Continuous Stiffness Measurement Research Articles

A new nanoindentation approach for determining both indentation size effect and continuous apparent activation volume during loading of nanocrystalline Ni and Ni-20 wt.% Fe alloy

A new nanoindentation approach is developed in this study to determine both indentation size effect (ISE) and continuous apparent activation volume () during loading of nanocrystalline nickel (NC Ni) and nanocrystalline nickel-20 wt.% iron alloy (NC Ni-Fe alloy). This approach involves conducting nanoindentation tests under loading modes controlled by both constant strain rate (CSR) and constant loading rate (CLR). Firstly, a new empirical expression for the parameter in the modified Nix-Gao model is established to study the strain rate dependence of the ISEs created in the CSR and CLR tests. Then, continuous data of each individual sample (indentation) during loading are obtained in the CLR test through the alternative use of continuous stiffness measurement technique. The stress dependence of is analyzed based on Duhamel et al.’s model, which considers the role of vacancies generated during inhomogeneous dislocation nucleation. Finally, based on the above experimental and theoretical work as well as transmission electron microscopy observation, the influences of loading mode, loading rate, and material properties (stacking fault energy) on resulting intrinsic hardness of NC Ni and NC Ni-Fe alloy are analyzed. The nanoindentation approach developed in this study provides profound insights into the mechanical behaviors during loading and underlying mechanisms of materials.

Increase in elastic and hardness anisotropy of titanium with oxygen uptake due to high temperature oxidation: A multimodal framework using high speed nanoindentation mapping

Titanium and its alloys combine an important mechanical anisotropy and a high capacity to dissolve oxygen. The detailed evolution of the elastic compliance of titanium as a function of its oxygen content is only partially known, despite its importance in structural applications. Here, high speed nanoindentation mapping (HSNM) was conducted on a grade 2 commercially pure titanium (CP-Ti) to probe elastic and hardness anisotropy as well as property evolution as a function of the oxygen content within Ti using pre-oxidized specimens. The oxygen concentration investigated ranged from 600 ppm to 20% atomic. Pre-oxidation of the CP-Ti was performed at 700 °C for 100 h under air to create a gradient of oxygen content within the metal, denoted oxygen-rich layer (ORL). Local oxygen content was quantified using microprobe analyses (EPMA) and crystal orientation using electron backscattered diffraction (EBSD). Reduced modulus and hardness maps were obtained on the pre-oxidized sample within the ORL and far from the ORL using large but highly resolved nanoindentation technique in continuous stiffness measurement (CSM) mode. Data merging techniques were used on this multi-modal dataset to statistically link local mechanical properties to chemical and crystal orientation information. Oxygen insertion in the Ti lattice was found to significantly increase the hardness and elastic moduli of titanium and was correlated to orientation of the c-axis of the α-Ti as a function of the nanoindentation loading direction. Using the Vlassak and Nix theory, it was possible to identify the evolution of the Cij terms of the stiffness matrix as a function of the oxygen content up to 20% at. in O.

Mechanical softening of CuX alloys at elevated temperatures studied via high temperature scanning indentation

The thermal stability and temperature dependent hardness of ultrafine-grained Cu-alloys CuSn5 and CuZn5 after high pressure torsion are investigated using the high temperature scanning indentation (HTSI) method. Fast indentations are carried out during thermal cycling of the samples (heating-holding-cooling) to measure hardness and strain rate sensitivity as a function of temperature and time. The microstructures after each thermal cycle are investigated to characterize the coarsening behaviour of both alloys.Results show that the thermal stability of the tested alloys can be expressed in terms of several temperature regimes: A fully stable regime, a transient regime in which growth of individual grains occurs, and finally a regime in which the microstructure is fully coarsened. The onset of grain growth is accompanied by high strain rate sensitivity on the order of 0.2–0.3. Furthermore, the obtained hardness and strain rate sensitivity values are in good agreement with continuous stiffness measurement (CSM) and strain rate jump (SRJ) experiments. This highlights the applicability of the HTSI method to the characterization of the thermomechanical properties of ultrafine-grained alloys.

