TY - JOUR

T1 - A micro-mechanics based extension of the GTN continuum model accounting for random void distributions

AU - Holte, I.

AU - Nielsen, K. L.

AU - Martínez-Pañeda, E.

AU - Niordson, C.F.

PY - 2024

Y1 - 2024

N2 - Randomness in the void distribution within a ductile metal complicates
quantitative modeling of damage following the void growth to coalescence
failure process. Though the sequence of micro-mechanisms leading to
ductile failure is known from unit cell models, often based on
assumptions of a regular distribution of voids, the effect of randomness
remains a challenge. In the present work, mesoscale unit cell models,
each containing an ensemble of four voids of equal size that are
randomly distributed, are used to find statistical effects on the yield
surface of the homogenized material. A yield locus is found based on a
mean yield surface and a standard deviation of yield points obtained
from 15 realizations of the four-void unit cells. It is found that the
classical GTN model very closely agrees with the mean of the yield
points extracted from the unit cell calculations with random void
distributions, while the standard deviation varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities , while it rapidly increases for triaxialities above , reaching maximum values of about at .
At even higher triaxialities it decreases slightly. The results
indicate that the dependence of the standard deviation on the stress
state follows from variations in the deformation mechanism since a
well-correlated variation is found for the volume fraction of the unit
cell that deforms plastically at yield. Thus, the random void
distribution activates different complex localization mechanisms at high
stress triaxialities that differ from the ligament thinning mechanism
forming the basis for the classical GTN model. A method for introducing
the effect of randomness into the GTN continuum model is presented, and
an excellent comparison to the unit cell yield locus is achieved.

AB - Randomness in the void distribution within a ductile metal complicates
quantitative modeling of damage following the void growth to coalescence
failure process. Though the sequence of micro-mechanisms leading to
ductile failure is known from unit cell models, often based on
assumptions of a regular distribution of voids, the effect of randomness
remains a challenge. In the present work, mesoscale unit cell models,
each containing an ensemble of four voids of equal size that are
randomly distributed, are used to find statistical effects on the yield
surface of the homogenized material. A yield locus is found based on a
mean yield surface and a standard deviation of yield points obtained
from 15 realizations of the four-void unit cells. It is found that the
classical GTN model very closely agrees with the mean of the yield
points extracted from the unit cell calculations with random void
distributions, while the standard deviation varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities , while it rapidly increases for triaxialities above , reaching maximum values of about at .
At even higher triaxialities it decreases slightly. The results
indicate that the dependence of the standard deviation on the stress
state follows from variations in the deformation mechanism since a
well-correlated variation is found for the volume fraction of the unit
cell that deforms plastically at yield. Thus, the random void
distribution activates different complex localization mechanisms at high
stress triaxialities that differ from the ligament thinning mechanism
forming the basis for the classical GTN model. A method for introducing
the effect of randomness into the GTN continuum model is presented, and
an excellent comparison to the unit cell yield locus is achieved.

KW - Ductile failure

KW - Gurson model

KW - Statistical variation

KW - Void growth

U2 - 10.1016/j.euromechsol.2023.105123

DO - 10.1016/j.euromechsol.2023.105123

M3 - Journal article

SN - 0997-7538

JO - European Journal of Mechanics A - Solids

JF - European Journal of Mechanics A - Solids

ER -