to the material’s original length

Equation: ε = ΔL/L₀

Units: unitless (often expressed as a %)

Young’s Modulus / Elastic Modulus (E)

Definition: Resistance to elastic deformation in tension or compression; measures stiffness

Equation: E = σ/ε

Units: Pa (usually Gpa)

• The slope of a stress-strain curve in the linear part is E

• Axial Loading

Shear Modulus / Modulus of Rigidity (G)

Definition: Resistance to deformation caused by a shearing force

Equation: G = τ / γ

Units: Pa (usually GPa)

Bulk Modulus (K)

Definition: Resistance to uniform compression or a change in volume

Equation: K = - ΔP / (ΔV / V₀)

Units: Pa (usually GPa)

Flexural Modulus

Definition: Measures a material’s resistance to bending or flexural deformation

Units: Pa (usually GPa)

Poisson’s Ratio (v)

Definition: Ratio of lateral strain to longitudinal strain when a material is stretched or compressed

Equation: v = - ε(lateral) / ε(longitudinal)

Units: Unitless

Elasticity

Definition: Ability to return to original shape after the load is removed

• The linear portion of the stress-strain curve

Plasticity

Definition: Ability to permanently deform without breaking

• The non-linear portion of the stress-strain curve

Yield Strength

Definition: Stress at which significant permanent (plastic) deformation begins

Units: Pa (usually MPa)

• Upper limit of the linear portion of the strain-stress curve

• Do not want to go beyond this point

Ultimate Tensile Stress (UTS) (σᵤₜₛ)

Definition: maximum tensile stress a material can withstand before failure (necking/fracture)

Equation: UTS = Fₘₐₓ / A₀

Units: Pa (usually MPa)

• Occurs at maximum of the stress-strain curve

Ductility (εf)

Definition: Ability to undergo significant plastic deformation before breaking

Equation: [ (ΔL-L₀) / L₀ ] * 100

• Percent Elongation

• It’s okay to go past yield stress if you want to shape the material

• Final point on the stress-strain curve

Brittleness

Definition: Tendency to fracture with little plastic deformation

Toughness

Definition: Ability to absorb energy before fracturing

Units: J/m³ or σε

• Energy per volume required to permanently break a material

• Integral of the entire strain-stress curve

Resilience

Definition: ability of a material to absorb energy elastically and release that energy when unloaded

Equation: Uᵣ = σᵧ² / 2

Units: J / m³

• Area underneath linear portion of the strain-stress curve

• Used for shock absorber, helmet, protective gear, etc.

Hardness

Definition: Resistance to indentation, scratching, or localized deformation

• Resistance to plastic deformation

• Surface Property of a material

• Depends on test (Brinell, Vickers, Rockwell, etc.)

Stiffness

Definition: resistance of an object to deformation when force is applied

• How much force (stress) does it take to flex the material

Equation: k = F / ΔL

Units: N / m

Tensile Test

Definition: Test where a specimen is pulled until it deforms and/or breaks to determine mechanical properties

Measures: Young’s Modulus, yield strength, UTS, ductility, toughness, etc.

Vickers Hardness Test

Definition: Hardness test that uses a diamond-shaped pyramid indenter pressed into the material. The size of the indentation is measured

• Softer material = easier to indent, deeper indentation

Moh’s Hardness Scale

Definition: Scale that ranks minerals based on their resistance to scratching