Indentation Technique Research Articles

Adhesive depth-sensing indentation tests: Slopes of the force–displacement curves

Depth-sensing indentation experiments are a very important tool for estimating mechanical properties of modern materials. A review of various aspects of contact problems that used as the theoretical basis for interpretation of depth-sensing nanoindentation experiments is presented. Usually, analytical treatment of the indentation tests is based on analysis of the slopes of the force–displacement curves according to the non-adhesive Hertz contact theory. However, molecular adhesion is crucially important for many physical processes at the micro/nano-scales. Here, depth-sensing indentation techniques are reviewed and analyzed using the recent results obtained for adhesive contact problems. Fundamental relations for adhesive nanoindentation tests are derived for both frictionless and no-slip boundary conditions within the contact region. It is argued that the adhesive effects may be very important for treatment of the nanoindentation tests because the slopes of the force–displacement curves may considerably differ from the slopes derived using the non-adhesive contact theory.

Instrumented indentation for determining stress and strain levels of pre-strained DC01 sheets

In classical mechanical testing, determining the stress and strain states of complex shape specimens turns out to be very challenging, especially in the most deformed regions. In the latter case, when not enough material is present, non-destructive testing is needed for determining the corresponding mechanical state. In this study, a novel approach, based on the local quasi-non-destructive instrumented indentation technique (IIT) coupled with the inverse analysis technique (IAT), is used to determine the stress and strain levels of pre-strained DC01 specimens using monotonic and non-monotonic loading paths. Monotonic and cyclic shear tests as well as Marciniak tests, in both plane and equi-biaxial strain states, are used to apply different pre-strain levels. For monotonic loading paths, i.e. monotonic shearing and Marcianiak tests, the applied methodology showed very satisfying results in determining the stress and strain states of the pre-strained specimens, especially for pre-strain values close to the representative indentation strain values. A maximum stress error of less than 15% was obtained in the case of the highest applied pre-strain value (29.04%). The purely isotropic Voce hardening law was adopted for determining the hardening behavior of the studied specimens in both cases: as-received and pre-strained. In the case of cyclic shear, a mixed isotropic-kinematic hardening law is to be used to determine the stress and strain states of the pre-strained specimens. Adopting a mixed isotropic-kinematic Chaboche hardening law led to satisfying results where the estimation errors of the applied pre-strain value and corresponding yield stress didn't exceed 6% and 1.3%, respectively. The obtained results show that the proposed indentation-based method can be very useful in estimating the work-hardening level and corresponding plastic deformation of pre-strained parts under various loading paths

Comparison of Oliver-Pharr and Work of Indentation Approach to Determine the Mechanical Properties of Melt-Spun Al-12%Wt.Si-0.5%Sb Alloy

In this research, the hardness and reduced modulus of Al-%wt.12-%wt.0.5Sb melt-spun alloy were evaluated by using depth sensing indentation and atomic force microscopy techniques. We considered two approaches, Oliver-Pharr and Work of Indentation, to analyse the load-displacement curves. The ratio of final depth to maximum depth was found to be higher than the reported critical value of 0.70, which mean that pile-up was dominant in the melt-spun. A pile-up around the deformed surface was observed from atomic force microscope, which is consistent with the aferomentioned result. The hardness calculated by Oliver-Pharr method was higher than that calculated by Work of Indentation Approach. According to the results, Work of Indentation Approach was more reliable than the Oliver-Pharr approach because of reducing pile-up affect.

Micromechanical properties of Dy3+ ion-doped (LuxY1-x)3Al5O12 (x = 0, 1/3, 1/2) single crystals by indentation and scratch tests

Three kinds of Dy3+ ion-doped (LuxY1-x)3Al5O12 (x = 0, 1/3, 1/2) single crystals fabricated by the Czochralski method with 4 at.% Dy3+ ion doping were investigated by indentation and scratch techniques under Vickers, Knoop, Berkovich, and spherical indenters to understand the influence of Lu ion on micromechanical properties and fracture behavior of Y3Al5O12 (i.e. YAG for x = 0) single crystals. The largest (or smallest) values of hardness, elastic modulus, and fracture toughness were found for x = 1/3 (or 1/2). The indentation size effect was explained by four different models with the Hays-Kendall approach being the most suitable one to determine the true hardness. Fracture toughness values of YAG crystals obtained by the Vickers hardness method agreed with those obtained by scratching with a spherical indenter based on linear elastic fracture mechanics.

