Indentation Stress-strain Curves Research Articles

Indentation stress–strain analysis and finite element simulation to determine elastoplastic properties of thin films decreasing the substrate contribution

AbstractThe mechanical performance of protective coatings is crucial in daily industrial environments, with transition metal nitrides being among the most commonly used hard coatings for machining tool protection. However, determining their elastoplastic properties via conventional methods can be challenging due to the thickness‐dependent response of film/substrate systems. In this study, we utilised two sputtering Ti‐Al‐N films as a model hard thin film/soft substrate system to showcase an alternative methodology to the Oliver and Pharr method. This alternative approach involves determining Young's modulus, yield stress and hardness through indentation stress–strain curves obtained from nanoindentation tests, effectively decreasing the substrate's contribution. This decrease was corroborated by finite element simulations conducted on films with thickness below 1.0 μm. The elastoplastic properties determined using our methodology fell within the range reported for typical Ti‐Al‐N films. Furthermore, by applying our methodology, we were able to correlate and discuss the observed differences in mechanical behaviour between the two films based solely on their microstructural, compositional and morphological properties. Thus, we have demonstrated a viable alternative methodology to address substrate contribution challenges in the mechanical characterisation of thin film/substrate systems when employing an indenter with a large radius of curvature (~650 nm). This research holds potential implications for the design of protective submicrometric films with industrial applications.

Study on correlation and scaling protocol between indentation stress-strain and uniaxial stress-strain

Most important mechanical structures produce complex local material changes during the moulding and servicing process. Obtaining the specific local mechanical properties of materials and conducting field tests are problems in structural integrity evaluation. The instrumented indentation technique (IIT) is a solution to these problems. However, the core challenge with the IIT is the quantitative correlation between indentation response and uniaxial stress-strain (USS) response. In this study, we investigate the scaling relationship between indentation stress-strain (ISS) and uniaxial stress-strain (USS). A new protocol for obtaining the mechanical properties of alloy steels using ISS curves is proposed, which can directly obtain the plastic stage of the USS curves from the ISS curves. We used a finite element inversion method based on existing theories. Models with different mechanical properties (USS curves) were established using the ABAQUS software to obtain the corresponding ISS curves. We then explored the relationship between the two; the strain-scaling factor and stress-scaling function were specifically identified. Our work proposes an ISS protocol for power-law-hardening materials. Two alloy steels (SA508 and 42CrMo) were experimentally verifieds. The predicted results are approximately consistent with the practical curves and the error was within ± 10%. Because of the universality and reliability of the protocols, it is expected to provide a theoretical reference and technical approach for the development of IITs and structural integrity evaluation of important mechanical structures.

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

Atomistic Understanding of the Competition between Dislocation and Twinning in Silver under Nanoindentation

In this study, the competition mechanisms between dislocation slip and twinning in silver with a low stacking fault energy using molecular dynamics (MD) simulation from an atomistic point of view are reported. Herein, three crystallographic surface orientations of , , and are considered and compared. The indentation stress–strain curves are successfully obtained from the load–displacement curves of nanoindentation. The stress of , , and orientations drops at the strains of 0.140, 0.133, and 0.136, which corresponds to the yield stress of 3.83, 4.33, and 4.99 GPa, respectively. Dislocation slip and twinning simultaneously form in silver as indicated by the total potential energy of the system. Furthermore, the typical four‐, two‐, and sixfold symmetries of the out‐of‐plane displacement as in copper are not observed for , , and orientations in silver. Hence, this observation can be supported by the simultaneous occurrence of dislocation slip and twinning in silver.