Elastic-plastic properties of ceramic matrix composites characterization by nanoindentation testing coupled with computer modeling

The nanoindentation test is utilized to measure the hardness and elastic modulus of various components within Ceramic Matrix Composites (CMCs), including continuous stiffness measurement (CSM) and quasi-static testing. To further characterize the elastic-plastic properties of CMCs, an efficient method is proposed by using backpropagation (BP) neural network inversion, which is based on the relationship between load and depth obtained by the nanoindentation experiment and Abaqus finite element simulation. As part of the analysis, the load-depth (p-h) curve is simplified to six characteristic parameters through the fitting of the experimental results. The pre-estimated elastic-plastic characteristics are utilized to model the nanoindentation test for CMCs. A BP neural network is used to perform deep learning on simulation data, which leads to a network structure that matches the trained parameters of the p-h curve and elastic-plastic properties. The experimental data for fiber is inputted into the network to acquire the elastic-plastic properties required in practice. The accuracy of the proposed method is verified by comparing the inversion results with the simulation outcomes.

Investigation of process-induced periodic structure on n-type 4H-SiC with corresponding mechanical characteristics estimation

A dicing process that combines the laser scribing and mechanical breaking procedures is demonstrated to achieve high-quality n-type 4 H-silicon carbide (SiC) without generating the edge defect and chipping phenomenon. Presented dicing process is successfully implemented on a 40 mm × 40 mm SiC workpiece with a thickness of 150 μm, and it separated 1 mm × 1 mm and 2 mm × 2 mm chips. However, the process-induced stress introduces stress-induced amorphization into the cut cross section of fabricated SiC. Moreover, vertical thermal cracking is found on the periodic tip region treated with laser scribing. To investigate the influence of stress-induced damage on mechanical characteristics of fabricated SiC, the nanoindentation technique is utilized to identify modulus gradient and mapping behavior. Analysis results reveal that damage-induced degradation on modulus behavior is observed from the edge of the periodic tip region to the hinterland region, which the measured reduced modulus results of aforementioned regions are 325.87±56.21 and 284.85±30.02 GPa, respectively. Moreover, the thickness of the damaged layer that covers the cut cross section is estimated to be at least 150 nm by utilizing continuous stiffness measurement (CSM) nanoindentation. The modulus mapping characteristics on the molten and unmolten regions are within the range of 90–160 GPa and 180–300 GPa, respectively. The composition of molten region is investigated by the EDS analysis and the corresponding reduced modulus results is revealed as 105.86±16.46 GPa.

Comparison of the Viscoelastic Properties and Plasticity of Early and Late Wood of Pine and Spruce by Continuous Stiffness Measurement during Nanoindentation

Comparison of the Viscoelastic Properties and Plasticity of Early and Late Wood of Pine and Spruce by Continuous Stiffness Measurement during Nanoindentation

Designing a Compact High-precision Positioner with Large Stroke Capability for Nanoindentation Devices

A new design of a fine positioner or high precision driven unit with a large positioning range is proposed for a custom-made in-situ indenter device equipped inside an SEM chamber. The design configuration of the proposed system is size-effective for the confined working area of the SEM chamber. The indentation depths can be precisely varied by controlling the fine positioner driven by a piezoelectric actuator. The main goal is to achieve very deep penetrations toward the bottom layers of tall or large-size scale specimens by single indentation, without the need for sequential indentations. Thus, the proposed design can eliminate the need for sequential adjustments of the specimen position with respect to the indenter tip as currently being practiced by the researchers. The specimen position adjustment after each indentation heavily depends on the coarse positioner and its accuracy level in a sub-millimeter regime which could result in position errors and unwanted lateral forces in the nanoindentation process. Therefore, the sequential indentations technique could lead to considerable variations in the outcomes of nanoindentation tests done on similar specimens. The proposed design will be realized to deploy in the Continuous Stiffness Measurement (CSM) techniques generally used to evaluate elastic properties as a function of continuous penetration depth with high-frequency loading and unloading cycles.

Effect of combined tobacco use and type 2 diabetes mellitus on prevalent fibrosis in patients with MASLD.

