Nanoindentation Deformation Research Articles

Physical phenomena during nanoindentation deformation of amorphous glassy polymers

We identify for visco-elasto-plastic (VEP) glassy polymers, physical phenomena during Berkovich nanoindentation, a locally imposed deformation. Live visuals via in situ nanoindentation indicate mainly sink-in during loading, with pile-up after unloading. Scanning Probe Microscopy (SPM) indicates significant volume conserving upflow below the tip, for these high ν, compliant materials, with compliance correlated high geometric fractional contact, hcΔhmΔ∼0.86−0.95. We adapt the ideal conical indentation framework to VEP Berkovich nanoindentation, to calculate the contact area and visually depict the upflow and the displacement paths, in the material. The combination of SPM and P−h data, indicates a mixed comparison with uniaxial modulus and yield stress, with conventionally defined hardness, H<3σy, and nanoindentation modulus, EN>E. By rationally removing viscoelastic (VE) effects from the loading P−h data, we find instant, zero-time hardness HL0>3σy. We apply the power law model to only the recovery onset, to estimate pure elastic recovery. We then deconvolute the VEP nanoindentation into the conventional EP (elasto-plastic) and elastic contributions, isolating the VE component. Constraint-induced sink-in, pile-up and VE recovery of the highly yielded tip-apex region, mirror the converse constrained deformation effects, governing the trends in the conventional EP EN and HL0 estimates for glassy polymers.

Exploring the Effect of Aluminium Solute Atoms on Nanomechanical Properties of Copper‐Aluminium System using Nanoindentation

In this work, nanomechanical properties for Cu and Cu–Al (where Al = 2, 4, 6, and 8 wt%) alloys are determined using nanoindentation with Berkovich tip. Nanoindentation experiments are performed using trapezoidal load function where maximum load (Pm) varies from 1000 to 9000 μN at an equal interval of 1000 μN by maintaining equal loading and unloading rate. It is found that Cu8Al sample shows lower depth of penetration (h) at any load (P) in comparison to other samples due to more pinning of dislocations or hinderance of the dislocation movement by solute (Al) atoms during nanoindentation deformation. In addition, it is observed that the recovery is maximum for Cu8Al sample among all samples; however, this recovery is reducing with the increasing Pm for all samples. Thereafter, the elasticity and plasticity index are calculated from the area under the P–h curves, which shows that the elastic index is maximum for Cu8Al and minimum for Cu. Furthermore, the nanomechanical properties (reduced elastic modulus [Er] and hardness [H]) are reported for all samples and significant indentation size effect is observed for Cu8Al due to dislocation structure during deformation.

A comparison of the mechanical properties of 3D-printed, milled, and conventional denture base resin materials.

This study investigated the mechanical properties of three denture base resin materials produced by three-dimensional (3D) printing (Group P), computer-aided design/computer-aided manufacturing milling (Group M), and conventional (Group C) methods. Three-point flexural tests were performed before and after thermocycling treatment to evaluate the mechanical properties. Additionally, nanoindentation and dynamic mechanical analysis (DMA) were used to analyze the behavior of the materials. After flexural strength tests, scanning electron microscopy (SEM) was performed to evaluate the fracture cross-section. The results consistently showed that Group P exhibited significantly higher flexural strength and modulus regardless of thermocycling than Groups C and M (p<0.05), along with a higher storage modulus in DMA and greater resistance and resilience to nanoindentation deformation. SEM analysis showed that Group C had a relatively smooth cross-section, whereas Groups M and P had torn cross-sections. This study suggests that the 3D-printed material has suitable mechanical properties for hard dental prosthesis applications.

Nano-indentation deformation behavior of heavy ion irradiated reduced activation ferritic/martensitic (RAFM) steels

