Modeling of Fatigue Crack Growth Closure Considering the Integrative Effect of Cyclic Stress Ratio,Specimen Thickness and Poisson's Ratio

Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since the FCG process is affected by various factors,no universal model exists due to the complexity of the mechanisms.Most of the existing models are obtained by fitting the experimental data and could hardly describe the integrative effect of most existing factors simultaneously.In order to account for the integrative effect of specimen parameters,material property and loading conditions on FCG process,a new model named integrative influence factor model（IIF） is proposed based on the plasticity-induced crack closure theory.Accordingly to the predictions of crack opening ratio（γ） and effective stress intensity factor range ratio（U） with different material under various loading conditions,predictions of γ and U by the IIF model are completely identical to the theoretical results from the plane stress state to the plane strain state when Poisson＇s ratio equals 1/3.When Poisson＇s ratio equals 0.3,predictions of γ and U by the IIF model are larger than the predictions by the existing model,and more close to the theoretical results.In addition,it describes the influence of R ratios on γ and U effectively in the whole region from-1.0 to 1.0.Moreover,several sets of test data of FCG rates in 5 kinds of aluminum alloys with various specimen thicknesses under different loading conditions are used to validate the IIF model,most of the test data are situated on the predicted curves or between the two curves that represent the specimen with different thicknesses under the same stress ratio.Some of the test data slightly departure from the predictions by the IIF model due to the surface roughness and errors in measurement.Besides,based on the analysis of the physical rule of crack opening ratios,a relative thickness of specimen is defined to describe the influence of material property,specimen thickness and so forth on FCG characteristics conveniently.In conclusion,the relative thickness of specimen simplifies the expression of FCG characteristic and provides a general parameter to analyze the fatigue characteristics of different materials with various thicknesses under different loading conditions.The IIF model describes the integrative effect of existing influence factors explicitly and quantitatively,and provides a helpful tool for fatigue property estimation of practical component and experiment design.

Critical Cyclic Stress Ratio of Undisturbed Saturated Soft Clay in the Yangtze Estuary under Complex Stress Conditions

There exists a critical cyclic stress ratio when sand or clay is subjected to cyclic loading. It is an index dis-tinguishing stable state or failure state. The soil static and dynamic universal triaxial and torsional shear apparatus de-veloped by Dalian University of Technology in China was employed to perform different types of tests on saturated soft marine clay in the Yangtze estuary. Undisturbed samples were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consoli-dation parameters. The effects of initial orientation angle of major principal stress, initial ratio of deviatoric stress,initial coefficient of intermediate principal stress and stress mode of cyclic shear on the critical cyclic stress ratio wereinvestigated. It is found that the critical cyclic stress ratio decreases significantly with increasing initial orientation angle of major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientationangle of major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate prin-cipal stress is less evident. Under the same consolidation condition, the critical cyclic stress ratio from the cyclic cou-pling shear test is lower than that from the cyclic torsional shear test, indicating that the stress mode of cyclic shear has an obvious effect on the critical cyclic stress ratio. The main reason is that the continuous rotation in principal stressdirections during cyclic coupling shear damages the original structure of soil more than the cyclic torsional shear does.

