Indentation Deformation Research Articles

3D Deformation Measurement of Soft Material under Indentation Using Improved Diffraction-Assisted Image Correlation

In inverse finite element-based analysis, complete experimental data collection is critical for multi-parameter identification and physical modeling of all kinds of materials. In this paper, diffraction-assisted image correlation (DAIC) is improved and proposed for the deformation measurement of a soft material under indentation with no blind area. A simple and convenient image-based 3D calibration method was developed, and more accurate formulations for 3D displacement measurement based on a more rigorous imaging model were derived. Using the improved DAIC, a newly developed imaging device with indenter-fixed loading and no blind area is proposed that allows 3D displacements of the whole upper surface of a soft silica gel specimen to be retrieved. The experimental results demonstrate that the proposed method is an accurate, efficient and convenient tool with a simple structure for 3D indentation deformation measurement and illustrate its capabilities to capture deformation in indentation tests with tough testing requirements, such as in situ measurement with limited access (high integration level) and dynamic testing (capturing of synchronously stereo images).

Computation of stress field in a polymer scaffold from optically measured deformation field using particle images

Different mechanical stimuli are applied to the substrate of a microchip and a cellular scaffold to simulate in vivo biomechanical environment, but few studies have been performed to measure the stress inside the substrate and the scaffold. In this study, a novel technique of computing the stress field inside a scaffold using optically measured deformation field has been developed. The effectiveness of our proposed technique is evaluated using a polymer block undergoing indentation deformation. The deformation field in the cross section of a block under indentation loading was measured using a particle image analysis method, and the accuracy of the displacement measurement method was verified. The measured displacement fields were mapped into the cross sectional surface of a block model, and FE analysis was performed to compute the stress fields. The stress field estimated from the inverse analysis using the measured displacement fields agree with that of the direct force loading simulation, and the relative error of maximum stress was less than 3%. The indentation forces also agreed well with those in the direct force loading FE analysis, and the errors were less than 8%.

Effects of rockfall on an elastic-plastic member: A novel compliance contact model and dynamic response

The study presents the dynamic structural response of steel member subjected to a localized impact from falling rock blocks in rockfall areas. A novel compliance contact model is derived for the interaction between the elastic-plastic member (the target) and an impacting rock block. Unlike other existing models, the proposed compliance contact model accurately evaluates the material properties of the rock block (considered as a deformable indenter) and of the steel target (considered as an elastic-plastic target of finite thickness). A simplified two degrees of freedom (2-DOF) lumped masses model accounting for nonlinear contact interaction and material nonlinearities is used to describe the dynamics of the phenomenon. The proposed contact law and the 2-DOF model are validated with detailed static and dynamic analyses conducted with finite element software ANSYS. The results are compared and commented in order to be implemented in future civil engineering applications.

Indentation behavior of the stiffest membrane mounted on a very compliant substrate: Graphene on PDMS

Graphene is the stiffest membrane and PDMS is one of the very compliant materials. The indentation response of a graphene monolayer mounted on a PDMS substrate (graphene/PDMS) is studied by both experimental and computational investigations. Due to the huge elastic modulus ratio between membrane and substrate (∼106) and the very large ratio of indentation depth to membrane thickness (∼103), the indentation deformation of graphene in the graphene/PDMS structure is analogous to that of free-standing (F-S) graphene but just with a relatively smaller indentation depth (i.e., the graphene deformation is insensitive to the appearance of PDMS substrate); the graphene can create a screening effect, which causes the PDMS substrate deformation to be insensitive to the tip geometry. In addition, with the aid of finite element method (FEM), the elastic modulus of graphene monolayer can be accurately determined from the overall indentation response of graphene/PDMS using an inverse analysis, which is determined as 0.982TPa (very close to previously reported values). The present approach can be also extended to other 2D materials.

