POISSON'S RATIO

                 If a body is subjected to a load its length changes, the ratio of change in length to the original length is called as linear or primary strain. Due to this load, the dimension of the body in all directions right angle to its line of application change; the strains thus produced are called lateral or secondary strain s and are of nature opposite to that of primary strain. For example, if tensile load is applied on a body, there will be increase in length and corresponding decrease in cross-sectional area of the body. In this case tensile strain is primary and compressive strain is lateral or secondary strain.

                It is defined as “the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load”. Since most common materials become thinner in cross section when stretched, Poisson's ratio for them is positive.

i.e., poisson's ratio,        μ or = 1/m

             Where, m is called a constant and its value varies between 3 and 4 for different materials. For a perfectly incompressible materials, the poisson's ratio would be exactly 0.5. Most practical engineering materials have 'V' between 0 and 0.5. Cork is close to 0 (zero), most steels are around 0.3, and rubber is almost 0.5. A poisson's ratio greater than 0.5 cannot be maintained for large amounts of strain because at a certain strain the material would reach zero volume, and any further strain would give the material negative volume.

Poisson’s ratio for different materials: 

Material	Poisson's ratio(μ )
rubber	0.4999
gold	0.42–0.44
saturated clay	0.40–0.49
magnesium	0.252-0.289
titanium	0.265-0.34
copper	0.33
aluminium-alloy	0.32
clay	0.30–0.45
stainless steel	0.30–0.31
steel	0.27–0.30
cast iron	0.21–0.26
sand	0.20–0.45
concrete	0.20
glass	0.18–0.3
foam	0.10–0.50
cork	~ 0.00

DESTRUCTIVE TESTS (MECHANICAL TESTS)

             As the name suggests, Destructive testing (DT) includes methods where your material is broken down in order to determine mechanical properties, such as Strength, Toughness and Hardness. In practice it means, for example, finding out if the quality of a weld is good enough to withstand extreme pressure or to verify the properties of a material.

              The following important mechanical tests give valuable information about metals and alloys as given below:

1	Tensile test	tensile strength, yield strength, elastic limit, young’s modulus, Ductility, toughness etc
2	Impact test	toughness of a material under shock loading condition.
3	Hardness test	wear resistance, indentation resistance, scratch resistance or cutting ability  of material.
4	Fatigue test	Behavior of a material under repeatedly applied stress and its endurance limit.
5	Creep test	Behavior of a material under a steady load over a long period of time and creep limit of a material.

TENSILE TEST

               The tensile test is one of the most widely used mechanical test.  There are many variations of this test to accommodate the widely differing character of materials such as metals, elastomers, plastics, and glasses. The tensile test on mild steel test piece is described below:

STRESS - STRAIN DIAGRAM:

Consider a rod of initial length L0 and area A0 which is subjected to a load F. The stress σ is the force per unit area, and strain is the change in length (δ) divided by the initial length. Thus,

Stress      σ  = F / A0

Strain      ε   = δ / L0

The σ-ε curve for a material (say mild steel) is shown in the Fig. 1.1. Up to the proportionality point A, the stress-strain variation is linear. Up to this point Hooke's law holds good.

i.e.,  σ α ε

    Or            

                        σ= E ε

Where, 

               E is Young's modulus commonly called modulus of elasticity

               Beyond point A and up to point B, material remains elastic i.e., the material remains to its original condition of the force acting on it is removed.

              If the specimen is stressed beyond point B, permanent set takes place and we enter plastic deformation region. In the plastic deformation region, the strain does not get fully removed even with the removal of the force causing it. If the force is increased further, point 'C' is reached, where the test specimen streches even when the stress is not increased. This point is called Yield point. In fact, there are two Yield points C and D which are called upper and lower yield points respectively.

             

               With further straining, the effect of this phenomenon called strain hardening or work hardening takes place. The material becomes stronger and harder and its load bearing capacity increases. The test specimen is therefore able to bear more stress. On progressively increasing the force acting on the specimen, point E is reached. This point is the highest point in the stress-strain curve and represents the point of maximum stress. It is, therefore, called Ultimate Tensile Strength (UTS) of the material. It is equal to the maximum load applied divided by the original cross-sectional area (A0) of the test specimen.

              Here, we must consider the effect of increasing load on the cross-sectional area of the test specimen. As plastic deformation increases, the cross-sectional area of the specimen decreases. However for calculation of the stress in the stress-strain graph, the original cross-sectional area is considered. It is for this reason, that the point of breakage F seems to occur at a lower stress level than the UTS point E. After UTS point E, a sharp reduction in cross-sectional area of the test specimen takes place and a "neck" is formed in the centre of the specimen. Ultimately the test specimen breaks in two pieces as the neck becomes thinner and thinner. The actual breaking stress is much higher than the UTS, if the reduced cross-sectional area of the test specimen is taken into account.

               The measure of the strength of a material is the ultimate tensile strength (σ at point E). However, from the point of view of a design engineer, the yield point is more important as the structure designed by him should withstand forces without yielding. Usually yield stress (σ at point D) is two-thirds of the UTS and this is referred to as yield-strength of the material.

                  In actual practice, to determine UTS, a tensile test is carried out on a tensile testing or a universal testing machine. In order that tests conducted in different laboratories on the same material may give identical test results, the test piece used for the tensile test has been standardized. A standard test piece is shown in Fig. 1.2.

             A stress-strain curve for brittle material is obtained by subjecting a test bar of such material in a tensile testing machine. The tensile load is gradually increased and the extension of the test piece is recorded. The stress-strain curve for a brittle material shows some marked differences as compared to the curve obtained for a ductile material. A typical stress-strain curve for a brittle material is shown in Fig.1.3.

             This curve displays no yield point, and the test specimen breaks suddenly without any appreciable necking or extension. In the absence of a yield point, concept of "proof-stress" has been evolved for measuring yield strength of a brittle material. For example, 0.2% proof-stress indicates the stress at which the test specimen 'suffers' a permanent elongation equal to 0.2% of initial gauge length and is denoted by σ 0.2.

              The tensile test and the stress-strain curve has been described above in some detail, because a lot of useful information with regard to other properties of material can be cleaned from it. It may be noted that most tensile testing machines are provided with equipment to carry out a compressive strength test as well.