Substituting Eqs。(I) (4) into  Eg。(5),  it  can  be obtained as follows:

Expanding Kpq。   = d-(-1 (12)

Bulging K„ ,     = d + 1 (13)

From Eqs。(10) (13), the relationships between the elon- gation é and the forming limits of tensile stamping operations can be observed。 It can be seen that it is the materials elon- gation (6) that mainly determines the forming limits of ten- site stamping operations。 While d varies with the length of specimen, the factors influencing d  should be  considered[‘"‘] in Eqs。(10) (13) in order to obtain scientific results。 Fortu- nately, the quantitative relationship between  d  and  the length of the specimen is given by a former Soviet scholar H。H。Basof, which can be expressed as  follows:

where, A and o are constants  related  to  the specimen mate- rial。 Take mild steel for example, fi——185 and n=0。4。 L is the length  of  the specimen。

Substituting   Eg。(14)   into  Eqs。(10)    (13),   the following

equations  can  be obtllined:

Prof。, Ph。D。, to whom correspondence should be addressed, E—mail: shzhangBimr。ac。en。

。I。  Mater。  Sci。  Technol。   Vol。20    No。3,  2004

Table   2    Comparisons  between  calculations   and experiments

lvI aterial Geornetricai coeffiCient  of forming limits

process

Beiitliiig 90‘

Al alloy (LY12) dimensions

t ——8 inin Nomogram

z。3 Experiment

2。s   2。s

Expanding lCr 18Ni9Ti 'f'32 mm, t ——1 mm 1。56 1。52

Low  carbon steel 'I'58 mm, t=0。8 mm 1。28 1。 26

Flaiiging 。Al alloy L=100 mm 0。86 0。82  0。87

Low- carbon steel 4'20 mm, t=0。5 mm 0。 72 0。73

Bulging 。4l alloy 4'70  mm, t=i,5 mm 1。 17 1。 19

Fig。1   Forming  limit  nomogram  of  tensile  stamping  operations

Through the comparisons, it can be observed that the re- sults obtained from the nomogram are close  to  the  results from experiments。 Therefore,  it  is  reasonable  to  determine the forming limits of tensile stamping operations through this analytic method, and the geometrical  dimension  of  blank is the main factor to control the forming  limit。  It  can  also be seen that the nomogram established in this paper satisfies the engineering  requirements。

ehere  L  is  the  deformation   length,   which  can  be  calculated