# What is the relationship of stress and strain

### NPTEL :: Mechanical Engineering - Strength of Materials

Stress is force per unit area - strain is the deformation of a solid due to stress. Stress – Strain Relationships. Tensile Testing. One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. A member is under axial loading when a force acts along its axis. The internal force is normal to the plane of the section and the corresponding.

Pp counteracts the effects of Pc. Thus, rock properties are controlled largely by the difference between Pc and Pp, or the differential pressure Pd.

**9. Physics - Elasticity - Relation Between Stress and Strain - by Ashish Arora**

A more exact form will account for the interaction of the fluid pressure with the pore space and minerals and result in an effective stress Pe law Deformation, strain and modulus Application of a single vertical stress is one typical experiment run to measure material mechanical properties Fig.

If this stress continues to increase, eventually the material will fail when the uniaxial compressive strength is reached see Rock failure relationships. For the rest of this topic, however, we will deal only with small deformations and stresses such that the rock remains in the elastic region. Vertical strain Restricting ourselves to small deformations and stresses, several important material properties can be defined. Normalizing this deformation by the original length of the sample, L, gives the vertical strain The lateral strain can then be defined Cijkl would then be a tensor with 81 components.

### Stress–strain curve - Wikipedia

However, because of symmetry considerations, only a maximum of 21 can be independent a thorough treatment of the tensor relations is provided in Nye [3]. For isotropic materials, this reduces to In fact, for isotropic materials, there are only two independent elastic parameters.

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.

## Stress strain relationships in rocks

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.

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.

A typical stress—strain curve is shown in Fig. Typical brittle materials like glass do not show any plastic deformation but fail while the deformation is elastic. One of the characteristics of a brittle failure is that the two broken parts can be reassembled to produce the same shape as the original component as there will not be a neck formation like in the case of ductile materials.

- Stress Strain Relation
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- Stress–strain curve

A typical stress—strain curve for a brittle material will be linear.