A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens is derived based on the Lemaitre strain equivalence hypothesis,which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

Mechanical properties and damage constitutive model of sandstone after acid corrosion and high temperature treatments

Aiming at the problem of temperature-mechanics-chemical(T-M-C)action encountered by rocks in underground engineering,sandstone was selected as the sample for acid corrosion treatment at pH 1,3,5 and 7,the acid corrosion treated samples were then subjected to high-temperature experiments at 25,300,600,and 900℃,and triaxial compression experiments were conducted in the laboratory.The experimental results show that the superposition of chemical damage and thermal damage has a significant impact on the quality,wave velocity,porosity and compression failure characteristics of the rock.Based on the Lemaitre strain equivalent hypothesis theory,the damage degree of rock material was described by introducing damage variables,and the spatial mobilized plane(SMP)criterion was adopted.The damage constitutive model can well reflect the stress-strain characteristics of the rock triaxial compression process,which verified the rationality and reliability of the model parameters.The experiment and constitutive model analyzed the change law of mechanical properties of rock after chemical corrosion and high temperature thermal damage,which had certain practical significance for rock engineering construction.

Creep characteristics and constitutive model for frozen mixed soils

The uniform settle caused by the permafrost creep is still the primary problem of engineering construction in cold region.To investigate the creep characteristics of frozen soils mixed with silty clay and coarse-grained sand,several triaxial creep tests of frozen mixed soils under different conditions(temperature,confining pressure,coarse-grained particle content) were performed,and the effects of the temperature,confining pressure and coarse particle content on the creep characteristics of frozen mixed soils were also analyzed.The results of the experiments indicated that when the confining pressure was low,the specimen exhibited an attenuation creep under a low-stress level(0.4-0.7) and a non-attenuation creep under a high-stress level(0.7-0.9).In contrast,when the confining pressure was high,the specimen had both initial and stable creep stages,but no the accelerated creep stage.The higher the content of coarse grains,the shorter the stable creep stage,and the easier to enter the accelerated creep stage for the specimen.Further,the long-term strength of frozen soils decreased with an increase in the content of coarse grains.Finally,a newly improved Nishihara model was proposed to consider both the hardening effect and damage effect by introducing both the hardening and damage variables,which can model the entire creep process of frozen soils modeled relatively easily.It was found that with the increasing content of coarse particle,both the strengthening and damaged effects in the creep process are reduced。

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale,as a kind of brittle rock,often exhibits different nonlinear stress-strain behavior,failure and timedependent behavior under different strain rates.To capture these features,this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1.The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates.These strain rate-dependent mechanical behaviors of shale are originated from damage growth,which is described by a damage parameter.When axial strain is the same,the damage parameter is positively correlated with strain rate.When strain rate is the same,with an increase of axial strain,the damage parameter decreases firstly from an initial value(about 0.1 to 0.2),soon reaches its minimum(about 0.1),and then increases to an asymptotic value of 0.8.Based on the experimental results,taking yield stress as the cut-off point and considering damage variable evolution,a new measure of micro-mechanical strength is proposed.Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength,a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established.Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process,nonlinear elements and creep damage are generally introduced in the model to resolve this issue.However,several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution.Nevertheless,the creep damage mechanism of rocks is still not clearly understood.In this study,a reasonable representation of the damage variables of solid materials is presented.Specifically,based on the Gurson damage model,the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established.Further,the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model.Finally,the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite.And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite.Overall,this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern,which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Rheological mechanical properties and its constitutive relation of soft rock considering influence of clay mineral composition and content

