Thermoplastic Multilayer Composites - ifm kit
Continuum mechanical modelling of deformation and failure mechanisms in thermoplastic multilayer composites Thomas Seelig Institute of Mechanics, Karlsruhe University, Germany, [email protected]
Introduction (a)
• tensile response of PC/SAN multilayer composites controlled by interacting micromechanisms - shear banding in (ductile) PC
PC
(b) PC
PC
- crazing / microcracking in (brittle) SAN - formation of network-like deformation pattern at small overall strain (a) • macroscopic behaviour: brittle failure of SAN-rich composites (PC content / relative layer thickness < 50%) due to early coalescence of microcracks ductile response of PC-rich composites (> 50 %), holes in SAN grown from microcracks are stabilised (b) (from: Gregory, B.L. et al., J. Mat. Sci. 1987, 22, 532-538)
objective of present study: gain additional understanding of interrelation between microstructure, micromechanisms and macroscopic behaviour from numerical (finite element) simulations
Modeling Bulk constitutive models:
- sample with alternating layers of PC and SAN, plane strain (2D) model - uniaxial overall loading in terms of prescribed macroscopic strain rate ε&
PC: finite strain viscoplasticity,
- cohesive surfaces as potential locations of failure cohesive failure modes: - crazing in SAN
.
ε SAN
PC
SAN
PC
- ductile rupture of PC upon large plastic deformation
SAN
σ SAN
intrinsic softening ( shear banding),
PC
rehardening due to molecular alignment
(uniaxial tension)
SAN: linear elastic (tension)
ε cohesive surfaces
Cohesive zone model for crazing: - initiation criterion (crit. normal stress)
SAN
PC
- rate-dependent traction-separation law
σc
∆& C (T&,T ;σ C )
∆c T
- craze widening resistance σ C (∆ C ) (micromechanics of fibrillation process) - craze-breakdown at crit. craze width
cr
∆c
Results - simulations with different realisations (statistically equivalent) of initial defect distribution in σ [MPa] SAN (lower craze initiation stress) 70 - composition-dependent overall brittle-to-ductile transition 60 reproduced 50 - localisation of damage in 40 SAN-rich composites (a) and early brittle failure 30 - spatially distributed damage in 20 PC-rich composites (b, c) and 10 ductile overall behaviour 0 - long-range extension of shear band network (scaling with relative PC layer thickness) plays pivotal role for delocalisation of damage
macroscopic response
contours of local plastic strain (c)
PC/SAN (3/1)
(b)
(b)
(a) εp
(c) ε
PC/SAN (1/3)
ε
0.5 0.4 0.3 0.2 0.1 0.0
(a) 0
0.05
p
0.1
0.15
p 0.5 0.4 0.3 0.2 0.1 0.0
ε PC/SAN(1/3)
PC/SAN(3/1)
1.2 1.0 0.8 0.6 0.4 0.2 0.0
∆c
Introduction (a)
• tensile response of PC/SAN multilayer composites controlled by interacting micromechanisms - shear banding in (ductile) PC
PC
(b) PC
PC
- crazing / microcracking in (brittle) SAN - formation of network-like deformation pattern at small overall strain (a) • macroscopic behaviour: brittle failure of SAN-rich composites (PC content / relative layer thickness < 50%) due to early coalescence of microcracks ductile response of PC-rich composites (> 50 %), holes in SAN grown from microcracks are stabilised (b) (from: Gregory, B.L. et al., J. Mat. Sci. 1987, 22, 532-538)
objective of present study: gain additional understanding of interrelation between microstructure, micromechanisms and macroscopic behaviour from numerical (finite element) simulations
Modeling Bulk constitutive models:
- sample with alternating layers of PC and SAN, plane strain (2D) model - uniaxial overall loading in terms of prescribed macroscopic strain rate ε&
PC: finite strain viscoplasticity,
- cohesive surfaces as potential locations of failure cohesive failure modes: - crazing in SAN
.
ε SAN
PC
SAN
PC
- ductile rupture of PC upon large plastic deformation
SAN
σ SAN
intrinsic softening ( shear banding),
PC
rehardening due to molecular alignment
(uniaxial tension)
SAN: linear elastic (tension)
ε cohesive surfaces
Cohesive zone model for crazing: - initiation criterion (crit. normal stress)
SAN
PC
- rate-dependent traction-separation law
σc
∆& C (T&,T ;σ C )
∆c T
- craze widening resistance σ C (∆ C ) (micromechanics of fibrillation process) - craze-breakdown at crit. craze width
cr
∆c
Results - simulations with different realisations (statistically equivalent) of initial defect distribution in σ [MPa] SAN (lower craze initiation stress) 70 - composition-dependent overall brittle-to-ductile transition 60 reproduced 50 - localisation of damage in 40 SAN-rich composites (a) and early brittle failure 30 - spatially distributed damage in 20 PC-rich composites (b, c) and 10 ductile overall behaviour 0 - long-range extension of shear band network (scaling with relative PC layer thickness) plays pivotal role for delocalisation of damage
macroscopic response
contours of local plastic strain (c)
PC/SAN (3/1)
(b)
(b)
(a) εp
(c) ε
PC/SAN (1/3)
ε
0.5 0.4 0.3 0.2 0.1 0.0
(a) 0
0.05
p
0.1
0.15
p 0.5 0.4 0.3 0.2 0.1 0.0
ε PC/SAN(1/3)
PC/SAN(3/1)
1.2 1.0 0.8 0.6 0.4 0.2 0.0
∆c
