Research on the energy evolution characteristics and the failure intensity of rocks

It is pretty challenging and difficult to quantitatively evaluate the intensity of dynamic disasters in deep mining engineering.Based on the uniaxial loading-unloading experiments for five types of rocks,this paper investigated the energy evolution characteristics,and identified the damage and crack propagation thresholds.Also,the fragment size distributions of the rocks after failure were analyzed.The energy release rate(Ge)and energy dissipation rate(Gd)were then proposed to describe the change of energies per unit volume and per unit strain.Results demonstrated that the more brittle rocks had the shorter stage of unstable crack growth and the lower induced damage at crack damage thresholds.The evolution characteristics of the strain energy rates can be easily identified by the crack propagation thresholds.The failure intensity index(FId),which equals to the values of Ge/Gd at the failure point,was further put forth.It can account for the brittleness of the rocks,the intensity of rock failure as well as the degree of rock fragmentation.It was revealed that a higher FId corresponded to a lower fractal dimension and stronger dynamic failure.

Study of Debond Fracture Toughness of Sandwich Composites with Metal Foam Core

Two types of experiments were designed and performed to evaluate the adhesive bond in metal foam composite sandwich structures. The tensile bond strength of face/core was determined through the flatwise tensile test （FWT）. The test results show that the interfacial peel strength is lower than the interlaminar peel strength in FWT test. The mode I interracial fracture toughness （GIC） of sandwich structures containing a pre-crack on the upper face/core interface is determined by modified cracked sandwich beam （MCSB） experiment. It is found that the crack propagates unsynchronously on the two side of the specimen and the propagation of interfacial debonding always stays on the face/core interface during the MCSB tests. In order to simulate the failure of metal foam composite sandwich structures, a computational model based on the Tsai-Hill failure criterion and cohesive zone model is used. By comparing with experiment results, it can be concluded that the computational model can validly simulate the interracial failure of metal foam composite sandwich structures with reasonable accuracy.

The energy release rate for hygrothermal coupling elastic materials

In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.

Experiment on Mode Ⅰ/Ⅱ Mixed Interfacial Fracture Characterization of Foam Core Sandwich Materials at Elevated Temperatures

Foam-cored sandwich materials have been widely used in the civil engineering due to their advantages such as lightweight,high strength,and excellent anti-corrosion ability. However,the interfacial bonding strength of foamcored sandwich materials is weakened at elevated temperatures. In practice,the effect of high temperature cannot be ignored,because the composites and foams are sensitive to the change of temperature in the environment. In this study,a series of single-leg bending beams were tested at different temperatures to evaluate the influences of high temperatures on Mode Ⅰ/Ⅱ mixed interfacial fracture of foam core sandwich materials. The temperature was from29 ℃ to 90 ℃,covered the glass transition temperature of composites and foam core,respectively. The Mode Ⅰ/Ⅱ mixed interfacial crack prorogation and its corresponding interfacial strain energy release rate were summarized.

FRACTURE ANALYSIS OF A FUNCTIONALLY GRADED STRIP UNDER PLANE DEFORMATION

In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.

MICROMECHANICAL DAMAGE MODEL FOR ROCKS AND CONCRETES SUBJECTED TO COUPLED TENSILE AND SHEAR STRESSES

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

Anisotropy in shear-sliding fracture behavior of layered shale under different normal stress conditions

Shear-sliding mode(mode Ⅱ)fracture of rocks is a vital failure form in deep underground engineering.To gain deep insight into the anisotropic shear fracture behaviors of a typical shale under high normal stress conditions,a series of direct shear tests were conducted on double-notched specimens in three typical bedding orientations(i.e.,the arrester,divider,short-transverse orientations)and under five normal stresses.The modeⅡfracture toughness(K_(Ⅱc))is found to exhibit a significant 3D anisotropy.The maximum K_(Ⅱc)is obtained in the divider orientation,followed by those in the arrester and short-transverse orientations.In contrast,the 3D anisotropy in the critical modeⅡenergy release rate(G_(Ⅱc))is not as significant as that in K_(Ⅱc),and G_(Ⅱc)in the arrester orientation is quite close to that in the divider orientation.The anisotropy in the prepeak input energy accumulated during shearing is found to be exactly consistent with that in G_(Ⅱc),which has not been noted before.Furthermore,the anisotropies in the modeⅡfracture resistances will,unexpectedly,not be weakened by the high normal stress.Owing to the layered structures,tensile cracks are involved during the modeⅡfracture process,resulting in the formation of rough fracture surfaces.

