Indentation Velocity Research Articles

Guided wave based detection of damage in honeycomb core sandwich structures

We report on the Lamb wave type guided wave propagation in honeycomb core sandwich structures. An experimental study supported by theoretical evaluation of the guided wave characteristics is presented that proves the potential of Lamb wave type guided wave for detection of damage in sandwich structures. A sandwich panel is fabricated with planar dimension of 600mm×600mm, having a core thickness of 7mm, cell size of 5mm and 0.1mm thick aluminum face sheets. Thin piezoelectric patch actuators and sensors are used to excite and sense a frequency band limited guided wave with a central frequency. A linear phased array of piezoelectric patch actuators is used to achieve higher signal strength and directivity. Group velocity dispersion curves and corresponding frequency response of sensed signal are obtained experimentally. Linearity between the excitation signal amplitude and the corresponding sensed signal amplitude is found for certain range of parameters. The nature of damping present in the sandwich panel is monitored by measuring the sensor signal amplitude at various different distances measured from the center of the linear phased array. Indentation and low velocity impact induced damages of increasing diameter covering several honeycomb cells are created. Crushing of honeycomb core with rupture of face sheet is observed while introducing the damage. The damages are then detected experimentally by pitch-catch interrogation with guided waves and wavelet transform of the sensed signal. Signal amplitudes are analyzed for various different sizes of damages to differentiate the damage size/severity. Monotonic changes in the sensor signal amplitude due to increase in the damage size has been established successfully. With this approach it is possible to locate and monitor the damages with the help of phased array and by tracking the wave packets scattered from the damages.

Multiscale simulations of nanoindentation and nanoscratch of single crystal copper

In this paper, a three-dimensional multiscale method coupling molecular dynamics (MD) and finite element (FE) analysis has been employed to study nanoindentation and nanoscratch processes of copper thin film. During the nanoindentation process, no discontinuities can be observed in the displacement gradient, which demonstrates a seamless coupling between MD and FE regions. The multiscale model of nanoindentation is further validated by the fact that the load–depth curves obtained from both multiscale and full MD simulations match each other reasonably well. The nanoindentation results using multiscale model are also compared with those using part MD model to elucidate the advantages of multiscale method. The multiscale simulation results of nanoindentation show that the indentation velocity has a great effect on the load–depth curve and hardness of copper. The continuity of displacement field during the nanoscratch also demonstrates a seamless information exchange between MD and FE regions. The deformation of substrate and forces in the nanoscratch process are also investigated using the multiscale method. The multiscale method can greatly expand the system size to be explored without significant increase in computational cost.

押込み試験とモデリングによるベキ乗則材料の単軸クリープに関する構成式の予測

Indentation creep tests and finite element simulations were performed on a model material to show that a constitutive equation for conventional uniaxial creep can be derived using the instrumented indentation testing technique. When the indentation pressure and the indentation creep rate maintain constant values of ps and εin(s), respectively, the contours of the equivalent stress and the equivalent plastic strain rate in the region beneath the conical indenter expand according to the increase in the indenter displacement while maintaining the geometrical self-similarity. These findings indicate that a pseudo-steady state deformation takes place around the indenter tip. The representative point exhibiting the creep behavior within the limited region, which actually determines the indenter velocity, is defined as the location where the equivalent stress σr is equal to ps/3. The equivalent plastic strain rate εr at this point is found to be εin(s)/3.6 in the case that the creep stress exponent is 3. The stress exponent and the activation energy for creep extracted from the results of Al-5.3 mol%Mg solid-solution alloy indentation tests are in close agreement with those of tensile creep tests reported in the literature. In addition, the values for σr and εr agree well with the values for the applied stress and the corresponding creep rate in tensile creep tests at the same temperature. The above results show not only that the creep characteristics of advanced materials, which are often available in minute quantities or as small-volume specimens, can be obtained from carefully designed indentation creep tests, but also that the constitutive equation for tensile creep can be predicted with sufficient precision through indentation creep test results.

