Increasing Indentation Depth Research Articles

Mechanical Properties and Fracture Mechanisms of Nanocomposites of Metal and Graphene with Overlapping Edges.

The fracture mechanism and mechanical response of Ni/graphene nanocomposites under nanoindentation are investigated by molecular dynamics simulations. We analyze the effect of the overlapping area on the microstructural transition, HCP atomic fraction, dislocation density, load-displacement relationship, and stress distribution. It was found that the maximum indentation depth of embedded graphene has a nonlinear dependence relation with the overlapping area, and it becomes smaller at the overlapping width comparable to the indenter diameter. The graphene layer is able to hinder the expansion of the dislocation into the interior of the Ni matrix in the initial stage. The densities of HCP atoms and dislocations in the composite gradually increase with increasing indentation depth. The stress concentration tends to cause nucleation of dislocations below the indentation surface. When the graphene is ruptured, the elastic recovery to some extent occurs in the deformed substrate. This work sheds light on modifying the mechanical properties of metal/graphene composites by tuning the overlapping boundary of graphene.

Molecular dynamics study on the edge effect of single crystal Ni with two indenters nanoindentation

The edge effect and the formation and evolution of dislocations in nanoindentation were studied using molecular dynamics methods. A series of molecular dynamics models of two indenter nanoindentation was constructed, and diamond indenters were used for indentation simulation. This paper analyzes the effects of two indenters distance and indentation depth on the edge side extrusion, surface collapse, indentation force, internal defects, and stress of single crystal Ni workpieces. The results show that the number of particles extruded from the side does not increase linearly with the indentation distance increasing, the magnitude of indentation force changes with the increase of indentation depth and is influenced by the distance between the indenters, and the internal defects of single crystal nickel workpieces change with the change of indentation distance and increase with the increase of indentation depth. This work has a positive impact on understanding the nanoindentation processing of single crystal Ni and can help to understand the mechanism of internal dislocation formation in workpieces under multiple indenters indentation.

Nanoindentation mechanical studies of bulk AlN single crystals with different orientations

Abstract This study utilized nanoindentation to perform nano-mechanical tests on freestanding aluminum nitride (AlN) single crystal substrates with (0002), (10–10), and (11–20) orientations prepared by the physical vapor transport (PVT) method with varying indentation depths. The results indicate that the c-plane exhibits greater hardness and smaller Young’s modulus compared to other orientations. Moreover, the mechanical properties of AlN with different orientations demonstrate consistency with the indentation size effect, showing a decrease in both hardness and Young’s modulus with increasing indentation depth. Surface morphology of the indentations was observed using SEM, revealing that at high loads, no obvious cracks were found in the c-plane indentation except for slight deformation, while the m-plane and a-plane indentations produced cracks extending along the a- and m-directions, respectively. Cathodoluminescence (CL) results demonstrated that dislocations and structural defects generated by the indentation produced the luminescence quenching. Notably, the inverted triangular dislocation slip region was clearly observed in the panchromatic CL images of c-plane indentation. The anisotropy of the phonon peaks at different crystal planes and the nature of the local stress at the indentation were further analyzed using Raman spectroscopy.

Effects of adhesive and frictional contacts on the nanoindentation of two-dimensional material drumheads

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.

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.

Nanoindentation responses of NiCoFe medium-entropy alloys from cryogenic to elevated temperatures

NiCoFe alloy, a medium-entropy alloy, shows potential for applications in extreme environments. However, there is a theoretical barrier concerning the unclear understanding of its high-temperature dislocation motion mechanism. The load response exhibits distinct signatures relevant to thermal activation, most notably a decrease in critical force (i.e., softening) from cryogenic to elevated temperatures, e.g., from 200 to 1000 K. The onset of plasticity is characterized by the nucleation of stacking faults and prismatic loops at low temperatures, whereas the surface nucleation of Shockley partial dislocations dominates plasticity at elevated temperatures. We show that thermal effects lead to non-uniform atom pile-ups and control the rate of phase transformation with increasing indentation depth. The findings in this work extend the understanding of the mechanical response of NiCoFe alloys under indentation at different temperatures, shedding light on the underlying dislocation motion mechanisms and surface deformation characteristics. The observed transformation-induced plasticity mechanism has implications for the properties of medium-entropy alloys and their potential applications in extreme environments.

