IFMASS10

340

deformation localization appears within the shear bands at micro-scale and, finally,

material separation by fracture occurs at macroscopic level. It is to mention that

significant simplifications are necessary here, which have to be proved as conservative

by experiments.

In Fig. 18 hierarchical simulation approach is presented, as devised for assessing and

optimizing the mechanical behaviour of Cybersteel /1/. At quantum scale, the failure

mechanism is initiated by bonds breaking at inclusions-matrix interface. The cohesive

strength, in terms of atoms separation, as function of traction force, governs the atomic

bonds breaking. The interface binding energy derived from this solution is regarded as

key design parameter of Cybersteel (Fig. 18.a). At nano-scale, the debonding on

inclusions-matrix interface is simulated by a concurrent method. The matrix and particles

regions are modeled by finite elements and the interface is modeled by molecular

dynamics. The debonding on interface triggers voids nucleation. Further, the dynamics

of voids development, which is dependent on voids volume fraction and the distribution

of nano-secondary particles, enables to simulate the constitutive law of deformation and

plastic flow rule in a nano-cell (Fig. 18.b).

At micro-scale (Fig. 18.c), the constitutive equations of deformation and the plastic

flow rule are simulated concurrently, similarly as in nano-scale cells, having incorpo-

rated the constitutive equations and plastic flow rule inherited and passed from nano-

scale simulation. The deformation behaviour of the matrix, according to its constituency

at micro-level, as well as of primary inclusions (of micro-size, by difference to secondary

particles of nano-size) is simulated as a continuum by FE. The debonding on

matrix/primary inclusions is simulated by MD with cohesive rule inherited from the

simulation at QM level (Fig. 18.a). Subsequently, the growth and eventually the

coalescence of voids, under increasing loading, are captured by FE simulation of the

matrix. The observed shear bands, as prelude to final fracture, are simulated at this level.

Under increased applied loading, continuum FE models of elastic-plastic fracture

mechanics are applied (Fig. 18.d). After significant prior plastic deformation at

macroscopic level, fracture appears as result of unstable plastic deformation, localized

into a critical cross-section which is normal to the maximum of the applied principal

tensile stress. Significant capacity of macroscopic plastic deformation under monoto-

nously increased loading, owing to optimized size and nature of primary and secondary

particles, coupled with high values of crack tip opening displacement demonstrated by

simulation, confer, from design stage, high toughness to Cybersteel, which was fully

confirmed by laboratory testing.

It should be remarked in this construct that the simulation of dislocations mecha-

nisms, which are involved at mesoscopic level, has been circumvented owing to the lack

of clarified physical models of dislocations, both as individual entities (e.g. the electrons

configuration of the dislocations core) and as dynamic ensembles. However, the details

of the physical process at mesoscopic scale are implicitly covered, globally, in the lower

scale-sizes models at quantum mechanics and MD levels.

Presented approach can be considered as further and very detailed extension of

previously developed crack significance assessment, involving high level of theoretically

based knowledge gathered at different scales, but in fact it does not treat the situation at

the crack tip. It demonstrates high level of applied theoretical background, capacity of

modelling and numerical analysis and obtained practical effects, proved experimentally.