Recommended symbols in forming technology: for use within scientific technical Committee "F" of C.I.R.P.

Recommended symbols in forming technology

Citation for published version (APA):

Kals, J. A. G. (1976). Recommended symbols in forming technology: for use within scientific technical Committee "F" of C.I.R.P. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0373). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1976

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RECOMMENDED SYMBOLS IN FORMING TECHNOLOGY.

for use within Scientific Technical Comnittee "Fllof C.I.R.P.

compiled by J.A.G. Kals

C.I.RP

INTERNATIONAL INSTITUTION FOR PRODUCTION ENGINEERING RESEARCH.

INTERNATIONALE FORSCHUNGSGEMEINSCHAFT FUR MECHANISCHE PRODUKTIONSTECHNIK.

COLLEGE INTERNATIONAL POUR L'ETUDE SCIENTIFIQUE DES TECHNIQUES DE PRODUCTION MECHANIQUE.

======================================================================-=================

===============================~========================================================

RECOMMENDED

SYMBOLS IN FORMING TECHNOLOGY

(international recommandation for use within S.T.C •. IIPI)

compi led by J.A.G. Kals, Techn. Seer. S.T.C. "F"

January

1976

SYMBOL pref. al t. a

x

etc. A a

Explanation: - Numbers in column 3 refer to terms and texts in C.I.R.P. dictionary (part 5)

in which the symbol of column 1 is used in a meaning which conforms to that in column 4;

C.I.R.P. dictionary

vol.

5

5302

EG

- different symbols and meanings (not only from the C. I.R.P. dictionary) are commented in the last column;

- + behind n~mber of term: no symbol mentioned in dictionary; (d) behind number of term: definition;

- E

=

Engl ish text only; G

=

German text only; F

=

French text only.

- references to symbols used in Japanese literature are based on the Japanese Industrial Standard JIS Z -

8202 - 1974.

RECOMt1ENDED MEANING COM~1ENTS

- acceleration

₅₄₄₅

_{G : a}

k

=

Kerbschlagz§higkeit. Beschleunigung

-- acceleration

-

area, cross-section

-

₅₃₀₂

_F,

₅₃₀₇

_{F etc: S = aire}

-

Fl§che, Querschnitt

_{- 5331}

_{F: A}

₌

_{al10ngement conventionnel} - ai re, section

_{- 5470}

EF:

a

=

AlS n

- sometimes A is used for work

- angle _{- a and}

_S

_{also for family of orthogonal} - \-linkel _character i 5 tics known as slip or shear

- angle lines

(5369

+)

- 5713:

20.

=

cone angle, Offnungswi nke 1,

-1-angle au sommet du cone de filage.

-

coefficient of linea i r the rma 1 expansion. - heat transfer coefficient.

January

1976

..

- width

b B

-

Breite

-

largeur

- angle - ex and 13 a I so for fami 1 y of orthogona 1

characteris-e

- Winke 1 tics known as slip or shear I j nes (5369 +)

- angle - Recommendat ion:

B

for geometrical dimensionless number indicating the broad formability in any forming process

(8

large if formability is good) for example limiting drawing ratio.

- coefficient of volumetric thermal expansion. - specific heat - also used for elastic stiffnesses, c ..

c - spezifische Warme

-

capital letter C is probably more wid~ly used

-

capacit~ _{calorifique specifique in U. S. A. for specific heat.}

n

(Ludwik's relationship) for example

- constant - (J

=

CE

C K

-

_Konstante

- constante _ al so in Japan C

=

heat capacity

- diameter - d and <5 used for differentials or increments

d D - Durchmesser. - Japan : d

=

thickness

- diametre

- 5442 G:

o

=

Bruchdehnung (also VD I

3137

a.o.) - often ~sed for differentials, increments or'

0 d iff e rences

- VOl

3137:0

=

Gleichmaszdehnun9 - in Japan

0

9

=

thickness

January

1976

,

- engineering strain

-

5331

F: A

=

allongement conventionnel

e

5331

E(d)

-

Dehnung (bezogen auf Ausgangs1ange) - e is a I so error, eccentricity and e == base of

- allongement brut (convent i onne 1) natural logs

2. ]182818

-

VD I

'3137:

£ instead of e, this is never used in English literature ( see £ be I ow)

- Young's modulus

E

-

Elastizitatsmodul - sometimes used for energy (see W)

- module d'Young

- natural strain (true strain)

- 5331

G : <p == Umformgrad

£

5331

EF(d) - Unformgrad (log. Formanderungsverh.) - Germany a.o.:£ = engineering strain

-

deformation vraie (def. rationelle)

-

the recommended meaning is always used in English literature, G notation inconsistent (see

5338

G,

5435

G and

5309)

.