An energy-consistent fracture model for ferroelectrics

The fracture behavior of ferroelectrics has been intensively studied in recent decades, though currently a widely accepted fracture mechanism is still lacking. In this work, enlightened by previous experimental observations that crack propagation in ferroelectrics is always accompanied by domain switching, we propose a micromechanical model in which both crack propagation and domain switching are controlled by energy-based criteria. Both electric energy and mechanical energy can induce domain switching, while only mechanical energy can drive crack propagation. Furthermore, constrained domain switching is considered in this model, leading to the gradient domain switching zone near the crack tip. Analysis results show that stress-induced ferroelastic switching always has a toughening effect as the mechanical energy release rate serves as the driving force for both fracture and domain switching. In comparison, the electric-field-induced switching may have either a toughening or detoughening effect. The proposed model can qualitatively agree with the existing experimental results.

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.

基于能量原理不同含水率下煤岩体变形破坏能量损伤演化机制

为探究不同含水率下煤岩体在变形破坏过程中的能量演化规律与损伤演化特征,对双马一矿煤岩体开展了在不同含水率条件下单轴压缩试验,基于能量计算及最小耗能原理,分析不同含水率下煤岩体能量耗散特征及损伤演化机制,结果表明:不同含水率下煤岩体力学性质不同,峰值应变与含水率呈正相关,抗压强度、弹性模量与含水率呈负相关;煤岩体含水率越高,其在峰值处弹性应变能及破坏吸收总应变能越小,耗散能占总应变能比例越高;基于最小耗能原理建立的损伤本构模型表明:随着煤岩体含水率增加,损伤门槛值逐渐降低;干燥状态下,煤岩体在应力峰值处损伤变量分别为0.36、0.28,当含水率增至自然状态时,煤岩体在应力峰值处损伤变量值分别下降0.09、0.18,但当含水率增至饱水状态时,煤岩体在应力峰值处损伤变量值反而分别大幅度上升0.102、0.49,总体呈先减后增的发展趋势;进一步建立了不同含水率煤岩损伤应变能释放率演化模型,低含水率煤岩较干燥煤岩的最大损伤应变能释放率大幅度下降,降幅分别为45.61%、31.29%,而随着含水率增加至饱水状态,其最大损伤应变能释放率增大幅度较平缓,分别为3.08%、8.80%,表明煤岩破坏剧烈程度并未大幅度增加。研究成果对煤岩矿柱水害预测评价与岩石损伤评估具有一定参考意义。

基于态基近场动力学的碳化硅陶瓷圆柱壳体断裂损伤分析

碳化硅(SiC)陶瓷材料具有优异的力学性能,广泛应用于各种工程部件中.然而,陶瓷是脆性材料,当发生脆断时会造成巨大的危害.因此对其断裂行为的准确预测显得极为重要.为了研究SiC陶瓷壳体在外载荷作用下的断裂损伤机理,首先通过准静态拉伸和压缩实验获得SiC陶瓷的临界能量释放率,建立了适用于拉伸和压缩损伤分析的常规态基近场动力学模型.然后,采用Fortran语言编程实现了陶瓷壳体在线性递增外载荷作用下断裂损伤行为的数值仿真,并将所获得的仿真值与理论预测值进行对比,验证了所建模型的准确性.最后,对仿真结果进行详细分析,揭示了壳体结构的损伤扩展演化规律.仿真结果表明:初始损伤区源于壳体内壁面的压缩断裂,且沿环向呈90°均匀分布.随着载荷的逐渐增加,壳体外壁面出现拉伸断裂损伤区,内外壁面的损伤区先沿着周向扩展,再向着壳体中面缓慢延伸,并在厚度方向贯穿整个壳体.随后,在壳体轴线方向出现拉-压损伤混合区,该损伤区沿着轴向扩展,最终将壳体分成4个断裂区.所建模型能够有效地描述复杂载荷作用下SiC陶瓷结构的断裂损伤演化过程,同时弥补了态基近场动力学在断裂分析方面的不足.