Rheological mechanical properties of the soft rock are afected signifcantly by its main physical characteristics-clay mineral.In this study,taking the mudstone on the roof and foor in four typical mining regions as the research object,frstly,the clay mineral characteristic was analyzed by the X-ray difraction test.Subsequently,rheological mechanical properties of mudstone samples under diferent confning pressures are studied through triaxial compression and creep tests.The results show that the clay mineral content of mudstone in diferent regions is diferent,which leads to signifcant diferences in its rheological properties,and these diferences have a good correlation with the content of montmorillonite and illite-montmorillonite mixed layer.Taking the montmorillonite content as an example,compared with the sample with 3.56%under the lower stress level,the initial creep deformation of the sample with 11.19%increased by 3.25 times,the viscosity coefcient and longterm strength decreased by 80.59%and 53.94%,respectively.Furthermore,based on the test results,the damage variation is constructed considering the montmorillonite content and stress level,and the M–S creep damage constitutive model of soft rock is established.Finally,the test results can be ftted with determination coefcients ranging from 0.9020 to 0.9741,which proves that the constitutive relation can refect the infuence of the clay mineral content in the samples preferably.This study has an important reference for revealing the long-term stability control mechanism of soft rock roadway rich in clay minerals.

Fracture and Damage Behaviors of Concrete in the Fractal Space

The fracture toughness, the driving force and the fracture energy for an infinite plate with a fractal crack are investigated in the fractal space in this work. The perimeter-area relation is adopted to derive the transforma-tion rule between damage variables in the fractal space and Euclidean space. A plasticity yield criterion is introduced and a damage variable tensor is decomposed into tensile and compressive components to describe the distinct behaviors in tension and compression. A plastic damage constitutive model for concrete in the Euclidean space is developed and generalized to fractal case according to the transformation rule of damage variables. Numerical calculations of the present model with and without fractal are conducted and compared with experimental data to verify the efficiency of this model and show the necessity of considering the fractal effect in the constitutive model of concrete. The structural response and mesh sensitivity of a notched unre-inforced concrete beam under 3-point bending test are theoretical studied and show good agreement with the experimental data.

A Constitutive Model of Granite Shear Creep under Moisture

Previous constitutive models of granite shear creep have two limitations：（1） although moisture greatly affects granite shear creep behavior, currently there are no constitutive models that include this factor;（2） there are also no models that include an acceleration stage. This paper presents an improved Burgers constitutive model with the addition of a damage parameter to characterize the moisture effect and uses a nonlinear relation equation between stress and strain for inclusion as the acceleration stage. The damage parameter is determined from granite creep experiment under four different moisture contents（0%, 0.22%, 0.49%, and 0.79%）. The nonlinear relation equation is obtained by fitting a dataset of stain versus time under five different loading stages. To verify the presented model, a creep experiment was conducted on other granite samples and the results show that the model agrees well with the experimental observation data.

Investigation on creep behavior of warm frozen silty sand under thermo-mechanical coupling loads

In cold regions,the creep characteristics of warm frozen silty sand have significant effect on the stability of slope and subgrade.To investigate the creep behavior of warm frozen silty sand under thermo-mechanical coupling loads,a series of triaxial creep tests were carried out under different temperatures and stresses.The test results reveal that the creep strains decrease as the consolidation stress increases,and finally tend to be equal under the same loading stress,regardless of whether the stress is isotropic or deviatoric.Additionally,warm frozen silty sand is highly sensitive to temperature,which greatly influences the creep strain both in the consolidation stage and loading stage.Furthermore,based on the creep test phenomena,a new creep model that considers the influence of the stress level,temperature,hardening,and damage effect was established and experimentally validated.Finally,the sensitivity of the model parameters was analyzed,and it was found that the creep curve transitions from the attenuation creep stage to the non-attenuation creep stage as the temperature coefficient and stress coefficient increases.The hardening effect gradually changes to the damage effect as the coupling coefficient of the hardening and damage increases.