Revealing the temperature-dependent hardening mechanisms of non-uniformly distributed defects for ion-irradiated metals: Experiments and modeling

In this work, an integrated approach including experimental examinations and theoretical modeling was employed to examine the temperature-dependent hardening of structural materials under ion irradiation. Experimental procedures involved the characterization of grain morphology and size distribution by electron backscatter diffraction (EBSD). Irradiation experiments were conducted utilizing high-energy Au-ions at elevated temperatures, with transmission electron microscopy (TEM) employed for observing irradiation-induced defects. Moreover, mechanical properties were assessed through high-temperature nano-indentation tests (HTNIT), revealing the concurrent occurrence of irradiation hardening and high-temperature softening in the considered materials. For theoretical modeling, a mechanistic model was developed to address the depth-dependent hardness. This model innovatively characterized the hardening mechanisms resulting from non-uniformly distributed defects in the irradiated layer while simultaneously incorporating the temperature effect. Calibration of the model demonstrated its capability to elucidate the hardness-depth relationships at different irradiation doses and testing temperatures. Further theoretical analyses indicated distinct evolution laws in irradiation hardening behavior with varying indentation depths, while the increment in temperature accelerated the expansion of the plastic zone, resulting in a moderate indentation size effect (ISE). With increasing indentation depth, the hardening contributions of geometrically necessary dislocations (GNDs) and irradiation-induced defects gradually diminished. At substantial indentation depths, the dominant hardening mechanism was then controlled by statistically stored dislocations (SSDs).

Effects of Ion Irradiation and Temperature on Mechanical Properties of GaN Single Crystals under Nanoindentation.

Understanding the impact of irradiation and temperature on the mechanical properties of GaN single crystals holds significant relevance for rational designs and applications of GaN-based transistors, lasers, and sensors. This study systematically investigates the influence of C-ion irradiation and temperature on pop-in events, hardness, Young's modulus, and fracture behavior of GaN single crystals through nanoindentation experiments. In comparison with unirradiated GaN samples, the pop-in phenomenon for ion-irradiated GaN samples is associated with a larger critical indentation load, which decreases with increasing temperature. Both unirradiated and ion-irradiated GaN samples exhibit a decline in hardness with increasing indentation depth, while Young's moduli do not exhibit a clear size effect. In addition, intrinsic hardness displays an inverse relationship with temperature, and ion-irradiated GaN single crystals exhibit greater intrinsic hardness than their unirradiated counterparts. Our analysis further underscores the significance of Peierls stress during indentation, with this stress decreasing as temperature rises. Examinations of optical micrographs of indentation-induced fractures demonstrate an irradiation embrittlement effect. This work provides valuable insights into the mechanical behavior of GaN single crystals under varying irradiation and temperature conditions.

Structural responses of heterogeneous FeB(P)CCu amorphous alloys under nanoindentation

The nano-scaled structural heterogeneity is closely associated with the magnetic softness and mechanical properties of Fe-based amorphous alloys. However, limited by the shape and size of ribbons, the details of the atomic-scale structural evolution in ribbons under external stimulation are still missing. In this work, Maxwell-Voigt model with 2 K units and 1 Mx unit was employed to investigate the structural response of FeBCCu amorphous ribbons by substitution of P for B during creeping process under nanoindentation. The P-added alloy exhibited a more sensitive mechanical response at various loading rates, especially for the reduction of hardness and the increase of maximum indentation depth and creep displacement. With the help of creep analysis using above Maxwell-Voigt model, both types of defects were inclined to be activated at a quasi-static loading mode in P-added alloy, and the small size defects seemed to be easily activated and finally coupled into large defects in the fast loading mode, revealing the atomic diffusion and reconstruction process of activated defects. These types of defects evolved into the response of structural heterogeneity to external stimulation, manifesting a large deformation behavior during creeping. This work enlightens the comprehensive insights into the evolution of structural defects in Fe-based amorphous ribbons and has certain guiding significance for the structural design of high-performance alloys.