An improved methodology for extracting uniaxial stress–strain curves from spherical indentation data

In the recent years, it has been shown that the Pathak–Kalidindi (P–K) spherical indentation protocol and its accompanying definition of the indentation strain has many advantages over the classical definition. In the present work, an improved methodology to obtain the uniaxial stress–strain curve from the spherical indentation stress–strain curve is proposed based on the P–K protocol. The classical definitions of the representative strain, ϵruni, which relates the indentation strain to an equivalent uniaxial strain, and the non-dimensional strain, ϵND, which relates the indentation strain to the uniaxial stress, are revised in this work. These revisions are made such that they are consistent with the P–K protocol, and are shown to have the similar relationships as the classical equations. Using non-dimensional analysis, a closed form expression is obtained for the uniaxial stress as a function of the elastic–plastic properties of the material and the indentation strain. Based on this expression, an inverse approach is then utilized using results of finite element simulations to develop a methodology to predict uniaxial stress–strain curves from spherical indentation data for a large range of elastic–plastic mechanical properties. This methodology is demonstrated on spherical indentation stress–strain curves obtained from a set of finite element simulations for materials with mechanical properties spanning those of widely used structural alloys. Finally, this method is shown to provide good estimates of the uniaxial stress–strain curves from experimental spherical microindentation tests.

High-throughput assessment of local mechanical properties of a selective-laser-melted non-weldable Ni-based superalloy by spherical nanoindentation

Additive manufacturing (AM) enables complex localized microstructure tailoring by layer-wise printing, which potentially offers exceptional mechanical performance. However, conventional mechanical testing methods are not optimal for interrogating the corresponding heterogeneous microstructure, limiting the in-depth understanding and exploitation of the structure-property linkages. Here, we leverage a spherical nanoindentation method to efficiently measure indentation stress-strain (ISS) curves at the microscale. This was demonstrated on a selective-laser-melted Ni-based superalloy (IN738LC) which has high economic value but suffers from hot-cracking. The measured average elastic modulus (193 ± 9 GPa) agrees with the literature data. The ISS curve is comparable with micro-pillar compression results with a similar size (stressed volume) and crystallographic orientation; however, it is higher than the bulk tensile test results because of the size effect. Furthermore, combined with surface morphology, elemental distribution, and crystallographic orientation analyses, abundant microstructure-mechanical property linkages were explored. The indentation yield stress weakly depends on the indentation direction but is sensitive to the local precipitation distribution. Grain boundaries (GBs) mediate the strain-hardening behavior when the indents are close to the GBs. The ISS curve is accessible even when the indent contains microcracks because the hydrostatic stress underneath the indenter suppresses crack propagation. Overall, the demonstrated spherical nanoindentation method is suitable for the high-throughput assessment of local mechanical properties of additively manufactured materials.

A comparative study of microstructures and nanomechanical properties of additively manufactured and commercial metallic stents

Additive manufacturing emerges as an innovative technology to fabricate medical stents used to treat blocked arteries. However, there is a lack of direct comparison of underlying microstructure and mechanical properties of additively manufactured and commercial stents. In this study, additively manufactured and commercial 316 L stainless steel stents were investigated comparatively, with electrochemical polishing being used to improve the surface finish of the former stent. Microstructural characterisation of both stents was carried out through optical microscopy, scanning electron microscopy, and electron backscatter diffraction. Their hardness and elastic modulus were studied using Berkovich nanoindentation, with an emphasis on the effect of grain orientation. In addition, spherical nanoindentation was used to generate indentation stress-strain curves based on load-displacement responses. The obtained results showed that electrochemical polishing was effective in diminishing the average surface roughness, with a reduction of Ra value from 8.45 µm to 5.96 µm. The additively manufactured stent demonstrated the hierarchical grain microstructure with columnar grains and cellular sub-grains, as opposed to equiaxed fine grains and twins in the commercial stent. The hardness and modulus of additively manufactured stents were higher than those of the commercial ones. The grains close to the (111) orientation exhibited the highest hardness and elastic modulus followed by (101) and (001) orientations. The indentation stress-strain curves, yield strength, and hardening behaviour were similar for the additively manufactured and commercial stents. This work provides a fundamental understanding of the microstructure and properties of the additively manufactured stent and represents an important step towards innovative manufacturing of stents.