The Nano-indentation deformation behavior of the heavy ion irradiated RAFMs is investigated in the present work. Specimens of the CLF-1 steel were irradiated with 123.4 MeV 20Ne ion at both -50 °C and 400 °C, respectively, to achieve a mean displacement damage level of 0.15 dpa. A quasi-uniform distribution of the displacement damage was produced in the specimens by utilizing an energy degrader at the irradiation chamber. The results of nano-indentation experiments indicate that during the loading stage, the irradiated materials exhibit a lower strain rate, but during the holding stage after reaching the maximum load, the irradiated materials show a higher strain rate than the un-irradiated material. Transmission electron microscopy observation showed that the low-temperature irradiation produced a high density of irradiation-induced dislocation loops, which impeded the glide of dislocation lines during the loading stage. However, as the load increases gradually to the holding stage, the dislocation lines can overcome the pinning by the dislocation loops. The strain that did not occur due to the pinned effect of the dislocation loops in the loading stage was released during the holding stage, resulting in a higher strain rate in the irradiated specimen during the holding stage. Based on the Peierls mechanism, a quantitative relationship between the number density of the irradiation-induced dislocation loops and the strain rate during the holding stage was established. The calculated results agree well with the experimentally obtained strain rate during the holding stage.

The Influence of Crystallographic Orientation and Grain Boundary on Nanoindentation Behavior of Inconel 718 Superalloy Based on Crystal Plasticity Theory

The crystal plasticity finite element method (CPFEM) is widely used to explore the microscopic mechanical behavior of materials and understand the deformation mechanism at the grain-level. However, few CPFEM simulation studies have been carried out to analyze the nanoindentation deformation mechanism of polycrystalline materials at the microscale level. In this study, a three-dimensional CPFEM-based nanoindentation simulation is performed on an Inconel 718 polycrystalline material to examine the influence of different crystallographic parameters on nanoindentation behavior. A representative volume element model is developed to calibrate the crystal plastic constitutive parameters by comparing the stress-strain data with the experimental results. The indentation force-displacement curves, stress distributions, and pile-up patterns are obtained by CPFEM simulation. The results show that the crystallographic orientation and grain boundary have little influence on the force-displacement curves of the nanoindentation, but significantly influence the local stress distributions and shape of the pile-up patterns. As the difference in crystallographic orientation between grains increases, changes in the pile-up patterns and stress distributions caused by this effect become more significant. In addition, the simulation results reveal that the existence of grain boundaries affects the continuity of the stress distribution. The obstruction on the continuity of stress distribution increases as the grain boundary angle increases. This research demonstrates that the proposed CPFEM model can well describe the microscopic compressive deformation behaviors of Inconel 718 under nanoindentation.

Effect of crystal orientation on the nanoindentation deformation behavior of TiN coating based on molecular dynamics

In order to investigate the mechanism of nanoindentation deformation of TiN and the protective properties of TiN coating in [001] and [111] crystal orientation, molecular dynamics simulations were established for single-crystal TiN and bilayer TiN/FeCrNi models in this study. The hardness and reduced elastic modulus were obtained by analyzing the indenter load displacement curves obtained from the simulations. Combined with the atomic-scale analysis, it was found that the trigonal defect structure generated in the [111] crystal orientation of the single-crystal TiN enhanced the hardness of the material. The analysis of the simulation results of bilayer TiN/FeCrNi found that the coating withstood high stresses to effectively protect the substrate from damage, and the lower substrate hardness also improved the plastic deformation of the coating to avoid fragmentation, which showed basically the same hardness in both crystal orientations. The results of the study can provide theoretical support for the preparation and application of TiN coatings and provide useful insights to defect-formation, defect/defect interactions and plausible strengthening mechanisms upon loading.

Nanoindentation study of δ-phase zirconium hydride using the crystal plasticity model

Zirconium hydride precipitation degrades the fracture toughness of nuclear reactor fuel cladding tube. Due to the difficulty of experiment, deep understanding on mechanical properties of zirconium hydride via numerical approaches is in a great need. To study the mechanical properties of zirconium hydride, the crystal plasticity finite element model considering geometrically necessary dislocations evolution is used to simulate the nanoindentation deformation behavior of single-crystal δ-hydride. The parameters in the crystal plasticity model are calibrated by Young's modulus along different crystallographic orientations and experimental stress-strain data at different strain rates. The predicted polycrystalline Young's modulus, Poisson's ratio, and nanoindentation hardness are in good agreement with the experimental results. The simulation results show that the nanoindentation hardness strongly depends on the indentation depth when it is smaller than 500 nm. Furthermore, the effects of crystallographic orientation and zirconium matrix on the indentation results are also studied. We find that the nanoindentation hardness of δ-hydride is slightly orientation dependent. For smaller hydride size or larger indentation depth, the surrounding zirconium matrix undergoes plastic deformation, which leads to a significant underestimate of the nanoindentation hardness of the hydride.

