Creep Deformation Research Articles

New insights into the hardening mechanism of calcium silicate hydrates under creep deformation: A reactive molecular simulation study

Understanding the time-dependent behaviour of calcium silicate hydrates (C-S-H) under stresses is crucial for unraveling the microscopic creep behavior of concrete and its consequences on the evolution of nanostructure of C-S-H. In this study, the structural evolution of C-S-H nanostructure under stress was investigated using reactive molecular dynamics and stress perturbation technique. Under sustained stress, C-S-H nanostructure undergoes a relaxation process leading to a creep deformation and transitioning the system towards a more energetically stable state. The process was comprehensively examined under shear stress through a detailed analysis of the system's potential energy. A hardening phenomenon was observed within calcium silicate layers throughout this relaxation process, categorizing in three distinct stages. in Stage I, structural reorganization occurred in the silicate chains, progressing towards a stable state by reducing non-bonded interactions. The calcium-oxygen ionic bonds within the intralayer were strengthened in Stage II, leading to a decrease in bonding energy. Finally, the interface between calcium silicate layers and the interlayer contributed to overall structural stability in StageIII.

Development of Binderless Graphite Compact for Bipolar Plate Production

Bipolar plates account for almost 29% of the fuel cell stack costs and hence cost-effective manufacturing methods for making the bipolar plates are of paramount importance. Current manufacturing technologies for graphite bipolar plates require consolidation of graphite precursor materials using compression or injection molding followed by high temperature treatment for baking and graphitization. In contrast, in this investigation, we demonstrate direct consolidation of graphite powders without the use of any coal, petroleum or polymer binders resulting in significant reduction of time during compression molding as well as elimination of the need for additional heat treatment. Graphite particles were electrolessly coated with copper particles and subject to uniaxial compression at 100°C to produce a highly dense compact with relative density of ~ 98%, The process resulted in improving the flexural strength of the compact by almost ~50%. TEM investigation of the graphite particle interfaces revealed that copper undergoes creep deformation that aids in strengthening the compacts. The paper will describe the underlying mechanisms for the binderless production of graphite compacts which could be potentially useful for energy and cost-effective production of bipolar plates for fuel cells and flow batteries.

Prediction method of long-term creep deformation of mobile phone resin lens module in a harsh temp environment

In recent years, the replacement cycle of digital products such as mobile phones in the market has significantly increased, and the accurate prediction of attenuation under long-term usage conditions of the lens module, storage, and other components has become important. The vast majority of mobile phone lens modules are processed from optical resins, and the degradation of their imaging performance is mainly caused by assembly deformation and long-term creep deformation after a high-temperature reliability test. Therefore, there is an urgent need for a reliable model to describe the long-term creep deformation of the mobile phone resin lens module in a harsh temperature environment. This study proposed a modified derivation method for the parameters of the Maxwell constitutive model to predict the long-term creep deformation of the mobile phone resin lens module in a high-temperature environment. The fitting accuracy of the modified generalized Maxwell model and the time-hardening model were compared through uniaxial compression creep experiments. Long-term creep simulations and experiments were conducted on the mobile phone resin lens module; the deformation law of each component of the mobile phone resin lens module was identified; and the creep deformation mechanism was elucidated. The result shows that the modified generalized Maxwell model has much higher accuracy than the time-hardening model in predicting the long-term creep deformation of different resin materials. When considering the influence of the creep phenomenon, the simulation result matches well with the experimental result, and the high-temperature creep mechanism of the mobile phone resin lens module was clarified. In addition, it was found that the maximum deformation of the lens occurred at the lens with the largest size, which was 2.1 µm, and the position with the largest surface deviation was at the edge of the lens. The prediction method proposed in this study can provide guidance and correction suggestions for the structural design of a mobile phone resin lens module and the rationality of optical design; thus, the imaging accuracy of lens modules will be guaranteed to the greatest extent possible.

Nanoindentation creep: The impact of water and artificial saliva storage on milled and 3D-printed resin composites.

