Load-penetration Depth Curves Research Articles

Size effects in spherical indentation of single crystal copper

A study of the size effects in the spherical indentation test of a copper single crystal is carried out. The main novelty of the approach is the analysis of a wide spectrum of parameters measured in the test that are predicted by the proposed model, and the prediction is verified experimentally for six different tip radii. Load-penetration depth curves, nominal hardness, pile-up and sink-in profiles, and the rotation and rotation gradient of the crystallographic lattice in the cross-section beneath the indenter have been measured and also calculated using 3D finite element simulations on the micro- and nanometer scale. Two gradient-effects are examined numerically within the Cosserat elastoplasticity framework with the gradient-enhanced hardening law. It is shown that a good prediction of the experimentally observed size effect on nominal hardness is achieved using the conventional power-hardening law, calibrated from the standard uniaxial compression test, enhanced with a term dependent on the lattice spin gradient term with no adjustable parameter. Furthermore, it has been found that the observed distribution of lattice rotation and decrease in the rotation magnitude with decreasing indenter radius can be qualitatively modelled by adjusting the coefficient of accumulated lattice curvature energy within the same framework.

Determination of gradient residual stress for elastoplastic materials by nanoindentation

Residual stress is an important manufacture factor affecting the working life of components and structures. In this paper, a dimensionless method is proposed to determine the residual stress profile by using the nanoindentation technique. An exponential function is formulated in a generalized form to describe the residual stress profile in the elastoplastic substrate material. A finite element (FE) model is created to simulate the entire process including the loading stage with the indenter penetrating into the substrate up to the maximum depth and also the subsequent unloading stage. For elastoplastic substrate materials following the power-law constitutive model, a wide range of FE predictions are made by considering various gradient residual stresses of interest. The results show that the applied load–penetration depth curve is highly consistent with the variation of gradient residual stress. Based on FE simulations, dimensionless functions considering the residual stress is derived for both the applied load and the total work done. Thereafter, a reverse algorithm is proposed to elegantly predict the gradient residual stress in elastoplastic materials. With several work examples, the proposed reverse algorithm is confirmed to be excellent for determining residual stresses by comparing the existing experimental results. More importantly, the proposed reverse algorithm can effectively determine the type and trend of gradient residual stresses, which helps to guide the optimization of manufacturing process for critical components and structures.

Indentation Reverse Algorithm of Mechanical Response for Elastoplastic Coatings Based on LSTM Deep Learning.

The load-penetration depth (P-h) curves of different metallic coating materials can be determined by nanoindentation experiments, and it is a challenge to obtain stress-strain response and elastoplastic properties directly using P-h curves. These problems can be solved by means of finite element (FE) simulation along with reverse analyses and methods, which, however, typically occupy a lengthy time, in addition to the low generality of FE methodologies for different metallic materials. To eliminate the challenges that exist in conventional FE simulations, a long short-term memory (LSTM) neural network is proposed in this study and implemented to deep learn the time series of P-h curves, which is capable of mapping P-h curves to the corresponding stress-strain responses for elastoplastic materials. Prior to the operation of the neural network, 1000 sets of indentation data of metallic coating materials were generated using the FE method as the training and validating sets. Each dataset contains a set of P-h curves as well as the corresponding stress-strain curves, which are used as input data for the network and as training targets. The proposed LSTM neural networks, with various numbers of hidden layers and hidden units, are evaluated to determine the optimal hyperparameters by comparing their loss curves. Based on the analysis of the prediction results of the network, it is concluded that the relationship between the P-h curves of metallic coating materials and their stress-strain responses is well predicted, and this relationship basically coincides with the power-law equation. Furthermore, the deep learning method based on LSTM is advantageous to interpret the elastoplastic behaviors of coating materials from indentation measurement, making the predictions of stress-strain responses much more efficient than FE analysis. The established LSTM neural network exhibits the prediction accuracy up to 97%, which is proved to reliably satisfy the engineering requirements in practice.