Molecular dynamics simulation of nanoindentation on nano-twinned FeCoCrNiCu high entropy alloy

ABSTRACT Twin boundary (TB) plays an important role in the deformation process of materials. In this paper, molecular dynamics (MD) simulation was used to investigate the nanoindentation deformation behaviour of single-crystal FeCoCrNiCu high entropy alloy (SC-HEA) and nano-twinned FeCoCrNiCu high entropy alloy (NT-HEA) with different twin spacings. It is found that the main characteristic of plastic deformation of SC-HEA is the dislocation loop emission. The dislocation movement and distribution of NT-HEA are very different from that of SC-HEA. We found that partial dislocation slip parallel to the twin boundary (PSPTB) and twin partial slip (TPS) can lead to alloy softening. The hindrance of the TB causes the dislocation to slip within a single layer (known as confined layer slip, CLS), which strengthens the material. In the process of nanoindentation, the softening and strengthening mechanisms are constantly competing. When the twin spacing is larger than 1.23 nm, CLS dominates the competition with the hardening mechanism, and the hardness of the material increases with the decrease of the twin spacing. When the twin spacing is less than 1.23 nm, the dominant mechanism of plastic deformation changes to the softening mechanism controlled by TPS, and the hardness thus decreases as twin spacing increases.

Molecular dynamics study of nano-indentation deformation behavior of Al/Al90Sm10 nanolaminate.

Molecular dynamics-based investigation has been carried out to simulate the nano-indentation loading in crystalline Al-amorphous Al90Sm10 metallic glass (MG) with an aim to investigate the effect orientation of crystalline-amorphous (C/A) interface orientation on the nano-indentation behavior of the C/A Al-Al90Sm10 nanolaminate for varying indenter speeds. Post-analysis techniques like adaptive-common neighbor analysis (a-CNA), atomic strain, dislocation extraction algorithm (DXA), and Voronoi polyhedral analysis (VP) have been employed to capture the structural evolution during simulated nano-indentation loading. C/A Al-Al90Sm10 nanolaminate with C/A interface orientated perpendicular to the indenter exhibits the presence of elastic regime followed by plastic curve, whereas load versus depth curve behaves plastically since the beginning in case of C/A Al-Al90Sm10 nanolaminate with C/A interface orientated parallel to the indenter. The dislocation density growth is slower in case of C/A Al-Al90Sm10 nanolaminate with C/A interface orientated perpendicular to the indenter attributed to the sinking of dislocations into MG counterpart of the nanolaminate, thereby triggering shear transformation zone activation. Whereas, the dislocation generation is delayed in case of C/A Al-Al90Sm10 nanolaminate with C/A interface orientated parallel to the indenter by virtue of amorphous Al90Sm10 MG coating on crystalline Al but is extensive and rapid. The disintegration of ICO-like structures and mixed clusters and growth of crystal-like clusters is discernible in C/A Al-Al90Sm10 nanolaminate with C/A interface orientated perpendicular to the indenter. On the other hand, the VP population exhibits cyclic variation in C/A Al-Al90Sm10 nanolaminate with C/A interface orientated parallel to the indenter. A transformation pathway of VPs has been mapped out for C/A Al-Al90Sm10 nanolaminate under nano-indentation loading. The simulations have been carried out by employing Molecular Dynamics using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) platform. Post-analysis techniques like adaptive-common neighbor analysis (a-CNA), atomic strain, dislocation extraction algorithm (DXA), and Voronoi polyhedral analysis (VP) have been employed to capture the structural evolution during simulated nano-indentation loading.

Nanoindentation deformation and fracture mechanisms of SiC/SiO2 thermally oxidized in plasma wind tunnel

Mechanical strain and delamination of surface oxide from substrate are important mechanisms leading to failure of thermal protection systems in hypersonic vehicles. In this work, the deformation and fracture mechanisms of a thermally oxidized SiC/SiO2, formed by dynamic oxidations inside a plasma wind tunnel, are studied by nanoindentation experiments and finite element modeling. The results show an amorphous and uniform SiO2 formation on β-SiC at 1200∼1400 °C in the plasma flow (pressure ≈6.5 kPa), after long-term single/repeated oxidations. In the plasma environment the passive oxidation of SiC is slow, as a result the as-formed SiO2 is very thin. The SiO2 thickness is only ≈680 nm after 8 × 500 s dynamic oxidation. SiC/SiO2 exhibits a strong depth dependent indentation behavior, and at a critical indentation depth, delamination of SiO2 oxide scale is triggered. Finite element modeling helps decouple the effects of SiC substrate, residual thermal stress and interfacial delamination on the nanoindentation response of SiC/SiO2. The results evidence that delamination has a negligible effect on the nanoindentation response, and the main contributions are the SiC substrate and residual thermal stress. This work may forward the fundamental understanding of deformation and fracture mechanisms of oxide scales on thermal protection materials in response to localized loading conditions.

