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An Automated Process Sequence Design and Finite Element Simulation of Axisymmetric Deep Drawn Components
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FE Simulation Module.
In this module, the obtained process sequence of the product is automatically simulated in Theabaqus/EXPLICIT finite element software. This module creates the ABAQUS input and submits it to theabaqus/EXPLICIT software to execute. The blank elements and the dies would be simulated using shell and rigid elements, respectively. The blank would be modeled in the first drawing stage, but in the next stages the node and element information of the blank at the end of the previous stage is imported as initial condition. Executing ABAQUS software automatically, the system gets the information of each interval. Using the forming limit diagram (FLD) or ductile fracture criterion the system checks whether the process is successful. If not successful, the system automatically changes the appropriate process parameters namely, punch arc radius, die arc radius, drawing ratio, friction coefficient, and blankholder force.
The blankholder force that initially is used in FE simulations is calculated using the Eq. (2) [36]：37166
(2)BHF=Pbh×Abh=10−3c[(R0rp−1)3+0.01R0t0]Su×π(R20−(rp+rd)2)
where Pbh is the blank holder pressure, Abh is the contact area between the blank-holder and blank, R0 is the initial blank radius, rp is the punch radius, t0 is the initial blank thickness, rd is the die arc radius, and Su is the tensile strength of the sheet material. The factor c is a constant that can be determined by the user (usually between 2 and 3). By default c is equal to 2. The FE simulation is performed by the calculated blank holder force. The system determines the distance of all nodes of the cup during drawing operation from the wrinkle free cup geometry in perpendicular direction to it. If there is a node that its distance is greater than a predefined value (which by default is 10% of sheet metal thickness), the cup is considered to be wrinkled. If wrinkling is observed in FE simulations, the system increases the c value which increases the blankholder force and FE simulation is performed again, with the new calculated blank holder force.
If fracture is predicted in FE simulations, the system first tests the die arc radius and punch arc radius to be in safe region. If they are not in safe region, the selected parameter is moved to safe region and the changes are applied in the process sequence. If they are safe, the drawing ratio is decreased and its effect on the next drawing stages is applied on the designed process sequence. The next drawing stages is simulated again and this procedure is carried out until all drawing stages are successful.
The current system uses the ductile fracture criterion and the FLDs obtained using the statistical and M-K methods to determine whether the drawing process is successful. In the following these methods are described briefly.
Ductile Fracture Criteria (DFC).
The Brozzo et al. criterion is used as one of the DFC criterion in the current system [33]. According to this criterion, the fracture occurs when Eq. (3) is satisfied
(3)∫ɛ¯f023(1−σhσmax)−1dɛ¯=C
where ɛ¯f is the equivalent strain at which the fracture occurs, σmax is the maximum normal stress, σh is the hydrostatic stress, and C is the material constant. To determine this constant, one destructive test has to be carried out on the sheet material. This could be simply the uniaxial tension test which is also required to determine the other necessary material properties.
Using the stresses and strains obtained by the Finite element simulation, the integral term is calculated for each element and each deformation step. The condition of fracture is satisfied when and where the integral term amounts to the value of C [33].
Statistical Forming Limit Diagram.
Stuart Keeler and William Brazier have developed a statistical model for generation of the FLD, based on the data collected for deep drawing quality steels [34]. Considering e1 and e2 as the major and minor engineering strain values of the points of the FLD expressed in percent, in right hand side of the FLD where e2>0, the values of e1 and e2 are related to each other as below equation