岩性差异对裂缝穿层扩展的率相关断裂特征影响

薄互层致密砂岩储层由于层间岩性差异、纵向非均质性强等原因,导致主裂缝难以垂向扩展,提高裂缝扩展速率可有效促进裂缝穿层扩展。为研究裂缝穿层断裂过程中的率效应机制,采用人工预制水泥-砂岩试件进行了三点弯断裂试验,通过数字图像法监测了裂缝扩展至层间接触界面处时的断裂过程区(fracture process zone,FPZ)发育特征;基于断裂动力学理论,提出了考虑率效应的裂缝扩展路径预测模型。研究结果表明:低速扩展时裂缝形态曲折,FPZ呈现短、宽的现象,高速扩展时裂缝平直,FPZ呈现长、窄的特点;FPZ存在离散性,且存在相互吸引的特点,裂缝从低弹性模量岩石向高弹性模量岩石低速扩展时层间接触界面处会提前产生高应变区,导致裂缝扩展至层间接触界面处时沿层扩展,高速扩展无此现象;岩石抗拉强度与裂缝穿越单元体的平均抗拉强度呈正相关关系,低扩展速率裂缝优先沿微缺陷扩展,导致岩石抗拉强度降低,高扩展速率裂缝优先沿自相似方向扩展,穿过大量高强度单元导致岩石抗拉强度增加;裂缝与层间接触界面夹角越大,裂缝越容易穿层扩展,裂缝与层间接触界面夹角为30°时,夹角影响效果最大,夹角超过30°时影响效果逐渐下降。研究结果对水力压裂参数优化、增加水力裂缝高度、提高薄互层致密砂岩油气产量具有重要意义。

皮质骨微观能量释放率与大鼠月龄关系

目的预测大鼠股骨皮质骨微观能量释放率,探究微观能量释放率随大鼠月龄的变化关系。方法依托前期实验数据,结合皮质骨断裂模拟数值方法,对比仿真与实验测得载荷-位移曲线及断裂模式,反演预测不同月龄大鼠股骨皮质骨的微观能量释放率。结果经预测得到1、3、5、7、9、11、15月龄大鼠股骨皮质骨微观能量释放率分别处于0.08~0.12、0.12~0.14、0.15~0.19、0.25~0.28、0.23~0.25、0.19~0.22、0.13~0.16 N/mm。结论微观能量释放率随月龄增长而下降导致失效载荷降低,说明微观能量释放率是决定骨折发生的主要因素之一,但断裂时刻却未观察到明显下降,说明微观能量释放率与结构断裂时刻未呈线性正比关系。研究结果能够从临床层面协助解释皮质骨的骨折发生机制。

含内聚裂纹弹性体的能量释放率与断裂能

根据内聚裂纹模型,含裂纹的弹性体在裂纹尖端附近存在一内聚区,内聚区断裂参数表达是其核心研究内容.该文假定弹性平板直线裂纹尖端存在一带状内聚区,并由一条虚拟线裂纹代替,其张开位移与内聚力存在确定的非线性函数关系.以Ⅰ型边裂纹为例,导出了满足虚拟裂纹条件的解析解;在此基础上给出了物理裂纹尖端扩展的能量释放率Ga、内聚裂纹尖端扩展的能量释放率Gb的计算公式;讨论了Gb,J积分和断裂能GF之间的关系;从理论上证明了临界能量释放率Gbc就是断裂能GF,Gbc可以作为含内聚区材料裂纹失稳扩展的断裂参数.提出的方法适用于所有含Ⅰ、Ⅱ、Ⅲ型内聚裂纹的弹性体.