Surface, Structural, and Mechanical Properties Enhancement of Cr2O3 and SiO2 Co-Deposited Coatings with W or Be.

Direct current (DC) and radio frequency (RF) magnetron sputtering methods were selected for conducting the deposition of structural materials, namely ceramic and metallic co-depositions. A total of six configurations were deposited: single thin layers of oxides (Cr2O3, SiO2) and co-deposition configurations (50:50 wt.%) as structural materials (W, Be)—(Cr2O3, SiO2), all deposited on 304L stainless steel (SS). A comprehensive evaluation such as surface topology, thermal desorption outgassing, and structural/chemical state was performed. Moreover, mechanical characterization evaluating properties such as adherence, nano indentation hardness, indentation modulus, and deformation relative to yielding, was performed. Experimental results show that, contrary to SiO2 matrix, the composite layers of Cr2O3 with Be and W exhibit surface smoothing with mitigation of artifacts, thus presenting a uniform and compact state with the best microstructure. These results are relevant in order to develop future dense coatings to be used in the fusion domain.

Orientation behavior in TRC-ZA21 magnesium alloy with fine grain size during nano-indentation process

The deformation behavior in magnesium alloy was greatly affected by grain orientation. It is crucial to analyze the relationship between deformation mechanism and grain orientation. In this study, the deformation behaviors in grains possessing different orientations for TRC-ZA21 alloy with fine grain size were investigated using the nano-indentation deformation coupling EBSD method. The effects of grain orientation and grain boundary on deformation behavior and propagation of deformation mechanism were discussed. The results illustrated that the irregular performance of the nano-mechanical properties could be attributed the inconsistency of grain orientation as well as the grain boundary misorientation angle. Grain orientation, followed by the criterion of Schmid factor, regulated the deformation mechanism of grains that were in direct contact with the nano-indenter. This signified the orientation dependence in plastic deformation. The deformation behavior in grains, induced by plastic deformation and indirectly in contact with the nano-indenter, was found to be influenced by the grain boundary. The orientation difference in adjacent grains determines the influence of grain boundary in plastic deformation, revealing the competitive and coordinative behavior associated with these deformation mechanisms. The c-axes angle between adjacent grains was the key factor to determine the influence of grain boundary on deformation propagation.

Ni/Ni3Al interface-dominated nanoindentation deformation and pop-in events

Nickel-based single crystal alloys have excellent mechanical properties due to its unique two-phase structure and interface. Therefore, molecular dynamics methods were used to simulate nanoindentation and microstructural evolution. We found the indenter reaction force and hardness of the Ni3Al phase is the largest. The pop-in event in Ni3Al phase is more obvious than that in the Ni phase and Ni/Ni3Al phase. Because lots of dislocations in the Ni3Al phase break through the barrier of the interface and cut into the Ni phase, while dislocations in the Ni phase only slip inside the Ni phase. Moreover, we found that the position of the starting point of the adhesion force recovery is mainly related to the elastic recovery of the material. The stronger the elastic recovery of the phase, the smaller the depth value corresponding to the starting point of the recovery. We further studied the variation of potential energy with indentation depth and found that the change of wave trough of the load–displacement (P–h) curve is related to stacking fault energy. This study has important theoretical guiding significance for the in-depth understanding and engineering application of the mechanical properties of nickel-based single crystal alloys.

