Sheet Metal Forming

x / Abbreviations and Symbols
D
p
punch diameter
D
0
diameter of initial blank
dc 
direct current
DCV 
directional control valve
DDS 
deep-drawing steel
DIN 
German Industry Standard
DP 
dual phase
DQ 
drawing quality
DQSK 
drawing quality, special killed
DR 
dent resistant, draw ratio
DS 
drawing steel
e
engineering strain, endpoint of 
tool motion, eccentricity of the 
load
e
t
total elongation
e
u
uniform elongation
E
Young’s modulus, elastic 
modulus, energy of deformation
E
’ 
Young’s modulus in plane
strain
E
cushion
cushion energy
E
D
elastic deflection
E
EM
electric motor energy
E
F
friction energy
E
forming
forming energy
E
M
machine energy
E
p

process energy
E
slide
slide energy
E
T
total energy
EA 
evolutionary algorithm
E-coating 
electrocathodic coating
EDDS 
extra-deep- drawing steel
EDDS+ 
extra-deep-drawing steel plus
EL 
elongation
EMF 
electromagnetic forming
EP 
extreme pressure
ERC/NSM Engineering Research Center for 
Net Shape Manufacturing
ET 
extreme temperature
f
friction factor
f 
‘ 
modified friction factor
f
b
, 
F
b
blankholder force
f
r
feed rate
F
force, applied load
F
b
bending force
F
BH
blankholder force
F
c
clamping force, clamping load 
F
d
deformation force
F
d,max
maximum punch force
F
draw,max
maximum drawing force
F
f
friction force
F
G
counterforce
F
H
horizontal force
F
N
normal force
F
P
punch force
F
R
ring force, radial force
F
S
blanking force
F
T
tangential force
F
V
vertical force
fcc 
face-centered cubic
F

index to define material flow
FE 
finite element
FEA 
finite-element analysis
FEM 
finite-element method, finite-
element modeling
FLC 
forming limit curve
FLD 
forming limit diagram
FRF 
flexible roll forming
h
clearance, depth of cup, slide 
position
h
conv

convective heat-transfer 
coefficient
h
d
bulge or dome height
h
eff

effective heat-transfer coefficient
h
o
original height
h
(
P
)

contact heat-transfer coefficient
h
rad

radiation heat-transfer coefficient
H
height, surface hardness
H
e
heat-transfer coefficient with air
H
t
heat-transfer coefficient 
HCO 
hem curved outboard
HDGA 
hot dip galvannealed
HDGI 
hot dip galvanized
HE 
hole expansion
HER 
hole expansion ratio
HF 
hot forming
HR 
hot rolled
HRB 
Rockwell B hardness
HRC 
Rockwell C hardness
HSLA 
high-strength, low-alloy
HSPR 
hydro-self-pierce riveting
HSS 
high-strength steel
HV 
Vickers hardness
I
moment of inertia, angular 
inertia, identity sensor
IE 
Erichsen index
IF 
interstitial free
IFU 
Institut für Umform-
technik (Institute of Forming 
Technology)
ISF 
incremental sheet forming
ISM 
inside of metal
ISO 
International Organization for 
Standardization
IUL 
Institut für Umformtechnik und 
Leichtbau (Institute of Forming 
Technology and Lightweight 
Construction)
J
deviatoric stress invariant
k 
empirical constant

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Abbreviations and Symbols / xi
k
stripping constant, heat 
conductivity, shear strength, 
bend allowance
k
f
flow stress
K
springback ratio, strength 
coefficient, wear coefficient, 
shear flow stress 
K-B 
Keeler-Breizer equation
KSIF 
kinematic incremental sheet 
forming
l
distance, length, roll spacing
l
F
total elongation at fracture
l
o
,
 l
0
original length
l
U 
 
uniform elongation
l
1

final length
L
length, sliding distance, load
L
d
draw-in length
L
hem
hem length
L
M
machine load
L
min
dimensions of smallest element
L
o
,
 L
0

initial length
L
p
process load
L
st
stripping force
LDH 
limiting dome height
LDR 
limiting draw ratio
LED 
light-emitting diode
LVDT 
linear variable differential 
transformer
m 
friction factor
m
friction shear factor, strain-rate 
sensitivity
m
r
modified shear factor
M 
index describing the shape of the 
yield loci
M
bending moment, tilting 
moment, torque
MPC 
multipoint cushion
MS 
martensitic steels
n
strain-hardening coefficient, 
strain exponent, speed of crank 
in revolutions per minute, 
number of strokes per minute
n
p
number of strokes per minute 
under load
n
0
number of strokes per minute 
when idle
OBI 
open-back inclinable press
OD 
outside diameter
OEM 
original equipment manufacturer
OSM 
outside of metal
p 
Cowper-Symonds coefficient
p
pressure, normal pressure, 
hydraulic pressure, magnetic 
pressure 
p
BH
blankholder pressure
p
I
internal pressure
p
max
maximum pressure
P
penetration, pressure, 
compression load, normal load, 
deformation power
P
b
blankholder pressure
P
e
interface pressure
P
f
fluid pressure
P
i
instantaneous pressure
PPG 
pulsed power generator
PTFE 
polytetrafluoroethylene
PVD 
physical vapor deposition
Q
̇
flow rate
QPF 
quick plastic forming
r
bending radius, tube radius, 
mean radius, instantaneous 
radius, plastic or normal 
anisotropy, plastic strain 
ratio or Lankford coefficient, 
eccentricity of the crank
r
avg
average strain ratio
r
c
die cavity radius
r
d
, 
r
D
die radius, die corner radius
r
f
die fillet radius
r
m
weighted average of strain
ratios
r
o
outer radius
r
p

