simulation of multi-layered composites forming · ^/dh> d/ke k& dh>d/ > z˝z˝˘...

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< sE>KK^dZ ^ >KDKs/ sZWK^d SIMULATION OF MULTI-LAYERED COMPOSITES FORMING

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Page 1: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

< �s�E�>KK^d�Z^ �>KDKs����/ �s�ZWK�^d

SIMULATION OF MULTI-LAYERED COMPOSITES FORMING

Page 2: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

K

/ � � �'D � � � � � � �� � � � � �/ � ����Yh^��^ � � � �

< �s ������W ��^�&KZD�

Page 3: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

/

& � � �� � � � � � �

� � � � � � � WW �

< �s ������W ��^�&KZD�

< �s � � K � � � � � � /��D�

Page 4: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

/

& � � � �� � � � � �

/ � � � � �� � � � � � �

< �s ������W ��^�&KZD�

Page 5: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

/

& � � � �� �

' �^ � � �, � ��

> � �E � � �

� � � � � � � � ��

< �s ������W ��^�&KZD�

W 1E �Q E h

K

Page 6: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

'

'

� � � �/ � � � � �&�D^ � � � � �

< �s ������W ��^�&KZD�

Page 7: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

D

t � �d � � � � �

< �s ������W ��^�&KZD�

d� � �

> � � � �� � �

Page 8: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� � �

W �

< �s ������W ��^�&KZD�

W ^

/ � � � ��

< �s � ��^�&KZD�

Page 9: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �>

< �s ������W ��^�&KZD�

W 1E �Q E h

K� � � � �WW� �d

K � � � �W � � � � � � � �� �

W �K d �� d � � �� / � � � �

�< �s � ��^�&KZD�

Page 10: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �>

< �s ������W ��^�&KZD�

W � � ��D � � � �� � �

s � � �� � � � � � � �

� � �� � K � �

W �d �

Page 11: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �� � � � � � � � � �

< �s ������W ��^�&KZD�

d � � � � � � � �

Page 12: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �

< �s ������W ��^�&KZD�

Assume traction is known but h is unknown and assume a constant interlayer thickness

The average thickness calculated for a variable thickness profile does not agree with the real average thickness!

Page 13: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �^

< �s ������W ��^�&KZD�

W

d

Page 14: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �d �

< �s ������W ��^�&KZD�

Wp W0 � k � v� �n 0 W � �� �

No need for value of K or the viscosity of the matrix

� � � < � < � � W Z

W

d

Page 15: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �d �

< �s ������W ��^�&KZD�

� � � � � � �W � � � � �

� �

� � � �W �d �

Page 16: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �� �d � � ^ �

< �s ������W ��^�&KZD�

� � � ��

� � � � �^ � ��

Page 17: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

/ � � � � ����Yh^^

< �s ������W ��^�&KZD�

Page 18: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

^

< �s ������W ��^�&KZD�

Z � �� � �

/ � � � � ����Yh^

Page 19: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �d � � � � � � � �

� �� �t

^

< �s ������W ��^�&KZD�

d � � � � � �� � � � � � �

� �

Page 20: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �^

< �s ������W ��^�&KZD�

Page 21: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �� � � � � � � � �d � � � � � � � � �

� � � � � �

^

< �s ������W ��^�&KZD�

KD � �

� �V � DW

����

Page 22: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� �� � � �&>� � � � � �

� �

^

< �s ������W ��^�&KZD�

KD � �

� �V � DW

����

Page 23: SIMULATION OF MULTI-LAYERED COMPOSITES FORMING · ^/Dh> d/KE K& Dh>d/ > z˝Z˝˘ KDWK^/d˝^ &KZD/E’ ˘ < s W ˝^ &KZD Assume traction is known but h is unknown and assume

^/Dh>�d/KE�K&�Dh>d/ >�z�Z����KDWK^/d�^�&KZD/E'

� � � � � � �� � �

d � � � � � �s&Z/�� ����Yh^d � � � � � �

� � �� � � � �

< �s ������W ��^�&KZD