This study evaluated the effects of artificial saliva and distilled water on the nanoindentation creep of different 3D-printed and milled CAD-CAM resin composites. Disk-shaped specimens were subtractively fabricated from polymer-infiltrated ceramic network (EN) and reinforced resin composite (B) and additively from resin composite (C) and hybrid resin composite (VS) using digital light processing (DLP). Specimens from each material were divided into two groups according to their storage conditions (artificial saliva or distilled water for 3 months). Creep was analyzed by nanoindentation testing. Statistical analysis was done using two-way ANOVA, one-way ANOVA, Bonferroni post hoc tests, and independent t-test (α = 0.05). The main effects of material and storage conditions, and their interaction were statistically significant on nanoindentation (p<0.001). Storage condition had the greatest influence (partial eta squared ηP 2 =0.370), followed by the material (ηP 2 = 0.359), and the interaction (ηP 2 = 0.329). The nanoindentation creep depths after artificial saliva storage ranged from 0.34 to 0.51µm and from 0.50 to 0.87µm after distilled water storage. One of the additively manufactured groups had higher nanoindentation creep depths in both storage conditions. All specimens showed comparable performance after artificial saliva storage, but increased nanoindentation creep after distilled water storage for 3 months. The subtractive CAD-CAM blocks showed superior dimensional stability in terms of nanoindentation creep depths in both storage conditions. Additively manufactured composite resins had lower dimensional stability than one of the subtractively manufactured composites, which was demonstrated as having higher creep deformation and maximum recovery. However, after artificial saliva storage, one of the additively manufactured resins had dimensional stability similar to that of subtractively manufactured.

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

Microstructural characterization and creep deformation response of an Inconel-600/Inconel-625 welded joint obtained by oscillating GMAW process.

This investigation presents the microstructural characterization and creep failure mechanism of a dissimilar weld (DW) of Inconel 600 (IN600) and Inconel 625 (IN625) at a temperature of 675 °C and different stress levels. Optical microscopy (OM), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and Vickers microhardness test were used to characterize the welded joint, the creep rupture features, and microstructural characteristics of the DW respectively. The experimental results show that the crept samples consistently broke on the base material of the IN600 side and that the failure was mainly controlled by the plastic deformation of coarser austenitic grains, dynamic recrystallization, and the coalescence and growth of microcracks that resulted from the evolution of the Cr-rich carbides along the grain boundaries that conducted to a transgranular fracture mode.

Scale and suction effects on compressibility and time-dependent deformation of mine waste rock material

Designing high mine waste rock piles for long-term behavior requires material mechanical characterization over a large range of stresses and variable environmental conditions. However, representative coarse samples cannot be handled by standard testing devices and the common approach is to test small-scaled samples at the laboratory, which might be affected by particle size effects when compared to the field material. Several reported results indicate that coarser samples present higher amount of particle crushing than small-scaled samples, thus lower dilatancy and higher compressibility. However, specific studies of size effects on time-dependent deformation are lacking. The aim of this paper is to identify the effects of particle size and suction on stress-deformation mechanism of partially saturated mine waste rock. Oedometric compression tests on two parallel graded samples are presented: the gravelly fraction (dmax=50 mm) and the sandy fraction (dmax=2.36 mm). Each stress increment triggers « instantaneous » and delayed strains. The results reveal the combined effects of particle size and humidity on the mechanical behavior. Coarser samples exhibit higher total compressibility and creep deformation, which also increases with the material humidity. The results give empirical support for the development of scaling laws and suggest that total deformation can be decoupled considering a suction dependent index for creep deformation.

