Strain Gradient Theory Studies On Mechanical Behaviors Of Micro And Nano Materials

The mechanic behavior of micro/nano-sized material is size-dependent; one dominant source is the interface constraint which results in the non-uniform deformation filed, the size-dependent phenomena displays when the characteristic wavelength of the non-uniform deformation field is the same order as the intrinsic material length. The interface constraint and its corresponding size-dependent mechanism are the important research concerns in the field of micro/nano-plasticity mechanics, and have theoretical importance.One side, the strain gradient theories succeeded in describing the effect of non-uniform deformation fields on the mechanical response of the micro/nano sized materials, however, the reasonable considerations of interface constraint within the strain gradient framework are still not satisfying, thus there are still some limitations in explaining the size-dependent mechanical behavior resulting from the interface constraint. It's necessary to develop a strain gradient model within the strain gradient plasticity framework by treating the interface in different ways with the detailed interface deformation characteristics and mechanisms.On the other side, the strain gradient theories are mostly phenomenological, and didn't give a careful and deep consideration for the microstructure evolution and underlying deformation mechanism related with the plastic deformation; meanwhile, there are no clear physical meanings to be endowed to intrinsic material length scales and microscopic stress balance equation. It's an open issue to establish a new strain gradient plasticity theory which should be physically reasonable and enriched with underlying consideration of microstructure related deformation mechanisms.In the present dissertation, we address the above two sides of strain gradient plasticity research. The main research contents and results are summarized as follows: 1,Three different interface models are proposed within the strain gradient theory framework depending on the deformation characteristics of the micro/nano-szied materials. In the compressed single crystalline micropillar, the interfaces lie between the slip layers which are in different deformation status due to asynchronous plastic yielding in the micropillar and play a role as the transition interfaces. In the compressed bi-crystalline micropillar, the grain boundary play a role as barrier to the movement of dislocations, and the interface energy is endowed to the grain boundary within the strain gradient plasticity framework, then the interfacial yielding rules are developed. In nanocrystalline solids, grain boundaries occupy significant volume fraction of the material, thus are treated as a separate phase endowed with balance equations and constitutive equations.2,Based on the strain gradient multilayer model, the "strain bursts" phenomena observed in single crystalline micropillar compression experiments are investigated. The higher-order stress, which is discontinuous at the interface between a plastic layer and its neighboring elastic layer but continuous when two neighboring layers begin deforming plastically, is the underlying mechanism responsible for the strain burst. The transition from discontinuity to continuity of the higher-order stress across the internal boundary between two neighboring layers results in the strain burst. Furthermore, the stress-strain response of the single crystal micropillar is dispersed; the strain gradient multilayer model could also capture the upper and lower bounds of the stress-strain curves.3,The compression behavior of the bi-crystalline micropillar is interpreted by considering the interface energy term in the grain plasticity framework. Grain boundary is the interface where higher order stress experiences a jump, thus it is modeled using interface energy, an "interfacial" yield criterion is deduced to describe the yielding behavior of grain boundary as a result. The tri-linear stress-strain curves obtained from the theory fit in well with experimental data of bi-crystal micropillars, and display two distinct "knee" at whichthe grain and grain boundary begin to yield.4,The mechanical behavior of the nanocrystalline is analyzed using the strain gradient model treating grain boundaries as a separate phase with a finite thickness. Grain boundary phase and grain phase interchange their role to accommodate deformation as the grain size varies from microsclae to nanoscale. Grain boundary phases could be either the obstacles or passage of the plastic deformation depending on the ratio of grain boundary thickness to the grain size. The "normal" to "abnormal" Hall-Petch transition is successfully captured by the present model; the critical grain size at which this transition occurs is also predicted with good agreement with the experiments.5,Based on the dislocation self-energy and interaction energy, a thermodynamics consistent work-conjugated higher-order strain gradient crystal plasticity theory is developed. The evolution of self energy based on rectangular dislocation loop is related with the image stress and self stress, and the interaction energy enables the back stress to be deduced. The final microscopic stress balance equation derived from virtual power principle describes the plastic flow of the crystalline material in separate slip system. It should be noted that the multiple intrinsic length scales introduced in present model are related with the characteristic sizes of micro structures in the material, so have specific physical meanings. Furthermore, the present dislocation energy based work-conjugated strain gradient theory is compared with Zbib's three-dimensional discrete dislocation dynamics (3D-DDD) framework and Evers-Bayley models of non-work-conjugated type, and correspondence between them are revealed.