Instrumented indentation based methods to assess fracture toughness (KIC) of self-compacting concrete: Influence of water to binder (w/b) ratio and type of concrete

The main objective of this paper is to compare the fracture toughness determined by instrumented indentation tests of a variety of self-compacting concretes (SCCs) and normal vibrated concretes (NVCs). For this purpose, five mixing compositions of self-compacting concrete (SCC) with different water/binder ratios of 0.33 to 0.41 (water/cement ratio = 0.44 to 0.56) and two mixing compositions of normal vibrated concrete (NVC) were prepared. The fracture behaviors of both (SCCs) and (NVCs) with laboratory-size specimens under the instrumented indentation test (IIT) were investigated. It was found that the fracture toughness values of the self-compacting concrete increased with the decreasing w/b ratio. The largest values of the stress intensity factor (KIC) were showed on the concretes with the lowest (w/b) ratio (w/b = 0.33, the case of SCC5). Moreover, it is confirmed that the self-compacting concretes exhibit larger fracture toughness than those of the normal vibrated concretes at the same compressive strength. The obtained results indicated that there existed a remarkable relationship between the water/binder (water/cement) ratio, fracture behavior and mechanical properties of these materials. It is shown that the instrumented indentation technique can be very useful for determination of the fracture parameters.

Evaluation of the ITZ modification efficiency via aggregate surface coating with nano SiO2 (NS) and its influence on properties

In order to effectively refine the porous microstructure of interfacial transition zone (ITZ) region in cement-based materials, the nano SiO2 (NS) was introduced into the mixture via aggregate pre-immerging in NS suspension to directly regulate the formation of ITZ microstructure. For comparison, a corresponding content of NS was directly added to the mixture during the casting process. The macro mechanical properties and micro pore structures of the specimens with varying modification methods and NS contents were assessed. The ITZ microstructures (in terms of porosity distribution and nano mechanical properties) were quantitatively characterized via the combination of BSE-SEM and nano indentation techniques. The results demonstrate that both modification methods could refine the microstructure of the bulk paste and ITZ. The directing adding method can more effectively modify the microstructure of the bulk paste with certain NS dosage (no more than 3%). At higher dosage, due to the agglomeration of the NS, the difference between two methods was not obvious. For ITZ modification, the aggregate pre-immerging method has more profound effect, from the aspects of reducing the ITZ thickness and decreasing the porosity of region in the extreme vicinity of aggregate surface (0–10 µm).

Direct Observation of Adhesion and Mechanical Behavior of a Single Poly(lactic-co-glycolic acid) (PLGA) Fiber Using an In Situ Technique for Tissue Engineering.

Nanometer- and submicrometer-sized fiber have been used as scaffolds for tissue engineering, because of their fundamental load-bearing properties in synergy with mechano-transduction. This study investigates a single biodegradable poly(lactic-co-glycolic acid) (PLGA) fiber's load-displacement behavior utilizing the nanoindentation technique coupled with a high-resolution in situ imaging system. It is demonstrated that a maximum force of ∼3 μN in the radial direction and displacement of at least 150% of fiber diameter should be applied to acquire the fiber's macroscopic mechanical properties for tissue engineering. The adhesion behavior of a single fiber is captured using a high-resolution camera. The digital image correlation (DIC) technique is adopted to quantify the adhesion force (∼25 μN) between the fiber and the tip. Adhesion force has also been quantified for the fiber after immersing in phosphate-buffered saline (PBS) to mimic the bioenvironment. A 4-fold increase in adhesion force after PBS treatment was observed due to water penetration and hydrolysis on the fiber's surface. A high similarity between mechanical properties of a single fiber and native tissues (elastic modulus of 10-25 kPa) and superior adhesion force (25-107.25 μN) was observed, which is excellent for promoting cell-matrix communication. Overall, this study examines the mechanics of a single fiber using innovative indentation and imaging processing techniques, disclosing its profound and striking roles in tissue engineering.