Significant reduction of anisotropy in stress relaxation aging and mechanical properties improvement for 2195 Al-Cu-Li alloy subjected to plastic loading

Although the plastic loading can enhance creep deformation and yield strength, the anisotropic Stress Relaxation Aging (SRA) behavior and mechanism under plastic loading remain unclear, which presents a significant challenge in accurately shaping aluminum alloy panels. In this study, the SRA behavior of 2195-T4 Al-Cu-Li alloys were thoroughly studied under initial loading stresses within the elastic (210/250 MPa) and plastic (380/420 MPa) ranges at 180 ℃ by stress relaxation and tensile tests as well as microstructure characterization. The findings reveal that compared with those under elastic loadings, in-plane anisotropy (IPA) values of the stress relaxation amount, yield strength and fracture elongation under plastic loadings are reduced by 60%-80%, 70%-90% and 72%-89%, respectively. Similarly, IPA values of precipitate size in grains and Precipitation-Free Zones (PFZ) width at grain boundaries under plastic loading decrease by 31.4% and 94.4% respectively. These results indicate plastic loading significantly weakens the anisotropic SRA behavior, owing to numerous uniformly distributed fine T1 phases and small IPA values of both T1 precipitates size and PFZ width in various loading directions. Compared with those of elastic loading-aged alloys, yield strength of plastic loading-aged alloys shows high strength-ductility because of the combined effect of closely dispersed fine T1 precipitates, narrowed PFZ and numerous sheared and rotated T1 phases at different locations during tensile process. The uniformly distributed larger Kernel Average Misorientation (KAM) and Schmidt factor values of the plastic loading-aged alloy, as well as the cross-slip generated, also help to enhance the strength and ductility of the alloy.

Significant creep-strength improvement in modified 9Cr-1Mo steel via microstructural control through laser powder bed fusion

Modified 9Cr-1Mo steel was manufactured using laser powder bed fusion (LPBF). The as-built LPBF-sample microstructure comprised columnar δ-ferrite grains and fine martensite grains. The δ-ferrite was a unique phase that formed under the significantly rapid LPBF-induced solidification. Creep testing was performed for the LPBF sample at 923 K for up to 10,000 h. The LPBF-sample time-to-rupture and minimum creep rate were at least 10 times longer and 100 times smaller, respectively, than those of conventional modified 9Cr-1Mo steels at 923 K under 100 MPa. Microstructural characterization of the creep-ruptured samples revealed that creep deformation preferentially occurred in the martensite. Thus, the δ-ferrite contributed significantly to the enhanced creep strength. The intrinsic creep resistance of the δ-ferrite phase exceeded that of the martensite. The microstructural stability of the δ-ferrite grains (attributed to dense MX-phase precipitation at the grain boundary) was a likely strengthening factor. Overall, the modified 9Cr-1Mo steel creep strength was successfully improved via unique microstructural control through LPBF. This achievement is expected to extend LPBF application as a novel microstructural control process for steels and alloys, avoiding the diffusional transformation kinetics that occur in conventional heat-treatment processes.

Microstructure Evolution and Creep Properties of AZ61 Magnesium Matrix Composites Reinforced with Bimodal-Sized SiC Particles

In the scope of this exploration, AZ61 magnesium matrix composites fortified with bimodal size SiC particles were synthesized using ultrasonic-assisted mixing in the semi-solid state, which exhibited optimal grain refinement and exceptional creep resistance. We examined the impact of bimodal SiC particles on the microscopic structure and creep deformation of the resulting composites. Our findings indicated that incorporating bimodal SiC particles resulted in the refinement of the matrix grains and alteration of the morphology of the Mg17Al12 phase. Furthermore, the micron-sized SiC particles exhibited a typical necklace-like particle distribution around the grain boundaries of the bimodal SiC particle/AZ61 composites, while the nano-sized SiC particles were mainly located around the micron-sized particles. As the volumetric percentage of micron SiC particles increased, the quantity of nano-sized particle clusters diminished noticeably. Creep analysis at 200 °C and 50 MPa revealed that the creep life of M−6+N−1 composite was increased by 111.9% compared to the AZ61 alloy. Additionally, the M−6+N−1 combination exhibited a significantly lower steady-state creep rate compared to the matrix alloy, with a reduction of approximately 11 times. These results indicate that the bimodal SiC particle/AZ61 composites have superior creep resistance, which is a consequence of the grain refinement and grain boundary pinning effects of SiC particles.

