Indentation Force-depth Curves Research Articles

Nanoindentation characteristics of nanocrystalline B2 CuZr shape memory alloy via large-scale atomistic simulation.

Nanoindentation tests are performed by molecular dynamics simulation to explore the mechanical properties of nanocrystalline B2 CuZr shape memory alloys with average grain sizes ranging from 6 to 18nm. Some paramount aspects are monitored, including indentation force-depth curve, hardness, yield strength, and elastic recovery. The results demonstrate an inverse Hall-Petch effect, i.e., the hardness decreases with the decrease in grain size. For the single crystalline B2 CuZr, dislocation nucleation and propagation are the major plastic mechanisms. However, grain cleavage, grain boundary compression, and grain rotation prevail over the plastic behaviors of nanocrystalline B2 CuZr alloys. The elastic recovery becomes stronger with the increase in grain size. Besides, the effects of temperature, indenter size, and indenter speed on the nanoindentation responses are evaluated quantitively.

New Inverse Method for Determining Uniaxial Flow Properties by Spherical Indentation Test

The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way. Current inverse methods mainly rely on extensive iterative calculations, which yield a considerable computational costs. In this paper, a database method is proposed to determine tensile flow properties from a single indentation force-depth curves to avoid iterative simulations. Firstly, a database that contain numerous indentation force-depth curves is established by inputting varied Ludwic material parameters into the indentation finite elements model. Secondly, for a given experimental indentation curve, a mean square error (MSE) is designated to evaluate the deviation between the experimental curve and each curve in the database. Finally, the true stresses at a series of plastic strain can be acquired by analyzing these deviations. To validate this new method, three different steels, i.e. A508, 2.25Cr1Mo and 316L are selected. Both simulated indentation curves and experimental indentation curves are used as inputs of the database to inversely acquire the flow properties. The result indicates that the proposed approach provides impressive accuracy when simulated indentation curves are used, but is less accurate when experimental curves are used. This new method can derive tensile properties in a much higher efficiency compared with traditional inverse method and are therefore more adaptive to engineering application.

Measurement of the interconnected turgor pressure and envelope elasticity of live bacterial cells.

Turgor pressure and envelope elasticity of bacterial cells are two mechanical parameters that play a dominant role in cellular deformation, division, and motility. However, a clear understanding of these two properties is lacking because of their strongly interconnected mechanisms. This study established a nanoindentation method to precisely measure the turgor pressure and envelope elasticity of live bacteria. The indentation force-depth curves of Klebsiella pneumoniae bacteria were recorded with atomic force microscopy. Through combination of dimensional analysis and numerical simulations, an explicit expression was derived to decouple the two properties of individual bacteria from the nanoindentation curves. We show that the Young's modulus of bacterial envelope is sensitive to the external osmotic environment, and the turgor pressure is significantly dependent on the external osmotic stress. This method can not only quantify the turgor pressure and envelope elasticity of bacteria, but also help resolve the mechanical behaviors of bacteria in different environments.

Estimation of tensile strengths of metals using spherical indentation test and database

The indentation technique provides a non-destructive characterization method for in-service equipment. Recent years have seen an increased interest in determination of tensile properties from spherical indentation test (SIT) through inverse optimization theory, while this approach is computational costing and time consuming. This paper aims to propose a novel method for estimation of strength properties based on the application of a database. Firstly, systematically varied Ludwik constitutive parameter vectors were used to establish a database that contains indentation force-depth curves (extracted from the simulated results of indentation test) and corresponding strength values (calculated with the parameter vectors). The indentation force-depth curve of a concerned material was then processed by the database, as a result of which the yield and ultimate strengths can be obtained. A series of virtual materials were used to validate the accuracy of this method. The results show that the database method provides an impressive accuracy and stability in estimating strengths. The database method was subsequently applied to eight real materials. It is found that the predicted strengths agree well with the values from uniaxial tests for most materials, while the database method may be not suitable for materials that show obvious tension-compression asymmetry.

