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.

Three-Dimensional simulation of deformation fields underneath vickers indenter:Effects of power-law Plasticity

The effects of power-law plasticity (yield strength and strain hardening exponent) on the plastic strain distribution underneath a Vickers indenter was systematically investigated by recourse to three-dimensional finite element analysis, motivated by the experimental macro-and micro-indentation on heat-treated Al-Zn-Mg alloy. For meaningful comparison between simulated and experimental results, the experimental heat treatment was carefully designed such that Al alloy achieve similar yield strength with different strain hardening exponent, and vice versa. On the other hand, full 3D simulation of Vickers indentation was conducted to capture subsurface strain distribution. Subtle differences and similarities were discussed based on the strain field shape, size and magnitude for the isolated effect of yield strength and strain hardening exponent.

Role of indenter angle on the plastic deformation underneath a sharp indenter and on representative strains: An experimental and numerical study

The subsurface microhardness mapping technique of Chaudhri was utilized to determine the shape, size and distribution of plastic strain underneath conical indenters of varying semi-apex angles, alpha (55 degrees, 65 degrees and 75 degrees). Results show that the elastic-plastic boundary under the indenters is elliptical in nature, contradicting the expanding cavity model, and the ellipticity increases with alpha. The maximum plastic strain immediately under the indenter was found to decrease with increasing alpha. Complementary finite-element analysis was conducted to examine the ability of simulations to capture the experimental observations. A comparison of computational and experimental results indicates that the plastic strain distributions as well as the maximum strains immediately beneath the indenter do not match, suggesting that simulation of sharp indentation requires further detailed studies for complete comprehension. Representative strains, epsilon(r), evaluated as the volume-average strains within the elastic-plastic boundary, decrease with increasing alpha and are in agreement with those estimated by using the dimensional analysis. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Nanoindentation behavior of nanotwinned Cu: Influence of indenter angle on hardness, strain rate sensitivity and activation volume

The influence of strain on the mechanical properties and deformation kinetic parameters of nanotwinned (at) copper is investigated by a series of nanoindentation experiments, which were performed by employing sharp indenters with five varying centerline-to-face angles (psi). Comparison experiments were also conducted on (1 1 0) single crystalline Cu. Experimental results indicate that, unlike coarsegrained materials, nt-Cu is prone to plastic flow softening with large material pile-up around the indentation impression at high levels of strains. Localized detwinning becomes more significant with decreasing psi, concomitant with reduced strain-rate sensitivity (m) and enhanced activation volume (V*). The m of nt-Cu is found to depend sensitively on psi with a variation of more than a factor of 3, whereas V* exhibits a much less sensitive trend. This paper discusses the validation of the experimental techniques and the implications of various deformation kinetic parameters on the underlying deformation mechanisms of nt-Ca. 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

An New Area Function for Sharp indenter Tips in Nanoindentation

A new area function is introduced and applied to a Berkovich tip in order to characterize the contact projected area between an indenter and indented material. The function can be related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentation experiments are performed on a commercial Nano Indenter XPsystem. The other two area functions introduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper for comparison. By comparison from experimental results among different area functions, the indenter tip described by the proposed area function here is very close to the experimental indenter.

Influence of Indenter Tip Roundness on Hardness Behavior in Nanoindentation

In this paper. the effect of indenter tip roundness on hardness behavior for two typical elastic perfectly plastic materials is studied by means of finite element simulation. A rigid conical indenter of semi apex angle 70.3 degrees fitted smoothly with a spherical tip is employed. It is shown that as the indentation depth increases hardness first rises from zero, reaches a maximum and then decreases slowly approaching asymptotically the limiting value equal to that due to a conical indenter of ideally sharp tip. The range within which hardness varies appreciably is comparable to the radius of the indenter tip. The difference between the maximum value and the limiting value depends on the yield stress over the Young's modulus ratio. The smaller this ratio the greater the difference is. Numerical simulation also provides an opportunity for checking the accuracy and limitations of the widely used Oliver-Pharr method.

The Capillary Force In Micro- And Nano-Indentation With Different Indenter Shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force. (c) 2008 Elsevier Ltd. All rights reserved.

On the initial unloading slope in indentation of elastic-plastic solids by an indenter with an axisymmetric smooth profile

A simple relationship between the initial unloading slope, the contact area, and the elastic modulus is derived for indentation in elastic-plastic solids by an indenter with an arbitrary axisymmetric smooth profile. Although the same expression was known to hold for elastic solids, the new derivation shows that it is also true for elastic-plastic solids with or without work hardening and residual stress. These results should provide a sound basis for the use of the relationship for mechanical property determination using indentation techniques. (C) 1997 American Institute of Physics.

Plastic deformation in Zr41 Ti14 Cu12.5 Ni10 Be22.5 bulk metal glass under vickers indenter

Vickers indentation was conducted on an as-cast Zr41Ti14Cu12.5Ni10Be22.5 bulk metal glass (BMG) to study shear band formation using a bonded interface technique. The results indicate that the plastic deformation in the BMG is accommodated by the semi-circular (primary) and radial (secondary) shear bands. The inter-band spacing of the semi-circular shear bands is found to be independent of the applied load. The measured size of the deformation zone is in good agreement with the prediction of the theoretical model proposed by Zhang et al.

Effect of structure relaxation on the plastic deformation behaviour in a Zr-based BMG under indenter

Vickers and nano indentations were performed on a structurally relaxed Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 bulk metallic glass (BMG), and the evolution of the shear bands in the relaxed BMG was investigated and compared to that in the as-cast alloy. Results indicate that the plastic deformation in the BMG with structure relaxation is accommodated by the semicircular (primary) and radial (secondary) as well as tertiary shear bands. Quantitatively, the shear band density in the relaxed alloy was much lower than that in the as-cast alloy. The annihilation of free volume caused by the annealing was responsible for the embrittlement of the sample with structure relaxation.

Plastic deformation in the annealed Zr41Ti14Cu12.5Ni10Be22.5 bulk metal glass under indenter

Vickers and nanoindentationswere carried out on an annealed Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 bulk metallic glass (BMG), and the evolution of the shear bands in the annealed BMG was investigated and compared to that in the as-cast alloy. Results indicate that the plastic deformation in the BMG with the structure relaxation is accommodated by the semicircular (primary) and radial (secondary) as well as tertiary shear bands. Quantitatively, the shear band density in the annealed alloywas much lower than that in the as-cast alloy. The load-displacement curve of nanoindentation test for the annealed alloy exhibited a more flat serrated flow. The annihilation of free volume caused by the annealing was responsible for the embrittlement of the annealed sample.

Plastic deformation in a partially crystallized Zr-based BMG under Vickers indenter

Vickers indentations were carried out on an anneal-introduced partially crystallized Zr₄₁Ti₁₄Cu_12.5 Ni₁₀Be_22.5 bulk metallic glass (BMG), and the evolution of the shear bands in this samplewas investigated and compared to the as-cast, aswell as the structurally relaxed counterparts. The results indicate that the plastic deformation in the partially crystallized BMG was accommodated by the semi-circular (primary) and radial (secondary) shear bands. A full crack or flake that was produced due to the spring back during the load removal was observed. The shear band density in the annealed alloy which was dispersed with crystalliteswas significantly lower than that of the as-cast alloy. The difference of the shear band features among the three kinds of alloy status, i.e., partially crystallized, structurally relaxed and as-cast alloys was discussed in terms of the free volume in the BMGs and the characteristics of nano-composites. It has been demonstrated that the plasticity for the three statuses of alloys queues in the descending order as the as-cast, annealed with partial crystallization, and annealed without crystallization.