Several studies have investigated the independent effect of cigarette smoking or type 2 diabetes mellitus (T2DM) on MASLD. However, the interaction effect between tobacco consumption and T2DM on MASLD severity remains underexplored. In this study, we assessed the combined effect of tobacco use and T2DM on hepatic fibrosis in MASLD. We conducted a single-center retrospective cross-sectional analysis of eligible participants from the Mass General Brigham Fibroscan© database. The participants were divided into 3 groups: those with T2DM and a history of tobacco use (primary exposure group), those with T2DM but no history of tobacco use (secondary exposure group), and those without T2DM and no history of tobacco use (reference group). An additional model was developed, which included a fourth group, participants with a history of tobacco use but no T2DM. The likelihood of fibrosis was determined using a defined fibrosis-4 index cutoff value of 1.3. In addition, we computed the estimated marginal means for liver stiffness measurement and compared the values among the exposure groups. Bivariable and multivariable logistic regression models were used to explore the associations between the exposure groups and the risk for hepatic fibrosis. Overall, 598 individuals were enrolled in the study. The bivariable logistic regression model revealed a significant independent association between T2DM, combined smoking and T2DM, and the outcome of interest, fibrosis. Age, sex, metabolic syndrome, aspirin use, statin use, hemoglobin A1C (A1C), and total bilirubin level were also significantly associated with fibrosis. In the adjusted fibrosis-4 multivariable model (comparing exposure groups to controls), cigarette smoking and T2DM interaction had higher odds of prevalent fibrosis (aOR, 3.04; 95% CI, 1.62-5.76), compared to those with T2DM alone (aOR 2.28; 95% CI, 1.37-3.85). The continuous liver stiffness measurement comparison across the exposure group showed an estimated marginal means of 6.26 (95% CL: 5.58-6.94), 7.54 (95% CL: 6.78-8.30), and 7.88 (6.78-8.99) for the reference group, T2DM only group, and tobacco-T2DM group, respectively. The diabetes-only group and the combined tobacco-T2DM group had statistically significant associations with liver stiffness measurement (p values: 0.013 and 0.014, respectively). Although diabetes is independently associated with hepatic fibrosis in patients with MASLD, the combination of tobacco consumption and diabetes is associated with a higher prevalence of fibrosis. Therefore, lifestyle change through tobacco use cessation in patients with diabetes could be beneficial in reducing the incidence of liver fibrosis among individuals with MASLD.

Microstructures and mechanical properties of Sb-doped ZnO thin films deposited on a-plane sapphire substrates

The structural features and nanomechanical properties of ZnO and Sb-doped (1.0 at%) ZnO (SbZO) thin films deposited on a-plane sapphire substrates by radio-frequency (RF) magnetron sputtering are comparatively investigated in this study. The X-ray diffraction and atomic force microscopy analyses indicated that both ZnO and SbZO thin films were highly (002)-oriented albeit with somewhat different grain structure and surface morphologies. Nanoindentation results of both films exhibited apparent discontinuities (so-called pop-ins) in the load-displacement curves (P-h curves), while no discontinuity was observed in the unloading segment of the P-h curves. By using a Berkovich nanoindenter operating with the continuous contact stiffness measurement mode, the obtained hardness and Young's modulus of ZnO (SbZO) thin films are 7.3 ± 0.2 (8.5 ± 0.4) GPa and 259.6 ± 17.8 (327.4 ± 13.9) GPa, respectively. Furthermore, the facture toughness and fracture energy of ZnO and SbZO thin films obtained by Vickers indentation were also compared.

A novel methodology to estimate hydrogen diffusivity and its applications in revealing hydrogen effects in CoCrNi medium-entropy alloy versus 316L stainless steel

Hydrogen diffusivity is one of the important factors affecting the susceptibility to hydrogen embrittlement of metals and alloys. Here, we proposed a novel approach to estimate hydrogen diffusivity in FCC alloys by performing nanoindentation experiments with continuous stiffness measurement. In consideration of the plastic zone size around the indentation, the relationship between hydrogen-induced hardness change and the depth from the sample surface was established for two typical FCC alloys—316L stainless steel (SS) and CoCrNi medium-entropy alloy (MEA)—subjected to hydrogen-charging and subsequent room-temperature aging. By combining with the estimation of the through-thickness distribution of hydrogen concentration, hydrogen diffusivity values were successfully determined, which agreed well with the literature data. It was revealed that CoCrNi MEA exhibited a hydrogen diffusivity ∼0.68 times higher than that in SS316L, and that hydrogen-induced softening upon long-term aging (at room temperature) was observed in CoCrNi but not in SS316L. The underlying mechanisms for the distinct hydrogen-related phenomena in CoCrNi MEA were elucidated based on the density functional theory calculations of hydrogen solution energy and vacancy formation energy.

