Representative indentation elastic modulus evaluated by unloading of nanoindentation made with a point sharp indenter

The conventional method to extract elastic modulus from the nanoindentation on isotropic linearly elastic solids is based on Sneddon’s solution (1965). However, it is known that the solution is valid only for incompressive elastic solids with the Poisson’s ratio ν of 0.5. This paper first proposes the modification of the solution in a wide range of ν from 0 to 0.5 through the numerical analysis on the unloading behavior of a simulated conical nanoindentation with a finite element method. As a result of the modification, the coefficient of linearity between the indentation elastic parameter k_e and Young’s modulus E is empirically given as a function of ν and the inclined face angle of the indenter, β, where k_e is defined as k_e ≡ P/h² with the indentation load P and penetration depth of the indenter h. According to the linear relationship between k_e and E, it is found that elastic rebound during unloading of a nanoindentation is uniquely characterized by a representative indentation elastic modulus E¹ defined in terms of E, ν and β, and that the value of E¹ can be evaluated from the P–h relationship with k_e and β. For an isotropic elastoplastic solid, the indentation unloading parameter k₂ defined as k₂ ≡ P/(h–h_r)² for a residual depth h_r is different from k_e even though a linearly elastic solid with k_e and elastoplastic solid with k₂ have a common E¹. In order to evaluate E¹ of an elastoplastic solid, the corresponding k_e is estimated from k₂ with an empirical equation as a function of the relative residual depth ξ defined as ξ ≡ h_r/h_max for the maximum penetration depth h_max. A nanoindentation experiment confirmed the validity of the numerical analysis for evaluating the elastic modulus.     

Size effect of indenter on determining modulus of nanowires using nanoindentation technique

This study uses a finite element modeling to simulate the behavior of copper nanowires submitted to nanoindentation and estimate their mechanical properties. The simulation results reveal that using the well-known Oliver-Pharr theory, generally applied for materials with semi-infinite half-space, yields an underestimate elastic modulus of the wire materials. Moreover, the radius of the indenter tip also influences the accuracy of the predicted elastic modulus. Such errors are mainly from the overestimate of the contact area between the indenter and the specimen. They can be corrected from the numerical modeling. The elastic modulus of the wires calculated from the corrected contact area is highly close to the bulk value.     

Nanomechanical characterization of thermally evaporated Cr thin films — FE analysis of the substrate effect

We study the substrate effect on the deformation and hardness behaviour of chromium thin films using nanoindentation technique. Two different substrates namely Si (100) and AISI-304 SS are used in order to obtain a soft film on a hard substrate and a hard film on a soft substrate combination. Typical hardness variations for the two combinations are obtained. It is also observed that Cr thin films deposited on two different substrates deform distinctly. Radial cracks are found to develop in the case of Cr film on Si whereas circumferential cracks are produced in the case of Cr film on SS substrate. Using 2-D finite element analysis, it is found that the substrate not only affects the development of plastic zone but also the stress distribution in the films which results in observed distinct hardness and deformation behaviour.     

On the use of hardness tests to estimate the extent of plastic deformation

The standard hardness test result is dependent to some extent on the surface condition of the material being assessed. In particular, since the measurement involves permanent deformation of the surface the state of stress or strain in the material will influence the result. Consequently the hardness test may be used as an indicator of prior plastic deformation. The present investigation was concerned with the phenomenon of buckle propagation in undersea pipelines and a theoretical model of the collapse process was developed. The model predicted the extent of the developing plastic zones around the cross-section of the collapsing pipe. Hardness measurements on the cross-sections of collapsed pipe have been used to estimate the extent of the plastic zones and comparisons with the theoretical analysis are given.     