Electrical-mechanical coupling performance of gallium arsenide under nanoindentation

In this research, the electrical-mechanical coupling performance of gallium arsenide (GaAs) crystalline has been investigated by carrying out the in situ electrical measurement experiments which enabled us to record precisely both the mechanical behavior of the nanodeformed GaAs and the accompanying electrical response during nanoindentation. An effective and precise In situ electrical measurement system has been set up by introducing a conductive diamond indenter and both traditional and cyclic nanoindentation experiments have been performed. The experimental results showed that the application of indentation force caused a significant increase in the current flow due to the pressure-induced metallic phase transition of GaAs, and the magnitude of current flow was increased with increasing either the applied force or voltage. Furthermore, the current flow showed symmetric changes with the indentation loading and unloading, indicating a fully reversible metallic phase transformation of GaAs in indentation. On the other hand, the externally applied voltage (electrical field) was observed to barely affect the indentation force-depth curve (mechanical performance) of GaAs in respect of Young’s modulus and hardness.

Prediction of Asymmetric Yield Strengths of Polymeric Materials at Tension and Compression Using Spherical Indentation

Engineering polymers generally exhibit asymmetric yield strength in tension and compression due to different arrangements of molecular structures in response to external loadings. For the polymeric materials whose plastic behavior follows the Drucker–Prager yield criterion, the present study proposes a new method to predict both tensile and compressive yield strength utilizing instrumented spherical indentation. Our method is decomposed into two parts based on the depth of indentation, shallow indentation, and deep indentation. The shallow indentation is targeted to study elastic deformation of materials, and is used to estimate Young's modulus and yield strength in compression; the deep indentation is used to achieve full plastic deformation of materials and extract the parameters in Drucker–Prager yield criterion associated with both tensile and compressive yield strength. Extensive numerical computations via finite element method (FEM) are performed to build a dimensionless function that can be employed to describe the quantitative relationship between indentation force-depth curves and material parameters of relevance to yield criterion. A reverse algorithm is developed to determine the material properties and its robustness is verified by performing both numerical and experimental analysis.

Molecular dynamics simulation of nano-indentation on Ti-V multilayered thin films

We developed a second nearest-neighbor modified embedded-atom method potential for binary Ti-V system. The potential parameters were identified by fitting the lattice parameter, cohesive energy and elastic constants of CsCl-type TiV, and further validated by reproducing the fundamental physical and mechanical properties of Ti-V systems with other crystal structures. In addition, we also performed molecular dynamics simulations of nano-indentation processes of pure Ti film, pure V film, and two kinds of four-layer Ti-V films, V-Ti-V-Ti and Ti-V-Ti-V. We found that the indentation force-depth curve for the pure V film turns flat at an indentation depth of 2.8nm, where a prismatic loop was observed. Such prismatic loop is not found in the V/Ti/V/Ti multilayer because the thickness of each layer is insufficient for the formation of such prismatic loops, which accounts for the increase of stress in the multilayer.

Surface residual stress in soda-lime glass evaluated using instrumented spherical indentation testing

Instrumented spherical indentation testing is proposed as a non-destructive way to evaluate surface residual stress in soda-lime glass. 10 μm-deep indentations with a spherical indenter of 250 μm radius do not reduce the strength of 3.5-mm-thick soda-lime glass as measured in four-point bending tests. We find good linearity between the compressive surface residual stress and the force difference at maximum indentation depth in the indentation force–depth curve, while hardness as measured by instrumented spherical indentation testing is independent of compressive surface residual stress introduced by bending and strengthening heat treatment.

