Instrumented Sharp Indentation Research Articles

A Correction Function to Improve the Accuracy of Measuring Elastic Modulus by Instrumented Spherical Indentation

Abstract Instrumented indentation combined with the classic Oliver–Pharr method has been widely utilized to measure elastic modulus of various materials. However, the elastic modulus measured by instrumented spherical indentation (ISI) is not as accurate as that measured by instrumented sharp indentation, especially at large indentation depth. In this work, the effect of the maximum indentation depth on measurement of elastic modulus by ISI was deeply investigated through finite element simulations and experiments. It was found that errors in measured elastic moduli increase significantly due to the inaccurate estimation of contact radius and excessive increase in initial unloading stiffness as maximum indentation depth increases. A correction function was then proposed to correct the measured elastic modulus. After correction, the errors were effectively reduced to within ±5 % for most cases. This work contributes to discovery of the error source in the measurement of elastic modulus by ISI, thereby improving the measurement accuracy.

A novel model for obtaining both equi-biaxial and uniaxial residual stress of metallic materials by instrumented sharp indentation

As a new method, the indentation technique has become popular for measuring residual stress and mechanical properties at surfaces due to its simplicity of use, in-situ applicability, and nano-to-macro range of measurements. In this study, a novel model for obtaining the surface residual stress of metallic materials is proposed by instrumented sharp indentation. The metallic material containing surface residual stress is equivalent to another non-stressed material with a different yield stress in Hollomon law from the perspective of indentation response. Thus, a unified equivalent material indentation (UEMI) model is established for measuring both equi-biaxial and uniaxial residual stresses within metallic structural materials. Additionally, only five parameters need to be calibrated via finite element analysis (FEA) in this model. Moreover, the novel model is successfully verified using lots of simulated materials from FEA and seven metallic materials experimental data found in the references. The results show that the predicted residual stress agrees well with the pre-applied residual stress which meeting the needs of engineering.

Evaluation of equibiaxial residual stress in metallic materials using the loading work of instrumented sharp indentation

<p indent="0mm">Residual stresses can significantly influence the mechanical performance of engineering structures. Therefore, the accurate evaluation of the equibiaxial residual stress in such structures is of great value. In the present work, the fractional change in the loading work was chosen as the analytical parameter. A linear relationship between the fractional change in the loading work and the normalized equibiaxial residual stress was determined via dimensional and finite element analyses. Based on numerous finite element simulations, new fitting equations were obtained for evaluating the equibiaxial residual stress by instrumented sharp indentation. Both numerical and experimental verifications were used to examine the accuracy and reliability of the newly proposed method. A biaxial stress-generating jig was designed to introduce equibiaxial residual stress into metallic specimens to mimic the residual stress. By comparing the residual stresses determined by the proposed method with the generated pre-stresses, the maximum relative error and absolute error were typically found within ±20% and <sc>30 MPa,</sc> respectively.

Determination of elastoplastic properties in anisotropic materials with cubic symmetry by instrumented indentation

Multi-dimensional finite element modelings of instrumented sharp indentation on materials with cubic symmetry are conducted. A novel reverse analysis algorithm for identifying elastoplastic properties is established for the cubic material, while the anisotropy of the material is determined by indentations on distinct orientations. Influences of elastic anisotropy and anisotropic yielding behavior are considered with the help of three-dimensional computations. Sensitivity analysis confirms the accuracy and robustness of the new method. The obtained results are compared and verified with experimental data of a nickel-base single crystal alloy.

Determination of Rate-Dependent Properties in Cohesive Frictional Materials by Instrumented Indentation

The extraction of the elastoplastic constitutive behavior from instrumented sharp indentation is still a subject of research. Several approaches have been proposed to solve this problem, mainly based on the use of numerical techniques. This work proposes an inverse analysis approach based on dimensional analysis calibrated with finite element modeling, to extract the elastoplastic properties from instrumented sharp indentation in rate- and pressure-dependent materials, which is the typical behavior that most polymers exhibit. Pressure sensitivity was modeled with a Drucker-Prager yield criterion, while rate dependency was introduced through a power-law dependence on strain rate of the yield stress. A set of master curves is proposed that relate the experimental metrics of instrumented indentation tests with the parameters of the proposed material model. Furthermore, the analysis was experimentally validated by testing several materials, including PMMA, coarse grain copper, and ultrafine grain copper. The predictions of the inverse analysis correlated well with the known material properties.

