Criterion of local energy release rate of gob instability in deep mines considering unloading stress path

The stress path characteristics of surrounding rock in the formation of gob were analyzed and the unloading was solved. Taking Chengchao Iron Mine as the engineering background, the model for analyzing the instability of deep gob was established based on the mechanism of stress relief in deep mining.The energy evolution law was analyzed by introducing the local energy release rate index(LERR), and the energy criterion of the instability of surrounding rock was established based on the cusp catastrophe theory. The results show that the evolution equation of the local energy release of the surrounding rock is a quartic function with one unknown and the release rate increases gradually during the mining process.The calculation results show that the gob is stable. The LERR per unit volume of the bottom structure is relatively smaller which means that the stability is better. The LERR distribution showed that there was main energy release in the horizontal direction and energy concentration in the vertical direction which meets the characteristics of deep mining. In summary, this model could effectively calculate the stability of surrounding rock in the formation of gob. The LERR could reflect the dynamic process of energy release,transfer and dissipation and that provided an important reference for the study of the stability of deep mined out area.

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.

Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.

ANALYSIS OF ENERGY RELEASE RATE FOR CRACKED LAMINATES

An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of chasical plate theory analysis. a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then. an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition. a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally. several different kinds of laminates are examined and the results obtained could be used in engineering applications.

RESEARCH FOR THE STRAIN ENERGY RELEASE RATE OF COMPLEX CRACKS BY USING POINT-BY-POINT CLOSED EXTRAPOLATION APPROACH

A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.

Energy Release Rates for Interface Cracks in Multilayered Structures

This paper examines the evolution of the interfacial deflection energy release rates in multilayered structures under four-point bending.The J-integral and the extended finite element method(XFEM)are adopted to investigate the evolution of the interfacial deflection energy release rates of composite structures.Numerical results not only verify the accuracy of analytical solutions for the steady-state interfacial deflection energy release rate,but also provide the evolutionary history of the interfacial deflection energy release rate under different crack lengths.In addition,non-dimensional parametric analyses are performed to discuss the effects of normalized ratios of the crack length,the elastic modulus,and the thickness on the interfacial deflection energy release rate.The results demonstrate that the elastic modulus ratio and thickness ratio have a distinct influence on the interfacial deflection energy release rate for multilayered beams.Furthermore,an unstable interfacial crack tends to occur for elastic multilayer beams with higher elastic modulus on the upper sub-beam under bending moments.The unstable interfacial fracture shows a decreasing interfacial deflection energy release rate with an increasing interfacial crack length.

ON CRACK-TIP STRAIA ENERGY RELEASE RATE IN NON-PRINCIPAL DIRECTIONS OF ELASTICITY FOR SIMPLE LAYER PLATE OF COMPOSITE MATERIALS

In this paper,the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied.The formulae of transformation between characteristic roots,coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived.Then,the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.

Energy Release Rate Measurement of Welded Bamboo Joints

Double cantilever beam tests were used to measure the energy release rates of linear vibrational welded moso bamboo joints.The influence of the length of the preserved cracks,the different combinations of the inner and outer bamboo surfaces and the moisture content is studied herein.The experimental compliance method,which is based on linear elastic fracture mechanics and has been shown to be an ideal method,was used to analyze data with the power equation.The results show that the preserved initial crack length does not have a significant effect on the final measured energy release rate,while the moso bamboo combination does affect the properties dramatically.The welded moso bamboo joints with inner-inner surfaces have the highest energy release rate of 122 J/m^2.The average energy release of the outer-outer combination was only 102 J/m^2.The expansion of the cracks also became easier when the moisture content of the welded joints was 18.5%compared to 4.5% and 10.1%.So the moisture resistance of the welded joints should be duly improved.

磁电弹性材料中含有带四条裂纹的正方形孔的反平面断裂问题

针对反平面剪切力作用下,磁电弹性材料中含有带四条裂纹的正方形孔口的断裂问题进行了深入地探索。基于线弹性断裂理论和Riemann-Schwarz解析延拓定理,利用复变函数方法和留数定理,通过构造合适的数值保角映射函数,将解析函数边值问题转化为柯西积分方程组进行解答,获得了磁电非渗透边界条件下裂纹尖端断裂力学参数的显式表达式。通过与已有结果的对比,验证了方法的有效性。利用数值算例描述了孔洞尺寸、四条裂纹长度和机–电–磁载荷等因素对裂纹扩展参数的影响规律。结果表明:水平右裂纹对孔口裂纹扩展影响更显著;垂直裂纹影响水平裂纹的扩展趋势;在磁电非渗透边界条件下,随着机械载荷的增大,裂纹尖端的应力强度因子变大,而电载荷和磁载荷对裂纹的扩展与机械载荷的大小和方向密切相关。该分析方法为求解复杂多连通域的智能复合材料问题提供了一条有效途径,研究成果为含裂纹的复合材料或结构的优化设计提供了科学依据。