Ion-irradiation induced hardening behavior of zirconium alloys: A combination of experimental and theoretical study

This study aimed to investigate the microstructure information and mechanical behavior of ion-irradiated zirconium (Zr) alloys through a combination of experimental measurements and theoretical analysis. Experimental procedures involved Au3+ irradiation of Zr-1.5Sn-0.2Fe-0.1Cr and Zr-1.0Sn-1.0Nb-0.1Fe at 3 displacements per atom (dpa) and 30 dpa. Transmission electron microscopy analysis revealed the formation of precipitates such as Zr(Fe, Cr)2 in Zr-1.5Sn-0.2Fe-0.1Cr, as well as β-Nb and Zr(Nb, Fe)2 in Zr-1.0Sn-1.0Nb-0.1Fe. These precipitates exhibited a transformation from crystalline state to partial or complete amorphization after ion-irradiation. Furthermore, macroscopic mechanical properties of the Zr alloys were characterized by nano-indentation tests, which revealed a significant indentation size effect (ISE) and irradiation hardening behavior. To provide a theoretical understanding of the depth-dependent hardness observed in ion-irradiated Zr alloys, a mechanistic model was developed to address the different expansion rates of the plastic zone in the irradiated and unirradiated region. The results indicated that the ISE phenomenon could be attributed to the reduction in the density of geometrically necessary dislocations (GNDs) caused by the expansion of the plastic zone. In addition, the irradiation hardening behavior primarily resulted from the contribution of irradiation-induced defects. With increasing indentation depth, the dominant hardening mechanisms changed from the contribution of irradiation-induced defects, GNDs and statistically stored dislocations (SSDs) in the irradiated region to SSDs in the unirradiated substrate.

The research on the influence mechanism of internal deformation for the performance of Bi-2212

Cable-in-conduit conductor (CICC), one of the most promising conductors for manufacturing magnets in magnetic confinement fusion devices, has attracted lots of attention. In the production of CICC, porosity control is necessary for its stability. The porosity control is usually realized by the diameter-reducing process, which would also lead to indentation damages to the elements of CICC-superconducting wires. In this article, systematic research of indentation damages was carried out on the next generation of high-temperature superconducting materials–Bi-2212 wires. The results indicate that the current carrying capacity of the indentation-damaged wire would first keep steady and then show exponential decline with the increase of indentation depth. The wires subjected to pre-overpressure (pre-OP) treatment exhibit slightly improved resistance against indentation damage at shallow indentation depths. However, their critical current (I c) deteriorates more rapidly at greater indentation depths when compared to wires that have not undergone the per-OP process. The following structural characterization analyzed the reasons for the property changes with the help of scanning electron microscopy, energy dispersive x-ray spectroscopy, computed tomography, and hardness tester. Misalignment between the Bi-2212 grains and shaped filaments was found in the indentation-damaged wires, with which the degradation in I c of the wires and the differences in properties of the two kinds of wires were further discussed.

Novel procedure to determine the stress-strain relation of Lithium-ion Batteries through indentation test

This study proposes a novel approach to convert the load–depth curve measured in the experimental indentation test into stress–strain curves. Due to the lack of the tensile test results for the cylindrical lithium-ion battery (LIB) cell, a combination of the analytical analysis and the inverse optimization approach is first conducted as a reference point to determine the elastoplastic constitutive equation, which can predict the response of cylindrical LIB cell cells under the cylindrical indenter. The obtained load-depth curves from the robust optimization algorithm are in good agreement with the experimental loading–unloading curves. This novel approach includes a new definition of the contact area between the cylindrical indenter and the cylindrical LIB cell. Finite element models validate the measured contact area values from the analytical approach. The analytical approach in this study can accurately capture the stress–strain curve validated with optimization results. Afterward, different single indentation tests are conducted to estimate the reduction of Young’s modulus through the increasing indentation depth. Noteworthy, a definition of the indentation strain can physically interpret the indentation strain in the case of two crossed cylinders. The cell voltage is measured during the indentation test to detect the internal short circuit in the LIB cell. In homogenized modeling, the damage of the LIB cell is considered, which is an essential indicator of the internal short circuit of a LIB cell and possible thermal runaway.

Anisotropy of nanoindentation in copper single crystals under different orientations

The anisotropy of nanoindentation in copper single crystals is studied through experiments and simulations. Nanoindentation tests with different orientations were carried out, and the depth was 20nm-500nm. Simulations were carried out using crystal plasticity finite element method. The results show that sample with different orientations present anisotropic with increase of indentation depth. The accumulated plastic strains of the samples with different orientations are different due to the different angle between the loading direct and the normal to the slip surface. The cumulative plastic strain of oriented samples is the smallest, and orientation is the largest. The amount of slip coefficients initiated simultaneously for samples with different orientations is responsible for the differences in nanoindentation properties.

