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Investigation of Creep Behavior Under Load During Indentation Experiments and its Influence on Hardness and Modulus Results
Abstract
To improve the accuracy and comparability of hardness and modulus results from nanoindentation experiments an evaluation of the creep behaviour is required. Creep depends on the material and normally diminishes to very low values within some seconds. Nevertheless, it influences the maximum depth and the upper part of the unloading curve in a way that measurement errors of more than 20% may occur. In this work, a detailed analysis of the creep behaviour for different film and substrate materials is done. In addition, the influence of loading time and hold period at maximum load on the hardness and modulus results is investigated. The results show that especially for materials with low hardness-to-modulus ratio (mostly metals), the modulus results are not reliable if the hold period is chosen too low. Hold periods are proposed in dependence on the material type that should be kept for high accuracy measurements.
... Indenter contact area A i Indenter Area C 1 , C 2 , C 3 , ……. . C 8 ...
... In the same way, the creep behavior of various alloys and glasses was examined using the indentation method by Ma et al. [7] and Chudoba et al. [8]. The shear creep behavior of viscoelastic-plastic materials such as Poly (methyl methacrylate) (PMMA) and polyvinyl chloride (PVC) was investigated by Peng et al. [9]. ...
... The non-dimensional parameters are defined in Eqs. (5) to (8). The creep displacement of materials is characterized by an exponential relationship involving various parameters. ...
Polymers have emerged as a novel class of engineered materials that find application in several domains, such as structural components, fittings, couplings, and more. Due to their viscoelastic nature, these materials experience a deformation dependent on time when subjected to an applied load. This paper presents a novel approach to address this research gap by introducing simplified and practical models for predicting creep and back creep displacement utilizing a non-destructive technique, specifically micro-indentation. A comprehensive experimental investigation of multi-cycle indentation testing has been conducted. The creep and back creep models that have been developed are expressed as nonlinear exponential equations, which include variables such as material properties determined using micro-indentation techniques, as well as experimental parameters like maximum load, loading and unloading rates, and the indenter’s hold time. The relationships discussed significantly influence the holding time at maximum and minimum loading conditions. One advantage of these exponential models is their ability to provide a simple mathematical representation. By utilizing this approach, there is no longer a requirement to conduct multiple single-cycle indentations or to depend only on conventional creep tests.
... If creep is not considered, it can have a remarkable effect on the calculation of hardness and the reduced modulus from analysing the unloading curve. It was found by Chudoba and Richter [104] that creep not only affects the measured depth but also the slope of the unloading curve at peak load, which is a key quantity to calculate the reduced modulus. ...
... The experiment conditions influencing the creep were examined. It was found that loading rate and the hold/dwell time at peak load govem not only the extent of creep but also the initial contact stiffness, which agreed with the findings by Chudoba and Richter [104]. It was also noticed that the higher the loading rate, the larger the creep, thus a longer dwell time will be required to allow for this deformation to take place as long as the full load is not applied abmptly, i.e. in less than 10 s, which can affect the initial contact stiffness. ...
... This indicates that short-time loading causes erroneous indentation data which seem to include undesired deformations. This explanation of bowing can be supported by the findings of Chudoba and Richter[104] who reported this bowing phenomenon when dwell time is zero and loading time is 92 s.The material behaviour in the case of short-time loading can be understood as a dynamic response to a high strain rate loading, in which the material seems stronger, compared with its response under static loading. Short time loading should thus be avoided during indentation to ensure more accurate results.Referring toFig. ...
p>The strength of welded joints has a vital effect on the structural response of a welded structure under severe loading conditions. The thermal nature of the weld process causes considerable changes in the microstructure across the weld regions, which leads to different material properties in these regions, namely, the parent metal, the weld fusion zone, and weld heat -affected zone. The reliability of predicting the real behaviour of the welded structure using finite element analysis depends on the accurate determination of the material properties across these regions which are essential input data in the model. Whilst conventional tensile testing is incapable of providing these properties on such a small scale, the instrumented micro/nano-hardness test lends itself for such a task. In this non-destructive technique a small indenter, which is spherical in this study, is pressed onto the sUlface of the material and then unloaded while load and depth of indentation are continuously measured. Several approaches have evolved to analyse the measured load indentation data to extract various material mechanical properties conesponding to each indent location. The primary objective sought from such an analysis is the determination of the contact area, which is then used to obtain material properties. While the existing analytical approaches assume the contact edges sink-in, soft metals, however, tend to pile-up resulting in possible large errors in the delived results. The available conection formulae attempt to predict pile-up based on a prior knowledge of the strain hardening exponent of the test material. In addition, they assume a constant ratio of the pile-up lip height to indentation depth, which they defined as a function of the strain hardening exponent. Thus they do not predict pile-up based solely on the indentation data. This study shows, based on detailed finite element modelling, that pile-up starts with a negative value (sink-in) in the early stages of an indentation experiment and then develops and builds up until it stabilises at a celiain level. An empilical relation is proposed to predict the extent of pile-up of an unknown material based on the residual to total indention depth ratio. This leads to a more accurate estimate of the contact area and thus the derived stress-strain curve. In addition, a characterisation model for an indenter of imperfect geometry is also proposed in this study which identifies the characte11stic strain for an imperfect sphere. An algorithm is suggested which incorporates the proposed characterisation analysis in a complex iteration technique in the frame compliance calibration routine to process the raw acquired data. The proposed characterisation technique has been verified on expe11mental data of test mate11als, and it has then been applied to indentation data on butt-welded steel spanning the distinct weld regions.</p
... For the SiN/Si structures, p max value was varied from 100 to 400 µN. In measurements involving nanometer-scale penetration depth and extended time periods, one should consider drift components such as thermal drift and creep [22,24,60,61]. Note that the energy transferred from the plastic deformation process can increase the temperature of the system, sometimes exceeding one hundred degrees near the contact surface [62,63]. ...
... By assuming that the rate of the change in h(t) due to creep and thermal drift is constant during a single loading/unloading cycle, one can implement the Maxwell model shown in figure 17(a). In this case, the measured S is expressed as follows [60], ...