AFM Reveals Age-Dependent Micromechanical Degradation of Cardiopulmonary Tissues in a Mouse Model of Marfan Syndrome

Marfan syndrome (MFS) is caused by mutation of the FBN1 gene encoding the extracellular matrix (ECM) protein fibrillin-1 that forms elastic microfibrils. This study aims to characterize the micromechanics of aortic and lung tissues from wild type (WT) and FBN1-deficient mutant (MT) mice to identify biophysical determinants of cardiopulmonary disease in MFS. For testing by atomic force microscopy (AFM), full-thickness sections of ascending aorta were dissected from young (0.5-mo) and adult (2-mo) WT and MT mice, mounted flat with the lumen facing up, and indented with a 15-μm spherical probe at 3-5 sites per sample from 1-4 animals per condition. Indentation force-depth curves were analyzed using a hybrid theoretical and finite element analysis to determine the elastic modulus of intima (Eint) and media (Emed) layers. The Kolmogorov-Smirnov test was performed for pairwise statistical analysis; p<0.008 was considered significant based on the Bonferroni correction. Emed at 0.5-mo showed no difference between WT (10.1±2.7kPa, n=8; mean±SEM for n-curves) and MT (7.5±0.6kPa, n=80). Emed increased with age (p<0.0006), but was significantly softer in MT (21.3±1.4kPa, n=112) vs WT (37.4±2.2kPa, n=65, p<0.0001). Eint also increased with age (p<0.003) from ∼2kPa to ∼5-10kPa, but showed no significant difference between WT and MT at matched ages. Similar nano-indentation studies, using a pyramidal probe on lung parenchyma isolated from 2-mo WT and MT mice, showed Elung for MT (1.7±0.1 kPa, n=92) was significantly softer than WT (4.8±0.3kPa, n=91, p<0.0001). In conclusion, AFM revealed age-dependent softening of micro-elastic modulus in elastin-rich tissues including lung parenchyma and aortic media, but not in the aortic intima. In contrast to macro-scale measurements of aortic stiffening in MFS, these micro-scale AFM findings appear consistent with histological observations of local disruption of ECM microstructure in MFS.

Instrumented indentation for determination of full range stress-strain curves

One common method for the determination of full range stress-strain curves by instrumented indentation is presented and validated for an aluminium alloy. This method relates properties describing the indentation force-depth curve with those describing the uniaxial stress-strain curve as traditionally obtained from a tensile test. The first aim of this paper is to explain the basic concepts of instrumented indentation. Next, the analysis method is presented and validated. This study ends with discussing the uniqueness of the obtained solution. It is concluded that accurate determination of stress-strain behaviour can be realized, but for certain materials two indentations are needed.

Material characterization by instrumented spherical indentation

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the sharp indentation response of materials. These issues are further extended for spherical indentation in the present study. Instrumented spherical indentation was performed by a parametric finite element analysis for a wide range of materials with maximum indentation depth-indenter radius ratios rising from 0.01 to 0.3 to investigate several fundamental features within the frame work of limit analysis. Frictional effects are taken into account. Regarding dimensional analyses and using a Taylor series expansion, a new set of dimensionless functions is constructed for spherical indentation parameters and hardness associated to a 70.3° conical indenter. Based on formulated functions, a reverse analysis procedure is suggested to extract material properties and hardness from spherical indentation force-depth curves with respect to two different indentation depth-indenter radius ratios. Effects of indenter compliance on indentation parameters and reverse results are considered. The accuracy of the proposed method is studied and discussed by carrying out reverse and sensitivity analyses for 22 representative materials with rigid and deformable indenters.

Spherical indentation for determining the phase transition properties of shape memory alloys

A spherical indentation method was developed to characterize the phase transition behaviors of shape memory alloys (SMAs). Based on deformation analysis, the measured indentation force-depth curves of SMAs can be converted to their nominal stress-strain curves. The predicted elastic modulus and phase transition stress of SMAs from spherical indentation agree well with those directly measured from tensile tests. This approach should be especially useful for characterizing the phase transition properties of SMA materials of small size or thin films.

