Nonlinear Creep Deformation Research Articles

A novel time-dependent damage constitutive model for hard rock materials

The mechanical behavior of deep hard rocks plays a crucial role in the long-term safety and stability of engineering structures. This work focuses on studying the instantaneous and time-dependent fracture propagation of hard rock materials from a theoretical perspective. A new unified constitutive model, based on a modified Mohr–Coulomb (M-C) criterion, is proposed to accurately represent the short and long-term mechanical properties of hard rocks. To capture the strain hardening and strain softening behaviors, damage is utilized as an internal mechanism-driven variable, controlling the expansion and contraction of the plastic yield surface. Additionally, a combination of time-dependent damage law and viscoplastic theory is employed to account for nonlinear creep deformation characteristics. By considering the time-dependent effects, the model can be applied to both instantaneous loading and creep conditions. The general algorithm format is derived in detail, and an explicit integration algorithm is utilized to update the time-dependent damage evolution. Finally, the proposed model is validated by comparing its predictions with the short and long-term mechanical responses of Beishan granite and Rumei dacite. This comprehensive constitutive model improves our understanding of continuum damage mechanics and provides a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering projects.

Thermomechanical Fatigue Life Prediction Method of the Trailing Edge Holes in the Turbine Blade for Turboshaft Engine

In this paper, a thermomechanical fatigue (TMF) life analysis method considering stress relaxation was established for turbine blade in a turboshaft engine. The nonlinear creep deformation of a superalloy is predicted by coupling creep damage in the framework of viscoplastic theory. The results revealed that the calculation error of the model for the elastic-plastic stress-strain curve was less than 5%, while the simulation accuracy for the creep curve is within the dispersion range of the inherent properties of material creep deformation. Based on the elastic-plastic creep analysis of a turbine blade, the creep damage and its evolution law of the leading edge and trailing edge of the blade are clarified, and a new method is provided for determining the local dangerous points on the blade. With the help of the linear damage cumulative life theory, the fatigue creep life of the trailing edge hole of a turbine blade considering the stress relaxation is obtained, which provides a more reasonable and better engineering application method for the blade life evaluation.

Monitoring aseismic fault creep using persistent urban geodetic markers generated from mobile laser scanning

High resolution and high accuracy distributed detection of fault creep deformation remains challenging given limited observations and associated change detection strategies. A mobile laser scanning-based change detection method that is capable of measuring centimeter-level near-field (<150 m from fault) deformation is described. The methodology leverages the use of man-made features in the built environment as geodetic markers that can be temporally tracked. The proposed framework consists of a RANSAC-based corresponding plane detector and a combined least squares displacement estimator. Using repeat mobile laser scanning data collected in 2015 and 2017 on a 2 ​km segment of the Hayward fault, near-field fault creep displacement and non-linear creep deformation are estimated. The detection results reveal 2.5 ​± ​1.5 ​cm of accumulated fault parallel creep displacement in the far-field. The laser scanning estimates of displacement match collocated alinement array observations at the 4 ​mm level in the near field. The proposed change detection framework is shown to be accurate and practical for fault creep displacement detection in the near field and the detected non-linear creep displacement patterns will help elucidate the complex physics of surface faulting.

Geomechanical simulation of energy storage in salt formations

A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.

Nonlinear Creep Deformation of Polycarbonate at High Stress Level: Experimental Investigation and Finite Element Modeling

It is well known that polycarbonate (PC) undergoes time-dependent deformation (i.e., creep deformation), and nonlinear creep deformation is often experienced at high stress level. Using the time–temperature–stress superposition principle (TTSSP), we obtain a new master curve, which covers higher stress level, and successfully establish a new modeling method of creep deformation of PC. First, to investigate the effect of applied stress level on the creep compliance (i.e., stress-dependent nonlinear creep deformation), this study conducted various creep tests with eight different stress levels. We found that the creep compliance curve strongly depended on the applied stress level; in particular, a higher stress level induced a larger difference in creep compliance. According to the TTSSP, the creep compliance curve at each stress level shifts with the creep time (i.e., stress reduced time). When we appropriately selected the stress reduced time, we obtained the master curve of creep compliance, which is unified with respect to various applied stresses. However, we found that the stress-shifted factor is not compliant with the previous TTSSP, especially in the higher stress regime. Therefore, this regime was also considered to obtain a new master curve that can cover a wide range of stress levels. Finally, our established creep model (master curve and stress shift factor) was introduced into FEM, and then this numerical model was verified by comparison with experimental data. Our model may be useful for predicting the creep deformation of PC subjected to a wide range of applied stresses.