CO_(2)−荷载耦合作用下煤体细观统计损伤本构模型及验证

CO_(2)吸附会对煤体产生损伤劣化作用进而降低其稳定性,对CO_(2)封存的长期安全性提出挑战,明确CO_(2)劣化作用并建立本构模型至关重要。采用损伤力学理论和统计理论推导出能够综合反映CO_(2)吸附和荷载耦合作用下煤体总损伤变量的计算公式,并重点考虑了压密段的影响,分段建立了CO_(2)作用下煤体的细观统计损伤本构方程,明确了模型各参数的确定方法。最后通过CT扫描实验系统、MTS 816实验系统确定了本构模型参数,并采用自主研制的气−固耦合实验系统对不同CO_(2)压力下煤体进行了单轴压缩实验,验证了模型的合理性。研究结果表明:①基于CT扫描获取的裂隙率和运用Weibull分布理论分别定义了吸附和受载作用下的损伤变量,结合损伤理论进一步得到二者耦合作用下的总损伤变量,并建立了细观统计损伤本构模型;②基于CT扫描技术的裂隙三维重构真实反映了CO_(2)作用前后裂隙扩展特征,CO_(2)压力越高,裂隙扩展越充分,煤样三维裂隙参数和损伤变量越大,所形成的空间裂隙网络越复杂;③CO_(2)对煤体力学性质劣化作用显著,煤体的抗压强度与弹性模量随CO_(2)压力增加分别降低了49.78%和22.63%,CO_(2)对煤体的溶胀效应、塑化效应和气楔效应的综合作用导致了力学参数的降低;④建立的CO_(2)作用下煤体细观统计损伤模型理论曲线与单轴实验曲线具有较高的吻合度,说明损伤本构模型能够较好地反映出CO_(2)对煤体力学特性的损伤劣化作用,体现了损伤本构模型及模型参数确定方法的合理性与适用性。

卸围压下弱胶结软岩分数阶蠕变损伤本构模型

为研究地下硐室开挖卸荷诱发的软岩蠕变损伤特征,以西部矿区弱胶结软岩为研究对象,利用GDS HPTAS开展了分级卸围压蠕变试验,研究了不同含水条件下弱胶结软岩卸围压下蠕变特征和蠕变速率特征。基于稳态蠕变速率倒数的方法,确定了弱胶结软岩长期强度和含水率的数学指数函数关系。基于蠕变速率曲线特征提出了一种确定衰减蠕变与等速蠕变分界点t_1和等速蠕变与加速蠕变分界点t_2的新方法。引入Riemann-Liouville分数阶积分算子和负时间指数损伤演化变量,定义了非线性损伤Abel黏壶,建立了一个包括弹性元件、黏弹性损伤元件、黏性元件和非线性黏塑性损伤元件的六元件分数阶蠕变损伤本构模型。基于试验结果,采用Trust-Region算法进行了模型参数识别和敏感性分析。结果表明,所建立的模型具有物理意义明确、与试验值吻合度较高等特点,可较为准确地反映开挖卸荷条件下弱胶结软岩蠕变损伤特性,对保障地下工程长期稳定性具有重要的意义。

钛合金室温受压蠕变损伤本构模型

为了解决工程上在评估深潜器耐压壳体安全可靠性时不考虑拉压蠕变破坏机理产生的差异,会导致较大计算误差问题,本文提出了适用于室温蠕变的蠕变损伤本构模型。通过分析钛合金材料蠕变特性,考虑了室温环境下位错堆积造成的蠕变阻力,并且位错堆积的现象与时间有关。基于微分自洽法提出了适用于室温环境下的钛合金蠕变本构模型,得到受压情况下TC4ELI的相关材料参数,并将该模型用USDFLD和CREEP子程序进行定义。研究表明:对于受压结构而言,使用通过拉伸蠕变实验得到的本构模型的计算结果会过于保守,对于含V型缺口平板受压时等效蠕变应变的相对误差为168.20%。本文所提出的模型适用于环肋耐压壳结构的蠕变损伤分析。