Comments on the paper “Modification of composite hardness models to incorporate indentation size effects in thin films”, D. Beegan, S. Chowdhury and M.T. Laugier, Thin Solid Films 516 (2008), 3813-3817

Since the original work of Bückle concerning the substrate influence on the hardness measurement of thin film, more than 20 models were proposed to separate the contribution of the substrate. Subsequently to the development of these numerous models, a question arises: Which is the most relevant models among them? Indeed, the authors usually consider that their proposed model leads to the best prediction of the film hardness which is probably correct for a given experimental condition applied to a particular material. In addition, the authors also assume that the other models are not so relevant. But to have a sound discussion about the existing models, it is necessary to correctly apply them according to the author statement. In this paper, we better specified the application of the Jönsson and Hogmark model and that of Chicot and Lesage applied to the results obtained on copper films by Beegan et al. Contrarily to these authors, we show that the above-mentioned models lead to a good representation of the experimental data and a good predicted value of the film hardness.     

On the resistance to penetration of stiffened plates,Part II: Numerical analysis

A series of indentation tests have been carried out quasi-statically on various configurations of stiffened panels. These represent hull plates in ships subjected to grounding or collision actions. The results of the scaled down tests are reported in the first part of this two-part companion paper. This part (II) presents results from numerical analyses with focus on fracture prediction.     

Residual stress in low temperature carburised layer of austenitic stainless steel

Microstructure, elements concentration and residual stress of a low temperature carburised layer on 316L austenitic stainless steel were investigated by optical microscopy, electron probe microanalysis, nanoindentation and X-ray diffraction (XRD). The results show that surface carbon concentration and nanohardness increase significantly after low temperature carburisation in the mixture gas of 30?vol.-% CO–30?vol.-% H₂–40?vol.-%N₂ at 743?K for 20?h, while Young’s modulus keeps unchanged. A finite element model was proposed to simulate the nanoindentation of unstressed carburised layer based on the results of nanoindentation experiments. Combined with the experimental and simulation results, the residual stress was calculated based on Suresh model, which agrees well with the corrected data by XRD method. The surface displacement around indenter was discussed.     

薄圆柱体高频感应温度场的测量和有限元模拟

本文利用自制的NiCr-NiAl热电偶精确地测量了薄圆柱工件端面高频感应温度场的分布;应用有限元分析软件ANSYS/Thermal对高频感应加热过程的温度场进行了模拟.热电偶测量的数据直观可信,但测取工件温度场分布费时费力;有限元分析则可较为快速获知工件各处的温度,弥补了实验工作的不足.本文研究结果显示,两种方法得出的结果具有可比性,能够相互参照.     

Alternative methods to determine the elastoplastic properties of sintered hydroxyapatite from nanoindentation testing

This study introduces alternative methods to determine the elastoplastic properties of bovine-derived Hydroxyapatite (HA) porous bone graft through a set of nanoindentation tests with a Berkovich indenter. Generally, experimental data obtained from nanoindentation tests are force displacement, hardness and elastic modulus. However, to determine plastic properties such as strength coefficient and work hardening exponent of bovine HA, analytical or inverse finite element models are required. In this paper, the effect of sintering temperature on these properties of HA is studied for the range of 1000–1400 °C. The direct and inverse Finite Element (FE) simulation models for nanoindentation tests were written in MSC, MARC^® software. A special algorithm for the inverse technique was developed to infer the most suitable elastoplastic material model for HA. A semi-empirical method was adapted to calculate the elastoplastic material properties of HA. The numerical results of harder hydroxyapatite showed better agreement with the experiments while the work hardening exponent, or n-value, and strength coefficient k of hard HA were found to be 0.23 and 8.05 GPa respectively. A comparison between the experimental and predicted load–displacement curves showed that the proposed inverse technique is effective in predicting the elastoplastic material properties from the nanoindentation test with error below 4% at maximum load.     

