W. W. Gerberich

Interpretations of Indentation Size Effects

For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly created surface and plastic strain energy dissipation. Also, the contact surface to plastic volume ratio was nearly constant for a range of shallow depths. Based on the above, an analytical model of hardness versus depth provides a satisfactory fit to the experimental data and correlates well with embedded atom simulations. @DOI: 10.1115/1.1469004#

Superhard silicon nanospheres

Abstract Successful deposition and mechanical probing of nearly spherical, defect-free silicon nanospheres has been accomplished. The results show silicon at this length scale to be up to four times harder than bulk silicon. Detailed measurements of plasticity evolution and the corresponding hardening response in normally brittle silicon is possible in these small volumes. Based upon a proposed length scale related to the size of nanospheres in the 20– 50 nm radii range, a prediction of observed hardnesses in the range of 20– 50 GPa is made. The ramifications of this to computational materials science studies on identical volumes are discussed.

Deconfinement leads to changes in the nanoscale plasticity of silicon

Silicon crystals have an important role in the electronics industry, and silicon nanoparticles have applications in areas such as nanoelectromechanical systems, photonics and biotechnology. However, the elastic-plastic transition observed in silicon is not fully understood; in particular, it is not known if the plasticity of silicon is determined by dislocations or by transformations between phases. Here, based on compression experiments and molecular dynamics simulations, we show that the mechanical properties of bulk silicon and silicon nanoparticles are significantly different. We find that bulk silicon exists in a state of relative constraint, with its plasticity dominated by phase transformations, whereas silicon nanoparticles are less constrained and display dislocation-driven plasticity. This transition, which we call deconfinement, can also explain the absence of phase transformations in deformed silicon nanowedges. Furthermore, the phenomenon is in agreement with effects observed in shape-memory alloy nanopillars, and provides insight into the origin of incipient plasticity.

Temperature effects on fatigue crack growth in polycarbonate

The fatigue behaviour of a high strength thermoplastic, polycarbonate, has been investigated as a function of temperature. Fatigue crack growth properties were measured in the temperature range of 100 to 373 K and were analysed using a fracture mechanics approach. Fatigue behaviour was found to be related to the fracture toughness of the material. This correlation with fracture toughness was used to develop an empirical model based on the toughness for describing the effect of temperature on fatigue crack growth, and to consider fatigue in terms of the secondary losses of the polymer.

Correlations of the craze profile in PMMA with Dugdale's plastic zone profile

The craze opening profile in PMMA has been determined as a function of stress intensity using interference optics and a special wedge loading device. An attempt was made to correlate the craze profile with the corresponding parameters (crack opening displacement and plastic zone length) predicted by the Dugdale model. Over the mid-range of stress intensities (KI=0.4 to 1.0 MPa m1/2), samples which were annealed after precracking were found to exhibit a profile similar in shape but smaller than that predicted by the Dugdale model. The lower limit of this range marks the critical stress intensity for crazing in PMMA. Both the craze length and the opening at the craze-crack interface increase with increasing stress intensity and, due to strain-hardening of the craze material, reach maximum values of about 40μm and 3μm respectively atKI=1.0 MPa m1/2. Experimental uncertainties cannot account for the profile difference and it is therefore concluded that the Dugdale model is not fully adequate to describe craze geometries in PMMA. The discrepency between the Dugdale model and the experimental data is suggested to be due to either fibril strain-hardening and/or the formation of a plane strain plastic zone ahead of the craze.

Smaller is tougher

“Smaller is stronger” is now a tenet generally consistent with the predominance of evidence. An equally accepted tenet is that fracture toughness almost always decreases with increasing yield strength. Can “smaller is tougher” then be consistent with these two tenets? It is taught in undergraduate engineering courses that one design parameter that allows for both increased strength and fracture toughness is reduced grain size. The present study on the very brittle semiconductor silicon proves this exception to the rule and demonstrates that smaller can be both stronger and tougher. Three nanostructures are considered theoretically and experimentally: thin films, nanospheres, and nanopillars. Using a simple work per unit fracture area approach, it is shown at small scale that toughness is inversely proportional to the square root of size. This is supported by experimental evidence from in situ electron microscopy nanoindentation at length scales of less than a micron. It is further suggested that dislocation shielding can explain both strength and toughness increases at the small scales.