单轴压缩下结构充填体的能耗特征及本构模型与验证

以矿山分层充填为背景,针对由不同力学性能基体组合而成的三层复合结构充填体,基于初始超声波速和耗散能演化特征,并借助Logistic模型,建立了能够描述考虑层间结构和荷载耦合作用下完整的损伤变量方程。进一步结合损伤力学理论和有效介质理论,构建了考虑压密段的结构充填体分段本构模型。结果表明:根据耗散能的演化特征可将结构充填体的变形破坏特征划分为三个阶段,即初始累积损伤阶段、快速损伤阶段和加速损伤阶段,损伤加速的转折点位置与中间层的力学性质有关;损伤变量呈现“S”形增长的演化规律,初始损伤与中间层灰砂比和高度比之间呈指数关系,最大损伤率随着中间层强度的降低而降低;建立的本构模型能够较好地描述应力-应变过程,与实测数据吻合度较高。

炭质板岩冻融后蠕变特性试验及损伤模型研究

为了揭示炭质板岩冻融后蠕变力学,以汶川-马尔康高速公路卓克基隧道炭质板岩为研究对象。开展了不同冻融循环次数下的三轴压缩蠕变试验。假设岩石受荷载作用下的时效损伤服从Weibull概率密度分布,由此定义受荷损伤变量,依据唯象损伤力学理论定义冻融损伤变量,考虑冻融与应力的耦合效应,构建冻融、受荷总损伤变量。基于炭质板岩蠕变行为表现,确定H-H|N-N|S蠕变模型结构,基于此进行了损伤演化,得到一个新的可反映冻融与应力耦合的蠕变损伤模型,拓展为三维应力状态。给出模型参数求解方法,并分析了损伤演化规律,采用所建模型识别炭质板岩蠕变数据,引入一个传统模型进行了对比,分析模拟对比曲线,验证新模型的可行性和合理性。结果表明:炭质板岩的蠕变试验曲线呈“台阶形”,轴向应变随着时间增长而递增;随着冻融作用的增强,长期强度随之递减,冻融循环作用可能会降低岩石蠕变破坏的难度;新模型对炭质板岩蠕变行为的模拟效果较好,平均R^(2)达0.9878,证明了新模型描述炭质板岩冻融后蠕变特性的可行性。冻融作用的加强,使得炭质板岩内部结构的损伤发展更快,对岩石蠕变破坏起一定促进作用。

混凝土重力坝结构损伤机理及演化规律研究

混凝土重力坝作为水利工程的主要坝型,其结构损伤机理及演化规律研究对确保大坝安全性和稳定性具有重要意义。针对混凝土重力坝在承载作用下可能面临的温度应力损伤、收缩徐变损伤和疲劳损伤等问题,采用理论分析、实验研究和数值模拟等方法,对混凝土重力坝结构损伤机理进行了深入研究。基于损伤力学理论,明确了损伤状态变量,提出了各项异性弹性受损材料的本构模型,分析了混凝土材料的微观损伤机理和性能特点,揭示了混凝土重力坝在不同损伤阶段下的应力应变变化规律。

浸水条件下含水率对粉砂质泥岩蠕变特性的影响研究

泥岩具有强度低、遇水易软化的特点,尤其是富水泥岩地层,对工程岩体的长期稳定性影响较大,但相关研究少有报道,因此亟待深入研究泥岩遇水蠕变特性。开展了不同初始含水率泥岩试样在天然和浸水条件下的分级加载蠕变试验,研究了水对岩体蠕变特性的影响机理,结合广义Kelvin模型,构建了考虑含水劣化效应的蠕变损伤本构模型,并将新模型嵌入FLAC3D有限差分软件中,模拟了不同工况下泥岩蠕变变形特性,并与室内试验结果进行了对比。结果表明:随着含水率的增大,岩体蠕变应变量增大,长期强度降低;相比天然条件,浸水环境使得岩体长期强度劣化更为严重,试样初始含水率越小,浸水条件对其蠕变变形影响越大;将岩体因水的劣化效应定义为蠕变参数的损伤因子,损伤因子随着含水率的增加而提高;考虑含水劣化效应的蠕变损伤本构模型数值模拟结果与室内试验结果基本吻合,验证了新模型的合理性。

