Increase In Indentation Depth Research Articles

Evaluating the electromigration effect on mechanical performance degradation of aluminum interconnection wires: A nanoindentation test with molecular dynamics simulation study

Electromigration (EM) is a crucial failure mode in Aluminum (Al) interconnection wires those are widely used in high density semiconductor packaging. This study systematically investigated the influence of EM on the mechanical properties of Al interconnects via nanoindentation experiments and molecular dynamics (MD) simulations. The results are list as follows. (1) The indentation depth gradually increases with the increase in indentation load, resulting in a gradual increase and stabilization of the Young’s modulus and hardness of the structure. Within a specific range, the influence of the loading rate on the indentation depth and mechanical properties is relatively small. (2) The region where Young’s modulus of the interconnect decreases correlates with the location where EM-induced voids initiate. EM-induced voids have a direct impact on the material’s mechanical properties, particularly the decrease in Young’s modulus. (3) These EM-induced voids affect the nucleation and formation of dislocations. With the increase in void concentration and indentation depth, The generation and slip of dislocations increase as the void concentration and indentation depth increase, leading to a decrease in the material’s mechanical properties over time. This comprehensive findings expand the knowledge on mechanical behavior degradation of Al interconnects when EM failure occurs, providing a scientific basis for designing and optimizing high density semiconductor packaging.

Atomistic insight of deformation mechanisms and mechanical characteristics of nano-scale silver (100) using nanoindentation

This work aims to utilize the widely adopted nanoindentation technique to explore the deformation behavior and mechanical characteristics of nanocrystalline silver (Ag) materials. Molecular Dynamics simulations were conducted to understand the material behavior at the nanometer scale. In this simulation, the effect of indentation velocity and indentation depth on defect formation and hardness during nanoindentation of Ag specimens was analyzed and discussed in detail. The results show that the deformation behavior of the Ag specimen was affected by different indentation velocities. These phenomena were confirmed by analyzing the load-displacement curve, which indicates elastic deformation by the appearance of a linear load-displacement at low indentation velocities. In contrast, plastic deformation was found by the presence of intensified serration in the load-displacement relationship at higher indentation velocities. In these cases, the hardness showed little variation when the indenter velocity was increased from 5 m/s to 10 m/s, whereas a significant increase in hardness was observed when the indentation velocity was further increased to 20 m/s. Importantly, the progression of load-displacement curves during nanoindentation demonstrates the occurrence of minor and major load drops, corresponding to an increase in indentation depth from 0.5 nm to 2 nm respectively. These findings were elucidated through dislocation extraction analysis (DXA), which revealed that a minor load drop at low indentation depths is attributed to the nucleation of an amorphous structure, while a major load drop at higher indentation depths is associated with the expansion of dislocation nucleation. Consequently, the hardness increased significantly as the indentation depth increased. This research, provides insight into atomistic investigation and offers guidelines for designing materials with excellent mechanical properties using nanoindentation.

Probing Fault Features of Lithium-Ion Battery Modules under Mechanical Deformation Loading

Electric vehicle battery systems are easily deformed following bottom or side pillar collisions. There is a knowledge gap regarding the fault features of minor mechanical deformation without ISC, which can be used for early warning of mechanical deformation. In this study, the fault features of a lithium-ion battery module under different degrees of mechanical deformation were studied from the perspective of voltage consistency. The results show that the capacity of the battery module declines with an increase in indentation depth, consistent with the capacity degradation of the indented cell. During the charging and discharging processes, the voltage of the indented cell deviates to a lower value compared to the other normal cells. At the end of the discharging process, the voltage sharply declines and exhibits a significant deviation from the other normal cells. The Mean Normalization (MN) method is employed to quantitatively describe the voltage consistency. The results indicate that the MN value of the indented cell’s voltage is distributed at the lowest during the charging period and sharply declines below −0.06 at the end of discharging. In the future, a fault detection method for mechanical abuse will be established based on these features.

