The ratio of stress to strain in the elastic region, E = σ/ε. It is set by interatomic bonding: about 200 GPa for steel and about 70 GPa for aluminum, and it hardly changes with heat treatment.
Japanese name: ヤング率
Young's modulus appears in 24 practice questions across 11 topics, including Composite materials, Biomaterials, Materials selection and design.
Young's modulus is determined by the curvature of the interatomic bonding potential (the stiffness of the bonds). It therefore tends to be larger for substances with strong bonds and high melting points: about 1000 GPa for diamond, about 410 GPa for tungsten, about 200 GPa for steel, about 120 GPa for copper, and about 70 GPa for aluminum and glass. Polymers are a few GPa or less and rubber is a few MPa, a range of about six orders of magnitude across material types. It is a basic design quantity that sets the stiffness, deflection and natural frequencies of parts.
It can be found from the slope of the elastic range in a tensile test, but the elastic strain is small, about 0.1%, and deflection of the machine is included, so the accuracy is not high. Accurate values are measured by the resonance method, which uses the resonant frequency of a specimen, or the ultrasonic pulse method, which uses the speed of ultrasound. The speed of longitudinal waves in a thin rod is √(E/ρ), about 5000 m/s for steel with a Young's modulus of 200 GPa and a density of 7850 kg/m³. For thin films and small regions, nanoindentation, which analyzes the unloading curve of an indenter, is used.
Young's modulus expresses resistance to deformation and is separate from resistance to failure (strength). Even when quenching increases the strength of steel several times, its Young's modulus hardly changes. If you want less deflection in a part, switching to a high-strength steel does nothing; you must change the cross-sectional shape or choose a material with a higher modulus. In a single crystal the value also varies with direction; for iron it is about 125 GPa in the <100> direction and about 273 GPa in the <111> direction. The value for a polycrystal is an average of these.
Deflections in tension and bending are inversely proportional to Young's modulus; for beams they are set by its product EI with the second moment of area I (the flexural rigidity). When lightness also matters, materials are compared by specific stiffness E/ρ, but steel (about 200 GPa, 7.85 g/cm³), aluminum alloys (about 70 GPa, 2.70 g/cm³) and titanium alloys (about 110 GPa, 4.5 g/cm³) all come to nearly the same value, about 25 GPa/(g/cm³). Among metals, therefore, designing the shape of plates and beams is what pays off, and a large increase in specific stiffness requires composites such as CFRP.
Answer: B. It is determined by the strength of interatomic bonding and changes little with heat treatment or working
Young's modulus is the ratio of stress to strain in the elastic region, E = σ/ε. It is set by the strength of interatomic bonding (the curvature of the interatomic potential) and is a structure-insensitive property. That is why it stays at around 200 GPa whether the steel is mild or quenched, and doubling the strength does not double the modulus. Yield strength and hardness are structure-sensitive properties governed by how easily dislocations move, and they change greatly with heat treatment and working. Young's modulus is the slope of the straight elastic line, distinct from the slope of the plastic region (the work-hardening rate). As temperature rises, bonding weakens and the modulus decreases gradually.
Answer: B. About 1.0 mm
From Hooke's law, the strain is ε = σ/E = 100×10⁶ / (200×10⁹) = 5.0×10⁻⁴. The elongation is ΔL = εL = 5.0×10⁻⁴ × 2000 mm = 1.0 mm. About 0.10 mm and about 10 mm are off by one order of magnitude from a slip in the GPa–MPa conversion (1 GPa = 1000 MPa) or the m–mm conversion. Even in a steel with a yield stress of several hundred MPa, the elastic strain stays at only about 0.1–0.2%. At the same stress, an aluminum alloy with about one third the modulus (about 70 GPa) stretches about three times as much, a difference that matters in stiffness-critical design.
For isotropic materials, G = E/(2(1 + ν)), where ν is Poisson's ratio. For steel (E = 200 GPa, ν = 0.3), G ≈ 77 GPa. Young's modulus expresses resistance to tensile deformation and the shear modulus resistance to shear.
The same as stress, Pa, and GPa is common for metals. Strain is dimensionless, so Young's modulus has the same unit as stress. Steel's roughly 200 GPa can also be written 2.0×10⁵ N/mm² (MPa).
Not necessarily. Hardness is resistance to plastic deformation and changes greatly with microstructure, such as how easily dislocations move, whereas Young's modulus is set by bond strength. Quenched and annealed steels differ greatly in hardness but have almost the same Young's modulus.
Young's modulus is the ratio of stress to strain in the elastic region, E = σ/ε.
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