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。

磁电弹性材料含正六边形纳米缺陷的表面效应研究

在磁电弹性材料断裂力学框架下,利用表面弹性理论和解析函数边值理论,解析研究了反平面机械载荷、面内电载荷和磁载荷耦合作用下磁电弹性体中正六边形孔边均布六条等长裂纹的Ⅲ型断裂力学问题,确定了考虑表面效应时纳米尺寸裂纹问题的精确解.基于以上解析解,通过数值算例揭示了表面效应、缺陷几何参数及所施加的损坏载荷分别在两种理想裂纹面电磁条件假设下对断裂参数的影响规律.研究发现:考虑表面效应时影响裂纹扩展的因素与经典弹性理论解答明显不同.各个物理分量呈现出显著的尺寸依赖效应,但随着缺陷尺寸的增加,表面效应的影响呈下降趋势,并趋于经典弹性理论值.研究可为该材料应用于微纳米结构和微机电系统提供理论指导.

磁电弹性体中正三角形孔口快速传播裂纹问题分析

目的探索含运动缺陷的磁电弹性材料的力学性能和断裂机理。方法基于磁电弹性材料断裂理论和广义复变函数理论展开力学行为研究,通过作伽利略变换,将磁电弹性材料的断裂问题转化为稳定裂纹动力学问题进行解答。结果获得了磁电非渗透边界条件下裂纹尖端处动态应力强度因子以及机械应变能释放率的解析表达式。结论磁电弹性材料损伤、断裂现象的发生不仅受缺陷的几何参数和损坏载荷的影响,还与缺陷的运动速度有密切关系。

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。

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。

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.

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.

贵州龙凤煤矿无烟煤自燃特性及动力学参数

为研究贵州龙凤煤矿采空区遗煤自燃特性,首先采用同步热分析(TG-DSC)试验装置,测试该矿无烟煤在不同升温速率和氧气浓度条件下特征温度和放热量的变化规律,然后使用Coats-Redfern积分公式定量分析活化能。结果表明:相同氧气浓度条件下,煤样特征温度点均随升温速率增大呈升高趋势;相同升温速率的煤样其特征温度点T_(2)随氧气浓度的增大出现波动性变化,T_(3)先增加后降低,而T_(1)、T_(4)、T_(5)和T_(6)则逐渐降低;随着升温速率的增大,煤样放热峰值、峰值温度及放热量逐渐增加;煤样初始放热温度和峰值温度随氧气浓度的增大而减小,而放热峰值和放热量则先增加后降低,并在15%氧气浓度时达到最大;煤样受热分解/燃烧阶段的最概然机理函数符合n=4的A-E方程,在21%氧气浓度、不同升温速率下的活化能分别为141.18,12984,118.03,102.05,84.38 kJ/mol,随升温速率升高而降低,而在10 K/min升温速率、不同氧气浓度下的活化能分别为85.24,97.79,114.51,125.18,129.84 kJ/mol,随氧气浓度升高而增大。试验结果为该矿的煤自燃防治提供了理论依据。

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

东欢坨矿切顶卸压沿空留巷聚能爆破关键参数研究

为确定切顶卸压沿空留巷合理的聚能爆破参数,实现成功留巷的目的,以东欢坨矿20221工作面倾斜中厚煤层为工程背景,采用理论分析、工程经验和现场试验研究相结合的方法,对双向聚能张拉爆破参数进行了研究,对不同爆破参数下单位长度爆破孔成缝率进行了分析。结果表明,在爆破孔深7.5 m、炮孔间距500 mm的情况下,“4-4-1”的装药结构爆破成缝效果明显,成缝率达到90%以上,在工作面回采过后顶板垮落及时,现场应用效果良好。

真三轴多面快速卸荷岩爆多余能量特征实验研究

利用自主研发的真三轴岩爆实验系统,进行了一系列真三轴高压加载下水平方向不同快速卸荷面数的滞后性岩爆实验。基于能量理论,实验研究了不同卸荷面数下的岩爆储能特征、多余能量(ΔE)、多余能量释放速度(EERR)以及AE裂纹演化特征。实验得出了以下主要结论:1)岩爆的发生相较于岩石单轴加载静态破坏,主要是由于多余能量ΔE的产生,多余能量ΔE取决于岩石在岩爆前所存储的弹性应变能、峰后设备输入的能量以及残余弹性应变能,随着卸荷面数的增加,ΔE逐渐减小,但多余能量释放速度EERR却增大,导致岩爆现象变得更为剧烈;2)在真三轴高压加载条件下进行快速卸荷,会使应力应变曲线出现卸荷平台,卸荷损伤主要以张拉破坏为主,并主要集中在临空面附近,随着卸荷面数的增加卸荷损伤逐渐增大;3)在砂岩的损伤演化过程中,拉伸裂纹占据主导地位,而在最终临近岩爆阶段,剪切裂纹曲线的斜率大于拉伸裂纹,表明剪切裂纹是导致试样失稳破坏的关键因素。