Comparing thin-sheet models with 3-D multilayer models for continental collision

Various models have been proposed to explain tectonic deformations during continent collision. A frequently applied model is the thin viscous sheet model which is however not fully 3-D and assumes a priori diffuse thickening as the dominant deformation style. We compare a fully 3-D multilayer numerical model with a corresponding thin viscous sheet numerical model for the scenario of continent indentation. In our comparison we focus on the three basic viscous deformation styles thickening, buckling (folding) and lateral crustal flow. Both numerical models are based on the finite element method (FEM) and employ either a linear or power-law viscous rheology. The 3-D model consists of four layers representing a simplified continental lithosphere: strong upper crust, weak lower crust, strong upper mantle and weak lower mantle. The effective viscosity depth-profile in the 3-D model is used to calculate the depth-averaged effective viscosity used in the thin-sheet model allowing a direct comparison of both models. We quantify the differences in the strain rate and velocity fields, and investigate the evolution of crustal thickening, buckling and crustal flow resulting from the two models for two different phases of deformation: (1) indentation with a constant velocity and (2) gravitational collapse after a decrease of the indenting velocity by a factor of 5. The results indicate that thin-sheet models approximate well the overall large-scale lithospheric deformation, especially during indentation and for a linear viscous rheology. However, in the 3-D model, additional processes such as multilayer buckling and lower crustal flow emerge, which are ignored in the thin-sheet model but dominate the deformation style in the 3-D model within a range of a few hundreds of kilometres around the collision zone and indenter corner. Differences between the 3-D and thin-sheet model are considerably larger for a power-law viscous than for a linear viscous rheology. Buckling and lower crustal flow are significant in the 3-D model with power-law viscous rheology. For example, fibre strain rates due to buckling can be several hundred per cent different to the depth-averaged strain rate and the lateral mass flow of lower crustal material can be up to six times more than the flow of upper crustal material. Our results also show that the horizontal velocity fields of the upper crust and upper mantle remain nearly identical in the 3-D model during indentation despite their mechanical decoupling due to an intermediate weak lower crust. This result questions the validity of using similarities between velocities from the surface global positioning system (GPS) and mantle shear wave splitting data as evidence for a mechanically coupled lithosphere. 3-D multilayer models provide a more complete picture of continental collision than thin-sheet models as they enable studying the timing, locality and relative importance of different processes simultaneously which is especially important for the hundreds of kilometre scale around the collision zone and indenter corners. 3-D models are, however, still computationally challenging and we, therefore, also present results of a computational performance test of several solution algorithms.

Mechanical characterization of nanoindented graphene via molecular dynamics simulations

The mechanical behavior of graphene under various indentation depths, velocities, and temperatures is studied using molecular dynamics analysis. The results show that the load, elastic and plastic energies, and relaxation force increased with increasing indentation depth and velocity. Nanoindentation induced pile ups and corrugations of the graphene. Resistance to deformation decreased at higher temperature. Strong adhesion caused topological defects and vacancies during the unloading process.

A hybrid model for multiscale simulations of nanoindentation

A numerical model for multiscale simulations of nanoindentation has been established by coupling molecular dynamics (MD) simulations with finite element analysis. The multiscale simulations are performed for two-dimensional nanoindentation of a cylindrical indenter against a copper (1 1 1) substrate. Results show that the load–depth curves obtained from both multiscale and full MD simulations match each other reasonably well and no visible discontinuity of deformation is observed in the handshake region. In the beginning, the normal load increases gradually, corresponding to elastic substrate deformation, followed by sudden drops in load–depth curves, which are related to the nucleation and movement of dislocations. The simulations also reveal that indenter radius and indentation velocity significantly affect the nanoindentation process. By the use of multiscale method, the system size to be explored can be greatly expanded without increasing computational cost.

Non-Invasive Test of Soft Tissue for Tissue Reaction in Needle Biopsy

Needle biopsy is a widely used medical procedure in which a tissue sample is cut and removed by needle for examination to identify and diagnose cancer and other diseases. Predictions of soft tissue deformation and reaction caused by needle insertion are important for the accuracy of this procedure. In this paper, in order to aquire the properties of soft tissue, indentation experiments of porcine livers are performed as non-invasive test to measure the force response depending on time in various indentation depth and indentation velocities conditions. A nonlinear least square method on Matlab have been created to fit the indentation results. According to the experimental and fitting indentation force-time curves, the coefficients of Neo-Hookean model and Kelvin model which are selected to develop the nonlinear model of porcine liver are acquired . Finally, a finite element model of liver based on experimental data is finally developed and succeeds in simulating the stress relaxation character and force-time curve. This finite element model and methodology can be used to investigate soft tissue reaction in needle biopsy.

