Experimental design for uniaxial tensile measurements at the microscale

Bone’s unique combination of mechanical properties like strength, stiffness, toughness and low weight are the result of its complex hierarchical structure spanning several length scales. Despite extensive research on bone, there is still a lack of understanding on how its micromechanical behavior relates to its macroscopic failure behavior. While recent research has mostly utilized microcompression and nanoindentation, pure tensile testing at the lamellar level has not yet been reported. Nevertheless, critical failure events in bone are often attributed to tensile stresses. In this study a tensile experiment is designed using an in-situ micromechanical testing platform (Alemnis AG, Switzerland). The setup consists of a translatable silicon gripper driven by a piezo motor and a movable sample stage mounted atop a load cell. The setup is compact and can be installed within an electron microscope for in-situ testing. Please click Additional Files below to see the full abstract

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future

Microtensile properties and failure mechanisms of cortical bone at the lamellar level.

Bone features a remarkable combination of toughness and strength which originates from its complex hierarchical structure and motivates its investigation on multiple length scales. Here, in situ microtensile experiments were performed on dry ovine osteonal bone for the first time at the length scale of a single lamella. The micromechanical response was brittle and revealed larger ultimate tensile strength compared to the macroscale (factor of 2.3). Ultimate tensile strength for axial and transverse specimens was 0.35 ± 0.05 GPa and 0.13 ± 0.02 GPa, respectively. A significantly greater strength anisotropy relative to compression was observed (axial to transverse strength ratio of 2.7:1 for tension, 1.3:1 for compression). Fracture surface and transmission electron microscopic analysis suggested that this may be rationalized by a change in failure mode from fibril-matrix interfacial shearing for axial specimens to fibril-matrix debonding in the transverse direction. An improved version of the classic Hashin's composite failure model was applied to describe lamellar bone strength as a function of fibril orientation. Together with our experimental observations, the model suggests that cortical bone strength at the lamellar level is remarkably tolerant to variations of fibrils orientation of about ±30°. This study highlights the importance of investigating bone's hierarchical organization at several length scales for gaining a deeper understanding of its macroscopic fracture behavior. STATEMENT OF SIGNIFICANCE: Understanding bone deformation and failure behavior at different length scales of its hierarchical structure is fundamental for the improvement of bone fracture prevention, as well as for the development of multifunctional bio-inspired materials combining toughness and strength. The experiments reported in this study shed light on the microtensile properties of dry primary osteonal bone and establish a baseline from which to start further investigations in more physiological conditions. Microtensile specimens were stronger than their macroscopic counterparts by a factor of 2.3. Lamellar bone strength seems remarkably tolerant to variations of the sub-lamellar fibril orientation with respect to the loading direction (±30°). This study underlines the importance of studying bone on all length scales for improving our understanding of bone's macroscopic mechanical response

Tension-compression strength asymmetry of bone extracellular matrix

Bone features a hierarchical architecture, as a result of which antagonistic properties like toughness and strength are achieved. On the macroscale, bone exhibits a distinct anisotropy and loading mode dependence, with a considerably lower strength in tension compared to compression. To better understand the mechanisms leading to this behavior, anisotropic tensile yield and failure properties of ovine bone were characterized on the length scale of a single lamella (3-7 μm) and then compared to compression data for the same scale [1]. In situ microtensile experiments were carried out using an improved testing methodology, developed to overcome typical issues encountered during small scale testing related to sample fabrication, sample handling and misalignment [2]. The methodology is based on self-aligning silicon grippers prepared by means of reactive ion etching and an optimized microtensile sample geometry that can be fabricated via focused ion beam (FIB) milling. The measured elastic modulus, strength, yield stress and strain at maximum stress are summarized in table 1. Please click Additional Files below to see the full abstract

Nanoscale compressive deformation mechanisms and yield properties of hydrated bone extracellular matrix

Bone features a hierarchical architecture combining antagonistic properties like toughness and strength. In order to better understand the mechanisms leading to this advantageous combination of properties, its postyield and failure behavior was analyzed on the length scale of a single lamella. Micropillars were compressed to large strains in saline solution to measure their anisotropic yield and post-yield behavior under near-physiological conditions. An increase in strength compared to the macroscale by a factor of 1.55 was observed in line with theory for size effects in quasi-brittle materials. Furthermore, a clear influence of hydration with a reduction by 60% compared to in vacuo results was found. This is well in line with literature nanoindentation data and the known change in properties of the organic phase upon hydration. Please click Additional Files below to see the full abstract

In-situ microcompression high cycle fatigue tests: Up to 1 kHz frequencies and 10 million oscillation cycles

