🧱Stress–Strain Curves - Tensile Test Animation, Young's Modulus, Thermal Stress

How to use Materials Properties & Stress–Strain Curves

1. 1On the Stress–strain tab pick a material, tap others to overlay them, and switch to the elastic zoom or true-stress curve if you like
2. 2Press Pull to watch the specimen stretch, neck and break, or drag the slider to any strain and read the stress and energy absorbed
3. 3On the Axial load tab enter the cross-section, length and force to get stress, elongation, lateral contraction, safety factors and buckling load
4. 4Use the Thermal tab for ΔL and thermal stress and to animate a heated bimetal strip, and the Ashby tab to compare specific stiffness and strength

FAQ

What do the key points on a stress–strain curve mean?

The slope of the straight part is Young's modulus E, the stiffness. Where the line ends and permanent deformation starts is the yield strength σ_y; many metals have no sharp yield point, so the 0.2% offset yield is used, where the curve meets a line of slope E shifted by a strain of 0.002. The highest point is the ultimate tensile strength σ_u, after which the specimen necks and the engineering stress falls. The strain at fracture is the elongation at break, a measure of ductility, and the area under the curve is the energy absorbed per unit volume before breaking, the toughness.

Why does engineering stress fall after necking? Is the material getting weaker?

No. Engineering stress divides the force by the original area. Once necking starts, deformation concentrates in a short region whose cross-section shrinks quickly, so the force needed drops. The true stress σ_t = σ(1+ε), based on the current area, keeps rising, showing the metal is still work hardening. The tool can overlay the true stress–true strain curve, but that conversion only holds for uniform deformation, before necking.

What is the difference between toughness and strength?

Strength is the highest stress a material can carry; toughness is the energy it absorbs before breaking, which depends on both strength and ductility. Glass and carbon fibre can be very strong but barely deform plastically, so the area under their curves is small and they are brittle. Mild steel is only moderately strong but stretches 20–30%, so it is very tough. Spider silk is famous because it combines strength close to high-strength steel with tens of percent of stretch, giving more toughness per unit volume than steel.

Why does a bimetallic strip bend when heated?

The two layers have different expansion coefficients, so on heating one wants to grow more than the other. Bonded together, they can only accommodate this by curving into an arc, with the more expansive layer on the outside. Timoshenko's 1925 formula gives the curvature κ = 6(α₂−α₁)ΔT(1+m)² / {h[3(1+m)² + (1+mn)(m² + 1/mn)]}, where m is the thickness ratio and n the modulus ratio. For equal thicknesses and moduli it reduces to κ = 3Δα·ΔT/2h. Invar barely expands, so paired with brass it bends strongly, which is why it is used in thermostats and dial thermometers.

How do I use the guide lines on the Ashby chart?

For lightweight design you compare performance per unit mass, not E or σ alone. A tie in tension should maximise E/ρ, a beam in bending E^{1/2}/ρ, and a panel in bending E^{1/3}/ρ. On log–log axes lines of constant index have slopes 1, 2 and 3. Materials on the same line perform equally, and those above and to the left do better. That is why wood and carbon fibre can beat steel for beams and panels, and how aircraft and bicycle materials are chosen.