The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, FE simulations to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson’s ratio =0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27m to 0.11m with a von Mises model, and from 0.09m to 0.02m with Drucker-Prager plasticity. We conclude that it is important to include friction in nanoindentation simulations of bone.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

Deformation behaviours of coarse-grained and nanocrystalline Mg-5wt% Al alloys

Magnesium alloys have been of growing interest to various engineering applications, such as the automobile, aerospace, communication and computer industries due to their low density, high specific strength, good machineability and availability as compared with other structural materials. However, most Mg alloys suffer from poor plasticity due to their Hexagonal Close Packed structure. Grain refinement has been proved to be an effective method to enhance the strength and alter the ductility of the materials. Several methods have been proposed to produce materials with nanocrystalline grain structures. So far, most of the research work on nanocrystalline materials has been carried out on Face-Centered Cubic and Body-Centered Cubic metals. However, there has been little investigation of nanocrystalline Mg alloys. In this study, bulk coarse-grained and nanocrystalline Mg alloys were fabricated by a mechanical alloying method. The mixed powder of Mg chips and Al powder was mechanically milled under argon atmosphere for different durations of 0 hours (MA0), 10 hours (MA10), 20 hours (MA20), 30 hours (MA30) and 40 hours (MA40), followed by compaction and sintering. Then the sintered billets were hot-extruded into metallic rods with a 7 mm diameter. The obtained Mg alloys have a nominal composition of Mg–5wt% Al, with grain sizes ranging from 13 μm down to 50 nm, depending on the milling durations. The microstructure characterization and evolution after deformation were carried out by means of Optical microscopy, X-Ray Diffraction, Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Probe Microscopy and Neutron Diffraction techniques. Nanoindentaion, compression and micro-compression tests on micro-pillars were used to study the size effects on the mechanical behaviour of the Mg alloys. Two kinds of size effects on the mechanical behaviours and deformation mechanisms were investigated: grain size effect and sample size effect. The nanoindentation tests were composed of constant strain rate, constant loading rate and indentation creep tests. The normally reported indentation size effect in single crystal and coarse-grained crystals was observed in both the coarse-grained and nanocrystalline Mg alloys. Since the indentation size effect is correlated to the Geometrically Necessary Dislocations under the indenter to accommodate the plastic deformation, the good agreement between the experimental results and the Indentation Size Effect model indicated that, in the current nanocrystalline MA20 and MA30, the dislocation plasticity was still the dominant deformation mechanism. Significant hardness enhancement with decreasing grain size, down to 58 nm, was found in the nanocrystalline Mg alloys. Further reduction of grain size would lead to a drop in the hardness values. The failure of grain refinement strengthening with the relatively high strain rate sensitivity of nanocrystalline Mg alloys suggested a change in the deformation mechanism. Indentation creep tests showed that the stress exponent was dependent on the loading rate during the loading section of the indentation, which was related to the dislocation structures before the creep starts. The influence of grain size on the mechanical behaviour and strength of extruded coarse-grained and nanocrystalline Mg alloys were investigated using uniaxial compression tests. The macroscopic response of the Mg alloys transited from strain hardening to strain softening behaviour, with grain size reduced from 13 ìm to 50 nm. The strain hardening was related to the twinning induced hardening and dislocation hardening effect, while the strain softening was attributed to the localized deformation in the nanocrystalline grains. The tension–compression yield asymmetry was noticed in the nanocrystalline region, demonstrating the twinning effect in the ultra-fine-grained and nanocrystalline region. The relationship k tensions < k compression failed in the nanocrystalline Mg alloys; this was attributed to the twofold effect of grain size on twinning. The nanocrystalline Mg alloys were found to exhibit increased strain rate sensitivity with decreasing grain size, with strain rate ranging from 0.0001/s to 0.01/s. Strain rate sensitivity of coarse-grained MA0 was increased by more than 10 times in MA40. The Hall-Petch relationship broke down at a critical grain size in the nanocrystalline region. The breakdown of the Hall-Petch relationship and the increased strain rate sensitivity were due to the localized dislocation activities (generalization and annihilation at grain boundaries) and the more significant contribution from grain boundary mediated mechanisms. In the micro-compression tests, the sample size effects on the mechanical behaviours were studied on MA0, MA20 and MA40 micro-pillars. In contrast to the bulk samples under compression, the stress-strain curves of MA0 and MA20 micro-pillars were characterized with a number of discrete strain burst events separated by nearly elastic strain segments. Unlike MA0 and MA20, the stress-strain curves of MA40 micro-pillars were smooth, without obvious strain bursts. The deformation mechanisms of the MA0 and MA20 micro-pillars under micro-compression tests were considered to be initially dominated by deformation twinning, followed by dislocation mechanisms. For MA40 pillars, the deformation mechanisms were believed to be localized dislocation activities and grain boundary related mechanisms. The strain hardening behaviours of the micro-pillars suggested that the grain boundaries in the nanocrystalline micro-pillars would reduce the source (nucleation sources for twins/dislocations) starvation hardening effect. The power law relationship of the yield strength on pillar dimensions in MA0, MA20 supported the fact that the twinning mechanism was correlated to the pre-existing defects, which can promote the nucleation of the twins. Then, we provided a latitudinal comparison of the results and conclusions derived from the different techniques used for testing the coarse-grained and nanocrystalline Mg alloy; this helps to better understand the deformation mechanisms of the Mg alloys as a whole. At the end, we summarized the thesis and highlighted the conclusions, contributions, innovations and outcomes of the research. Finally, it outlined recommendations for future work.

