Time-dependent Plastic Deformation Research Articles

Assessment of mineral compositions on geo-mechanical time dependent plastic creep deformation

Understanding rock mechanical time-dependent plastic deformation enables the researchers to accurately predict rock responses during loading and unloading. This research focuses on the geomechanical aspects of hydrogen storage, particularly rock resistance to creep deformation under varying stresses and pressures. Modelling creep deformation in underground storage mediums has been overlooked and requires further consideration, as it is a critical, cyclical, time-dependent phenomenon essential for hydrogen containment. The study's novelty is demonstrated in its focus on geomechanical properties of rock minerals, providing insights that aid in site-selection criteria for hydrogen storage A creep deformation model with varying mineral compositions is used to assess creep deformation strain. In homogenous cases, calcite showed the highest resistance to creep deformation after three loading cycles, primarily due to its high Young's Modulus. As for the heterogenous cases, the results indicated that the mixture of calcite and quartz was the most creep-resistant rock composition. In terms of rock types, basalt samples demonstrated the highest resistance to creep deformation, while siltstone exhibited the highest susceptibility to deformation. It was observed that as the number of cycles increase, the rock mechanical stability decreases, hence optimizing the number of cycles is a must to ensure hydrogen geo-containment.

Rate of change of J‐integral in creep‐fatigue condition

AbstractThe operational conditions in next generation power plants and other high temperature applications such as turbine blades in jet engines demand the component to perform under extreme conditions where metallic materials show time dependent deformation under cyclic loading conditions. Under creep‐fatigue loading condition, the crack tip is exposed to both time dependent and independent plastic deformation. Conventional crack characterizing parameters such as (C ) has shown good correlation with dominant damage‐based crack velocity, (d /d ) . However, the true definition or prediction of crack driving forces under such scenario are vague due to limited theoretical validity of the conventional crack tip characterizing parameters, such as or C . In this work, the concept of configurational forces are applied for the first time to understand the creep‐fatigue crack growth behavior. The crack growth is simulated using node‐release technique and the configurational forces are calculated using post processing the finite element results for calculation of d /d .

Nanoindentation creep behavior of diverse microstructures in a pre-strained interstitial high-entropy alloy by high-throughput mapping

Time-dependent plastic deformation, also known as creep, can occur in high-melting-point materials at room temperature when subjected to submicron plastic contact (e.g., components in micro-electronic mechanical systems) due to the extremely high stress conditions. Previous investigations of creep behavior at submicron scale mainly focus on uniform microstructures, whereas recently developed high-performance structural materials usually show complex microstructural heterogeneities. Here, we demonstrate a high-throughput nanoindentation approach to unveil the creep behavior of locally diverse microstructures, via a case study on an interstitial high-entropy alloy (iHEA). The prototype iHEA specimen was firstly pre-strained by severe cold-rolling to achieve diverse microstructure features including dense dislocations, nanotwins and nanograins. Nanoindentation mapping with 144 indents is conducted to collect creep data from all types of diverse microstructures, followed by systematical calculations based on power-law analysis. Then intuitive contour maps of nanohardness (H), strain rate (ε˙) and stress exponent (n) are attained. The individual creep mechanism of each microstructure variant is evaluated by correlating local microstructure features with corresponding creep responses from these contour maps. With the increase of n value for different sample regions, the ε˙ value inversely reduces and the corresponding dominant creep mechanism gradually converts from diffusion-mediated mode to dislocation-controlled one. The presence of nanograins and nanotwins significantly hinders dislocation interactions and promotes stress-induced diffusion. This work verifies that nanoindentation creep behavior is highly correlated with local microstructure features, and the mapping approach is feasible for evaluating creep-resistance of locally diverse microstructures under extremely high-stress conditions.