Recently, plasma process-induced damage (PID) has garnered significant interest in the design of thin dielectric films implemented in semiconductor devices. Silicon nitride (SiN) films, a material of interest in strain engineering, are found to suffer from PID because they are exposed to various plasmas during device manufacturing processes. Only a limited amount of experimental evidence is available at present regarding plasma-induced mechanical property changes of SiN films. In this study, we investigated the mechanical property change in SiN and SiO2 films using a cyclic nanoindentation technique. We focused on the contact stiffness (S) as the principal mechanical property parameter. Firstly, a single loading/unloading test confirmed an increase in S after Ar and He plasma exposures. Subsequently, we examined the time-dependent features of damaged SiN and SiO2 films under cyclic loading/unloading. From the cyclic test, an increase in S was seen with the number of loading/unloading cycles (N) for both SiN and SiO2 films. A larger increase in S was observed for the damaged SiN, while no significant increase was seen for the damaged SiO2 films. The observed increase in S and its time dependence are attributed to the strain developed by the created defects (e.g. interstitial species) and the reconstruction and stabilization of plasma-damaged Si–N networks with created defects, respectively. The time-dependent S analysis under cyclic loading/unloading is useful for evaluating the effects of PID on the mechanical properties of thin films.
... That is, creep appears when the load is held constant and the depth increases as the indenter 'sinks' into the samples, see Figure 2.4. Chudoba and Richter have studied the creep influence behavior on nanoindentation measurements of hardness and elastic modulus [15]. [15]. ...
... Chudoba and Richter have studied the creep influence behavior on nanoindentation measurements of hardness and elastic modulus [15]. [15]. Their research indicates that the creep influence can be minimized by holding the load constant for a fixed period of time the experimentally calculated period at the maximum load which will allow to the creep to be fading. ...
... S value is calculated by using For elastoplastic materials, the unloaded P À h data is pure elastic but viscous materials show time-dependent behavior during unloading, i.e., viscous deformation and viscoelastic recovery. In the case of viscous deformation, the material extends during unloading and results in an increment of depth of penetration which looks like a nose-shape (Ref 11, [14][15][16][17]. Due to this depth increment, the elastic S cannot be acquired at the onset of the unloading. ...
... Hence, it is important to eliminate or minimize this viscous deformation. Therefore, many researchers (Ref 11,14,15,18,19) have suggested to follow a longer holding time, until the viscous deformation rate during holding (Ref 20) becomes less than 1%, so that there will be no viscous deformation during unloading. In addition, Ngan et al. (Ref 16) have reported an empirical formula to estimate the elastic S without providing a longer holding time. ...
We have determined Young’s modulus (EN) value via nanoindentation experiments for thermoplastic glassy polymers; polycarbonate (PC) and poly(methyl methacrylate) (PMMA). Four types of load functions are followed to examine the viscous behavior effect on unloaded data which affects EN estimation. It is seen that the viscous deformation during unloading is ~ 10% for PMMA and ~ 3.5% for PC with a no-hold + slow-unloading rate and by following a fast unloading rate it reduces to < 1%. The viscoelastic recovery is less for a fast unloading rate. We have estimated the elastic stiffness (S) value via hold + fast-unloading rate data to eliminate the viscous deformation and minimize the viscoelastic recovery. We show that the fitting range of unloaded data from which S value is estimated, is not universal to avail EN equal to tensile modulus (E). Our results show that the fitting range depends on the applied load, choice of the load function, contact area estimation, phenomenological correction factor, and viscous behavior of the material.
... For this purpose, once the load reaches the maximum load, it is then held for a period of approximately 60s, this results in further increase in depth because of epoxy's viscoelastic nature. This creep, if not applied, effects the unloading behavior of materials, which in turn has a negative influence on results [40]. The Indentation applied load vs. depth graphs for all the samples, and is shown in Figure 7. ...
... For this purpose, once the load reaches the maximum load, it is then held for a period of approximately 60s, this results in further increase in depth because of epoxy's viscoelastic nature. This creep, if not applied, effects the unloading behavior of materials, which in turn has a negative influence on results [40]. All the prepared epoxy coatings were subjected to similar testing conditions. ...
This research paper presents the fabrication of epoxy coatings along with the hybrid combination of SiO2 and ZrO2. The epoxy resin is incorporated with SiO2 as the primary pigment and ZrO2 as the synergist pigment. The study delves into the adhesion, barrier, and anti-corrosion properties of these coatings, enriched with silica and zirconium nanoparticles, and investigates their impact on the final properties of the epoxy coating. The epoxy resin, a Diglycidyl ether bisphenol-A (DGEBA) type, is cured with a polyamidoamine adduct-based curing agent. To evaluate the protective performance of silica SiO2 and zirconia ZrO2 nanoparticles in epoxy coatings, the coated samples were tested in a 3.5% NaCl solution. The experimental results clearly demonstrate a remarkable improvement in the ultimate tensile strength (UTS), yield strength (YS), and Elastic Modulus. In comparison to using SiO2 separately, the incorporation of both ZrO2 and SiO2 resulted in a substantial increase of 43.5% in UTS, 74.2% in YS, and 8.2% in Elastic Modulus. The corrosion test results revealed that the combination of DGEBA, SiO2, and ZrO2 significantly enhanced the anti-corrosion efficiency of the organic coatings. Both these pigments exhibited superior anti-corrosion effects and mechanical properties compared to conventional epoxy coatings, leading to a substantial increase in the anti-corrosion efficiency of the developed coating. This research focuses the potential of SiO2 and ZrO2 in hybrid combination for applications, where mechanical, corrosion and higher adhesion to the substrates are of prime importance.
... Consequently, if the creep indentation is not adequately considered, it can have a significant effect on the Young's modulus and hardness results. In this case, it is worth noting that the applied dwell time of 25 s during the creep nanoindentation is typically a sufficient period for marginal influence of creep on the calculation of the hardness and Young's modulus of the three samples [55]. ...
... Hence, the creep effects likely affect the unloading process and then cause an overestimation of the contact stiffness, which in turn influence the measured Young's modulus. Indeed, to avoid such drawbacks and for high accuracy of the measured hardness and Young's modulus, the holding time was taken equal to 25 s, which was considered as sufficient dwell time (higher than at least 10 s) [55], for which the drift rate is estimated at 0.01 nm/s, which is typically low to overcome any possible creep effects on the determined values of hardness and Young's modulus. ...