Cyclic behavior of reinforced sand under principal stress rotation

Although the cyclic rotation of the principal stress direction is important,its effect on the deformation behavior and dynamic properties of the reinforced soil has not been reported to date.Tests carried out on large-scale hollow cylinder samples reveal that the cyclic rotation of the principal stress direction results in significant variations of strain components(ε,ε,εand γ) with periodic characteristics despite the deviatoric stress being constant during tests.This oscillation can be related to the corresponding variations in the stress components and the anisotropic fabric that rotate continuously along the principal stress direction.Sand under rotation appears to develop a plastic strain.Similar trends are observed for reinforced sand,but the shear interaction,the interlocking between particles and reinforcement layer,and the confinement result in significant reductions in the induced strains and associated irrecoverable plastic strains.Most of the strains occur in the first cycle,and as the number of cycles increases,the presence of strains becomes very small,which is almost insignificant.This indicates that the soil has reached anisotropic critical state(ACS),where a stable structure is formed after continuous orientation,realignment and rearrangement of the particles accompanied with increasing cyclic rotation.Rotation in the range of 60°-135° produces more induced strains even in the presence of the reinforcement,when compared with other ranges.This relates to the extension mode of the test in this range in which σ>σand to the relative approach between the mobilized plane and the weakest horizontal plane.Reinforcement results in an increase in shear modulus while it appears to have no effect on the damping ratio.Continuous cycles of rotation result in an increase in shear modulus and lower damping ratio due to the densification that causes a decrease in shear strain and less dissipation of energy.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Dynamic behaviour of weathered red mudstone in Sichuan(China)under triaxial cyclic loading

The construction of a high-speed railway(HSR) in Southwest China is being hindered by a severe shortage of high-quality subgrade materials. However, red mudstone is widely distributed in the Sichuan Basin of China. The ability to use weathered red mudstone(WRM) to fill subgrade beds by controlling its critical stress and cumulative strain would enable substantial savings in project investments and mitigate damage to the ecological environment. To better understand the dynamic behaviour of WRM, both monotonic and cyclic triaxial tests were performed. The evolution of the cumulative strain vs. increased loading cycles was measured. The influences of confining pressure and loading cycles on the dynamic modulus, damping ratio, critical cyclic stress ratio(CSR), and dynamic stress level(DSL) were investigated. The relationship between the CSR and loading cycles under different failure strain criteria(0.1%-1.0%) was analysed. The prediction model of cumulative strain was also evaluated. The results indicated that the shear strength of WRM sufficiently meets the static strength requirements of subgrade. The critical dynamic stress of WRM can thus satisfy the dynamic stress-bearing requirement of the HSR subgrade. The critical CSR decreases and displays a power function with increasing confining pressure. As the confining pressure increases, the DSL remains relatively stable, ranging between 0.153 and 0.163. Furthermore, the relationship between the dynamic strength and loading cycles required to cause failure was established. Finally, a newly developed model for determining cumulative strain was established. A prediction exercise showed that the model is in good agreement with the experimental data.

Pore water pressure increment model for saturated Nanjing fine sand subject to cyclic loading

Three groups of dynamic triaxial tests were performed for saturated Nanjing fine sand subjected to uniform cyclic loading. The tested curves of the excess pore water pressure （EPWP） ratio variation with the ratio of the number of cycles are provided. The concept of the EPWP increment ratio is introduced and two new concepts of the effective dynamic shear stress ratio and the log decrement of effective stress are defined. It is found that the development of the EPWP increment ratio can be divided into three stages： descending, stable and ascending. Furthermore, at the stable and ascending stages, a satisfactory linear relationship is obtained between the accumulative EPWP increment ratio and natural logarithm of the effective dynamic shear stress ratio. Accordingly, the EPWP increment ratio at the number of cycles N has been deduced that is proportional to the log decrement of effective stress at the cycle number N-l, but is independent of the cyclic stress amplitude. Based on the analysis, a new EPWP increment model for saturated Nanjing fine sand is developed from tested data fitting, which provides a better prediction of the curves of EPWP generation, the number of cycles required for initial liquefaction and the liquefaction resistance.

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Hexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio(α) and the cyclic dynamic stress ratio(η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1.For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex stress paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitutive models.