Contact nanomechanics of a capped nanotube indented on graphite and diamond surfaces

Contact behaviour of a capped single-walled carbon nanotube (SWCNT) indented into the surface of graphite sheets and diamond is studied using molecular dynamics simulation. The interactions between SWCNT, graphite and diamond atoms are described by the Tersoff–Brenner potential, and the Lennard–Jones potential function is employed to simulate the interactions between the indenter and the graphite and diamond atoms. The simulation results show that the maximum contact force increases with increasing indentation velocity and with decreasing indentation temperature. In addition, the diamond appears a greater force exerted on the indenter than the graphite sheets.

Design, construction and validation of a computer controlled system for functional loading of soft tissue

Osteoarthritis is a chronic degenerative disease affecting body joints. Abnormal mechanical loading could be an initiating factor of cartilage damage, by influencing chondrocytes activity. To date, devices performing mechanical studies of viable tissues are mostly uniaxial. In this work, we developed and validated a multi-axial device for static and dynamic mechanical testing of viable soft tissues. The system, named RPETS, is composed of a motor driven indenter, moving vertically and horizontally along the bottom of a tank containing tissue samples and it can apply combined compression, sliding, and rolling on viable samples. Validation studies were performed with standard rubber and bovine nasal cartilage tissue. Static tests demonstrated that the system is comparable to existing uniaxial devices, with a maximum force control error smaller than 0.5 N and a positioning resolution of 5 μm. Dynamic tests performed with different motion profiles showed that the system can exert a load of 100 N with a maximum velocity of 100 mm/s maintaining the force control error within 10% of the desired value. Sinusoidal motion frequency can vary between 0.05 and 0.5 Hz. In practical tests, viability staining of dynamically loaded cartilage slices showed extents of cell death to depend on the indenter velocity.

A molecular dynamics simulation of the mechanical characteristics of a C 60-filled carbon nanotube under nanoindentation using various carbon nanotube tips

The mechanical characteristics of a single-walled carbon nanotube (SWCNT) filled with C 60 fullerene subject to nanoindentation is studied using molecular dynamics (MD) simulations. The effects of temperature, indentation velocity, adhesion, and tip sizes were evaluated. The simulated results clearly show that the exerted load, Young’s modulus, elastic energy, and plastic energy decrease significantly with increasing temperature and decreasing indentation velocity and tip size. C 60 fullerenes can effectively increase the mechanical strength of a SWCNT because they act as a “barrier” to resist the radial deformation, as well as an inner wall in a double-walled carbon nanotube. With the same indentation depth, the ratio of elastic energy to plastic energy for a material gradually increases with the increase in the radius of the tip. This indicates that the elastic recovery of a material is better when the tip has a larger radius.

Yield shear stress dependence on nanoindentation strain rate in bulk GaN crystal

AbstractThe strain rate controlled nanoindentation was performed in c‐plane (0001) and m‐plane (10–10) GaN crystals. The indentation velocity was ranged from 0.16 to 800 nm/s. The significant displacement bursts were detected after every perfect elastically deformations and they allowed us to calculate the maximum shear stress τmax. The τmax dependences on strain rate in two crystal orientations involved that the two perpendicular compressions induced the same plastic deformation mechanism. Comparing the obtained τmax with the Peierls potential and maximum shear stress in each slip system, {10–11} 〈11–20〉 dislocation nucleation may support the origin of the plastic deformation in GaN crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Material characterization of ex vivo prostate tissue via spherical indentation in the clinic