The contribution of seat components to seat hardness and the interface between human occupant and a driver seat

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper comprises: a study investigating the component mechanical behaviour of a spring-suspended, production level seat when indented by SAE J826 type, human thigh-buttock representing hard shell; a model of seated human buttock shape for improved indenter design using a multivariate representation of Australian population thigh-buttock anthropometry; and a finite-element study simulating the deflection of human buttock and thigh soft tissue when seated, based on seated MRI. The results of the three studies provide a description of the mechanical properties of the driver-seat interface, and allow validation of future dynamic simulations, involving multi-body and finite-element (FE) DHM in virtual ergonomic studies.

A new tip area function for instrumented nanoindentation at extremely small contact depths

The accuracy of measurement of mechanical properties of a material using instrumented nanoindentation at extremely small penetration depths heavily relies on the determination of the contact area of the indenter. Our experiments have demonstrated that the conventional area function could lead to a significant error when the contact depth was below 40. nm, due to the singularity in the first derivation of the function in this region and thus, the resultant unreasonable sharp peak on the function curve. In this paper, we proposed a new area function that was used to calculate the contact area for the indentations where the contact depths varied from 10 to 40. nm. The experimental results have shown that the new area function has produced better results than the conventional function. © 2011 Elsevier B.V.

Experimental study on mechanical properties of pumpkin tissue

Purpose: The purpose of this study was to calculate mechanical properties of tough skinned vegetables as a part of Finite Element Modelling (FEM) and simulation of tissue damage during mechanical peeling of tough skinned vegetables. Design/methodology: There are some previous studies on mechanical properties of fruits and vegetables however, behaviour of tissue under different processing operations will be different. In this study indentation test was performed on Peel, Flesh and Unpeeled samples of pumpkin as a tough skinned vegetable. Additionally, the test performed in three different loading rates for peel: 1.25, 10, 20 mm/min and 20 mm/min for flesh and unpeeled samples respectively. The spherical end indenter with 8mm diameter used for the experimental tests. Samples prepare from defect free and ripped pumpkin purchased from local shops in Brisbane, Australia. Humidity and temperature were 20-55% and 20-250C respectively. Findings: Consequently, force deformation and stress and strain of samples were calculated and shown in presented figures. Relative contribution (%) of skin to different mechanical properties is computed and compared with data available from literature. According the results, peel samples had the highest value of rupture force (291N) and as well as highest value of firmness (1411Nm-1). Research limitations/implications: The proposed study focused on one type of tough skinned vegetables and one variety of pumpkin however, more tests will give better understandings of behaviours of tissue. Additionally, the behaviours of peel, unpeeled and flesh samples in different speed of loading will provide more details of tissue damages during mechanical loading. Originality/value: Mechanical properties of pumpkin tissue calculated using the results of indentation test, specifically the behaviours of peel, flesh and unpeeled samples were explored which is a new approach in Finite Element Modelling (FEM) of food processes. Keywords: Finite Element Modelling (FEM), relative contribution, firmness, toughness and rupture force.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