Computational modeling reveals a vital role for proximity-driven additive and synergistic cell-cell interactions in increasing cancer invasiveness.

Solid-tumor cell invasion typically occurs by collective migration of attached cell-cohorts, yet we show here that indirect cell-interactions through the substrate can also drive invasiveness. We have previously shown that well-spaced, invasive cancer cells push-into and indent gels to depths of 10 µm, while closely adjacent, non-contacting cancer cells may reach up to 18 µm, potentially relying on cell-cell interactions through the gel-substrate. To test that, we developed finite element models of indenting cells, using experimental gel mechanics, cell mechanostructure, and force magnitudes. We show that under 50-350 nN of combined traction and normal forces, a stiff nucleus-region is essential in facilitating 5-10 µm single-cell indentations, while uniformly soft cells attain 1.6-fold smaller indentations. We observe that indentation depths of cells in close proximity (0.5-50 µm distance) increase relative to well-spaced cells, due to additive, continuum mechanics-driven contributions. Specifically, 2-3 cells applying 220 nN normal forces gained up to 3% in depth, which interestingly increased to 7.8% when two cells, 10 µm apart, applied unequal force-magnitudes (i.e., 220 and 350 nN). Such additive, energy-free contributions can reduce cell mechanical energy -output required for invasiveness, yet the experimentally observed 10-18 µm depths likely necessitate synergistic, mechanobiological changes, which may be mechanically triggered. We note that nucleus stiffening or cytoplasm softening by 25-50% increased indentation depths by only 1-7%, while depths increase nearly linearly with force-magnitude even to two-fold levels. Hence, cell-proximity triggered, synergistic and additive cell-interactions through the substrate can drive collective cancer-cell invasiveness, even without direct cell-cell interactions. STATEMENT OF SIGNIFICANCE: Metastatic cancer invasion typically occurs collectively in attached cell-cohorts. We have previously shown increased invasiveness in closely adjacent cancer cells that are able to push-into and indent soft-gels more deeply than single, well-spaced cells. Using finite element models, we reveal mechanisms of cell-proximity driven invasiveness, demonstrating an important role for the stiff nucleus. Cell-proximity can additively induce small increase in indentation depth via continuum mechanics contributions, especially when adjacent cells apply unequal forces, and without requiring increased cell-mechanical-energy-output. Concurrently, proximity-triggered synergistic interactions that produce changes in cell mechanics or capacity for increased force-levels can facilitate deep invasive-indentations. Thus, we reveal concurrent additive and synergistic mechanisms to drive collective cancer-cell invasiveness even without direct cell-cell interactions.

The rock fragmentation and crack propagation under TBM tunneling based on particle flow code

Abstract The rock fragmentation and crack propagation of anisotropic rock induced by tunnel boring machine (TBM) tunneling is studied in this paper. First, a numerical model based on the 2D particle flow code (PFC2D) is established and calibrated to reveal the four stages of rock fragmentation. In Stage I (indentation depth 0–0.4 mm), the indentation force beneath the cutterhead increases and decreases dramatically with the accumulation and release of mechanical energy. Such a phenomenon indicates that a hydrostatic core (crushed zone) can be observed. In Stage II (indentation depth 0.4–1.1 mm), many median cracks propagate dramatically with the indentation force. Meanwhile, the hydrostatic core is pushed because the mechanical energy of the cutterhead is reaccumulated in the specimen. In Stage III (indentation depth 1.1–2.6 mm), lateral cracks begin to develop due to the further increase in indentation depth. In Stage IV (indentation depth 2.6–5 mm), the lateral cracks and median cracks continue to propagate, and rock chips can be found on the sides of the cutterhead. Then, with increasing confining pressure, lateral cracks begin to gradually develop and the maximum angle of lateral cracks is 70.5°. Furthermore, the magnitude of the intrusion velocity can seriously influence the evolution of the indentation force during Stages III and IV because of the accumulation and release of mechanical energy. The accumulation and release of mechanical energy are more obvious with a higher intrusion velocity of the cutterhead.