Background The mechanical characterization of prostate tissue has not received much attention and is often disconnected from the clinic, where samples are readily attained. Methods We developed a spherical indenter for the clinic to generate force–displacement data from ex vivo prostate tissue. Indentation velocity, depth, and sphere diameter, and four means of estimating elastic modulus (EM) were validated. EM was then estimated for 26 prostate specimens obtained via prostatectomy and 6 samples obtained from autopsy. Prostatectomy prostates were evaluated clinically upon digital rectal exam and pathologically post-extirpation. Findings Whole-mount measurements yielded median EM of 43.2 kPa (SD = 59.8 kPa). Once sliced into cross-sections, median EM for stage T2 and T3 glands were 30.9 and 71.0 kPa, respectively, but not significantly different. Furthermore, we compared within-organ EM difference for prostates with (median = 46.5 kPa, SD = 22.2 kPa) and without (median = 31.0 kPa, SD = 63.1 kPa) palpable abnormalities. Interpretation This work finds that diseased prostate tissue is stiffer than normal tissue, stiffness increases with disease severity, and large variability exists between samples, even though disease differences within a prostate are detectable. A further study of late-stage cancers would help to strengthen the findings presented in this work.

MOLECULAR DYNAMICS OF NANOINDENTATION WITH CONICAL CARBON INDENTERS ON GRAPHITE AND DIAMOND

Molecular dynamics (MD) simulation of nanoindentation with a conical carbon indenter on graphite sheets and diamond is performed. The interactions of carbon indenter, graphite, and diamond atoms are described by the Tersoff–Brenner potential. Also, the Lennard–Jones potential function is employed to simulate the interactions between the indenter and the graphite and diamond atoms. The simulation results show that the maximum contact force increases with increasing conical angle due to an increase in the contact area. As the indentation velocity increases, the maximum contact force increases. However, the force decreases when the substrate temperature increases because of the weak interaction force between the atoms. Furthermore, the maximum contact force of nanoindentation with a conical indenter on the diamond was larger than that on the graphite sheets at the same indentation depth, velocity, and temperature.

Direct observation of amophization in load rate dependent nanoindentation studies of crystalline Si

Indentation at very low load rate showed region of constant volume with releasing load in crystalline (c-)Si, indicating a direct observation of liquidlike amorphous phase which is incompressible under pressure. Signature of amorphization is also confirmed from load dependent indentation study where increased amount of amorphized phase is made responsible for the increasing elastic recovery of the sample with increasing load. Ex situ Raman study confirmed the presence of amorphous phase at the center of indentation. The molecular dynamic simulation has been employed to demonstrate that the effect of indentation velocities has a direct influence on c-Si during nanoindentation processes.

Method for identification of the filled polymer material relaxation kernel in millisecond time range

The filled polymer materials exhibit viscoelastic properties in a wide time range including the millisecond range (∼10−2–10 ms) characteristic of different shock loadings of structures made of these materials. We propose a method for the identification of the filled polymer material relaxation kernel in the millisecond time range; this method is based on a shock loading test of a cylindrical sample made of this material. In this test, the disk indenter acceleration is measured by using a piezotransducer. The test scheme does not impose any rigid constraints on the sample dimensions. In particular, it is possible to use samples of typical dimensions of the order of 10 cm, for which the conditions that the sample material is representative of the structure material are necessarily satisfied. The relaxation kernel parameters are identified by numerical minimization of the theoretically predicted indenter velocity deviation from the velocity-time dependence obtained by integrating the acceleration transducer readings. The minimization problem is solved by using a genetic algorithm. The problem of theoretical prediction of the indenter velocity is solved numerically by using a reduced computational scheme whose parameters are chosen from the minimum condition for the deviation from the prediction obtained in the framework of the detailed computational scheme. The use of the reduced computational scheme permits decreasing the computational costs by 3–4 orders of magnitude compared with the detailed computational scheme, which is a necessary condition for the practical applicability of the genetic algorithm in identification problems. We present examples of relaxation kernel identification in the range of 0.1–10ms from the results of the test where the disk indenter raised to the height of 1m falls on the sample end surface.

Computer simulations of nanoindentation in Mg–Cu and Cu–Zr metallic glasses

The formation of shear bands during plastic deformation of Cu0.50Zr0.50 and Mg0.85Cu0.15 metallic glasses is studied using atomic-scale computer simulations. The atomic interactions are described using realistic many-body potentials within the effective medium theory, and are compared with similar simulations using a Lennard-Jones description of the material. The metallic glasses are deformed both in simple shear and in a simulated nanoindentation experiment. Plastic shear localizes into shear bands with a width of approximately 5 nm in CuZr and 8 nm in MgCu. In simple shear, the shear band formation is very clear, whereas only incipient shear bands are seen in nanoindentation. The shear band formation during nanoindentation is sensitive to the indentation velocity, indenter radius and the cooling rate during the formation of the metallic glass. For comparison, a similar nanoindentation simulation was made with a nanocrystalline sample, showing how the presence of a polycrystalline structure leads to a different and more spatially distributed deformation pattern, where dislocation avalanches play an important role.

