Why is polystyrene brittle and polycarbonate tough and what can we do about it? R.J.M. Smit, W.A.M. Brekelmans, H.E.H. Meijer Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, NL 5600 MB Eindhoven

90 MPa Introduction 84 MPa Polycarbonate: at a global 78 MPa 72 MPa On a macroscale, polystyrene (PS) is brittle and poly- strain of 1.1%,thenotchtip 66 MPa 60 MPa carbonate (PC) is tough. On a microscale, however, causes critical dilative stresses 54 MPa 48 MPa craze craze fibrils (length scale nm) break after 300% (> 90MPa) → PC crazes 42 MPa 1 36 MPa strain in PS and 100% in PC . This contradictory PC, dilative stress 30 MPa

behaviour is elucidated and the toughening by the 2 PS is brittle because of high defect sensitivity addition of cavitating rubbery particles is explained. 2 PC is tough because of low defect sensitivity Intrinsic material behaviour Improving toughness 2,3 Uniaxial compression experiments and model fits Enhance toughness by minimizing defect sensitivity. (true stress versus compressive strain,λ =draw ratio): Possible routes: 80 c 90 70 80 1. reduce yield stress: minimizes (unstable) strain d e 60 70 1. softening and reduces triaxial stresses 60 50 b 50 2. improve (stabilizing) strain hardening

[MPa] 40 [MPa] zz zz 40 σ σ

− 30 150 − 30 20 20 10 a PC 10 PS 0 0 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 −(λ2−1/λ) −(λ2−1/λ) 100 2: Deformation stages: (a-b) linear elastic; (b-c) non- −crosslinking linear viscoelastic (c) yield; (c-d) strain softening; (d- −preorientation 1: −blending with rubber e) strain hardening. −predeformations 50 −addition of plasticizers True stress [MPa]

2 strain softening: decreasing stress results in −creation of surface (voids) increasing strain → unstable deformation −addition of heterogeneities

0 2 strain hardening: increase in stress needed for 0 50 100 150 200 increase in strain → stable deformation Linear strain [%] 3. avoid high triaxial stress states by incorporation of

2 PS: more strain softening, less strain hardening 3. voids or cavitating rubbery particles → Polystyrene shows intrinsically a less stable → deformation behaviour than polycarbonate Rubber toughening is successful because: - cavitating rubbery particles reduce triaxial stresses 6 2 crazes initiate after yield, triaxial stress level during - heterogeneous microstructure eliminates softening 4,5 craze initiation in PS≈ 40 MPa and PC≈ 90 MPa - rubbery particles improve strain hardening

2 model offers accurate description of yield- and Conclusion post-yield behaviour in arbitrary 3D stress states3,4 Brittleness of glassy polymers depends on unstable Consequence for toughness post-yield behaviour and triaxial crazing stress. Re- ducing softening, improving hardening and avoiding Deformation of a notched bar of PS and PC with a high triaxialities are the keys to enhanced toughness. minor defect to model realistic (imperfect) specimen: defect References ↓ 1. Donald, A.M. and Kramer, E.J. (1982). Deformation zones and entanglements in glassy poly- mers. Polymer, 23, 1183-1188. 2. Hasan, O.A. and Boyce, M.C. (1993). Energy storage during inelastic deformation of glassy polymers. Polymer, 34, 5085-5092 45 MPa 3. Timmermans, P.H.M. (1997), Evaluation of a constitutive model for solid polymeric materials: 43.5 MPa Model selection and parameter quantification. Ph.D. thesis, Eindhoven University of Technology. Polystyrene: at a global strain 42 MPa 4. Tervoort, T.A. (1996) Constitutive modelling of polymer glasses: Finite, nonlinear viscoelastic 40.5 MPa behaviour of polycarbonate. Ph.D. thesis, Eindhoven University of Technology. of 0.22%,thedefect triggers lo- 39 MPa 5. Narisawa, I. and Yee, A.F. (1993), Crazing and Fracture of Polymers. In: Cahn, R.W., Haasen, 37.5 MPa P., and Kramer, E.J., editors, Materials Science and Technology. A Comprehensive Treatment, cal yielding, resulting in a critical 36 MPa Vol. 12: Structure and Properties of Polymers, vol.ed.: E.L. Thomas. page 699. VCH, Weinheim. 34.5 MPa 6. Smit, R.J.M., Brekelmans, W.A.M., and Meijer, H.E.H., Prediction of the large-strain mechanical > 33 MPa response of heterogeneous polymer systems. Part 1. J. Mech. Phys. Solids, submitted. dilative stresses ( 40MPa) 31.5 MPa → PS crazes PS, dilative stress 30 MPa