This study investigates the impact of Mg doping concentration in GaN thin films on their physical and mechanical properties, specifically on their conductivity transition, luminescence, hardness, Young's modulus, and creep behavior. Mg-doped GaN layers were grown on sapphire substrates using the MOCVD technique, with trimethylgallium (TMG) and bis(cyclopentadienyl) magnesium (Cp2Mg) as precursors for Ga and Mg, respectively. The TMG flow rate was set at 20 μmol/min, while the Mg flow rate was adjusted by tuning the temperature of the thermostatic bath of Cp2Mg. Three different Cp2Mg flow rates: 2, 7 and 9 μmol/min were utilized to explore their effects on the physical and mechanical properties of the grown epilayers. The results demonstrate that an increase in the Mg concentration leads to a conductivity transition from n-type to p-type, with the highest hole concentration (4.5 ± 0.2) × 1e+17 cm−3 and blue luminescence attained with Mg concentration equal to 2.1 × 1e+19 atoms/cm3. Moreover, the hardness, Young's modulus and the intensity of compressive stress increase with the Cp2Mg flow rate due to the evolution of pre-existing dislocation density and point defects incorporation. Additionally, this study evaluates the creep behavior of the Mg-doped GaN thin films. It shows that both the creep stress exponent and the maximal creep depth decrease with the increase of the Cp2Mg flow rate. This is attributed to dislocation glides and climbs governing the creep mechanism. Accordingly, this investigation highlights the importance of understanding the relationship between physical properties and mechanical characteristics of Mg-doped GaN thin films, which have potential implications for various technological applications.
... This error is referred to as thermal drift. The phenomenon of thermal drift is well known in the nanoindentation field and significantly limits the use of such instrument for long time measurements such as creep and high temperature experiments [6][7][8][9][10][11]. Conventionally, the thermal drift measurement is done before loading [12,13] or at 90% of unloading segment [2,14]. In this method, the drift is monitored for 40 s and a linear equation (for LC mode: h = nt, where n is slope and t represents time) is fitted to the data of last 20 s. ...
... From the preceding discussion, we can conclude that the conventional methods [12,13] of drift correction are inadequate for longer duration experiments. Here, we present a new method for drift correction, called prior drift monitoring, that is applicable for both LC and DC mode of experiments and is independent of the mechanical response of the sample being tested. ...
Nanoindentation is widely used for characterizing mechanical properties of materials at small length scales. Thermal drift effects during indentation are well-known, and are typically corrected using a linear relationship between displacement and time. However, this method has serious drawbacks for measuring thermal drift for long duration experiments even at room temperature. We show that for experiments in displacement control (DC) mode, conventional methods to measure thermal drift are inaccurate. Changes in value due to thermal drift occur in load data, not in displacement data since displacement is controlled by transducer in DC experiments. In addition, we find that thermal drift rate may not be constant even for 100 s duration experiments. Drift correction methods that require post-monitoring of displacement lead to errors since unloading behavior is influenced by elastic response of the sample being tested. We propose a novel scheme that involves prior drift monitoring, which alleviates all problems.Graphic abstract
... Also, the nanoindentation technique has gained popularity in studying the mechanical properties of CBMs (such as indentation modulus M, hardness H, fracture toughness K, and creep modulus), since it has the advantages of short test time and high test accuracy compared to the macro properties tests [3,[11][12][13][14][15][16]. Additionally, the nanoindentation can be used to test the micro creep of CBMs [17][18][19][20][21], and the micro creep performance obtained by the test is comparable to the results of traditional methods. Furthermore, the micromechanical properties of CBMs obtained through nanoindentation testing are an important foundation for establishing numerical models. ...
... Chudoba et al. analyzed the creep behavior of an Al film on BK7 glass using nanoindentation methods. They investigated the behavior of H and E of these materials in terms of holding time and loading time [29]. ...
Polymers are the latest designed materials used in structural, fitting, joint, and other applications. Three thermoplastic polymers, named Polyether ether ketone (PEEK), Poly (methyl methacrylate) (PMMA), and Poly-tetra-fluoro-ethylene (PTFE), have been subjected to the constant load multicycle (CLMC) micro-indentation method. In this study, the fatigue and creep behaviour of the materials has been assessed using the load-displacement curve produced from the indentation method. The primary goal of this paper is to examine the polymer's cycle fatigue behaviour by taking into account the repetitive loading and the resulting hysteresis loop. A technique based on stress and energy was used to study the polymer's fatigue behaviour. In these stress- and energy-based techniques, respectively, hardness (H) and plastic energy (EP) correspond with fatigue life (N). In the fatigue life prediction of polymers, the fatigue toughness, or a total of hysteresis energy, was studied. In addition, these viscoelastic polymers experience time-dependent deformation when a force is applied. By examining the depth (h) with holding time (tH) data, multicycle micro indentation is utilised to determine the creep behaviour of polymers. This study discusses developing a simple and practical approach for calculating the creep and back creep displacement of polymers with the holding time at maximum and minimum load. The fatigue and creep properties of the polymer can be assessed simultaneously using a CLMC indentation.
... This creep behavior influences the maximum depth and slope of the upper portion of the unloading load. As a result, if this creep is not considered, It will affect the final calculated results [19]. ...
Zirconia (ZrO 2) nanoparticles (1-3 wt.%) were incorporated into the epoxy matrix using the ultra-sonication mixing method of dispersion to manufacture nanocomposite coatings. An automatic applicator was used to prepare the coating samples on a stainless steel substrate. The influence of ZrO 2 nanoparticles on the physicochemical characteristics of epoxy coatings was evaluated using energy dispersive X-ray spectroscopy (EDS), field emission scanning electron microscopy (FE-SEM), Fourier-transform infrared spectroscopy (FTIR), thermos-gravimetric analysis (TGA), elastic modulus, and micro-hardness measurement with the nano-indentation technique. The corrosion stability during immersion in 3.5% NaCl solution was monitored using electrochemical impedance spectroscopy (EIS). All ZrO 2-containing coatings showed better corrosion stability and adhesion than pure epoxy coating. Epoxy coating incorporated with 2% ZrO 2 exhibited the greatest values of corrosion resistance and adhesion due to the effect of nanoparticle properties and their better de-agglomeration in the epoxy matrix than pure epoxy coating.
