Determination of crack spacing and penetration due to shrinkage of a solidifying layer

International Journal of Solids and Structures

Volumn 46, Issue 5, 2009, Pages 1078-1084

  Jenkins, D R ^a  

^a CSIRO   (Australia)

Author keywords

Regular crack array; Solidification; Strain energy; Thermoelasticity

Indexed keywords

BOUNDARY VALUE PROBLEMS; CRYSTALLIZATION; ELASTICITY; SOLIDIFICATION; STRAIN ENERGY; THERMOELASTICITY;

CRACK PATTERNS; CRACK SPACINGS; INTERNAL STRESSES; KEY FEATURES; LAYER OF MATERIALS; MINIMUM ENERGIES; NUMERICAL COMPARISONS; PERIOD DOUBLING; REGULAR ARRAYS; REGULAR CRACK ARRAY; SOLIDIFICATION MODELS; SOLIDIFICATION PROCESSES; TEMPERATURE PROFILES; THERMAL PROFILES; TIME PROGRESSES;

CRACKS;

EID: 58249138397     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.10.017     Document Type: Article

References (37)

1. Akiyama T., Liu H., and Hayakawa K.-I. Hygrostress-multicrack formation and propagation in cylindrical viscoelastic food undergoing heat and moisture transfer processes. Int. J. Heat Mass Trans. 40 7 (1997) 1601-1609
2. Bahr H.-A., Weiss H.-J., Maschje H.G., and Meissner F. Multiple crack propagation in a strip caused by thermal shock. Theor. Appl. Fracture Mech. 10 (1988) 219-226
3. Bažant Z.P., Ohtsubo H., and Aoh K. Stability and post-critical growth of a system of cooling or shrinkage cracks. Int. J. Fracture 15 5 (1979) 443-456
4. Bažant Z.P., Kim J.-K., and Jeon S.-E. Cohesive fracturing and stresses caused by hydration heat in massive concrete wall. J. Eng. Mech. 129 1 (2003) 21-30
5. Brener E.A., Mu{combining double acute accent}ller-Krumbhaar H., and Spatschek R. Coarsening of cracks in a uniaxially strained solid. Phys. Rev. Lett. 86 7 (2001) 1291-1294
6. Carslaw H.S., and Jaeger J.C. Conduction of Heat in Solids. Second ed. (1959), Clarendon, Oxford, CH XI
7. Chan Y., Lu X., Chen E.Q., and Mi Y. Micropatterning from drying micelle solution of di-block copolymers: strap-structure, quadrate farmland-structure and biomimetic structure. Polymer 45 (2004) 3465-3471
8. Chertkov V.Y. Modelling cracking stages of saturated soils as they dry and shrink. Eur. J. Soil Sci. 53 (2002) 105-118
9. Chertkov V.Y., and Ravina I. Morphology of horizontal cracks in swelling soils. Theor. Appl. Fracture Mech. 31 (1999) 19-29
10. Choules B.D., Kokini K., and Taylor T.A. Thermal fracture of ceramic thermal barrier coatings under high heat flux with time-dependent behavior. Mater. Sci. Eng. A 299 (2001) 296-304
11. Dance M., Hancock P.L., Sparks R.S.J., and Wallman A. Fracture and surface crust development in a Holocene pahoehoe lava flow on the Island of Tenerife, Canaries. J. Struct. Geol. 23 (2001) 165-182
12. Goehring L., and Morris S.W. Experimental investigation of the scaling of columnar joints. Phys. Rev. E 74 (2006) 036115
13. Grossenbacher K.A., and McDuffie S.M. Conductive cooling of lava: columnar joint diameter and stria width as functions of cooling rate and thermal gradient. J. Volcan. Geotherm. Res. 69 (1995) 95
14. Hong A.P., Li Y.N., and Bažant P. Theory of crack spacing in concrete pavements. J. Eng. Mech. ASCE 123 3 (1997) 267-275
15. Hu M.S., and Evans A.G. The cracking and decohesion of thin films on ductile substrate. Acta Metall. 37 3 (1989) 917-925
16. Jagla E.A. Stable propagation of an ordered array of cracks during directional drying. Phys. Rev. E 65 (2002) 046147
