Indentation Load-displacement Curves Research Articles

On elastoplastic behavior of porous enamel – an indentation and numerical study

The micro/nano pores in natural mineralized tissues can, to a certain extent, affect their responses to mechanical loading but are generally ignored in existing indentation analysis. In this study, we first examined the void volume fraction of sound and caries lesion enamels through micro-computed tomography (micro-CT). A Berkovich indentation study was then carried out to characterize the effect of porous microstructure on the mechanical behavior of the human enamels. The indentation tests were also modeled using the nonlinear finite element analysis technique to simulate indentation load-displacement curves, which showed reasonable agreement with the experimental measurements. From the simulation results, the extent of densification in the plastic zone was identified and the corresponding stress and contact pressure evolutions were quantified. Further, a conventional elastic-perfectly plastic material model without considering micropores was also developed to investigate the compaction effect of the porous structure. The simulation results reveal that conventional elastic perfect-plastic constitutive models become less reliable to model the mechanical behavior of carious lesion enamel with increasing loss of mineral content as it underestimates the yield stress and plastic energy dissipation. This study divulges the importance of compaction of porous enamel structure beneath the indented area. Note that understanding the effect of porous microstructures on plastic behavior is vital as the involved inelastic deformation mechanism associated with irreversible processes such as localized microcracking has a significant bearing on wear and fatigue behavior of enamel. Statement of significanceBased on micro-CT and nano-indentation characterization, a numerical model was developed aiming to precisely describe the deformation behavior of naturally porous enamel. Inelastic properties and energy dissipation characteristics of porous enamel were investigated in detail. This work demonstrated that the existence of micro-pores in White Spot Lesions (WSLs) contributes to mechanical stability, which can mitigate the reduction in Young's modulus and fracture toughness resulting from loss of mineral components. The knowledge gained from this study can be used to explain the mechanisms related to irreversible processes, such as contact induced cracking and wear, and strengthen understanding of the mechanical behavior of porous mineralized tissues.

Residual stress indentation model based on material equivalence

A novel residual stress indentation model for conical indentation loading is proposed to describe the relationship between the residual stress, material constitutive parameters, load, and displacement for materials with a uniaxial constitutive relationship that obeys Hollomon’s power law (H-law). The novel model was established based on the principle that the equivalent material without residual stress corresponds to the original material with residual stress, conical indentation theoretical model based on energy density equivalence, and an assumed power-law relationship between the dimensionless residual stress and relative difference of the yield stresses of the equivalent material and original material. Sixty imaginary H-law materials with ten equibiaxial and ten uniaxial residual stresses were investigated by Finite Element Analysis (FEA). The residual stresses predicted by the novel model from the indentation load–displacement curves simulated for the imaginary materials are in close agreement with those applied by the FEA. Finally, indentation tests for Cr12MoV steel, 45 steel, and 6061-T6511 aluminum alloy were carried out on their specimens without residual stress and their bending specimens with equibiaxial and uniaxial residual stresses. The residual stresses predicted by the novel model according to the indentation load–displacement test curves are in good agreement with those applied by the tests.

Finite element modelling to predict hardness of Mg alloy reinforced with Ti/Hydroxyapatite hybrid composites – An axisymmetric approach

Magnesium based MMCs are widely investigated for orthopaedic applications because of its degradable property. In order to reduce the experimental trials on designing these composites that mimic the natural human bone, Finite element method has been widely employed. This work analyses finite element model of Mg-3Zn alloy matrix reinforced with micron sized 1% Ti particles/ 1.5 % hydroxyapatite particles (hybrid reinforcements) to predict hardness indentation load displacement curves as these composites can be used as load bearing support for fractured bone. Local mechanical responses measured by indentation technique by local measurements are correlated. Stiffness response of the composite to indentation sensitivity is analysed with constitutive parameters. Relations between influence of reinforcements and the material property to aid experimentation are addressed. Critical differences and similarities in strain fields shape, magnitude and size are established. It was observed that the experimental hardness results of the composites are in good agreement with the simulated results.

