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

> Compare stress–strain curves of 15 materials with an animated tensile test: E, yield, UTS, toughness. Axial load, thermal stress, bimetal strip and Ashby chart.

- URL: https://qilingtools.com/en/physics/materials
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

See typical stress–strain curves for structural steel, high-strength steel, aluminium, copper, titanium, cast iron, glass, concrete, rubber, nylon, polyethylene, wood, carbon fibre, bone and spider silk on one chart. An animated tensile specimen goes through elastic stretching, yielding, necking and fracture while the area under the curve (toughness) fills in. There is also an axial load calculator (stress, strain, elongation, Poisson contraction, G and K, safety factors, Euler buckling), thermal expansion and constrained thermal stress, a bimetallic strip that bends by Timoshenko's formula, and an Ashby chart of modulus against density.

## How to use

1. On 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. Press Pull to watch the specimen stretch, neck and break, or drag the slider to any strain and read the stress and energy absorbed
3. On the Axial load tab enter the cross-section, length and force to get stress, elongation, lateral contraction, safety factors and buckling load
4. Use 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

## Features

- Model curves for 15 materials: yield plateau, work hardening, necking, cold drawing, rubber hyperelasticity, concrete in compression
- Tensile specimen animation: uniform thinning at constant volume, necking in metals, a travelling neck in polymers, brittle or ductile fracture
- E, 0.2% offset yield, σ_u, elongation, toughness, resilience, specific stiffness and specific strength
- Axial tension and compression: σ, ε, ΔL, Poisson contraction, volume change, G, K, safety factors and Euler load, with plastic strain read from the curve
- Thermal expansion, fixed-end thermal stress and Timoshenko bimetal curvature with an animated tip deflection
- Ashby chart (E or strength against density, log–log) with E/ρ, E^½/ρ and E^⅓/ρ guide lines, plus a property table

## 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.

## Related tools

- [Unit Converter](https://qilingtools.com/en/math/unit): Free online unit converter: length, area, volume, weight, temperature, time, speed, data, pressure, energy and angle — one value converts every unit at once.
- [Vector Calculator](https://qilingtools.com/en/math/vector): Free online vector calculator for 2D and 3D: addition, scalar multiples, dot and cross products, magnitude, angle, unit vector and projections, with checks.
- [Significant Figures Calculator](https://qilingtools.com/en/math/significant-figures): Free online sig fig calculator: count significant figures digit by digit, round to N sig figs or decimals with six rounding modes, and compute by sig fig rules.
- [Tone Generator](https://qilingtools.com/en/audio/tone-generator): Free online tone generator: sine, square, sawtooth and triangle waves from 1 to 20,000 Hz, a note picker, sweeps, white/pink/brown noise and a WAV download.
- [Audio Spectrogram](https://qilingtools.com/en/audio/spectrogram): Free online spectrogram generator: see time, frequency and level from a Hann-windowed STFT, with FFT size, log axis, dB range and colour maps. Exports PNG.
- [Decibel Meter](https://qilingtools.com/en/audio/decibel): Free online decibel meter: measure noise with your mic in real time, A/C/Z weighting, fast/slow response, min/max/average/Leq, 60-second graph and calibration.
- [Physics Formula Calculator](https://qilingtools.com/en/physics/physics): Physics formulas solved with steps: SUVAT, projectiles, Newton’s laws, inclines, energy, Ohm’s law, resistors, RC, buoyancy, waves, lenses, gravity.
- [Fourier Series & FFT Visualizer](https://qilingtools.com/en/math/fourier): Fourier series coefficients and animated partial sums for square, sawtooth, triangle or any function (Gibbs), draw-your-own epicycles and FFT spectra.