Defects controlled rejuvenation in the Zr47.5Cu47.5Al5 metallic glass

The rejuvenation which is the reverse of the physical aging is expected to solve the problems of brittleness and physical aging of MGs. Although numerous studies try to reveal the origin of deep cryogenic treatment (DCT) induced rejuvenation, the origin of rejuvenation is now somewhat controversial. Here, thermal cycling on the time-dependent plastic deformation and structure dynamic of a Zr47.5Cu47.5Al5 metallic glass (MG) with different states is investigated. The results show that rejuvenation or improvement of creep deformation is ascribed to the activation of STZ volume which is controlled by total defects number in Zr47.5Cu47.5Al5 MG. Moreover, neutron total scattering reveals that the thermal cycling can induce the change of medium-range order (MRO), which is independent with the initial states of the samples.

The loading speed facilitating stress relaxation behaviors of surface-modified silicon: a molecular dynamics study.

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.

Enhancement in creep resistance of pristine polystyrene with incorporation of exfoliated 2D graphene nanosheets at low filler loading

Determination of the reliability and durability of polymers in structural applications is highly dependent on the resistance to time-dependent plastic deformation. In this study, creep behaviour and enhancement in creep resistance of polystyrene-graphene nanocomposites is investigated at low filler loading. Herein, 2D material (graphene) is synthesised by the liquid-phase exfoliation method ( LPE) using the tetrahydrofuran ( THF) solvent via batch sonication. Samples are characterised by Scanning Electron Microscopy ( SEM) for morphology analysis and X-rays Diffraction ( XRD) for identification of polystyrene-graphene (PS-G) peaks in nanocomposites. Additionally, Atomic Force Microscopy ( AFM) is employed to quantify sheet’s thickness and Optical Microscopy ( OM) to corroborate the dispersion of 2D sheets. The creep resistance of PS-G nanocomposites is measured at room temperature (25°C) by incorporating 2D sheets of flake length ∼359 μm with 0.1, 0.3, 0.5, 0.7 and 0.9 wt.%. A significant enhancement in the time to withstand constant creep load (1 N) is observed. The creep resistance of the samples exhibits a maximum increase of 79%, 258.24%, 647.25%, 417.58% and 760.44%, respectively, compared to pristine polystyrene. This increase in creep resistance resulted from intense interfacial contact between polymer chains and filler accompanied by adequate scattering/dispersion in the polymer matrix.

Revealing thickness dependence of hardness, strain rate sensitivity, and creep resistance of nano-crystalline magnesium/titanium multilayers by nanoindentation

The size effect on mechanical properties of hcp/hcp multilayer has been short of understanding hitherto. In this study, we prepared Magnesium/Titanium (Mg/Ti) multilayers with various individual layer thicknesses (h = 50, 100, 150, 200 nm) by magnetron sputtering. Relying on nanoindentation, hardness and elastic modulus were little changed for the multilayers with h of 50 ∼ 150 nm, while they were evidently lower when h increased to 200 nm. The determined strain rate sensitivities were 0.029, 0.032, 0.035, and 0.062 for the samples with h = 50, 100, 150, 200 nm, respectively. According to evolution of grain size, it suggests that Hall-Petch law dominates the strengthen effect of this hcp/hcp multilayers, rather than blocking effect of interface and decrease of dislocation content by reducing individual layer thickness. On the other hand, creep resistance was gradually promoted as reducing h. It indicates that interface and dislocation content could be important for the time-dependent plastic deformation. The room-temperature creep mechanism was discussed based on the strain rate sensitivity of steady-state creep flow. It indicates that dislocation glide could be suppressed and grain boundary glide, dislocation climb, and even interface glade could be plausible when h decreased to 50 nm.

Ambient-temperature time-dependent deformation of cast and additive manufactured Al-Cu-Mg-Ag-TiB2 (A205)

A dual-stage indentation test at ambient temperature including a constant indentation load rate followed by a constant indentation load-hold segment was employed to assess the time-dependent plastic deformation of cast and additive manufactured Al-Cu-Mg-Ag-TiB2 alloys in as-fabricated and T7 conditions at room temperature. Optical microscopy, scanning electron microscopy, electron backscattered diffraction, and transmission electron microscopy techniques were used to study the microstructure of the samples and to correlate the microstructure with the creep properties. That is, the indentation load/displacement/time data from depth-sensing indentation creep were combined with the advanced microstructural assessments to analyze the controlling mechanisms of creep in as-cast, as-built, and T7 samples. Expectedly, the microstructure of samples manufactured by different methods was substantially different in terms of the grain size and the distribution of TiB2 particles. The θ’’, θ’ and Ω phase were formed in all heat-treated samples; however, the density of Ω phase was higher in the cast-T7 samples. Distinct microstructure and precipitation density resulted in different indentation-derived properties, both cast and AM samples at T7 condition showed enhanced creep resistance compared to their as-manufactured counterparts. The main controlling mechanism of creep deformation was found to be dislocation creep based on the indentation-derived creep stress exponent values.