- natural strain rate - see aboven for £

£

5334

EF(d)

-

Formanderungsgeschwindigkeit

-

(€ .. )

== strain rate tensor ( i , j = 1 , 2,

3,

or

- vitesse de deformation I J

x, y, z)

- 5334

G: ~

=

zeitliche Anderung der Formanderung - equivalent (effect ive, generalized)strain

- 5338

G: d£ = Vergleichsformanderungszuwachs (etc

-

v

£ 5338 EF(d) - Vergleichsformanderung

- subscr j pt eff. could have a more general meaning

-deformation equivalente

- bar is sometimes used as mean or average but this

)

.

is not recommended here (see subscript m)

.

- equivalent strain rate

-£ - Vergleichsformanderungsgeschwindigkeit - vitesse de deformation equivalente

- efficiency factor, work rat io factor

- 5330

(d) : T) == efficiency of deformation,

F

T)

5330

- Wirkungsgrad _{Umformwirkungsgrad}

- coe ff i c i en t de rendement rapport de formage

January 1976 4

-- components of deviatoric strain increment -- one subscri pt (1,2,3); principal stress

] tensor - double subscript (11,22,33) or (xx,yy,zz):

Qe: ••

-

_{Komponenten des infinitesimalen devia- general normal stress}

IJ

torischen Formanderungs-tensors _{- double subscript (12,23,31) or (xy,yz, zx):} - composantes du tenseur d'viatorique des general shear stress.

dtHormat Ions infinitesimales

- frequency _{- often used as Coulomb's friction coefficient for}

f - Frequenz· the past few years f is connected with another

-

frequence _{frictional concept in the U.S.A.}

- VDI 3137: f

=

Federweg

-

force (load) _{5301 E, 5302 E, 5305} E: L

=

load F L 5301 GF(d) - Kraft (Belastung)

-

force (effort)

- average value of natural strain - 5363 (Mohr figure): 11

=

angle

cp _{- mittlerer Umformgrad - cp is often used for (spher i ca 1) coordinate}

-

valeur moyenne de la d'formation vraie

- 5331 G : I I i

' I == n -10

- often used for orientation of s lip lines . - 5334 G

.

·

- average natural strain rate : cp

= Formanderungsgeschwindigkeit

•

- mi tt lere (logarlthmische)

Formanderungs-cp

geschwindigkeit

- valeur moyenne de la vitesse de d'for-mat ion

- average total equivalent strain

-cp - mittlere Vergleichsformanderung

- valuer moyenne de la deformation totale 'quivalente

·

- average equivalent strain rate

-<p - mittlere Vergleichsformanderungsgeschwin-digkeit

-

valeur moyenne de la vitesse de deforma-tion equivalente

5

-January 1976

-

shear modulus - a Iso used for force of gravity

G - Schubmodul

- module de cisaiJlernent

5331

-

shea range 1 , engineering shear strain

-

5331 EGF, 5338 EGF, shear stra in

y

-

Schiebung(s winkel), Gleitungswinkel - different meanings in Japan. 5338 - angle de glissement, deformation de

c i sa i 11 ernen t

- engineering shear strain rate

.

_{- Schiebungsgeschwindigkeit}

y

- vitesse de deformation de cisail1ement

- height - VOl 3137: h

=

Kraftweg etc.

h H

-

Hohe

-

in U.S.A.: h or H = enthalpy

- hauteur

-

in Japan: heat transfer coefficient

5304 (d) + - stroke - 5305: s

=

Stroke, Stoszelweg, deplacement

H h 5651 (d) ₊ - Hub

- A =

stroke speed (also

h)

5654 + - course - VOl ₃₁₃₇ : hA

=

Auswerferhub

H

=

Hub {Maximalwert}

I 1

-

tensor invariants - usually for strain tensors

'2

- Tensorinvarianten - by way of exception the suffixes do not indicate

'3

-

invariants du tenseur direct i on; cannot introduce any misunderstanding.

-

In Japan: I

=

mechanical energy

_I

a

January 1976 k K (or dA)

c

L 5348 (d) 5349 (d) 5331 5736 etc. - tensor invariants - Tensorinvarianten - invariants du tenseur

- yield stress in shear - $chubflieszspannung

- limite d'elasticite au cisaillement

- constant - Konstante - constante - length - Uinge - longeur

- factor of proportionality in incremental stress·strain relations.