Study of structural changes of pumpkin tissue before and after mechanical loading

The texture of agricultural crops changes during harvesting, post harvesting and processing stages due to different loading processes. There are different source of loading that deform agricultural crop tissues and these include impact, compression, and tension. Scanning Electron Microscope (SEM) method is a common way of analysing cellular changes of materials before and after these loading operations. This paper examines the structural changes of pumpkin peel and flesh tissues under mechanical loading. Compression and indentation tests were performed on peel and flesh samples. Samples structure were then fixed and dehydrated in order to capture the cellular changes under SEM. The results were compared with the images of normal peel and flesh tissues. The findings suggest that normal flesh tissue had bigger size cells, while the cellular arrangement of peel was smaller. Structural damage was clearly observed in tissue structure after compression and indentation. However, the damages that resulted from the flat end indenter was much more severe than that from the spherical end indenter and compression test. An integrated deformed tissue layer was observed in compressed tissue, while the indentation tests shaped a deformed area under the indenter and left the rest of the tissue unharmed. There was an obvious broken layer of cells on the walls of the hole after the flat end indentations, whereas the spherical indenter created a squashed layer all around the hole. Furthermore, the influence of loading was lower on peel samples in comparison with the flesh samples. The experiments have shown that the rate of damage on tissue under constant rate of loading is highly dependent on the shape of equipment. This fact and observed structural changes after loading underline the significance of deigning post harvesting equipments to reduce the rate of damage on agricultural crop tissues.

Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

Seat Comfort. M4-M6.

Hardness is defined as the resistance and load bearing capability of an item. Seat hardness is an important factor in seat comfort as it impacts on a number of variables including seat postural stability, postural control, pressure comfort as a result of tissue deformation, and occupant vibration. The development of the test rig further on described in this report will enable Futuris Automotive to develop their current comfort testing procedures and thus increase the comfort of their automotive seats. The test rig consists of a buttock indenter, which produces a controlled application of a load to a seat cushion with measured displacement via a linear indenter. In parallel with the physical property presented, an analytic (software) finite element tool was developed to simulate seat pressure in an ANSYS Workbench V13 environment. This report also details the procedure required for Futuris to accurately and precisely measure cushion hardness which will enhance their comfort testing procedures, product development and target settings. The report is divided into three main sections: 1 Test equipment specification (M4) - A detailed description of the process used to build the seat cushion indenter and a description of the indenter mechanical structure and electrical functionality (chapter 2). 2 Analytic tool specification (M5) – A detailed description of the CAE seat and indenter software tool, developed as a finite element model (FEM) under ANSYS Workbench V13 to simulate indentation of a physical seat cushion similar to the hardware tool (chapter 3). 3 Product Development and Comfort Design Procedure (M6) - The cushion hardness testing procedure to be used with the physical indenter. This milestone is partially incomplete, as it covers a description of the test procedure to be applied, however not the operating system (control software) required to operate the physical property (chapter 4). Although outside the scope of this project, this report also details the testing procedures required to measure overall seatback hardness.

Nanoindentation study of the mechanical behavior of TiO2 nanotube arrays

Titanium dioxide (TiO2) nanotube arrays are attracting increasing attention for use in solar cells, lithium-ion batteries, and biomedical implants. To take full advantage of their unique physical properties, such arrays need to maintain adequate mechanical integrity in applications. However, the mechanical performance of TiO2 nanotube arrays is not well understood. In this work, we investigate the deformation and failure of TiO2 nanotube arrays using the nanoindentation technique. We found that the load–displacement response of the arrays strongly depends on the indentation depth and indenter shape. Substrate-independent elastic modulus and hardness can be obtained when the indentation depth is less than 2.5% of the array height. The deformation mechanisms of TiO2 nanotube arrays by Berkovich and conical indenters are closely associated with the densification of TiO2 nanotubes under compression. A theoretical model for deformation of the arrays under a largeradius conical indenter is also proposed.