Application of Nanoindentation in the Characterization of a Porous Material with a Clastic Texture.

In materials science and engineering, a significant amount of research has been carried out using indentation techniques in order to characterize the mechanical properties and microstructure of a broad range of natural and engineered materials. However, there are many unresearched or partly researched areas, such as, for example, the investigation of the shape of the indentation load–displacement curve, the associated mechanism in porous materials with clastic texture, and the influence of the texture on the constitutive behavior of the materials. In the present study, nanoindentation is employed in the analysis of the mechanical behavior of a benchmark material composed of plaster of Paris, which represents a brand of highly porous-clastic materials with a complex structure; such materials may find many applications in medicine, production industry, and energy sectors. The focus of the study is directed at the examination of the influence of the porous structure on the load–displacement response in loading and unloading phases based on nanoindentation experiments, as well as the variation with repeating the indentation in already indented locations. Events such as pop-in in the loading phase and bowing out and elbowing in the unloading phase of a given nanoindentation test are studied. Modulus, hardness, and the elastic stiffness values were additionally examined. The repeated indentation tests provided validations of various mechanisms in the loading and unloading phases of the indentation tests. The results from this study provide some fundamental insights into the interpretation of the nanoindentation behavior and the viscoelastic nature of porous-clastic materials. Some insights on the influence of indentation spacing to depth ratio were also obtained, providing scope for further studies.

Indentation-induced cracking behavior of a Cu(In,Ga)Se2 films on Mo substrate

Abstract Cu(In,Ga)Se2 (CIGS) light absorption films were synthesized by co-sputtering method on Mo/soda-lime glass, and the mechanical behavior of the films was investigated by nanoindentation. The Young's modulus and hardness of the films were approximately 88.5 ± 2.2 and 5.89 ± 0.23 GPa, respectively. The comparison graph of indentation load–displacement curve with the curve based on the theoretical elastic films, while considering the curvature of the indenter tip, revealed that cracks initiated in the CIGS films at approximately 25 mN indentation load. The transmission electron microscopy (TEM) analysis revealed that most of the cracks exhibited intergranular fracture, and the fracture toughness of the films was ~0.22 MPa√m, which is greater than the brittleness of soda-lime glass. Both Palmqvist radial and lateral cracks are observed. Results also reveal that the indentation pressure caused grain subdivision (before cracking initiated), and indentation stress may be absorbed by relatively less dense microstructures of the films.

Indentation model to obtain residual stress based on deviator stress equivalence and its application

Residual stress on the surface of a structure component can be effectively small-invasive evaluated using the indentation method, which is important for evaluating the safety of a service structure. In this study, a novel indentation model based on the deviator stress equivalence was proposed to determine the residual stress in metallic materials that obey Hollomon's power law (H-law). The model described the relationship between equibiaxial or uniaxial residual stresses, H-law parameters, load, and displacement. Finite element analysis (FEA) was used to obtain the indentation load–displacement curves within various equibiaxial or uniaxial residual stresses for several H-law materials. The residual stresses predicted using the model were close to the reference residual stress given by FEA. For three types of the materials, the equibiaxial and uniaxial residual stresses with multilevel were applied to cross and single beams by bending loading, and conical indentation tests were performed. According to the experimental load–displacement curves, the residual stresses predicted by the model proposed were in good agreement with the applied residual stresses.

