Stress-strain & Hooke's law
About this app
Tensile bar under load plus the stress-strain diagram σ-ε with the Hooke line (Young's modulus), proportionality/yield limits, plastic region and fracture; the operating point moves along the curve.
The basics
In a tensile test a bar is stretched while the force is measured. Plotting stress σ = F/A₀ against strain ε = ΔL/L₀ gives the stress-strain curve. In the elastic range Hooke’s law σ = E·ε applies, and the slope of the line is Young’s modulus E. Unloaded here, the specimen springs back completely. Above the yield strength R_e the material starts to flow and the deformation becomes permanent. The peak of the curve is the ultimate tensile strength R_m. After that the specimen necks locally until it fractures.
What the app shows
On the left a tensile bar elongates under the chosen load; on the right the operating point moves along the σ-ε diagram. The Hooke line, the proportional limit R_p, the yield strength R_e, the tensile strength R_m and the fracture point are marked. A phase label tells you whether you are in the elastic range, at yield, in the plastic range, necking or at fracture. You can choose structural steel with a yield plateau, or aluminium and copper with a smooth transition; the values are typical textbook figures.
Things to try
Increase the load step by step and watch where the operating point leaves the Hooke line. The buttons “Elastic limit” and “To fracture” jump straight to those points. Compare the three materials: steel has the largest modulus and therefore the steepest line, while copper stretches the most before it breaks.
Frequently asked questions
- What does a stress-strain curve show?
- It shows how a material responds to load in a tensile test, plotting stress σ against strain ε. From it you read Young’s modulus, yield strength, tensile strength and elongation at fracture. These values are the basis of every strength calculation.
- What is the difference between yield strength and tensile strength?
- Yield strength R_e is the stress at which the material begins to flow and permanent deformation sets in. Ultimate tensile strength R_m is the highest stress on the curve, based on the original cross-section. Materials without a distinct yield point are described by the 0.2 % offset yield strength R_p0.2.
- What does Hooke’s law state?
- In the elastic range stress is proportional to strain: σ = E·ε. Young’s modulus E is a material property, about 210 GPa for steel and about 70 GPa for aluminium. In this range the deformation disappears completely when the load is removed.
- Which materials can I compare in the app?
- The app offers structural steel, aluminium and copper. You control the load with a slider or jump to the elastic limit or to fracture with a button. It shows stress, strain, force, Young’s modulus and the values R_p, R_e and R_m.
Subject: Engineering mechanics
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