Determination of the parameters of material models using dynamic indentation test and artificial neural network

Stress-strain curves of materials normally change with strain rate and temperature and are normally defined by material models. In this study, a new technique was developed for determining the constants of material models. This technique was based on dynamic indentation test, numerical simulation using Ls-dyna code and artificial neural network. An indenter of tapered shape was shot against the materials as the target by a gas gun. The experiments were carried out for four strain rates and four temperatures. The target was made of pure copper. The penetration depth-time and load-time histories were captured by a LVDT and a piezoelectric load-cell, respectively and the load-penetration depth curve (P-h) was obtained. This curve is characterized by five parameters which are determined for each indentation test. On the other hand, the indentation test was simulated using Ls-dyna hydrocode. From the simulations, the P-h curves were obtained using Johnson-Cook (J-C) and Zerilli-Armstrong (Z-A) material models and the characterizing parameters of the numerical P-h curves were also identified. Finally, an artificial neural network (ANN) was trained by the numerical P-h curves parameters as the input and the constants of J-C and Z-A models as the output. The trained neural network was then tested by the experimental p-h curves parameters as the input and the constants of J-C and Z-A models as the output. Moreover, a number of dynamic compression tests were performed using the well-known Split Hopkinson Bar at the same strain rates and temperatures used for indentation tests and the stress-strain curves of material were obtained. A reasonable agreement was observed between the stress-strain curves predicted by neural network and the Split Hopkinson Bar. The proposed method does not need sophisticated instrumentation and in fact, the load-time and indentation depth-time histories are directly converted to stress-strain of material using an artificial neural network.

Microstructural examination and mechanical characterization of Ti/HA and Ti/SiO2 functionally graded materials fabricated at different loading rates

Functionally graded material (FGM) is a heterogeneous composite material that consists of two or more constituent phases with continuous changes in the microstructure from one material to another with adjustable through thickness properties. FGMs are utilized in medical applications, such as dental implants, due to their excellent mechanical and tribological properties. In this study, the powder metallurgy method (PMM) is used to produce Titanum/Hydroxyapatite (Ti/HA) and Titanum/Silicon dioxide (Ti/SiO2) FGM samples. A new designed blender is employed to mix the particles constituting the FGM samples. The mixed particles are then compacted at different strain rates from quasi static loading, using a universal testing apparatus, to dynamic loadings, using a drop hammer and a split Hopkinson bar. The effect of strain rate on mechanical properties and microstructure of specimens is studied by conducting various tests such as indentation and compression tests and by microstructural examinations using scanning electron microscopy (SEM). The results showed that the relative density of fabricated specimens was increased with the increase of the strain rate. The highest relative density for the Ti/HA composite was achieved for the specimens produced by the split Hopkinson bar. For both of Ti/HA and Ti/SiO2 FGMs the maximum indentation force and indentation energy, obtained from the load-penetration depth curve, and the ultimate strength, obtained from the compressive stress-strain curve, were increased with the increase in strain rate. The results also indicated that the increase in volume fraction of reinforcing ceramic particles (HA or SiO2) led to the decrease of the maximum indentation force and indentation energy.

Mechanical properties of α-quartz using nanoindentation tests and molecular dynamics simulations

Understanding the mechanical properties of α-quartz is of vital importance to rock engineering because α-quartz is the main component of igneous, metamorphic and sedimentary rocks. Molecular dynamics simulations (MDs) of nanoindentation tests on α-quartz were performed to investigate the effects of indenter tip radius and penetration depth on the mechanical properties of α-quartz. Indentation load-penetration depth (P-h) curves were plotted, from which Reduced Young’s modulus ( E r ) , hardness ( H ) were obtained and these mechanical parameters were then compared with the laboratory nanoindentation results. The mechanical results obtained from MDs are in good agreement with the experimental values. It can be found that E r and H increase with indentation depth at shallow contact depth while they decrease with indenter tip size. To the authors’ knowledge, this is the first MDs of nanoindentation test of hard rock-forming minerals reported and we believe that this study can shed light on the precise measurement of the mechanical properties of rock minerals at micro- and nano-scales.

Effect of indenter tip radius on indentation hardness by finite element analysis

In this study, the indentation hardness test is performed by elastic-plastic finite element (FE) analysis. In order to investigate the effect of the wear of indenter tip on the load-penetration depth curve ([Formula: see text] curve), indentation simulation is made by changing the indenter tip radius. The [Formula: see text] curve obtained by finite element method (FEM) is in good agreement with the experimental results. The calculation shows that the indentation plastic work [Formula: see text] corresponding to the area in the [Formula: see text] curve is hardly affected by the indenter tip radius.