Surface finishing and tool wear in single point diamond turning of chemical vapour deposited tungsten carbide hard coatings

Precision-engineered components which operate in demanding conditions often require the application of hard coatings such as tungsten carbide (WC) to improve their functional properties. Following the coating deposition process, a surface finishing or machining operation is often required to correct the sizing or achieve adherence to geometrical tolerancing and surface finish requirements. Single point diamond turning (SPDT) is a widely used ultraprecision machining technique for the fabrication of high-end engineering components made up of ductile materials, making it a desirable technique as a post-coating machining or finishing process. In this study the machinability of hard CVD W/WC coatings with a hardness of 1120 ± 15 HV and a thickness of 100 μm using SPDT was investigated. Here we report the results of axial and transverse turning using a cutting speed of 600 rpm and feed rates of 1 and 5 μm respectively. Experimental results show that an Ra of 0.2 μm is achieved with a diamond tool having a 0.5 mm nose radius. Significant tool wear was observed at the rake/flank edge of the diamond tool due to the coating's hardness. Surface and cross-sectional analysis of the samples' machined areas revealed presence of adhesive and abrasive wear. The occurrence of material pile-up due to tool loading on the surface of the coating was investigated through the indentation technique which demonstrated the occurrence of material deformation contributing to the overall surface roughness.

The dependency of work hardening on dislocation statistics in cold rolled 1050 aluminum alloy

In this contribution, the phenomenon of work hardening is studied as a function of the nature of dislocation evolution with change in the level of deformation for commercially available 1050 Al alloy. To investigate the nature of dislocations in the cold-rolled aluminum alloy, total dislocation density was calculated using the indentation technique as well as by implementing two numerical approaches. For estimation of a statistically representative value of geometrically necessary dislocations (GND), electron backscattering diffraction measurements were performed over a large area (~ 0.5 mm2). The GND density of deformed samples was quantified by the implementation of a modified kernel average misorientation technique as well as by using Nye's dislocation density tensor for corresponding lattice curvature. The values of statistically stored dislocations (SSD) are obtained based on the assessment of the total dislocation density and GND values after different straining levels. The study provides both qualitative and quantitative illustrations of the mechanism of dislocation multiplication as thickness reduction increases, thereby, increasing the hardness of the samples. The results obtained reveal that the hardening of rolled materials is majorly governed by the SSD density at lower deformation. However, as the deformation level approaches the value of ~0.4, the density of GNDs rises and its contribution becomes significantly accountable for the strain hardening of the material. On the other hand, it has been observed that at lower straining levels the generated GNDs are trapped at grain boundaries and have a high contribution towards forest dislocations but with an increase of strain, the GNDs have a tendency to contribute nearly equally to mobile and forest dislocations. The estimated stored energies for samples subjected to rolling reduction ranging between 5.3 and 76% tend to change between the 5.6 kJ/m3 and 343.3 kJ/m3.

Cylindrical Indentation to Selectively Stress Nanoscale CMOS Transistors

Advanced indentation techniques have been introduced to study the effects of multiple stresses on the transistor characteristics with using a cylindrical tip with various alignments. Particularly, controlling the cylinder tip orientation relative to the transistor channel direction is proposed to selectively strain the silicon channels in order to induce very different selectively controlled stresses. Several tip alignments allow to shift the stresses from uniaxial towards biaxial stress as well as to induce shear stress. Ring oscillator circuits based on NAND and NOR gates are used to monitor the stress effects on the characteristic circuit frequency as well as on the individual transistors. Finite Element simulations help to identify optimized setup properties for the targeted application. Comparison with previous indentation experiments derives the specific influence of each stress tensor component on the transistor characteristics.