Multiresolution investigations of thermally aged steels using spherical indentation stress-strain protocols and image analysis

In recent work, our research group has developed and demonstrated novel multi-resolution protocols capable of extracting indentation stress-strain (ISS) curves from tests on individual microscale constituents (e.g., phases, grains) as well as bulk properties of material microstructures. In addition, we recently developed protocols for design of consistent segmentation of micrographs. This work combines these recent advances in multi-resolution spherical indentation and image segmentation protocols to address the current challenges in the critical evaluation and advancement of physics-based composite models. These new research avenues are identified and demonstrated through a case study on thermally aged ferrite-pearlite steel samples, where the respective indentation yield strengths of the microscale constituents (i.e., ferrite, and pearlite) and the bulk yield strength of the samples were estimated from ISS tests measurements. The constituent volume fractions were extracted from segmented optical microscopy images. It is shown that the multi-resolution indentation yield strength and volume fraction measurements are highly consistent with the homogenization estimates from simple composite theories.

Effects of ball size and microstructures on indentation curves of Fe9Cr model alloys and tempered martensitic steel Eurofer97

Nano-indentation with spherical indenters is a test technique largely used to determine the elastic–plastic behavior of a very small volume of material. In this work, the indentation size effects under spherical indentation were investigated for Fe9Cr model alloys and reduced activation tempered martensitic steel Eurofer97. Experimental tests and finite element method (FEM) simulations were performed. Results and analysis of the experimental results and FEM simulations revealed that the indentation size effects depend on both the spherical indenter radius and the microstructures characterized by the initial dislocation density and the grain size of the tested materials. The observed difference in the indentation stress–strain curves was qualitatively discussed in terms of the relative effects associated with the ball radius and the microstructural length scale.

Effect of irradiation damage and indenter radius on pop-in and indentation stress-strain relations: Crystal plasticity finite element simulation

In this work, a crystal plasticity finite element model is developed to simulate the spherical nano-indentation of ion-irradiated metallic materials. Two critical features are addressed by the proposed theoretical framework, which include the pop-in event observed in the loading force-indentation depth (P−h) relations and irradiation hardening characterized by the transformed indentation stress-strain (ISS) curves. For the former, the pop-in event is dominated by the dislocation nucleation mechanisms, which are affected by both the density of irradiation-induced dislocation nucleation sites and indenter radii. For the latter, irradiation hardening is closely related to the heterogeneously distributed irradiation-induced defects within the irradiated layer with a limited depth. By applying the developed model to the spherical nano-indentation of helium-irradiated single crystal tungsten, it is informed that the simulated results can match well with corresponding experimental data, which include the unirradiated and irradiated P−h and ISS relations at different indenter radii. Moreover, the evolution of different hardening mechanisms during the indentation process is systematically analyzed, which can help comprehend the fundamental deformation mechanisms of ion-irradiated materials under spherical nano-indentation.

Mechanical Responses of Primary-α Ti Grains in Polycrystalline Samples: Part I—Measurements of Spherical Indentation Stress–Strain Curves

Mechanical Responses of Primary-α Ti Grains in Polycrystalline Samples: Part I—Measurements of Spherical Indentation Stress–Strain Curves

Uncertainties in the representative indentation stress and strain using spherical nanoindentation

In this study, we reviewed the definitions of indentation strain and stress proposed from earlier studies and then calculated indentation strain–stress curves according to 20 combinations of five indentation strain definitions and four indentation stress definitions. The finite element method was applied to predict the load–displacement curves and the force–displacement for spherical nanoindentation and tensile test, respectively. Thus, the load–displacement data were used to determine indentation strain–stress curves, which were compared with the stress–strain curve, obtained from the tensile test simulation. Comparing with the tensile stress–strain curve, three combinations of σX − ɛK, σO − ɛA, and σH − ɛM reveal better fitting curves than the other combinations, where the subscripts of X, K, O, A, H, M are denoted as Xu and Chen (J Mater Res 25:2297-2307, 2010), Kalidindi and Pathak (Acta Mater 56:3523-3532, 2008), Oliver and Pharr (J Mater Res 7:1564-1583, 1992, J Mater Res 19:3-20, 2004), Ahn and Kwon (J Mater Res 16:3170-3178, 2001), Hill et al. (P R Soc Lond 423:301-330, 1989), and Milman et al. (Acta Metal Mater 41:2523-2532, 1993), respectively. The limitation of the indentation strain is at 0.06, 0.03, and 0.01 for combinations of σX − ɛK, σO − ɛA, and σH − ɛM. The stress constraint factor (called the ratio of mean contact pressure to tensile stress) for combinations of σX − ɛK, σO − ɛA, and σH − ɛM is 3.4, 3.4, and 2.6 to obtain the optimized fitting indentation stress–strain curves with the parameter n of the power law of 0.306, 0.248 and 0.173, which reveal the deviation of 43.0%, 15.9%, and 19.2%, respectively, in comparison with that of the tensile flow curve. Considering the best fitting curve by the combination of σO − ɛA, together with the stress constraint factor $$\psi$$ of 3.4, the fitting parameters of n and K are 0.248 and 588.56 corresponding to the deviation of 15.9% and 7.7% in terms of these parameters in the tensile flow curve.

