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1. Flexural properties
The behaviors shown by textile
materials (fibre, yarn and fabric), when
it is subjected to bending, are known
as flexural properties.

2. a) Flexural rigidity:
Flexural rigidity is the resistance of a textile fibre against
bending. It can also be defined as the couple required to bend the
fibre to unit curvature. The unit of flexural rigidity is N-mm2, N-
m2 etc.
Mathematically, Flexural rigidity, Rf = 1 x ηЕT2
4∏ ρ
Where, η = Shape factor
Е = Specific shear modulus (in N/tex)
T = Linear density (in tex)
ρ = Density (in gram/cm3)

3. Specific flexural rigidity:
The specific flexural rigidity is the flexural rigidity of a
textile fiber of unit linear density. Specific flexural rigidity is
usually expressed as N-mm2/tex, N-m2/tex etc.
Mathematically, Specific flexural rigidity = 1 x ηЕ(1)2
= 1 x ηЕ 4∏ ρ
4∏ ρ

4. b) Bending recovery:
The power of recovery from an immediate
curvature of textile fiber is known as bending recovery.
For example, nylon of 15 denier shows 100% recovery
from a small curvature, whereas only 20% recovery is
obtained from a large curvature.

5. c) Bending modulus:
Bending modulus can be defined as the
ratio between bending stress and bending strain. Here,
bending strain is usually expressed as degree or radian.
So, Bending modulus = Bending stress
Bending strain

6. Shape factor:
Shape factor is a quantity or number that indicates the
thickness or cross-section(shape) of a fibre. Shape factor
is usually expressed by η.
If η =1, then the fiber is completely round shaped.
If η >1, then the fiber thickness is increased while
bending.
If η <1, then the fiber thickness is reduced while
bending.

7. Shape factor of different fibres:
Fibre Shape factor Fibre Shape factor
Viscose 0.74 Acetate 0.67
Wool 0.80 Nylon 0.91
Silk 0.59 Glass 1.0

8. Torsional Properties
The behaviors shown by textile fiber,
when it is subjected to twisting is
known as torsional properties.

9. a) Torsional rigidity:
Torsional rigidity is the resistance of a textile fiber against
twisting. It can also be defined as the torque applied to insert unit
twist per unit length of fiber. The unit of torsional rigidity is N-
mm2, N-m2 etc.
Mathematically, Rt = ηЕT2
ρ
Where, η = Shape factor
Е = Specific shear modulus (in N/tex)
T = Linear density (in tex)
ρ = Density (in gram/cm3)

10. b) Specific torsional rigidity:
The specific torsional rigidity is the torsional rigidity of a
textile fibre of unit linear density. Specific torsional rigidity is
usually expressed as N-mm2/tex, N-m2/tex etc.
Mathematically, Specific torsional rigidity = ηЕ (1)2 = ηЕ
ρ ρ

11. Specific torsional rigidity of different fibres:
Fibre Specific torsional rigidity
(mN-mm2/tex)
Cotton 0.16
Wool 0.12
Silk 0.16
Viscose 0.085
Nylon-6.6 0.06
Polyester 0.067

12. c) Breaking twist:
Breaking twist is the twist for which a textile fibre will
break. Breaking twist can also be defined as the number of turns
or twists required to break a fibre. Breaking twist depends upon
the diameter of fibre and is inversely proportional to the
diameter.
So, Breaking twist, Tb ∞1/d [d = fibre diameter]

13. d) Breaking twist angle:
The angle through which the outer layers of fibres are
sheared at breaking is known as breaking twist angle. Breaking
twist angle is usually expressed as α.
Mathematically, Breaking twist angle, α = tan-1 (∏ d Tb)
Where, d = Fibre diameter & Tb = Breaking twist per unit length
of fibre.
D=0.2mm, Tb=20/inch, a=?

14. Breaking twist angle of different fibres:
Fibre Breaking twist
angle (α)
Fibre Breaking twist
angle (α)
Cotton 350 Wool 400
Viscose 330 Silk 390
Polyester 500 Glass 40

15. C) Shear modulus:
Shear modulus can be defined as the ratio between shear
stress and shear strain.
So, Shear modulus = Shear stress
Shear strain
Shear strain is usually measured in radian. Shear modulus of
a fibre is expressed as kN/mm2. For example, shear modulus of
wool is 1.3 kN/mm2.