Description of step loads at high temperature creep of metallic materials

Abstract In metallic materials under high-temperature creep conditions, the damage evolution occurs. To describe it, Kachanov and Rabotnov proposed the concept of damage. In this paper, the damage parameter is defined as the relative change in material density, serving as an integral measure of damage. By incorporating the damage parameter and the mass conservation law, are we formulated interrelated kinetic equations for rate of creep deformation and the damage parameter. The case of variable loads is crucial both theoretically and practically, as most structural components typically operate under such conditions. Therefore, solutions of considered equations are derived for the case of two-stage loading. The received solutions and experimental results on the creep of titanium alloy under variable loads at 500°C were compared. There is a good agreement between the theoretical results and experimental data.

Co-, Ni- and Fe-rich grain-boundary phases enhance creep resistance in θ′-strengthened Al-Cu alloys

Microstructural evolution and creep response were investigated in the cast Al-5.0Cu-0.3Mn-0.2Zr (wt.%) alloy with and without addition of slow-diffusing, intermetallic-forming elements Fe, Ni, or Co. Baseline Al-5.0Cu-0.3Mn-0.2Zr alloy exhibits high creep resistance at 300 °C, up to ∼75 MPa, which is attributed to high-aspect-ratio, intragranular θ′-Al2Cu precipitates that effectively suppress dislocation climb. However, θ′-Al2Cu precipitate-free zones form along grain boundaries upon heat treatment, whose extent is amplified during subsequent creep. Such weak regions experience dislocation creep, leading to strain localization and acceleration of grain-boundary sliding. Adding Ni and Co, individually or in combination, leads to the formation of grain-boundary precipitates (Al9Co2, Al3Ni2) which are resistant to coarsening, thus suppressing the formation of θ′-Al2Cu precipitate-free zones. This microstructure provides high creep resistance at stresses up to 75–80 MPa, with strain rates much lower than in unmodified Al-5.0Cu-0.3Mn-0.2Zr. Adding Fe, which results in extensive decoration of grain boundaries with coarsening-resistant Al7Cu2Fe, and then increasing the Cu content to compensate for the Cu loss to this new phase, leads to a new Al-7.4Cu-1.6Fe-0.3Mn-0.2Zr alloy with creep resistance at 300 °C that surpasses known cast aluminum alloys. Adding Fe to improve the creep resistance of Al-Cu alloys is both cost-effective and sustainable. Our findings offer guidelines applicable to various alloy systems on controlling the evolution of precipitate-free zones and its ensuing effects on creep deformation.

Unusual indentation depth dependent hardness and creep behaviors in NbMoTaW films at the nanoscale

Herein, nanocrystalline NbMoTaW and (NbMoTaW)N thin films were prepared via magnetron sputtering and investigated using nanoindentation creep tests at various indentation loads (P). The hardness (H) of films increases with P, exhibiting an abnormal indentation size effect (ISE). At the same time, with decreasing indentation depth (h), the creep rate and the creep rate sensitivity (m) both increase. Under a critical h (hc) for each film, m sharply increases. The diffusion between the indenter/film interface dominates the creep mechanism at h lower than hc, whereas the dislocation–grain boundary interaction dominates the creep deformation at h higher than hc. The coble creep and lattice diffusion were both excluded as the main deformation mechanism. The escape of screw dislocations to the surface leads to the softening of the film, whereas the pile-up of screw dislocations leads to hardening, explaining the abnormal ISE on H. The effect of residual stress, grain boundary structures, substrate, and impurities are also discussed.

