Criterion of mechanical instabilities for dislocation structures

To understand the nature of mechanical instabilities of dislocation structures, which plays a central role, for example, in determining the plastic behavior and fatigue in crystalline metals, it is essential to investigate a critical condition in which a dislocation structure collapses. A criterion for the mechanical instability of arbitrary dislocation structures is proposed in this paper. According to the criterion, the mechanical instability can be described by the positiveness of the minimum eigenvalue of the Hessian matrix, which is composed by the second-order differential of potential energy of the system with respect to the dislocation coordinates. In addition, the collapse mode can be simultaneously determined by the eigenvector of the minimum eigenvalue. We applied the proposed criterion to the veins and dislocation walls under external loading, and it successfully describes the onset of instabilities and the corresponding collapse modes, regardless of the difference in structures and sizes. This success in the criterion paves the way to address the mechanical instability issues on more complex dislocation structures

Experimental characterization at nanoscale of single crystal silicon fracture toughness

The work reviews some preliminary recent micromechanical tests aimed at the evaluation of the fracture toughness of silicon. Pre-cracked nano specimens and alternatively notched nano specimens combined with the theory of critical distances (TCD) are compared. The results show that the fracture toughness of silicon is approximately 1 MPa·m0.5, regardless of the procedure involved (i.e., pre-cracked samples or TCD). This value agrees with macro counterpart, i.e., 0.75-1.08 MPa·m0.5, and therefore the KIC is independent of the size and crystal orientation. However, by employing the TCD, the accurate control of the final crack tip which is currently very challenging, is overcome by using notched specimens. Additionally, the results give information about the crack propagation at the nanoscale. It seems that although the specimen axis deviates from the (011), the crack propagates along the cleavage plane (011) and the process develops very fast by breaking covalent bond at the crack tip. A brief discussion on beyond the breakdown of continuum theory and challenges toward nanometer scale fracture mechanics concludes the paper

Experimental characterization at nanoscale of single crystal silicon fracture toughness

The work reviews some preliminary recent micromechanical tests aimed at the evaluation of the fracture toughness of silicon. Pre-cracked nano specimens and alternatively notched nano specimens combined with the theory of critical distances (TCD) are compared. The results show that the fracture toughness of silicon is approximately 1 MPam0.5, regardless of the procedure involved (i.e., pre-cracked samples or TCD). This value agrees with macro counterpart, i.e., 0.75-1.08 MPa෷m0.5, and therefore the KIC is independent of the size and crystal orientation. However, by employing the TCD, the accurate control of the final crack tip which is currently very challenging, is overcome by using notched specimens. Additionally, the results give information about the crack propagation at the nanoscale. It seems that although the specimen axis deviates from the (011), the crack propagates along the cleavage plane (011) and the process develops very fast by breaking covalent bond at the crack tip. A brief discussion on beyond the breakdown of continuum theory and challenges toward nanometer scale fracture mechanics concludes the pape

Cu/Si interface fracture due to fatigue of copper film in nanometer scale

In order to investigate the fatigue behavior of metals in nanoscale, a cyclic bending experiment is carried out using a nano-specimen. The specimen includes a copper film with a thickness of 20 nm constrained by highly rigid materials, which yields a high strain region with a size of a few nanometers near the interface edge. The specimen broke before the maximum load in the 7th cycle under fatigue (load range of 18 μN). The load-displacement curve shows nonlinear behavior and a distinct hysteresis loop, indicating plasticity in the Cu film. Reverse yielding appearing after the 2nd cycle suggests the development of a cyclic substructure in the Cu film. The cumulative plastic strain in the Cu film at fracture is more than three times larger than that under monotonic loading. These results indicate that the specimen breaks owing to fatigue of the Cu film on the nanoscale

Delamination crack initiation from copper/silicon nitride interface edge with nanoscale singular stress field

In order to investigate delamination crack initiation from an interfacial edge in nanoscale component with the singular stress field, we conduct mechanical experiments using four kinds of cantilever specimens with the nanoscale singular stress field at the copper/silicon nitride interface. The results reveal that regardless of the specimen dimensions, the critical magnitude of the plastic stress intensity parameter, K[interface edge] (C), is constant (112 MPa m[0.179]) within the singular stress field range of approximately 25 nm. This indicates that in the nano-sized component, a delamination crack initiation is dominated by a nanoscale singular stress field near the interface edge

Cohesive zone criterion for cracking along the Cu/Si interface in nanoscale components

Crack initiation and propagation along the Cu/Si interface in multilayered films (Si/Cu/SiN) with different thicknesses of the Cu layer (20 and 200 nm) are experimentally investigated using a nano-cantilever and millimeter-sized four-point bending specimens. To examine the cohesive zone model (CZM) criterion for interfacial delamination along the Cu/Si interface in nanoscale stress concentration, an exponential type of CZM is utilized to simulate the observed delamination processes using the finite element method. After the CZM parameters for the Cu/Si interface are calibrated by experiment, interface cracking in other experiments is predicted. This indicates that the CZM criterion is universally applicable for describing cracking along the interface regardless of specimen dimensions and film thickness which include the differences in plastic behavior and residual stress. The CZM criterion can also predict interfacial cracking along Cu/Si interfaces with different stress singularities

Nonsingular Stress Distribution of Edge Dislocations near Zero-Traction Boundary

Among many types of defects present in crystalline materials, dislocations are the most influential in determining the deformation process and various physical properties of the materials. However, the mathematical description of the elastic field generated around dislocations is challenging because of various theoretical difficulties, such as physically irrelevant singularities near the dislocation-core and nontrivial modulation in the spatial distribution near the material interface. As a theoretical solution to this problem, in the present study, we develop an explicit formulation for the nonsingular stress field generated by an edge dislocation near the zero-traction surface of an elastic medium. The obtained stress field is free from nonphysical divergence near the dislocation-core, as compared to classical solutions. Because of the nonsingular property, our results allow the accurate estimation of the effect of the zero-traction surface on the near-surface stress distribution, as well as its dependence on the orientation of the Burgers vector. Finally, the degree of surface-induced modulation in the stress field is evaluated using the concept of the L2-norm for function spaces and the comparison with the stress field in an infinitely large system without any surface

Evaluation on plastic deformation property of copper nano-film by nano-scale cantilever specimen

We investigate the elasto-plastic deformation properties of a 20-nm-thick copper (Cu) thin film. A nano-scale cantilever specimen is fabricated from multilayer thin films, where the Cu thin film is sandwiched between a silicon nitride layer and a silicon substrate. During bending, the load, P, and displacement, d, are carefully monitored using an electron microscope, and a distinct non-linearity is observed. The plastic constitutive equation of the Cu thin film, which is assumed to obey a power hardening law (σ = Rεn (σ > σy)), is inversely derived by finite element method fitting the experimental results. The residual stress in each layer is experimentally examined, and the effect is included in the inverse analysis. We obtain σ = 3316ε0.29 [MPa] and a yield stress of 765 MPa for the Cu film. The yield stress is about 10 times higher than that of the bulk, and the exponent is also larger. Moreover, inverse analysis based on the bending experiment data, without considering the residual stress, gives a good approximation of the plastic law. This is because the plastic deformation preferentially takes place at the top and bottom surfaces, where the residual stress is relieved during fabrication of the specimen