Calibration and data-analysis routines for nanoindentation with spherical tips

Instrumented spherical nanoindentation with a continuous stiffness measurement has gained increased popularity in microphysical investigations of grain boundaries, twins, dislocation densities, ion-induced damage, and more. These studies rely on different methodologies for instrument and tip calibration. Here, we test, integrate, and re-adapt published strategies for tip and machine-stiffness calibration for spherical tips. We propose a routine for independently calibrating the effective tip radius and the machine stiffness using standard reference materials, which requires the parametrization of the effective radius as a function of load. We validate our proposed workflow against key benchmarks and apply the resulting calibrations to data collected in materials with varying ductility to extract indentation stress–strain curves. We also test the impact of the machine stiffness on recently proposed methods for identification of yield stress. Finally, we synthesize these analyses in a single workflow for use in future studies aiming to extract and process data from spherical nanoindentation.Graphic abstract

Investigation of dynamic micromechanical properties of biodegradable elastic material by continuous stiffness measurement analysis

Micromechanical properties of polymeric materials play a critical role in various biological applications in terms of their biocompatibility and mechanical durability. Apart from material properties such as modulus and density, viscoelastic properties play a crucial role during the design and fabrication of devices. Here, we investigated the viscoelastic properties of poly (glycerol sebacate) (PGS), a widely used bioresorbable elastic material, through the nanoindentation technique, configured by the continuous stiffness measurement (CSM) method at frequencies from 10 Hz to 50 Hz. The results revealed that the storage modulus (E’) depends on the test frequency and cannot be ignored as the results showed significant changes. Additionally, increasing the curing temperature of PGS specimens between 150 to 170°C allows modifying the storage modulus of samples between 0.52 MPa and 1.05 MPa at 10 Hz. The results were also confirmed using the dynamic mechanical measurements to validate the reliability of the CSM nanoindentation technique.

Elastic modulus identification of particles in particulate composite through nanoindentation

The characterization of the constitutive behavior of embedded particles is crucial for the mechanical analysis of functional particulate composites. However, current methods for identifying the elastic parameters through instrumented indentation tests lack robust theoretical foundations. In this study, a series-connection analytical model was proposed to determine the Young's modulus of the embedded particles based on the Oliver-Pharr (O-P) model. Additionally, a simplified regression function was derived from the complete analytical model.To validate the accuracy of these methods in estimating the Young's modulus, 2D indentation simulations were conducted. Furthermore, in order to facilitate practical engineering applications, a data processing strategy was developed and implemented to determine the statistical value of the Young's modulus for LiNixMnyCozO2 (NMC) particles in the cathode of a Lithium-ion battery (LIB). Moreover, data obtained from continuous stiffness measurement (CSM) of a single embedded NMC particle were utilized to verify the reliability of the simplified regression function. The simplified regression function was found to possess significant engineering potential in related studies, as it enables a quick and reliable approximation of the Young's modulus of embedded particles without requiring detailed experimental information.