Comprehensive investigation on the durability and safety performances of lithium-ion batteries under slight mechanical deformation

Mechanical abuse is a general abuse behavior in electric vehicles. To prevent the safety risk from mechanical deformation, it is necessary to understand its failure mechanism and its effects on battery performance. There is a knowledge gap in the influence of slight mechanical deformation on the durability and safety of lithium-ion batteries. This study comprehensively investigates the changes in electrochemical properties, morphology, and thermal stability in commercial ternary/graphite lithium-ion batteries by multiple techniques. Tested cells are indented from 4 mm to 6.8 mm and cycled for 620 cycles. The results of cycle aging exhibit that indentation can improve the cycle performance of tested cells, but the effect turns negative for the cells when the indentation depth exceeds 6.5 mm. The electrochemical impedance spectroscopy measurements exhibit that indentation retarded the increase of impedance of indented cells during the aging process. It could be due to the increase of compact density weakening the degradation in the anode electrode. But the degradation in the cathode electrode is aggravated by mechanical deformation. During the cycle aging of tested cells, the loss of lithium inventory dominates the degradation of indented cells in the first 500 cycles and then follows the loss of active material damage. The apparent morphology of electrodes in deformed and aged cells exhibits that active material particles are compacted in the dented area, and cracks are formed in the fold area. After cycle aging, the compressed area surrounding the dent is covered by a layer of reaction products of electrolyte with lithium at the anode electrode. The adiabatic tests show the thermal stability of indented cells reduces firstly and then increases with the increase of indentation depth, as well as the aged cells.

Atomistic investigation of the mechanical and tribological responses of the ferrite-cementite interface with a Bagaryatskii orientation

The excellent tribological properties of pearlitic steel can be tracked to the synergistic effect between ferrite and cementite phases. However, owing to the lack of full understanding of the plastic carrier-interface interaction mechanism, the essential role of the interface in the mechanical and tribological response is indistinct. In this study, the deformation response of cementite/ferrite (Fe3C/α-Fe) interface under a mechanical load was explored by leveraging molecular dynamics simulation. The results showed that the Fe3C/α-Fe interface significantly hinders the shear deformation propagation and can effectively relax the strain/stress concentration. With the increasing indentation depth, the cementite phase undergoes an amorphous transformation and rejuvenation, and the ferrite phase undergoes a phase transformation to HCP, thus synergistically enhancing the plasticity of pearlite. On this basis, we revealed the underlying origin for the decreased growth rate of friction coefficient with the increasing friction depth. In particular, the tribological properties change periodically in the scratch direction due to the effect of interfacial dislocations, and the friction mechanism is also affected by the interfacial dislocation structure, showing a dendritic shear banding deformation. Our work is a step forward in understanding the relationship between the Fe3C/α-Fe interface and the micro-mechanism of friction.

Local wrinkles of van der Waals heterostructures under nanoindentation

Probing van der Waals (vdW) heterostructures to characterize their properties, especially the stability and durability is of vital importance due to the weak interactions between two-dimensional materials. However, the wrinkling behavior of vdW heterostructures under nanoindentation is still unclear, which hinders the accuracy and development of probing methods at the nanoscale. Herein, the wrinkles of vdW heterostructures composed of graphene and molybdenum disulfide (MoS2) under indentation are studied through molecular simulation and theoretical analysis. It is found that wrinkles occur when the hoop strain of the upper layer reaches the critical value for the graphene film-single layer MoS2 substrate system. By fitting the force–displacement relationship, we estimate the predicted elastic modulus of the vdW heterostructure, and uncover that the wrinkling phenomena have ignorable effect on the probing results. It is interesting to find a transition from a sinusoidal wrinkling to a period-doubling bifurcation of vdW heterostructures with the increase of indentation depth. What is more, the wrinkling morphology of vdW heterostructures can be tuned through choosing suitable indentation depth, indenter size, upper film size as well as applied pretension. The present findings should be useful for the developing probing methods of vdW heterostructures, and serve as a guide for their blooming applications.

Revealing the length-scale dependence of the spatial mechanical heterogeneity and shear transformation zone size in metallic glassy films

Mechanical heterogeneity in metallic glasses at the nanoscale has been widely investigated but remains to date not well understood. In this study, metallic glassy films with an ultra-smooth and defect-free surface were prepared via a magnetron sputtering method. Grid nanoindentation tests were conducted to study the statistical distributions of hardness, elastic modulus, and yield stress, as well as their spatial fluctuation at varying indentation depths. The results revealed locally “strong” and “weak” regions with a characteristic length of 5–10 μm uniformly distributed at an indentation depth of 50 nm. The spatial mechanical heterogeneity was shown to be greatly suppressed with increasing indentation depth. Using the statistical law of yield shear stress, the shear transformation zone (STZ) size was determined and was found to rapidly increase with increasing indentation depth. Along the planar direction, mechanical heterogeneity and STZ size were shown to be independent of the length scale.