A novel combined dual-conical indentation model for determining plastic properties of metallic materials

Based on the equivalent energy principle (EEP), an explicit theoretical model between conical indentation response and uniaxial mechanical parameters is derived. In order to avoid the defect that sharp indentation technique always requires at least two indenters to penetrate different positions successively and the compatibility between the indentation points, an energy-based combined dual-conical indentation (CDI) model is created by using a novel combined indenter with dual conical surfaces. A typical piecewise load-depth curve is observed during the combined dual-conical indentation and two characteristic loading curvatures are respectively acquired from the single penetration response. Numerical verifications for the novel method are conducted by finite element analysis (FEA) within a large range of elastic–plastic materials. For six kinds of metallic materials, based on the stable load-depth curves obtained by the combined indentation tests, the uniaxial stress–strain curves as well as the yield stress, strain hardening exponent and tensile strength are predicted by CDI model. The results show that the predictions of CDI method are consistent with those from uniaxial tension. The novel method is expected to be more convenient for mechanical testing and evaluation of materials or structures.

Numerical and analytical study to the uniqueness problem in identification of uniaxial parameters through spherical indentation

In the identification of uniaxial parameters using indentation techniques, it is usually difficult for numerical optimization methods to converge to the experiment result due to the uniqueness problem which manifests as hard-to-distinguish load-penetration (L-h) curves for notably different stress-strain curves. In this paper, an efficient and easy-to-use optimization scheme named local optimization-fitting (LOF) approach is established and applied to spherical indentation, which can not only give an accurate identification to the uniaxial parameters, but also provide the possible hard-to-distinguish materials of the tested material and their distribution on the parameter plane. Based on the distributions of hard-to-distinguish materials given by LOF, a plastic-strain-energy-density (PSED) assumption is proposed and verified analytically. By applying the PSED assumption, uniqueness problem is studied beyond the limitation of power law stress-plastic strain relation. Other influencing factors to uniqueness problems such as friction and strain gradient hardening are also discussed.

Interpretable Machine Learning Approach for Identifying the Tip Sharpness in Atomic Force Microscopy

Atomic force microscopy (AFM) is routinely used with indentation techniques to characterize the plastic deformation of materials. The accurate quantification of the features associated with the indent, which is used to quantify the hardness and indentation deformation mechanisms, depends on the sharpness of the AFM tip used for imaging. However, identifying the tip-sharpness of an atomic force microscope requires non-trivial measurements. Here, using machine learning, we develop a model to predict the tip sharpness of the AFM cantilever directly from the indent images. Further, we employ explainable machine learning models, such as integrated gradients and gradient shap, to interpret the features learned by the model. Altogether, we show that machine learning approaches can accelerate experiments by providing non-trivial information about the instrument performance, thereby enabling researchers to perform better quality experiments.

A Continuum-Tensegrity Computational Model for Chondrocyte Biomechanics in AFM Indentation and Micropipette Aspiration

Mechanical stimuli are fundamental in the development of organs and tissues, their growth, regeneration or disease. They influence the biochemical signals produced by the cells, and, consequently, the development and spreading of a disease. Moreover, tumour cells are usually characterized by a decrease in the cell mechanical properties that may be directly linked to their metastatic potential. Thus, recently, the experimental and computational study of cell biomechanics is facing a growing interest. Various experimental approaches have been implemented to describe the passive response of cells; however, cell variability and complex experimental procedures may affect the obtained mechanical properties. For this reason, in-silico computational models have been developed through the years, to overcome such limitations, while proposing valuable tools to understand cell mechanical behaviour. This being the case, we propose a combined continuous-tensegrity finite element (FE) model to analyse the mechanical response of a cell and its subcomponents, observing how every part contributes to the overall mechanical behaviour. We modelled both Atomic Force Microscopy (AFM) indentation and micropipette aspiration techniques, as common mechanical tests for cells and elucidated also the role of cell cytoplasm and cytoskeleton in the global cell mechanical response.