... Nevertheless, this assumption is not always valid due to thermal drift effects, and creep effects can cause an overestimation of the contact stiffness, thereby influencing the measured Young's modulus. To obtain accurate measurements of the hardness and Young's modulus, a holding time of 30 s was considered sufficient to mitigate any potential creep effects on the measured values, as suggested by Chudoba et al. [36]. The drift rate during this time was estimated to be 0.01 nm/s, which is typically low. ...
This paper investigates the mechanical properties and creep behavior of undoped and Mg-doped GaN thin films grown on sapphire substrates using metal–organic chemical vapor deposition (MOCVD) with trimethylgallium (TMG) and bis(cyclopentadienyl)magnesium (Cp2Mg) as the precursors for Ga and Mg, respectively. The Mg-doped GaN layer, with a [Mg]/[TMG] ratio of 0.33, was systematically analyzed to compare its mechanical properties and creep behavior to those of the undoped GaN thin film, marking the first investigation into the creep behavior of both GaN and Mg-doped GaN thin films. The results show that the incorporated [Mg]/[TMG] ratio was sufficient for the transition from n-type to p-type conductivity with higher hole concentration around 4.6×1017 cm−3. Additionally, it was observed that Mg doping impacted the hardness and Young’s modulus, leading to an approximately 20% increase in these mechanical properties. The creep exponent is also affected due to the introduction of Mg atoms. This, in turn, contributes to an increase in pre-existing dislocation density from 2 × 108 cm−2 for undoped GaN to 5 × 109 cm−2 for the Mg-doped GaN layer. The assessment of the creep behavior of GaN and Mg-doped GaN thin films reveals an inherent creep mechanism governed by dislocation glides and climbs, highlighting the significance of Mg doping concentration in GaN thin films and its potential impact on various technological applications.
... Chemical composition of each point at the position shown in Fig. 9 (atomic fraction, at%). atoms, resulting in a transient negative strain rate [25,26], this is known as the Portevine-Le-Chatelier (PLC) effect [27]. The values of hardness and Young's modulus are derived according to the method developed by Oliver, which is determined by the projected product of the maximum load and the indentation on the contact surface [28,29]: ...
... However, even with the application of a holding period, the deformation may continue to grow upon unloading before the gradually diminishing of the delayed strain response (Fig. 7c) [48]. Nonetheless, the effect of delayed response on the unloading portion may be neglected if the penetration depth grows by less than 1% per minute [49]. ...
Biological tissues have developed structures that fulfil their various specific requirements. Mineralized tissues, such as tooth and bone, are often of mechanical competence for load bearing. Tooth enamel is the hardest and toughest mineralized tissue. Despite a few millimeters thick and with minimal regenerative capacity, human tooth enamel maintains its functions throughout a lifetime. Bone provides skeletal support and essential metabolism to our body. Degenerative diseases and ageing induce the loss of mechanical integrity of the bone, increasing the susceptibility to fractures. Tooth and bone share certain commonalities in chemical components and material characteristics, both consisting of nanocrystalline apatite and matrix proteins as their basic foundational structural units. Although the mechanical properties of such mineralized hard tissues remain unclear, it is plausible that they have an inherent toughening mechanism. Nanoindentation is able to characterize the mechanical properties of tooth enamel and bone at multiscale levels, and the results suggest that such toughening mechanisms of enamel and bone may be mainly associated with the smallest-scale structure–function relationships. These findings will benefit the development of advanced biomaterials in the field of material science and will further our understanding of degenerative bone disease in the clinical community.
... Even if it was found that the loading time has a significant influence by increasing modulus and hardness error, it was also determined that above 45 seconds of hold, this error became negligible. [20] In Figure 3b is displayed the penetration depth of the tip as a function of time, where we can identify the creep behavior of both samples between 30 and 150s, when the holding period is applied. Each curve is taken from 1 out of the 10 tests made on each sample so it is mainly valuable to discuss the shape of the curves. ...
Wet etching of polytetrafluoroethylene by sodium naphthalenide dissolved in diglyme solution was investigated experimentally and theoretically. First, the irreversible modification of the polymer surface was analyzed by Raman and XPS spectroscopies, water wetting angle measurements and AFM observations. The drastic changes brought to the surface of PTFE could be clearly demonstrated by these analytical methods. Then, first principle calculations coupled to molecular dynamics (FPMD) were performed to simulate the first steps of the reaction involved in the process of surface modification. It has been shown that fluorine directly attacks vicinal sodium with formation of a pair of sodium fluoride ions without grafting of the naphthalene moiety onto the modified surface. While the formation of the alkene and alkyne bond can be modelized, no spectroscopic signature is observed after rinsing etched PTFE.
... As already shown, the composite hardness of the coatings depends on the applied load ( Figures 5 and 6). The load-dependence of composite hardness is called the indentation size effect (ISE) [54][55][56][57][58][59]. This effect can be modeled in two ways: empirically (according to Meyer's power law relationship [16,20,[57][58][59]) or according to the PSR model [54], i.e., as a linear function between the hardness and the reciprocal value of indentation diagonal. ...
Mechanical (hardness and adhesion) and electrical (sheet resistance) characteristics of electrolytically produced copper coatings have been investigated. Morphologies of Cu coatings produced galvanostatically at two current densities from the basic sulfate electrolyte and from an electrolyte containing levelling/brightening additives without and with application of ultrasound for the electrolyte stirring were characterized by SEM and AFM techniques. Mechanical characteristics were examined by Vickers microindentation using the Chen–Gao (C–G) composite hardness model, while electrical characteristics were examined by the four-point probe method. Application of ultrasound achieved benefits on both hardness and adhesion of the Cu coatings, thereby the use of both the larger current density and additive-free electrolyte improved these mechanical characteristics. The hardness of Cu coatings calculated according to the C–G model was in the 1.1844–1.2303 GPa range for fine-grained Cu coatings obtained from the sulfate electrolyte and in the 0.8572–1.1507 GPa range for smooth Cu coatings obtained from the electrolyte with additives. Analysis of the electrical characteristics of Cu coatings after an aging period of 4 years showed differences in the sheet resistance between the top and the bottom sides of the coating, which is attributed to the formation of a thin oxide layer on the coating surface area.