On the effect of substrate properties on the indentation behaviour of coated systems

The indentation behaviour of an elastoplastic coating–substrate system is investigated using a combination of dimensional and finite element analyses. Scaling functions relating the indentation load–depth curves to coating and substrate mechanical properties are given. Based on these scaling functions, the indentation behaviour of various coated systems is examined. The critical indentation depth to coating thickness ratio below which the substrate material has a negligible effect on the indentation response of the coated system is identified for various generic coating–substrate systems. Such ratio is given in terms of the yield strength and Young’s modulus of the coating and substrate, i.e. σ_yc/σ_ys and E_c/E_s. The results of parametric studies revealed that the commonly used rule that the maximum indentation depth should be less than 10% of the coating thickness, is applicable only when σ_yc/σ_ys<10. However, indentation experiments should be carried out up to a maximum depth of 5% of the film thickness to avoid any influence from the substrate when σ_yc/σ_ys≥10 and E_c/E_s>0.1.     

影响金属薄膜沉积初期因素的有限单元法模拟

利用有限单元法对影响金属薄膜沉积初期的因素进行了计算机模拟.按膜料为Pt、Pt-Ru、Pt-Ti、Pt-Ni、Pt-Al等五种模式,采用刚性球入射到C或Si基底,重点研究了沉积原子的半径差异比、沉积原子能量和原子入射角等参数对薄膜沉积的影响,同时检验了有限元方法在微观领域中的合理性和适用性.     

Development of semi-empirical formulation for extracting materials properties from nanoindentation measurements: Residual stresses, substrate effect, and creep

Nanoindentation is one of the most popular techniques for characterizing the mechanical properties of micro- or nano-structured metals or dielectric thin films. However, the obtained experimental data can only provide the relationship between the applied load and the penetration depth. Mechanics models are therefore required to convert the test data into the corresponding material properties. In this work, the effect of residual stress, the substrate effect, and the creep of materials subjected to the indentation test are discussed in order to establish appropriate conversion formulas or criteria for extracting the interested material properties. Dimensional analyses are firstly performed to find the governing parameters and to obtain scaling relationships for subsequent finite element analysis. With the described procedure, models have been developed to convert nanoindentation test data into the desired material properties. Those models provide useful tools for extracting specific material properties, such as residual stress, creep exponent, and stress relaxation time constant. Specifically, this investigation also shows that for the situation of soft film/hard substrate combination, the indentation behavior is essentially identical if the modulus of the substrate is 10 times higher than that of the corresponding film and the response deviates consistently from that of bulk material with increasing of indentation depth. For penetration depth less than 10% of the film thickness, the deviation could be acceptable. On the other hand, significant deviation is observed for hard film/soft substrate systems. In summary, by integrating the models proposed by this work and data from standard tests, it is possible to obtain the Young's modulus, hardness, and the viscoelastic properties as well as the residual stress for a specific material through indentation characterization.     

A novel method for the preparation of Al-Mg intermetallic coating

A novel method has been suggested to obtain an Al-Mg intermetallic compound coating on the ZL102 Al alloy by Al-Mg twin-wire arc spraying and gas tungsten arc melting (GTAM) post treatment. The composition and the morphology of the coating are characterized by X-ray diffraction (XRD) and scanning electron microscope (SEM) and the corrosion behavior is investigated by potentiodynamic electrochemical tests respectively. The results show that the components of the coating after GTAM are Mg₁₇Al₁₂, Al₃Mg₂ and Al. According to polarization curves and micro-hardness tests, the Al-Mg intermetallic coating exhibits good corrosion resistance and high micro-hardness.     

Numerical Study on the Effects of Equi-biaxial Residual Stress on Mechanical Properties of Nickel Film by Means of Nanoindentation

In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic residual stress and residual stress exceeded the yield stress for fixed indentation depth.Indentation profiles changed monotonously with compressive and tensile stresses at peak force which determinates contact area observed directly by finite element modeling (FEM).The elastic residual stress h...     

