### Stress–strain curve - Wikipedia

What is strain? Stress Strain relationship. Learn about the terms related to stress, strain and more only @ BYJU'S. Physics · Physics Article; Stress And Strain. Elasticity, Stress, and Strain. Elasticity is a measure of how much an object deforms (strain) when a given stress (force) is applied. Tensile strength is the breaking stress that will cause permanent deformation or fracture of a . [link] shows a stress-strain relationship for a human tendon.

Forces that act parallel to the cross-section do not change the length of an object. The only difference from the tensile situation is that for compressive stress and strain, we take absolute values of the right-hand sides in Equation When an object is in either tension or compression, the net force on it is zero, but the object deforms by changing its original length L0.

In both cases, the deforming force acts along the length of the rod and perpendicular to its cross-section. In the linear range of low stress, the cross-sectional area of the rod does not change.

Find the compressive stress at the cross-section located 3. The normal force that acts on the cross-section located 3. Once we have the normal force, we use Equation Thus, if the pillar has a uniform cross-sectional area along its length, the stress is largest at its base.

### Stress, Strain, and Elastic Modulus (Part 1) - Physics LibreTexts

Check Your Understanding Ignoring the weight of the rod, what is the tensile stress in the rod and the elongation of the rod under the stress? Strategy First we compute the tensile stress in the rod under the weight of the platform in accordance with Equation Therefore, the stress needed to initiate the movement will be large.

As long as the dislocation escape from the pinning, stress needed to continue it is less. After the yield point, the curve typically decreases slightly because of dislocations escaping from Cottrell atmospheres. As deformation continues, the stress increases on account of strain hardening until it reaches the ultimate tensile stress. Until this point, the cross-sectional area decreases uniformly and randomly because of Poisson contractions.

The actual fracture point is in the same vertical line as the visual fracture point.

However, beyond this point a neck forms where the local cross-sectional area becomes significantly smaller than the original. If the specimen is subjected to progressively increasing tensile force it reaches the ultimate tensile stress and then necking and elongation occur rapidly until fracture. If the specimen is subjected to progressively increasing length it is possible to observe the progressive necking and elongation, and to measure the decreasing tensile force in the specimen.

The appearance of necking in ductile materials is associated with geometrical instability in the system. Due to the natural inhomogeneity of the material, it is common to find some regions with small inclusions or porosity within it or surface, where strain will concentrate, leading to a locally smaller area than other regions. For strain less than the ultimate tensile strain, the increase of work-hardening rate in this region will be greater than the area reduction rate, thereby make this region harder to be further deform than others, so that the instability will be removed, i.

## Stress Strain Relation

However, as the strain become larger, the work hardening rate will decreases, so that for now the region with smaller area is weaker than other region, therefore reduction in area will concentrate in this region and the neck becomes more and more pronounced until fracture.

After the neck has formed in the materials, further plastic deformation is concentrated in the neck while the remainder of the material undergoes elastic contraction owing to the decrease in tensile force.

The stress-strain curve for a ductile material can be approximated using the Ramberg-Osgood equation. Brittle materials[ edit ] Brittle materials, which includes cast iron, glass, and stone, are characterized by the fact that rupture occurs without any noticeable prior change in the rate of elongation. Therefore, the ultimate strength and breaking strength are the same.