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Measuring Fracture Toughness in Engineering Plastics: Insights and Methods

This chapter delves into the various standardized methods for measuring fracture toughness in engineering plastics, as detailed in the book "Polymer Testing". It covers important specimen types including single-edge notched bend (SENB), single-edge notched tension (SENT), and compact tension (CT), providing crucial equations and parameters for assessing material properties. The insights presented by Grellmann and Seidler offer a comprehensive understanding of how fracture toughness impacts the performance and durability of polymer materials in engineering applications.

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Measuring Fracture Toughness in Engineering Plastics: Insights and Methods

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  1. s N s y s x s z mode I r y  x mode II z mode III mode II r » 0 mode I s N B Fig.: 5.1 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  2. SENB specimen (single-edge-notched bend specimen) F W = 10 mm B = 2 … 10 mm L = 80 mm s = 40 … 70 mm a = 0.5 … 7.5 mm N = 2 mm W a F/2 F/2 N s L/2 L/2 a F s K = f I 3/2 W B W 9 7 1 5 3 a a a a a a 2 2 2 2 2 f = 2.9 − 4.6 + 21.8 − 37.6 + 38.7 W W W W W W 2 a a a a 1.99 − 1 − 2.15 − 3.93 + 2.7 W W W a W 3 a f = 3 W 2 W a a 2 1− 1+2 W W Fig.: 5.2a Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  3. SENT specimen (single-edge-notched tension specimen) W = 40 mm H = 150 mm s = 120 mm D = 10 mm a = 18 … 22 mm N = 3 mm B = 2 … 10 mm F W/2 H/2 W s a N H/2 O D 1/2 a F a K = f I W B W F 4 2 3 a a a a a f = 1.99 − 0.41 + 18.7 − 38.48 + 53.85 W W W W W Fig.: 5.2b Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  4. CT specimen (compact tension specimen) F W = 40 mm H = 48 mm G = 50 mm s = 22 mm D = 10 mm a = 18 … 22 mm N = 2 mm B = 2 … 34 mm l = 1.5 mm H/2 l s O D N H/2 a W F G a F K = f I 1/2 W B W 9 1 3 7 5 a a a a a a 2 2 2 2 2 f = 29.6 − 185.5 + 655.7 − 1017 + 638.9 W W W W W W Fig.: 5.2c Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  5. b 260 K a 240 c 1/2 240 K Ic 210 220 K ; K (MPamm ) 180 SENT 1/2 200 Ic 150 B EDZ min c K ; K (MPamm ) 180 120 B ESZ/EDZ Ic 160 90 10 20 30 0 c K c B (mm) 140 60 K Ic 120 B CT min 100 0 2 4 6 8 1 0 B (mm) B ( m m ) Fig.: 5.3

