0 Introduction The second chapter is divided into sections devoted to micromechanisms of brittle,quasi-brittle and ductile fracture under static (low strain rate)and dynamic (high strain rate)loading.The leading theme of the first topic is the geometrically-induced crack tip shielding effect and the related fracture micromechanism.A two-scale analytical model based on quantitative fractog- raphy and mixed-mode fracture mechanics is applied to explain the fracture behaviour of borosilicate glasses.In order to quantify the quasi-brittle frac- ture,the geometrically-induced shielding effect is related to the ratio of a characteristic microstructure dimension and the crack-tip plastic zone size (the size ratio)in a two-scale analytical model based on quantitative frac- tography and fracture mechanics.This model is employed to describe the anomalous fracture behaviour of UHSLA steels as well as to assess the value of fracture energy of grain boundaries with segregated phosphorus in ferritic al- loys.Finally,analytical three-scale models of ductile fracture processes based on dislocation dynamics,microvoids formation kinetics and fracture mechan- ics are presented.These models are able to predict the fracture strain in the tensile testing of ductile metallic materials and to assess the values of fracture toughness for steels exhibiting the ductile fracture micromechanism. The last chapter is dedicated to fatigue fracture of metallic materials.The micromechanisms of mechanical hysteresis,crack initiation and crack prop- agation under all modes of crack-tip loading are described in the multiscale concept from nanoscale to mesoscale levels.An analytical multiscale model of crack closure was developed in order to evaluate individual crack-tip shield- ing components and to assess the intrinsic fatigue threshold value under the opening loading mode.Micromechanisms of crack propagation under shear and mixed-mode loading are also discussed from the point of view of both theoretical and experimental approaches.For example,a two-scale model connecting three-dimensional topology with linear-elastic fracture mechan- ics is able to explain a formation of factory-roof morphological patterns on the fracture surfaces generated by cyclic torsion.The initiation and propaga- tion of fish-eye cracks is studied under combined bending-torsion loading in specimens made of nitrided steel.A method enabling a quantitative recon- stitution of the fatigue process from the fracture morphology is described in the final part of the chapter.This method of engineering failure analysis was successfully applied in many practical cases. The book is complemented by three appendices devoted to ab initio meth- ods utilized in atomistic models,criteria employed in mixed-mode fracture and derivation of void-induced dislocation dynamics in the model of ductile fracture.0 Introduction 7 The second chapter is divided into sections devoted to micromechanisms of brittle, quasi-brittle and ductile fracture under static (low strain rate) and dynamic (high strain rate) loading. The leading theme of the first topic is the geometrically-induced crack tip shielding effect and the related fracture micromechanism. A two-scale analytical model based on quantitative fractog￾raphy and mixed-mode fracture mechanics is applied to explain the fracture behaviour of borosilicate glasses. In order to quantify the quasi-brittle frac￾ture, the geometrically-induced shielding effect is related to the ratio of a characteristic microstructure dimension and the crack-tip plastic zone size (the size ratio) in a two-scale analytical model based on quantitative frac￾tography and fracture mechanics. This model is employed to describe the anomalous fracture behaviour of UHSLA steels as well as to assess the value of fracture energy of grain boundaries with segregated phosphorus in ferritic al￾loys. Finally, analytical three-scale models of ductile fracture processes based on dislocation dynamics, microvoids formation kinetics and fracture mechan￾ics are presented. These models are able to predict the fracture strain in the tensile testing of ductile metallic materials and to assess the values of fracture toughness for steels exhibiting the ductile fracture micromechanism. The last chapter is dedicated to fatigue fracture of metallic materials. The micromechanisms of mechanical hysteresis, crack initiation and crack prop￾agation under all modes of crack-tip loading are described in the multiscale concept from nanoscale to mesoscale levels. An analytical multiscale model of crack closure was developed in order to evaluate individual crack-tip shield￾ing components and to assess the intrinsic fatigue threshold value under the opening loading mode. Micromechanisms of crack propagation under shear and mixed-mode loading are also discussed from the point of view of both theoretical and experimental approaches. For example, a two-scale model connecting three-dimensional topology with linear–elastic fracture mechan￾ics is able to explain a formation of factory-roof morphological patterns on the fracture surfaces generated by cyclic torsion. The initiation and propaga￾tion of fish-eye cracks is studied under combined bending-torsion loading in specimens made of nitrided steel. A method enabling a quantitative recon￾stitution of the fatigue process from the fracture morphology is described in the final part of the chapter. This method of engineering failure analysis was successfully applied in many practical cases. The book is complemented by three appendices devoted to ab initio meth￾ods utilized in atomistic models, criteria employed in mixed-mode fracture and derivation of void-induced dislocation dynamics in the model of ductile fracture