Creep Analysis of Axially Loaded Fiber Reinforced Polymer-Confined Concrete Columns

An analytical model is developed to study the time-dependent behavior of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) and fiber-wrapped concrete columns (FWCC) under sustained axial loads. The model utilizes the double power law creep function for concrete in the framework of rate of flow method, and the linear viscoelastic creep model for FRP. It follows geometric compatibility and static equilibrium, and considers the effects of sealed concrete, multiaxial state of stresses, creep Poisson’s ratio, stress redistribution, variable creep stress history, and creep rupture. The model is verified against previous creep tests by the writers on FWCC and CFFT columns. It is then used to study the practical design parameters that may affect creep of FRP-confined concrete under service loads, or lead to creep rupture at high levels of sustained load. Creep of FWCC is shown to be close to that of sealed concrete of the same mix, as the effect of confinement on creep of concrete is not very significant. CFFT columns, on the other hand, creep much less than FWCC, mainly due to axial stress redistribution. As the stiffness of the tube increases relative to the concrete core, larger stress redistributions take place further reducing the creep. However, there is a threshold, beyond which, stiffer tubes would not significantly lower the creep of concrete. Creep rupture life expectancy of CFFT columns is shown to be quite acceptable.     

泥质粉砂岩蠕变特性及非线性蠕变模型研究

为揭示地下岩体非线性蠕变力学特性,对中风化泥质粉砂岩开展分级单轴加载蠕变试验。泥质粉砂岩典型蠕变曲线可划分为减速蠕变、稳态蠕变和加速蠕变阶段,使用给定蠕变速率阈值法求得的岩石长期强度为14.3 MPa。为了描述岩石非线性蠕变特性,引入了一个与时间应力水平相关的非线性黏塑性元件,将其与广义Kelvin体和带开关的黏性体串联,得到了改进的非线性黏弹塑性蠕变模型。使用Origin平台的Levenberg-Marquardt非线性最小二乘法反演得到模型的蠕变力学参数,通过将广义Kelvin蠕变模型、伯格斯蠕变模型和改进黏弹塑性蠕变模型与试验曲线进行比较,分析了各自的适用特点。结果表明：本研究提出的改进黏弹塑性蠕变模型可以较好地描述中风化泥质粉砂岩加速蠕变阶段特征,揭示了泥质粉砂岩的非线性蠕变力学特性。     

Comparison of Continuum Damage Laws Under Uniaxial Creep for an AISI 316 Stainless Steel

Parameters of five popular continuum damage models are fit to match their creep rate and time to rupture predictions with that of a validated micro-mechanisms based model at a high nominal stress for an austenitic stainless steel. Their predictions are then compared with that of the micro-mechanisms based model at lower stress levels. The creep-strain rate and time to failure predictions of the model due to Wen et al. (Eng Fract Mech 98:169–184, 2013) best agrees with that of the micro-mechanisms based model in the regime of dominance of creep deformation processes. At still lower stress levels, where cavitation-rate is determined by diffusion processes, the Wen et al. model predictions of creep lifetimes become excessively non-conservative. A correction based on a formula due to Cocks and Ashby (Prog Mater Sci 27:189–244, 1982) has been proposed for this regime.     

Numerical Model for Time-Dependent Fracturing of Concrete

A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.     

Refinement of a Design-Oriented Stress–Strain Model for FRP-Confined Concrete

This paper presents the results of a recent study conducted to refine the design-oriented stress–strain model originally proposed by Lam and Teng for fiber-reinforced polymer (FRP)-confined concrete under axial compression. More accurate expressions for the ultimate axial strain and the compressive strength are proposed for use in this model. These new expressions are based on results from recent tests conducted by the writers’ group under well-defined conditions and on results from a parametric study using an accurate analysis-oriented stress–strain model for FRP-confined concrete. They allow the effects of confinement stiffness and the jacket strain capacity to be separately reflected and accounts for the effect of confinement stiffness explicitly instead of having it reflected only through the confinement ratio. The new expressions can be easily incorporated into Lam and Teng’s model for more accurate predictions. Based on these new expressions, two modified versions of Lam and Teng’s model are presented. The first version involves only the updating of the ultimate axial strain and compressive strength equations. The second version caters to stress–strain curves with a descending branch, which is not covered by the original model.     