Investigation of softening induced indentation size effect in Nanoglass and Metallic glasss

In this work, binary Cu60Zr40 nanoglasses (NGs) and melt spun ribbons (MGs) are synthesized by using magnetron sputtering in an inert gas condensation (IGC) system and standard melt-spinning, respectively. The bonded interface experiments through micro-indentation, and nanoindentation experiments at different peak loads are conducted on both glasses. In addition, complementary finite element (FE) simulations are performed using finite strain viscoplastic constitutive theory for amorphous metals. The bonded interface experiments reveal smooth and almost semi-circular shaped shear bands in MG, while the formation of wavy shear bands is observed in NG. Further, the primary shear band densities in the MG is higher than that in NG, while the plastic zone size below the indenter is larger in the latter than the former. Furthermore, nanoindentation experiments show that the hardness in NGs as well as MGs decreases with increase in indentation depth signifying both alloys exhibiting the indentation size effect (ISE). However, the ISE is found to be more pronounced in MGs than NGs. The FE simulations show that the less pronounced ISE in NGs is due to the slower softening primarily because of higher friction coefficient, μ in them.

Mechanical characterization of shale matrix minerals using phase-positioned nanoindentation and nano-dynamic mechanical analysis

The accurate determination of mechanical parameters (namely, Young's modulus and hardness) of shale-constitutive minerals is crucial for predicting the macroscale mechanical parameters of shale composites. This study employed an advanced nanoindentation apparatus equipped with a high-resolution microscope (4000×) and a newly emerging nano-dynamic mechanical analysis (nano-DMA) module to conduct mineral-positioned indentation and investigate the depth profiles of mechanical parameters of shale matrix minerals, with the objective of obtaining their intrinsic mechanical values. To conduct mineral-positioned nanoindentation, various matrix minerals were pre-discerned under the optical microscope based on their particle shapes, surface features, and reflection colors. The mechanical response curves show that silicates (quartz and feldspar) exhibit significant elastic characteristics, whereas carbonates (dolomite and calcite) and clay minerals exhibit a combined deformation behavior of elasticity and plasticity based on the elastic recovery ratio and plastic work ratio. The mechanical depth profiles produced by nano-DMA show that the mechanical parameters of all aforementioned minerals decrease rapidly with respective to the increase in indentation depth, before reaching stable values. This variation pattern for the mechanical parameters is a result of the indentation size effect (ISE), which comes from the internal structure (or texture) adjustment of the indented material in small deformed volumes during indenter invasion. Whereas the platform section represents the indenter overcoming the ISE layer and actually probing the material as it is, the mechanical values measured at this stage can be recognized as the true values for the indented materials. In addition, the tested mineral grains would be easily affected by the substrate phases at a much larger indentation depth, and the mechanical parameters would correspondingly change in the mechanical depth profiles after the plateau stage. Overall, our findings identify reliable Young's moduli and hardnesses for different matrix minerals: 30 GPa and 1.5 GPa for clay minerals, 105–110 GPa and 14–16 GPa for quartz, 75–85 GPa and 9–10 GPa for feldspar, 70–75 GPa and 2–3 GPa for calcite, and 115–120 GPa and 7–8 GPa for dolomite.

Resistance spot weldability of TBF steel sheets with dissimilar thickness

This paper presents an experimental study on weldability of TBF steel sheets with dissimilar thickness. Nominal thickness of TBF sheets were 0.95 and 1.55 mm. Optical microscope was used to observe the cracks formed in the weld zone. The indentation depths were determined by ultrasonic technique. Tensile shear tests were applied to the welded specimens in order to determine the mechanical properties. Higher weld current and time resulted in higher nugget size and indentation depth. This increase in nugget size and indentation depth with increasing of weld current and weld time was almost linearly. The liquid metal embrittlement crack sensitivity in the HAZ was very high on TBF spot welds. The liquid metal embrittlement cracks were much deeper and wider along the weld periphery regions compared to the nugget regions. These cracks were occurred easily with a higher heat input and the crack depth increased almost linearly with increasing of heat input. Weld strength of the specimens was governed by crack formation in the HAZ. Lower weld currents and weld times resulted in higher tensile shear properties. The highest tensile shear load (18.50 kN) and energy absorption (37.5 J) were achieved at 6 kA for 20 cycles. This weld exhibited interfacial failure mode.

