Modelling the behaviour of plastics for design under impact G. Dean and L. Crocker MPP IAG Meeting 6 October 24
Land Rover door trim
Loading stages and selected regions
Project MPP7.9 Main tasks Tests on regions cut from component Tests on specimens - standard, injection moulded - cut from component Analysis of test data - material properties - model parameters Comparison FEA simulation - 3 materials models Implement cavitation model in Abaqus
Stress-strain curves for Dow polymer - injection moulded specimens 35 3 compression 25 true stress (MPa) 2 15 shear tension 1 5 effective plastic strain rate.1 s -1 along specimen axis transverse to specimen axis.2.4.6.8.1.12 true strain
Results for specimens cut from door trim 25.6 2.5.4 stress (MPa) 15 1 tensile M1S2A shear.3 Poisson's ratio poisson's ratio.2 5.1.2.4.6.8.1.12.14.16.18.2 strain
Elastic-plastic models 45 4 35 3 ε e ε p stress (MPa) 25 2 15 1 first yield stress 5.2.4.6.8.1.12.14 strain
Tensile hardening curve 25 2 tension stress (MPa) 15 1 5.1.2.3.4.5.6.7.8.9.1 plastic strain
Plastic behaviour Stresses are related by a yield criterion Simplest criterion is von Mises σ e is the effective shear stress ) ( p T e ε σ = σ + + = 2 1 3 2 3 2 2 2 1 2 ) ( ) ( ) ( 2 1 σ σ σ σ σ σ σ e
Predictions using the von Mises model 35 3 compression 25 tension stress (MPa) 2 15 shear 1 modelled shear modelled compression 5.2.4.6.8.1.12.14.16.18.2 strain
Prediction of Poisson s ratio.6.5 von Mises calculated.4 poisson's ratio.3.2.1.2.4.6.8.1.12.14.16.18.2 tensile strain
A more accurate yield criterion Yielding in plastics is sensitive to the hydrostatic component of stress σ µ ( σ T µσ 3 e = 1+ ) m µ is a material parameter σ m is the hydrostatic stress 1 σ m = ( σ1 + σ 2 + 3 σ 3 )
Determination of the parameter µ 25 2 tension stress (MPa) 15 1 shear 5 equivalent data.2.4.6.8.1.12 plastic strain
Predictions using the Drucker-Prager model 5 45 4 35 compression µ=1. stress (MPa) 3 25 2 tension 15 1 shear modelled shear modelled compression 5.2.4.6.8.1.12.14.16.18.2 strain
An elastic-plastic model with cavitation Under stress states with a hydrostatic component, cavities form in the polymer These promote yielding in the regions between cavities The yield criterion depends on cavity volume fraction Expressed in terms of the shear hardening curve
Parameters in the cavitation model E, ν e σ o (ε p ) hardening curve from shear data µ from shear and compression data µ from Poisson s ratio V ra from materials supplier k from variation of yield stress with rubber volume ε 1v ε 2 v from optimum fit to tensile data β
Compressive behaviour cavitation model 35 3 compression stress (MPa) 25 2 15 1 calculated compression measured compression 5.2.4.6.8.1.12.14 compression strain
Tensile behaviour - cavitation model 25 tensile stress (MPa) 2 15 1 5 calculated using cavitation model measured.2.4.6.8.1.12.14.16.18.2 tensile strain
Poisson s ratio cavitation model Poisson's ratio.45.4.35.3.25.2.15.1.5 calculated using cavitation model measured.5.1.15.2.25.3.35.4 tensile strain
Determination of properties at high strain rates see IAG minutes March 4 Measure stress/strain curves at low and moderate strain rates Model hardening behaviour Extrapolate to high strain rates
Tensile hardening curves at different strain rates 35 3 25 true stress (MPa) 2 15 1 5 strain rate 12 s-1 strain rate 1.5 s-1 strain rate.15 s-1 strain rate.13 s-1 strain rate.1 s-1 calculated extrapolated 1 s-1 extrapolated 1 s-1.2.4.6.8.1.12.14.16.18.2 true plastic strain
Development of an ISO Standard ISO/CD 18872 Determination of tensile properties at high strain rates Comments from the CD ballot will be discussed at the ISO meeting in October
NPL Report DEPC-MPR 7 Determination of Material Properties and Parameters Required for the Simulation of Impact Performance of Plastics Using Finite Element Analysis G. Dean and R. Mera July 24
FE Modelling Have obtained parameters for Von Mises Linear Drucker-Prager Cavitation model Plus rate-dependant data Rate-dependence is newly implemented in the cavitation model
Verification of rate-dependant cavitation model Use plate analysis ABS material Indentation speeds Slow (.1 mm/s) Fast (1 m/s)
