A Multi-scale Investigation On Fracture And Dislocation Mechanism Of Heterogeneous Materials

Macroscopic, mesoscopic and microscopic theories of fracture of solid materials are all very important for solid mechanics, solid physics and material science, and they have important theoretical significance and scientific value in investigation of mechanism of strengthening and toughening, fatigue and fracture. The method using uniformity of macroscopy and meso-microscopy is an important channel of study on materials failure.The dislocation emitted from blunt crack tip was often neglected in investigation of plastic fracture, and the dislocation plasticity was always neglected in switching of ferroelectric material and martensitic phase transformation of TRIP steel. However, the dislocations, micro cracks and inclusions generated in process of manufacture and use are the key factors affecting material properties, especially the dislocation emission is looked upon as the key of toughness-brittleness transition of solid material. So I introduce dislocations in steel, film, intelligent ceramics and so on, and carry out multi-scale theoretical study on mechanism of strengthening and toughening and essence of failure of heterogeneous materials in this paper. Some novel complex potential methods in investigation of complex multiply connected domain and intricate crack of have been created, and the closed form solution of a series of models has been obtained, the fracture mechanism is investgated in macroscopic scale. Applying mechanics of continious medium to microscopic scale, the mechanism of strengthening and toughening of nanoscale inhomogeneity or film has been study by applying theory of mismatch dislocation nucleation, the compatible of dislocations and visco-elatic-plastic fracture in heterogeneous materials has been investigated. Taking macroscopic loads, mesoscopic domain switching and phase transformation and microscopic dislocations into consideration, the competition and interaction between dislocation emission and crack propagation induced by domain switching in ferroelectric ceramics subjected to external load and dislocation theory of stress-induced martensitic transformation for a TRIP steel subjected to external load have been studied in multi-scale, respectively. The detail achievements obtained in this paper are expressed as follows.Thermal elastic effect on typical macroscopic cracks of heterogeneous materials is dealt with. Two problems are considered:Anti-plane fracture mechanism of a lip shaped bonded a strained reinforcement layer; Interaction between heat dipole and circular inclusion with an interfacial crack. The analytical expressions of stress field, displacement field, temperature field and stress intensity factor have been derived. The influence of loads, geometric parameters of interfacial crack, properties of materials and shape of inclusion on stress intensity factor is discussed. The results show that the increase of ratio of semi-minor axis and semi-major axis can weak the stress concentration of crack tip. The interfacial stresses can be further intensified or diminished by the adjacent material having a higher or lower stiffness. The increase of arm of heat dipole can increase the stress concentration.The interaction between dislocation/disclination and typical macroscopy defects is dealt with. Four problems are considered:Interaction between a moving screw dislocation and an interfacial crack in two dissimilar orthotropic media; Interaction between edge dislocation and a lip shaped crack; Interaction between a wedge disclination dipole and a circular inclusion with an interfacial crack; Interaction between a screw dislocation dipole and a crack crossing interface. The analytical expressions of dislocation stress field, stress intensity factor and dislocation force have been obtained. The influence of dislocation velocity, geometric parameters of crack and properties of materials on dislocation shielding, anti-shielding effect and dislocation force is discussed. The results show that dislocation moving away from the crack tip can decrease the shielding effect and the minimum strain energy density near the crack tip. The increase of ratio of semi-minor axis and semi-major axis can weak the stress concentration of crack tip. The increase of arm of heat dipole can increase the shielding and anti-shielding effect.The mismatch dislocation nucleation near the interface between nanoscale inhomogeneity or film and matrix is studied. Two problems are considered:Mismatch screw dislocation dipole nucleation near the interface between buried strained nanoscale inhomogeneity and viscoelastic matrix; Mismatch screw dislocation nucleation near the interface between nanoscale film and nano-pore. The analytical expressions of dislocation equilibrium position and critical dimensions of inhomogeneity or film for dislocation nucleation have been derived. The results show that the nucleated dislocations are not always located at the interface. If dimensions of inhomogeneity or film are smaller than the critical values, dislocations can not be nucleated and the strength of structure is improved greatly.The compatible of dislocations and visco-elastic-plastic fracture is dealt with. Two problems are considered:The compatible of screw dislocations and visco-elastic fracture of edge interfacial blunt crack in bimaterial; The compatible of edge dislocations and visco-elastic-plastic fracture of blunt crack. The analytical expressions of stress intensity factor, COD, number of dislocations and dimension of plastic zone are obtained. The influence of viscosity of interface or material on the fracture characteristic and dislocations is discussed. The results show that screw dislocation shielding effect can decrease with relaxing of interface, and the edge dislocation shielding effect can decrease with time lapse. The number of edge dislocations can first increase and then decrease with increase of dimension of dislocation zone, and can decrease with the increase of ratio of semi-minor axis and semi-major axis, and can increase and tend to be a constant with time lapse.The competition and interaction between dislocation emission and crack propagation induced by domain switching in ferroelectric ceramics is investigated. The analytical expressions of boundary equations of switching, stress intensity factor of switching, critical applied electric field of dislocation nucleation, number of emitted dislocations and critical applied electric field of crack propagation are obtained. The influence of dislocation shielding effect on crack tip is discussed. The results show that negative electric field can induce domain switching around crack tip, then the switching can induce dislocation nucleation and emission and drive crack propagation. There is interaction between dislocation emission and crack propagation beside competition, the shield effect of emitted dislocations is remarkable, the fracture toughness can be increased.Dislocation theory of stress-induced martensitic transformation toughening near crack tip in high strength steel is dealt with. The analytical expressions of boundary equations of martensitic transformation zone, stress intensity factor of transformation, absorbed energy of martensitic transformation, critical applied stress intensity factor of dislocation nucleation, number of emitted dislocations and critical applied stress intensity factor of crack propagation are obtained. The effect of shear strain of martensitic transformation on toughening is analyzed. The results show that shear strain of martensitic transformation absorbing energy is the key reason of toughening for high strength steel. The martensitic transformation toughening can be simulated by dislocation nucleation and emission.