Dynamic Indentation Characteristics for Various Spacings and Indentation Depths: A Study Based on Laboratory and Numerical Tests

Laboratory and numerical study tests were conducted to investigate the dynamic indentation characteristics for various spacings and indentation depths. First, laboratory tests indicate that the increase in the indentation depth first resulted in enlarged groove volumes, caused by fiercer rock breakages between indentations for a fixed spacing; then, the groove volume slightly increased for further increase in indentation depth, whereas the increase in spacing restrained rock breakages and resulted in shrunken grooves. In addition, the numerical study agreed well with laboratory tests that small chips formed at the shallow part of the rock specimen at the early indentation stage, and then, larger chips formed by the crack propagation at deeper parts of the rock specimens when the indentation depth increased. With further increase in indentation depth, crushed powders instead of chips formed. Moreover, the numerical analysis indicates that crack propagation usually leads to the decrease of the indentation force and the dissipation of the stress concentrations at crack tips, whereas the cessation of crack propagation frequently resulted in the increase of the indentation force and the stress concentrations at crack tip with the increase in indentation depth.

Spatial Variation of Mechanical Properties of ZnO Thin Films RF-Sputtered in Various Gas Environment

ZnO thin films were deposited on quartz substrates by RF sputtering under argon, oxygen and nitrogen gas environment. The as deposited films showed hexagonal wurtzite structure with (002) orientation along c-axis. The mechanical properties of films with thickness ranging from 842[Formula: see text]nm to 1067[Formula: see text]nm and grain size 94–124[Formula: see text]nm were studied using nanoindentation technique. The Young’s modulus and hardness of the films were in the range 76–257[Formula: see text]GPa and 5–18[Formula: see text]GPa, respectively. Both parameters decreased with increase in indentation depth of the films. The spatial distribution of these parameters were strongly dependent on the gas environment used for film deposition.

Molecular dynamics simulation of plasticity in VN(001) crystals under nanoindentation with a spherical indenter

We perform molecular dynamics simulations of the nanoindentation on VN (001) films with a spherical indenter to elucidate the initial plastic deformation and the formation mechanisms of dislocation loops during nanoindentation. We find that the nucleation and movement of partial dislocations are the main mechanism of the inelastic deformation at the initial plastic stage of nanoindentation, when the “dislocation flower” consisting of several {111} stacking fault planes and the 〈110〉 stair rod dislocation lines are observed. With the increase in indentation depth, the newly nucleated dislocations react with the existing ones, forming four kinds of dislocation loops. Moreover, we also conduct a systematic analysis of the formation process of the dislocation flower and the four kinds of dislocation loops.

Characterization of diamond wire-cutting performance for lifetime estimation and process optimization

Diamond abrasive-coated wire is a tool for the precise multi-wire sawing of mono-crystal ingots to manufacture substrates. This tool is used to cut hard materials such as silicon carbide, gallium nitride, sapphire and silicon. The cutting performance of diamond wires strongly influences the accuracy of substrates in terms of roughness, total thickness variation and BOW. Nonetheless, changes in cutting performance as a result of gradual wear through repeated contact complicate the optimization of diamond wire use. A characterization method is proposed for the cutting performance and lifetime of a diamond wire based on mathematical modeling and experimental results. The theoretical model predicts that cutting accelerates with the application of a strong feed force and small abrasives due to an increase in indentation depth for each abrasive. Experimental results showed that a wire with a low concentration exhibited an increased material removal rate. However, the lifetime of the wire displayed an opposite trend; that of a diamond wire can be classified into two regimes. The first one is an increased loss of abrasives as a result of rapid wear attributed to a low concentration; the second regime is caused by a drop in actual contact pressure due to the enlarged contact area between the workpiece and the bonding material enveloping the abrasives.