Role of Ti3AlC2 MAX phase on characteristics of in-situ synthesized TiAl intermetallics. Part IV: mechanical properties

In this study, the 4th part of a series of publications on the sintering and characterization of TiAl-Ti3AlC2 composite materials, the mechanical properties were measured and discussed. For this purpose, different contents of synthesized Ti3AlC2 reinforcement (10, 15, 20, 25, and 30 wt%) were added to metallic Ti and Al powders, then ball-milled and manufactured by spark plasma sintering (SPS) for 420 s at 900 ºC under 40 MPa. Flexural strength, fracture toughness and Vickers hardness were measured by 3-point technique, SENB method, and indentation technique, respectively. Increasing the Ti3AlC2 content resulted in improvement of the mechanical properties, so that TiAl-25 wt% Ti3AlC2 composite showed the best flexural strength and Vickers hardness (270 MPa and 4.11 GPa, respectively). Increasing amount of Ti3AlC additive had no significant effect on fracture toughness. Densification improvement, in-situ formation of Ti2AlC, and limitation of grain growth were recognized as the reasons of mechanical properties enhancement. In contrast, further addition of Ti3AlC2 (30 wt%) decreased the mechanical properties due to the reduction of density and formation of more Ti2AlC agglomerates in grain boundaries.

Crack-healing behaviour of MoSi2 dispersed Yb2Si2O7 environmental barrier coatings

MoSi2 doped Yb2Si2O7 composites were designed to extend the lifetime of Yb2Si2O7 environmental barrier coatings (EBCs) via self-healing cracks during high-temperature applications. Yb2Si2O7–Yb2SiO5–MoSi2 composites with different mass fractions were prepared by applying spark plasma sintering. X-ray diffraction results confirmed that the composites consisted of Yb2Si2O7, Yb2SiO5, and MoSi2. The thermal expansion coefficients (CTEs) of the composites increased with an increase in the MoSi2 content. The average CTE of the 15 wt% MoSi2 doped Yb2Si2O7 composite was 5.24 × 10−6 K−1, indicating that it still meets the CTE requirement of EBC materials. After being pre-cracked by using the Vickers indentation technique, the samples were annealed for 0.5 h at 1100 or 1300 °C to evaluate the crack-healing ability. Microstructural studies showed that cracks in 15 wt% MoSi2 doped Yb2Si2O7 composites were fully healed during annealing at 1300 °C. Two mechanisms may be responsible for crack healing. First, the cracks were filled with SiO2 glass formed by MoSi2 oxidation. Second, the formed SiO2 continued to react with Yb2SiO5 to form Yb2Si2O7, which can cause cracks to heal owing to volumetric expansion. The Yb2Si2O7 formation with smaller volume expansion is more beneficial.

Impact of Micro-Indentation on Hardness and Indentation Depth of Ni-Cr Super Alloys

ABSTRACT A material’s (metal, composite, polymer, etc.) behaviour is greatly influenced by the indentation hardness and elastic modulus during any operation (sliding, fretting, turning, etc.). To measure the micromechanical properties of surfaces, subsurfaces and coated thin layers of materials, depth-sensing measurement indentation techniques are most commonly used. The present study aims to develop a compressive model to investigate the influence of indentation parameters on the indentation hardness and indentation depth of Ni-Cr superalloy during indentation experiments. Experiments were conducted based on model L18 (21*32) full factorial design with a mixed orthogonal array using a microhardness tester. The experiments revealed that indentation hardness values show a normal indentation size effect with respect to indentation load. Indentation depth values increase with the increase in indentation load. Taguchi's approach and the regression analysis were used to model the indentation hardness and indentation depth with respect to indentation parameters. Analysis of variance was employed to check the effect of input parameters on performance outputs. The experimental and predicted values show a good degree of proximity. However, indentation load (79.22% and 52.34%) was found to be the most dominant parameter affecting indentation hardness and indentation depth, respectively, followed by dwell time.