Cooling and Annealing Effect on Indentation Response of Lead-Free Solder

With the development of lead-free solders in the electronic packing industry, Sn–Ag–Cu solders are one of the most promising lead-free alloys to be applied due to their outstanding mechanical property and wettability. By performing indentation experiments, the effect of cooling rate on the mechanical properties of Sn–3.0Ag–0.5Cu (SAC305) solder is investigated in typical cooling conditions (i.e., furnace cooled and water quenched) and compared with the as-machined samples of bulk solder bars from the industry. Based on continuous stiffness measurement technique, Young’s modulus and hardness are reduced by 2.3–3.9[Formula: see text]GPa and 0.053–0.085[Formula: see text]GPa, respectively, after annealing treatment for the indentation depth between 1000[Formula: see text]nm and 1100[Formula: see text]nm in samples after cooling, however, the value of hardness is independent of cooling condition. By defining the contact stiffness to represent residual stress in solder samples after cooling and annealing process, an exponential-based Oliver–Pharr model is employed to fit the unloading responses of indentation. It is found that the smaller cooling rate induces less contact stiffness and thus less residual stress. Despite different cooling conditions, the contact stiffness of unannealed and annealed solder samples are 711.8–842.5[Formula: see text][Formula: see text]N/nm and 655.2–673.4[Formula: see text][Formula: see text]N/nm, respectively. Thus, annealing treatment of 210[Formula: see text]C for 6[Formula: see text]h can effectively alleviate residual stress to a similar level for SAC305 solder samples with different cooling conditions. This conclusion is supported by the alleviation of pile-up deformation in the residual indentation after annealing treatment.

Amplified effect of mild plastic anisotropy on residual stress and strain anisotropy

Axisymmetric indentation of a geometrically axisymmetric disk produced residual stresses by non-uniform plastic deformation. The 2024 aluminum plate used to make the disk exhibited mild plastic anisotropy with about 10% lower strength in the transverse direction compared to the rolling and through-thickness directions. Residual stresses and strains in the disk were measured with neutron diffraction, slitting, the contour method, x-ray diffraction and hole drilling. Surprisingly, the residual-stress anisotropy measured in the disk was about 40%, the residual-strain anisotropy was an impressive 100%, and the residual stresses were higher in the weaker direction. The high residual stress anisotropy relative to the mild plastic anisotropy and the direction of the highest stress are explained by considering the mechanics of indentation: constraint on deformation provided by the material surrounding the indentation and preferential deformation in the most compliant direction for incremental deformation. By contrast, the much larger anisotropy in residual strain compared to that in residual stress is independent of the fabrication process and is instead explained by considering Hookean elasticity. For Poisson's ratio of 1/3, the relationship simplifies to the residual strain anisotropy equaling the square of the residual stress anisotropy, which matches the observed results (2 ≈ 1.4^2). A lesson from this study is that to accurately predict residual stresses and strains, one must be wary of seemingly reasonable simplifying assumptions such as neglecting mild plastic anisotropy.

Produce mirror-shining surface of electrogalvanized steel with significantly elevated scratch resistance through combined nanoelectrodeposition and passivation treatment

This article reports a study on production of mirror-shining surface of electrogalvanized steel with significantly elevated scratch resistance, achieved by combined nano-electrodeposition and passivation treatment. Roughness, indentation deformation, elastic modulus and micro-scratch resistance of the treated electrogalvanized steel surface were investigated. Through in situ property mapping using a multi-mode atomic force microscope, surface properties of passivation films on coarse-grained and nanocrystalline zinc coatings were evaluated. It was demonstrated that the combination of nano-electrodeposition and passivation treatment greatly improved the passive film on the zinc coating with mirror brightness and significantly raised resistance to scratch, which is about two orders of magnitude higher than that of oxide film on conventional electrogalvanized steel.

Material dimensionality effects on the nanoindentation behavior of Al/a-Si core-shell nanostructures

The nanoindentation behavior of hemispherical Al/a-Si core-shell nanostructures (CSNs), horizontally-aligned Al/a-Si core-shell nanorods (CSRs) with various lengths, and an Al/a-Si layered thin film has been studied to understand the effects of geometrical confinement of the Al core on the CSN deformation behavior. When loaded beyond the elastic limit, the CSNs have an unconventional load-displacement behavior with no residual displacement after unloading, resulting in no net shape change after indentation. This behavior is enabled by dislocation activities within the confined Al core, as indicated by discontinuous indentation signatures (load-drops and load-jumps) observed in the load-displacement data. When the geometrical confinement of the core is slightly reduced, as in the case of CSRs with the shortest rod length, the discontinuous indentation signatures and deformation resistance are heavily reduced. Further decreases in core confinement result in conventional nanoindentation behavior, regardless of geometry. Supporting molecular dynamics simulations show that dislocations nucleated in the core of a CSN are more effectively removed during unloading compared to CSRs, which supports the hypothesis that the unique deformation resistance of Al/a-Si CSNs are enabled by 3-dimensional confinement of the Al core.

Effect of the Elastic Deformation of a Point-Sharp Indenter on Nanoindentation Behavior.