Investigation of Elasto-Plastic Deformation Behavior of Haynes242 Alloy Subjected to Nanoscale Loads Through Indentation Experiments

The deformation behavior of Haynes242 alloy subjected to nanoscale loads was investigated through nanoindentation experiments with strain rates varying from 0.05 to 0.20 s−1 and an indentation depth of 2000 nm. The strain rate jump tests have been carried out to examine the strain rate sensitivity on mechanical properties at ambient temperature. Strain rate sensitivity measured from these tests was observed to be 0.112 indicating its influence on mechanical properties. Elastic properties such as indentation hardness and Young’s modulus decreased with increase in indentation depth at different strain rates representing strong indentation size effect (ISE). It was observed that, the hardness at nanoscale loads increased with increasing strain rate, however, the influence of strain rate on Young’s modulus is not predominant. The ISE was also studied through Nix and Gao model. The H2 versus 1/h for Haynes242 exhibited a better linear relationship, which is in agreement with the behavior of Ti-6Al-4V. The study of plastic behaviour revealed that, strain rates had no predominant effect on strain hardening exponent, however, it had a significant influence on yield stress.

The effect of work-hardening and pile-up on nanoindentation measurements

Nanoindentation is performed on the cross-section of copper samples subjected to surface mechanical attrition treatment (SMAT). The cross-section of the SMAT samples provides a unique microstructure with varying amounts of work-hardening depending on the distance from the SMAT surface. Results show that for a given indentation load the pile-up height decreases and the indentation depth increases as the distance from the SMAT surface increases, both following a power law relationship. Based on image analysis of the indented surface this increase in the pile-up height and decrease in indentation depth is attributed to the localization of plastic strain due to the increased resistance to dislocation motion in the work-hardened region. For a given amount of work-hardening (in terms of distance from SMAT surface), the indentation depth increased with the indentation load obeying a power law relationship with the exponent ranging from 0.58 to 0.68. However, the pile-up height increased linearly with the load, with the rate (slope) increasing with the amount of work-hardening. The observed linear increase in pile-up height with indentation load would naturally introduce an indentation size effect (ISE) if the hardness is corrected for the pile-up. Interestingly, this ISE associated with pile-up increased with an increase in indentation depth, in contradiction to the ISE associated with strain gradient. Deviation of the hardness values corrected for pile-up from the bulk behavior due to surface effect is highlighted and a method to obtain a bulk-equivalent hardness quantity representing the bulk behavior is proposed.

Temperature variations at nano-scale level in phase transformed nanocrystalline NiTi shape memory alloys adjacent to graphene layers

The detection and control of the temperature variation at the nano-scale level of thermo-mechanical materials during a compression process have been challenging issues. In this paper, an empirical method is proposed to predict the temperature at the nano-scale level during the solid-state phase transition phenomenon in NiTi shape memory alloys. Isothermal data was used as a reference to determine the temperature change at different loading rates. The temperature of the phase transformed zone underneath the tip increased by ∼3 to 40 °C as the loading rate increased. The temperature approached a constant with further increase in indentation depth. A few layers of graphene were used to enhance the cooling process at different loading rates. Due to the presence of graphene layers the temperature beneath the tip decreased by a further ∼3 to 10 °C depending on the loading rate. Compared with highly polished NiTi, deeper indentation depths were also observed during the solid-state phase transition, especially at the rate dependent zones. Larger superelastic deformations confirmed that the latent heat transfer through the deposited graphene layers allowed a larger phase transition volume and, therefore, more stress relaxation and penetration depth.

