Physical pharmaceutics -ii unit-iii deformation of solid B-pharmacy

1. DEFORMATION OF SOLID

2. OBJECTIVE
 Plastic Deformation
 Elastic Deformation
 Heckel Equation
 Stress
 Strain
 Elastic Modulus

3. What is deformation of solid?
 It is defined as change in the size and shape of an object. When
applied a external force.
 It is term of the concept of Strain and stress.

4.  What is stress ?
 Stress (σ) is the force per unit area that applies to an object to
deform it.
 Stress (σ) = Force/Area
 Its unit is Nm-2 or Pa
o Types of stress
 There are three type of stress
1) Direct stress
2) Indirect stress
3) Combined stress

5.  Types of stress
 Direct Stress:
1) This stress produced under direct loading condition
2) i.e force will be in line with the axis of member.
3) It is force acting on body.
4) It may be tensile or compressive or shear stresses

6. Direct Stress
Tensile
stress
• Define:- Tensile
force acting per unit
area of the body.
• It is the ratio of
change in length to
the original length.
Compressive
stress
• Define:-
Compressive force
acting per unit area
of the body.
Shear stress
• Define:-Shear force
acting per unit area
of the body.
Indirect Stress :- This stress occur due to torque produced in the body.
Combined Stress :-This stress are the combination of above two types
of stress.

7. What is strain ?
 Strain is the measure of the amount of deformation.
 For E.X- If the Bar has original length(L) and when the load is
applied on a bar the length of bar will change which is indicated as
(∆L)
Strain= ∆L/L
 It has no unit.
o Types of strain
 There are three type of strain
1) Tensile strain
2) Compressive strain
3) Shear strain

8.  Types of strain
Tensile
strain
• It is defined as
ratio of increased
in length to
original length of
bar.
Compressive
strain
• It is defined as
ratio of decrease
in length of
original length of
bar.
Shear strain
• The strain
produced by
shear force is
called shear
strain.

9.  What is Elastic modulus?
 The constant of proportionality depends on the material being
deformed and the nature of the deformation.
 This constant is called as elastic modulus.
 Elastic modulus determine the amount of force required per unit
deformation.
 The elastic modulus under the law of Hooke’s law.
 This law state that “, In an elastic member stress is directly proportional
to the strain within elastic limit”.
σ α ε
σ=E.ε
or E= σ/ε
Where,
E is constant known as modulus of elasticity or young modulus
σ is stress
ε is strain

10. Fig- stress strain relationship for elastic solid

11. stress strain relationship for elastic solid
 Young modulus will have to identify how much the material is elastic.
 The elastic limit of substance is defined as the maximum stress that can be
apply to the substance before it deform permanently.
Initially, a stress strain curve is a
straight line
As the stress is increase, the curve is
no longer straight.
When the stress exceed the elastic limit, the object is
permanently distorted and does not return to it original
shape after the stress is removed.
Hence, the shape of the object is
permanently changed.
As a stress is increased even further,
the material ultimately breaks.

12. Type of
deformation
Stress applied Deformation
Removal of
stress
Elastic
deformation
Plastic
deformation

13. Elastic Deformation
The material return to its original shape
when force is removed.
It is reversible
In elastic deformation the chemical bond of
substance undergo stretching and bending
It is time dependent
It occurs in metals within elastic limits
Plastic Deformation
The material does not return to its original
shape when force is removed.
It is Irreversible
In plastic deformation the chemical bond of
substance undergo breakage
It is time in-dependent
It occur beyond plastic limits.

14.  What is Heckle equation?
1. The Heckle analysis is a most useful method for estimating the volume
reduction under the compression pressure in pharmacy.
2. Heckle plots can be affected by the time of compression, the degree of
lubrication and size of the die. The effect of these variables should be
taken into consideration.
3. The basic assumption of heckle equation is that the densification of the
bulk powder on applying force obeys first-order kinetics. The Heckle
equation is expressed as ;
In
1
𝜀
= KP + A
where, ε = Tablet porosity.
P = Applied pressure.
A = Constant related to particle re-arrangement and fragmentation.
K = Slope of the linear part of the relationship reflects yield stress
or yield pressure (Py) for the particles:

15.  What is Heckle equation?
 Reciprocal of the K (1/k) value is calculated and reflects yield stress or yield
pressure (Py) for the particles:
In
1
𝜀
=
𝑃
𝑃𝑦
+ A
 Heckle profile depicting on initial curvature (region 1) associated with
particle fragmentation and particle rearrangement. The relationship is
linear most of the time for a range of pressure applied (region 2) and therby
follow the expression.
 The linear part reveals a situation where compression process is influenced
by particle deformation. From the gradient of this linear part, the yield
pressure can be determine. When the profile again deviates from the linear
relationship (region 3), the resultant curvature suggest deformation of the
complete tablet.

16.  What is Heckle equation?
Significance of heckle plots:
1. It is used to characterize single material and
as well as can also be used for powder
mixture.
2. Region 1-Heckle plot usually exhibit a
higher final slope than region 2.
3. This indicate that the Region 1 have a lower
yield pressure.
4. The two region of Heckle plots in region 2
represent the initial repacking stage and
subsequent deformation process
5. The crushing strength of tablets is also correlated with the value of K of the
heckle plot.
6. Larger K Values indicate harder tablet. The knowledge of this can be used to
select binder during designing of tablets.