Dilatancy and liquefaction behaviour of clean sand at wide range of confining stresses

The state of clean sand was mainly dependent on its void ratio(density)and confining stress that greatly influenced the mechanical behavior(compression,dilatancy and liquefaction)of clean sand.Confirming whether the confining stress was a state variable of sand required precise element tests at different confining stress,especially the tests under very low confining stress whose test data were very limited.In this study,static-dynamic characteristics of clean sand was comprehensively investigated by a unified test program under low and normal confining stress ranging from 5 to 98 kPa,under monotonic/cyclic and drained/undrained conditions,together with the literature available data under confining stress of 1.0 to 3.0 MPa.For monotonic loading tests,the contraction/dilation phase transition was observed for loose sand at low confining stress,and dilatancy angles were stress-dependent.In addition,the liquefaction resistance was observed to increase with reducing of confining stress,and the axial strain varied from compressive to dilative when confining stress increased.Special attention was also paid to the enhancement effect of membrane,and it was observed that its influence on the test results was limited.In addition,the experimental results were proved reliable by reproducibility.

Study on one—dimensional consolidation of saturated soil with semi—pervious boundaries and under cyclic loading

The variation of effective stress ratio of stratfied soil with semi pervious boundaries and under cyclic loading was analyzed on the basis of Terzaghi's one dimensional consolidation assumptions. A solution by Laplace Transform was obtained for the case when the soil was under time varied loading. With numerical inversion of Laplace Transform, some useful results were obtained for several kinds of commonly encountered loadings. The results can be meaningful in engineering practice.

重塑黄土的往返加卸载真三轴试验研究

针对不同应力路径往返加卸载条件下黄土累积塑性应变发展特性,以重塑黄土为研究对象,利用真三轴仪开展不同应力路径的往返加卸载试验研究,探究不同应力路径、应力幅值下黄土的循环应力时程曲线、滞回曲线、骨干曲线及累积塑性应变曲线的影响规律。揭示了应力路径对重塑黄土力学特性的影响,描述了各主应力与中主应力比b和应力幅值的相关性,提出了重塑黄土的滞回曲线近似呈椭圆形,长轴斜率随中主应力比b值的增大而增大,随应力幅值的增大而减小;随着中主应力比b值的增大,循环应力-应变骨干曲线随之硬化,累积塑性应变曲线依次降低,且累积塑性应变发展更早的进入平缓阶段,为解决相关黄土工程问题提供了参考。

速度脉冲型地震动作用下局部可液化场地响应

为研究速度脉冲效应对可液化场地的影响,基于OpenSees平台建立有限元模型,对近断层速度脉冲型地震动与无速度脉冲地震动作用下局部可液化场地的竖向位移、加速度时程、土体剪应力-应变、超孔隙水压力比、循环应力比等土体的响应差异进行研究。数值计算结果表明:相同输入地震动幅值前提下,无脉冲地震动作用下可液化土体的竖向永久位移与位移发展持时平均值比速度脉冲型地震动作用分别大13%、19%;而速度脉冲型地震动作用下土体最大剪应变是无速度脉冲地震动的约5.4倍,最大剪应力约1.7倍;速度脉冲效应使土体的剪应力-剪应变滞回圈所围面积更大但滞回圈数量较少,且不同深度土体具有更大的循环应力比,从而促进土体发生液化;非液化密砂层放大地震动加速度幅值;液化松砂层对地震加速度时程进行了高频滤波,使地表加速度时程更为平滑且稀疏;速度脉冲效应作用下液化土层超孔隙水压力比整体较小,表明土体剪胀效应更加强烈。

不均匀波浪荷载作用下海积软黏土的动力特性

为研究饱和海积黏土在均匀与不均匀波浪荷载作用下的循环特性,利用GDS空心圆柱扭剪仪进行了一系列不排水试验,在相同的初始固结状态下,对试样施加不同最大偏应力q_(max)、最小偏应力q_(min)的圆形及螺旋形应力路径的轴—扭联合循环载荷。分析了在考虑主应力轴旋转时,这两种不同应力路径的循环应力比R_(CS)与动应力比δ=q_(mim)/q_(max)对循环加载期间土体动力特性的影响。试验结果表明:R_(CS)与δ的增大均能提升黏土在波浪荷载下的孔压、轴向应变、双幅剪切应变及其速率,同时也能使土体轴向回弹模量与动剪切模量的衰减更严重,且δ的作用效果会随R_(CS)的增大而增大。当R_(CS)≤0.05时,土体在循环期间保持为“弹性安定或塑性安定”状态;而当R_(CS)≥0.06时,土体会处于“疲劳破坏”或“塑性蠕变”状态,其具体形式由R_(CS)与δ共同决定。土体在循环过程中的轴向回弹模量与动剪切模量近似呈一定比例。