Nanoindentation creep of supercrystalline nanocomposites

Supercrystalline nanocomposites (SCNCs) are inorganic-organic hybrid materials with a unique periodic nanostructure, and thus they have been gaining growing attention for their intriguing functional properties and parallelisms with hierarchical biomaterials. Their mechanical behavior remains, however, poorly understood, even though its understanding and control are important to allow SCNCs’ implementation into devices. An important aspect that has not been tackled yet is their time-dependent deformation behavior, which is nevertheless expected to play an important role in materials containing such a distribution of organic phase. Hereby, we report on the creep of ceramic-organic SCNCs with varying degrees of organic crosslinking, as assessed via nanoindentation. Creep strains and their partial recoverability are observed, hinting at the co-presence of viscoelasticity and viscoplasticity, and a clear effect of crosslinking in decreasing the overall material deformability emerges. We rationalize our experimental observations with the analysis of stress exponent and activation volume, resulting in a power-law breakdown behavior and governing deformation mechanisms occurring at the organic sub-nm interfaces scale, as rearrangement of organic ligands. The set of results is reinforced by the evaluation of the strain rate sensitivity via strain rate jump tests, and the assessment of the effect of oscillations during continuous stiffness measurement mode.

Microindentation analysis of mechanical properties evolution during an artificial hydrocarbon generation process

The last decade witnessed rapid growth of shale oil and gas production. Increasing numbers of shale reservoirs have been explored and developed. Since hydrocarbon generation is an important process in forming a shale reservoir, it has attracted great attention from researchers. However, previous works mainly focus on geochemical changes during the hydrocarbon generation process, and investigations of the change of other parameters are insufficient. In this study, we intend to fill this gap in the literature by examining the mechanical properties evolution of organic-rich shales during an artificial hydrocarbon generation experiment. Continuous stiffness measurement (CSM) and microindentation test are used to measure the mechanical properties of rocks. The result of CSM shows the influence of indentation depth on Young's modulus. Three stages are identified, and a displacement of 4000 nm–6000 nm is determined to be appropriate for measuring bulk mechanical properties. Microindentation results of shales at different hydrocarbon generation stages exhibit a hill-like trend. The Young's modulus with an initial value of 42.15 GPa increases as the hydrocarbon generation proceeds, reaches a maximum value of 46.49 GPa, and then begins to decrease and reaches the lowest value of 37.41 GPa. Indentation hardness and estimated fracture toughness by an energy-based method show similar trends to Young's modulus. Scanning electron microscope observation of post-hydrocarbon-generation samples may provide an explanation of the hill-like trend.

A multi-technique and multi-scale analysis of the thermal degradation of PEEK in laser heating

The present work studies the thermal degradation of laser-heated poly-ether-ether-ketone (PEEK) as the heating duration increases. Its damage morphology, chemical composition, crystallinity content, and mechanical properties are examined with optical microscopy, attenuated total reflection-Fourier transform infrared spectroscopy, differential scanning calorimetry, Raman spectroscopy, and continuous stiffness measurement nanoindentation. The applicability of those methods in detecting the thermal degradation of laser-heated PEEK and assessing the induced thermal damage is highlighted. Results show that short-time laser heating acts as an annealing process that improves the crystallinity and hardness on the affected surface of PEEK by up to 5.1% and 10.8% respectively. With a further increase in the heating duration, surface carbonisation occurs and a char layer is formed. Surface carbonisation is associated with the thermal limits of PEEK in laser heating decreasing by up to 50% its hardness and by 45% its indentation modulus. Finally, the char layer is found to act as a shielding mechanism that protects the bulk PEEK from the applied thermal load, resulting in mostly superficial thermally induced damage.

Nanoindentation creep behavior of nanocrystalline Ni and Ni-20 wt% Fe alloy and underlying mechanisms revealed by apparent activation volumes

Nanoindentation creep behavior and underlying mechanisms of nanocrystalline (NC) Ni and NC Ni-20 wt% Fe (Ni-Fe) alloy were investigated at room temperature by a new testing method. The continuous creep strain rate versus creep stress data and hence the continuous apparent activation volume versus creep stress data in the entire holding stage on each single sample were achieved under a loading rate-controlled mode by a cooperative use of the continuous stiffness measurement (CSM) technique. Furthermore, the dependence of the apparent activation volume on the creep stress was interpreted by performing a theoretical analysis. Based on the above experimental and theoretical results and the high-resolution transmission electron microscope observation of the microstructures, the effects of the loading rate and stacking fault energy on the nanoindentation creep behavior of NC Ni and NC Ni-Fe alloy and the underlying mechanisms were analyzed. It was demonstrated that NC Ni-Fe alloy shows higher creep resistance in the transient regime, but lower creep resistance in the steady-state regime compared to NC Ni. The contact stiffness data obtained by the CSM technique in a strain rate-controlled mode can be used to determine the creep stress data from the creep displacement data obtained in a loading rate-controlled mode.

