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Table of Contents
                            Preface  Metal Forming - Process, Tools, Design
Section 1  
01  Hydroforming Process: Identification of
the Material’s Characteristics and
Reliability Analysis
02  Stamping-Forging Processing
of Sheet Metal Parts
03  Developments in Sheet Hydroforming for
Complex Industrial Parts
04  Forming of Sandwich Sheets Considering
Changing Damping Properties
Section 2  
05  Impact of Surface Topography of
Tools and Materials in Micro-Sheet
Metal Forming
06  Towards Benign Metal-Forming:
The Assessment of the Environmental
Performance of Metal-Sheet For
Section 3  Design
07  The Design of a Programmable Metal
Forming Press and Its Ram Motion
08  Self-Consistent Homogenization Methods for
Predicting Forming Limits of Sheet Metal
Document Text Contents
Page 1


Edited by Mohsen Kazeminezhad

Page 2

Metal Forming – Process, Tools, Design
Edited by Mohsen Kazeminezhad

A. El Hami, B. Radi, A. Cherouat, Xin-Yun Wang, Jun-song Jin, Lei Deng, Qiu Zheng,
M. Bakhshi-Jooybari, A. Gorji, M. Elyasi, Bernd Engel, Johannes Buhl, Tetsuhide Shimizu,
Ming Yang, Ken-ichi Manabe, Marta Oliveira, Weizhong Guo, Feng Gao, Javier W. Signorelli,
María de los Angeles Bertinetti

Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia

Copyright © 2012 InTech
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any damage or injury to persons or property arising out of the use of any materials,
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Publishing Process Manager Oliver Kurelic
Typesetting InTech Prepress, Novi Sad
Cover InTech Design Team

First published October, 2012
Printed in Croatia

A free online edition of this book is available at
Additional hard copies can be obtained from [email protected]

Metal Forming – Process, Tools, Design, Edited by Mohsen Kazeminezhad
p. cm.
ISBN 978-953-51-0804-7

Page 109

Forming of Sandwich Sheets Considering Changing Damping Properties 101

The Euler representation with the function ���(�� � � + ��) is used with the damped angular
frequency ��. From experimental tests it is well known, that the decay based on
displacement behaves ��� � ����� [35].
With ���, the value of the displacement at time � = 0:

�(�) = ��� � ������� � ���(�� � � + ��) (39)
With the following characteristics of:

Damping/ Decay constant:

� = ������������ � � � � (40)
Resonance quality:

� = ������������� (41)

Damping ratio:

�� = ������������� (42)
The natural angular frequency of damped oscillation ω� is calculated of angular frequency
ω� and damping constant δ.

�� = ���� − �� (43)
Due to the viscous damping, only the physically significant context ω�� − δ� > 0 is
considered further. With the dimensionless damping ratio D, the decay and input angular
frequency can be compared:

� = ��� (44)

5.3. Damping-behavior of a three layer sandwich

Ross, Kerwin and Unger (1959) [36] calculated with their approach "Damping Model" the
damping behavior of a three-layer composite. Many modification has been made [37], [38],
[39] with are summarized in [40]. Starting with the elastic bending moment M of the three-
layer sheet, the shear forces and shear strains are calculated:

� = � ���� = ∑ ���

� + ∑ ������� (45)

Where B is the flexural rigidity per unit width of the composite plate, Mii the Moment of
exerted by the forces on the ith layer about its own neutral plane, Fi the net extensional
force on the layer and Hio the distance from the center of the ith layer to the neutral plane
of the composite beam. [33] predicted the loss of "thick plates with a thin intermediate

Page 110

Metal Forming – Process, Tools, Design 102

������������ = ����� ∙ �∙���������∙�����)∙�]���∙�∙����∙����������]� (46)

With the "geometric parameter" 1/h, the distance between the neutral fiber of the sandwich
structure and the coversheets is described.

�� =

�� ∙ �

+ ���∙��� (47)

And a „shear-parameter“ g:

� = ��

∙ � ���∙�� +


� (48)

Parameter “a” is the distance of the neutral fibers of the cover plates:

� � �� + ������)� (49)

And the number of wave k:

� = ��
� �

� (50)

With the mass per unit length m':

�� = � ∙ � (51)
The cross-sectional area S:

�� = ����� + ��) (52)
And with the specific total bending stiffness B':

�� = ���� + ���) ∙ �� + �∙����∙����∙�����)� (53)

Wherein the specific bending stiffness Bi for a plane sheet layer can be calculated as:

��� = ��� ∙ �� ∙ ��
� (54)

5.4. Influence of forming on damping-behavior of three layer sandwich sheet

As seen in chapter 0 the bending stiffness �� for a sheet layer is significant for decay-
behavior. With increasing stiffness of the cover layers, the total loss factor of the sandwich
sheet decreases. Accordingly, the forming geometry has a big influence on the damping
behavior. Cover-sheets with a thickness of �� = ��� = ���� and a width and length with
� = � = ����� and the viscoelastic interlayer (calculated adhesive, Figure 15) are shown in
Figure 19. No. 1 shows the decay curve of an unformed sheet in contrast to a sheet with
bended edges and a v-profile. All three sheets have the same initial width b. A great
influence of the bending stiffness can be seen.

Page 217

Self-Consistent Homogenization Methods for Predicting Forming Limits of Sheet Metal 209

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