The effect of the elastic deformation of a point-sharp indenter on the relationship between the indentation load P and penetration depth h (P-h curve) is examined through the numerical analysis of conical indentations simulated with the finite element method. The elastic deformation appears as a decrease in the inclined face angle β, which is determined as a function of the elastic modulus of the indenter, the parabolic coefficient of the P-h loading curve and relative residual depth, regardless of h. This indicates that nominal indentations made using an elastic indenter are physically equivalent to indentations made using a rigid indenter with the decreased β. The P-h curves for a rigid indenter with the decreased β can be estimated from the nominal P-h curves obtained with an elastic indenter by using a procedure proposed in this study. The elastic modulus, yield stress, and indentation hardness can be correctly derived from the estimated P-h curves.

Origin of a Nanoindentation Pop-in Event in Silicon Crystal.

The Letter concerns surface nanodeformation of Si crystal using atomistic simulation. Our results account for both the occurrence and absence of pop-in events during nanoindentation. We have identified two distinct processes responsible for indentation deformation based on load-depth response, stress-induced evolution of crystalline structure and surface profile. The first, resulting in a pop-in, consists of the extrusion of the crystalline high pressure Si-III/XII phase, while the second, without a pop-in, relies on a flow of amorphized Si to the crystal surface. Of particular interest to silicon technology will be our clarification of the interplay among amorphization, crystal-to-crystal transition, and extrusion of transformed material to the surface.

The Influence of Indenter Tip Imperfection and Deformability on Analysing Instrumented Indentation Tests at Shallow Depths of Penetration on Stiff and Hard Materials

We report on the difficulties of extracting plastic parameters from constitutive equations derived by instrumented indentation tests on hard and stiff materials at shallow depths of penetration. As a general rule, we refer here to materials with an elastic stiffness more than 10 % of that of the indenter and a yield strain higher than 1 %, as well as to penetration depths less than ∼ 5 times the characteristic tip defect length of the indenter. We experimentally tested such a material (an amorphous alloy) by nanoindentation. To describe the mechanical response of the test, namely the force-displacement curve, it is necessary to consider the combined effects of indenter tip imperfections and indenter deformability. For this purpose, an identification procedure has been carried out by performing numerical simulations (using Finite Element Analysis) with constitutive equations that are known to satisfactorily describe the behaviour of the tested material. We propose a straightforward procedure to address indenter tip imperfection and deformability, which consists of firstly taking account of a deformable indenter in the numerical simulations. This procedure also involves modifying the experimental curve by considering a truncated length to create artificially the material’s response to a perfectly sharp indentation. The truncated length is determined directly from the loading part of the force-displacement curve. We also show that ignoring one or both of these issues results in large errors in the plastic parameters extracted from the data.

Vickers Indentation Cracking of Ion-Exchanged Glasses: Quasi-Static vs. Dynamic Contact

The indentation deformation and cracking responses of ion-exchanged glasses were measured using quasi-static and dynamic loading cycles. Two glass types were compared, a normal glass that deforms to a large extent by a shearing mechanism and a damage resistant glass that comparatively deforms with less shear and more densification. The quasi-static indentation cracking threshold for median/radial cracks for the ion-exchanged normal glass was determined to be 7 kilograms force (kgf), while the ion-exchanged damage resistant glass required loads exceeding 30 kgf. The increased cracking threshold of the damage resistant glass composition is attributed to the deformation mechanism, i.e. deformation with greater densification/less shear results in less subsurface damage and less residual stress. Both glass types were also subjected to dynamic indentation where the contact event time was more than 10,000 times shorter than the quasi-static condition. Under dynamic loading conditions, the cracking thresholds of the ion-exchanged normal and damage resistant glasses increased to greater than 50 kgf and greater than 150 kgf, respectively. The stress induced optical retardation was compared for quasi-static and dynamic indents made at sub-cracking threshold loads for both glasses. For indents made at the same sub-cracking threshold load in the normal glass, optical retardation mapping indicates less residual stress surrounding dynamic indents when compared to quasi-static indents. This suggests a rate dependence on the deformation mechanism in normal glasses with higher rates promoting densification in favor of shear. However, for damage resistant glass, the stress induced optical retardation is the same for indents made at both quasi-static and dynamic indentation rates.