  6. a residual fracture area b damage area stable crack growth (fracture mirror length) machined notch (razor blade notch) 100 µm B Fig.: 5.4 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  7. s y s y d x r a pl s Fig.: 5.5 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  8. a b 200 µm 50 µm Fig.: 5.6 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  9. s/2 d/2 2 3 (W a) W 1 1 n max f 1 hinge point 2 sharp notch 3 support Fig.: 5.7 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  10. y 2 s/2 1 d SZH d/2 x SZH 3 100 µm SZW a stable crack growth 5 µm b stretch zone brittle fracture initial crack SZW 10 µm SZH c d Fig.: 5.8 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  11. T y n a b I dR 1 a 1 I 2 a F 2 I Riss 3 a crack 3 x 1 2 A R G f (i=1...3) i f resp. v c d J Ic I I I 1 2 3 J A I G B f 3 a ¶A f 1 1 G 2 f ¶a B a a 1 3 2 a f resp. v Fig.: 5.9 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  12. loading parameter blunting Line J; d technical crack initiation J ; d 0.2 0.2 resistance against crack propagation crack propagation physical crack initiation resistance against crack initiation crack initiation J ; d i i crack blunting Da Da = 0.2 mm SZW stable crack growth Da Fig.: 5.10 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  13. junction diode laser collecting lens F deflection mirror CT specimen start v F semiconductor prism motor t stop evaluation and graphics rotating mirror Fig.: 5.11 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  14. type II type I 5 % 5 % F max T T F max F F Q Q F F S S a v v c c v; v ; f v; v ; f L L Fig.: 5.12 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  15. crack initiation crack propagation 5 4 b c crack blunting 3 200 µm 1 mm 2 a 1 50 µm 0 0 1 2 3 4 5 -2 F/(B(W−a )) (Nmm ) f (mm) eff Fig.: 5.13 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  16. unnotched specimen notched specimen F F max max F (N) F (N) A A G 0 v ; f v ; f 0 L0 max Lmax v ; f (mm) v ; f (mm) L L Fig.: 5.14 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  17. load–deflection diagram Charpy impact tester ICIT-4J AG = Apl + Ael Fmax striker load (F) - transducer Fgy load F (N) t specimen F1 Apl AR personal computer tB ; fmax fgy time resp. deflection (ms; mm) analysis of F–f diagram amplifier digital oscilloscope - checking of experimental conditions tB > 3t F1 < Fmax AH > 3 AG - SEM analysis of fracture surface - fracture mechanics concept support - checking of geometry - independence of fracture mechanics values photooptical transducer deflection (f) - sensor KId ; dId ; JId Fig.: 5.15 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  18. Fmax II I III Fmax Fmax Fgy FF AG = Apl + Ael Fgy Apl F AG Ael AG fgy fmax fmax fmax fgy Fmax Ia IIa IIIa Fmax Fmax Fgy FF Fgy Apl AR AG AR AG Ael AR fmax fmax fmax fgy fgy f Fig.: 5.16 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  19. a/W = 0.45 a/W = 0.2 F = 53 N max -1 F = 36 N F = 36 N 1 1 F = 28 N v = 2.9 ms max I F = 62 N max -1 F = 36 N max v = 1 ms I F = 8 N F = 8 N 1 1 Fig.: 5.17 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  20. F A W a s L B B B 0.05 < a/W < 0.15 0.1 < a/W < 0.4 0.3 < a/W < 0.7 Fig.: 5.18 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  21. 3.0 PVCC BL J 2.5 -1 FEM J v = 1.5 ms I s/W = 4 RT 2.0 J-integral ratio MC J 1.5 FEM J 1.0 ST J FEM J 0.5 RPM J FEM J 0 0 0.2 0.4 0.6 0.8 Fig.: 5.19 a/W Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  22. 100 -1.73 b = 3466 K I 10 b 1 0.1 100 1000 10 1/2 K ; K (MPamm ) Id Ic Fig.: 5.20 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  23. 10000 -0.94 e = 224 J I 1000 e 100 10 1 1 10 100 0.1 -1 J ; J (Nmm ) Id Ic Fig.: 5.21 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  24. 100 -0.83  = 3.6 d Idk  10 0.1 1 0.01 d [mm] Idk Fig.: 5.22 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  25. spring F acceleration unit drop weigth strain gauge lifting device clamped test sheet cross-head masses controller instrumented drop weigth support temperature chamber Fig.: 5.23 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  26. PA 6 + impact modifier 25 0 wt.-% 5 wt.-% 10 wt.-% 20 wt.-% 25 wt.-% 20 15 10 5 0 70 90 10 30 -30 50 -70 -50 -10 T (°C) ST J (Nmm-1) d Fig.: 5.24 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  27. 