Determination of static elastic constant “E” (young’s modulus) and poison ratio for a given sample of rock.

Scope:-

From this test we calculate the young’s modulus of rock sample. It is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. Poison ratio and bulk modulus can also calculate from this test by using stress-strain graph that helps in selection of materials for particular structural applications. It is used to measure elastic constants which are very impartment for design parameter during construction and mining activity.

Apparatus:-

• Extensometer
• Strain gauges(more efficient then extensor meter)
• Strain meters
• Universal testing machine
• Computer attachments

Related Theory

Stress:-

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body.

σ = F/A

Where

F=Applied Force

A=Area

Units:-

The dimension of stress is that of pressure, and therefore the SI unit for stress is the pascal (symbol Pa), which is equivalent to one newton (force) per square meter (unit area), that is N/m2. In Imperial units, stress is measured in pound-force per square inch, which is abbreviated as psi.

Strain:-

Strain is a description of deformation in terms of relative displacement of particles in the body. Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body. It is unit less.

Young’s Modulus:-

Young's modulus, also known as the tensile modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the un axial strain in the range of stress in which Hooke's Law holds.^[1] In solid mechanics, the slope of the stress-strain curve at any point is called the tangent modulus. The tangent modulus of the initial, linear portion of a stress-strain curve is called Young's modulus. It can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. In anisotropic materials, Young's modulus may have different values depending on the direction of the applied force with respect to the material's structure.

It is also commonly called the elastic modulus or modulus of elasticity, because Young's modulus is the most common elastic modulus used, but there are other elastic moduli measured, too, such as the bulk modulus and the shear modulus.

Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic (initial, linear) portion of the stress strain curves:

Where;

E is the Young's modulus (modulus of elasticity)

F is the force exerted on an object under tension;

A₀ is the original cross-sectional area through which the force is applied;

ΔL is the amount by which the length of the object changes;

L₀ is the original length of the object

Poisson's ratio:-

It is named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain (perpendicular to the applied load), to the extension or axial strain (in the direction of the applied load).

When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio (nu) is a measure of the Poisson effect. The Poisson ratio is the ratio of the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes.

Procedure:-

• Take a rock sample of standard dimensions.
• 2 gauges are attached with the rock sample. One in the vertical direction that gives the value of longitudinal strain and other one in the horizontal that gives the lateral or diametric strain.
• Connect the whole system with computer to get readings from strain gauges.

  

                         

• Now apply the load and take the readings every 500 kg force.
  
• Plot the graph using excel and measure the values of UCS, youngs modulus and poison ratio.
  

  Precautions:-

  1. Lapping of sample should be done carefully.
  2. Dimensions should be measure carefully.
  3. Sample should be moisture free.
  4. Sample shouldn’t be cracked.
  5. Sample axis should be perpendicular to each other.

  Comments:-

  Young’s modulus of rock gives us an idea about the behavior of rock under tensile or compressive loads. It gives us an idea that how much the material expands and contrast under tension and compression respectively. With the help of bulk modulus we can measures the substance's resistance to uniform compression. So, we can say that with the help of this test we can estimate the behavior of rock under loading or under forces.