Effect of re-melting on the cladding coating of Fe-based composite powder

The aim of this paper is to investigate the influence of laser re-melting on the geometry and overlapping pores of cladding coating. In this study, Fe-based alloy mixed with 5 wt.% Cr₃C₂ powder was used as cladding material to obtain high hardness and strength coating. However, this coating has overlapping pores and a rough surface. Therefore, re-melting process is explored systematically. The geometry, microhardness and microstructure of the coatings have been analyzed and compared subsequently. Besides, a 3D finite element model has been built to provide a thermal field analysis for laser re-melting. Finally, it is found that re-melting process is an effective method to improve the surface smoothness of cladding layer, which could reduce the process cycle and cost of secondary operations. More importantly, it could remove the overlapping pores easily.     

Radial locations of strain gages for accurate measurement of mode I stress intensity factor

Strain gage methods are popular in experimental determination of stress intensity factors (SIFs). Radial location of gages with respect to the crack tip plays an important role in accuracy of strain measurements and thus accurate determination of SIFs. The present work proposes a finite element based simple, accurate and consistent method for determination of the limiting value of the radial distance (r_max) of a strain gage. This parameter is in turn useful in deciding the valid strain gage location for accurate measurement of opening mode SIF. The results obtained from the present investigation agree well with the theoretical predictions and could be used for experimental determination of SIFs for both single ended and double ended cracked specimens. The r_max values of center cracked and edge cracked plates with different crack length to width ratio are estimated. The results of the present investigation show that the relative size of the crack length and net ligament length strongly influences the r_max value and the effect of Poisson’s ratio is marginal on the r_max value.     

Rethinking the role that the “step” in the load-displacement curves can play in measurement of fracture toughness for hard coatings

The “step” in the load-displacement curves during nanoindentation of hard coatings has been regarded as a representation of the energy dissipated during fracture of the coating thus is used in measuring the fracture toughness of this coating. This paper scrutinizes the “step” and finds that the “step” is a gap artificially bridged up with a straight line and that the “step” size corresponds with the thickness of the coating in testing. It is realized that the gap is formed due to loss of contact of the indenter with the sample. Upon catastrophic fracture of the coating, the indenter undergoes a freefall of a distance about the thickness of the coating. The size of such a “step” has no logic relationship with the energy dissipation that fractures the coating before the freefall of the indenter takes place.     

Digital element approach for simulating impact and penetration of textiles

A micro-scale computational tool, based upon an explicit digital element method (DEM), has been developed for numerical simulation of ballistic impact and penetration of textile fabrics. In this approach, each yarn is digitized as an assembly of digital fibers. Each digital fiber is further digitized into a short digital rod element chain connected by frictionless pins (nodes). A search is conducted to find contacts between adjacent digital fibers. If a contact is detected, compressive and frictional forces between fibers will be determined, based upon contact stiffness and friction coefficient. Nodal forces are calculated for each time step. Nodal displacements are determined using an explicit procedure. Because the digital element approach operates on a sub-yarn micro-scale, one can determine textile penetration resistance based upon sub-yarn scale properties, such as inter-fiber compression, friction, and fiber strength. Research presented in this paper includes three parts. First, the explicit digital element algorithm used in dynamic simulation is explained. Second, the approach is used to generate 2-D woven fabric micro-geometries and to simulate ballistic penetration processes. Third, numerical results are compared to high resolution experimental impact and ballistic test data.     

Individual factors affecting the risk of death for rear-seated passengers in road crashes

We studied the effect of age, gender, use of restraint systems and seat position on the risk of death for rear-seated passengers of cars involved in road crashes. The data source was the Spanish register of traffic crashes with victims compiled by the Government's General Traffic Directorate. Data for crashes recorded from 1993 to 2002, inclusive, were studied. We used a matched cohort design to analyze all 5260 rear-seated passengers in vehicles occupied by two or three rear-seated passengers for accidents in which at least one of these passengers was killed. Conditional Poisson regression with death as the dependent variable was used. An increased risk of death was observed for females and children aged <3 years. For passengers aged 25 years and older, the risk increased with age. The use of restraint systems and central and right-side seats was associated with a lower risk. These results should be considered in research focused on passenger fragility and strategies to prevent injury and death.