- Proportional itatsfaktor der konstitutiven

Gleichungen. .

- coefficient de proportionalite entre la deformation infinitesimale et les con-traintes.

6

-- usua 11 y for st ress tensors

I

- by way of exception the suffixes do not indicate a direction; cannot introduce any misunderstanding.

- 5470 G: k

f = kf .~n

o

- 5349

G: k

13=

k

f

=

Flieszgrenze (kf

=

2k, Tresca)

- 5349

EF: k I

3

=

Y

=

yield stress in tension

=

limite d'elasticite au tension

- VOl 3137 : k

f

=

Flieszspannung

- K is used for stiffness matrix and heat conductivi ty

- very often used for stress intensity factor in fracture mechanics

- compression modulus, bulk modulus - see

F

also

- A

often used for wavelength and for first Lame constant

January 1976

- mass

I

-

constant friction factor - IIfriction factor"

=

shear stress/yield shear

m - Masse

_I

(Tresca) stress

- masse

I

- coefficient de friction

-

Reibungsbeiwert - m often used as strain rate sensitivity exponent .!. m

I

I

in

-

cr

=

C E

I

- m is used as the Wei bull flow density constant t determine the probability of failure of brittle

I

materi a Is

o

- moment - bending moment _{t~B '} torsion moment MT

M - Moment

- moment

-

Coulomb's coefficient of friction - )1 is used for Lode's parameter too

)1 .v 5381 (d)

-

Reibungsbeiwert (Reibwert) - )1 is the 2nd Larre's constant and is convenient t o

- coe ff i c i en t de frottement use were

G

is taken as the Gibbs free energy - also )1 viscosity

-

strain hardening exponent

-

n, m, I often used as direction cosines of the n 5470 (d) - Verfestigungsexponent normal to a plane

- coefficient d'ecrouissage - defining relation cr

=

CEn attributed to Ludwik - VOl 3137: n

=

Verfestigungsexponent + Hubzahl - Poisson rat io _{- v often used for frequency and kinematic viscosi ty}

v - PoissonzahJ - Lode's parameter

- coefficient de Poisson - angular velocity

w

- WinkeJgeschwindigkeit

- vitesse angulaire

- pressure

-

in Japan p is used for moment

p 5302

-

Flachenpressung (Druck) - also to be used for hydrostatic pressu re - pression - often used as primary principal stress

-

power (work per unit time)

-

in Japan: P := pressure

•

p _{W - Leistung}

- puissance

January 1976 r R p s t S (J •• IJ

- radius (polar coordinate) - Radius (Polkoordinate) - rayon (coordinee polaire)

r---~---_{- area reduction ratio}

5309 EF(d) - bezogene Querschnittsanderung - variation relative de la section

transversale

- anisotropy parameter - Kennwert fUr Anisotropie - coefficient d'anisotropie

1

-- extrusion ratio

5308 EF(d) - Querschnittsverhaltnis bei Flieszpressen - rapport de filage

5339 (d)

5341 (d)

- radius (of curvature,. bending radius) - (Krummungs)radius, Biegeradius

- rayon (de courbure, rayon de pI iage) - thickness - Dicke, Blechstarke - epaisseur - area, cross-section - Flache, Querschnitt - aire, section

- components of stress tensor - Komponenten des Spannungstensors

- composantes du tenseur des contraintes

8

-I

- sometimes strain ratio in deep drawing (I.D.D.R.G.)

- often p

=

density

- 5305 : s = Stosselweg, stroke, deplacement - s is used as engineering stress i.e. load

divided by original cross-section - VDI 3137 : s

=

Stauchverhaltnis

s

=

Wanddicke

- 5302 F, 5307 F, 5308 F : section transversale - S often used for entropy.

- one subscript (1,2,3) ~ principal stress - double subscript (11,22,33) or ~x,yy,zz) ~

general normal stress

- double subscript (12,23,31) or (xy,yz,zx) ~

January 1976

9

-- components of deviatoric (reduced) stressl -- one subscript (1,2,3) + principal stress

tensor - double subscript (11,22,33) or (xx,yy,zz) + I

5344 (d) - Komponenten des deviatorischen{reduzierten} general normal stress (J ..