Time-dependent deformation mechanism of metallic glass in different structural states at different temperatures

There is limited understanding of time-dependent plastic deformation behavior of amorphous alloys as a function of their structural state. Here, the creep behavior of Zr52.5Ti5Cu17.9Ni14.6Al10 bulk metallic glass was investigated in its as-cast and relaxed states using nanoindentation technique with applied load in the range of 500–1500 mN and temperature in the range of room temperature to 573 K. The creep displacement increased with increasing load and temperature since the creep process is thermally activated and diffusion rate is enhanced at elevated temperature and higher load. The creep strain rate sensitivity, which is a measure of the creep mechanism, increased with increase in temperature and decrease in applied load. This was attributed to the transition from localized to more homogeneous creep. Reduction in free volume for the relaxed alloy resulted in lower creep displacement and larger strain rate sensitivity compared to its as-cast counterpart. The results suggest that diffusion-based deformation dominate at higher temperature in contrast to shear transformation mediated plasticity at room temperature. The volume of shear transformation zone for the metallic glass was calculated using cooperative shearing model and correlated with the structural state for fundamental insights into the deformation process as a function of temperature and load.

Curve Fitting for Damage Evolution through Regression Analysis for the Kachanov-Rabotnov Model to the Norton-Bailey Creep Law of SS-316 Material.

In a number of circumstances, the Kachanov–Rabotnov isotropic creep damage constitutive model has been utilized to assess the creep deformation of high-temperature components. Secondary creep behavior is usually studied using analytical methods, whereas tertiary creep damage constants are determined by the combination of experiments and numerical optimization. To obtain the tertiary creep damage constants, these methods necessitate extensive computational effort and time to determine the tertiary creep damage constants. In this study, a curve-fitting technique was proposed for applying the Kachanov–Rabotnov model into the built-in Norton–Bailey model in Abaqus. It extrapolates the creep behaviour by fitting the Kachanov–Rabotnov model to the limited creep data obtained from the Omega-Norton–Bailey regression model and then simulates beyond the available data points. Through the Omega creep model, several creep strain rates for SS-316 were calculated using API-579/ASME FFS-1 standards. These are dependent on the type of the material, the flow stress, and the temperature. In the present work, FEA creep assessment was carried out on the SS-316 dog bone specimen, which was used as a material coupon to forecast time-dependent permanent plastic deformation as well as creep behavior at elevated temperatures and under uniform stress. The model was validated with the help of published experimental creep test data, and data optimization for sensitivity study was conducted by applying response surface methodology (RSM) and ANOVA techniques. The results showed that the specimen underwent secondary creep deformation for most of the analysis period. Hence, the method is useful in predicting the complete creep behavior of the material and in generating a creep curve.

Creep Parameters Determination by Omega Model to Norton Bailey Law by Regression Analysis for Austenitic Steel SS-304