Microstructural and Mechanical Characterization of Thin-Walled Tube Manufactured with Selective Laser Melting for Stent Application

This paper focuses on microstructural and mechanical characterization of metallic thin-walled tube produced with additive manufacturing (AM), as a promising alternative technique for the manufacturing of tubes as a feedstock for stents micromachining. Tubes, with a wall thickness of 500 μm, were made of 316L stainless steel using selective laser melting. Its surface roughness, constituting phases, underlying microstructures and chemical composition were analyzed. The dependence of hardness and elastic modulus on the crystallographic orientation were investigated using electron backscatter diffraction and nanoindentation. Spherical nanoindentation was performed to extract the indentation stress–strain curve from the load–displacement data. The obtained results were compared with those for a commercial 316L stainless steel stent. Both tube and commercial stent samples were fully austenitic, and the as-fabricated surface finish for the tube was much rougher than the stent. Microstructural characterization revealed that the tube had a columnar and coarse grain microstructure, compared to equiaxed grains in the commercial stent. Berkovich nanoindentation suggested an effect for the grain orientation on the hardness and Young’s modulus. The stress–strain curves and the indentation yield strength for the tube and stent were similar. The work is an important step toward AM of patient-specific stents.

Protocols for studying the time-dependent mechanical response of viscoelastic materials using spherical indentation stress-strain curves

Spherical nanoindentation has been used successfully to extract meaningful indentation stress-strain curves in hard materials such as metals and ceramics. These methods have not yet been applied on viscoelastic-viscoplastic polymer samples. This study explores the potential of the current spherical nanoindentation analysis protocols in extracting indentation stress-strain curves and viscoelastic properties on samples exhibiting time-dependent material response at room temperature. These new protocols were tested on polymethyl methacrylate, polycarbonate, and low-density polyethylene. The properties extracted under different loading rates and indenter tip sizes conditions were observed to be consistent. It is further demonstrated that it is possible to recover the compression stress-strain curves for polymethyl methacrylate and low-density polyethylene from the measured indentation stress-strain curves. This study establishes some of the foundations needed for the development of protocols needed to reliably investigate the local time-dependent mechanical response of materials using spherical nanoindentation.

Mechanical Responses of Primary-α Ti Grains in Polycrystalline Samples: Part I – Measurements of Spherical Indentation Stress-Strain Curves

Recently established spherical indentation stress-strain protocols have demonstrated the feasibility of measuring reliably the mechanical responses at different material structure length scales in a broad range of structural alloys. In the present study, we apply these high-throughput protocols on the primary α-phase grains in polycrystalline samples of Ti-5Al-2.5Sn, Ti-8Al-1Mo-1V, Ti-6Al-4V, Ti-6Al-2Sn-4Zr-2Mo and Ti-6Al-2Sn-4Zr-6Mo to aggregate a large experimental dataset that documents systematically the effects of α-phase chemical composition and grain orientation on the measured values of indentation modulus and the indentation yield strength. This dataset is being offered to the materials community in an open repository to allow further analyses of the effect of chemical composition of the α-phase on its single crystal elastic and plastic properties. This study establishes the feasibility and tremendous value of spherical indentation stress-strain protocols for documenting the grain-scale anisotropic mechanical responses of different α-phase compositions in high-throughput assays. In part II of this paper, the dataset is analyzed with advanced statistical approaches to estimate the single crystal elastic stiffness constants and the critical resolved shear strengths (CRSS) of the different Ti alloys studied.