Nanomechanical tests are moving beyond hardness and modulus to encompass host of different mechanical properties like strain rate sensitivity 1,2, stress relaxation 3, creep and fracture toughness by taking advantage of focused ion beam milled geometries and well known stress state during testing. Adding high cycle fatigue (HCF) properties to this list will be useful to extend the gamut of properties studied at the micro/nanoscale. There have been several reports of repeated impact and sinus mode (also referred to as “continuous stiffness mode”) nanoindentation tests for studying the contact fatigue properties of films and coatings. Though promising for studying contact fatigue properties, these measurements suffer from low oscillation frequencies (less than ~ 50 Hz) and, consequently, long duration tests. Merle et al. 4 reported micropillar compression-compression fatigue tests on nanocrystalline Cu at 40Hz and required ~ 7 hours to reach 1 million cycles. For a technique like nanoindentation that typically comprises of thermal drift rates of ~ 3nm/min at room temperature, this amounts to a total displacement drift of 1.2µm over the entire duration of the test (7 hours). Therefore, pushing the frequencies of sinus oscillation tests higher seems to be the key towards minimizing artefacts of measurements and to reach high cycle contact fatigue regime in shorter time spans. This presentation will report the development of micropillar HCF tests with oscillation frequencies up to 1kHz and compression-compression fatigue tests up to 10 million cycles. Micropillar HCF tests performed on single crystal silicon (reference sample, does not exhibit fatigue at high frequencies) showed no change in unloading stiffness over 10 million cycles, suggesting the reliability of the developed experimental technique. The associated instrumentation and technique development, design of the fatigue tests at the micron scale, data analysis methodology, experimental protocol and challenges will be discussed. Compression-compression high cycle micropillar fatigue of nanocrystalline nickel will be presented and the experimental results will be discussed in light of existing literature data, particularly the operative deformation mechanism(s). The fatigue tests were performed both below and above the 0.2% offset yield strength. Prolonged fatigue tests resulted in grain growth and microstructural changes in nanocrystalline nickel. The associated changes in mechanical deformation data (unloading stiffness, load and displacement amplitudes) will be discussed. The convolution of time dependent plasticity in such tests will be addressed by comparing both load and displacement controlled fatigue tests at high frequencies. It is hoped that this study will pave way for routine high cycle fatigue tests of metals at the micron scale and provide clues for designing similar indentation based fatigue tests. Please click Additional Files below to see the full abstract

High temperature nanoindentation up to 800°C for characterizing high temperature properties of materials

One of the primary motivations for development of instrumented indentation was to measure the mechanical properties of thin films. Characterization of thin film mechanical properties as a function of temperature is of immense industrial and scientific interest. The major bottlenecks in variable temperature measurements have been thermal drift, signal stability (noise) and oxidation of/condensation on the surfaces. Thermal drift is a measurement artifact that arises due to thermal expansion/contraction of indenter tip and loading column. This gets superimposed on the mechanical behavior data precluding accurate extraction of mechanical properties of the sample at elevated temperatures. Vacuum is essential to prevent sample/tip oxidation at elevated temperatures. In this poster, the design and development of a novel nanoindentation system that can perform reliable load-displacement measurements over a wide temperature ranges (from -150 to 800 °C) will be presented emphasizing the procedures and techniques for carrying out accurate nanomechanical measurements. This system is based on the Ultra Nanoindentation Tester (UNHT) that utilizes an active surface referencing technique comprising of two independent axes, one for surface referencing and another for indentation. The differential depth measurement technology results in negligible compliance of the system and very low thermal drift rates at high temperatures. The sample, indenter and reference tip are heated/cooled separately and the surface temperatures matched to obtain drift rates as low as 1nm/min at 800 °C without correction. Instrumentation development, system characterization, experimental protocol, operational refinements and thermal drift characteristics over the temperature range will be presented, together with a range of results on different materials. Please click Additional Files below to see the full abstract

A new push‐pull sample design for microscale mode 1 fracture toughness measurements under uniaxial tension

The miniaturization of microelectronic devices and the use of thin hard coatings have led to an increased demand for knowledge on the fracture behaviour of microscopic structures. A new geometry called Micro-SENT is proposed in this work that allows performing experiments in uniaxial tension on the microscale using a standard flat punch indenter by making use of a symmetric push-pull sample design. This enables the measurement of mode 1 fracture toughness under uniform tensional far-field loading as opposed to current state of the art approaches based on cantilever bending or micropillar splitting. Please click Additional Files below to see the full abstract

Development of novel indentation-based stress relaxation tests to study transient plasticity in metals

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