In the material’s creep failure analysis, the difficulty of assessing the applied thermo-mechanical boundary conditions makes it critically important. Numerous creep laws have been established over the years to predict the creep deformation, damage evolution and rupture of the materials subjected to creep phenomena. The omega model developed by the American Petroleum Institute and Material Properties Council is one of the most commonly used creep material models for numerical analysis over the years. It is good in defining the fitness of mechanical equipment for service engineering evaluation to ensure the reliable service life of the equipment. The Omega model, however, is not readily accessible and specifically incorporated for creep evaluation in FEA software codes and creep data is always scarce for the complete analysis. Therefore, extrapolation of creep behavior was performed by fitting various types of creep models with a limited amount of creep data and then simulating them, beyond the available data points. In conjunction with the Norton Bailey model, based on API-579/ASME FFS-1 standards, a curve fitting technique was employed called regression analysis. From the MPC project omega model, different creep strain rates were obtained based on material, stress and temperature-dependent data. In addition, as the strain rates increased exponentially with the increase in stresses, regression analysis was used for predicting creep parameters, that can curve fit the data into the embedded Norton Bailey model. The uncertainties in extrapolations and material constants has highlighted to necessitate conservative safety factors for design requirement. In this case study, FEA creep assessment was performed on the material SS-304 dog bone specimen, considered as a material coupon to predict time-dependent plastic deformation along with creep behavior at elevated temperatures and under constant stresses. The results indicated that the specimen underwent secondary creep deformation for most of the period.

Indentation-derived creep response of cast and laser powder bed fused AlSi10Mg alloy: Air temperature

Compared with time-consuming conventional uniaxial tensile/compressive creep experiments, depth-sensing indentation testing is considered a reliable, and convenient testing technique to assess the time-dependent plastic deformation of materials in a reasonable time scale. In the present study, we report the ambient (room) temperature indentation creep properties of additively manufactured (i.e., laser-powder bed fused) and cast AlSi10Mg alloy at as-fabricated and different post-fabrication heat treatment states. The indentation creep testing parameters (i.e., dwell time, peak indentation load, and indenter shape) were optimized to adequately represent the creep response (time-displacement) variations for different material conditions. To this end, dual-stage, constant loading rate followed by constant-load holding, pyramidal indentation experiments were performed at a loading rate of 10 mN/s, a peak load of 200 mN, and a dwell time of 400 s. Besides, electron backscattered diffraction was performed to evaluate the manufacturing process (selective laser melted versus cast)/ post-fabrication heat treatment/ texture/ creep properties relationships for the studied AlSi10Mg alloy. Also, the indentation hardness, indentation strain rate sensitivity, indentation creep exponent, and activation volume were analyzed to study and confirm the mechanism of indentation creep. The calculated high values of creep stress exponents (i.e., >10) are attributed to dislocation-reinforcing particle interaction as the controlling mechanism of the creep which agrees with this assumption that AlSi10Mg is indeed an in-situ metal matrix composite with eutectic silicon as the reinforcing particles.

Effect of thermal creep on the behavior of flush end-plate connection under transient conditions of fire

The properties of steel material become dependent on the temperature and duration of heating during a fire event. Thermal creep strain is a time-dependent plastic deformation that becomes significant under constant load and high temperatures. The goal of this study is to understand the thermal creep effect on the behavior of a beam-column flush end-plate connection subjected to transient fire conditions. Finite element models were developed and validated against experimental work available in the literature. Parametric studies were conducted to study the overall response of the connection with and without the explicit consideration of thermal creep. The parameters included are heating/cooling rate, beam length, load ratio, plate thickness, bolt size, column axial compressive force, and creep effect in bolts. The thermal creep effect decreases the beam thermal induced compressive forces and simultaneously causes larger mid-span deflections at high heating temperatures. At slow heating rates, the effect of thermal creep can significantly reduce the compressive force at the end of heating while generating high tensile forces at the end of cooling. Neglecting the thermal creep in the analysis may cause inaccurate prediction of the tying forces and rotational demand of the connection.

Micromechanics and indentation creep of magnesium carbon nanotube nanocomposites: 298 K–573 K

