# STRESS-STRAIN DIAGRAM AND STRENGTH PARAMETERS

You must have noticed that there are certain objects that you can stretch easily. Let’s say a rubber band. However, can you stretch an iron rod? Sound’s impossible right? Why? In this chapter, we will look at these properties of solids in greater details.

## STRESS-STRAIN BEHAVIOR OF MATERIAL

All engineering materials do not show same sort of behavior when subjected to tension as well as compression. There exist some materials like metals, alloys etc., which are more or less equally strong in both tension and compression. And these materials are generally tested in tension again concrete, stones, bricks etc., are such type of materials which are weaker in tension and stronger in compression. Hence, these materials are tested in compression.

Now the stress-strain characteristics of mild steel are of specific importance to the community dealing with basic engineering science.

### Stress :

It is the ratio of the internal force F, produced when the substance is deformed, to the area A over which this force acts. In equilibrium, this force is equal in magnitude to the externally applied force.

The SI Unit of stress is newton per square meter (Nm-2)

Types of Stress

• Normal stress: It is the restoring force per unit area perpendicular to the surface of the body.  It is of two types: tensile and compressive stress.
• (Tangential stress: When the elastic restoring force or deforming force acts parallel to the surface area, the stress is called tangential stress.

### Strain :

It is the ratio of the change in size or shape to the original size or shape. It has no dimensions, it is just a number.

Types of Strain

• Longitudinal strain: If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain or tensile strain.
• Volumetric strain: If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain.
• Shear strain: The angle tilt caused in the body due to tangential stress expressed is called shear strain.

#### STRESS-STRAIN CHARACTERISTICS OF MILD STEEL (M.S)

In order to obtain stress-strain behavior of M.S, a specimen of uniform circular cross-section is prepared following the specification laid in IS 1608:2005 identical to ISO 6892:1998. A specific length of maximum 4 inch or 100 mm is generally selected in the well-middle part of the specimen and this length is designated as gauge length, over which the amount of elongation is studied.

Now the specimen, suitably fitted in extensometer, mounted on the machine where loading is started gradually from zero till failure. Following is a stress-strain curve of M.S specimen having gauge length 100 mm, tested in Amsler Universal Testing Machine of capacity 20T . Various points on stress-strain curve are marked in Figure 2.

PROPORTIONAL LIMIT

It is the point on the stress-strain curve, up to which the plot is a straight line and stress is proportional to strain. Up to proportional limit, the material remains elastic and strictly follows Hooke’s Law.

ELASTIC LIMIT

In the stress-strain curve, it is the point just beyond proportional limit. From proportional limit to elastic limit, the material remains elastic but does not follow Hooke’s Law and so, stress and strain are not proportional.

YIELD POINT

When the specimen is loaded beyond elastic limit, it enters into elasto-plastic zone. In this region, elongation of specimen occurs by considerable amount without any perceivable amount of increase in load. Sometimes this yielding is accompanied by an abrupt reduction of load and thereby stress. In this case the upper and lower limits of stress are called upper yield point or stress and lower yield point or stress, respectively.

Lower yield stress is normally considered as yield stress σy of material, because upper yield stress is affected by speed of testing, form of specimen and shape of cross-section.

PROOF STRESS

Some materials like High Strength Deformed (HSD) steel, brass, duralumin etc., do not show any well defined yield point. For these materials, proof stress serves as analogous to yield stress.

Proof stress is the stress that is just sufficient to produce under load, a defined amount of permanent residual strain, which a material can have without appreciable structural damage. This arbitrary value will be different for different material or different uses of same material.

It is determined from the stress-strain curve by drawing a line parallel to initial straight part or tangent of the curve and at a distance from the origin by an amount representing the defined residual strain (normally 0.1% or 0.2%) thus determining the stress at which the line cuts the curve.

In specifying proof stress, the amount of permanent strain considered, should be mentioned, i.e.,0.1% proof stress, 0.2% proof stress etc.

ULTIMATE STRESS

Yield point serves as the gateway to plastic zone. Beyond yield point, due to sudden decrease in load, material begins to strain-harden and recover some of the elastic property. And by virtue of that, gradual up rise of stress-strain curve occurs and terminates at a point, called ultimate stress. This is the maximum stress, the specimen can withstand, without any appreciable damage or permanent deformation.

BREAKING STRESS

While ultimate stress is the maximum stress with standing capacity prior to failure, further increase of ultimate stress leads to failure of the specimen and this occurs at breaking stress. Here the value of breaking stress lower than ultimate stress, as appearing in the stress-strain diagram obtained during experiment, of ductile material, is somehow misleading.

What happens in reality is that, beyond ultimate stress, there occurs a reduction in area of cross-section near at the middle of gauge length. This phenomenon is called formation of neck or formation of waist. As the grips of extensometer are attached at the end of gauge length, the effect of neck formation thereby the reduction in diameter of the specimen cannot be taken into account. By reason of which breaking stress exhibits value lower than ultimate stress. And this breaking stress is called Nominal Breaking Stress.

When the reduced cross-sectional area at neck is considered to compute actual stress, it is found that breaking stress is pretty higher than ultimate stress. And this is called True Breaking Stress. In case of brittle material, ultimate stress is same as breaking stress.

DUCTILITY

It is the property of a material which allows of its being drawn out by tension to a small section. Brittleness is the lack of ductility.

MALLEABILITY

It is the property of a material by virtue of which it can be turned to a very thin sheet by the application of pressure.

TOUGHNESS

It can be said, in general, resistance to deformation. This deformation may be due to impact, abrasive force, punch etc.