17. Jagla E.A., and Rojo A.G. Sequential fragmentation: the origin of columnar quasihexagonal patterns. Phys. Rev. E 65 (2002) 026203
18. Jenkins D.R. Optimal spacing and penetration of cracks in a shrinking slab. Phys. Rev. E 71 (2005) 056117
19. Kang W., and Lee N.-H. Mathematical modeling to predict drying deformation and stress due to the differential shrinkage within a tree disk. Wood Sci. Tech. 36 (2002) 463-476
20. Lawn B.R., and Wilshaw T.R. Fracture of Brittle Solids (1975), Cambridge UP, Cambridge
21. Loison R., Foch P., and Boyer A. Coke: quality and production. Second ed. (1989), Butterworths, London
22. Lore J., Aydin A., and Goodson K. A deterministic methodology for prediction of fracture distribution in basaltic multiflows. J. Geophys. Res. 106 B4 (2001) 6447
23. Mahoney, M., Jenkins, D.R., Keating, J., LeBas, A., McGuire, S., 2004. Factors affecting coke size and fissuring during cokemaking. In: Proceedings of the Second International Meeting on Ironmaking, Vitoria, Brazil September 12-15, 2004, ABM (Associacao Brasileira de Metalurgia e Materiais), pp. 871-880.
24. Mu{combining double acute accent}ller G. Starch columns: Analog model for basalt columns. J. Geophys. Res. 103 B7 (1998) 15293
25. Mu{combining double acute accent}ller G. Experimental simulations of basalt columns. J. Volcan. Geotherm. Res. 86 (1998) 93
26. Moës N., and Belytschko T. Extended finite element method for cohesive crack growth. Int. J. Num. Meth. Eng. 46 (2002) 131-150
27. Nemat-Nasser S., Keer L.M., and Parihar K.S. Unstable growth of thermally induced interacting cracks in brittle solids. Int. J. Solids Struct. 14 (1978) 409-430
28. Nemat-Nasser S., Sumi Y., and Keer L.M. Unstable growth of tension cracks in brittle solids: stable and unstable bifurcations, snap-through, and imperfection sensitivity. Int. J. Solids Struct. 16 (1980) 1017-1035
29. Parbrook P.J., Wang T., Whitehead M.A., Harrison C.N., Lynch R.J., and Murray R.T. Crack formation and development in AlGaN/GaN structures. Phys. Stat. Sol. (c) 7 (2003) 2055-2058
30. Plummer P.S., and Gostin V.A. Shrinkage cracks: desiccation or synaeresis?. J. Sedim. Petrol. 51 4 (1981) 1147-1156
31. Saliba R., and Jagla E.A. Analysis of columnar joint patterns from three-dimensional stress modeling. J. Geophys. Res. 108 B10 (2003) 2476
32. Schaefer C.J., and Kattenhorn S.A. Characterization and evolution of fractures in low-volume pahoehoe lava flows, eastern Snake River Plain, Idaho. GSA Bull. 116 3/4 (2004) 322
33. Sletten R.S., Hallet B., and Fletcher R.C. Resurfacing time of terrestrial surfaces by the formation and maturation of polygonal patterned ground. J. Geophys. Res. 108 E4 (2001) 8044
34. Timm D.H., Guzina B.B., and Voller V.R. Prediction of thermal crack spacing. Int. J. Solids Struct. 40 (2003) 125-142
35. Toramaru, A., Matsumoto, T., 2004. Columnar joint morphology and cooling rate: a starch-water mixture experiment. J. Geophys. Res. 109, B02205, doi:10.1029/2003JB002686.
36. Walker G.P.L. Basaltic-volcano systems. In: Prichard H., et al. (Ed). Magmatic Processes and Plate Tectonics vol. 76 (1993), Geol. Soc. Spec. Publ. 3-38
37. Weinberger R. Initiation and growth of cracks during desiccation of stratified muddy sediments. J. Struct. Geol. 21 (1999) 379-386