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.

A new criterion of rock burst proneness based on residual energy release rate index

The natural property of rock material,whether impact occurs,is the key influencing factor of the occurrence of rock burst disaster.To accurately assess rock burst proneness,this study focuses on typical sandstone as the research object.Uniaxial cyclic loading and unloading tests were conducted to measure the elastic strain energy accumulated in sandstone under different stress levels and a relationship between elastic strain energy and stress level was established.The results show that:(1)The peak stress under cyclic loading and unloading conditions is slightly lower than the uniaxial compressive strength.With an increase in the number of cycles,the internal damage of sandstone continues to accumulate,and the mechanical properties such as compressive strength continue to deteriorate;(2)With an increase in stress,the input strain energy,elastic strain energy,and dissipated strain energy also increase;(3)When the stress is low,the increase in elastic strain energy is large and shows a steady growth;with an increase in stress,the increase of elastic strain energy decreases;(4)The square of stress at any time has a good linear relationship with elastic strain energy.According to the relationship obtained from the test,the elastic strain energy at the peak stress time can be obtained;(5)A new criterion for assessing rock burst proneness is proposed:residual energy release rate index W_(T),which characterizes the energy release per unit time when the rock burst occurs.The intervals for evaluating the rock burst proneness of the residual energy release rate index W_(T) are as follows:W_(T)<0.025,indicating no rock burst proneness;0.025≤W_(T)<0.15,indicating weak rock burst proneness;0.15≤W_(T)<2,indicating medium rock burst proneness;W_(T)>2,indicating strong rock burst proneness;and(6)The rationality of the proposed residual energy release rate index W_(T) is verified by the multi-index method and the multi-sample method,and the proposed residual energy release rate index is used to determine the rock burst proneness of 10 kinds of rock samples.The evaluation accuracy is shown to be high,and it can reflect the actual rock burst proneness.

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.

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.

ANALYSIS OF ELASTO-PLASTIC POSTBUCKLING AND ENERGY RELEASE RATE FOR DELAMINATED FIBER METAL LAMINATED BEAMS IN THERMAL ENVIRONMENT

The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed in this paper. Considering geometrical nonlinearity, thermal environment and geometrical initial imperfection, the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established, which are solved using the differential quadrature method and iterative method. Based on these, according to the J-integral theory, the elasto-plastic energy release rate is studied. The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.

Dynamic simulation for tempo-spatial distribution of strain energy density in inhomogeneous stratified crust

Through simulating the research on dynamic variations of strain energy density (SED) in seismogenic model with hard inclusion, the authors have gained further knowledge to such problems as the process of earthquake preparation, initial rupture, conditions of the initial rupture and fracture propagation direction, etc. Results of the research show that SED (strain energy density) in soft inclusion is very high during the initial period of earthquake preparation. And the increment of SED in the soft area decreases at the later stage of the process. Meanwhile, the increment increases quickly in hard inclusion and in the intersection zone of the inclusion with an erecting fault, where the increment of SED is maximum. Thus, the intersection zone between hard inclusion with larger elastic modulus and erecting fault becomes the place where the initial rupture or earthquake occurs. The fracture in the end part of the hard inclusion spreads along a direction nearly vertical to the erecting fault, so the theoretical fracture direction is consistent with that calculated by digital simulation.

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。

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。

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。