Verification of rate-dependant cavitation model Four different materials models Single rate cavitation Rate-dependent cavitation Rate-dependent cavitation with cavitation turned off (equivalent to linear Drucker-Prager) Rate-dependent linear Drucker-Prager Compare no cavitation cavitation model with ABAQUS linear Drucker-Prager model to verify the implementation of ratedependent data in the cavitation model Use explicit analysis good for dynamic events and high deformation situations
Verification of rate-dependant cavitation model Explicit analysis Lengthy analysis for slow rate small time increments Initial results poor rounding errors To speed up analysis Increase maximum stable time increment Increasing mesh size Increasing material density Decreasing material stiffness Best to increase density (*mass scaling factor) Can cause inertial effects Lose contact between 9 and 13 mm
Plate predictions 1 m/s 14 12 1 Standard Rate-dependent No cavitation Explicit Rate-dependent No cavitation Explicit Rate-dependent Linear Drucker-Prager Explicit Rate-dependent Cavitation Explicit Single rate Cavitation Good match between explicit and standard no cavitation predictions and ABAQUS linear Drucker-Prager model force (kn) 8 6 4 2 Single rate and rate-dependent model predictions are similar due to choice of single rate curve Cavitation model predictions are lower than linear Drucker-Prager model Fast rate 1 m/s 5 1 15 2 25 3 deflection (mm)
Plate predictions 1 m/s Same trends in stress and strain predictions 8 Fast rate 1 m/s.3 Standard Rate-dependent No cavitation Explicit Rate-dependent No cavitation 6.25 Explicit Rate-dependent Linear Drucker- Prager Explicit Rate-dependent Cavitation 4.2 Explicit Single rate Cavitation 2 stress (MPa) 1 2 3 4 5 6 strain.15.1-2 -4-6 Standard Rate-dependent No cavitation Explicit Rate-dependent No cavitation Explicit Rate-dependent Linear Drucker-Prager Explicit Rate-dependent Cavitation Explicit Single rate Cavitation position along plate radius.5 Fast rate 1 m/s 1 2 3 4 5 6 position along plate radius
Plate predictions.1 mm/s 1 8 Slow rate.1mm/s Good match between standard no cavitation predictions and ABAQUS linear Drucker-Prager model. Explicit no cavitation predictions are poorer at higher deflections force (kn) 6 4 Standard no cavitation Explicit no cavitataion 2 Explicit linear Drucker-Prager Explicit single rate Explicit rate-dependent experimental 5 1 15 2 25 3 35 deflection (mm) Single rate and rate-dependent model predictions are similar due to choice of single rate curve Cavitation model predictions are lower than linear Drucker-Prager model Experimental data match linear Drucker-Prager suggests material does not cavitate See results of inertial effects
Plate predictions.1 mm/s.6 Same trends in stress and strain predictions Explicit rate-dependent results are poorer away from centre of the plate.35.5.4 slow rate.1 mm/s.3 Standard no cavitation Explicit no cavitation Explicit linear Drucker-Prager Explicit single rate Explicit rate-dependent.3.25.2 stress (MPa).1 1 2 3 4 5 6 strain.2.15 -.1 Standard no cavitation -.2 Explicit no cavitation.1 -.3 -.4 Explicit linear Drucker-Prager Explicit single rate Explicit rate-dependent.5 slow rate.1 mm/s -.5 position along plate radius 1 2 3 4 5 6 position along plate radius
FEA of component parts Experimental results 25 25 Toptrim indentation Armrest indentation 2 2 15 15 Load (N) Load (N) 1 1 AQKE1 (.1 mm/s) AQKE11 (.1 mm/s) 5 AQKE3 (.1 mm/s) AQKE4 (1 mm/s) AQKE6 (1 mm/s) 5 AQKE12 (.1 mm/s) AQKE13 (1 mm/s) AQKE15 (1 mm/s) 5 1 15 2 25 3 35 4 Cross-head displacement (mm) 1 2 3 4 5 Crosshead displacement (mm)
FEA of component parts FEA Meshes toptrim armrest
FEA of component parts Two models: Explicit rate-dependent linear Drucker-Prager Explicit rate-dependent cavitation model Three test speeds.1 mm/s, 1 mm/s and 1 m/s
FEA of component parts Armrest 25 2 AQKE1 (.1 mm/s) AQKE3 (.1 mm/s) AQKE4 (1 mm/s) AQKE6 (1 mm/s).1 mm/s prediction 1 mm/s prediction 15 Load (N) 1 5 5 1 15 2 25 3 35 4 Cross-head displacement (mm)
Toptrim FEA of component parts 25 Toptrim indentation 2 15 Load (N) 1 5 AQKE11 (.1 mm/s) AQKE12 (.1 mm/s) AQKE13 (1 mm/s) AQKE15 (1 mm/s).1 mm/s prediction 1 2 3 4 5 Crosshead displacement (mm)
FEA of component parts Further work Complete linear Drucker-Prager predictions Analysis of component parts with: Rate-dependent cavitation model Von Mises Land Rover to analyse parts using their preferred model FE sensitivity analysis look at effects of changes in parameters etc