STRESS AND STRAIN

STRESS:

                 Stress is defined as the force per unit area and strain is the fractional change in length, area or volume. Obviously, this is the resistance of the body to deformation due to the application of external force.

              Stress describes the intensity of a force that acts on a unit area. Its units are N/mm2 or N/m2 . which is called pascal in SI Units and denoted by pa. When the force acting over an area is uniformly distributed, we have

            In several cases, such uniformly distributed loads are not present and therefore stress is non-uniform. This is why, the stress is always referred to a point and in a body the stress varies from point to point over any section. If F is the total load acting on the original cross-sectional area , then normal stress, 

                Obviously, stress is the intensity of internal force. The stress is said to be normal if load p is normal to the surface and tangential or shearing, if load is tangential to this surface. The normal or direct(tensile or compressive) stress is produced over a section when force is acting normal to the section. If the force is acting away from the section, the stress is tensile, if it is acting towards the section the section is compressive.

In general, the stress at any point will have six components and its nature is different than that of force and area both. In fact, stress at a point is a tensor quantity and needs the following specifications for complete specification: 

 (i) Magnitude  

(ii) Plane passing through the point, on which stress is being defined and,

(iii) The direction in which stress is acting.

STRAIN:

                Strain is the deformation produced per unit length of a body due to the effect of stress on it. It is the ratio of the change in length of the specimen to its original length. If L is the original length of the sample and  l is the change in length, then

            Strain is simply a ratio and has no unit and it is a dimensionless quantity. Depending upon the type of load, strain can be lateral strain or shear strain.

As there are different types of stresses, thee are different types of strains, e.g., 

                  (i) Compressive strain,

                  (ii) Shear or Transverse strain and

                  (iii) Volumetric strain.

    The strain associated with the change in length is called the elongation strain (l/L).Similarly  v/V  is the volumetric strain, where V is the volume. When there is a change in shape and no change in volume, corresponding strain is called shear strain. The shear strain is measured by the angle. The behavior of a material within the elastic limit is the same under compression as under tension.

Corresponding to elastic and plastic properties of materials, we have two classes of strain; (a) Elastic strain and (b) Plastic strain

(a) Elastic strain: It is the change in dimension of a body when it is subjected to a load. This is reversible phenomenon, i.e., elastic strain disappears after the applied load is removed. This is proportional to the stress applied.

(b) Plastic strain:  This is the permanent change in the body when subjected to a load. The change remains even after the applied load is removed.

The amount of elongation, expressed as a percentage of the original gauge length is called as the percentage elongation;

 

HOOKE'S LAW

                  In 1678, Robert Hooke, for the first time suggested that within elastic limits, stress is directly proportional to strain, i.e.,

   F µ e

Þ F = ke

The ratio of stress to strain is a constant characteristic of a material, and this proportionality constant is called modulus of the material. It differs from material to material, and for different nature of stresses.

When the stress applied is tensile or compressive, the constant is called Young's modulus of elasticity. The slope of stress-strain diagram up to the limit of proportionality is called Young's modulus of elasticity (Y or E).

When shear stress and strain are used, it is called modulus of rigidity (G). It is given by

TESTING OF MATERIALS

Introduction:

Metals are  tested for one or more of the following purposes:

     (1) To access numerically the fundamental mechanical properties of ductility, malleability, toughness, fatigue etc.,

          (2) To check chemical composition.

          (3) To determine which metal is suitable for which purpose.

          (4) To determine the life cycle of machine parts.

          (5) To determine the internal or surface defects in materials. 

CLASSIFICATION OF TESTS

Tests on materials may be classified as:

                1. Non-destructive tests.               2.Destructive tests (or) Mechanical tests.

In non-destructive testing a component does not break and so even after being tested it can be used for the purpose for which it was made.

EXAMPLE: Radiography, Ultrasonic inspection,Liquid penetration etc.,

In destructive testing the component or specimen either breaks or remains no longer useful for further use.

EXAMPLE: Tensile test, Impact test, Torsion test etc.,

NON-DESTRUCTIVE TEST

                      Non-Destructive tests (NDT) may be defined as those in which the test specimen would not damage such that it is rendered useless for future for which it was originally meant.

                       While studying various mechanical tests in previous sections, we have noted the effects of cracks and flaws. These should be detected at the early stages and the component replaced otherwise disaster will result. One can detect all microscopic flaws by NDT. NDT is the the method of detection and measurement of properties or condition of material, structures, machines without damaging (or) destroying their operational capabilities. Examples of NDT are: radiography, magnetic particle inspection, ultrasonic test, penetrating liquid method, electrical method, damping. All NDTs are used to detect various types of flaws on the surface of material or internal inclusions of impurities and these techniques are also very useful during preventing maintenance and repair. There are few techniques which do not require any special apparatus and are quite simple to handle and only a moderate skill being required. Some of the applications of NDTs are detecting: (i) surface cracks (ii) material composition (iii) internal inclusions (iv) internal voids and discontinuities and (v) condition of internal stress.

Now, we describe the various methods used for Non-destructive testing are as follows:

• X-Ray radiography
• Gamma radiography
• Magnetic particle inspection
• Ultrasonic testing
• Liquid penetration test
• Electrical method
• Damping

X-RAY RADIOGRAPHY

           Radiography technique is based on exposing the components to short wavelength radiations in the form of X-Rays, Gamma rays and radio-isotope welds. This method is used to check internal cracks, shrinkage cavities, slag inclusions, defects in materials and welds. These defects are of special importance designed to withstand high temperature and pressure employed in power plants, atomic reactors, pressure vessels and oil refining equipment; because they cause stress concentration which may frequently lead to part failure. Nowadays, radiography techniques are finding more extensive applications in the field of physical metallurgy and in the treatment of various diseases.

           Rays are absorbed by the materials through which they are passed in the proportion of their density. The rays, after passing through the components, show a picture on a fluorescent screen or on a photographic plate. The cracks, blow holes and cavities appear lighter, where as inclusions of impurities appear darker than the metal component. Developed photographic film show lighter and darker areas to represent the radiograph of defects in the component.

                  In X-Ray radiography, the portion of the casting where defects are suspected is exposed to X-Rays emitted from the X-ray tube. A cassette containing X-ray film is placed behind and in contact with the casting perpendicular to rays. X-rays after allowing through the blow hole in a casting, will be absorbed to lesser extent than X-rays which allowed to pass through sound metal, therefore, film appears to be more dark where defects are in line of X-ray beam. The exposed and developed X-ray film showing light and dark areas is termed as Radiograph. X-rays are useful only for small thickness material as their penetration power is less than that of gamma rays.