Self-healing capacity of Mullite-Yb2SiO5 environmental barrier coating material with embedded Ti2AlC MAX phase particles

Repetitive heating and cooling cycles inevitably cause crack damage of hot gas components of gas turbine engines, such as blades and vanes. In this study the self-healing capacity is investigated of mullite + ytterbium monosilicate (Yb2SiO5) as EBC material with Ti2AlC MAX phase particles embedded as a crack-healing agent. The effect of Ti2AlC in the EBC was compared with the self-healing ability of the mullite + Yb2SiO5 material. After introducing cracks by Vickers indentation on the surface of each sample, crack healing was realized by controlling the temperature and time during the post-heat-treatment process. For the mullite + Yb2SiO5 composite with Ti2AlC particles, crack healing occurred at 1000 °C, while in the case of the mullite + Yb2SiO5 composite without Ti2AlC, a sustained temperature of 1300 °C or higher was required. Compared with the healing of the mullite + Yb2SiO5 composite by the formation of a eutectic phase, the addition of Ti2AlC promoted healing via the oxidation of Ti and Al. Notably, the surface formation of a ternary oxide of Ti–Yb–O was confirmed, which completely covered the damage area. Consequently, the addition of a Ti2AlC MAX phase to the EBC composite resulted in a complete strength recovery, while the mullite + Yb2SiO5 composite without Ti2AlC showed a strength recovery of about 80%. Furthermore, by analyzing the indentation load–displacement curve to indicate the role of Ti2AlC, the addition of Ti2AlC improved both the hardness and stiffness of the composite.

Determining the constitutive behavior of nonlinear visco-elastic-plastic PMMA thin films using nanoindentation and finite element simulation

Understanding the nonlinear visco-elastic-plastic behavior and properties of PMMA thin films during nanoindentation is helpful for predicting the plastic deformation of thermoplastic polymer products during manufacture and evaluating stress to predict the reliability and failure behavior of their service structures. This article reports a study on the nanoindentation of PMMA thin films via instrumented indentation testing and numerical simulation to determine its constitutive behavior. It is found that both the loading curve and the unloading curve at any depth can be generated from one indentation depth for the indentation tests of PMMA thin films with Berkovich indenter. By coupling experimental investigation and finite element simulation, we investigated the possibility of applying the Oyen-Cook constitutive equation to nonlinear viscous-elastic-plastic PMMA thin films. The results of finite element analysis show that the time-dependent elastic-plastic deformation of the unloading curves becomes more conspicuous when the quadratic viscosity term of the Oyen-Cook constitutive equation is decreased. Finite element simulations using the Oyen-Cook constitutive model reproduce the experimentally-measured indentation load-displacement curves with reasonable accuracy.

A paradox in mechanical property characterization of multilayer 2D materials based on existing indentation bending model

Elastic modulus of multiple layer two-dimensional (2D) materials is typically measured in indentation testing via existing indentation bending model of a beam/plate, in which the sample is assumed to be a doubly clamped beam/plate under a central point load. However, a paradox is commonly found in indentation testing of multiple layer 2D materials: the measured indentation load-displacement curve has a much longer linear regime than the corresponding theoretical counterpart; in addition, the elastic modulus determined is significantly lower than its theoretical counterpart. Based on the theoretical and numerical analyses, the above paradox can be well explained via the separation of the adhesive boundary of 2D materials in indentation tests, resulting in that the freestanding portion of sample behaves like a pure bending beam/plate, instead of a doubly clamped beam/plate subjected to a central point load. These results agree with the reported experimental results very well, and thus, the indentation response of multiple layer 2D materials should be analyzed via the pure bending model instead of the existing indentation bending model of beam/plate.

Application of a portable indentation rig with Rockwell indenter to determine mechanical properties and residual stresses on an aluminum plate

Measuring residual stresses is still a dilemma in many engineering applications. It is even more crucial when the industrial requirements demand for a non-destructive technique in order to avoid compromising the structural integrity of the engineering components. Furthermore, estimating the mechanical properties of the materials, especially when the components are aged, is of importance. Instrumented indentation has gained much interest in recent years. There are many studies in the literature which are focused on measuring residual stresses or mechanical properties using instrumented indentation. Since in many cases there is no possibility of transferring large samples or those under service, for possible measurements, having a portable rig can be very useful. Furthermore, indentation procedure is a low-cost non-destructive method with high accuracy which is able to measure the plastic properties of material as well as its residual stresses on which the designing and construction of the portable apparatus were based. The instrumented indentation testing details were followed according to the ASTM E2546-15 standard practice. In this research, a wide range of simulations were performed on a group of aluminum alloys in order to estimate the equi-biaxial residual stresses by analyzing the indentation load–displacement curves which were obtained from the experimental outcomes. Then neural networks were employed to estimate the unknown parameters. The performance accuracy of the designed portable apparatus and the acceptable precision of the introduced method were then verified with experimental tests performed on Al 2024-T351.