Study on Micromechanical Properties of Duplex Microstructure of Martensite/Bainite in Hot Stamping Via the Reverse Algorithms in Instrumented Sharp Indentation

Study on Micromechanical Properties of Duplex Microstructure of Martensite/Bainite in Hot Stamping Via the Reverse Algorithms in Instrumented Sharp Indentation

Assessment of Elastic–Plastic and Electrical Properties of Printed Silver-Based Interconnects for Flexible Electronics

In this work, the elastic–plastic properties of the printed interconnects on a glass substrate with Ag-filled polymer-conductor ink are evaluated through a theoretical framework based on finite element (FE) modeling of instrumented sharp indentation, experimental indentation, the concept of the representative strain, and dimensional analysis. Besides, the influences of the ink-solvent content and temperature on the elastic–plastic and electrical properties of the printed Ag-based interconnects are also addressed. First of all, parametric FE indentation analyses are carried out over a wide range of elastic–plastic material parameters. These parametric results together with the concept of the representative strain are used via dimensional analysis to constitute a number of dimensionless functions, and further the forward/reverse algorithms. The forward algorithm is used for describing the indentation load–depth relationship and the reverse for predicting the elastic–plastic parameters of the printed Ag-based interconnects. The proposed algorithms are validated through the correct predictions of the plastic properties of three known metals. At last, their surface morphology, microstructure, and elemental composition are experimentally characterized. Results show that the elastic–plastic properties and electrical sheet resistance of the printed Ag-based interconnects increase with the ink-solvent content, mainly due to the increase of carbon element as a result of the increased ink-solvent residue, whereas their elastic–plastic properties and electrical performance decreases with the temperature.

Estimation of surface equi-biaxial residual stress by using instrumented sharp indentation

Herein, we describe a method that can be used to estimate the surface equi-biaxial residual stress of a material using instrumented sharp indentation. In this method, the fractional change in the loading curvature, rather than the contact area, was chosen as the analytical parameter; this fractional change can be more precisely obtained. A linear relationship between the fractional change in the loading curvature and the normalized equi-biaxial residual stress was found via dimensional and finite element analysis, and this linear relationship greatly simplifies the formulas associated with this method. Moreover, the proposed method was successfully verified using experimental data from our laboratory and from the literature.

Characterization of the viscoelastic-plastic properties of UPVC by instrumented sharp indentation

The yielding behavior of glassy polymers may be sensitive to the hydrostatic pressure and also be influenced by the strain rate. Thus, the yield strength is a function of hydrostatic pressure and strain rate instead of a constant. In this paper, using dimensional analysis and finite element simulations, we established a method to estimate the yield strength of glassy polymers by instrumented indentation. Together with the method for determining shear creep compliance proposed in our previous work, the viscoelastic-plastic properties of glassy polymers can be extracted from a single indentation load-depth curve. Applications were illustrated on unplasticized polyvinyl chloride (UPVC). The shear creep compliance and yield strength of UPVC were successfully determined by a single indentation test. Using these parameters, the true stress–strain curves of UPVC under different strain rates were approximately predicted according to a linear viscoelastic-perfectly plastic constitutive description.

Effect of Strain Rate on Load-Displacement Relations by Instrumented Sharp Indentation

Effect of Strain Rate on Load-Displacement Relations by Instrumented Sharp Indentation

An Inverse Approach for Extracting Elastic–plastic Properties of Thin Films from Small Scale Sharp Indentation

An inverse method for extracting the elastic-plastic properties of metallic thin films from instrumented sharp indentation has been proposed in terms of dimensional analysis and finite element modeling. A wide range of materials with different elastic modulus, yield strength, and strain-hardening exponent were examined. Similar to the Nix-Gao model for the depth dependence of hardness H, ( H H 0 ) 2 = 1 + h H * h , the relationship between elastic modulus E and indentation depth h can be expressed as ( E E 0 ) 4 = 1 + h E * h . By combining these two formulas, we find that there is a relationship between yield stress σ y 0 and indentation depth h: σ y = σ y 0 ⋅ ( 1 + h H * h ) f ( n ) ⋅ ( 1 + h E * h ) [ 0.25 − 0.54 f ( n ) ] where σ y0 is the yield strength associated with the strain-hardening exponent n, the true hardness H0 and the true elastic modulus E0. f ( n ) = 1 2 ( 1 − n ) is constant, which is only related to n, and h H * and h E * are characteristic lengths for hardness and elastic modulus. The results obtained from inverse analysis show that the elastic-plastic properties of thin films can be uniquely extracted from the solution of this relationship when the indentation size effect has to be taken into account.