Microscale fracture toughness degradation of notched solder microcantilevers under varied accelerated aging process

Experimental fracture mechanics at the microscale became an indispensable tool for understanding and analyzing the solder joint degradation in microelectronics packaging, which is facing severe temperature swings and is prone to failure due to the delamination induced by the microcracks. In this work, we studied the fracture behavior of the widely used Sn-based solder on microscale with the notched microcantilevers fabricated using the focused ion beam (FIB) milling. The microcantilever bending tests were performed to demonstrate the fracture process by the nanoindentation system. Besides, the continuous stiffness measurement (CSM) for the dynamic stiffness was applied to assess the crack behavior. Crack resistance was obtained from the J-Δa curves and the fracture toughness was calculated from the bending tests based on the elastic-plastic fracture mechanics. The results indicated that the fracture toughness decreased after the thermal cycling test. Compared to the specimen without aging, the resistance to rupture decreases rapidly and tends to a low variation against the increased aging cycles. Moreover, the grain orientations and dislocation densities were analyzed using electron back-scatter diffraction (EBSD). It was found that the dislocation density and misorientations of the aged specimens correlated closely to fracture toughness. Furthermore, the stress distribution of the crack tip and the deformation in the plastic zone were analyzed by the finite element simulations. This work provided new insight into the degradation of fracture and deformation behavior of solder material on microscale and revealed the relationship of crack resistance and thermal cycling aging.

Discrepancies in Nanoindentation Hardness and Modulus with a Berkovich, a Cube-corner, and a Conical Tip in a Cu(In,Ga)Se2 Light-Absorption Layer

In this study, we tried to understand the difference in the mechanical properties (elastic modulus, E & hardness, H) values of CIGS compound semiconductors measured using the Berkovich indenter and the sharper cube corner and conical indenter. Adopted continuous stiffness measurement technique to characterize it along with the indentation depth. The depth was up to 1000 nm, and E and H values w ere obtained according to the depth. The projected contact area of the cube edge and the conical indenter was calculated assuming the two indenters had an ideal shape. In the case of the Berkovich indenter, which is the subject of comparison, both calculated values assuming an ideal shape and experimental values were used. Cube-corner and conical tip showed lower load at the same depth of 1000 nm compared to Berkovich indenter. This means that the same depth of indentation was achieved even at a low load, which could affect the value of the mechanical properties of the thin film. The cube-corner tip and the conical tip have a sharp shape with a projected contact area about 6 times smaller than that of the Berkovich tip. It was observed that not only the effect of grain boundaries of the microstructure of the CIGS thin film, but also the effect of reflecting the characteristics of the Mo substrate had a significant effect on the mechanical properties of the CIGS thin film.

Effects of a porous boron nitride nanofiber on nano-mechanical properties in shallow surface of WC-Si3N4 composite

The nanoindentation technique has been applied to materials research for decades, such as WC, Si3N4, and other ceramics or composites. However, nano-mechanical properties in shallow surfaces were often unstable, especially for ceramics-based composites. In this paper, the mechanical properties of WC-10 wt.% Si3N4 without and with the addition of ultrafine porous boron nitride nanofiber were investigated by nanoindentation continuous stiffness measurement in this study. The effects of the porous fiber on elastic modulus and hardness were revealed, which led to more stable and regular profiles of the elastic modulus and hardness versus displacement curves. The curves were cut out and shown before the 30 nm displacement of the tip, which displayed the regularity of the profiles caused by the porous fiber more directly. The values were statistically analyzed at intervals of 10 nm after 30 nm displacement, and then lower standard deviations were observed. The different Si3N4 cracks made from Vickers indentation on the composites were photographed and associated with the regularity of the curves after the fiber addition. It’s considered that the regularity effects on mechanical properties of the porous boron nitride nanofiber on ceramics composites can be helpful in thin film studies, which are also in difficulties of mechanical properties scattering on the nanometer scale using continuous stiffness measurement.