• Niordson, Christian Frithiof
• Holte, Ingrid
• Nielsen, Kl
• Martínez-Pañeda, E.

Abstract

Randomness in the void distribution within a ductile metal complicatesquantitative modeling of damage following the void growth to coalescencefailure process. Though the sequence of micro-mechanisms leading toductile failure is known from unit cell models, often based onassumptions of a regular distribution of voids, the effect of randomnessremains a challenge. In the present work, mesoscale unit cell models,each containing an ensemble of four voids of equal size that arerandomly distributed, are used to find statistical effects on the yieldsurface of the homogenized material. A yield locus is found based on amean yield surface and a standard deviation of yield points obtainedfrom 15 realizations of the four-void unit cells. It is found that theclassical GTN model very closely agrees with the mean of the yieldpoints extracted from the unit cell calculations with random voiddistributions, while the standard deviationvaries 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 aboutat .At even higher triaxialities it decreases slightly. The resultsindicate that the dependence of the standard deviation on the stressstate follows from variations in the deformation mechanism since awell-correlated variation is found for the volume fraction of the unitcell that deforms plastically at yield. Thus, the random voiddistribution activates different complex localization mechanisms at highstress triaxialities that differ from the ligament thinning mechanismforming the basis for the classical GTN model. A method for introducingthe effect of randomness into the GTN continuum model is presented, andan excellent comparison to the unit cell yield locus is achieved.

Topics

• impedance spectroscopy
• surface
• forming
• random
• void
• deformation mechanism