Testing and analysis on nonlinear creep behaviour of concrete-filled steel tubes with circular cross-section

Owing to the excellent seismic resistance of circular concrete-filled steel tubes (CFST), no specific limitation on their in-service axial load level is provided in Chinese codes. Therefore, nonlinear creep could occur in Chinese CFST applications. This study intends to experimentally investigate the nonlinear creep behaviour and the creep failure behaviour of CFST columns. Fourteen specimens were subjected to sustained loading for 200–500 days. The sustained loading level ranged between 40% and 80% of the cross-sectional strength of the specimens. The strain state of steel tubes was monitored to determine how the confinement effects vary with time. Ultimate loading tests were finally conducted on all specimens immediately after the long-term tests to investigate the nonlinear creep effects on the cross-sectional capacity and ductility of the CFST specimens. A method was then proposed for the nonlinear creep analysis of circular CFST members with consideration of the beneficial contribution of confinement effects. Existing nonlinear models were benchmarked against available experimental results to evaluate their adequacy in predicting the nonlinear creep responses of CFST members. Experimental results indicated that nonlinear creep could lead to a 58–200% increase in the creep coefficient, in which case the linear creep model will underestimate the long-term deformation by 37–67%. Owing to the vertical stress redistribution between the concrete core and the steel tube and the confinement effects, no creep failure occurred during the 500-day tests, and the nonlinear creep barely influenced the cross-sectional capacity of the specimens. A model was recommended to predict the nonlinear creep deformation of CFST members.

Optimization of thermo-mechanical reliability of solder joints in crystalline silicon solar cell assembly

A robust solder joint in crystalline silicon solar cell assembly is necessary to ensure its thermo-mechanical reliability. The solder joint formed using optimal parameter setting accumulates minimal creep strain energy density which leads to longer fatigue life. In this study, thermo-mechanical reliability of solder joint in crystalline silicon solar cell assembly is evaluated using finite element modelling (FEM) and Taguchi method. Geometric models of the crystalline silicon solar cell assembly are built and subjected to accelerated thermal cycling utilizing IEC 61215 standard for photovoltaic panels. In order to obtain the model with minimum accumulated creep strain energy density, the L9 (33) orthogonal array was applied to Taguchi design of experiments (DOE) to investigate the effects of IMC thickness (IMCT), solder joint width (SJW) and solder joint thickness (SJT) on the thermo-mechanical reliability of solder joints. The solder material used in this study is Sn3.8Ag0.7Cu and its non-linear creep deformation is simulated using Garofalo-Arrhenius creep model. The results obtained indicate that solder joint thickness has the most significant effect on the thermo-mechanical reliability of solder joints. Analysis of results selected towards thermo-mechanical reliability improvement shows the design with optimal parameter setting to be: solder joint thickness — 20μm, solder joint width — 1000μm, and IMC thickness — 2.5μm. Furthermore, the optimized model has the least damage in the solder joint and shows a reduction of 47.96% in accumulated creep strain energy density per cycle compared to the worst case original model. Moreover, the optimized model has 16,264cycles to failure compared with the expected 13,688cycles to failure of a PV module designed to last for 25years.

Anisotropic creep modeling of coated textile membrane using finite element analysis

Coated textile membranes (CTMs) form a class of flexible textile composites undergoing viscoelastic deformation because they consist of a polymeric reinforcement and matrix and are tensioned in service. In most CTMs, woven fabrics are frequently used as a reinforcement structure, causing anisotropic mechanical behavior including time dependent viscoelastic deformation. To describe such anisotropic and nonlinear time dependent deformation, the creep potential with three orthotropic parameters was introduced and incorporated into finite element software through a user material subroutine. The three parameters included in the creep potential were determined by carrying out off-axis coupon creep tests and using various mathematical formulae for the effective creep compliance. To validate the current creep modeling and its implementation in finite element software, off-axis coupon creep tests were re-simulated and compared with the experiments, showing that the present modeling can describe the anisotropic and nonlinear creep deformation of CTM with acceptable accuracy.

