Computational Methods for Debonding in Composites

More documents

Recommendations

Info

36 R. Rolfes et al. Unit cell (a) Scan of NCF (b) Discretization Fig. 2.7 Mesomechanical non-crimp fabric unit cell resin pocket 2 Stitch yarn Fiber orientation 1 b H r N 5 mm Fig. 2.8 Geometry of mesomechanical unit cell for non-crimp fabric of the stitch yarn has no significant influence, because of its small diameter and minor material properties of the PES-yarn compared to the glass-fibers that lie in the same plane. The discretization of the unit cell is shown in Fig. 2.7b, it consists of 200 × 200 × 1 elements. The fiber bundle structure in thickness direction is neglected, hence only one element is used in this direction. Figure 2.8 shows the different components, fiber bundle, epoxy resin pocket and stitching yarn, of the unit cell and their dimensions. The resin pocket is LH = 3.5 mm long and bH = 0.3mm wide, the radius of the stitch yarn is rN = 0.054 mm. 2.2.4.2 Weft-Knitted Fabrics Compared to the non-crimp fabric described above the yarn in weft-knitted fabrics presented here plays a bigger role, although still the yarn diameter is smaller than the fiber bundle diameter. Firstly the loops of the yarn are denser and secondly the yarn is stronger, because it consists of glass fibers instead of polyester and has a larger diameter. Secondly the material structure of the weft-knitted fabric is much more heterogeneous, the individual fiber bundles are clearly identifiable. Therefore in the draping process layers of weft-knitted fabric penetrate each other, as can be seen in Fig. 2.9. Thus the smallest unit cell of the weft-knitted fabric, see Fig. 2.9 includes 5 mm L
2 Material and Failure Models for Textile Composites 37 Fig. 2.9 Geometry of mesomechanical unit cell for two weft-knitted fabrics, epoxy resin is removed on right side two fabrics. It consists of fiber bundles in warp- and fill-direction, the knitting yarn and the epoxy resin. The fiber bundles and epoxy resin are discretized with volume elements, whereas the knitting yarn, is modelled with truss elements, because of its lower diameter. On the right hand side of Fig. 2.9 the epoxy resin is removed to make the knitting yarn visible. 2.3 Material Models In order to describe the specific phenomena of textile composites, special material models are developed on micro- and mesoscale. The fibers are represented by a linear elastic material model. For epoxy resin, an isotropic elastic-plastic material model with an isotropic damage formulation is presented in Sect. 2.3.1. Modelling the transversely isotropic behavior of the fiber bundles, a transversely isotropic elastic-plastic material model with damage is developed in Sect. 2.3.2. 2.3.1 Isotropic Elastic-Plastic Material Model for Epoxy Resin Considering the micromechanical unit cell, epoxy resin turns out as the determining material concerning the overall mechanical behavior of the unit cell. Especially the plastic behavior and the fracture characteristic of epoxy resin prove to be the governing material parameters. Therefore, special care has to be taken to find a good representation of all experimentally observed characteristics of epoxy resin in the material model. An isotropic elastic-plastic material model with an isotropic damage formulation is considered as the best approach for modelling epoxy resin in the micromechanical unit cell. 2.3.1.1 Yield Surface Generally, epoxy resin is a visco-elastic-plastic material, whereas the development of viscosity and plasticity varies depending on the type of epoxy resin and the
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 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 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 102 and 103:
4 Analytical and Numerical Investig
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 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Chapter 8 A Numerical Material Mode
Page 176 and 177:
8 A Numerical Material Model for Pr
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
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 204 and 205:
192 N. Zobeiry et al. where g f is
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 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
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

Create successful ePaper yourself

Delete template?

Save as template?