循环荷载对粉土海床中单桩横向承载特性的影响

在较大的波浪荷载作用下,海洋单桩会出现承载力降低、甚至失稳现象。利用GDS三轴仪对杭州湾重塑海相粉土进行了静三轴、动三轴和循环后静三轴不排水剪试验,研究了循环荷载作用对循环后粉土变形和不排水强度特性的影响,分别建立了动孔压比与循环应力比和循环次数、动孔压比与循环后不排水强度比及割线模量比的经验关系式。在此基础上,根据波浪荷载在海床深度方向的剪应力比分布,得到了桩侧粉土刚度和强度的衰减比深度分布,计算了波浪荷载对单桩横向承载特性的影响。在本算例条件下,波浪荷载对粉土海床的强度和刚度弱化随深度急剧衰减,影响深度约40 m,海床浅部约5 m深度有液化现象,循环荷载后桩身的刚性反应增强、位移和反弯点深度增加,弯矩和侧压力减小,总的横向承载力降低约40%。

循环荷载下饱和黄土的剪切特性与破坏模式

饱和黄土的破坏模式和剪切特性是分析黄土地基及其构筑物地震变形的基础,为了揭示循环荷载下黄土独特的强度衰减和变形劣化规律,本文开展了饱和黄土不排水动三轴试验,控制初始剪应力(q_(s))和循环剪应力(q_(c)),研究了不同初始应力状态下饱和黄土的动强度、孔压发展规律及破坏模式。试验结果表明:当q_(s)<q_(c)时,重塑和原状黄土试样表现为循环迁移型破坏,当q_(s)≥q_(c)时,重塑黄土试样表现为流动型破坏,而原状黄土试样则表现为塑性应变累积型破坏;黄土试样的循环应力比(R_(CS))、循环阻力比(R_(CR,10))随着初始剪应力比(R_(SS))的增大呈先增大后减小的趋势;循环迁移型和塑性应变累积型破坏在循环加载的初始阶段孔压上升迅速,孔压增长曲线分别呈“风琴”状和“喇叭”状,而流动型破坏的初始阶段孔压增长速率较慢,当到达某一振次后孔压突然增长,孔压增长曲线呈“镰刀”状。基于初始阶段孔压发展指标(K_(1-2))与初始应力状态(q_(s)/q_(c))提出了图表法,可用于预测循环荷载下饱和黄土的破坏模式。

重载铁路基床级配碎石动弹性模量及颗粒破碎试验研究

针对级配碎石的动力特性以及颗粒破碎性质,采用室内动三轴试验,研究其在循环荷载作用下循环应力比(cyclic stress ratio,CSR)、围压以及加载次数对累积动应变、动弹性模量、颗粒形状系数和颗粒破碎的影响。研究结果表明,不同CSR条件下,加载次数达到10000次时,累积动应变基本完成。随着加载次数的增加,不同CSR下的动弹性模量逐渐减小,滞回圈面积逐渐增加后保持稳定。低围压下,CSR对动弹性模量影响不显著,动弹性模量增加幅度较少;高围压下,动弹性模量随着CSR的增加而增长较大。循环荷载作用下,颗粒破碎方式主要为研磨;颗粒粒径越大,试验后的颗粒形状系数球度越大,颗粒越靠近球形,其轮廓线越圆滑。当CSR小于0.3时,影响颗粒破碎的主要因素为动应力大小,而围压影响不显著;当CSR大于0.3时,颗粒破碎主要因素受动应力和围压共同影响。

