Transcript Bending of Sheet and Plate

Bending of Sheet and Plate
• Bending is done to form flanges, etc.
• Also for giving stiffness to a sheet part
• Length of neutral axis
– l0  ( R  T )
2
– l f  ( R  T )
– e0 
–
l f  l0
l0

lf
l0
1
( R  T )
1


( R  T / 2)  2 R  
 T   1
 

• In bending outer fibers are in tension and
inner fibers are in compression
• Strain is usually equal in magnitude
1
– e0  ei 
2 R / T   1
R=bend radius
T=thickness
• But in effect e0 is larger than ei because of
neutral axis shift to inner surface
• With R/T
e0-ei=
Minimum Bend Radius
• We can see that as R/T decreases tensile
strain at the outer surface increases.
• Radius ‘R’ at which cracks appear on the
outer surface is called “minimum bending
radius”
• Min. bending radius is expressed in terms of
T (2T, 3T, etc.)
• True strain at outer fiber for cracking = true
fracture strain in tension test.
• Spring back
– Elastic recovery after the removal of load.
(Finite modulus of elasticity) Rods, sheets,
bars, etc.
– Radius of bending increases when load is
removed.
– Springback factor Ks.
• Bend Allowance
T
T


–   Ri  i   R f  
2
2


–
f
 f (2Ri / T )  1
Ks 
Ks 

i
 i (2 R f / T )  1
• Since recovery depends on the stress level
and modulus of elasticity ‘E’ we can
recalculate Ri/Rf.
–
3
Ri
 R Y   3R Y 
 4 i    i   1
Rf
 ET   ET 
Where ‘Y’ is the yield
stress of the material
• Bendability can be improved
– Heating the area
– Applying hydrostatic pressure
– Reducing outer tensile strain by compressive
force
• As R/T decreases, narrow sheets (smaller
length of bend) crack at the edge and move
towards center. Wide sheet crack at center.
• Rough edges can also cause reduction of
bendability (stress raisers).
Operations
•
•
•
•
•
Beading
Flanging
Hemming
Roll Forming
Tube Bending
Bead Forming
TUBE BENDING
STRETCH FORMING
FLANGING
Spinning
• Conventional Spinning
– As large as 6m (20 ft)
• Shear Spinning
– Missile nose cones, rocket parts.
t

t
sin

0
•
Ft  ut0 f sin 
• Tube Spinning
u=specific energy
of deformation
High Energy Rate Forming
• Diffusion and Super plastic formation
– A “hot” research area
• Honeycomb material
• Deep Drawing
– Pure drawing
– Stretching
– ironing
Superplastic Forming
• Same fine grained alloys can elongate as much as
2000%
– E.g. Zn-Al, titanium can be formed into very complex
shapes.
• High ductility, low strength
• Very strain rate sensitive
• Extremely slow forming
– 10-4 to 10-2 s
• Some times forming can take hours
HONEY COMB STRUCTURE
Super Plastic Forming