Determination of Mechanical and Fracture Properties of Silicon Single Crystal from Indentation Experiments and Finite Element Modelling

It is well-known that cracks are observed around the impression during indentation of brittle materials. The cracks inception depends on load conditions, material and indenter geometry. The paper aims to use experimental micro-indentation data, FE simulations with cohesive zone modelling, and an optimisation procedure to determine the cohesive energy density of silicon single crystals. While previous studies available in the literature, which use cohesive zone finite element techniques for simulation of indentation cracks in brittle solids, tried to improve methods for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, this study focuses on the evaluation of the cohesive energy density 2Γ from which the material toughness can be easily determined using the well-known Griffith-Irwin formula. There is no need to control the premise of the linear fracture mechanics that the cohesive zone is much shorter than the crack length. Hence, the developed approach is suitable also for short cracks for which the linear fracture mechanics premise is violated.

Revealing the nanoindentation response of a single cell using a 3D structural finite element model

Changes in the apparent moduli of cells have been reported to correlate with cell abnormalities and disease. Indentation is commonly used to measure these moduli; however, there is evidence to suggest that the indentation protocol employed affects the measured moduli, which can affect our understanding of how physiological conditions regulate cell mechanics. Most studies treat the cell as a homogeneous material or a simple core–shell structure consisting of cytoplasm and a nucleus: both are far from the real structure of cells. To study indentation protocol-dependent cell mechanics, a finite element model of key intracellular components (cortex layer, cytoplasm, actin stress fibres, microtubules, and nucleus) has instead been developed. Results have shown that the apparent moduli obtained with conical indenters decreased with increasing cone angle; however, this change was less significant for spherical indenters of increasing radii. Furthermore, the interplay between indenter geometry and intracellular components has also been studied, which is useful for understanding structure-mechanics-function relationships of cells.

CCM pilot study overview: geometrical measurement of the Rockwell diamond indenter

This paper describes an overview of the capability of the NMIs that participated on the CCM Pilot Study measurement systems, conducted by the CIPM/CCM/Working Group on Hardness, to characterize the Rockwell hardness diamond indenter geometry, by measuring the included cone angle, the straightness of the generatrix, the spherical tip radius, the deviation of the local radius and the tilt angle. <br />Nine NMIs took part in this study: INMETRO (Brazil); INRiM (Italy); KRISS (South Korea); NIM/PR (China); NIMT (Thailand); NIST (USA); PTB (Germany); TUBITAK UME (Turkey); VNIIFTRI (Russia), where INMETRO (Brazil) served as pilot laboratory.

Nanoindentation of Aluminum Single Crystals: Experimental Study on Influencing Factors

Results from nanoindentation of aluminum single crystals deliver valuable information as model systems for understanding technical aluminum alloys. The effect of the crystal orientation and the azimuthal indenter orientation on indentation hardness and modulus was studied by Vickers indentation (max. load 10 mN) on single crystal surfaces with (100), (110), and (111) orientations. The average indentation hardness varied, depending on the crystallographic orientation, by 1.8%. The anisotropy of the elastic modulus (1.1% of the average modulus) is lowered (indentation averaging effect). This is predicted by explicit approximation of the contact problem (conical indenter, orthotropic material). It was found that indentation hardness and modulus vary periodically with the azimuthal indenter orientation on (100)- and (110)-oriented surfaces (relative amplitude of 1.8% for indentation hardness and 2.6% of the modulus). This is attributed to the combined effect of the indenter geometry and crystal symmetry. For the first time, this effect was quantified for aluminum single crystals.

Pre-stress of actin cortices is important for the viscoelastic response of living cells

Shape, dynamics, and viscoelastic properties of eukaryotic cells are primarily governed by a thin, reversibly cross-linked actomyosin cortex located directly beneath the plasma membrane. We obtain time-dependent rheological responses of fibroblasts and MDCK II cells from deformation-relaxation curves using an atomic force microscope to access the dependence of cortex fluidity on pre-stress. We introduce a viscoelastic model that treats the cell as a composite shell and assumes that relaxation of the cortex follows a power law giving access to cortical pre-stress, area compressibility modulus, and the power law (fluidity) exponent. Cortex fluidity is modulated by interfering with myosin activity. We find that the power law exponent of the cell cortex decreases with increasing intrinsic pre-stress and area compressibility modulus, in accordance with previous finding for isolated actin networks subject to external stress. Extrapolation to zero tension returns the theoretically predicted power law exponent for transiently cross-linked polymer networks. In contrast to the widely used Hertzian mechanics, our model provides viscoelastic parameters independent of indenter geometry and compression velocity.

Hardness–Yield Strength Relationships in Al-Zn-Mg(-Cu) Alloys

Mean pressure developed during Vickers and Rockwell hardness testing of Al-Zn-MgCualloys is reviewed. Relationships between mean pressure and yield strength are introduced for these alloys by using both Vickers and Rockwell hardness data from the literature. Results have shown that the slope of the mean pressure–yield strength relationships is 0.355 for Vickers tests and 0.264 for Rockwell B tests. The y-intercepts calculated for best fits are all negative, implying that the representative strains in both tests have exceeded the yield strain. Results also have indicated that mean pressure is affected by the indenter geometry and therefore is not a universal hardness number.

The influence of upper-plate advance and erosion on overriding plate deformation in orogen syntaxes

Focused, rapid exhumation of rocks is observed at some orogen syntaxes, but the driving mechanisms remain poorly understood and contested. In this study, we use a fully coupled thermomechanical numerical model to investigate the effect of upper-plate advance and different erosion scenarios on overriding plate deformation. The subducting slab in the model is curved in 3-D, analogous to the indenter geometry observed in seismic studies. We find that the amount of upper-plate advance toward the trench dramatically changes the orientation of major shear zones in the upper plate and the location of rock uplift. Shear along the subduction interface facilitates the formation of a basal detachment situated above the indenter, causing localized rock uplift there. We conclude that the change in orientation and dip angle set by the indenter geometry creates a region of localized uplift as long as subduction of the down-going plate is active. Switching from flat (total) erosion to more realistic fluvial erosion using a landscape evolution model leads to variations in rock uplift at the scale of large catchments. In this case, deepest exhumation again occurs above the indenter apex, but tectonic uplift is modulated on even smaller scales by lithostatic pressure from the overburden of the growing orogen. Highest rock uplift can occur when a strong tectonic uplift field spatially coincides with large erosion potential. This implies that both the geometry of the subducting plate and the geomorphic and climatic conditions are important for the creation of focused, rapid exhumation.