Abstract
A multi-scale hierarchical constitutive model is developed for establishing the relationship between quantum mechanical, micromechanical, and overall strength/toughness properties in steel design. Focused on the design of ultra-high strength, high toughness steels, a two-level cell model is used to represent two groups of hard particles (inclusions) in an alloy matrix which is characteristic of such Fe-based alloys. Primary inclusion particles, which are greater than a micron in size, are handled by a microcell. Secondary inclusion particles which are tens of nanometers in size are modeled by a sub-microcell. In the sub-microcell, the matrix constitutive behavior is given by quantum mechanics computation of bcc-iron calibrated according to experiments. In the microcell, the matrix constitutive behavior is given by the stress–strain response of the sub-microcell, characterized by a plastic flow potential based on the numerical simulation of the representative cell. In turn, the plastic flow potential generated by the stress–strain response of the microcell is used as the constitutive response at the continuum macro level for simulation of ductile fracture and for the assessments of toughness. The interfacial debonding between the matrix and the primary and the secondary inclusion particles are modeled using decohesion potentials computed through quantum mechanics calculation together with a mechanical model of normal separation and gliding induced dislocation, which also provides quantitative explanations why practice strength of a steel is much lower than the atomic separation force and how plasticity occurs in steels.
The ductile fracture simulations on an ASTM standard center cracked specimen lead to the generation, for the first time, of a toughness, strength, adhesion diagram based on computer simulation and which establishes the relationship between alloy matrix strength, interfacial decohesion energy, and fracture toughness.