Modelling of damage and failure in short glass-fibre-reinforced
polypropylene
Citation for published version (APA):
Geers, M. G. D., Borst, de, R., Brekelmans, W. A. M., Peijs, A. A. J. M., & Peerlings, R. H. J. (1996). Modelling of damage and failure in short glass-fibre-reinforced polypropylene. Poster session presented at MaTe Poster Award 1996 : first annual poster contest.
Document status and date: Published: 01/01/1996
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Accepted manuscript including changes made at the peer-review stage
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erials
a echnology
Modelling of damage and failure in short
glass-fibre-reinforced polypropylene
M.G.D. Geers, R. de Borst, W.A.M. Brekelmans, T. Peijs, R.H.J. Peerlings Eindhoven University of Technology,
Faculty of Mechanical Engineering, Section Materials Technology, P.O. Box 513, NL 5600 MB Eindhoven
tue
Experimental analysis
on SGFPP
The damage and failure behaviour
of short glass-fibre-reinforced
polypropylene (SGFPP) has been investigated with an optical parti-cle tracking method on Compact-Tension specimens. CT - specimen Strain Distribution Video Hentschel 1.2 W 0.325W 0.275W 0.25W 0.25W 1.25 W an Thickness 3.8 mm W/50
Measured displacements fields
are converted to strain fields and related to the principal fail-ure mechanisms: matrix cracking, fibre-matrix debonding and fibre pull-out. 0 10 20 30 40 50 60 0 10 20 30 40 50 60 X−dir. [mm] Y−dir. [mm] CT−test − W = 50 [mm] − Force 1120 [N] 0 0.005 0.01 0.015 0.02 0.025 εyy 200 mµ
The propagation of the process zone can be traced throughout the CT-test. 20 40 60 20 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm] Sample 1 − Force 813.6 [N] εyy 20 40 60 20 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm] Sample 2 − Force 1220 [N] εyy 20 40 60 20 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm] Sample 3 − Force 1101 [N] εyy 20 40 60 20 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm] Sample 4 − Force 477.3 [N] εyy
Numerical modelling
Gradient damage models with an invariable length parameter suffer from unrealistic damage and strain widening when used in cracked and highly damaged zones, as illustrated for a cracking one-dimensional tensile bar with a cen-tred imperfection. 20 40 60 80start end 0 0.5 1 X−coord [mm] Evolution Damage 20 40 60 80start end 0 0.5 1 X−coord [mm] Evolution
Local equivalent strain
A strain-based transient-gradient damage model has been pro-posed to remedy this shortcoming.
~ ~ ~ u e ς Equilibrium Nonlocal averaging ∇ =.rσ rf e− ∇ =ς 2e e Gradient activity ς=ζ Solve σ =(1−D)4C:ε External load Constraints Restraints Boundary Conditions Compute D=f( )e ε Compute ζ =f ( )e e=Computef ( )ε
Equivalent strain definition
Damage evolution law
Gradient activity evolution law
Update and check for convergence
YES
NO
u = nodal displacement ζ= integration point gradient activity
e = nodal nonlocal equivalent strain D = Damage variable
ς= nodal gradient activity (controls nonlocal effect) σ= stress tensor ε= strain tensor e = local equivalent strain
Reliable results are obtained upon mesh refinement and no damage widening is observed in severely cracked two-dimensional notched specimens. L an wn t h 0 1 2 3 4 5 6 0 500 1000 1500 2000 2500 Displacement [mm] Force [N] Coarse mesh Medium mesh Fine mesh Force = 1895 [N] Displ. = 1.08 [mm] 0 0.2 0.4 0.6 0.8 D Force = 1327 [N] Displ. = 2.33 [mm] 0 0.2 0.4 0.6 0.8 1 D Force = 506 [N] Displ. = 3.86 [mm] 0 0.2 0.4 0.6 0.8 1 D Force = 66 [N] Displ. = 10.5 [mm] 0 0.2 0.4 0.6 0.8 1 D
Experimental
verification
Global results can be well fitted for different specimen sizes and notch depths of the CT-specimen.
0 1 2 3 4 5 6 0 200 400 600 800 1000 1200 1400 1600 Displacement [mm] Force [N] CT−test − W = 50 [mm] − an = 10 [mm] Experimental results Numerical simulation 0 1 2 3 4 5 6 0 200 400 600 800 1000 1200 1400 Displacement [mm] Force [N] CT−test − W = 50 [mm] − an = 15 [mm] Experimental results Numerical simulation 0 2 4 6 8 10 0 500 1000 1500 2000 Displacement [mm] Force [N] CT−test − W = 75 [mm] − an = 15 [mm] Experimental results Numerical simulation 0 2 4 6 8 10 0 200 400 600 800 1000 1200 1400 1600 1800 Displacement [mm] Force [N] CT−test − W = 75 [mm] − an = 22.5 [mm] Experimental results Numerical simulation
The correspondence of the local strain fields is good and mainly depends on the proper estimation of the nonlocal parameters which govern the failure behaviour.
30 40 50 20 30 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm]
Experimental results − Force 1225 [N]
εyy 30 40 50 20 30 40 0 0.02 0.04 X−dir. [mm] Y−dir. [mm]
Numerical simulation − Force 1207 [N]
εyy 25 30 35 40 45 50 55 −0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 X−dir. [mm] Experimental results − Force 1225 [N]
εyy 25 30 35 40 45 50 55 −0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 X−dir. [mm] Numerical simulation − Force 1207 [N]
εyy
Large crack openings can be com-puted within a continuous FEM-framework.