Size effect in nanoindentation: Taylor hardening or dislocation source-limited effect?

In the present work, a 3D discrete dislocation dynamics (DDD) method was used to explore the indentation size effect (ISE) in the nanoindentation of single crystals. The distribution of geometrically necessary dislocation (GND) underneath the indent obtained from the DDD simulations was compared with that in experiments. The results show that the GND density increases as the indentation depth increases, which is inconsistent with the Nix-Gao model that is usually used to interpret the ISE phenomenon. The spatial-temporal evolution of dislocation structures indicates that the available dislocation sources are limited at smaller indentation depths, thus requiring higher stress to accommodate the plastic deformation. The authors do not have permission to share data. • The indentation size effect was investigated by 3D discrete dislocation dynamics. • The patterns of GNDs are correlated with the dislocation motions on slip planes. • The GND density increases as the indentation depth increases. • The indentation size effect is caused by the limitation of dislocation sources.

Indentation of elastomeric membranes by sphere-tipped indenters: Snap-through instability, shrinkage, and puncture

Elastomeric membranes are flexible and stretchable, commonly found in soft devices, soft robotics, and flexible electronics. The indentation of free-standing elastomeric membranes induces large transverse deflection, leading to the puncture of elastomeric membranes. In this paper, we study the indentation and puncture of elastomeric membranes by sphere-tipped indenters. Effects of the indenter tip size, indenter-membrane friction, and equi-biaxial pre-stretch of the membrane on the indentation depth-force curve, deformed membrane profile, puncture depth and force, and shape of the puncture site are studied both experimentally and theoretically. In the experiments, we observe an abnormal decrease of indentation force with increasing indentation depth, similar to the spontaneous expansion of a rubber balloon at a critical pressure. We call this phenomenon the snap-through instability in the indentation of elastomeric membranes. The profile of the lubricated membrane shrinks around the indenter tip with increasing indentation depth. The puncture depth and force of lubricated membranes are smaller than those of pristine membranes by several times. Indenters prefer to penetrate lubricated membranes by a line crack instead of a circular hole for pristine membranes. Our theoretical model successfully predicts the snap-through instability, puncture depth and force, and shrinkage of elastomeric membranes. Also, the shape of the membrane's puncture site is explained. These experimental findings and theoretical formulations reveal the new characteristics of the indentation and puncture of elastomeric membranes.

Temperature-dependent hardening of zirconium alloys under heavy ion-irradiation: Experimental observation and theoretical analysis

In this work, microstructure observation and thermo-mechanical property characterization of ion-irradiated Zr-0.5Sn-0.5Nb-0.3Fe-0.015Si alloys were addressed by both experimental measurements and theoretical analyses. In experiments, 6 MeV Au3+ irradiation was carried out for Zr alloys with the irradiation dose up to 30 displacements per atoms (dpa). Transmission electron microscopy (TEM) indicated the addition of solute elements could facilitate the formation of second phase particles (SPPs) like (Zr, Nb)2Fe, Zr(Nb, Fe)2 and Zr-Nb-Fe-Si precipitates in the unirradiated matrix, which were then transformed from the crystalline to amorphous state during the irradiation process. Moreover, it was indicated that there existed microband structures with different orientations inside the grains, and the actual irradiation depth had exceeded the value predicted by the SRIM simulation. The influence of irradiation-induced defects on the macroscopic mechanical behaviors of Zr alloys was characterized by both nano-indentation test (NIT) at 298 K and high-temperature nano-indentation test (HTNIT) at 573 K and 673 K. To theoretically address the hardness-indentation depth relations of ion-irradiated Zr alloys at elevated temperatures, a mechanistic model considering the underlying hardening mechanisms was developed. It was revealed that the irradiation hardening behavior was attributed to the contribution of irradiation-induced defects, while the decrease of hardness at elevated temperatures was ascribed to the weakening of all hardening mechanisms. In addition, with increasing indentation depth, the dominant hardening mechanisms changed from the contribution of irradiation-induced defects and geometrically necessary dislocations (GNDs) to those of statistically stored dislocations (SSDs).