Plastic deformation of pentagonal silver nanowires: Comparison between AFM nanoindentation and atomistic simulations

The plastic deformation of a pentagonal silver nanowire is studied by nanoindentation using an atomic force microscope (AFM). AFM images of the residual indent reveal the formation of a neck and surface atomic steps. To study the microscopic deformation mechanism, the indentation force-depth curve is converted to an indentation stress-strain curve and compared to the tensile stress-strain curves predicted by the atomistic simulations of pentagonal silver nanowires. The indentation stress-strain curve exhibits a series of yielding events, attributed to the nucleation and movement of dislocations. The maximum stress measured during nanoindentation (2 GPa) is comparable to the tensile yield strength predicted by atomistic simulations.

A study on the determination of plastic properties of metals by instrumented indentation using two sharp indenters

An earlier optimisation approach proposed by Luo et al. [Luo, J., Lin, J., Dean, T. A., 2006. A Study on the Determination of Mechanical Properties of a power-law Material by Its Indentation Force-Depth Curve. Philosophical Magazine, 86(19), 2881-2905], which is based on the assumption that the instrumented indentation force-depth response of an elastic–plastic material is a linear combination of the corresponding elastic and elastic–perfect plastic materials, is extended in this work to extract mechanical properties of a power-law material from two given experimental indentation P– h curves for conical indenters of half included angles of 60° and 70.3°. It was found that the non-uniqueness problem encountered in the single P– h curve optimisation approach is effectively removed by the two P– h curves optimisation. The appropriateness of the use of second half included angle of 60° is discussed. For the five representative materials Al, Ti, Fe, Ni and steel, it was found that the maximum relative prediction errors for E, σ y and n are 2%, 10.4% and 11.3%, respectively. The prediction accuracy of mechanical properties E, σ y and n is generally better than other methods reported in the literature.

A study on the determination of mechanical properties of a power law material by its indentation force–depth curve

In this study a novel optimization approach is proposed to extract mechanical properties of a power law material whose stress–strain relationship may be expressed as a power law from its given experimental indentation P–h curve. A set of equations have been established to relate the P–h curve to mechanical properties E, σ y and n of the material. For the loading part of a P–h curve this approach is based on the assumption that the indentation response of an elastic–plastic material is a linear combination of the corresponding elastic and elastic–perfect plastic materials. For the unloading part of the P–h curve it is based on the assumption that the unloading response of the elastic–plastic material is a linear combination of the full contact straight line and the purely elastic curve. Using the proposed optimization approach it was found that the mechanical properties of an elastic–plastic material usually cannot be decided uniquely by using only a single indentation P–h curve of the material. This is because in general a few matched sets of mechanical properties were found to produce a given P–h curve. It is however possible to identify the best matched set of mechanical properties by knowing some background information of the material. If the best matched material is identified, the predictions of mechanical properties are quite accurate.

Assessing Micromechanical Properties of Cells with Atomic Force Microscopy: Importance of the Contact Point

Mechanical properties are obtainable from atomic force microscopy (AFM) indentation force-depth curves, which are calculated from relationships between tip deflection and cantilever position, i.e. deflection curves. Indentation depth is the difference between tip deflections on a rigid and a soft material for the same amount of cantilever advancement, after contact is made. Since the contact point cannot be unequivocally identified from experimental data, there is some uncertainty in estimating material properties. Using simulations, this study examines some important issues related to the influence of contact point identification on estimated material properties. Simulations for linear materials using a typical stiffness for an AFM cantilever demonstrate that certain portions of the post-contact region of deflection curves for soft and very stiff materials can be approximated by quadratic and linear functions, respectively. Based on these findings, we first develop and verify an objective, automatic method to identify the contact point for materials with linear properties. We then assess the effect of misidentifying the contact point, with and without noise. If the contact point is missed by <50 nm, material properties for small indentations are erroneous but the error decreases asymptotically beyond 200 nm of indentation and the correct estimate of material stiffness is obtained. If the contact point is missed by >100 nm, however, the true material properties cannot be estimated accurately. Noise adds to uncertainty in material properties at small indentations but the combined effect of missing the contact point and noise is dominated by the former. Even though the algorithm was developed for linear materials, it is also suitable for certain nonlinear materials making it more generally applicable.