Void growth in power-law creeping solids: Effect of surface diffusion and surface energy

This paper addresses the growth of a void in a nonlinearly creeping material in the presence of the void-surface energy effect and void-surface diffusion driven by surface curvature gradients. Large strain finite element analysis of the coupled problem indicates that microstructural variables (porosity and void aspect ratio), as well as macroscopic deformation rates are strongly affected by the relative strength of the void-surface energy effect and the void-surface diffusion process vis-a-vis the rate of creep deformation in the bulk of the solid. The phenomenon is characterized by two-dimensionless groups, one measuring the strength of the surface diffusion process with respect to the nonlinear creep deformation in the interior of the solid, and the other the magnitude of the surface energy of the void in relation to the applied load and the size of the void. The computations reveal a rich variety of solutions that reflect a wide range of external load, material, and geometric parameters. Classical void growth studies that ignore both surface diffusion and surface energy effects are shown to recover only one case of this family of solutions. The computations also serve to quantitatively evaluate recent constitutive theories for porous nonlinear materials that account for continuously evolving microstructure, but do not include surface diffusion or surface energy effects.

Time-Dependent Nonlinearity of Compression Softening in Concrete

As nonlinear post-peak mechanics is time dependent in nature and the transient process of collapse is influenced by loading rates, post-peak analyses have to be conducted considering softened structural concrete under varying rates of straining. To meet this challenge, a new time-dependent constitutive model, which encompasses both near- and post-peak regions in concrete compression, is proposed. Towards better evaluation of structural collapse under extreme loads, a coupled plastic-damaging law is presented. For the purpose of identifying evolution laws of plasticity and continuum damage, experimental investigation into rate-dependent nonlinearity was performed under different levels of lateral confinement. The plastic and damage evolutions were formulated with respect to paths of intrinsic stress intensity of damage continua and time. The combined law of short-term elasto-plastic and fracture successfully convey nonlinear creep deformation and rate dependent strength, as well as delayed creep rupture of material instability.

A creep analysis of the deflection test for evaluating oxide growth stresses

During isothermal oxidation of one surface of a metal strip, growth-induced stresses will produce curvature of the metal/oxide composite sample. This observation has been used extensively elsewhere to evaluate the average stress developed within the oxide layer, but previous estimates have been based on an elastic stress analysis of the bending composite. At typical oxidation temperatures, creep deformation of both oxide and metal phases is much more likely. The present paper provides a stress analysis assuming such non-linear creep deformation. It considers the situation where the oxide experiences a net compressive stress and the metal a net tensile stress. The oxide neutral axis may be located either within the oxide layer or outside it, in the gas phase, depending on the thickness of the oxide and the relative creep strengths of the oxide layer and metal substrate. Evaluation of the stress distribution and average stress values in both the metal and oxide phases is provided for notional mechanical properties, within which the metal creep strength is varied widely. It is also shown how the assumption of elastic deformation can lead to large overestimates of stress values.

Polymer crystallinity and its effect on the non-linear bending creep rate for a polyphenylene sulphide thermoplastic composite

Recent developments have led to the introduction of advanced thermoplastic composites such as Polyphenylene Sulphide (PPS), which can be used structurally at higher temperatures. Because of its thermoplastic nature, it can also be hot worked by bringing the working temperature considerably above the glass transition temperature. However, such annealing processes also affect its degree of crystallinity, which in turn affect the properties of the material. This paper reports on the effect of matrix crystallinity on the rate of creep deformation in three point bending of some reinforced PPS composites. This work was based on a non-linear approach based on a Power law creep model creep deformation analysis. The effect of annealing on the non-linear creep deformation of the PPS composite specimens has been analysed using a Power Law creep model. Results indicate that the creep deformation for both 20 and 40% reinforced samples were relatively similar despite the difference in the amount of fibre reinforcement. In contrast, the value of the creep component decreased exponentially with the % crystallinity. for both 20 and 40%, reinforced samples.

Nonlinear creep deformation analysis of a radiation-cured wood-polymer composite

A wood-polymer composite has been produced by impregnating the wood with the monomer and subsequently polymerizing it by exposure to a gamma radiation source. To compare the improvement in creep deformation of the wood due to the polymer impregnation, a nonlinear Norton-Bailey isothermal mathematical function has been used to model the bending creep deformation of the wood-polymer composites. Results show that the impregnation significantly improves the creep resistance of the wood. The maximum creep resistance is obtained when the amount of polymer impregnation exceeds about 30%. An interfacial interaction between the wood cell wall and the polymer could explain the creep deformation improvement, as well as the maximum impregnation level beyond which little improvement occurs. The results indicate that polymer impregnation is a viable method for improving the poor creep properties of wood.