Unstable and limited crack propagation
Numerical modelling and parametric analysis
DOI:
https://doi.org/10.13052/REMN.17.663-675Keywords:
unstable crack propagation, pop-in, non-linear solver, cohesive zone modelsAbstract
We consider in this paper the unstable and limited extension of brittle cracks when they initiate near or in local brittle zones and extend through them towards tougher material zones. Our aim is to predict their arrest and in this case, one observes the so-called “pop-in” phenomenon. We use the cohesive zone models as constitutive law of brittle cracks, which are numerically modelled using interface-type elements. Non-linear solvers including loading step adaptive strategy are developed, that is necessary to overcome convergence difficulties during the pop-in. Some numerical aspects specifically related to the pop-in modelling are discussed. Parametric studies on CT specimens are carried out to point out the influential numerical, plastic and fracture parameters. As an example, the yield strength mismatch between the local brittle zone and the tougher material plays a very important role on the pop-in phenomenon and makes its modelling dependent upon the element size at the crack-tip.
Downloads
References
Adouani H., Tie B., Berdin C., Aubry D., “Adaptive numerical modelling of dynamic crack
propagation”, 8th International conference on mechanical and physical: Behavior of
materials under dynamic loading, September 2006, Dijon, France.
Adouani H., Tie B., Berdin C., « Modélisation numérique de la propagation instable et limitée
de fissure due à la présence de zones locales fragiles », 8e Colloque National en Calcul
des Structures, Mai 2007, Giens, France.
ASTM 1999, Standard test method for measurement of fracture toughness, ASTM E 1820-
Barrenblatt G. I, “The mathematical theory of equilibrium of cracks in brittle fracture”, Adv.
Appl. Mech., 7, 1962, p. 55-129.
Borst R. de, “Numerical aspects of cohesive zone models”, Engineering Fracture Mechanics,
, 2003, p. 1743-1757.
Camacho G.T., Ortiz M., “Computational modeling of impact damage in brittle materials”,
International Journal of Solids and Structures, 33, 1996, p. 2899-2938.
Chaboche J.L., Feyel F., Monerie Y., “Interface debonding models: a viscous regularization
with a limited rate dependency”, International Journal of Solids and Structures, 38, 2001,
p. 3127-3160.
Chandra N., Li H., Shet C., Ghonem H., “Some issues in the application of cohesive zone
models for metal-ceramic interfaces”, International Journal of Solids and Structures, 39,
, p. 2827-2855.
Crisfield M. A., Jelenic G., Mi Y., Zhong H.-G., Fan Z., “Some aspects of the non-linear
finite element method”, Finite Elements in Analysis and Design, 27, 1997, p. 19-40.
Dugdale D. S., “Yielding of steel sheets containing slits”, J. Mech. Phys. Solids, 8, 1960,
p. 100-104.
Falk M.-L., Needleman A., Rice J.-R., “A critical evaluation of cohesive zone models of
dynamic fracture”, 5th European Mecahnics of Materials Conference, March 2001, Delft,
Netherlands, Journal de Physique IV France, vol. 11, p. Pr5-43-50.
Moës N., Belytschko T., “Extended finite element method for cohesive crack growth”,
Engng. Fract Mech, 2002, 69, p. 813-33.
Riks E., Rankin C., Brogan F.A., “On the solution of mode jumping phenomena in thinwalled
shell structures”, Comp. Meth. Appl. Mech. Eng., 136, 1996, p. 54-92.
Siegmund T., Needleman A., “A numerical study on dynamic crack growth in elasticviscoplastic
solids”, Int. J. Solids Struct., 43, 1997, p. 769-787.
Valoroso N., Champaney L., “A damage-mechanics-based approach for modelling
decohesion in adhesively bonded assembles”, Eng. Frac. Mech., 73, 2006, p. 2774-2801.
Xu X.P., Needleman A., “Numerical simulations of fast crack growth in brittle solids”,
Journal of the Mechanics and Physics of Solids, 42, 1994, p. 1397-1434.