Powder Metallurgical Processing of Sn-Reinforced Al-Cu-Fe Quasicrystals: Structure, Microstructure and Toughening Behavior

The present work deals with powder metallurgical processing of Sn-reinforced Al-Cu-Fe icosahedral quasicrystalline (IQC) composites processed through mechanical milling (MM) followed by hot pressing and pressureless sintering. The structure, microstructure and toughening behavior of the nanocomposite powders and bulk samples were investigated through X-ray diffraction (XRD), optical metallography (OM), scanning electron microscopy (SEM) and indentation techniques. The XRD pattern suggested the coexistence of IQC and λ-Al13Fe4 (mC102; a = 1.549 nm, b = 0.808 nm, c = 1.248 nm) and B2-type Al (Cu, Fe) (cP2; a = 0.29 nm) crystalline phases in milled as well as sintered samples. The face-centered icosahedral (FCI) ordering was persistent even after 40 h of milling and sintering. The structural transformation during MM influences the indentation behavior of IQC-Sn nanocomposite powders, and the microhardness was found to be in the range of ~5.3 to 7.3 GPa. Further, efforts were made to study the indentation behavior of IQC-Sn composite prepared by pressureless sintering and hot pressing. The fracture toughness of the IQC-10Sn hot-pressed sample was found to be ~1.92 MPa.√m, which is ~22% higher than that of the as-cast and annealed IQC. The enhancement in the fracture toughness resulted mainly from the inhibition of cracks by Sn reinforcement particles. This suggests that powder metallurgical processing can produce the IQC-Sn composite with an optimal combination of microhardness and fracture toughness.

Microstructure and load bearing capacity of TiN/NbN superlattice coatings deposited on medical grade CoCrMo alloy by HIPIMS

In recent years significant progress has been made in the application of various ceramic, namely Metal nitride (MeN) functional coatings to engineer the surfaces of medical implants utilising metal-on-metal (MoM) articulation. This article reports on the load bearing capacity and structural response of TiN/NbN superlattice coatings deposited on medical grade CoCrMo alloy substrate under the application of localised load and the subsequent crack formation mechanism. The coatings have been deposited by mixed High Power Impulse Magnetron Sputtering-Unbalanced Magnetron Sputtering (HIPIMS-UBM) process. In the case of TiN/NbN coating deposited on CoCrMo substrate where Ecoating/Esubstrate is as high as 1.81 indicating that the substrate does not provide the necessary load bearing support for the brittle thin film, the utilisation of the Berkovich indentation technique proved to be a potent approach to study coating material as well as structural response to applied concentrated load. FIB/SEM analyses of the indented coatings revealed that in the hard-on-soft material systems cracks will initiate due to sub-coating substrate deformation and then propagate towards the coating surface. The FIB/SEM and low magnification XTEM analysis showed that an exceptionally strong TiN/NbN coating substrate adhesion bonding was achieved due to the utilisation of the HIPIMS pre-treatment. High resolution XTEM analyses revealed, for the first time, that during the indentation a collective rotation and alignment of the individual layers of the superlattice stack takes place without compromising coatings integrity which is clear evidence for the exeptionally high coating fracture toughness. The high toughness of the superlattice structured TiN/NbN coatings combined with their exceptionally high adhesion on madical grade CoCrMo ranks them as a strong candidate for medical implant applications.

Assessment of Mechanical Properties of Aged Composite Propellant Using Non‐Destructive Indentation Technique in Solid Propellant Rocket Motor

AbstractAgeing study of composite propellant is one of the important aspects for the long term usage of a solid propellant rocket motor (SPRM). The assessment of mechanical properties is essential to predict the structural performance of rocket motors before its flight test. Mostly, the study of ageing behavior of composite propellant is limited to sample level which is subjected to either for normal ageing or accelerated ageing. In the present study, an attempt was made to assess the aging behavior of HTPB based composite propellant at full scale rocket motor level using a non‐destructive indentation technique. The mechanical properties of naturally aged HTPB based composite propellant samples were comprehensively studied by both Universal Testing Machine (UTM) and indentation technique. The mathematical correlation was developed using least square method between UTM and indentation data. An attempt was made to establish the method to assess the aging behavior of composite propellant by indentation technique directly. The developed correlation was validated on aged composite propellant samples. Further, indentation technique was used to assess the mechanical properties of the propellant of in‐flight fielded SPRM which was 11 years old.