punch corner radius
r
R
die corner radius
r
z

radius of curvature in the 
longitudinal direction
r
0

parallel to the rolling direction
r
45

 
diagonal to the rolling direction
r
90

transverse to the rolling direction
r
θ
bulge radius, radius of curvature 
in the hoop direction
r
θ
o 

tube radius prior to deformation
r
, 
R
normal anisotropy
∆
r
planar anisotropy
R
rake, radius, bending radius, 
bend die radius, instantaneous 
outside radius, stress ratio, total 
eccentricity
R
c
radius of die ring
R
d
die radius, bulge radius
R
i
initial radius, inner bending 
radius 
R
m
mean bending radius, tensile 
strength
R
min
minimum bend radius
R
n
neutral radius
R
o
outer bending radius
R
p
punch radius, punch tip radius
RD 
rolling direction
RT 
room temperature

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xii / Abbreviations and Symbols
s
instantaneous sheet flange 
thickness, stroke, recoil
s
h
flange height
s
ij
deviatoric stress state
s
max
maximum stroke
s
0
initial sheet thickness, wall 
thickness, blank thickness
s
1

instantaneous sheet wall 
thickness
S
strength, arc length of inner curve,
yield stress, microstructure, 
stroke length, slide
S
r
pressure release displacement 
time
S
s
shear strength
S
th
theoretical displacement time
S
u
ultimate tensile strength
SB 
stretch bend
SDT 
strip drawing test
SF 
self-feeding
SHF-D 
sheet hydroforming with die
SHF-P 
sheet hydroforming with punch
SMA 
simplified modeling approach
SPIF 
single-point incremental forming
spm, SPM 
strokes per minute
SPR 
self-piercing riveting
SQ 
surface quality, structural quality
SS 
structural steel
t
thickness, sheet thickness, time
t
d
thickness at apex of bulge
t
o,
 t
0

initial thickness
t
p
time under pressure
t
γ

austenitization time
T
thickness, sheet thickness, 
tension stress, temperature, 
applied torque
T
e
temperature of environment
T
f
temperature at forming
T
F
tension load, tension force, final 
thickness
T
i
initial temperature
T
O
original thickness
T
punch
punch temperature
T
t
tool temperature
T
u
temperature of contact plates
T
y
tension required for yield
T
γ

austenitization temperature
T
0
initial temperature
TCT 
twist compression test
TD 
transverse direction, thermal 
diffusion
TDC 
top dead center
THF 
tube hydroforming
TPIF 
two-point incremental forming
TRB 
tailored rolled blanks
TRIP 
transformation-induced plasticity
TS 
tensile strength
TSA 
thickness strain analysis
TW 
tendency of wrinkling
TWIP 
twinning-induced plasticity
u·
instantaneous material point 
velocity in the 
x
-direction
u
D
punch-die clearance
U
d
constant speed 
U
D

die clearance
UHS 
ultra-high speed
UHSS 
ultrahigh-strength steel
UTS 
ultimate tensile strength
v
distribution of tool motion, 
sliding velocity
ν
·
instantaneous material point 
velocity in the 
y
-direction
v
p
punch velocity
V
velocity, volume 
V
p
slide velocity under pressure
V
punch
punch velocity
V
ϕ

angle distribution 
VPB 
viscous pressure bulge
w
width, depth of warp
w·
instantaneous material point 
velocity in the 
z
-direction
W
width, V-die opening, worn 
volume 
W
d
, 
W
D
die opening width
W
o
original width
y
distance
Y
yield strength
YS 
yield strength
z
b
,
 Z
b
burr zone
z
f
,
 Z
f
fracture/rupture zone
z
r
,
 Z
r
rollover zone
z
s
,
 Z
s
shear zone
α
angle, measured angle, bending 
angle, crank angle, angular 
deflection, thermal expansion, 
heat-transfer coefficient, stress 
ratio, cone angle, real contact 
area ratio
α
d
die angle
α
N
design angle
α
p
punch tip angle
β
camera angle, spinning ratio, 
depressor angle
γ
clearance angle
∆
r
planar anisotropy
ε
strain, true or natural strain
ε
·
strain rate
ε
b
bending strain
ε
e
elastic strain
ε
el
elastic strain

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