In the present study, the time-dependent plastic deformation (creep) response of magnesium/carbon nanotube (CNT) nanocomposites containing 0.25, 0.5, and 0.75 vol% of CNTs is investigated through instrumented indentation tests against monolithic pure magnesium. The Mg-CNT nanocomposites were synthesized via powder metallurgy coupled with microwave sintering followed by hot extrusion. Indentation creep tests were performed at 298, 373, 473, and 573 K with a cubic boron nitride Berkovich indenter. Creep tests are dual-stage, i.e., all tests involve loading to a prescribed peak load (50 mN), holding this peak load constant for a set dwell period (120 s), and finally unloading. Three load rates of 0.5, 5, and 50 mN/s were tested. Results are explained through hardness, microstructure, and CNT volume fraction in each sample. Mg reinforced with 0.25–0.5 vol% CNTs exhibit the best creep resistance. At the ambient temperature of 298 K, dislocation creep is the dominant creep mechanism. At elevated temperatures, multiple creep mechanisms are identified. However, diffusion creep mechanisms are expected to prevail when temperatures exceed 573 K. These materials are promising candidates for aerospace, automotive, military, and many other industrial applications. To this end, the findings of this study can be used for material selection in these industries. This work may also be used as a baseline for future high-temperature nanoindentation creep studies on other nanocomposites.

Revealing the Plastic Mode of Time-Dependent Deformation of a LiTaO3 Single Crystal by Nanoindentation.

Recently, instrumental nanoindentation has been widely applied to detect time-dependent plastic deformation or creep behavior in numerous materials, particularly thin films and heterogeneous materials. However, deformation mechanism at nanoindentation holding stage has not been well revealed hitherto. In the current work, nanoindentation holding tests with high loads were performed on a brittle LiTaO3 single crystal. The surface morphologies of residual impressions with various holding times were investigated. It was indicated that generation of secondary cracks and propagation of both main and secondary cracks were the dominating mechanism for time-dependent plastic deformation at the initial holding stage, and the density and length of cracks were invariable at the steady-state holding stage, which suggested a nonlocalized plastic deformation beneath the indenter. It could be concluded that time-dependent plastic deformation of brittle ceramic under nanoindentation is composed of instant cracking as the continuation of loading sequence and homogeneous creep flow by high shear-compression stress at room temperature.

Investigation on the microstructural and mechanical properties of a Polytetrafluoroethylene thin film by radio frequency magnetron sputtering

Relying on magnetron sputtering technology, a Polytetrafluoroethylene (PTFE) thin film was deposited on silicon substrate. We systematically investigated the atomic bonding, growth mode, and surface morphology of the as-prepared PTFE thin films by different nominal deposition power with different thicknesses. The mechanical properties including elastic modulus, hardness, strain rate sensitivity and creep resistance were carefully detected in a thick (1270 nm) PTFE film by an instrumental nanoindentation. In comparison to its bulk counterpart, PTFE thin film owns much higher elastic modulus and stronger resistances to the plastic and time-dependent plastic deformation. The results of its chemistry and mechanical properties show the films are hydrophobic and of higher mechanical strength. The enhanced mechanical properties of PTFE thin film could be intrinsically tied to its complex fluorocarbon groups which generated from the breakage and re-organization of C-F chains during sputtering process. The creep resistance of PTFE thin film was approximately two times stronger than the bulk PTFE.

Time-Resolved Digital Image Correlation in the Scanning Electron Microscope for Analysis of Time-Dependent Mechanisms

Background: Advancements in the Digitial Image Correlation (DIC) technique over the past decade have greatly improved spatial resolution. However, many processes, such as plastic deformation, have a temporal component spanning from fractions of a second to minutes that has not yet been addressed in detail, particularly for DIC conducted in-situ in the scanning electron microscope (SEM). Objective: To develop a methodology for conducting time-resolved digital image correlation in the SEM for analysis of time-dependent mechanical deformation phenomena. Methods: Microscope and electron beam scanning parameters that influence the rate at which time-resolved DIC information is mapped are experimentally investigated, providing a guide for use over a range of timescales and resolutions. Results: Time-resolved DIC imaging is demonstrated on a Ti-7Al alloy, where slip band propagation is resolved with imaging dwell times of seconds. The limits of strain resolution and strain collection speeds are analyzed. Conclusions: The new developed methodology can be applied to a wide range of materials loaded in-situ to quantify time-dependent plastic deformation phenomena.

High-Temperature Nano-Indentation Creep of Reduced Activity High Entropy Alloys Based on 4-5-6 Elemental Palette.