Reaction synthesis of gradient coatings by annealing of three-layer Ti–Ni–Ti nanolaminate magnetron sputtered on the TiNi substrate

In this work, Ti-Ni-Ti nanolaminate was deposited on a TiNi substrate by magnetron sputtering. Subsequent synthesis in Ar at temperatures of 500, 700 and 900 °C was carried out. To investigate the effect of the reaction synthesis temperature for obtaining a dense thin intermetallic biofunctional coating, a comparative analysis of the morphology, structure, phase composition, mechanical properties and wettability of the coatings was carried out. It was found that crystallization processes have a different impact on the amorphous Ti and Ni layers depending on temperature. In all cases, multilayer gradient crystalline coatings were formed that bound to the substrate by the diffusion zone. The reaction synthesis temperatures of 500 and 700 °C are insufficient for reaction completion and complete transformation; therefore, the obtained thin loose layers are unstable under stresses caused by the substrate. Reaction synthesis in Ti – Ni – Ti nanolaminate at 900 °С formed a dense two-layer gradient coating 2 µm thick, which reliably protects the matrix from further diffusion of interstitial impurities and segregation of Ni atoms onto the surface. An analysis of the nano-indentation deformation diagrams showed that the coatings do not prevent the viscoelastic deformation of the TiNi substrate.

Toward revealing full atomic picture of nanoindentation deformation mechanisms in Li2O-2SiO2 glass-ceramics

Obtaining full understanding of deformation mechanisms in Li2O-2SiO2 glass-ceramics subjected to sharp contact loading is a pressing need for many industrial applications. We herein conduct systematic molecular dynamics simulations to reveal atomic details that are otherwise extremely challenging to probe experimentally. Our study shows that glass-ceramics exhibit a dramatically different plastic deformation map compared to glass, where the nanocrystalline phase dictates the plastic zone shape. Shear flow preferentially nucleates and travels along the interfaces before moving to the surrounding glass and nanocrystals. Dislocations, amorphization zones around the indenter, and shear flow at glass and crystal interfaces help to dissipate contact energy and deconcentrate the deformation, thereby increasing fracture toughness and discouraging the development of catastrophic cracks. Additionally, extensive discussions on the effect of LS2 nanocrystal aspect ratio, location and orientation with respect to indenter in shaping the plastic zone also help to establish a solid knowledge in understanding surface damage behaviors of glass-ceramics as observed in many real applications.

Molecular dynamics simulation on deformation behavior of DLC films based on γ-Fe/CrN matrix

In this paper, the nano-indentation deformation behavior of DLC films with three densities (2.0 g/cm3, 2.8 g/cm3 and 3.5 g/cm3) on γ-Fe/CrN were simulated by molecular dynamics. Firstly, the energy loss rate, hardness and Young’s modulus of γ-Fe/CrN/DLC film were calculated. Meanwhile, the deformation behavior of DLC films on γ-Fe/CrN was analyzed by load-depth curve and indentation morphology. Finally, deformation mechanism of DLC film was analyzed by hybridization state and radial distribution function. The results show that, during the loading process, when the indentation depth is 12 Å, with the increase of density, the maximum normal loads are 325.4 nN, 550 nN and 428 nN, respectively. After unloading, the residual depths are 5.93 Å, 5.91 Å and 6.10 Å, respectively, which indicates the anti-deformability of DLC film with density of 2.8 g/cm3 is the highest. Meanwhile, the hardness, Young’s modulus of 2.8 g/cm3 DLC film is the largest. It is also found that the content of sp3-C in 2.8g/cm3 DLC film is highest after unloading, and the position of the first and second nearest neighbor peaks is hardly changed, which further provides the reason that the anti-deformability of 2.8 g/cm3 DLC film is the highest.

Electron microscopy and atom probe tomography of nanoindentation deformation in oxide dispersion strengthened steels

Oxide Dispersion Strengthened (ODS) steels are candidates for fuel cladding materials in sodium-cooled fast reactors and for structural materials in nuclear fusion power reactors. The effect yttrium-titanium-oxygen (Y-Ti-O) nano-oxide precipitates within ODS steels have on the micromechanical deformation mechanisms has been investigated. The aim is to assess the extent of any direct link between the Y-Ti-O dispersion and nanoindentation hardness, using electron backscatter diffraction, transmission electron microscopy (TEM), and atom probe tomography (APT) studies of a Fe-14Cr-3W-0.2Ti-0.25Y2O3 (wt%) ODS steel at room temperature. Y-Ti-O nanoclusters had a non-uniform distribution and average number density that ranged from 5.8 ± 0.1 × 1023 to 1.3 ± 0.1 × 1024 m−3 and Guinier radii ranging from 1.8 ± 0.2 nm to 2.1 ± 0.2 nm. Surprisingly, the local Y-Ti-O distribution did not correlate strongly with the nanohardness, indicating that the dominant hardening mechanisms was at best only weakly related to the Y-Ti-O distribution. Instead, scanning TEM and APT confirmed that the dominant hardening mechanism was due to the grain boundary refinement, and was further enhanced by tungsten enrichment to ~3.5 at.% at grain boundaries.