Mechanical Behavior of CFRP Lattice Core Sandwich Bolted Corner Joints

The lattice core sandwich structures have drawn more attention for the integration of load capacity and multifunctional applications. However, the connection of carbon fibers reinforced polymer composite (CFRP) lattice core sandwich structure hinders its application. In this paper, a typical connection of two lattice core sandwich panels, named as corner joint or L-joint, was investigated by experiment and finite element method (FEM). The mechanical behavior and failure mode of the corner joints were discussed. The results showed that the main deformation pattern and failure mode of the lattice core sandwich bolted corner joints structure were the deformation of metal connector and indentation of the face sheet in the bolt holes. The metal connectors played an important role in bolted corner joints structure. In order to save the calculation resource, a continuum model of pyramid lattice core was used to replace the exact structure. The computation results were consistent with experiment, and the maximum error was 19%. The FEM demonstrated the deflection process of the bolted corner joints structure visually. So the simplified FEM can be used for further analysis of the bolted corner joints structure in engineering.

Study on the deformation behavior of β phase in Ti–10V–2Fe–3Al alloy by micro-indentation

The Ti–10V–2Fe–3Al alloy composed of β phases was varied by the β-solution treatment. In order to characterize the indentation deformation behavior of β phase, the micro-indentation tests were conducted in the indenter load ranging from 50 mN to 450 mN and the loading rates range from 4.84 mN/s to 19.36 mN/s at ambient temperature. The influences of β-solution treatment temperature, loading rate and indenter load on the micromechanics properties were investigated. The results showed that both the micro-hardness and Young's modulus of β phase declined drastically with the increase of indenter load, while remained the same level when the indenter load was above 300 mN. It was observed that the specimen under β-solution treatment of 820 °C and the loading rate of 19.36 mN/s possessed a higher micro-hardness and Young's modulus than that of others. The plastic energy dissipation, which was significantly influenced by the β-solution treatment temperature and loading rate, increased with the growth of indenter load exerted on the specimens and can be expressed in a power-law function of indenter load for β phase. In addition, the average plastic energy dissipation density in the micro-indentation was a linear function of the micro-hardness and its decrease with indenter load is attributed to the decline of geometrically necessary dislocations (GNDs).

An extended GTN model for indentation-induced damage

The damage of metallic alloys induced by tensile deformation can be well described by Gurson-Tvergaard-Needleman (GTN) model. However, damage growth under intense shear loading, which has been found in micro-/macro-indentation tests, cannot be captured by this model. In this paper, an extension to GTN model is proposed to explain the damage induced by spherical indentation deformation. The nucleation of the secondary voids and the shear softening and localization due to the existing voids are taken into account. An independent law is proposed for the evolution of damage as a function of porosity. An implicit numerical integration using the generalized mid-point algorithm is formulated in the presented paper. Based on the extended GTN model, indentation simulations are performed. It is found that the coexistence of the shear softening and the nucleation of the secondary void mechanism is adequate to explain the damage induced by indentation as a result of the good agreement between the experimental measurement and the simulation prediction.

Vertically aligned CNT arrays: structural integrity and surface properties

Purpose Carbon nanotube-based architectures have increased the scientific interest owning to their exceptional performance rendering them promising candidates for advanced industrial applications in the nanotechnology field. Despite individual CNTs being considered as one of the most known strong materials, much less is known about other CNT forms, such as CNT arrays, in terms of their mechanical performance. The paper aims to discuss these issues. Design/methodology/approach In this work, thermal CVD method is employed to produce VA-MWCNT carpets. Their structural properties were studied by means of SEM, XRD and Raman spectroscopy, while their hydrophobic behavior was investigated via contact angle measurements. The resistance to indentation deformation of VA-MWCNT carpets was investigated through nanoindentation technique. Findings The synthesized VA-MWCNTs carpets consisted of well-aligned MWCNTs. Static contact angle measurements were performed with water and glycerol, revealing a rather super-hydrophobic behavior. Originality/value The structural analysis, hydrophobic behavior and indentation response of VA-MWCNTs carpets synthesized via CVD method are clearly demonstrated.

The Relationship between the Deformation of Spherical Indentation and Tensile Deformation

The paper is devoted to the definition of the deformation during indentation of the sphere and its relationship with the tensile deformation. Proposed by different authors methods of determining the deformation of the contact are considered. The results of their researches may vary significantly. It is shown that in the last decade to determine the deformation, the finite element analysis taking into account the "sink-in/pile-up", i.e. an elastic sinking in and plastic piling up of the material on the edges of the indent during the indentation process is widely used. The purpose of this research is to determine the relationship between tension deformation and sphere indentation deformation with taking into account the last achievements in the field of finite-element modeling of elastic-plastic sphere indentation. It is considered two methods of determining of deformation. One uses the equation proposed by S.I. Bulychev, in which the Mayer’s index is determined from the results of finite element analysis. The second method use the energy concept of hardness. It is based on the assumption that within the range of uniform deformation during uniaxial tension and during sphere indentation, the same energy is consumed to the plastic displacement of the part of the material volume out of limits of initial volume. They have close results. The corresponding graphic relations are shown.