There is a strong demand for materials with inherently high creep resistance in the harsh environment of next-generation nuclear reactors. High entropy alloys have drawn intense attention in this regard due to their excellent elevated temperature properties and irradiation resistance. Here, the time-dependent plastic deformation behavior of two refractory high entropy alloys was investigated, namely HfTaTiVZr and TaTiVWZr. These alloys are based on reduced activity metals from the 4-5-6 elemental palette that would allow easy post-service recycling after use in nuclear reactors. The creep behavior was investigated using nano-indentation over the temperature range of 298 K to 573 K under static and dynamic loads up to 5 N. Creep stress exponent for HfTaTiVZr and TaTiVWZr was found to be in the range of 20–140 and the activation volume was ~16–20b3, indicating dislocation dominated mechanism. The stress exponent increased with increasing indentation depth due to a higher density of dislocations and their entanglement at larger depth and the exponent decreased with increasing temperature due to thermally activated dislocations. Smaller creep displacement and higher activation energy for the two high entropy alloys indicate superior creep resistance compared to refractory pure metals like tungsten.

High-Temperature Nano-Indentation Creep Behavior of Multi-Principal Element Alloys under Static and Dynamic Loads

Creep is a serious concern reducing the efficiency and service life of components in various structural applications. Multi-principal element alloys are attractive as a new generation of structural materials due to their desirable elevated temperature mechanical properties. Here, time-dependent plastic deformation behavior of two multi-principal element alloys, CoCrNi and CoCrFeMnNi, was investigated using nano-indentation technique over the temperature range of 298 K to 573 K under static and dynamic loads with applied load up to 1000 mN. The stress exponent was determined to be in the range of 15 to 135 indicating dislocation creep as the dominant mechanism. The activation volume was ~25b3 for both CoCrNi and CoCrFeMnNi alloys, which is in the range indicating dislocation glide. The stress exponent increased with increasing indentation depth due to higher density and entanglement of dislocations, and decreased with increasing temperature owing to thermally activated dislocations. The results for the two multi-principal element alloys were compared with pure Ni. CoCrNi showed the smallest creep displacement and the highest activation energy among the three systems studied indicating its superior creep resistance.

Indentation-based characterization of creep and hardness behavior of magnesium carbon nanotube nanocomposites at room temperature

The time-dependent plastic deformation response of magnesium/carbon nanotube (CNT) nanocomposites containing 0.25, 0.5, and 0.75 vol% of carbon nanotubes is investigated through depth nanoindentation tests against monolithic pure magnesium in the present study. The Mg-CNT nanocomposite materials were successfully synthesized via a powder metallurgy technique coupled with microwave sintering followed by hot extrusion to produce 8-mm diameter, long solid bars. All depth-sensing indentation creep tests were conducted at ambient (room) temperature employing a diamond Berkovich pyramidal indenter. These tests are dual-stage, i.e., loading to a prescribed peak load of 50 mN, holding the peak load constant for a dwell period of 500 s, and finally unloading. Various strain rates of 0.01, 0.1, 1, and 10 s−1 were performed to assess the effects of strain rate and dwell time on the ambient temperature creep response of the Mg-CNT nanocomposites. The outcomes of these tests are explained through material hardness, microstructure, the extent of CNT content in each material, and strain rate sensitivity. Upon analyzing the nanoindentation creep tests, the dominant creep mechanism at room temperature was found to be a dislocation creep mechanism. It is also found that CNTs increase the creep resistance of magnesium. Findings of this study can be used as a starting point for a high-temperature creep study on Mg-CNT nanocomposites. This paper is a continued study from our group on time-dependent plastic deformation of Mg nanocomposites (i.e., see Haghshenas et al., Journal of Composite Materials, https://doi.org/10.1177/0021998318808358 ). The short-term goal is to provide a compressive picture of the controlling creep mechanisms and their dependency upon, time, temperature, strain rate, volume fraction of the nanoparticles, and the type of the nanoparticles. Mg, in general, is a notorious material for high-temperature application; therefore, the long-term objective is to propose Mg nanocomposite as reliable replacements for Mg when lightweight and creep resistance are needed. However, to be able to confidently suggest such a replacement detailed understanding on the controlling phenomena, mention as short-term goals, are required.