Three mechanisms of hydrogen-induced dislocation pinning in tungsten

The high-flux deuterium plasma impinging on a divertor degrades the long-term thermo-mechanical performance of its tungsten plasma-facing components. A prime actor in this is hydrogen embrittlement, a degradation phenomenon that involves the interactions between hydrogen and dislocations, the primary carriers of plasticity. Measuring such nanoscale interactions is still very challenging, which limits our understanding. Here, we demonstrate an experimental approach that combines thermal desorption spectroscopy (TDS) and nanoindentation, allowing to investigate the effect of hydrogen on the dislocation mobility in tungsten. Dislocation mobility was found to be reduced after deuterium injection, which is manifested as a ‘pop-in’ in the indentation stress-strain curve, with an average activation stress for dislocation mobility that was more than doubled. All experimental results can be confidently explained, in conjunction with experimental and numerical literature findings, by the simultaneous activation of three mechanisms responsible for dislocation pinning: (i) hydrogen trapping at pre-existing dislocations, (ii) hydrogen-induced vacancies, and (iii) stabilization of vacancies by hydrogen, contributing respectively 38%, 52%, and 34% to the extra activation stress. These mechanisms are considered to be essential for the proper understanding and modeling of hydrogen embrittlement in tungsten.

Stress−strain curves and derived mechanical parameters of P91 steel from spherical nanoindentation at a range of temperatures

This work compares different measurement and analysis protocols of spherical nanoindentation tests performed at different temperatures on a ferritic/martensitic P91 grade steel, in order to derive meaningful indentation stress−strain curves (ISSC) and estimate material parameters such as indentation modulus, yield strength, work hardening exponent and ultimate tensile strength. Quasi-static multi-cycle and dynamic continuous stiffness measurement indentation using a spherical indenter with a tip radius of 20 μm has been carried out from room temperature to 600 °C in vacuum in a set-up where thermal drift has been minimised by an active surface referencing system and accurate temperature stabilization in the contact area. The methodology used to determine the contact radius is critical to achieve consistent results. The application of different combinations of definitions of contact radius and indentation-induced strain to nanoindentation data obtained by the quasi-static and dynamic measurements reveals that Tabor's approach combined with a geometrically determined contact radius best represents the ISSC relationship for the P91 characterized. This method is then extended to predict the high temperature tensile properties of the steel from nanoindentation results.

Mechanical Responses of Primary-Α Ti Grains in Polycrystalline Samples: Part I – Measurements of Spherical Indentation Stress-Strain Curves

Mechanical Responses of Primary-Α Ti Grains in Polycrystalline Samples: Part I – Measurements of Spherical Indentation Stress-Strain Curves

Mechanical Properties of White Etching Areas in Carburized Bearing Steel Using Spherical Nanoindentation

The indentation stress–strain curves of nanocrystalline white etching areas (WEAs) in fatigue-damaged bearing steels were measured through the Pathak–Kalidindi spherical indentation protocols. Although the hardness of WEAs has been reported as greater than the matrix, the indentation yield strength is 36 ± 6 pct smaller and the Young’s modulus is 34 ± 11 pct smaller than the matrix. Using a Voigt–Reuss–Hill approximation, the measured reduction in Young’s modulus is consistent with the effective modulus of nanocrystalline grains within the WEAs.

Cold Sprayed Coatings for Repairing Damaged Metallic Structures

Metallic infrastructures suffer deterioration during their service life. When the metallic component reaches a limit level of damage, it is replaced by a new one. This generates high costs of maintenance and residues management. However, the deposition of coatings by the cold spray technique would allow the repairing of these damaged components and extent their service life. In this work the effect of the spraying temperature and pressure on the mechanical behavior of 316L stainless steel coatings deposited on carbon steel by the cold-spray technique has been analyzed. Spraying gas temperatures of 800oC, 900oC and 1000oC combined with gas pressures of 50 and 60 bars were selected. Indentation stress-strain curves were determined for each spraying conditions. The results showed a significant effect of both spraying parameters on the work hardening of the coatings.