A theory for creep by interfacial flaw growth in ceramics and ceramic composites

The nucleation and growth of flaws along grain boundaries and interfaces are known to cause significant reductions in elastic moduli and to play an important role in determining the deformation characteristics of ceramic materials at elevated temperatures. This paper presents an analysis of the creep behavior of deteriorating elastic solids where the principal mechanism of deformation is the growth of intergranular or interfacial flaws. The changes in elastic moduli induced by the growth of internal damage are used to derive the stress exponent in the power-law creep regime. When the flaws advance at a rate which is proportional to the local normal stress or normal strain, a power-law creep exponent of 2 is predicted for short time, steady-state creep for a population of aligned slit cracks and randomly oriented penny-shaped cracks. For long-time creep, the variation of nonsteady state creep strain rate as a function of the far-field stress and time is explicitly determined. General solutions for creep strain rates are also presented for situations where the microcrack growth rate has a power-law dependence on the local normal stress or stress intensity factor. The predicted dependence of creep strain rate on the far-field stress, the progression of damage and the consequent reduction in elastic moduli, overall creep ductility, and implications pertaining to microstructural and temperature effects on creep are found to be in accord with a wide variety of experimental observations for ceramics and ceramic composites. The temperature, stress and material conditions for which the proposed mechanism is applicable are discussed and a general theory of creep damage in progressively microfracturing elastic brittle solids is developed.     

Creep-behavior modeling of the single-crystal superalloy CMSX-4

An investigation has been undertaken into the creep behavior of the single-crystal superalloy CMSX-4. Creep deformation in the alloy occurs largely through dislocation activity in the γ channels. Shearing of the γ′ dislocations is observed, but, at higher temperatures, this does not occur until late in life via the passage of superpartial dislocation pairs. At lower temperatures (1023 K) and high stress levels, shearing of the γ′ precipitates is observed relatively early in the creep curve through the passage of {111}〈112〉 dislocations, which leave superlattice stacking faults (SSFs) in the precipitates. The stress-rupture behavior of CMSX-4 has been modeled using a damage-mechanics technique, where the level of damage required to cause failure is defined by the effective stress reaching the material’s ultimate tensile strength (UTS). This technique ensures that short-term rupture data extrapolate back to the UTS. High-temperature steady-state and tertiary creep are modeled using modified damage-mechanics equations, where the strain and damage rates are similar functions of stress. At intermediate operating temperatures of 1023 to 1123 K, the material exhibits pronounced sigmoidal primary creep of up to 4 pct strain, which cannot be modeled using a conventional approach. This transient behavior has been explained by the effect of internal stresses acting on dislocations in the gamma matrix; such an internal stress has been included in the creep law and evolves as a function of the damage-state variable.     

Creep-Effect on Mechanical Behavior of Concrete Confined by FRP under Axial Compression

Despite many successes in concrete creep studies, its effect on the mechanical behavior of concrete members is far from a thorough case-specific understanding. For the members that have been subjected to a long-term load, the classical stress-strain models describing the short-term behavior of either confined or unconfined concrete are unsuitable. In order to investigate this creep-effect, an experiment on eight concrete cylindrical columns confined by fiber-reinforced polymer (FRP) is carried out. Based on the theory of plasticity for concrete, a constitutive model that takes into account the effect of creep on mechanical behavior of concrete confined by FRP is presented. In the model, the creep law inspired in the microprestress-solidification theory is generalized to triaxial stress condition for the calculation of the creep of the concrete columns confined by FRP. The predictions of the model agree well with the experimental results. The present study indicates that the creep increases the elastic modulus, slightly decreases the compressive strength, and degrades the deformation capability of the concrete confined by FRP.     

P92钢的蠕变损伤容许量系数及蠕变断裂机理

利用P92钢在595、610、640、670℃的高应力试验条件下的蠕变试验数据,得出其Norton应力指数,依据Norton应力指数的大小判定其蠕变机理为位错蠕变。同时结合1种新的蠕变变形及断裂模型,引入将蠕变损伤看作1个内在的阶段变量的蠕变损伤容许量系数,根据蠕变损伤容许量λ=2.94,判断其蠕变变形和断裂是位错运动控制的。微观组织的观察也表明,蠕变后的试样中位错密度大大降低,高密度位错是P92钢持久强度高的原因,伴随着位错密度的下降,P92钢持久强度降低直至断裂。     

Creep strengthening of low carbon grade type 316LN stainless steel by nitrogen

Nitrogen-alloyed 316LN stainless steel is used as a structural material for high temperature fast breeder reactor components. With a view to increase the design life of the components up to 60 years and beyond, studies are being carried out to develop nitrogen alloyed 316LN stainless steel with superior tensile, creep and low cycle fatigue properties. This paper presents the results from studies on the influence of nitrogen on the high temperature creep properties of this material. The influence of nitrogen on the creep behaviour of 316LN stainless steel has been studied at nitrogen levels of 0.07, 0.11, 0.14 and 0.22 wt%. Creep tests were carried out at 923 K at stress levels 140, 175, 200 and 225 MPa. Creep rupture strength increased substantially with increase in nitrogen content. The variation of steady state creep rate with stress showed a power law relationship. The power law exponent varied between 6.4 and 13.7 depending upon the nitrogen content. Rupture ductility was generally above 40% at all the test conditions and for all the nitrogen contents. It was observed that the internal creep damage and surface damage decreased with increase in nitrogen content. Fracture mode was found to generally shift from intergranular failure to transgranular failure with increasing nitrogen content.     