A unified statistical model for indentation pop-in: Effects of indenter radius and microstructure density on the transition from homogeneous nucleation to heterogeneous nucleation to bulk plasticity

Indentation pop-in, i.e. a sudden displacement burst on the measured load-penetration depth curves, has been known as the onset of elastic-plastic deformation for crystalline materials. Depending on the indenter radius or density of pre-existing dislocation nucleation sources, the evolution of pop-in shear stress can generally be categorized into three deformation stages, i.e. the homogeneous dislocation nucleation stage, heterogeneous dislocation nucleation stage and bulk plasticity stage. For the former, the fluctuation of pop-in stress is dominated by the thermally activated nucleation process. For the middle, a size-dependent pop-in behavior with stress fluctuation is informed over a wide range of indenter radius and microstructure density. For the later, the materials strength is determined by the critical resolved shear stress for the motion of existing dislocations. Here, we find two additional transition stages between the adjacent deformation stages that can be effectively addressed by a novel competition mechanism, and the transition points are affected by the density of dislocation nucleation sites. All these critical features are well characterized by a unified statistical model proposed in this work. Moreover, a mechanistic model with closed-form formulas is developed for the size-dependent pop-in behavior during the heterogeneous dislocation nucleation stage. By comparing both the calibrated and predicted theoretical results with different sets of experimental data, good agreements are achieved that can rationally verify the proposed model. This work presents a theoretical framework to characterize the fundamental pop-in mechanisms, and provides an avenue towards the prediction of transition points distinguishing different plasticity deformation regimes.

Elastic constants determination of anisotropic materials by depth-sensing indentation

Depth-sensing indentation is a useful and powerful tool for the mechanical characterization of materials at the micro and nano scale. This technique allows the determination of the Young modulus from the analysis of the load-penetration depth curve according to specific theoretical models. One of the most used models is that one proposed by Oliver and Pharr. However, when a material with anisotropic mechanical properties is tested, Oliver and Pharr’s theory is no longer suitable to describe the contact mechanics between the indenter tip and the tested material. This paper provides an overview of the theoretical models developed for the evaluation of the elastic constants of anisotropic materials through depth-sensing indentation. Specifically, the cases of generally anisotropic and orthotropic materials are described in order to cover the entire range of anisotropy. Examples on how these models can be applied for the mechanical characterization of generally anisotropic topological insulators and transversely isotropic pyrolytic carbon are also reported. This topical overview represents a useful tutorial for the evaluation of the elastic constants of anisotropic materials by depth-sensing indentation by shading light on the contact mechanics at the micro and nano scale.

Indentation for investigation of strain rate effect on mechanical properties in structural steel weld zone

In this study, instrumented indentation testing was conducted at room temperature for the investigation of the effect of strain rate on the hardness and yield strength in the weld zone of a commonly used structural steel, SM520. A number of indentation tests were undertaken at a number of strain rate values from 0.02 s-1 to 0.2 s-1 in the weld metal (WM), heat-affected zone (HAZ), and base metal (BM) regions of the weld zone. The mechanical properties including yield strength (σy) and hardness (H) in WM, HAZ, and BM were then computed from the applied load-penetration depth curves using a proposed method. As the result, the effects of strain rate indentation on yield strength and hardness in all regions of the weld zone were evaluated. The results displayed that hardness and yield strength in the weld zone’s components are influenced on the strain rate, where both hardness and yield strength decrease with the decreasing strain rate.
 Keywords:
 indentation; mechanical properties; strain rate effect; structural steel; weld zone.

Size effects in wedge indentation predicted by a gradient-enhanced crystal-plasticity model

A recently developed gradient-enhanced crystal-plasticity model is applied to predict the size effects in wedge indentation. In the model, the internal length scale is defined through standard quantities that appear in the underlying non-gradient hardening law. A careful calibration of the non-gradient hardening law is thus performed, and the model is validated against published experimental results. To this end, a comprehensive computational study of wedge indentation into a nickel single crystal is performed, and the obtained results show a good agreement with the experiment in terms of the load–penetration depth curves for three wedge angles, as well as in terms of the distributions of lattice rotation, GND density, and net Burgers vector. For the indentation depth of about 200 μm, as employed in the experiment, the predicted size effects are insignificant. Accordingly, the size effects are next studied for the indentation depth varied between 200 μm and 1 μm. As an intermediate result, apparently not published to date, the general 3D crystal plasticity model with anisotropic hardening is consistently reduced to a 2D plane-strain model in which plastic deformation is realized by three effective in-plane slip systems, each representing two crystallographic slip systems.

