# Elongation and strain relationship

### Chapter 6. Mechanical Properties of Metals

Property Information. Elongation. Overview. Elongation to failure is a measure of the ductility of a materials, in other words it is the amount of strain it can. [link] shows the Hooke's law relationship between the extension \Delta L For example, a guitar string made of nylon stretches when it is tightened, and the elongation \Delta L . [link] shows a stress-strain relationship for a human tendon . However, using the relationships we previously discussed, loads and Percent Elongation - The strain at fracture in tension, expressed as a percentage.

E is large for ceramics stronger ionic bond and small for polymers weak covalent bond. Since the interatomic distances depend on direction in the crystal, E depends on direction i.

### Property Information

For randomly oriented policrystals, E is isotropic. Anelasticity Here the behavior is elastic but not the stress-strain curve is not immediately reversible.

It takes a while for the strain to return to zero. The effect is normally small for metals but can be significant for polymers. Elastic Properties of Materials Materials subject to tension shrink laterally.

Those subject to compression, bulge. The ratio of lateral and axial strains is called the Poisson's ratio n. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently plastically. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress, and is an important measure of the mechanical properties of materials.

In practice, the yield stress is chosen as that causing a permanent strain of 0. The yield stress measures the resistance to plastic deformation. The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds.

Stress Strain Curve of A Mild Steel // Stress Strain Curve for Mild Steel //

Plastic deformation is caused by the motion of dislocations. When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength sTSand then falls as the material starts to develop a neck and it finally breaks at the fracture point Fig.

Note that it is called strength, not stress, but the units are the same, MPa. For structural applications, the yield stress is usually a more important property than the tensile strength, since once the it is passed, the structure has deformed beyond acceptable limits.

The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation emax or maximum area reduction.

## Engineering Stress-strain Curve

Capacity to absorb energy elastically. The energy per unit volume is the area under the strain-stress curve in the elastic region. Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve. It is measured by an impact test Ch. True Stress and Strain When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking the transverse area decreases but the stress cannot increase beyond sTS.

The ratio of the force to the initial area, what we normally do, is called the engineering stress. If the ratio is to the actual area that changes with stress one obtains the true stress. Elastic Recovery During Plastic Deformation If a material is taken beyond the yield point it is deformed plastically and the stress is then released, the material ends up with a permanent strain.

If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point strain hardening, Ch. The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery Fig.

The first two are strength parameters; the last two indicate ductility. An engineering stress-strain curve is constructed from the load elongation measurements Fig. The engineering stress-strain curve It is obtained by dividing the load by the original area of the cross section of the specimen.

The two curves are frequently used interchangeably. The shape and magnitude of the stress-strain curve of a metal will depend on its composition, heat treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress imposed during the testing.

### Stress–strain curve - Wikipedia

The general shape of the engineering stress-strain curve Fig. In the elastic region stress is linearly proportional to strain. When the load exceeds a value corresponding to the yield strength, the specimen undergoes gross plastic deformation. It is permanently deformed if the load is released to zero. The stress to produce continued plastic deformation increases with increasing plastic strain, i. Initially the strain hardening more than compensates for this decrease in area and the engineering stress proportional to load P continues to rise with increasing strain.

Eventually a point is reached where the decrease in specimen cross-sectional area is greater than the increase in deformation load arising from strain hardening. This condition will be reached first at some point in the specimen that is slightly weaker than the rest. All further plastic deformation is concentrated in this region, and the specimen begins to neck or thin down locally.

Because the cross-sectional area now is decreasing far more rapidly than strain hardening increases the deformation load, the actual load required to deform the specimen falls off and the engineering stress likewise continues to decrease until fracture occurs. Tensile Strength The tensile strength, or ultimate tensile strength UTSis the maximum load divided by the original cross-sectional area of the specimen. For ductile metals the tensile strength should be regarded as a measure of the maximum load, which a metal can withstand under the very restrictive conditions of uniaxial loading.

It will be shown that this value bears little relation to the useful strength of the metal under the more complex conditions of stress, which are usually encountered.

For many years it was customary to base the strength of members on the tensile strength, suitably reduced by a factor of safety. The current trend is to the more rational approach of basing the static design of ductile metals on the yield strength. However, because of the long practice of using the tensile strength to determine the strength of materials, it has become a very familiar property, and as such it is a very useful identification of a material in the same sense that the chemical composition serves to identify a metal or alloy.

Further, because the tensile strength is easy to determine and is a quite reproducible property, it is useful for the purposes of specifications and for quality control of a product. Extensive empirical correlations between tensile strength and properties such as hardness and fatigue strength are often quite useful.

For brittle materials, the tensile strength is a valid criterion for design.

Measures of Yielding The stress at which plastic deformation or yielding is observed to begin depends on the sensitivity of the strain measurements. With most materials there is a gradual transition from elastic to plastic behavior, and the point at which plastic deformation begins is hard to define with precision.