Study of mechanical deformation of Zr55Cu30Al10Ni5 bulk metallic glass through instrumented indentation

Abstract Instrumented sharp indentation experiments using both conical and Vickers diamond pyramidal indenters were carried out to study deformation characteristics of Zr55Cu30Al10Ni5 bulk metallic glass. Finite element simulations of instrumented indentation were also performed to formulate an overall constitutive response. Comparing the experimentally obtained results with the finite element predictions, it can be stated that mechanical deformation of the bulk metallic glass can be described well by both Mohr–Coulomb and Drucker–Prager constitutive criteria. Using these criteria, the extent of material pile-up observed around the indenter was also estimated very well.

Calculation of the Mechanical Properties of FeB Layer's by Finite Element Method

Surface treatments of engineering materials are important for serviceable engineering components. One of the thermo-chemical surface treatments of steel based materials is the boriding process. In this study, low alloy steel substrates were borided by pack boriding process at 900 °C. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine, under applied peak loads of 800 mN, 1000 mN, 1200 mN and 1400 mN. To get the mechanical properties of FeB layers, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curve-fitted in Kick’s and Meyer’s law for the loading and the unloading part of the load-unload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods. These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n. The mechanical characterization of samples, finite element modeling was applied to simulate the mechanical response of FeB layer on low alloy steel substrate by using ABAQUS software package program.

A Model for the Calculation of Mechanical Properties of Hydroxyapatite Coatings on Ti6Al4V Substrate Using Finite Element Methods

The scope of this study is to find out yield curve on the coating-substrate system of hydroxyapatite (HA) by finite element modeling. With this regard, Hydroxyapatite (HA) coatings were successfully formed on Ti6Al4V substrates by using biomimetic technique. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine. In finite element modeling (FEM), mechanical properties of coatings were determined by using ABAQUS software package. This numerical study was carried out using an axisymmetric FEM model. To calculate the mechanical properties of coating, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curvefitted in Kick’s and Meyer’s law for the loading and the unloading part of the loadunload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n.

Residual stress measurement at the micrometer scale: focused ion beam (FIB) milling and nanoindentation testing

We present a new procedure for the determination of surface elastic residual stress by instrumented sharp indentation, based on nanoindentation testing on focused ion beam (FIB) milled micro-pillars. Finite element modeling (FEM) of strain relief after FIB milling of annular trenches demonstrates that full relaxation of pre-existing residual stress state occurs when the depth of the trench approaches the diameter of the remaining pillar. Considering this, the average residual stress present in the sample material can be calculated by the comparison of two different sets of load–depth curves, the first one obtained at the center of stress relieved pillars, the second on the undisturbed (residually stressed) surface. Analytical modeling of the contact stress distribution in non-halfspace conditions was adopted to take into consideration the additional boundary conditions given by the edges of pillars and the elastic properties of the substrate (in case of coatings). The results are presented for residual stress evaluation of a 3.8-µm TiN coating on WC–Co substrate obtained by cathodic arc evaporation-physical vapor deposition (CAE-PVD) techniques, showing an average compressive stress state of −5.63 GPa. This result is in close agreement with the estimation obtained by XRD (sin2 ψ method) analysis of −5.84 GPa of the same sample, adopting the same elastic constants.

Improved reverse analysis for material characterization with dual sharp indenters

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the indentation response of materials to single and dual sharp indenters. These issues are further extended in the present study. A parametric finite element analysis was performed to investigate the conical indentation response of elasto-plastic solids. Frictional effects are studied. Conical indenters of half-included angles from 50° to 88° are considered to examine several fundamental features of instrumented sharp indentation within the frame work of limit analysis. Regarding dimensional analysis, it is found that a Taylor series expansion according to the elastic indentation work-total indentation work ratio W e / W t can be used to improve dimensionless functions. Within this context, a new set of dimensionless functions is explicitly constructed for hardness and indentation parameters of single and dual indenters. Based on formulated functions, a reverse analysis with dual sharp indenters, which was previously proposed by the author, is improved to extract mechanical properties of materials.