... us, to not only consider the time-dependent deformation during the load-holding period at 10% of the peak load but also to avoid the influence of this error of equipment-temperature drift, the thermal equilibrium time of the Aton Pharr NHT3 system equiped with Berkovich indenter was more than 1 h, and compensations were autumatically formulated [35]. Both the thermal equilibrium and compensations were done previously based on other materials and the thermal drift also reaches much less than 0.01 nm/s [35], since we found the deformation of rocks (shale, mudstone, and coal) during the holding period of 10% of the maximum load is time-dependent rather a linear increase [36], which is too large to be ignored. After compensating, three random indentations were made on each rock sample to research the time-dependent deformation characteristics. ...
Recently, the holding states of nanoindentation experiments have been widely used to analyze the time-dependent deformations of various rocks, and the dynamic mechanical analysis (DMA) method seems to be more applicable than the quasi-static mechanical analysis (QMA) method when the influence of creep deformation on mechanical properties of rocks was analyzed. However, the former method causes an abnormal behavior during the creep holding stages that was not clearly interpreted.2 Consequently, in this study, by amplifying the oscillation of the DMA method, the mechanical mechanism of this phenomenon was explained. Experimental results confirm that the rheological deformation of rocks consists of the creep deformation (depth increasing) and the elastic aftereffect deformation (depth decreasing) during the creep time with small oscillation; once the elastic aftereffect deformation exceeds the creep deformation, the abnormal behavior can be observed. Besides, some other abnormal behaviors might be found for other rock materials when the DMA method with different oscillations is used, which illustrates the complexity and limitation of applying this method. Thus, the QMA method was recommended to investigate the above questions in future studies.
In this study, we investigate the mechanical properties of gold (Au) materials using molecular dynamics simulations. In this simulation, the nanoindentation process was performed to analyze the deformation defects and hardness properties of Au under different indentation velocities. The results suggest that the deformation behavior of the Au specimen was affected by different indentation velocities. These findings were confirmed by examining the load-displacement curve, which indicated elastic deformation through the appearance of a linear load-displacement relationship at low indentation velocities. In contrast, plastic deformation was identified by the presence of intensified serrations in the load-displacement curve at higher indentation velocities. Under such conditions, the hardness exhibited minimal variation when the indenter velocity increased from 5 mls to 10 mls. However, a significant increase in hardness was noted when the indentation velocity was further raised to 15 mls.
We propose an optimized load function designed to acquire the elastic aspect during nanoindentation for two viscous polymers, i.e., polycarbonate (PC) and poly (methyl methacrylate) (PMMA). To do so, various load functions are followed where constant strain rate (Pdot/P) varies from 0.05 /s to 50.0 /s, maximum load (Pm) from 1000 μN to 9000 μN and unloading rate (PdotUL) from 9.0 x 10^2 μN/s to 10^7 μN/s. Depending upon the Pdot/P, extent of viscous deformation varies during loading, e.g., slow Pdot/P shows more viscous deformation due to sufficient loading time and vice-versa. However, for fast Pdot/P, a large amount of viscous deformation is observed only when the tip decelerates at the end of loading since the deceleration zone is the favor of viscous deformation. During holding, it is seen that a large amount of viscous deformation takes place for fast Pdot/P at any Pm. Because viscous deformation could not take place during loading due to insufficient time that is why it takes place during holding. In addition, at high Pm large amount of viscous deformation takes place than low Pm. Since it is observed that different time is required for various Pdot/P and Pm to saturate the viscous deformation during holding; hence, a novel method is suggested to estimate the required time for any Pdot/P and Pm indentation. During unloading, it is noticed that for fast PdotUL less amount of viscoelastic recovery takes place towards Pm, hence, it is recommended that 95%–40% and 95%–60% unloading range should be considered to evaluate the elastic aspect for PC and PMMA, respectively.
Creep refers to the capacity of a material to bear load and it represents a fundamental property for material design. Indentation appears as a most convenient tool for the study of creep behavior in polymers. The present work gathers information on the indentation creep response of a wide variety of polymers, taken from different sources, and offers a comprehensive overview of the factors that can influence creep. It is shown that viscoplastic behavior assessed by the traditional technique is influenced by the internal polymer characteristics and also by external factors. As a general rule, chain stiffness, chain branching, crystallinity, physical ageing and rigid-filler addition promote creep resistance. The advent of modern instrumented indenters allowed analysis of viscoelastic flow. Interestingly, it is found that the creep parameters obtained from traditional and instrumented testing are in close agreement provided the viscoplastic regime prevails. Graphene-polymer nanocomposites are used to illustrate the reduced creep rate, creep extent and strain rate sensitivity found upon addition of the rigid filler to a number of thermoplastic matrices.
Stress relaxation is defined as a decrease in stress that is dependent on time under strain, which is constant in nature. A fixed amount of deformation is applied to the specimen and load is measured, which is required to maintain it as a function of time to study this characteristic nature of the polymer. In static and dynamic applications, the demand for fiber-reinforced plastic composites is increasing because of increase in mechanical performance. Glass fiber-reinforced polymers have wide applications in automotive sectors, aircraft industries, medical technology, and electronic appliances. It is possible to investigate microstructural behavior with the help of X-ray computed tomography combined with in situ loading. To study the effect of hostile solutions on the stress relaxation behavior of carbon fiber-reinforced polymers, solutions selected were hydrochloride acid and sodium hydroxide. Stress relaxation performance of high density polyethylene, which was based on injection-molded composites, was studied. The composites under study contained four types of natural fibers (i.e., wood, flour, rice hills, newsprint, and kenaf fiber). From pineapple leaf fiber and low density polyethylene, cost-effective and ecofriendly composite materials were developed. Injection molding and hot pressing of the thermoplastics between the wood fiber were used to produce wood fiber polypropylene and wood fiber waste polyethylene composites. Cylindrical macroindentation was used to investigate time-dependent mechanical behavior of three materials from the fluorocarbon family.
