Quasi-continuum Method Of Nano-scale Adhesive Contact And Crack Extension

Studying the special mechanical behavior of nano-scale materials is a complex task that involves the displine of material and physical science. There are three typical and meaningful areas of research in nanoscale. First, mechanical behavior of nano-scale material is quite distinguishive from marco-scale material as a result of anisotropy, adhesive force and the surface energy. These factors are of great importance for the study of nano-scale devices. Sencond, In what way do some material parameters such as the stacking fault energy and the twinning fault energy influence or determine the deformation mechanism of materials. What is the connection between these parameters and mechanical behavior? Third, are some models for marco-scale under the assumption of continnum still suitable for nano-scale models? If not, where is the boundary between applicable and not applicable?In order to shed some light on these three interesting and challenging issues, we study three aspects of FCC or BCC materials using the quasicontinnum method. We first study indentation and retraction processes between Ni indenter and Cu substrate. We also focus on the anisotropic behavior of noncontact between Ni indenter and Cu substrate. Second, the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) are investigated to reveal deformation mechanism of mode II type crack tip of BCC metal tantalum (Ta). Third, we make a detailed research on the different deformation mechanism of mode I type crack tip of Ta crystal under four different crystal orientations. Through careful study we find that:A tip with a radius much larger than those used in MD is chosen to study nanocontact. By examing atomic configurations and the load-depth curve, a large plastic zone is observed during indentation and retraction processes. After deep neck facture, the surface of Cu substrate is severely damaged and plastic deformation in the Cu substrate does not disappear completely.This implies that strong adhesive force might lead to the damage of materials or nano-scale devices during nanocontact. The GPF curve of Cu reveals that the energy barrier (γutf-γsf) required for deformation twinning is smaller than the energy barrierγusf required for the formation of stacking fault. Therefore, deformation twinning tends to be one of the dominant deformation mechanism duing nanocontact. Two different fracture mechanisms are responsible for load jump at different stages. At the initial stage, fracture occurs by atomic rearrangement. As neck elongates, fracture occurs in the middle of Cu neck. Homogeneous shear along one (111) plane over another is the dominant fracture mechanism.Comparing the critical adhesive force (Fc) and the critical contact radius (ac)for Cu neck fracture with JKR model, we find that there is deviation existing between theoretical values and numerical results. The simulation results are roughtly two times larger than the theoretical results.The generalized planar fault energy, including the generalized stacking fault (GSF) and the generalized twinning fault energy (GTF) of BCC metal tantalum (Ta) are investigated. The GSF of Ta reveals that no evident energy minimum is observed in the energy curve. This implies that full dislocations emitt on {112} slip plane rather than partical dislocations. The GTF predicts that the minimum thickness of a metastable twin is four layers and five layered twin is more stable. The incipient twin Ta tends to grow thick once it comes into being. To confirm the significance of the GSF and GTF in revealing incipient plasticity, plastic deformation of crackt tip of single Ta crystal under modeⅡloading is investigated. The results shows that deformation twin and full dislocation along <111> direction on {112} plane are two co-existent mechanisms of crack tip plastic deformation of Ta. The initial four layered twin quickly extends into five layers and much more layers with further loading. A full dislocation emitted into the front of the crack tip on {112} plane. These two plastic deformation mechanisms are well explained by the GTF and the GSF respectively.The deformation mechanisms of initial crack propagation of Ta crystal orientated in four different ways are examined under load modeⅡ. The results distinguish from each other surprisingly. (1) In the case of x[010], y[100] and z[0 01], the initial crack plane has high surface and there are no slip planes. Therefore, the crack changes its original direction and extends in a brittle manner on (110) plane which has a lower surface energy. (2) In the case of x[110],y[110] and z[00 1], no slip plane is available in the front of crack tip and the initial crack plane has low surface. The crack propagagtes along its original plane brittlely when the stress intensity factor is 2.41 K*1c. (3) For the case of x[100], y[011]and z[011], there are two slip planes in the front of crack tip. The crack tip is blunded as two full dislocations are emitted in the direction of [111] and[111]. The effect of blunting is further strengthened by phrase transformation near the crack tip. It is much more difficult for crack to propagate ans the BCC lattice changes into HCP at the crack tip in this case. (4) In the last cases of x[110], y[001]and z[110], the first plastic deformation occurs at 3.29K*1c-Deformation twinning is the most important way of plastic deformation near crack tip. The twinning band becomes wider as load continues and the crack tends to propagate along the grain boundary.Based on the four different way of crack propagation, a parameterξis proposed as the criterion of brittle or ductile fracture. The parameter is not only related with the surface enery of initial crack plane and unstable stacking fault energy but also related with the direction of slip plane. The largerξis, the much likely crack will propagate brittlely. The smallerξis, the crack will propagate in a ductile manner. Our simulation results confirm the validity of the criterion.