Analysis of nanoindentation curves in the case of bulk amorphous polymers

Abstract Load versus displacement curves obtained from nanoindentation experiments on polymers are particularly difficult to analyze due to their complex mechanical and especially time-dependent behavior. The indentation curves obtained on two amorphous polymers (polycarbonate (PC) and polymethyl methacrylate (PMMA)) show an increase in the indentation depth during load hold time. A non-linear time-dependent model shows that this phenomenon could be decomposed in a first part due to a viscoelastic response and a second part assigned both to a viscoelastic and a viscoplastic response. If the first part is not achieved, the values of the elastic modulus computed using the Oliver and Pharr method are abnormally high. If it is achieved, the beginning of the unloading curve presents an abnormality that is linked to the increase in indentation depth during hold load time. Nevertheless, if the load hold time is high enough and if the contact stiffness is calculated from the initial slope of the power fit of the unloading curve, the values of the elastic modulus computed using the Oliver and Pharr method are close to those obtained by tensile tests.

OS16-5-5 Fracture Strength of Porous Ceramics by Sphere Indentation

Due to its filterability and thermostability, porous ceramics have a large attention as a suitable material for filters such as a diesel particulate filter. Since damages induced by contact stress on filters cause serious degradation of their strength and life span, the standardization of sphere indentation test is necessity to evaluate the indentation strength of porous ceramics quantitatively. The sphere indentation examination was carried out to investigate the effects of pore diameter on indentation strength under different conditions of indentation sphere sizes and indentation speed. Three porous ceramics were tested; each porous ceramic contains different pore diameter. The result shows that indentation load increased monotonically along with an increase in indentation depth when the porous ceramics has small pore diameter. However, with large pore diameter, the graph of load-displacement displays load increases with vertical fluctuation along with increasing indentation depth. The strength of specimen with large pore diameter relies on indentation sphere size not depending on indentation sphere material. While the fracture strength of specimen with small pore stays constant, the strength of specimen with large pores rises with increasing sphere diameter. The strength of specimen with large pore is also dependent on indentation speed. The strength of specimen with large pore rises in the company of increasing indentation speed, although the strength of specimen with small pore is relatively constant.

2735 球圧子押込みによる多孔質セラミックスの破壊強度に及ぼす気孔径の影響(S28-2 セラミックスおよびセラミックス系複合材料(2),S28 セラミックスおよびセラミックス系複合材料)

Due to its filterability and thermostability, porous ceramics have a large attention as a suitable material for filters such as a diesel particulate filter. Since damages induced by contact stress on filters cause serious degradation of their strength and life span, the standardization of sphere indentation test is necessity to evaluate the indentation strength of porous ceramics quantitatively. The sphere indentation examination was carried out to investigate the effects of pore diameter on indentation strength. Three porous ceramics were tested ; each porous ceramic contains different pore diameter. The result shows that indentation load increased monotonically along with an increase in indentation depth when the porous ceramic has small diameter. However, with a larger diameter, the graph of load-displacement displays load non-monotonically increases with vertical fluctuation. The strength of specimen with larger pore diameter relies on indentation sphere size. While the ceramics strength with smaller pore diameter stays constant, the strength of larger one rises with increasing sphere diameter.

Dynamic observation of indentation process: A possibility of local temperature rise

Abstract Indentation experiments so far performed show that in a dynamic indentation test the rate of growth of the indentation size is highly dependent on the collision velocity of the indenter. Larger collision velocities yield higher rates of initial increase in indentation depth. The overall growth curves of the indentation depth are well modelled by a viscoelastic Voigt system. This model indicates that the viscosity of the sample reduces more rapidly as the collision velocity increases, suggesting the possibility of local temperature rise. In order to check this possibility, the temperature rise was observed with an infrared radiation thermosensor using a barium fluroide sample that is transparent to the infrared rays. The temperature was observed to increase in a wide area after the indenter collided with the sample. The temperature rise observed was small (less than 1K). Taking the limitation in the resolution of the sensor into account, the observed temperature was interpreted as that of the surf...