Spherical indentations on hafnium carbide- and silicon-carbide-coated carbon–carbon composites after thermal shock test in air

In this study, high-temperature oxidations and indentations on silicon carbide (SiC)- and hafnium carbide (HfC)-coated carbon–carbon (C/C) composites were investigated to prevent the oxidation of C/C composites in air. The SiC and HfC layers were coated to protect the composite from oxidizing in air at a high temperature. High-temperature oxidation tests were performed at 500 °C, 1,000 °C, 1,350 °C, and 1,500 °C for 1 h in air and then cooled to room temperature by thermal shock. This cycle was repeated until the coating layer was damaged. As a result of measuring the weight change according to the thermal cycle and observing the fiber damage in the C/C composites, the oxidation resistance of HfC was evaluated to be superior to that of SiC. The change of the mechanical behavior was investigated using an indentation test with a tungsten carbide ball with a radius of either 3.18 or 7.93 mm before and after the high-temperature oxidation test by thermal shock. The relative elastic modulus was predicted based on the slope of the indentation load–displacement curve during loading or that of the curve during unloading. The relative hardness was also analyzed based on residual displacement after indentation. The hardness and elastic modulus of the HfC and SiC coating were higher than those of C/C composites and the mechanical properties of the HfC-coated C/C composite were relatively good compared with those of the SiC-coated composites prior to the thermal shock test. In particular, in this study, it was found that the mechanical behaviors of HfC-coated C/C composites exposed to temperatures >1,000 °C in air were transferred from elastic to quasi-plastic. The quasi-plasticity of the HfC coating layer was evaluated to be excellent regarding its resistance to mechanical damage as the coating layer was not easily delaminated or damaged even by oxidation.

Amorphization and dislocation evolution mechanisms of single crystalline 6H-SiC

The amorphization and dislocation evolution mechanisms of a single crystal 6H-SiC were systematically investigated by using nano-indentation, high-resolution transmitted electron microscope (HRTEM), molecular dynamics (MD) simulations and the generalized stacking fault (GSF) energy surface analysis. Two major plastic deformation mechanisms of 6H-SiC under nano-indentation were revealed by HRTEM, i.e., (1) an amorphization region near the residual indentation mark, and (2) dislocations below the amorphization region in both the basal and prismatic planes. MD results showed that the amorphization process corresponds to the first “pop-in” event of the indentation load-displacement curve, while the dislocation nucleation and propagation are related to the consequent “pop-in” events. The amorphization is confirmed to achieve via an initial transformation from wurtzite structure to an intermediate structure, and then a further amorphization process.

Amorphization and Dislocation Evolution Mechanisms of Single Crystalline 6H-SiC

The amorphization and dislocation evolution mechanisms of a single crystal 6H-SiC were systematically investigated by using nano-indentation, high-resolution transmitted electron microscope (HRTEM), molecular dynamics (MD) simulations and the generalized stacking fault (GSF) energy surface analysis. Two major plastic deformation mechanisms of 6H-SiC under nano-indentation were revealed by HRTEM, i.e., (1) an amorphization region near the residual indentation mark, and (2) dislocations below the amorphization region in both the basal and prismatic planes. MD results showed that the amorphization process corresponds to the first “pop-in” event of the indentation load-displacement curve, while the dislocation nucleation and propagation are related to the consequent “pop-in” events. The amorphization is confirmed to achieve via an initial transformation from wurtzite structure to an intermediate structure, and then a further amorphization process.

