TY - JOUR
T1 - On the applicability of linear elastic fracture mechanics scaling relations in the analysis of intergranular fracture of brittle polycrystals
AU - Shabir, Zahid
AU - Van der Giessen, Erik
AU - Duarte, C. Armando
AU - Simone, Angelo
PY - 2019
Y1 - 2019
N2 - Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary length. It is shown that load–displacement curves for specimens with the same microstructure and for various cohesive law parameters can be obtained from a master load–displacement curve by means of simple linear elastic fracture mechanics scaling relations. This property is a consequence of the independence of intergranular crack paths from cohesive law parameters. Perfect scaling is obtained for cases characterized by the same grain boundary brittleness number, irrespective of its value, whereas scaling is approximated for cases with different but relatively large values of the grain boundary brittleness number. The former case corresponds to grain boundary traction profiles that are identical apart from a scale factor; in the latter case, a large grain boundary brittleness number implies similar, apart from a scale factor, traction profiles. By exploiting this property, it is demonstrated that computationally expensive simulations can be avoided above a certain grain boundary brittleness threshold value.
AB - Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary length. It is shown that load–displacement curves for specimens with the same microstructure and for various cohesive law parameters can be obtained from a master load–displacement curve by means of simple linear elastic fracture mechanics scaling relations. This property is a consequence of the independence of intergranular crack paths from cohesive law parameters. Perfect scaling is obtained for cases characterized by the same grain boundary brittleness number, irrespective of its value, whereas scaling is approximated for cases with different but relatively large values of the grain boundary brittleness number. The former case corresponds to grain boundary traction profiles that are identical apart from a scale factor; in the latter case, a large grain boundary brittleness number implies similar, apart from a scale factor, traction profiles. By exploiting this property, it is demonstrated that computationally expensive simulations can be avoided above a certain grain boundary brittleness threshold value.
KW - Brittle fracture
KW - Generalized finite element method
KW - Linear elastic fracture mechanics
KW - Polycrystals
KW - Scaling
UR - http://www.scopus.com/inward/record.url?scp=85069483463&partnerID=8YFLogxK
U2 - 10.1007/s10704-019-00381-x
DO - 10.1007/s10704-019-00381-x
M3 - Article
AN - SCOPUS:85069483463
SN - 0376-9429
VL - 220
SP - 205
EP - 219
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 2
ER -