Mechanical Properties of Solids Flashcards
Deforming Force
A force which changes the size or shape of a body
Elasticity
Property of body being able to regain original size and shape after the removal of deforming force
Perfectly elastic
Body regains its original size and shape completely and immediately after the removal of deforming force
Plasticity
If a body does not regain its orginal size and shape even after the removal of deforming force
Equilibrium Separation
For some particular separation (r), potential energy is minimum and interatomic force is zero
Explain elastic behaviour in terms of interatomic force
- When interatomic r is large, potential energy is negative, interatomic force is attractive
- Becomes minimum at equilibrium separation
- When separation below r, potential energy increases and interatomic force is repulsive
Strain
Ratio of change in any dimension produced in the body to original dimension
Strain = Change in dimension / Original dimension
Stress
Internal restoring force setup per unit area of cross - section of the deformed body
Stress = Applied Force / Area
Longitudinal strain
Increase in lenth per unit original length
= delta l / l
Volumetric Strain
Change in volume per unit orignal volume
= delta V / V
Shear strain
Angle theta through which a face originally perpendicular to the fixed face turned on applying tangential deforming force
= Relative displacement between 2 parallel planes / Distance between parallel planes
Elastic limit
Maximum stress within which the body completely regains its original size and shape after the removal of deforming fortce
Hooke’s Law
Extension in a wire is directly proportional to the load applied
Stress / Strain = Constant
Modulus of elasticity
Ratio of stress to the corresponding striain, within the elastic limit
E = Stress / Strain
Young’s Modulus of elasticity
Within the elastic limit, ratio of longitudinal stress to the longitudinal strain
Young’s Modulus Formula
Y = [F / pi (r^2)] * [l / delta l]
Proportional limit
Highest stress at which stress and strain are directly proportional
Yield strength
Point at which the material transforms from elastic to plastic
Permanent Set
Deformation that stays in the material after the applied stress is removed
Elastic Hysteresis
Difference between strain energy required to generate a given stress and material’s elastic energy
Tensile strength
Maximum load to which the wire may be subjected by slowly increasing the load to the original area of cross-section
Fracture point
The fracture point is the point of strain where a material physically separates or breaks apart. It is the maximum strain value at which a material can withstand stress before failing or rupturing
Young’s modulus of experimental wire
Y = Stress / Strain
= L / (pi)r^2 tan theta
Elastomers
Materials which can be elastically stretched to large values of strain
Plastomers
- Behaviour having both elastic and plastic behaviour
- Elasticity and plasticity
Bulk’s Modulus of elasticity
Ratio of normal stress to the volumetric strain
Bulk’s modulus of elasticity formula
k = - F / A * V / delta V
= - pV / delta V
Compressibility
The reciprocal of the bulk modulus of a material
Modulus of rigidity / Shear modulus
Ratio of tangential stress to shear strain
Modulus of rigidity formula
F / A * l / delta l
Why is shear modulus of a material considerably smaller than Young modulus
Easier to slide layers of atoms of solids over one another than to pull them apart or to squeeze them close together
Elastic after effect
Delay in regaining the original state by a body on the removal of the deforming force
*
Elastic fatigue
Defined as loss in strength of a material caused due to repeated alternating strains to which the material is subjected
PE stored per unit volume of a stretched wire
U = 1/2 Young’s Modulus * strain^2
Total PE
u = 1/2 * Y * strain^2 * volume
u = 1/2 * F * delta l
Poisson’s ratio
Within the elastic limit, the ratio of lateral strain to the longitudinal strain
Poisson’s formula
sigma = - (l / D) * (delta D) / (delta l)
Relation between modulus of rigidity and Young’s Modulus
G = Y / 3
A sphere contracts in volume by 0.01% when taken to the bottom of sea 1km deep. Find bulk modulus given density as 10^3 kgm^-3
9.8 * 10^10 Nm^-2
Poisson’s ratio fo a material of a wire whose volume remains constant under an external normal stress
V = pi (D^2 / 4) * l
We know differentiation gives 0 (as volume is constant)
0 = (pi)(l)/4 * 2D * dD + (pi)(D^2)/4 * dl
-ldD = Ddl or dD/D = -1/2 dl / l
sigma = -(dD / D) / dl / l = +1/2 (SIGN watch out)
Relation between Y, k, shear modulus, poissson’s ratio
(9/Y) = 3 / (shear) + 1 / k
Y = 2 (shear) ( 1 + poisson)
Relation between elasticity and compressibility
More incompressible = Less strain = More elastic
