Erik G. Herbert

On the measurement of stress–strain curves by spherical indentation

Abstract It has been proposed that with the appropriate models, instrumented indentation test (IIT) data can be reduced to yield the uniaxial stress–strain behavior of the test material. However, very little work has been done to directly compare the results from uniaxial tension and spherical indentation experiments. In this work, indentation and uniaxial tension experiments have been performed on the aluminum alloy 6061-T6. The purpose of these experiments was to specifically explore the accuracy with which the analytical models can be applied to IIT data to predict the uniaxial stress–strain behavior of the aluminum alloy. Despite not being able to reproduce the physical shape of the uniaxial stress–strain curve, the results do indicate that spherical indentation can be successfully used to establish an engineering estimate of the elastic modulus and yield strength of 6061-T6.

Nanoindentation and the dynamic characterization of viscoelastic solids

Using a high-damping thermoplastic as a standard reference material, the purpose of this work is to compare measured values of the complex modulus as determined by dynamic nanoindentation and dynamic mechanical analysis (DMA). Experiments were performed at approximately 22 °C and seven frequencies over the range 1-50 Hz. The indentation measurements were performed using a 103 μm diameter flat punch and a newly developed test method that optimizes the accuracy and precision of the measured stiffness and damping. As determined by dynamic nanoindentation, values of the storage modulus and loss factor (tangent delta) ranged from 4.2 to 10.2 MPa, and 0.28 to 1.05, respectively. Over the range 1-25 Hz, DMA confirmed the nanoindentation results to within 15% or better. Collectively, these data and the testing methods used to generate them should help future investigators make more accurate and precise measurements of the dynamic properties of viscoelastic solids using nanoindentation.

Increasing duration of type 1 diabetes perturbs the strength-structure relationship and increases brittleness of bone.

Type 1 diabetes (T1DM) increases the likelihood of a fracture. Despite serious complications in the healing of fractures among those with diabetes, the underlying causes are not delineated for the effect of diabetes on the fracture resistance of bone. Therefore, in a mouse model of T1DM, we have investigated the possibility that a prolonged state of diabetes perturbs the relationship between bone strength and structure (i.e., affects tissue properties). At 10, 15, and 18 weeks following injection of streptozotocin to induce diabetes, diabetic male mice and age-matched controls were examined for measures of skeletal integrity. We assessed 1) the moment of inertia (I(MIN)) of the cortical bone within diaphysis, trabecular bone architecture of the metaphysis, and mineralization density of the tissue (TMD) for each compartment of the femur by micro-computed tomography and 2) biomechanical properties by three-point bending test (femur) and nanoindentation (tibia). In the metaphysis, a significant decrease in trabecular bone volume fraction and trabecular TMD was apparent after 10 weeks of diabetes. For cortical bone, type 1 diabetes was associated with decreased cortical TMD, I(MIN), rigidity, and peak moment as well as a lack of normal age-related increases in the biomechanical properties. However, there were only modest differences in material properties between diabetic and normal mice at both whole bone and tissue-levels. As the duration of diabetes increased, bone toughness decreased relative to control. If the sole effect of diabetes on bone strength was due to a reduction in bone size, then I(MIN) would be the only significant variable explaining the variance in the maximum moment. However, general linear modeling found that the relationship between peak moment and I(MIN) depended on whether the bone was from a diabetic mouse and the duration of diabetes. Thus, these findings suggest that the elevated fracture risk among diabetics is impacted by complex changes in tissue properties that ultimately reduce the fracture resistance of bone.

On the measurement of yield strength by spherical indentation

Over the past 10 years, a number of investigators have proposed methods to measure the yield strength of metals using instrumented indentation experiments performed with a sphere [Ma et al., J. Appl. Phys. 94 288 (2003); Cao and Lu, Acta Mater. 52 4023 (2004); Yu and Blanchard, J. Mater. Res. 11 2358 (1996); Field and Swain, J. Mater. Res. 10 101 (1995)]. Most of these proposed methods have yet to be rigorously verified experimentally. The objective of this work is to contribute to experimental verification by testing four contemporary models against their ability to accurately determine the yield strength of the aluminium alloy 6061-T6 using the smallest sphere commercially available. The four models selected for this review are those in the references mentioned above. The tensile and indentation samples were taken from the same 3.175-mm thick sheet and the surface of the indentation sample was given the best possible mechanical polishing. The indentation experiments were performed using a 90° diamond cone with a mechanically polished radius of 385 nm. The procedures proposed by Ma et al. and Cao and Lu were inconsistent with experimental observations and could not be implemented. Yu and Blanchards model overestimated the yield strength by approximately 55%. Field and Swains procedure overestimated the tensile flow curve by roughly 40%, which precluded obtaining a meaningful estimate of the yield strength. Among the most likely explanations for these surprisingly poor results are the effects of roughness and contaminants on the surface, and the possibility of an indentation size effect.

A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings

The fracture toughness of thin ceramic films is an important material property that plays a role in determining the in-service mechanical performance and adhesion of this important class of engineering materials. Unfortunately, measurement of thin film fracture toughness is affected by influences from the substrate and the large residual stresses that can exist in the films. In this paper, we explore a promising new technique that potentially overcomes these issues based on nanoindentation testing of micro-pillars produced by focused ion beam milling of the films. By making the pillar diameter approximately equal to its length, the residual stress in the upper portion of the pillar is almost fully relaxed, and when indented with a sharp Berkovich indenter, the pillars fracture by splitting at reproducible loads that are readily quantified by a sudden displacement excursion in the load displacement behaviour. Cohesive finite element simulations are used for analysis and development of a simple relationship between the critical load at failure, pillar radius and fracture toughness for a given material. The main novel aspect of this work is that neither crack geometries nor crack sizes need to be measured post test. In addition, the residual stress can be measured at the same time with toughness, by comparison of the indentation results obtained on the stress-free pillars and the as-deposited film. The method is tested on three different hard coatings created by physical vapour deposition, namely titanium nitride, chromium nitride and a CrAlN/Si3N4 nanocomposite. Results compare well to independently measured values of fracture toughness for the three brittle films. The technique offers several benefits over existing methods.

On the Measurement of Stress-Strain Curves by Spherical Indentation

It has been proposed that with the appropriate models, instrumented indentation test (IIT) data can be reduced to yield the uniaxial stress-strain behavior of the test material. However, very little work has been done to directly compare the results from uniaxial tension and spherical indentation experiments. In this work, indentation and uniaxial tension experiments have been performed on the aluminum alloy 6061-T6. The purpose of these experiments was to specifically explore the accuracy with which the analytical models can be applied to IIT data to predict the uniaxial stress-strain behavior of the aluminum alloy.