Elastic, plastic or viscoelastic: three ways of responding to a load that can be identified in a single chart.
The most direct way to understand how a material behaves mechanically is to apply a load and measure its response. This is what a tensile test does.
The specimen is held between two grips and stretched at a controlled rate. Two signals are recorded simultaneously: the force exerted by the material, measured with a load cell, and its elongation, measured with an extensometer. Plotting one against the other gives the force–deformation curve, a true mechanical fingerprint of the material.
From force to stress
This curve depends on the dimensions of the specimen: a bar with twice the cross-section withstands twice the force, even though the material is the same. To compare materials rather than specific parts, both quantities are normalised:
This change of scale does not alter the shape of the chart, but the chart no longer describes a specific part: it describes the material. Strictly speaking, the raw curve is a force–elongation curve and the normalised one a stress–strain curve. In practice, both names are used almost interchangeably.
The tensile test, step by step
In the next panel a material can be selected and the test started. The specimen stretches while the curve is drawn, just as it would appear on the screen of a testing machine.
Tensile test
Elastic deformation: a reversible process
The first section of almost every curve is a straight line. In this region the material behaves like a spring: stress is proportional to strain and, when the load is removed, the specimen returns exactly to its initial length.
This is Hooke’s law. The slope of the line is Young’s modulus (E), which indicates the stiffness of the material.
At atomic scale, the bonds between atoms stretch slightly without breaking. When the load is removed, each atom returns to its equilibrium position and the energy supplied is fully recovered.
Plastic deformation: a permanent change
If the load keeps increasing, the line starts to curve. That point is the yield strength.
Beyond it, planes of atoms slide relative to one another. In metals this slip advances step by step through the movement of lattice defects called dislocations. The atoms remain in their new positions and, even when the load is removed, that part of the elongation is not recovered.
The next panel makes this visible. Once the amount of stretch has been chosen, the return path can be followed. Unloading runs parallel to the elastic line, and the point where it meets the horizontal axis indicates the permanent deformation.
Loading and unloading
If the part is loaded again, the curve rises along the same unloading line. The material does not start to yield until it reaches the maximum stress previously attained: it has become stronger, at the expense of ductility.
This phenomenon is known as strain hardening. It explains, for example, why a wire becomes progressively harder when it is bent back and forth several times.
In many metals the transition is so gradual that there is no clear point where the line ends. By convention, the stress that produces 0.2 % permanent strain is used. This is the proof strength, Rp0.2, defined in ISO 6892-1.
Each family of materials, its own curve
Comparison
- Ceramics and glasses. They are very stiff and their curve is an almost perfect straight line to the end. They break without warning and without noticeable plastic deformation: this is known as brittle fracture.
- Ductile metals. After the elastic region, they harden as they deform until they reach a maximum stress. Necking then appears: the deformation concentrates in a neck. The curve drops because the force is still divided by the initial cross-section, even though the real one keeps getting smaller.
- Ductile polymers. After yielding, they form a neck that propagates along the specimen at almost constant stress. Meanwhile, the molecular chains disentangle and align. They can reach several times their initial length.
- Elastomers. Rubber accepts very large and almost fully recoverable deformations, but its curve is not straight: it is S-shaped.
| Material | Young’s modulus | Yield strength | Elongation at break |
|---|---|---|---|
| S275 structural steel | 210 GPa | 275 MPa | ≈ 22 % |
| 6061-T6 aluminium | 69 GPa | ≈ 275 MPa | ≈ 12 % |
| Soda-lime glass | ≈ 70 GPa | Does not yield: breaks | < 0.1 % |
| High-density polyethylene (HDPE) | ≈ 1 GPa | 20–30 MPa | > 500 % |
| Natural rubber | 1–10 MPa | No yielding | 500–800 % |
Viscoelasticity: when time comes into play
So far it has been assumed that the response of the material does not depend on the test speed. In polymers, foams, rubbers, asphalt or biological tissue, that assumption no longer holds.
These materials behave partly as an elastic solid, which stores energy, and partly as a viscous fluid, which dissipates it. For this reason they are called viscoelastic.
This behaviour has two consequences. The first is that the curve changes with test speed. The second is that the loading and unloading paths do not coincide: they form a hysteresis loop, whose area is the energy dissipated as heat in each cycle.
Loading and unloading cycle
Bouncing putty illustrates this well. Thrown at the floor, it bounces like a ball; left on a table, it gradually spreads like a thick liquid.
Creep and stress relaxation
Time also matters when the load is held constant. Under a sustained force, a viscoelastic material continues to deform gradually: this is creep.
If the strain is held constant instead, the stress gradually decreases: this is stress relaxation. It is the reason why a newly fitted nylon guitar string goes out of tune during the first few days.
Creep of a viscoelastic foam
The jumper example is useful here as well. A stretched garment recovers part of its shape after washing, which shows that time, temperature and humidity also play a role in fabrics. In many real materials, plastic and viscoelastic behaviour coexist.
Key points
- Elastic: the deformation disappears when the load is removed and the energy is recovered.
- Plastic: beyond the yield strength, part of the deformation is permanent. The jumper has been stretched out of shape.
- Viscoelastic: the response depends on time and speed, and part of the energy is dissipated in every cycle.
Measuring well is half the job
Instrumentation for test benches
A curve is only as reliable as the signals behind it: a load cell suited to the range, a well-chosen extensometer, a controlled test speed and a sampling rate high enough to capture the fracture. At Adecua we design and integrate measurement systems for this type of test.