汽轮机部件多轴蠕变-疲劳寿命评估方法

汽轮机汽缸、转子等高温部件运行中受到疲劳损伤和蠕变损伤,二者的损伤机制会互相影响,有必要对疲劳损伤和蠕变损伤以及二者的耦合作用进行评估。在Ohno-Wang循环塑性模型基础上进行了拓展,提出了一种统一黏弹塑性循环材料本构模型,在ABAQUS平台上采用UMAT用户子程序开发了多轴蠕变-疲劳耦合分析程序。采用该程序对1 000 MW超超临界机组高温转子进行了多轴蠕变-疲劳寿命评估,结果显示损伤最大的位置出现在第1级动叶叶根轮槽位置。研究成果可为汽轮机高温部件的寿命评估提供技术支撑。

固体推进剂长期贮存损伤性能研究进展

主要从发动机装药结构的损伤性能有限元仿真分析方法、蠕变损伤试验设计以及蠕变损伤研究方法等3个方面综述了固体推进剂蠕变损伤性能研究进展,指出蠕变效应会导致推进剂内部含能颗粒与基体之间出现脱湿细观损伤,进一步总结了现今蠕变试验研究和宏细观蠕变性能数值模拟中的不足。分析认为,蠕变损伤试验研究的难点在于研究推进剂材料级试验结果与实际装药结构中推进剂蠕变效应的对应性和数据映射关系,推进剂损伤数值模拟的难点是推进剂含损伤蠕变多尺度本构模型的建立,以及在自重载荷下药柱形变预测计算的应用计算问题。最后提出的建议可以为开展长期贮存条件下推进剂蠕变损伤性能研究提供一定的参考。

高应力状态下岩石蠕变本构模型的研究

为探究高应力状态下岩石蠕变损伤本构的问题,开展不同应力水平蠕变试验。通过理论分析提出了一种新的损伤表达式,利用其修正了蠕变参数,建立了一种考虑损伤全过程的蠕变本构模型,并结合试验结果分析了模型参数规律。结果表明:高应力状态下,随着应力的增大,岩石在单调加载过程中引起的初始损伤分别为0.21、0.31和0.4,对应蠕变寿命,其随着蠕变应力水平的增大而减小;新模型能够较好地反映蠕变应变三阶段特征,尤其是在稳态段应变的增长趋势与试验结果更为一致,相关性系数均≥0.98;蠕变段弹性模量与黏弹性系数均随着应力比的增大呈现先快后慢的非线性减小趋势。

EBSD parameter assessment and constitutive models of crept HR3C austenitic steel

Creep damage and evolution of HR3C steel at 650℃ were investigated using electron backscatter diffraction(EBSD),and EBSD-based parameter assessments were conducted.EBSD analyses show that the grain size is almost unchanged and no obvious texture formed after creep at different creep rates.The lowest proportion of low Σ coincidence site lattice grain boundaries under 150 MPa implies that the primary twin structures are preserved under the low stress level,while some twin structures evolved into general grain boundaries at the high creep level.Two main damage features of microcracks and cavities can be seen along the grain boundaries:the former emerged at higher stress levels,while the latter appeared at the lower stress level,and both were shown under medium stress.Band contrast shows that the most severe creep damage is present at 170 MPa.It implies that the creep mechanism differs distinctly under different stress levels,and the transition point is around 170 MPa.Kernel average misorientation is better to describe the local plastic deformation related to the strain distribution while grain reference orientation deviation describes the inhomogeneous strain distribution.Creep lifetime prediction models including the isothermal method,Larson-Miller parameter method and Monkman–Grant relation were evaluated by the experimental data and literature data,and they are valid for predicting creep behavior.