Dislocation mechanisms in creep of Ni3Al at intermediate temperature

The creep behaviour and dislocation structure of polycrystalline Ni₃Al have been investigated at intermediate temperatures. At a temperature just below the peak strength temperature T_p different creep responses occurred with relatively low and high stress levels respectively. Under high stress, creep exhibited a normal primary creep regime and then an inverse creep regime. At low stress, however, no visible inverse creep was displayed. With variation in temperature, an anomalous temperature-dependence of creep strength was confirmed. Microstructural observation indicates that superdislocations slip on the cube cross-slip plane more easily at lower temperatures in the temperature regime investigated in the present study, which is considered to be one of the reasons for the creep strength varying anomalously with temperature. Moreover, although inverse creep is produced by the operation of cube cross-slip, the operation of cube cross-slip does not necessarily lead to inverse creep.     

Transitional Thermal Creep of Early Age Concrete

Couplings between creep of hardened concrete and temperature∕water effects are well-known. Both the level and the gradients in time of temperature or water content influence the creep properties. In early age concrete the internal drying and the heat development due to hydration increase the effect of these couplings. The purpose of this work is to set up a mathematical model for creep of concrete that includes the transitional thermal effect. The model governs both early age concrete and hardened concrete. The development of the material properties in the model is assumed to depend on the hydration process and the thermal activation of water in the microstructure. The thermal activation is assumed to be governed by the Arrhenius principle, and the activation energy of the viscosity of water is found applicable in the analysis of the experimental data. Changes in temperature create an imbalance in the microstructure termed the microprestresses, which reduce the stiffness of the concrete and increase the creep rate. The aging material is modeled in an incremental way reflecting the hydration process in which new layers of cement gel solidify in a stress free state and add stiffness to the material. Analysis of experimental results for creep of early age and hardened concrete either at different constant temperature levels or for varying temperature histories illustrate the model.     

干/湿状态下HFRP搭接接头的剪切蠕变试验及分数阶导数流变模型

搭接是纤维增强复合材料(FRP)的重要连接方式,长期性能是该技术实际工程应用的关键.对不同恒定应力和湿度状态下混杂FRP (HFRP)双搭接接头的剪切蠕变性能进行了试验研究.试验观测到了明显的蠕变变形,测定了蠕变与恒定应力及湿度的关系.进一步采用分数阶导数流变模型对试件的蠕变进行模拟.根据模型所包含的Mittag-Leffler函数的性质采用了改进的Powell优化算法,并确定了合理的初值,结合试验曲线拟合得到模型各参数值.根据搭接接头蠕变的特点,在经典分数阶流变模型中引入了表征应力水平对搭接接头非线性蠕变特性影响的函数,提出了一种改进的分数阶蠕变柔量计算公式.研究结果表明,该流变模型能够采用简单的表达形式和较少的参数对试件的非线性蠕变行为进行拟合,在30%~70%恒定应力范围内准确模拟了双剪搭接接头的蠕变曲线.      

Creep deformation and damage evaluation of service exposed reformer tube

Abstract

This paper aims at studying the creep deformation behaviour and quantifying creep damage of ～11 years service exposed primary hydrogen reformer tube made of HP40 grade of steel in a petrochemical industry, in terms of Kachanov’s continuum damage mechanics model (K model) and Bogdanoff model (B model) based on Markov process. Hot tensile, conventional creep deformation under identical test conditions, optical microscopy and fractography were extensively carried out. The as received tubes did not possess any sign of degradation including voids or creep cavitations and decarburisation. There was indeed loss of tensile strength from room temperature to 870°C for the bottom portion of the tube due to aging and overheating. Accumulation of damage due to creep has been quantified through microstructural studies in terms of two damage parameters A and A*. Experimental scatter observed in creep deformation and creep strain rate curves of the material at 870°C and at various stress conditions, is probably due to scatter in creep cavitations/voids and also due to variation in the mode of fracture in top as well as bottom portion of the tube. From statistical point of view, Weibull distribution pattern for analysing probability of rupture due to void area, shifts with increase in true strain towards the higher population of void. The estimation of average time to reach a specific damage state from K model and B model is in close agreement with that of experimental data and can describe the sudden changes of the creep damage in the tertiary region as well.     