Viscoelasticity of pore-spanning polymer membranes derived from giant polymersomes

We show how the viscoelastic properties of membranes formed from poly(butadiene)-block-poly(ethylene oxide) (PB130-b-PEO66) block copolymers can be locally accessed by atomic force microscopy. Polymer membranes are spread on microstructured porous silicon substrates from PB130-b-PEO66 vesicles by decreasing the osmotic pressure of the solution. Local viscoelastic properties of the pore-spanning polymer membranes were obtained from site-specific indentation experiments. Elastic moduli of these membranes were in the order of few MPa, while the elastic moduli of cross-linked membranes considerably increased to few GPa. Furthermore, the energy dissipation and velocity dependence of the hysteresis between indentation and relaxation were quantified and compared with a modified Kelvin–Voigt model. Relaxation times were in the order of hundreds of milliseconds explaining why the stiffness of the membrane increases with increasing indentation velocity.

Local Membrane Mechanics of Pore-Spanning Bilayers

The mechanical behavior of lipid bilayers spanning the pores of highly ordered porous silicon substrates was scrutinized by local indentation experiments as a function of surface functionalization, lipid composition, solvent content, indentation velocity, and pore radius. Solvent-containing nano black lipid membranes (nano-BLMs) as well as solvent-free pore-spanning bilayers were imaged by fluorescence and atomic force microscopy prior to force curve acquisition, which allows distinguishing between membrane-covered and uncovered pores. Force indentation curves on pore-spanning bilayers attached to functionalized hydrophobic porous silicon substrates reveal a predominately linear response that is mainly attributed to prestress in the membranes. This is in agreement with the observation that indentation leads to membrane lysis well below 5% area dilatation. However, membrane bending and lateral tension dominate over prestress and stretching if solvent-free supported membranes obtained from spreading giant liposomes on hydrophilic porous silicon are indented. An elastic regime diagram is presented that readily allows determining the dominant contribution to the mechanical response upon indentation as a function of load and pore radius.

Nanoindentation of thin films: Simulations and experiments

Atomistic simulations of nanoindentation of a 20-nm-thick Ni thin film oriented in the [111] direction were carried out to study the effects of indenter velocity and radii, interatomic potentials, and the boundary conditions used to represent the substrate. The simulation results were compared directly with experimental results of Ni thin film of the same thickness and orientation. It was found that the high indenter velocity does not affect the hardness value significantly. Different radii used for indentation also have negligible effects on the hardness value. Two different interatomic potentials were tested, giving significantly different hardness values but both within 20% of the experimental result. Different boundary conditions used to represent the substrate have a significant effect for relatively deep indentation simulations.

Analysis on pseudo-steady indentation creep

Theoretical analysis and finite element (FE) simulation have been carried out for a constant specific load rate (CSLR) indentation creep test. Analytical results indicate that both the representative stress and the indentation strain rate become constant after a transient period. Moreover, the FE simulation reveals that both the contours of equivalent stress and equivalent plastic strain rate underneath the indenter evolve with geometrical self-similarity. This suggests that pseudo-steady indentation creep occurs in the region beneath the indenter. The representative points in the region are defined as the ones with the equivalent stress equal to the representative stress. In addition, it is revealed that the proportionality between indentation strain rate and equivalent plastic strain rate holds at the representative points during the pseudo-steady indentation creep of a power law material. A control volume (CV) beneath the indenter, which governs the indenter velocity, is identified. The size of the CV at the indented surface is approximately 2.5 times the size of the impression. The stress exponent for creep can be obtained from the pseudo-steady indentation creep data. These results demonstrate that the CSLR testing technique can be used to evaluate creep parameters with the same accuracy as conventional uniaxial creep tests.