Ni2Al3 intermetallic coating: microstructure and mechanical properties

The Ni-Al intermetallic coating was prepared by adopting a two-step method, which consist of electroplating nickel previously and then by pack aluminizing. The mechanical properties, namely the hardness (H) and elastic modulus (E), were measured by the nanoindentation test. The X-ray diffraction analysis shows that the coating is mainly composed of Ni2Al3. The thickness of the Ni2Al3 intermetallic coating prepared on the substrate is about 35 μm, and it has a good metallurgical bond with the substrate from the SEM morphology. The hardness and elastic modulus of the Ni2Al3 intermetallic coating are about 14.66 and 229.03 GPa, which are obviously higher than that of the substrate. The area surrounded by the load-penetration depth curve of the Ni2Al3 coating is more compact than that of the substrate. The indentation creep of the coating is also small.

Mechanical Properties of Cubic‐BN(111) Bulk Single Crystal Evaluated by Nanoindentation

We performed nanoindentation measurements on the (111) plane of a cubic boron nitride (c‐BN) bulk single crystal and a c‐BN sintered compact at room temperature to evaluate the intrinsic mechanical properties of c‐BN. Our load–penetration depth curves for bulk single crystal feature a low noise level and small variation in the data. These features reflect the perfect phase purity and high crystal coherency of the c‐BN bulk crystal. The hardness and Young's modulus are determined to be 61 ± 1 and 1070 ± 30 GPa, respectively. These values are larger than those corresponding to the c‐BN sintered compact. The obtained Young's modulus followed a similar trend to previous experimental and calculation studies. Hence, we demonstrate the effectiveness of this evaluation method based on high‐quality bulk single crystals. We also compared the mechanical properties with our results for wurtzite boron nitride (w‐BN) bulk crystal.

Assessment of the Local Residual Stresses of 7050-T7452 Aluminum Alloy in Microzones by the Instrumented Indentation with the Berkovich Indenter

The local residual stresses in microzones are investigated by the instrumented indentation method with the Berkovich indenter. The parameters required for determination of residual stresses are obtained from indentation load–penetration depth curves constructed during instrumented indentation tests on flat square 7050-T7452 aluminum alloy specimens with a central hole containing the compressive residual stresses generated by the cold extrusion process. The force balance system with account of the tensile and compressive residual stresses is used to explain the phenomenon of different contact areas produced by the same indentation load. The effect of strain-hardening exponent on the residual stress is tuned-off by application of the representative stress $$\sigma_{0.033}$$ in the average contact pressure assessment using the $$\varPi$$ theorem, while the yield stress value is obtained from the constitutive function. Finally, the residual stresses are calculated according to the proposed equations of the force balance system, and their feasibility is corroborated by the XRD measurements.

Thermodynamic behaviour and formation mechanism of novel titanium carbide dendritic crystals within a molten pool of selective laser melting TiC/Ti–Ni composites

Selective laser melting (SLM) was applied to prepare TiC/Ti–Ni composites by using a mixed powder composed of titanium powder, nickel powder and titanium carbide powder. The result indicated that fine TiC particles were transformed into in situ Ti6C3.75 dendrites based on the complete melting mechanism and coarse TiC particles just partly experienced melting to form epitaxial dendrites along the margin of the remaining TiC particles. Besides, laser scan speed was found to have a significant influence on Ti6C3.75 dendrite growth. To give a better insight into the thermodynamic behaviour of TiC within the mesoscopic molten pool which was difficult to be monitored by experimental methods, a numerical simulation method was used. Due to the existence of differences in thermal conductivity between TiC and the matrix, reverse thermal hysteresis within TiC particles was predicted, influencing the temperature and its gradient on the TiC particles. Furthermore, the melting mechanism of TiC particles and growth processes of Ti6C3.75 dendrites were discussed. Moreover, nanoindentation load–penetration depth curves were also measured, reaching a value of 6.84 GPa at the applied v of 350 mm s−1.