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids − Part II: Validation for material design

Part II of the paper presents comprehensive investigations aimed at demonstrating the validation and effectiveness of the proposed integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids for material design. Quantitative comparisons between the model’s predictions of void area fraction in a 2D cross-section and experimental results using Alloy 201, a commercially pure nickel, demonstrated a high degree of agreement. Furthermore, the numerical simulation results align with theoretical equations, affirming the model’s validity and its capacity to represent complex phenomena accurately. Although traditional laboratory testing for pure Coble creep is challenging due to constraints such as time and equipment limitations, the proposed model offers a distinct advantage, allowing numerical simulation of Coble creep in materials with arbitrary polycrystalline morphologies under various environmental conditions. Leveraging this capability, the study conducted comprehensive numerical simulations to quantitatively explore the effects of environmental and polycrystalline morphology factors on Coble creep deformation and void nucleation/growth in polycrystalline solids. These aspects, which have not been comprehensively addressed in existing studies, were thoroughly investigated. The findings presented here establish a novel foundation for designing heat-resistant materials applicable across diverse equipment scenarios.

A Coupled Model of Multiscaled Creep Deformation and Gas Flow for Predicting Gas Depletion Characteristics of Shale Reservoir at the Field Scale

The viscoelastic behavior of shale reservoirs indeed impacts permeability evolution and further gas flow characteristics, which have been experimentally and numerically investigated. However, its impact on the gas depletion profile at the field scale has seldom been addressed. To compensate for this deficiency, we propose a multiscaled viscoelasticity constitutive model, and furthermore, a full reservoir deformation–fluid flow coupled model is formed under the frame of the classical triple-porosity approach. In the proposed approach, a novel friction-based creep model comprising two distinct series of parameters is developed to generate the strain–time profiles for hydraulic fracture and natural fracture systems. Specifically, an equation considering the long-term deformation of hydraulic fracture, represented by the softness of Young’s modulus, is proposed to describe the conductivity evolution of hydraulic fractures. In addition, an effective strain permeability model is employed to replicate the permeability evolution of a natural fracture system considering viscoelasticity. The coupled model was implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The proposed model was first verified using a series of gas production data collected from the Barnett shale, resulting in good fitting results. Subsequently, a numerical analysis was conducted to investigate the impacts of the newly proposed parameters on the production process. The transient creep stage significantly affects the initial permeability, and its contribution to the permeability evolution remains invariable. Conversely, the second stage controls the long-term permeability evolution, with its dominant role increasing over time. Creep deformation lowers the gas flow rate, and hydraulic fracturing plays a predominant role in the early term, as the viscoelastic behavior of the natural fracture system substantially impacts the long-term gas flow rate. A higher in situ stress and greater formation depth result in significant creep deformation and, therefore, a lower gas flow rate. This work provides a new tool for estimating long-term gas flow rates at the field scale.

Calculation of creep deformation of stiffness-degraded RC beams after strengthening with increased cross-section

The strengthening of existing reinforced concrete beams (RCBs) has mainly focused on short-term mechanical properties such as flexural resistance and shear resistance, while long-term deflection of RCBs has seldom been studied. In this study, six RCBs with different types and degrees of damage were designed and strengthened by the section enlargement method. Mid-span deflection and concrete strain were used to evaluate the influence of stiffness degradation due to fatigue or corrosion damage on the creep behavior of strengthened RCBs (SRCBs). The experiment results revealed that time-varying curves of creep deformation from fatigue or from corrosion-damaged SRCBs were consistent among the six specimens. Creep in a damaged SRCB was found to increase faster than that in an undamaged beam, and to reach over 90 % of final creep in about six months. Based on the mean curvature method and creep models, taking fatigue and corrosion damage as examples of stiffness degradation, a calculation method for creep deformation of SRCBs was established, and sensitivity analysis of stress levels, reinforcement height, consolidation time, and other parameters were carried out. The research results can provide a theoretical basis and guidance for evaluating creep deformation of stiffness-degraded RCBs after reinforcement with increased cross-section.