Relevance. Crystalline and amorphous lithium tetraborate (Li2B4O7) has a wide range of practical applications due to its physical properties. The knowledge of the mechanical characteristics of the surface layers of these materials, which are studied by nanoindentation, is necessary for optimising the technological processes for obtaining “optically perfect” samples. Aim. A comparative study of the mechanical properties and deformation mechanisms of glassy and crystalline Li2B4O7 samples in a wide range of applied loads. Methodology. The elastic-plastic properties of crystalline and glassy lithium tetraborate were investigated using the multiple-loading cyclic nanoindentation method. The samples were measured at maximum loading forces of 50, 100, 150, 200, 250, 300, 350, 400, 450, and 500 mN. Four measurements (in the form of a 2x2 matrix) were made at a distance of 50 µm from each other on each sample and at each load. Young’s modulus, hardness, and Poisson’s ratio of Li2B4O7 glass were also calculated using the Makishima-Mackenzie theory. Results. The load-displacement curves and graphs of the dependence of the average contact pressure on the displacement of the diamond Berkovich indenter were obtained, which have a “smooth” shape and no anomalies associated with “pop-in” or “pop-out” effects. The indentation modulus (Young’s modulus E) and hardness H of the studied samples were obtained from the experimental P-h load-displacement diagrams. The measured values mainly depend on the applied load or the contact depth of the indenter penetration into the crystalline and vitreous lithium tetraborate. Conclusions. Both the hardness and Young’s modulus of Li2B4O7 glass are lower than those of the single crystal, indicating a lower resistance of amorphous lithium tetraborate to elastic and plastic deformations. The obtained experimental values of hardness and Young’s modulus of Li2B4O7 glass correlate well with the results of the calculation within the framework of the Makishima-Mackenzie theory. Multiple-loading cyclic nanoindentation leads to deformation densification of glassy Li2B4O7 due to changes in the angles and lengths of chemical bonds, which leads to a decrease in the free volume in the medium-order structure of glass, as well as a change in the coordination of Boron atoms relative to Oxygen, i.e., the transformation of three-coordinated Boron into four-coordinated Boron
The gut microbiome impacts bone mass, which implies a disruption to bone homeostasis. However, it is not yet clear how the gut microbiome affects the regulation of bone mass and bone quality. We hypothesized that germ-free (GF) mice have increased bone mass and decreased bone toughness compared with conventionally-housed mice. We tested this hypothesis using adult (20 to 21-week-old) C57BL/6J GF and conventionally-raised female and male mice (n=6-10/group). Trabecular microarchitecture and cortical geometry were measured from microCT of the femur distal metaphysis and cortical midshaft. Whole-femur strength and estimated material properties were measured using three-point bending and notched fracture toughness. Bone matrix properties were measured for the cortical femur by quantitative backscattered electron imaging, nanoindentation, Raman spectroscopy, and for the humerus by fluorescent advanced glycation end-product assay (fAGEs). Shifts in cortical tissue metabolism were measured from the contralateral humerus. GF mice had reduced bone resorption, increased trabecular bone microarchitecture, increased tissue strength that was not explained by differences in bone size, increased tissue mineralization and fAGEs, and altered collagen structure that did not decrease fracture toughness. We observed several sex differences in GF mice, most notably for bone tissue metabolism. Male GF mice had a greater signature of amino acid metabolism and female GF mice had a greater signature of lipid metabolism, exceeding the metabolic sex differences of the conventional mice. Together, these data demonstrate that the GF state in C57BL/6J mice alters bone mass and matrix properties but does not decrease bone fracture resistance.
The gut microbiome impacts bone mass, implying a disruption to bone homeostasis, yet significant uncertainty remains regarding the impacts of the gut microbiome on remodeling bone cells. The gut microbiome is thought to be essential for normal biomineralization, but the specific consequences of the absent gut microbiome on tissue mineralization and multiscale bone quality are not determined. We hypothesized that bone homeostasis and tissue-scale metabolism, tissue mineralization, and whole-bone biomechanics are altered in germ-free (GF) C57BL/6J mice. Further, because many characteristics of the gut microbiome are sexually dimorphic, we hypothesized that the gut microbiome would show important sex differences with regards to its impact on bone quality. Differences between GF and conventional mouse bone extended from bone tissue metabolism to whole bone biomechanics. Cortical bone tissue from male mice had a greater signature of amino acid metabolism whereas female cells had a greater signature of lipid metabolism. These sex differences were also present in GF mice and were indeed even more stark. GF increased cortical femur bone formation for both sexes and decreased bone resorption and osteoclast density only in females. GF similarly increased cortical femur tissue mineralization and altered collagen structure for both sexes but led to greater gains in distal femur trabecular microarchitecture for males. Whole femur strength was similarly increased with GF for both sexes, but males had a greater increase in modulus. GF did not impact fracture toughness for either sex. The altered bone quality with GF is multifactorial and is likely contributed to by differences in tissue-scale composition as well as lower cortical porosity. Together, these data demonstrate that the gut microbiome influences bone cells and multiscale bone quality, but that the specific relationships that underlie these effects to bone are different for females and males.
Nanoindentation studies on bulk and epitaxial semiconductor crystals have been reviewed in general. The common materials of technological interest such as Si, Ge, GaAs, GaN, InP, CdZnTe, HgCdTe etc. have been included. Issues related with the measurement and analysis of load–displacement characteristics have been discussed in detail, including those for cyclic nanoindentation and continuous stiffness measurements. Common mistakes/oversights in the extraction of mechanical properties, particularly for the elastic modulus, have been highlighted. Various features observed in load–displacement curves are discussed in connection with different semiconductor materials. These include pop-in/pop-out events and serrations observed in general, and the open-jaw and hysteresis like features in cyclic nanoindentation. Cathodoluminescence studies on indented surfaces have also been included to highlight the deformation behaviour of some of the crystalline semiconductor materials.
Long-lasting constant loading commonly exists in silicon-based microelectronic contact and can lead to the appearance of plastic deformation. Stress relaxation behaviors of monocrystalline silicon coated with amorphous SiO2 film during nanoindentation are probed using molecular dynamics simulation by varying the indenter’s size. The results show that the indentation force (stress) declines sharply at the initial and decreases almost linearly toward the end of holding for tested samples. The amount of stress relaxation of SiO2/Si samples indented with different indenters during holding increases with growing indenter size, and the corresponding plastic deformation characteristics are carefully analyzed. The deformation mechanism for confined amorphous SiO2 film is depicted based on the amorphous plasticity theories, revealing that the more activated shear transformation zones(STZs) and free volume within indented SiO2 film promote stress relaxation. The phase transformation takes place to monocrystalline silicon, the generated atoms of Si-II and bct-5 phases within monocrystalline silicon substrate during holding are much higher than those for smaller indenter.