Molecular dynamics simulation on the deformation mechanism of monocrystalline and nano-twinned TiN under nanoindentation

In this research work, MD simulations are performed to investigate the nanoindentation deformation mechanisms of monocrystalline and nano-twinned TiN with various twin thicknesses. It is found that the nanoindentation plastic deformation of monocrystalline TiN with loading on the (111) surface is mainly due to the formation of triangular pyramid stacking faults, embryonic dislocation loop and then the ribbon dislocation loops. As for the nano-twinned TiN films with large twin thickness, the twin boundaries can efficiently block the propagation of dislocations, which could contribute to hardening. As for the nano-twinned TiN films with small twin thickness, the twin boundary could contribute to hardening in the initial plastic deformation due to the twin boundary-induced dislocation blockage, but the twin boundary could cause the softening effect in the middle and later stage of plastic deformation due to the following two aspects: (1) the formation of steps and local damaged regions in the twin boundary; (2) the steps and local damaged regions in the twin boundary serve as new sites for dislocations nucleation. Overall, twin boundary-induced softening mechanism dominates the deformation of nano-twinned TiN with small twin thickness during nanoindentation. Thus, nano-twinned TiN films with various twin thicknesses present the inverse Hall-Petch type relationship.

Molecular dynamics simulation of nanoindentation on amorphous/amorphous nanolaminates

The nanoindentation deformation behaviors of Cu80Zr20 (A)/Cu20Zr80 (B) amorphous/amorphous nanolaminates were studied by using molecular dynamics (MD) simulation, aiming to investigate the effects of heterogeneous interface and layer thickness on the hardness. It was found that there is a strong length-scale-dependence for the mechanical properties of amorphous/amorphous nanolaminates. There is a critical range of layer thickness h (~1 nm < h < 2 nm), within which the hardness of nanolaminates is minimized. By analyzing the shear strain and atomic displacement vector, the interface strengthening effect was found to be prominent when the layer thickness is less than 1 nm. We also revealed that the hardness of nanolaminates is mainly contributed by the surface layer when the layer thickness is larger than 1 nm, which should not be ignored when evaluating the mechanical properties at nanoscale. The current work highlights the influence of interface on the shear localized deformation through MD simulations, and shows that the amorphous/amorphous nanolaminates could be an important candidate for high performance materials at room temperature.

The effect of crystal anisotropy and pre-existing defects on the incipient plasticity of FCC single crystals during nanoindentation

Molecular dynamics simulation is used to identify and quantify the initial plastic deformation mechanisms of gold as a model face-centered cubic (fcc) metal in the nanoindentation process. The coupling effects of crystallographic orientation and internal structural defects on the resulting load distribution at the onset of plasticity are investigated to clarify the anisotropic characteristics of material responses to crystallographic orientation. Homogenous defect nucleation is studied by correlating the indentation force-displacement curve with the instantaneous defect structure. In the absence of pre-existing defects, nanoindentation deformation is dominated by nucleation of Shockley partial dislocations regardless of crystal orientation. Various forms of dislocation propagation are observed in different crystal orientations. The elastic-plastic transition point appears later for the [111]-oriented surface than the ones for [001]-, and [011]-oriented surfaces. The relation of hardening and dislocation density shows that conventional Taylor hardening captures the plasticity after a certain amount of indentation depth in the presence of enough dislocation density. The crystal's sensitivity to the presence of internal structural faults is strongly dependent on the crystallographic orientation. Nanoindentation simulations in the presence of sessile dislocation loops in the structure show that the most significant reduction in the pop-in load happens for the [111] oriented sample. Our simulations suggest that the indentation near a defect can lead to small, subcritical events that lead to a smoother "pop- in" at the onset of plasticity. Since internal defects in materials are nearly inevitable, a defect-based model can be useful to understand the stochastic pop- in loads in nanoindentation tests.