Time-Dependent Behavior of Concrete-Filled Steel Tubular Arch Bridge

This paper develops a simplified method using a summation procedure and a related computer program to calculate the time-dependent behavior of a concrete filled steel tubular (CFST) arch bridge based on the geometric compatibility principle, a step-by-step time incremental process, and self-equilibrium equations. An experimental test on a scaled (1:5) segmental model of the main arch ribs of the Maocaojie Bridge was used to confirm the effectiveness of the proposed calculation method for evaluating the long-term behavior of CFST arch bridge under sustained load. It is concluded that: (1) the numerical results were in good agreement with the experimental results, demonstrating that the proposed analytical model is capable of predicting long-term effects for CFST arch bridges; (2) the stresses in the steel tubes increased, and the compressive stresses in the concrete decreased due to the effects of concrete creep and shrinkage. The maximum relaxation of the compressive stress in concrete due to concrete creep was 52.7% of the initial concrete stress, and the maximum increase of stress in the steel tubes was 27.3%; and (3) more than 90% of the total creep of the concrete took place in the first year. Subsequent creep of the concrete was limited because of the lack of water exchange between the structure and atmosphere and the reduction of compressive stress in the concrete.     

New approach to predict the long-term creep behaviour and evolution of precipitate back-stress of 9–12% chromium steels

Modern advanced 9–12 % Cr steels are complex alloys with excellent creep strength even at high temperatures up to 620°C. The mechanical properties of these steels are significantly influenced by the presence and stability of various precipitate populations. Numerous secondary phases grow, coarsen and, sometimes, dissolve again during heat treatment and service, which leads to a varying obstacle effect of these precipitates on dislocation movement. In this work, the experimentally observed creep rupture strength of an modified 9–12% Cr steel developed in the European COST Group is compared to the calculated maximal obstacle effect (Orowan stress) caused by the precipitates present in these steels for different heat treatment conditions. It is shown that the differences in creep rupture strength caused by different heat treatments disappear after long time service. This observation is discussed on the basis of the calculated evolution of the precipitate microstructure. The concept of boosting long-term creep rupture strength by maximizing the initial creep strength with optimum quality heat treatment parameters for precipitation strengthening is critically assessed.     

Advanced Testing and Characterization of Asphalt Concrete Materials in Tension

The modeling of asphalt concrete materials is currently handled using linear viscoelasticity (VE) and viscoplasticity (VP) with damage. Exploratory frequency sweep and creep and recovery test results indicate that the linear VE with damage theory cannot represent the material response unless damage–healing is also included in the formulation. Therefore, the concept of effective stress, used for modeling damage, is extended to include additional nonlinear effects. A new theory of nonlinear VE with damage and VP is presented for uniaxial loading conditions in tension. A special load transfer device is described. It allows very fast unloading and very long recovery periods with complete unloading. It permits better separation between VE and VP components. Using this device, a uniaxial tension creep and recovery test is conducted and analyzed. The nonlinear material response is illustrated and a calibration of the damage function is presented. The formulation is being extended to three-dimensional conditions.     

Anisotropic Damage Model for Concrete

In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.     

循环加卸载下闪长玢岩蠕变特性及损伤本构模型

分级加载压缩蠕变试验未能充分考虑稳定蠕变中的黏塑性应变，故采用三轴循环加卸载压缩蠕变试验来实现岩石的黏弹、塑性应变分离，从而使岩石黏弹、塑性应变在岩石蠕变的各个阶段得以充分考虑。以某水电站闪长玢岩为例，探讨该类岩石蠕变特性。在破坏前，岩石的瞬时弹性应变以及瞬时塑性应变随着偏应力逐级增大呈线性增长；随着偏应力的增加，黏弹性应变和黏塑性应变呈非线性增长。引入一个分数阶Abel黏壶与Kelvin模型串联形成新型黏弹性模型；用分数阶Abel黏壶代替传统的黏塑性模型中的线性牛顿体并基于损伤建立黏塑性损伤模型。然后将新型黏弹性模型和黏塑性损伤模型与瞬时弹性模型和瞬时塑性模型串联组成一个新的岩石蠕变损伤模型。最后将该模型与岩石蠕变曲线进行拟合，从而证明该模型的适用性。