STRESS

BY ANKUR SAHAY

REG NO:-16MT001278

INTRODUCTION

• STRESSIt is the internal resistance of the metal/rock /soil specimen offered against loading or deformation.

• UNIT N/mm2 or Mpa

• STRENGTHMaximum value of stress at which material fails.

DIFFERENT KINDS OF STRESS ON ROCK Lithostatic stress:Rock beneath the Earth's surface experiences equal pressure exerted on it from all directions because of the weight of the overlying rock. It is like the hydrostatic stress (water pressure) that a person feels pressing all around their body when diving down deep in water

Differential (deviatoric) stress: In many cases, rock may experience an additional,unequal stress due to tectonic forces.  There are three basic kinds. tensional stress (stretching) compressional stress (squeezing) shearing stress (side to side shearing)

Strain - Rock Deformation in Response to Stress:-Rock responds to stress differently depending on the pressure and temperature (depth in Earth) and mineralogic composition of the rock.

Elastic deformation: For small differential stresses, less than the yield strength, rock deforms like a spring. It changes shape by a very small amount in response to the stress, but the deformation is not permanent. If the stress could be reversed the rock would return to its original shape.

Brittle deformation: Near the Earth's surface rock behaves in its familiar brittle fashion. If a differential stress is applied that is greater than the rock's yield strength, the rock fractures, it breaks. Note: the part of the rock that didn't break springs back to its original shape. This elastic rebound is what causes earthquakes.

Ductile deformation: Deeper than 10-20 km the enormous litho static stress makes it nearly impossible to produce a fracture (crack - with space between masses of rock) but the high temperature makes rock softer, less brittle, more malleable. Rock undergoes plastic deformation when a differential stress is applied that is stronger than its yield strength. It flows. This occurs in the lower continental crust and in the mantle

STRESS STRAIN CURVE FOR DUCTILE MATERIAL

YOUNG’S MODULUS A measure of elasticity, equal to the ratio of the stress acting on a substance to the strain produced.

ELASTIC LIMIT The maximum extent to which a solid may be stretched without permanent alteration of size or shape.

PLASTIC REGION If a material is forced beyond the elastic region, it experiences plastic deformation.

ULTIMATE STRENGTHIt is the capacity of a material or structure to withstand loads tending to elongate, as opposed to compressive strength, which withstands loads tending to reduce size.

RESILIENCE is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading.

PROOF RESILIENCE is defined as the maximum energy that can be absorbed within the elastic limit, without creating a permanent distortion.

TOUGHNESSIt is the maximum strain energy which can be stored in material before fracture.

DUCTILITY is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire.

BRITTLENESS A material is brittle if, when subjected to stress, it breaks without significant deformation.

Malleability is the quality of something that can be shaped into something else without breaking, like the malleability of clay. CREEP –It is a plastic deformation which is permanent in nature and it occurs with time at constant loading.

Fatigue is the weakening of a material caused by repeatedly applied loads. It is the progressive and localised structural damage that occurs when a material is subjected to cyclic loading.

3-D STRESS ELEMENTStress is a tensor quantity means it is bidirectional.

In 3-D stress element, there are 9 stress component can be expressed in the form of matrix.

In 2-D loading there will be only 4 stress elements.

ELASTIC CONSTANT1. MODULUS OF ELASTICITY OR YOUNG’S MODULUS

Ratio of stress to strain within the elastic limit is a constant which is defined by Hooke as the Modulus of elasticity or Young’s modulus (E).

2. SHEAR MODULUS OR MODULUS OF RIGIDITYDenoted by G, or sometimes S , is defined as the ratio of shear stress to

the shear strain.

3. BULK MODULUS(K) It is defined as the ratio of direct stress and volumetric strain.

4. POISSON’S RATIO Defined as the ratio of lateral strain and longitudinal strain.

INTER RELATIONSHIP B/W ELASTIC CONSTANTS

UNCONFINED COMPRESSIVE STRENGTH OF ROCK SAMPLE

SHEAR STRENGTH OF ROCK The compressive strength of rock is a function of the confining pressure. As the confining pressure increases so does the strength. The variation of peak stress with confining pressure is referred as rock criterion of failure.The simplest and the best known method is Mohr Coulomb criterion : the linear approximation of variation of peak stress with confining pressure.

MOHR CIRCLE

• Graphical construction that visualize the relationship between the principal stresses and tractions on a boundary (like a fault).

COULOMB LAW OF FAILURE

t

c

sn

Coulomb equation tc = c + tan f sn

Where,tc = critical shear stress required for faulting (shear strength)

c = cohesive strength

tan f = coefficient of internal friction = m

f

MOHR-COLOUMB FAILURE CRITERION

MOHR STRESS DIAGRAM

a) Mohr circle radius = ½(s1 – s3] that is centered on ½(s1 + s3] from the origin.

b) The Mohr circle radius, ½(s1 - s2] is the maximum shear stress ss max.

c) The stress difference (s1 – s3), called differential stress is indicated by sd

BYERLEE'S LAWByerlee's law, also known as Byerlee's friction law concerns the shear stress (τ)

required to slide one rock over another.

For a given experiment and at normal stresses (σn) below about 200 MPa the shear

stress increases approximately linearly with the normal stress (τ = 0.85 σn) and is highly

dependent on rock type and the character (roughness) of the surfaces . Byerlee's law states

that with increased normal stress the required shear stress continues to increase, but

the rate of increase decreases (τ = 0.5 + 0.6 σn), and becomes nearly independent of rock

type.

The law describes an important property of crustal rock, and can be used to

determine when slip along a geological fault takes place.

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