Influence of indenter tip geometry on elastic deformation during nanoindentation

Nanoindentation with a Berkovich indenter is commonly used to investigate the mechanical behavior of small volumes of materials. To date, most investigators have made the simplifying assumption that the tip is spherical. In reality, indenter tips are much more complex. Here, we develop a new method to describe the tip shape using the experimentally determined area function of the indenter at small depths (0-100 nm). Our analysis accurately predicts the elastic load-displacement curve and allows the theoretical strength of a material to be determined from pop-in data. Application of our new method to single crystal Cr3Si shows that the predicted theoretical strengths are within 12% of the ideal strength G/2pi, where G is the shear modulus.     

Effective elastic modulus of film-on-substrate systems under normal and tangential contact

Load and depth sensing indentation methods have been widely used to characterize the mechanical properties of the thin film-substrate systems. The measurement accuracy critically depends on our knowledge of the effective elastic modulus of this heterogeneous system. In this work, based on the exact solution of the Green's function in Fourier space, we have derived an analytical relationship between the surface tractions and displacements, which depends on the ratio of the film thickness to contact size and the generalized Dundurs parameters that describe the modulus mismatch between the film and substrate materials. The use of the cumulative superposition method shows that the contact stiffness of any axisymmetric contact is the same as that of a flat-ended punch contact. Therefore, assuming a surface traction of the form of [1−(r/a)²]^−1/2 with radial coordinate r and contact size a, we can obtain an approximate representation of the effective elastic moduli, which agree extremely well with the finite element simulations for both normal and tangential contacts. Motivated by a recently developed multidimensional nanocontact system, we also explore the dependence of the ratio of tangential to normal contact stiffness on the ratio of film thickness to contact radius and the Dundurs parameters. The analytical representations of the correction factors in the relationship between the contact stiffness and effective modulus are derived at infinite friction conditions.     

Nanoindentation of biodegradable cellulose diacetate‐graft‐poly(L‐lactide) copolymers: Effect of molecular composition and thermal aging on mechanical properties

Nanoindentation of cellulose diacetate‐graft‐poly(lactide)s (CDA‐g‐PLLAs) synthesized by ring opening graft copolymerization of L ‐lactide in bulk onto the residual hydroxyl positions on CDA were conducted to investigate the effect of the molecular composition and thermal aging on mechanical properties and creep behavior. Continuous stiffness measurement (CSM) technique was used to obtained hardness and elastic modulus. These material properties were expressed as a mean value from 100 to 300 nm depths and an unloading value at final indentation depth. The hardness and elastic modulus in all CDA‐g‐PLLAs were higher than those in pure CDA, indicating that the introduction of PLLA increases the hardness and elastic modulus. With an increase of crystallinity by thermal aging, the hardness and elastic modulus were increased in both CDA‐g‐PLLA and PLLA. The creep test performed by CSM showed that the creep strain of CDA was decreased by the grafting of PLLA. Thermal aging decreased the creep strain of CDA‐g‐PLLA and PLLA. With an increase of holding time, hardness was decreased, whereas elastic modulus was kept almost constant. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1114–1121, 2007     

Photochemistry of furyl- and thienyldiazomethanes: spectroscopic characterization of triplet 3-thienylcarbene

Photolysis (λ > 543 nm) of 3-thienyldiazomethane (1), matrix isolated in Ar or N(2) at 10 K, yields triplet 3-thienylcarbene (13) and α-thial-methylenecyclopropene (9). Carbene 13 was characterized by IR, UV/vis, and EPR spectroscopy. The conformational isomers of 3-thienylcarbene (s-E and s-Z) exhibit an unusually large difference in zero-field splitting parameters in the triplet EPR spectrum (|D/hc| = 0.508 cm(-1), |E/hc| = 0.0554 cm(-1); |D/hc| = 0.579 cm(-1), |E/hc| = 0.0315 cm(-1)). Natural Bond Orbital (NBO) calculations reveal substantially differing spin densities in the 3-thienyl ring at the positions adjacent to the carbene center, which is one factor contributing to the large difference in D values. NBO calculations also reveal a stabilizing interaction between the sp orbital of the carbene carbon in the s-Z rotamer of 13 and the antibonding σ orbital between sulfur and the neighboring carbon-an interaction that is not observed in the s-E rotamer of 13. In contrast to the EPR spectra, the electronic absorption spectra of the rotamers of triplet 3-thienylcarbene (13) are indistinguishable under our experimental conditions. The carbene exhibits a weak electronic absorption in the visible spectrum (λ(max) = 467 nm) that is characteristic of triplet arylcarbenes. Although studies of 2-thienyldiazomethane (2), 3-furyldiazomethane (3), or 2-furyldiazomethane (4) provided further insight into the photochemical interconversions among C(5)H(4)S or C(5)H(4)O isomers, these studies did not lead to the spectroscopic detection of the corresponding triplet carbenes (2-thienylcarbene (11), 3-furylcarbene (23), or 2-furylcarbene (22), respectively).     

Nanoindentation of Fused Quartz at Loads Near the Cracking Threshold

Experimental Mechanics - Nanoindentation with triangular pyramidal indenters with centerline-to-face angles of 35.3°, 45°, 55°, 65.3° and 75° at loads in the range...     

Size effects and stochastic behavior of nanoindentation pop in

A statistical model for pop in initiated at preexisting dislocations during nanoindentation is developed to explain size-dependent pop-in stresses. To verify theoretical predictions of this model, experiments were performed on single-crystal Mo, utilizing indenter radii that vary by over 3 orders of magnitude. The stress where plastic deformation begins ranges from the theoretical strength in small volumes, to 1 order of magnitude lower in larger volumes. An intermediate regime shows wide variability in the stress to initiate plastic deformation. Our theory accurately reproduces the experimental cumulative probability distributions, and predicts a scaling behavior that matches experimental behavior.     

Association of Molybdenum Ionic Species with Alumina Surface

The adsorption isotherms at 25, 45, and 65 degrees C of molybdenum solutions of concentration ranges between 10(-3) and 3x10(-2) M(Mo) (pH 4-5) on different alumina samples are investigated. The analysis is conducted using a modified Frumkin isotherm which takes a more realistic account of the lateral interaction between adsorbed species and considers that the adsorption takes place on the most basic OH groups on the surface of alumina. The results are discussed in view of the difference in solutions speciation, and the changes in the pH of the remaining supernatant solutions. The solution temperature, PZC of the used aluminas, the configuration of the basic OH groups on their surface, and the pore structure have been shown to intervene effectively. Copyright 2000 Academic Press.     

The correlation of the indentation size effect measured with indenters of various shapes

Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results.