Micro-Scale Effect On Damage Of Ductile Materials And Its Mechanism

With the rapid development of Micro Electromechanical System (i.e. MEMS) in recent years, various micro-apparatus and micro-machines have been widely used. A series of micro-mechanical tests and analytic results have already indicated that the mechanical behaviors show strong scale effect when the sample falls within the micron size range. At the micron scale, the strength analyses and structure optimization based on the classical independent-scale constitutive relation usually fail to be efficient. Thus, deep and systemic researches on damage and deformation behavior at the micron scale are of fundamental importance not only in understanding the damage mechanism of solids but also in engineering application.In the present dissertation, the micro-scale effect on damage and deformation behavior is investigated by both the strain gradient theory and the discrete dislocation dynamic modeling. The results from two kinds of methods are complementary with each other, which introduce more information about the subject to us. The main results are shown as follows:Based on the SG strain gradient deformation theory and the infinite model with an isolated spheroidal void, the size and shape effects on void growth in triaxial stress field are carefully investigated. It is found that (1) there exists a"critical void radius", the void is difficult to grow by plastic flow in the matrix material when the equivalent radius of micro-void approach or is lower than the"critical radius"; (2) the"critical radius"is independent of the void shape and the remote stress statue, and approximately equals to the material intrinsic length associated with the stretch strain gradient; (3)the void size effect and shape effect is coupled with each other, generally, the shape effect can enhance the scale effect. In addition, this coupling is closely related to the remote stress triaxiality.Based on the strain gradient deformation theory and the representative volume element (RVE) model, a scale-dependent macroscopic plastic potential of porous material is deduced, which generalizes application of the classical Gurson model to the micron size range. Further analyses show that(1)at a given void volume fraction, the growth rate of micron sized void is lower than that predicated by the traditional R-T model and Gurson model; (2) the yield locus of porous materials expands outwards with the void size decreasing.The effects of particle size and shape on the stress distribution at the particle/matrix interface and within the particle are investigated by employing the scale-dependent strain gradient SG theory to provide a better understanding to the micro-particle reinforcement mechanism. By solving a axial-symmetrical boundary value problem consisting of a infinite solid and an isolated spheriodal particle embedded in an infinite matrix, some interesting results are found as follow: (1) at the micron scale, the smaller the particle is, the higher the stresses at the matrix/inclusion interface and within the particle are; (2) this size effect is more remarkable with decreasing the stress triaxiality and increasing the remote equivalent strain. To reasonably equilibrate the double stress traction at the particle-matrix interface, a new parameter named"interfacial energy density"is introduced. The influence of"interfacial energy density"on the stress distribution is also investigated.A program for discrete dislocation dynamic modeling is developed. Using this program, the growth of an isolated void embedded in an infinite FCC single crystal is investigated. The emphasis is focused on the size effect of void growth and its intrinsic mechanism. The calculation results show that: (1) the expansion of dislocation shear loop and reaching the void surface is main mechanism controlling the void growth in single crystal; (2) the void growth vs. the remote strain curves are continuous and smooth for the larger voids, but there are some steps on the curves for the smaller void, so the internal mechanism controlling the void growth is different for the voids with various sizes; (3)this size effect is closely associated with the dislocation mobility and the number of dislocation sources activated around the void; (4) the discreteness of void growth is inherent and significant for the micron sized void.Based on the well-known Rice-Thomson model, dislocation emission and void growth induced by it are considered for elliptic voids with various sizes and different directions. The results indicate that: (1) there exist a"critical stress", when the applied stress is lower than this"critical stress", dislocations can not be emitted from the void surface, while when the applied stress is larger than the"critical stress", the dislocation emission is activated and can introduce the nano-void to grow suddenly; (2) within the nanometer size range, the dislocation emission"critical stress"for elliptic void is size dependent, i.e. the smaller the void is, the higher the critical stress is, and at a given equivalent radius, the critical stress for the elliptic voids is lower than that for the circular voids; (3) the dislocation emission and the void growth induced by it are closely related to the direction angle between the slip plane and the axis of the elliptic void.By employing the 2D discrete dislocation dynamic modeling, the stress distribution in the vicinity of an isolate circular particle embedded in an infinite FCC matrix is investigated, and the void nucleation mechanism is discussed. The results are shown that: (1) due to the dislocation obstruction and pile-ups near the interface, there are a series of peaks for the interfacial normal stress at the particle-matrix interface; (2) the number of interfacial stress peak and the magnitude of these peaks increases with increasing the inclusion radius. These results indicate that, within the micron scale range, the void nucleation at the matrix/particle interface seems to be related to the number and magnitude of the interfacial stress peak. According to this assumption, some experiment observations can be explained, i.e. the smaller the particle is, the more difficult the void nucleation is.