On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test

A novel methodology is proposed for estimating the strain hardening exponent of a metal single crystal directly from the spherical indentation test, without the need of solving the relevant inverse problem. The attention is focused on anisotropic piling-up and sinking-in that occur simultaneously in different directions, in contrast to the standard case of axial symmetry for isotropic materials. To correlate surface topography parameters with the value of material hardening exponent, a finite-element study of spherical indentation has been performed within a selected penetration depth range using a finite-strain crystal plasticity model. It is shown how the power-law hardening exponent can be estimated from the measured pile-up/sink-in pattern around the residual impression after indentation in a (001)-oriented fcc single crystal of a small initial yield stress. For this purpose, a new parameter of surface topography is defined as the normalized material volume displaced around the nominal contact zone, calculated by integration of the local residual height (positive or negative) over a centered circular ring. That indicator can be easily determined from an experimental topography map available in a digital form. Comparison is made with the estimates based on measurements of the contact area and the slope of the load–penetration depth curve in logarithmic coordinates. The proposed methodology is extended to estimation of the hardening exponent simultaneously with the initial yield stress when the latter is not negligible. Experimental verification for a Cu single crystal leads to promising conclusions.

Comparison and discussion on fragmentation behavior of soft rock in multi-indentation tests by a single TBM disc cutter

This paper is to investigate the mechanical responses and failure characteristics of soft rock in multi-indentation tests by a single TBM constant cross section (CCS) disc cutter. Different pre-set penetration depths and totally three cycles of indentation processes were employed in the repeated indentation tests conducted on the cubic cement mortar specimens. The load-penetration depth curve, penetration load, peak-load penetration depth, rock breakage work and compacted zone depth for the three indentation processes were analyzed. The strength and deformation properties and failure behavior of soft rock under different indentation conditions were revealed. The rock breakage behavior after several indentation processes still presents brittle failure characteristic with small pre-set penetration depths, but the specimens with large pre-set penetration depths appear obvious plastic failure mode. Approximately equal leap loads are obtained from both the intact specimen in direct indentation failure test and the weakened specimens after several indentation processes with different pre-set penetration depths, but the peak-load penetration depths for specimens with different pre-set penetration depths are varying. Curves of the cumulative penetration depth and cumulative rock breakage work both reach the corresponding peak values for one certain pre-set penetration depth. Along with this most unfavourable pre-set penetration depth, rock breakage efficiency is the lowest and energy consumption is the highest.

The Research of Nano-Mechanical Properties of Mono-Crystalline Silicon

The research of the nano-mechanical properties on mono-crystalline silicon by nanoindention technology is reported in this paper . Using the calculation method given by Oliver and Pharr, the hardness and the elastic modulus of mono-crystalline silicon are gained from the load-penetration depth curve. The simulation on mono-crystalline silicon in the plastic phase is carried out by ABAQUS. Based on the bilinear constitutive law and approximate relationship between the hardness and the yield strength, the obtained load-penetration depth curve through the finite element method is compared with the materials actual load-penetration depth curve and good correlation is achieved.

A method to take account of the geometrical imperfections of quasi-spherical indenters

Perfect indenter geometry is quite difficult to manufacture, especially in the nano and macro scales. Indentation curves obtained with imperfect indenter geometry can show strong differences with those obtained with assumed perfect indenter geometry, thereby leading to erroneous data exploitation results.This numerical study brings out the effect of imperfect spherical indenter geometry on indentation load–penetration depth curves, and on the mechanical properties identified by a reverse analysis model based on ideal spherical geometry. It is shown that a method to take account of geometrical imperfections is essential. Two correction methods based on geometrical and physical considerations are assessed, as well as the relevance of the use of the penetration data or the contact data. A method based on the equality of mean contact pressures and indenter volumes under the contact surface is found to be most relevant, as confirmed by the quality results obtained after application of a reverse analysis model.The proposed method is of particular interest in the case of the use of an imperfect indenter whose profile is accurately known.

Region-dependent micro damage of enamel under indentation

The objective of this investigation is to explore the region-dependent damage behavior of enamel, as well as to develop a good understanding of the deformation mechanisms of enamel with numerical modeling. Nanoindentation experiments have been performed to investigate the load-penetration depth responses for outer and inner enamel. Results show that the unloading curve does not follow the loading curve, and degradation of stiffness in the unloading curve is observed. Based on the experimental data, a physical quantity, the chain density in protein, has been introduced to the Drucker-Prager plastic model. Numerical simulations show that the simulated load-penetration depth curves agree with the experiments, and the stiffness degradation behaviors of outer and inner enamel are captured by the numerical model. The region-dependent damage behavior of enamel could be revealed by the numerical model. The micro damage affected area at inner enamel is larger than that at outer enamel, indicating that the inner enamel experiences more micro damage than the outer one. Compared with its outer counterpart, the inner enamel which is rich in organic protein could break more internal protein chains to dissipate energy and to enhance its resistance to fracture accordingly.