7 6 5 4 PVC/chalk 3 PP/chalk PVC/SiO 2 2 PE/SiO 2 PE/BW 1 PE/HP 0 0.3 0.1 0.2 0.4 0 j v ST J (Nmm-1) d Fig.: 5.25 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  28. a b 2.0 500 1.8 450 1.6 400 1.4 350 1.2 300 f (mm) F (N) max 1.0 PVC/chalk max 250 PP/chalk 0.8 200 PVC/SiO 2 0.6 PE/SiO 2 150 PE/BW 0.4 PE/HP 100 0.2 0.3 0.3 0.1 0.1 0.2 0.2 0.4 0.4 0 0 50 j j 0 v v Fig.: 5.26 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  29. 1.6 stearic acid surfactant 1.4  = 0.9  = 1.5 a b 1.2 1.0 5 µm 2 µm 0.8 0 0.25 0.50 0.75 1.00 1.25 1.50 coupling agent content (wt.-%) M ST J /J Id Fig.: 5.27 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  30. 110 PVC P V C 100 j PVC + chalk (j = 0.17) P V C + K r e i d e ( = 0 , 1 7 ) v v 90 d (10-3 mm) 80 Id 70 60 50 40 30 20 -150 -100 -50 0 50 1 2 3 1 7 3 2 2 3 2 7 3 3 2 3 T (°C) T ( K ) Fig.: 5.28 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  31. b a 450 0.45 400 0.40 350 f (mm) F (N) max max 300 0.35 250 0.30 200 0 0.1 0.2 0.3 0 0.1 0.2 0.3 j j v v 5 c d 210 K (a ) ld eff 4 180 1/2 -1 150 J (Nmm ) K (MPamm ) 3 K (a ) ld 0 Id 120 Id 2 90 1 60 0 0.1 0.2 0.3 0 0.1 0.2 0.3 j j Fig.: 5.29 v v Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  32. 2.5 2.0 PP/GF 1.5 Id M PE/GF J /J Id 1.0 0.5 ; experiment model 0 0 0.3 0.1 0.2 j v Fig.: 5.30 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  33. F F G G 100 N M 100 N f A /A f A /A R 1.2 R M 0.8 mm 0.8 mm 1.0 100 µm 0.8 PP + glass-fiber 0.6 (j = 0.13) v 0.4 100 µm 0 0.25 0.50 0.75 1.00 coupling agent content (wt.-%) Fig.: 5.31 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  34. 4 E/P copolymer + 10 wt.-% GF with 0.4 wt.-% CA 3 J (Nmm-1) 2 without CA 1 0 0.2 0.6 0.4 0 0.8 Da (mm) CA – coupling agent content Fig.: 5.32 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  35. ; experiment ; model 100 80 with coupling agent -2 60 a (kJm ) cN without coupling agent 40 20 0 80 100 0 20 40 60 PE content (wt.-%) Fig.: 5.33 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  36. TPU/ABS blends Da Da 9 min max TPU/ABS 50/50 7 TPU/ABS 20/80 -1 J (Nmm ) 5 ABS 3 1 0 0.4 0.2 0.6 0.8 Da (mm) Fig.: 5.34 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  37. 4 -1 3 T = 30 °C A  1.4 µm J (Nmm ) c 16 0.2 A = 2.00 µm 2 A = 1.45 µm A = 1.40 µm 12 1 A = 1.30 µm 2.0 1.0 1.5 A = 1.20 µm Da A (µm) min -1 J (Nmm ) 8 4 Da max 0 0.8 0.2 0.4 0.6 0 Da (mm) Fig.: 5.35 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  38. 10 8 -1 A  0.4 µm 6 J (Nmm ) c T = 23 °C 4 30 0.2 2 Da max 0 0.6 0.9 1.2 0.3 A (µm) 20 A = 1.00 µm A = 0.57 µm -1 A = 0.54 µm J (Nmm ) A = 0.40 µm Da min A = 0.39 µm A = 0.36 µm 10 0 0.8 0.6 0 0.2 0.4 Da (mm) Fig.: 5.36 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  39. copolymer 1 (30 °C) 8 copolymer 2 (20 °C) -1 6 J (Nmm ) 7 4 0.2 2 6 0 3 1 2 4 0 5 A/D 4 brittle copolymer 1 3 tough 2 copolymer 2 1 high impact 0 20 -30 10 -20 -10 40 0 30 50 T (°C) (A/D) c Fig.: 5.37 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  40. energy - determined 100 80 high impact 60 j (wt.-%) tough EPR 40 20 brittle 0 -80 -60 0 -40 20 -20 40 T (°C) ST J J Id 0.2 Fig.: 5.38 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  41. 175 composition 1 150 1/2 K (MPamm ) 125 Id 100 composition 2 75 0 10 30 20 40 50 t (min) w Fig.: 5.39 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  42. 2 µm Fig.: 5.40 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  43. carbon black content (phr) 0 10 20 30 40 50 60 J (Nmm-1) d 200 carbon black 150 sulfur 100 50 0 1.0 1.5 2.0 2.5 sulfur content (phr) Fig.: 5.41 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

  44. material selection dimensioning fracture behavior strength verification strain verification e >e e < e s <s s >s brittle tough undefined zul zul zul zul Charpy impact strength unsufficient sufficient demands on technology velocity- manufacturing monitoring temperature- realizable unrealizable shifting-concept unsufficient sufficient fracture mechanics concept realization K < K K > K I I zul I I zul or J > J J < J I I zul I I zul Fig.: 5.42 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

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