纯弯曲Sandwich梁试样界面裂纹扩展的应变能释放率

纯弯曲的Ｓａｎｄｗｉｃｈ梁试样在评价界面断裂抗力方面有重要作用。利用能量的叠加原理和截面转换方法，本文导出了纯弯曲Ｓａｎｄｗｉｃｈ梁试样界面裂纹扩展应变能释放率的显式解，并根据实验测得的界面裂纹扩展的临界载荷，用其计算出了四点弯曲Ｓｉ３Ｎ４／Ａｌ／Ｓｉ３Ｎ４试样Ｓｉ３Ｎ４／Ａｌ扩散连接界面的断裂韧度。

不同倾角单裂隙对非均质岩石失稳演化研究

岩体中的裂隙对岩石的力学行为、能量演化和失稳破坏有显著影响。为阐明不同倾角单裂隙对岩石能量演化和失稳破坏机理,基于颗粒流PFC2D方法,建立了不同倾角单裂隙砂质泥岩数值模型,模拟了不同倾角单裂隙下砂质泥岩的单轴压缩试验。研究表明,随着单裂隙倾角变大,砂质泥岩的强度与弹性模量先降低后增大,预制裂纹会影响断裂面的裂纹起始位置,并加速断裂面的形成;声发射事件在岩样破坏前存在小范围沉寂期,该特征可作为岩石破坏的前兆判据;随着裂隙倾角的增大,总能量持续增大,弹性能和耗散能呈现先增加后减小的趋势,倾角30°时,岩石试样冲击倾向性最弱,有利于降低冲击地压危险,倾角为90°时,岩石试样冲击倾向性相对最强,不利于冲击地压的防治。

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.

An Elastoplastic Damage Constitutive Model for Concrete

An elastoplastic damage constitutive model to simulate nonlinear behavior of concrete is presented. Similar to traditional plastic theory, the irreversible deformation is modeled in effective stress space. In order to better describe different stiffness degradation mechanisms of concrete under tensile and compressive loading conditions, two damage variables, i.e., tension and compression are introduced, to quantitatively evaluate the degree of deterioration of concrete structure. The rate dependent behavior is taken into account, and this model is derived firmly in the framework of irreversible thermodynamics. Fully implicit backward-Euler algorithm is suggested to perform constitutive integration. Numerical results of the model accord well with the test results for specimens under uniaxial tension and compression, biaxial loading and triaxial loading. Failure processes of double-edge-notched （DEN） specimen are also simulated to further validate the proposed model.

A novel formulation of material nonlinear analysis in structural mechanics

This article demonstrates a novel approach for material nonlinear analysis.This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior.Use of elastic moduli is eliminated.Instead,stress and strain functions are used as the material input in the analysis procedure.These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting.This way,the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior.It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results,easy to adopt and simple in calculations.The method eliminates all types of linearity assumptions in basic derivations of equations and hence,eliminates all types of possibility of errors in the analysis procedure as well.As it is required to know stress distribution in the structural body by proper modelling and structural idealization,the proposed analysis approach can be regarded as stress-based analysis procedure.Basic problems such as uniaxial problem,beam bending,and torsion problems are solved.It is found that approach is very suitable for solving the problems of fracture mechanics.Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated.The approach solves the fracture problem with relative ease in strength of material style calculations.For all problems,results are compared with the classical displacement-based liner theory.

高应力卸荷条件下硬岩能量演化研究

为探究引水隧洞在开挖过程中岩石破坏过程的能量演化规律,选取磁铁矿石开展了常规三轴及三轴峰前恒轴压卸围压试验。结果表明,在常规三轴试验中,岩石在峰值应力前以弹性应变能存储和耗散应变能消耗为主,在峰值应力后以弹性应变能释放和耗散应变能消耗为主;随着围压的增加,峰前剪切断裂能高于峰后;在卸围压试验中,耗散应变能均以指数函数趋势增加,卸荷速率越快,卸荷段经历时间较短,卸荷点与跌落点之间的耗散能在单位时间内能量增量变化速率越高;基于岩爆动力学M-C准则及卸荷路径下岩石内聚力丧失与岩石耗散应变能,新定义了岩石卸荷过程中的损伤变量,从能量角度揭示了岩石变形破坏的损伤程度。