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids - Part I: Theoretical framework

This study proposes an integrated model for simulating Coble creep deformation and void nucleation/growth in a 3D polycrystalline solid. Part I of the paper provides a theoretical framework for the proposed model. A representative volume element approach is employed to predict the effects of 3D polycrystalline morphology. The model comprises two distinct but interconnected stages: deformation and void nucleation/growth. The deformation stage of the proposed model comprises two sub-models: grain boundary (GB) migration and GB diffusion. The void nucleation/growth stage is composed of three consecutive calculations: void nucleation, void growth, and postprocessing. The process simulated in the void nucleation/growth stage is driven by relative GB velocity of the respective GBFs and diffusional fluxes between adjacent GBFs, which are provided from the deformation stage. The void nucleation rate is quantified using the relative GB velocity, and the initial void size is determined based on the stability condition for void existence derived from Helmholtz free energy. The void growth rate is evaluated by the atomic diffusion on the GBF and the surface of each void.

Study on the fractional creep model of roadway filling paste under the coupling effect of pore water pressure and stress

Filling paste in deep roadways is significantly affected by groundwater, especially high pore water pressure, which increases the complexity and variability of the filling paste's mechanical properties. To explore the creep characteristics and long-term stability of filling paste under varying pore water pressure, the MTS815.03 test system is used to conduct creep tests under different pore water pressures and stress. Then the creep deformation of the filling paste under the complex pressure field of static pore water pressures is analyzed. Finally, through the one-to-one correspondence between the numerical simulation of the creep model and the characteristic points of the creep curve, a method for determining the creep parameters under the complex pressure field of static pore water pressures is proposed. Results show that the creep test curves of filling paste under different pore water pressures and stress are in good agreement with the model curves. This shows that the creep constitutive model in this research can better reflect the whole process of creep deformation of filling paste. The result also verifies the rationality of the proposed method to determine creep model parameters. The newly proposed creep model can effectively compensate for the traditional Nishihara model, which is inability to reflect the acceleration of creep and can more accurately describe the creep characteristics of the primary and steady-state creep stages.

Investigation on the room temperature compressive creep behavior of TC4 titanium alloy joints with vacuum electron beam welding

The room temperature compressive creep behavior is a key issue for the titanium alloys welded structural components served in deep-sea environment. In the present work, the compressive creep behavior of different areas for TC4 titanium alloy joints with vacuum electron beam welding was systematically studied, and it is found that the fusion zone (FZ) of TC4 titanium alloy joints has the minimum creep strain rate. This is mainly because the creep deformation of TC4 titanium alloy is mainly controlled by the movement of dislocations in the α or α′ phases, the size of α′ phase in FZ is small, and thus the dislocation slip is limited. MD simulation results have further revealed that the room temperature compressive creep nature of α-Ti can be regarded as a dynamic hysteresis phenomenon in plastic strain and is dominated by the dislocation movement.

Numerical assessment of the time-dependent behaviour of a tunnel with a yielding support system for a potential repository in claystone

For the disposal of heat-generating radioactive waste and spent fuel in claystone formations, support structures for underground excavations are essential for the operational safety of geological disposal facilities (GDF). Claystone formations of moderate strength, at considerable depths, are characterised by their squeezing, creeping, and, sometimes, swelling behaviour that results in continuous tunnel convergence over time. Under these conditions, a rigid support system can be subjected to very high loads, requiring a considerable thickness and/or high-performance concretes. Therefore, yielding support systems are being currently investigated as a promising alternative for GDF. This work presents a numerical study of the behaviour of a tunnel in a claystone formation with a yielding support system. The use of a compressible mortar between the rock and the lining is assumed, as a means of reducing loads and mitigating the effects of creep deformations. A key aspect of the analyses is that the host rock is characterised by a constitutive model that includes a number of features that are relevant for the satisfactory description of the hydro-mechanical behaviour of stiff clayey materials, such as mechanical anisotropy, creep, strain softening, and its ability to simulate localised deformations through a nonlocal regularisation. An elastoplastic constitutive model was also developed to represent the behaviour of the compressible mortar. Results provide relevant insights into the performance of the adopted yielding support system, particularly regarding the effect of time-dependent deformations and the additional relaxation of the rock on the fractured zone near the excavation.