As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AEAs discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in t
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
(AE 2 + ED2 ) 1/2
AE
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
(AE 2 + ED2 ) 1/2
AE ) = 1 + )--~
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulusAs discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
(AE 2 + ED2 ) 1/2
AE ) = 1 + )--~
dimension of die
Swelling Ratios Due to Shear Stresses
(a) Long Capillary
Fig. 5.10 shows an annular element of fluid of radius r and thickness dr
subjected to a shear stress in the capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
(AE 2 + ED2 ) 1/2
AE ) = 1 + )--~
dimension of dieSwelling Ratios Due to Shear Stresses(a) Long CapillaryFig. 5.10 shows an annular element of fluid of radius r and thickness drsubjected to a shear stress in the capillary. When the element of fluid emergesfrom the die it will recover to the form shown by ABCD.If the shear strain at radius r is Yr thenEDYr "-- tan c~ ----AEarea of swollen annulusAlso =initial area of annulus2rrr dr 1 AD2rcr dr AE(AE 2 + ED2 ) 1/2AE ) = 1 + )--~
1/2
he capillary. When the element of fluid emerges
from the die it will recover to the form shown by ABCD.
If the shear strain at radius r is Yr then
ED
Yr "-- tan c~ ----
AE
area of swollen annulus
Also =
initial area of annulus
2rrr dr 1 AD
2rcr dr AE
(AE 2 + ED2 )
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
area of swollen annulus
Also =
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
area of swollen annulus
Also =
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die
area of swollen annulus
Also =
initial area of annul
As discussed earlier, polymer melts can also exhibit elasticity. During flow
they have the ability to store strain energy and when the stresses are removed,
this strain is recoverable. A good example of elastic recovery is post extrusion
swelling. After extrusion the dimensions of the extrudate are larger than those
of the die, which may present problems if the dimensions of the extrudate
are critical. In these circumstances some knowledge of the amount of swelling
likely to occur is essential for die design. If the die is of a non-uniform section
(tapered, for example) then there will be recoverable tensile and shear strains.
If the die has a uniform cross-section and is long in relation to its transverse
dimensions then any tensile stresses which were set up at the die entry for
example, normally relax out so that only the shear component contributes to
the swelling at the die exit. If the die is very short (ideally of zero length) then
no shear stresses will be set up and the swelling at the die exit will be the
result of recoverable tensile strains only. In order to analyse the phenomenon
of post extrusion swelling it is usual to define the swelling ratio, B, as
dimension of extrudate
B=
dimension of die