An energy-based nanoindentation method to assess localized residual stresses and mechanical properties on shot-peened materials

Abstract

Critical strain of the sharp indentation through serration behavior with strain rate

The indentation test is often used to determine the mechanical properties of materials, and its results are typically compared with uniaxial test results. However, the relationship between the indentation and uniaxial tests is unclear. Previously, the limit at which the indentation and uniaxial tests can be related has been determined by finite element simulation and termed the critical strain of indentation. In the critical strain concept, the high strain of the stress–strain curve has a negligible effect on the indentation load–displacement curve. To date, the effect of critical strain has not been addressed in indentation experiments. In this study, the serration behavior of an Al-Zn-Mg alloy during natural aging was investigated using uniaxial tensile and indentation tests in order to clarify (i) the relationship between these tests and (ii) the critical strain of indentation. Similar to uniaxial tests, the serration behavior of indentation was affected by the strain rate effect. However, it was found that the serration behavior observed at high strain in the uniaxial test could not be observed in the indentation test, as indicated by the concept of critical strain. With aging, the serrations of the indentation disappeared; however, they were observed in the uniaxial tests. It was confirmed that the migration of Mg atoms affected the serration behavior of indentation. The critical strain was experimentally found by comparing uniaxial test and indentation test results.

Analysis of the mechanisms of deformation of topocomposites by modeling of the indentation load-displacement curves

The use of materials with a surface layered structure (solid bodies with a thin coating, so-called topocomposites) in friction units makes it possible to extend significantly the possibilities of tribologists in developing materials with a required set of tribological characteristics. The main mechanical characteristics of the materials of friction pairs are presented by the elastic modulus and hardness (microhardness). For topocomposites, these characteristics depending on the thickness of the coating are variable. They vary more significantly, the greater the difference between the mechanical characteristics of the components (coating, substrate) composing the layered material. Modern procedures of the standard experimental determination of the hardness of a surface covered with a protective coating involve depth-sensing indentation. In this study, a theoretical description of the indentation load-displacement curves for materials with a surface coating or a hardened surface layer has been obtained. The analysis of the deformation process taking into account the topocomposite structure of the surface is carried out. The phenomenon of additional plastic deformation of the base material of the topocomposite is established.

Characterization of hardness, elastic modulus and fracture toughness of RB-SiC ceramics at elevated temperature by Vickers test

In this paper, mechanical properties of RB-SiC ceramics, such as hardness, elastic modulus and fracture toughness, are characterized through indentation technique using a Vickers indenter at elevated temperatures ranging from room temperature to1200 °C realized by laser heating. The indentation size effect, load-displacement curves and relationship between crack length and applied load are studied in order to determine hardness, elastic modulus and fracture toughness accurately. The results show that the Meyer’s index and Vickers hardness decrease with the increase temperature. It indicates that the permanent plastic deformation of RB-SiC ceramics is mainly responsible for the indentation size effect and the reduction of hardness at elevated temperature. Both material softening and plastic deformation will contribute to the indentation creep at elevated temperature as shown in the load-displacement curves. The elastic modulus decreases with the increase of temperature due to increase of contact depth as a result of less elastic recovery. In the indentation test for calculating fracture toughness, only radial-median cracks are identified by the relationship between crack length and applied load at all temperatures, although the fracture mode observed at the indent corner changes from transgranular at room temperature to intergranular at elevated temperature. As more energy is consumed by intergranular facture and cracking-healing takes place due to oxidation, only short crack length appears in the indentation test which implies an increase of fracture toughness with the increase of temperature. However, this tendency has an exception at the highest temperature of 1200 °C. This is because the free Si softening in RB-SiC specimen fails to resist crack propagation at extremely high temperature. Consequently, the crack length increases again which leads to the increase of the calculating fracture toughness at the highest temperature. These variations of hardness, elastic modulus and fracture toughness with temperatures will account for the possible change of material removal regimes occurred in some thermal-involved hybrid machining of RB-SiC ceramics.