Material characterization by dual sharp indenters

In a recent study, Le [Le, M.-Q., 2008. A computational study on the instrumented sharp indentations with dual indenters. International Journal of Solids and Structures, 45 (10), 2818–2835.] demonstrated that the yield strength Y can be replaced by the loading curvature C and hence the reduced elastic modulus-loading curvature ratio E ∗ / C and strain hardening exponent n can be used to govern characteristic parameters of indentation load–depth curves. Extending Le’s approach and regarding dimensional analysis, it is found that C / Y and E ∗ / Y can be used to investigate fundamental issues in instrumented sharp indentation. Based on extensive finite element analysis, a set of dimensionless functions are constructed for cone indenters of half included angles of 60° and 70.3°. Dimensionless relationships with respect to dual indenters are further explored. Several features of hardness are also considered. An inverse analysis procedure is suggested to estimate material properties, giving good inverse results for experimental data from the literature and representative materials. Sensitivity of inverse solution are studied and discussed. The results show that the proposed dual indenter method is quite robust and can be applied to a wide range of materials.

유한선단반경을 갖는 원뿔형 압입자에 의한 영률평가 수치접근법

본 연구에서는 원뿔형 압입자를 이용한 압입시험의 기초 유한요소해석으로부터 자기유사성을 나타내는 Kick's law 계수 C의 영향을 조사하고, 선단반경의 변화가 하중-변위 곡선에 미치는 영향을 회귀분석을 통해 살펴보았다. 아울러 항복강도와 변형경화지수 등의 변수들이 재료 영률평가에 미치는 영향을 분석하였다. 기존 영률 평가에 널리 사용되는 탄성이론에 기초한 Pharr 등의식을 일반적인 탄소성 금속재료에 적용하기 위하여 다양한 재료에 대한 유한요소해석을 수행하였다. 재료 영률평가 시 압입자 선단반경과 압입깊이의 영향을 최소화하기 위해 Pharr 등의 식에 수정된 보정계수 κ를 도입한 영률예측식을 제시하였다. 새로운 영률예측식은 텅스텐 카바이드와 다이아몬드 압입자일 때 모두 2%내의 평균 오차범위에서 각 재료의 영률을 평가할 수 있다.

An FIB study of sharp indentation testing on plasma-sprayed TiO 2

Instrumented sharp indentation is often employed for micromechanical investigation of thermal-spray coatings. However, rather complex dependencies of measured values on indentation load have been reported. To verify the possible influence of sub-surface cracking, Vickers and Berkovich indentations on plasma-spray TiO 2 were sectioned by FIB. Remarkable sub-surface cracking was found for indentations performed on the coating cross-section, even for rather low loads (1 N). Much less sub-surface cracking occurs when indenting the top surface, indicating material anisotropy. This preliminary investigation highlights the need for thorough studies of sub-surface cracking during instrumented sharp indentation.

A multi-cell FE-model for compressive behaviour analysis of heterogeneous Al-alloy foam

Compressive mechanical behaviours of closed cell Al-alloy foams produced by melt based and powder metallurgical methods were investigated by a finite element model composed of multiple unit lattices. The unit lattice consists of spherical and cubic sections possessing a thickness ratio between them. A Gaussian distribution of the relative density among the lattices and the random allocation of lattices were implemented in the model to address the structural heterogeneity. The constitutive relation for the lattice material was determined by a nondestructive instrumented sharp indentation test on the cell wall. The simulated compressive stress–strain curves for the ductile Al–Si–Ca foam were found to be in good agreement with the experimental ones over the entire strain range while the resistance of brittle Al–Si–Cu–Mg foam to the deformation turned out to be lower than that predicted by the model after about 0.50 strain. The discrepancy between experimental and simulation results for Al–Si–Cu–Mg foam in high strain range was associated with the disintegration of cell walls broken by the large deformation.