循环荷载作用下含水合物粉细砂的残余变形

本文针对不同饱和度和不同围压水平的含水合物粉细砂进行了一系列不排水循环三轴剪切试验,研究了轴向应变和孔隙水压力的发展,分析了影响含水合物粉细砂残余应变的主要因素:循环应力比、有效围压和水合物饱和度。在Monismith公式的基础上,提出了一种新的经验公式,能够预测循环荷载作用下含水合物粉细砂的残余变形,预测结果与实验结果的对比表明该经验公式具有良好的适用性。

纳米CaCO_(3)影响下重塑软黏土动力特性及微观孔隙结构研究

为研究循环荷载下纳米CaCO_(3)重塑软黏土的动力特性与微观形态,进行GDS动三轴、NMR试验,分析其动应力-动应变、动弹性模量、阻尼比及微观孔隙变化规律。结果表明:随着纳米CaCO_(3)掺量增加、围压增大,软黏土的动应变逐渐减小,动弹性模量逐渐增大;固结应力比增大使纳米CaCO_(3)重塑软黏土动应变先减小后增大,动弹性模量先增加后减小;围压和固结应力比的提高均可有效降低软黏土的阻尼比;软黏土滞回耗能与动应变呈现明显的非线性关系;纳米CaCO_(3)重塑软黏土T2分布曲线主峰峰值及峰面积相比于素软黏土显著降低,孔隙比减小使土体结构更加稳定。所进行的纳米CaCO_(3)重塑软黏土动力特性研究,可为实际工程提供参考。

循环荷载下粉煤灰群桩复合地基承载性能试验研究

在不同的循环荷载比和循环次数下进行循环荷载室内模型试验,从桩顶累积沉降、桩身应力、桩间粉煤灰应力和桩土应力比等方面分析循环次数和循环荷载比等因素对粉煤灰复合地基承载特性的影响。在循环荷载作用下,桩顶累积沉降与循环荷载比呈非线性相关关系,桩顶累积沉降曲线主要分为稳定型和发展型等2种变化形态;随着循环次数的增加,桩身应力和桩间粉煤灰应力均呈现先增大后稳定的趋势;当循环次数超过临界次数时,桩土应力比的减小速率将出现收敛;循环荷载比的增大会导致土拱效应发挥不稳定。

基于静力触探测试的国内外砂土液化判别方法

在砂土或粉土分布广泛的地区,地震液化是导致地基失稳和上部结构受损的直接原因之一。因此,判定地基土液化可能性是抗震勘察设计中的一个重大课题。由于获得高质量"未扰动"砂土样的困难和试验成本的限制,基于静力触探(CPT)的原位测试方法通常用于砂土液化势的评价。孔压静力触探(CPTU)作为一种新型的原位测试技术,采用其测试指标进行砂土液化势的评价日益受到人们的重视。目前,基于CPT测试资料已经提出了许多砂土液化势的评价方法,但国内外采用CPT判别砂土液化的方法是不同的。在对我国《建筑抗震设计规范》(GB50011–2001)中砂土液化判别方法与国外修正的Seed简化法的原理、方法及参数进行分析的基础上,将其2种方法进行比较,进而讨论了2种方法的差异。由于这些差异的存在,采用不同方法判别砂土液化可能性时会得出不同的、甚至是相反的结果。结合济宁—徐州高速公路砂土场地的CPT和CPTU测试资料,采用我国规范判别法、Seed简化法进行了液化判别分析,并进行了对比验算。其中Robertson法与Olsen法所得到的结论基本一致,而且Robertson法似乎比Olsen法稍微精确一些,而采用规范法所判定的结果偏于保守,这与锥尖阻力基准值的取值大小有关。

上海粉土液化特性及孔压模型的试验研究

根据循环三轴试验,分析了上海原状及重塑粉土的液化特性,提出了原状粉土的孔压上升模型,并与细砂的液化特性和孔丘模型进行了对比。