Extracting the isotropic uniaxial stress-strain relationship of hyperelastic soft materials based on new nonlinear indentation strain and stress measure

Instrumented indentation technique has been increasingly utilized to measure the mechanical properties of soft polymers and biological tissues. However, the indentation behaviors of these materials has not been well understood, especially the parameter identification of their hyperelastic material properties. In this paper, we developed a spherical indentation data analysis method to directly extract the isotropic uniaxial stress-strain relationship of hyperelastic soft materials from the measured spherical indentation load-displacement curves. The proposed method mainly included new measure of indentation stress and strain, which was built based on the Hertz load-displacement relationship and further revised by considering the non-Hertzian effects of neo-Hookean hyperelastic contact problems. Numerical and actual indentation experiments showed the proposed definition of indentation strain can properly evaluate the amount of nonlinear strain for neo-Hookean, Yeoh and Arruda-Boyce hyperelastic materials. Meanwhile, the proposed spherical indentation data analysis method was applicable only in certain deformation range for Yeoh and Arruda-Boyce hyperelastic materials, because their nonlinear material parameters might cause very complicated contact pressure distributions. Building a universal data processing technique for characterizing the hyperelastic mechanical properties of soft materials through indentation experiments still needed further investigations.

Deformation behaviors of Cu29Zr32Ti15Al5Ni19 high entropy bulk metallic glass during nanoindentation

The deformation behaviors of Cu29Zr32Ti15Al5Ni19 high entropy bulk metallic glass (HE-BMG) during the nanoindentation are presented via the large-scale molecular dynamics (MD) simulations. The indentation tests are carried out using spherical rigid indenter to investigate the microstructural evolution on the mechanical properties of HE-BMGs in terms of shear strain, indentation force, and surface morphology as well as radial distribution function (RDF). Based on the Hertzian fitting the load-displacement curve, HE-BMG Cu29Zr32Ti15Al5Ni19 has the Young's modulus of 93.1 GPa and hardness of 8.8 GPa. The indentation force requiring for the continual increasing contacted area between the indenter and the substrate goes up with the increasing of indentation depth. In addition, the symmetrical distribution of atomic displacement reveals the isotropic of HE-BMG after the indentation treatment. In the deformation region, the Al element would lead to the serious fluctuation in the first peak of RDF, which is much stronger than the other elements. The severe distortion from the atomic size difference maybe reduce the activation energy to the occurrence of shear deformation in HE-BMG, leading to the transition from brittle to ductile observed by the whole sliding of the local atom group. Through the indentation load-displacement curves at various temperatures, the softening of HE-BMG at high temperatures is in qualitative agreement with the experimental findings. Moreover, this effective strategy is used to accelerate the discovery of excellent mechanical properties of HE-BMGs by means of MD simulation, as well as understand the fundamental nanoindentation response of HE-BMGs.

On the fracture toughness of bulk metallic glasses under Berkovich nanoindentation

Measurements of fracture toughness from the crack tip opening displacement (CTOD) testing methods are complex and paramount important for a range of bulk metallic glasses (BMGs). In this work, we attempted to propose an indentation protocol to evaluate indentation fracture toughness based on two key considerations: First, the plastic deformation induced damage to the characteristic fracture initiation point calculated from integrating the indentation load-displacement curves is obtained and used to estimate indentation fracture toughness. Second, the continuum damage mechanics theory has been adopted to identify the characteristic fracture initiation point. To verify the applicability of the suggested approach, fracture toughness values of BMGs were estimated and compared with those from CTOD tests in the literature. The estimated fracture toughness values KC obtained from the indentation tests agreed well with those KQ from the CTOD tests within an approximately relative difference of 10%. We also found that KQ linearly correlates with KC (KQ=1.1KC−3.7). The value of KQ in Al-based BMG is predicted to be ~35MPa√m.