IJ _{Spannungstensors - double subscript (12,23,31) or (xy,yz,zx) +}

- composantes du tenseur d~viatorique general shea r st ress ( redu it) des contraintes

- hydrostatic or mean stress

_{- 53}

LI3 ( d) (J

=

hydrost. Spannungszustand,

(J - hydrostatischer Spannungszustand hydrostatic stress,

m _{- contrainte hydrostatique}

contrainte hydrostatique

- effect ive (generalized, equivalent) stress - 5345 G :(Jv := Vergleichspannung

-(J

(Jeff 5345 E{d) - Vergleichsspannung - 5345 F :(J

=

contrainte ~quivalente - contrainte equivalente (effective,

g~n~ra-1 i see)

- shear stress T •• ( i ,& j) for shear stress components of stress

T 5342 (d) - Schubspannung 1 J tensor

- contrainte de cisai llement

- time

I

- thickness - sometimes used for resulting stressor

stress-t - Zeit

I

- Dicke components (t .. ) •

- temps

I

- epaisseur 1 J

I

- temperature (oC

,

oK of oR)

.,

,

- period

T - Temperatur - torque

- temp~rature

- angle - also used for (Kelvin) temperature and

e

- Winkel volumetric strain (Japan)

10 -January 1976

- displacement

I

velocity

I :

- u x' u y' u z

u - Verschiebung Geschwindigkeit

- d~placement J - vitesse - often u, v, w, instead of u x' u y' u

- often U z

I

- often used for velocity in x-direction

I

- see below for v

-

instantenious yield stress (in tension) _{- 5438 kf}

₌

_{Fl ieszspannung} k

f 5438 EF(d) - Flieszspannung (Augenblickswert im _{Zugversuch) -} G:

- y.s.

₌

yield stress in U.S.A.

-

limite elastique (cont ra in _{te d ' ecoulement) - y}

=

yield st ress in U. K.

- d i sp lacement

I _

ve loc i ty - 5306 EF: V

=

velocity~ vi tesse

v 5306 G - Verschiebung

I -

Geschwindigkeit - often used for velocity in y-direction - deplacement

_1-

vitesse - see above for u

I

-

volume - 5306 EF: V = velocity, vitesse (see also 5348,

V - Volumen, Rauminhalt 5349, 5470)

- volume

- displacement

I _

velocity - sometimes deformation work per unit volume w - Verschiebung

I -

Geschwindigkeit - often used for velocity in z-direction

-

deplacement

_{I -}

vitesse - see u and v

I

- work, energy - weight in Japanese 1 iterature

W - Arbeit, Energ i e - often work per unit volume

January 1976

Pref. meaning

-

Bedeutung - signification - axial a - Axial - axial - width b - Brei te

-

largeur - bending B

-

Biegung - pI iage

- cri t i ca I .

I

_IC sometimes used for

c - kritisch

_I

"compressive n - critique I

I

- deformat ion : ex: Tdef def - Umform

I

- deformat i on

I

- effecti ve eff - Effektivwert - effectif - elastic el - elastisch - elas t ique GENERAL SUBSCRIPTS ALLGEMEINE INDIZES SYMBOLES INDICES Pref. meaning

-- optimal opt. - Optimalwert ... optimal - plastic pI - plastisch - plastique

-

radial r - Radial

-

radial

-

relative re I - Relativ

-

re)atif - torsion T - Torsion

-

torsion Bedeutung

-

signification

I

I

I

I

I -

tangential

I -

Tangential

I -

tangential

- final - maximum

e - Endwert max - Maximatwert, Grenzwert

- final - maximum

- friction

f-

_{see 5349 G} k} f f - Reibung

L

VOl

5470 G

- f rot temen t 3137: Fliesz (also F)

I

. - minimum

min

-

Minimalwert, Grenzwert - minimum

- height - normal

I

_I

h - Hohe - hauteur

n - Normal

I

ex: normal Force

=

Fn - normal

I

- denoting components of a tensor

-

initial

i ,j

-

Bezeichnung fUr Tensorkomponente 0 - Anfangswert

-

indices des composants dlun tenseur

-

initial

-

ideal x

-

in direction x etc.

i d

-

idee 11 .y

-

in x-Richtung usw.

-

idlSal z - en direction x etc.

, ₁ - principal

1-

_{5340 : 1,2 , 3} 2 -Haupt

1-

VOl 3137: 1,2,3

3

- principal

I

-

length 1

-

lSnge (langskomponente)

-

longeur - average m - Kittelwert - moyenne