Competing Indentation Deformation Mechanisms in Glass Using Different Strengthening Methods

Chemical strengthening via ion exchange, thermal tempering, and lamination are proven techniques for strengthening of oxide glasses. For each of these techniques, the strengthening mechanism is conventionally ascribed to the linear superposition of the compressive stress profile on the glass surface. However, in this work we use molecular dynamics simulations to reveal the underlying indentation deformation mechanism beyond the simple linear superposition of compressive and indentation stresses. In particular, the plastic zone can be dramatically different from the commonly assumed hemispherical shape, which leads to a completely different stress field and resulting crack system. We show that the indentation-induced fracture is controlled by two competing mechanisms: the compressive stress itself and a potential reduction in free volume that can increase the driving force for crack formation. Chemical strengthening via ion exchange tends to escalate the competition between these two effects, while thermal tempering tends to reduce it. Lamination of glasses with differential thermal expansion falls in between. The crack system also depends on the indenter geometry and the loading stage, i.e., loading vs. after unloading. It is observed that combining thermal tempering or high free volume content with ion exchange or lamination can impart a relatively high compressive stress and reduce the driving force for crack formation. Therefore, such a combined approach might offer the best overall crack resistance for oxide glasses.

Surface analysis and mechanical behaviour mapping of vertically aligned CNT forest array through nanoindentation

Carbon nanotube (CNT) based architectures have increased the scientific interest owning to their exceptional performance rendering them promising candidates for advanced industrial applications in the nanotechnology field. Despite individual CNTs being considered as one of the most known strong materials, much less is known about other CNT forms, such as CNT arrays, in terms of their mechanical performance (integrity). In this work, thermal chemical vapor deposition (CVD) method is employed to produce vertically aligned multiwall (VA-MW) CNT carpets. Their structural properties were studied by means of scanning electron microscopy (SEM), X-Ray diffraction (XRD) and Raman spectroscopy, while their hydrophobic behavior was investigated via contact angle measurements. The resistance to indentation deformation of VA-MWCNT carpets was investigated through nanoindentation technique. The synthesized VA-MWCNTs carpets consisted of well-aligned MWCNTs. Static contact angle measurements were performed with water and glycerol, revealing a rather super-hydrophobic behavior. The structural analysis, hydrophobic behavior and indentation response of VA-MWCNTs carpets synthesized via CVD method are clearly demonstrated. Additionally, cycle indentation load-depth curve was applied and hysteresis loops were observed in the indenter loading–unloading cycle due to the local stress distribution. Hardness (as resistance to applied load) and modulus mapping, at 200nm of displacement for a grid of 70μm2 is presented. Through trajection, the resistance is clearly divided in 2 regions, namely the MWCNT probing and the in-between area MWCNT − MWCNT interface.

Quantifying deformation processes near grain boundaries in α titanium using nanoindentation and crystal plasticity modeling

The influence of grain boundaries on plastic deformation was studied by carrying out nanoindentation near grain boundaries (GBs). Surface topographies of indentations near grain boundaries were characterized using atomic force microscopy (AFM) and compared to corresponding single crystal indent topographies collected from indentations in grain interiors. Comparison of the single crystal indents to indents adjacent to low-angle boundaries shows that these boundaries have limited effect on the size and shape of the indent topography. Higher angle boundaries result in a decrease in the pile-up topography observed in the receiving grain, and in some cases increases in the topographic height in the indented grain, indicating deformation transfer across these boundaries is more difficult. A crystal plasticity finite element (CPFE) model of the indentation geometry was built to simulate both the single crystal and the near grain boundary indentation (bi-crystal indentation) deformation process. The accuracy of the model is evaluated by comparing the point-wise volumetric differences between simulated and experimentally measured topographies. Good agreement, in both single and bi-crystal cases, suggests that the crystal plasticity kinematics plays a dominant role in single crystal indentation deformation, and is also essential to bi-crystal indentation. Despite the good agreement, some differences between experimental and simulated topographies were observed. These discrepancies have been rationalized in terms of reverse plasticity and the inability of the model to capture the full resistance of the boundary to slip. This is discussed in terms of dislocation nucleation versus glide in the model and in the physics of the slip transfer process.