Based on plasticity theory and physical experiments, the quantitative relationships between elongation 6 obtained by uniaxial tensile test and forming limits of tensile stamping operations are given, which mainly resolves the problem that forming limits can be derived from simple tensile test。  The forming  limit nomogram of tensile stamping  operations is also established to apply to engineering。79936

KEY  WORDS:  Nomogram,  Tensile  test,  Forming  limit,  Tensile  stamping

1。Introduction

The coefficient of forming limit is a main parameter to represent the forming ability of a stamping operation, which usually   is  olitained  by  trials  and  errors。   \Vhether  it  can   be

determined  by  analytic  method  has  great  meaning  in  theory

Table I Parameters to describe the deformation de- gree of stamping operations

Process Diagram   Description  of  deformation degree

(coefficient of forming limilts) Name Function

and practice。 A scholar of former Soviet Union obtained the coefficient of  hole  hanging  by  elongation  d[',  while  the  er- ror is verified zith the hole diameter for d is not a constant。 Tensile stamping operations including hole Clanging, expand- ing;, bulging, bending (outer layer) , share the same mechanical features, so fac。tors influencing their forming limits are similar and  the  main  factor  is  the  material  plasticity["']。   Therefore, it is possible  to  obtain  the  forming  limits  of  tensile  stamp- ing operations through a unitized analytic method。 How to realize Ihis itlea  is  the  major  consideration  of this   paper。

Relative bending ,

radius Coefficient of hanging

Ratio  of expanding A Coefficient of R expanding

Coefficient  of bulging  K

2。Theoretical  Analysis

As discussed above, tensile stamping operations share the same mechanical features, in which the maximum strain oc- curs under the dominating and compelling tensile principal stress,  and the stress-strain  state at  the critical section   that

Expanding Kp  < d + 1 (8)

Bulging K  <  6 + 1 (9)

From Eqs。(6) (9), the relationships between the coeffi- cients of forming limit ( ;---¡—, , Grimm, Kbq。, , K+。,) and the elongation (d) can be obtained as follows:

determines the forming limit can be considered to be uniaxial tensile stress-strain state。 So it is possible to represent the forming limits of t,ensile stamping operations by a parameter obtainetl through simple tensile test。

Parameters   used  to  describe  the  deformation   degree  of

stamping operations are shown in Table 1。 The relationships between the pitrameters  (Table  1)  and  the  maximum strain (ci„ ,。) occur  on the blank  can be presented  as follows:

Bending Hole banging

According to materials plasticity theory, the relation be- tween maximum strain (c„„x ) and materials elongation d should  be satisfied as: