Computational Methods for Debonding in Composites

More documents

Recommendations

Info

192 N. Zobeiry et al. where g f is the energy release rate density which is the area under the stress-strain curve, and c is the multiplier which represents the relation between the height of damage (hc) and the length parameter (l) and is roughly equal to hc/l. Thevalue of c mainly depends on the definition of the weight function and for the function defined in Eq. (9.4), it ranges between 2 to 2.5. Numerical simulations that are based on non-local averaging not only resolve the mesh size dependency problem but lead to more realistic prediction of the local strain/stress fields including the size of the damage zone. An added benefit of the non-local approach is that it improves the mesh orientation bias for damage propagation direction [1]. The LS-DYNA software provides non-local averaging capability for a select number of built-in material models. Unfortunately, this tool is currently not available for either built-in anisotropic damage models or user-defined damage models. Therefore, in the presented analyses the MAT PLASTICITY WITH DAMAGE material model which uses a scalar damage model (SDM) for isotropic materials is adopted. Figure 9.9 shows the longitudinal strain contours in an OCT simulation of a [0/ ± 45]4 braided composite material [15] using an effective isotropic Young’s modulus of 12.5 GPa, peak stress of 110 MPa, and a fracture energy release rate (G f ) of 45 kJ/m 2 . It can be seen that the height of the zone with localized strain defining the damage zone is almost constant during the analysis. By changing the length parameter (l), the predicted height of damage can be adjusted to fit the experimental measurements. To illustrate the mesh orientation dependency of local damage models and the resulting improvement using a non-local damage approach, an example of the OCT simulation is carried out with an inclined mesh introduced ahead of the notch. (a (a) (c) a= 16 mm (POD=1.87 mm) a= 26 mm (POD=2.53 mm) (b (b) (d (d) a= 20 mm (POD=2.12 mm) a= a= 30 mm (POD=2.83 mm) Fringe Levels 8. 8.00e-3 6. 6.67e-3 5.33e-3 4.00e-3 2.67e-3 1.33e-3 0.00e+0 h =14 mm Fig. 9.9 Predicted longitudinal strain (εy) contours and crack length values, ∆a, intheOCT simulation of a [0/ ± 45]4 braided CFRP at various levels of pin opening displacement (POD)
9 Progressive Damage Modeling of Composite Materials 193 (a) Using local scalar damage formulation (b) Using non-local scalar damage formulation Fig. 9.10 Predicted damage/crack pattern in an OCT test Figures 9.10a, b show the predicted damage/crack pattern in local and non-local simulations, respectively. It is seen that the non-local averaging can significantly improve the dependency of the FE predictions on mesh orientation as the crack follows the expected path (i.e. along the axis of the notch). 9.6 Conclusions A previously developed continuum damage mechanics based constitutive model, CODAM, has been further modified to account for the distinct damage mechanisms that occur under compressive loading of fibre reinforced composite materials. The proposed extension has been guided by the development of a simple mechanical analogue model that through special arrangement of basic elements describes the one-dimensional non-linear response of composite laminates under both in-plane tension and compression loading. The calibration of the tensile damage parameters of the model using an Overheight Compact Tension (OCT) test setup have been discussed. Results presented here show the efficacy of the model in predicting the overall damage zone size and force-displacement response of quasi-statically loaded OCT and open hole compression test panels. Finally, the limitations of local smeared crack (crack band) approaches in modeling damage propagation and its numerical implications have been discussed. It is shown that a non-local integral approach is an efficient remedy for problems stemming from the so-called localization and mesh orientation bias that local approaches suffer from. Acknowledgements The authors would like to acknowledge the financial support provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The contributions made to this work by many of the past members of the Composites Group at UBC are also gratefully acknowledged.
Page 2 and 3:
Mechanical Response of Composites
Page 4 and 5:
Pedro P. Camanho • C.G. Dávila S
Page 6 and 7:
Preface The methodology for designi
Page 8 and 9:
Acknowledgements The Editors of thi
Page 10 and 11:
x Contents 3 Practical Challenges i
Page 12 and 13:
xii Contents 8.2.4 Modelling Effect
Page 14 and 15:
xiv Contents 13.1.2 EffectiveProper
Page 16 and 17:
xvi List of Contributors Clara Schu
Page 18 and 19:
Chapter 1 Computational Methods for
Page 20 and 21:
1 Computational Methods for Debondi
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
28 R. Rolfes et al. functions by me
Page 46 and 47:
30 R. Rolfes et al. Microscale fibe
Page 48 and 49:
32 R. Rolfes et al. symmetric, whic
Page 50 and 51:
34 R. Rolfes et al. Fig. 2.5 Discre
Page 52 and 53:
36 R. Rolfes et al. Unit cell (a) S
Page 54 and 55:
38 R. Rolfes et al. stress state. T
Page 56 and 57:
40 R. Rolfes et al. biaxial compres
Page 58 and 59:
42 R. Rolfes et al. Damage Evolutio
Page 60 and 61:
44 R. Rolfes et al. Fig. 2.14 Radia
Page 62 and 63:
46 R. Rolfes et al. Table 2.2 Elast
Page 64 and 65:
48 R. Rolfes et al. A dev is the de
Page 66 and 67:
50 R. Rolfes et al. uniaxial compre
Page 68 and 69:
52 R. Rolfes et al. Stress in MPa -
Page 70 and 71:
54 R. Rolfes et al. 2.4.2 Results o
Page 72 and 73:
56 R. Rolfes et al. 12. Hughes TJR
Page 74 and 75:
58 B.N. Cox et al. inform models; a
Page 76 and 77:
60 B.N. Cox et al. 3.2 The Structur
Page 78 and 79:
62 B.N. Cox et al. be successfully
Page 80 and 81:
64 B.N. Cox et al. high fluxes of c
Page 82 and 83:
66 B.N. Cox et al. provides poor in
Page 84 and 85:
68 B.N. Cox et al. For example, a c
Page 86 and 87:
70 B.N. Cox et al. failures in comp
Page 88 and 89:
72 B.N. Cox et al. mixed-mode crack
Page 90 and 91:
74 B.N. Cox et al. 24. Elices M, Gu
Page 92 and 93:
Chapter 4 Analytical and Numerical
Page 94 and 95:
4 Analytical and Numerical Investig
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
100 C. Schuecker and H.E. Petterman
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Chapter 6 Study of Delamination in
Page 134 and 135:
6 Study of Delamination with in Com
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155: Chapter 7 Interaction Between Intra
Page 156 and 157: 7 Interaction Between Intraply and
Page 174 and 175: Chapter 8 A Numerical Material Mode
Page 176 and 177: 8 A Numerical Material Model for Pr
Page 192 and 193: 180 N. Zobeiry et al. There are sev
Page 194 and 195: 182 N. Zobeiry et al. for construct
Page 196 and 197: 184 N. Zobeiry et al. In compressio
Page 198 and 199: 186 N. Zobeiry et al. c = 38.7 mm h
Page 200 and 201: 188 N. Zobeiry et al. displacement
Page 202 and 203: 190 N. Zobeiry et al. No Notched St
Page 206 and 207: 194 N. Zobeiry et al. References 1.
Page 208 and 209: Chapter 10 Elastoplastic Modeling o
Page 210 and 211: 10 Elastoplastic Modeling of Multi-
Page 234 and 235: 224 J.A. Oliveira et al. 11.1 Intro
Page 236 and 237: 226 J.A. Oliveira et al. written as
Page 238 and 239: 228 J.A. Oliveira et al. asymptotic
Page 240 and 241: 230 J.A. Oliveira et al. χ jk i (0
Page 242 and 243: 232 J.A. Oliveira et al. (a) (b) Fi
Page 244 and 245: 234 J.A. Oliveira et al. Fig. 11.7
Page 246 and 247: 236 J.A. Oliveira et al. Fig. 11.10
Page 248 and 249: 238 J.A. Oliveira et al. (a) (b) (c
Page 250 and 251: 240 J.A. Oliveira et al. (a) (b) (c
Page 252 and 253: 242 J.A. Oliveira et al. 20. Suquet
Page 254 and 255:
244 E. Lund and L.S. Johansen In th
Page 256 and 257:
246 E. Lund and L.S. Johansen 12.2.
Page 258 and 259:
248 E. Lund and L.S. Johansen The D
Page 260 and 261:
250 E. Lund and L.S. Johansen Subje
Page 262 and 263:
252 E. Lund and L.S. Johansen Table
Page 264 and 265:
254 E. Lund and L.S. Johansen Layer
Page 266 and 267:
256 E. Lund and L.S. Johansen λ1 =
Page 268 and 269:
258 E. Lund and L.S. Johansen 12.6
Page 270 and 271:
260 E. Lund and L.S. Johansen 34. T
Page 272 and 273:
262 M. Kästner et al. Micro-level
Page 274 and 275:
264 M. Kästner et al. elastic stra
Page 276 and 277:
266 M. Kästner et al. 13.1.1.2 Per
Page 278 and 279:
268 M. Kästner et al. 13.1.2 Effec
Page 280 and 281:
270 M. Kästner et al. including pr
Page 282 and 283:
272 M. Kästner et al. In order to
Page 284 and 285:
274 M. Kästner et al. x2 x 3 x1 Br
Page 286 and 287:
276 M. Kästner et al. Fig. 13.12 I
Page 288 and 289:
278 M. Kästner et al. Table 13.4 C
Page 290 and 291:
Chapter 14 Development of Domain Su
Page 292 and 293:
14 Development of DST for the Model
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
294 H. Miled et al. for this type o
Page 304 and 305:
296 H. Miled et al. Fig. 15.2 Diffe
Page 306 and 307:
298 H. Miled et al. Each member of
Page 308 and 309:
300 H. Miled et al. temperature is
Page 310 and 311:
302 H. Miled et al. Fig. 15.7 Compa
Page 312 and 313:
304 H. Miled et al. Table 15.3 Prop
Page 314 and 315:
306 H. Miled et al. Eqs. 15.28 and
Page 316 and 317:
308 H. Miled et al. 15.4.2 Effectiv
Page 318 and 319:
310 H. Miled et al. Fig. 15.13 Comp
Page 320 and 321:
312 H. Miled et al. 9. Carreau P, D
show all

Computational Methods for Debonding in Composites

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?