Time-dependent plastic deformation commonly exists in silicon-based microelectronic contact. The stress relaxation behaviors of SiO2/Si bilayer composite are studied using molecular dynamics simulation by varying loading speed. The results imply that the indentation force decreases sharply at the initial and linearly towards the end of holding, and the amount of stress relaxation increases with the increasing loading speed. The plastic deformation of confined amorphous SiO2 film is carefully analyzed based on the amorphous plasticity theories; variations of coordinated silicon atoms and Si-O bond number indicate that the films are further densified at different degrees depending upon loading speed during holding. The densification is strengthened at a higher speed because much more activated shear transformation zones (STZs) and accumulated free volume generate within films indented at higher speed. The phase transformation of monocrystalline silicon is observed in indented silicon during holding; the Si-II and bct-5 silicon atoms increase with time and loading speed.
High-performance, anisotropic, single Kevlar fibers, K29, KM2, and K119, are evaluated by a newly developed modified Curved Area Function (mCAF). Indentations at various loads and depths are carried out to obtain the mechanical properties across the diameter of the fibers. To avoid substrate effects, the 10% substrate thickness rule of thumb was followed. Targeted Poisson ratios are assumed in the calculations of the indentation area function to match published data. The indentation moduli of Kevlar fibers at 10% fiber thickness measures: KM2 at 5.10 ± 0.4 GPa (ν = 0.30) and 4.91 ± 0.4 GPa (ν = 0.35), K29 at 2.95 ± 0.3 GPa (ν = 0.30) and 2.84 ± 0.3 GPa (ν = 0.35), and K119 at 2.43 ± 0.4 GPa (ν = 0.27). For all studied cases, the indentation moduli do not differ by more than ± 0.4 GPa, indicating a small measurement error, contrasting the ± 0.86 to ± 1.0 GPa error range attained by traditional area function calculations. The results are compared with the semi-plane analysis proposed by Oliver and Pharr to illustrate the necessity of the mCAF method. The fibers' indentation moduli are calculated at 2-13%, 7-13%, and 25-40% indentation depth of each fiber diameter using both the corrected and the traditional contact areas. The indentation moduli computed from the flat area function are generally less than those determined from the mCAF. As expected, maximum indentation moduli measurements occur closer to the surface of the fibers.
We report on an investigation of the suitability of SiO 2 thin films for use as calibration standards for the measurement of elastic modulus by laser-acoustic measuring devices. Film thicknesses for a range of thin film standards, originally developed for the calibration of ellipsometers, were obtained by X-ray reflectometry, ellipsometry, and metrological scanning force microscopy. Using the calibrated values of film thickness, a laser-acoustic method was used to obtain the elastic moduli of the thin films. Nanoindentation of the films, performed at two different laboratories was used to provide an independent measure of the elastic modulus values. The modulus values determined by nanoindentation and the laser-acoustic method were found to agree within 4.6 %, which was within the calculated uncertainty of the measurements performed. As a result of their high homogeneity with respect to film thickness and elastic modulus, their low surface roughness and the good laser-acoustic signal quality, the thin films investigated appear to hold promise as standards for laser-acoustic measuring devices.
Various sources of errors in the standard procedure according to the ISO 14577 draft for the iteration of elastic modulus and hardness of solid materials, with reference to fused quartz with its particular and unique indentation response, are pointed out on the basis of practical examples. Similar objections exist towards the use of the S2FN– 1 parameter, where S is the stiffness and FN is the normal force. It is suggested to use unambiguous mechanic characterization (at least additionally) by quantitative analysis of the loading curves in nanoindentations. These exhibit a general dependence between normal force and (displacement)3/2, the proportionality constant k being a non-iterated nanoindentation coefficient with dimension [force/length3/2] and unit [μN/nm3/2] that depends on the indenter tip geometry (pyramidal or conospherical) and is a characteristic material’s property. The validity has been demonstrated for virtually all types of materials (metals, semimetals, oxides, salts, organic molecular crystals, polymers) independent of their different bonding states. Pressure-induced phase transitions are detected by kinks in the linear plots for the loading curves well in the nanoindentation region. Crystalline materials, such as strontium titanate, exhibit far-reaching anisotropic effects along lattice axes that would strongly forbid the reference to an amorphous standard. The nanoindentation coefficient characterizes the different polymorphs and the face anisotropies. Another unambiguous mechanical characterization is given by the full work of indentation (as differentiated from the less secure plastic work of indentation). It also characterizes the face anisotropies with high precision for a given indenter as it is found proportional to (normal force)3/2, which allows for useful extrapolations.
Multiple partial unloading indentation is a useful technique for depth-dependent nanoindentation yielding up to 20 hardness and modulus values of different depth with one single measurement. A comparison between multiple partial unloading indentation and conventional single unloading technique is presented. A representative selection of materials (sapphire, TiN, DLC, tool steel, Ti alloy and aluminium) has been tested and it is found that both methods give comparable results. Soft materials as Al or Ti show certain deviations of about + 11 ± 4% in hardness and + 3.1 ± 1.2% for the modulus. For all other materials, the difference is + 2.2 ± 1.0% for the hardness and –2.1 ± 2.2% for the modulus. Possible reasons for these small systematic deviations will be discussed.
A simple method for measuring the Young's modulus of thermoplastic polymers at the nanoscale is proposed. Nanoindentation tests have been carried out on three polymers (ABS, PET and PP) using the Berkovich indenter tip. The elasticity moduli obtained from the reduced moduli thanks to the slope of the initial part of the discharge curve were greater than the real moduli of these polymers. For this, a simple method is proposed to minimize the error made on the determination of the modulus which is based on the calculation of several stiffnesses between 10 and 98% of the maximum load on the experimental unloading curve. The results show that the calculated moduli at a load less than 50% of the maximum load were close to the macroscopic moduli and the effect of viscosity was minimized. In the end, the elastic Young's modulus obtained by our approach is in very good agreement with the result of the tensile tests.