Prediction of interfacial crack path: a direct boundary integral approach and experimental study

This paper presents the development of a higher-order direct boundary integral-displacement discontinuity method for crack propagation in layered elastic materials. The method is based on the dual boundary integral equations of linear elasticity which are solved by means of a quadratic boundary element formulation. The analytical solution for a point force within a bonded half-plane region is used to derive the kernel functions of the boundary integral equations. Square-root displacement-discontinuity elements are used to model the crack tips, and stress intensity factors may be computed using the numerically predicted values of the displacement discontinuity components at the midpoints of these crack-tip elements. An algorithm based on the maximum tensile-stress criterion is then developed and incorporated into the boundary element model to predict the paths of cracks propagating in layered elastic materials.In the experimental part of this study, crack profiles for straight-through-cracked, compact-tension specimens of the anodically bonded silicon/Pyrex glass system are measured by profilometry. The plane strain prediction of the crack-propagation path is compared with the experimentally measured crack profiles. Consistent with the prediction, the interfacial crack is observed to kink away from the strong, anodically-bonded interface and propagate into the more compliant glass layer. The predicted initial kink angle of 26° agrees very well with the average measured value of 28°. The measured path of the crack is also in very good agreement with the predicted path over about the first 120 microns of crack growth with increasing deviation observed beyond that.

Toughness, fracture markings, and losses in bisphenol-A polycarbonate at high strainrate

As-received and heat-treated specimens of bisphenol-A polycarbonate were impacted at temperatures ranging from −196 to +100° C. The critical stress intensity has been calculated for the as-received case from the impact energy data by making a strain-rate correction. To make this correction, the time-temperature superposition principle has been applied to existing dynamic mechanical measurements of the storage modulus and loss modulus (tan δ). Critical stress intensity values of 2.2 to 3.9 MPa m1/2 were found to be comparable with those obtained from instrumented impact and low strain-rate test techniques. Resulting fracture surfaces of the specimens were studied with the scanning electron microscope. Specifically, the morphology of the regions in which sharp striations were present was investigated and the width of the striations have been reported as a function of testing temperature for both as-received and heat-treated cases. There appears to be a direct correlation between the strain-energy release rate, the stress intensity, the striation spacing and the loss curve (tan δ) for the as-received case.

An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events

Small volume deformation can produce two types of plastic instability events. The first involves dislocation nucleation as a dislocation by dislocation event and occurs in nanoparticles or bulk single crystals deformed by atomic force microscopy or small nanoindenter forces. For the second instability event, this involves larger scale nanocontacts into single crystals or their films wherein multiple dislocations cooperate to form a large displacement excursion or load drop. With dislocation work, surface work, and stored elastic energy, one can account for the energy expended in both single and multiple dislocation events. This leads to an energy balance criterion which can model both the displacement excursion and load drop in either constant load or fixed displacement experiments. Nanoindentation of Fe-3% Si (100) crystals with various oxide film thicknesses supports the proposed approach.

Molecular dynamics simulation of delamination of a stiff, body-centered-cubic crystalline film from a compliant Si substrate

Compliant substrate technology offers an effective approach to grow high-quality multilayered films, of importance to microelectronics and microelectromechanical systems devices. By using a thin, soft substrate to relieve the mismatch strain of an epitaxial film, the critical thickness of misfit dislocation formation in the overlayer is effectively increased. Experiments have indicated that stiff films deposited onto Si substrates can delaminate at the interface. However, the atomic mechanisms of the deformation and the fracture of the films have not been well studied. Here, we have applied molecular dynamics simulations to study the delamination of a stiff body-centered-cubic crystalline film from a compliant Si substrate due to tensile loading. The observed mechanical behavior is shown to be relatively independent of small changes in temperature, loading rate, and system size. Fracture occurs at the interface between the two materials resulting in nearly atomically clean surfaces. Dislocations are seen ...