Tensile Test Simulator: Stress-Strain Curve, Yield, UTS and Necking
Free tensile test simulator: pull steel, aluminium, cast iron, glass, plastics, rubber and more until they break and watch the stress-strain curve being drawn: yield, 0.2% offset, Lüders plateau, UTS, necking, unloading, true stress, resilience and toughness. Compare three materials.
Your own material
Start from a material in the list and change what you know. Yield is not used for brittle materials or rubber.
Type what you know
Any four values give the rest. The value you typed last always stays; an older one is worked out again when the newer ones fix it. Clear a box (×) to leave it unknown.
Side by side
The curves are a model fitted to each material's typical Young's modulus, yield strength, tensile strength and elongation (Hollomon / Ramberg–Osgood hardening, a Lüders plateau for mild steel). Specimen: a standard round bar, 12.5 mm across with a 50 mm gauge length (0.500 in and 2.000 in in US units). Real curves also depend on the test speed, temperature and the exact alloy.
For an isotropic material (the same in every direction) any two elastic constants fix all the others. Wood, carbon fibre laminates and bone are not isotropic, so these formulas do not link their E, G and ν.
Click a row to use that material in every tool. Click a column heading to sort.
Stiffness against weight
Both scales are logarithmic (each step is ten times the last). Click a dot to use that material. Dashed lines join materials with the same stiffness per kilogram (E/ρ): steel, aluminium and titanium sit on the same line.
Where the numbers come from
These are typical room-temperature values for learning and first estimates. They change with the exact alloy, heat treatment, temper, bar size, moisture (wood, nylon), direction (wood, composites, bone) and supplier. Yield and tensile strengths of the A36 steel are the specification minimums. Elongation is in a 50 mm (2 in) gauge length. Reduction of area is a rough figure that only shapes the neck in the tensile test.
Sources: published supplier data sheets (Special Metals for nickel alloys, mill and distributor sheets for steels, aluminium and copper alloys), the ASTM / UNS property collections summarised by MatWeb and MakeItFrom, ASM handbooks, the USDA Forest Products Laboratory Wood Handbook (clear wood at 12% moisture), ACI and Eurocode figures for concrete, textbook tables (Hibbeler, Gere & Goodno, Callister) and biomechanics reviews for bone. For design, use the certified values for your material and the rules of your design code.
For learning and first estimates. Real parts need certified material values, the design code that applies (AISC, Eurocode, ASME…) and a check by a qualified engineer.
Tensile test simulator: the stress-strain curve, step by step
A tensile test pulls a standard bar (here a round bar 12.5 mm across with a 50 mm gauge length, like ASTM E8 / ISO 6892-1) until it breaks, and plots the force against the stretch as a stress-strain curve. Press Start and watch the bar stretch in the grips while the curve is drawn point by point. Drag the slider to go back and forth, press Unload here to take the load off at any point, compare up to three materials on one chart, switch on the true stress-strain curve and see the resilience and toughness shaded. Steels, aluminium, titanium, copper, cast iron, glass, wood, plastics, rubber, carbon fibre and bone are in the list, or type your own material.
What the curve shows
- Elastic part: a straight line whose slope is Young's modulus, \(E = \sigma / \varepsilon\). Unload here and the bar goes back to its old length.
- Yield: most metals bend over smoothly, so the yield strength is taken where a line parallel to the elastic part, starting at 0.2% strain, meets the curve (the 0.2% offset rule, drawn dashed). Mild steel is different: it has an upper yield point, drops to a lower yield point and stretches at an almost constant force (the Lüders plateau) before it hardens.
- Strain hardening: the metal gets stronger as it is stretched, roughly \(\sigma_t = K\,\varepsilon_p^{\,n}\) in true stress and plastic strain (Hollomon). Unload from here and the line comes down with slope E, leaving a permanent set; load it again and it stays elastic up to the higher stress.
- Tensile strength (UTS) and necking: the highest point of the engineering curve. After it the bar thins in one place, so the force falls even though the metal in the neck keeps hardening. Necking starts when the hardening can no longer keep up with the loss of area, \(d\sigma_t / d\varepsilon_t = \sigma_t\) (Considère), which for the Hollomon law is at a true strain of about n.
- Fracture: ductile metals break with a cup-and-cone surface after a long neck; brittle materials (cast iron, glass, concrete, wood along the grain, carbon fibre) break with no yield and no neck.
Resilience and toughness
The area under the curve is energy per unit volume. The green triangle is the modulus of resilience, the energy the bar can store and give back: \(U_r = \sigma_y^2 / (2E)\). For A36 steel that is 250² ÷ (2 × 200,000) = 0.156 MJ/m³. The blue area is the toughness, the energy needed to break it, \(U_t = \int \sigma\,d\varepsilon\): about 80 MJ/m³ for A36, five hundred times the resilience. A quick estimate for a ductile metal is the average of the yield and tensile strengths times the elongation: (250 + 400) ÷ 2 × 0.23 ≈ 75 MJ/m³.
Engineering and true stress
Engineering stress divides the force by the original area, \(\sigma = F / A_0\); true stress divides it by the area the bar has now, \(\sigma_t = \sigma\,(1 + \varepsilon)\), with the true strain \(\varepsilon_t = \ln(1 + \varepsilon)\). The two formulas hold while the bar stretches evenly; after necking the true stress is worked out from the area of the neck (dashed).
How the curves are made
Each curve is fitted to the material's typical Young's modulus, yield strength, tensile strength and elongation at break, so the simulator hits those numbers exactly: the hardening exponent n and strength coefficient K come out of the fit and are shown. Real tests also depend on the test speed, temperature, the exact alloy and its heat treatment, so treat the curves as a typical shape, not a certificate.
Questions
What is the difference between yield strength and tensile strength?
Yield strength is where permanent stretching starts; tensile strength is the highest stress the bar takes before it necks and breaks. Parts are designed to stay below yield, with a safety factor.
Why does the curve go down before it breaks?
Because engineering stress uses the original area. Once the neck forms, the area there shrinks fast, so the force needed to keep stretching falls. The true stress in the neck keeps rising.
What is elongation at break?
How much longer the gauge length is when the pieces are fitted together after the break, in percent. It measures ductility: about 20 to 25% for structural steel, 12% for 6061-T6 aluminium, under 1% for cast iron. The elastic part springs back after the break, so it is a little less than the strain at the moment of fracture.
Why do plastics look so different?
Many plastics reach a yield peak, then a neck forms and travels along the bar at a steady force (cold drawing) until the whole bar is drawn out; HDPE can stretch to several times its length. Rubber has no yield at all: it is soft at first and stiffens as its chains straighten, and it springs back completely.