Behavior of the mechanical properties of the Au thin film deposited by pulsed laser sputtering technique was studied using nanoindentation at different values of maximum indentation load. The investigation was supplemented by the measurement of the coating thickness and research of the surface relief using scanning electron microscopy. The microgeometrical parameters of the Au film were calculated using 3D optical microscopy. The behavior of the diagrams, demonstrating dependencies of indentation depth on the load applied, was analyzed using the observation of indentation imprints on the optical microscope.
View Video Presentation: https://doi.org/10.2514/6.2021-3491.vid Rib turbulated cooling has become a common mechanism of heat transfer augmentation in modern gas turbine engines. Increasing the heat transfer capabilities of these engines allows for higher inlet temperatures, thus improving the engine efficiency. Over the years, numerous experiments have been conducted to quantify the relative heat transfer performance of various rib designs. In addition, studies have indicated towards a good correlation between experimental results and computational fluid dynamical simulations for conjugate heat transfer (CHT) analysis for this cooling mechanism. Unfortunately, even though the turbulators provide better heat transfer performance, they also become sources of localized creep and stress concentrations. This, in turn, degrades the creep and fatigue performance of the turbine blades. There exists a scope for studying the interaction of fluid-flow/heat transfer and structural creep performance of such designs. This paper studies the structural effects of different rib designs using the one-way Fluid-Structure Interaction (FSI) method. The designs are the straight rib (90 to channel wall) and angled (45 to channel wall) configurations. The pitch-rib width (P/e) ratios of 5 and 10 are analyzed, with P/e 5 being the baseline. The channel aspect ratio is 2:1. In the baseline analysis, the maximum gas-path temperature is kept as 1650°C. The internal cooling air inlet velocity is adjusted for the baseline such that the wall temperature profile from the conjugate heat transfer analysis would result in a 3% creep strain in the structural analysis. The results show that by increasing the P/e ratio from 5 to 10, the gas-path temperature can be raised by nearly 60°C using the same internal cooling power for a straight rib model. The angled rib design is an improvement itself from the straight rib design, with the P/e 5 angled configuration having an increase of 133°C from its straight rib equivalent. However, when the P/e ratio of the angled rib design is raised to 10, there is only an increase of 33°C from the baseline. These results highlight the importance of analyzing and appreciating the interaction between the wall temperature due to cooling-air induced heat transfer and the notch effect of the rib geometries, with a special focus on creep and fatigue performance.
The deformation and structure stability of graphite cathodes are of importance for its service lifetime. The time dependence and coupling of deformation, elastoplastic property change and microstructure evolution of graphite cathodes were investigated under constant pressure at 940 °C. The deformations from early expansion transiting to the rapid and latter steady creep were found with increased hardness and modulus, in parallel with decreasing interplanar spacing of graphite (002) planes (d002) and increasing crystallite size along c-axis of graphite lattice (Lc). The inner fracture among (002) planes may be related to the kink bands structure in graphite. It is clarified that no Na–C intercalation compounds get involved in change of graphite lattice. The crystallite size along a-axis (La) can play an important role in structure stability with deformation-hardening effect on elastoplastic property and pinning effect on creep resistance. The deformation mechanism and the influencing factors on long-term structure stability of graphite cathode are also discussed in detail.
In this paper, the solid-solid diffusion reaction and growth kinetics of Ni-Zn system were investigated using diffusion couple technique. Three intermetallic compounds (IMCs), β1 (NiZn), γ (Ni2Zn11) and δ (Ni3Zn22) were observed at the diffusion zone with the annealing temperature range between 598 K and 673 K. The results indicate that the growth process of reaction zone was dominated by volume diffusion. And the growth constants, integrated diffusion coefficients, growth activation energies and diffusion activation energies of γ and δ were evaluated based on thickness of the phases, reaction temperatures and annealing times. The Young’s modulus and Vickers hardness of the three phases were evaluated from the displacement-loading curve by nanoindenter testing. The Young's modulus and hardness of the IMCs increased firstly and then decreased with the increasing of Zn concentration, where γ phase has the highest Young's modulus (183.3 GPa) and highest hardness (6.05 GPa) among the three phases. Finally, the bulk modulus (B), shear modulus (G), Young's modulus (E), and Poisson's ratio (v) of the Ni-Zn IMCs were calculated by the first-principles calculations. The tendency of calculated Young's modulus varying with the composition of Zn was consistent with that of experimental results.
Description
Concisely appraises the understanding and application of microindentation techniques in materials research, mechanical surface property testing, and quality control in metals, ceramics, and polymers. Examines the use of indentation methods in the study of intrinsic deformation properties, residual stress states, thin-film adhesion, and fracture properties.
The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.
Metrologia 28 (1991) 463. w2x European Commission Programme: Standards, Measurements and Testing (SMT) Determination of hardness and modulus of thin films and coatings by nanoindentation – INDICOAT, contract SMT4, CT98y2249, Project report to be published
- T J Bell
- A Bendeli
- J S Field
- M V Swain
- E G Thwaite
- W C Oliver
- G M Pharr
w1x T.J. Bell, A. Bendeli, J.S. Field, M.V. Swain, E.G. Thwaite, Metrologia 28 (1991) 463. w2x European Commission Programme: Standards, Measurements and Testing (SMT) Determination of hardness and modulus of thin films and coatings by nanoindentation – INDICOAT, contract SMT4, CT98y2249, Project report to be published 2001. w3x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564. w4x H. Buckle, Metallurgical Reviews 4, Institute of Metals, London, ¨ 1959, p. 49. w5x P. Haasen, Physikalische Metallkunde, Akademie-Verlag, Berlin, 1985. w6x G.E. Schulze, Metallphysik, Akademie-Verlag, Berlin, 1974. w7x H.M. Pollock, D. Maugis, M. Barquins, in: P.J. Blau, B.R. Lawn (Eds.), Microindentation Techniques in Materials Science and Engineering, ASTM STP 889, Philadelphia, 1986, pp. 47–71.
- T J Bell
- A Bendeli
- J S Field
- M V Swain
- E G Thwaite
T.J. Bell, A. Bendeli, J.S. Field, M.V. Swain, E.G. Thwaite,
Metrologia 28 (1991) 463.
- W C Oliver
- G M Pharr
W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564.
- H Buckle
H. Buckle, Metallurgical Reviews 4, Institute of Metals, London,
1959, p. 49.