Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC STRESS INTENSITY FACTOR

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS

The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material （FGPM）. It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors.

Dynamic stress concentration of an elliptical cavity in a semi-elliptical hill under SH-waves

The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.

基于功率谱形心SWF的SRM复合材料壳体脱粘缺陷识别方法

针对SRM复合材料粘接结构间隙型脱粘和紧贴型脱粘的识别问题,运用声-超声的方法进行检测,在综合分析不同脱粘类型时域和频域波形的基础上,提出采用功率谱形心SWF表征脱粘类型。实验结果表明,功率谱形心SWF能有效地对两种脱粘类型进行识别。

Research Review of Principles and Methods for Ultrasonic Measurement of Axial Stress in Bolts

Bolts are important fasteners indispensable in the manufacturing field for their advantages, which include convenient assembly and disassembly, easy maintenance, refastenability to prevent looseness, and the avoidance of a phase change in the connected material composition. The precise control of the tightening force in bolts is closely related to the safety and reliability of the connected equipment or structure. Although there are many methods for estimating the tightening force applied to a bolt during assembly, poor accuracy in controlling the preload during the tightening process and a lack of monitoring to determine the residual axial force in service remain issues in evaluating the safety of bolted assemblies. As a nondestructive testing technology, ultrasonic measurement can be applied to successfully address these issues. In order to help researchers understand the theoretical basis and technological development in this field and to equip them to conduct further in-depth research, in this review, the basic knowledge describing the state of stress and deformation of bolts, as well as conventional testing methods are summarized and analyzed. Then, through a review of recent research of the ultrasonic measurement of the axial stress in bolts, the influence of the e ective stressed length and temperature are analyzed and proposed methods of calibration and compensation are reviewed. In order to avoid coupling errors caused by traditional piezoelectric transducers, two newly proposed ultrasonic coupling technologies, the electromagnetic acoustic transducer(EMAT) and the permanent mounted transducer system(PMTS), are reviewed. Finally, the new direction of research of the detection of residual axial stress in in-service bolts that have been assembled to yield is discussed.

SHEAR WAVE SCATTERING FROM A PARTIALLY DEBONDED PIEZOELECTRIC CYLINDRICAL INCLUSION

The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.

Scattering of elastic wave by a cylindrical shell deeply embeded in saturated soils

The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave （fast compressional wave） by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.

SCATTERING OF ANTI-PLANE SHEAR WAVES BY A SINGLE CRACK IN AN UNBOUNDED TRANSVERSELY ISOTROPIC ELECTRO-MAGNETO-ELASTIC MEDIUM

A theoretical treatment of the scattering of anti-plane shear(SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.

Scattering of SH-wave from interface cylindrical elastic inclusion with a semicircular disconnected curve

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green＇s function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green＇s function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed.

Surface Effects on the Scatter of SH-Wave by a Shallow Buried the Elliptical Hole

The methods of complex function, multi-polar coordinate system, and conformal mapping are used to solve dynamic stress concentration factor. The surface elasticity theory is applied to obtain the stress boundary conditions on the surface. The effects of frequency and the ration of the major and minor axis of the ellipse on the dynamic stress concentration factor around the elliptical nano-hole are discussed in detail. When the size of elliptical hole shrinks to nanometers, the numerical results show that the surface effect has a significant effect on the scattering of SH-wave.

Dynamic Analysis of Nanosized Arbitrary Shape Inclusion under SH Waves

The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress and displacement are given by classical elastic theory. Secondly, the arbitrary shape inclusion in the two-dimensional plane is transformed into a unit circle domain by conformal mapping, the incident wave field and the scattered wave field are presented. Next, the stress and displacement boundary conditions are established by considering surface elasticity theory, The infinite algebraic equations for solving the unknown coefficients of the scattered and standing waves are obtained. Finally, the influence of surface effect, non-dimensional wave number, Shear modulus and hole curvature on the dynamic stress concentration factor are analyzed by some examples, the numerical results show that the surface effect weakens the dynamic stress concentration. With the increase of wave number, the dynamic stress concentration factor (DSCF) decreases. Shear modulus and hole curvature have significant effects on DSCF.

梯度围岩结构应力波透射模型与传播衰减规律

锚杆支护与钻孔卸压等方式改变巷道围岩介质属性,形成具有三介质两结构面的巷道梯度围岩结构,增加对应力波的吸收与衰减能力,防止巷道冲击破坏。为揭示巷道梯度围岩结构中应力波传播衰减规律,建立了梯度围岩结构应力波透射模型,从弹性波在介质交界面处的波场分解和能量分配角度出发,分析了卸压带密度以及应力波入射角度对能量系数的影响,发现梯度围岩卸压带的密度和入射角对各折反射波的能量系数具有显著影响,揭示了梯度围岩结构的吸能防冲力学机理。基于不同梯度围岩结构模型的数值计算,综合应力波的波幅衰减系数、波阻抗匹配系数、能量吸收占比、能量衰减系数等参量,对比分析巷道梯度围岩结构对应力波传播衰减的影响规律。研究结果表明:梯度围岩结构卸压带宽度增加,应力波振动频率降低,波幅衰减系数随之增加,能量衰减系数呈上升趋势,提高了梯度围岩结构的缓冲与隔震性能,增强了巷道的防冲能力;卸压带宽度较小时,会引起应力波在梯度结构中的复杂叠加,使得应力波在局部区域幅值激增,合理的卸压带宽度能够避免应力波在三介质两结构面结构中的复杂叠加。卸压带内钻孔间排距减小,梯度围岩结构卸压带中介质的弹性模量与密度下降,能量吸收占比增加,提高了对应力波的吸波性能。梯度围岩结构中“三带”的波阻抗匹配系数越大,能量衰减系数越大,即“三带”的介质性质差异越大,梯度围岩对于应力波的吸收衰减效果越好,通过调控卸压钻孔的深度与间排距改变卸压带的尺寸和物理力学性能,可有效提高梯度围岩结构的吸波、缓冲、隔震性能。结合工程实例分析证实了梯度围岩结构可有效吸收冲击地压产生的应力波能量,避免冲击地压灾害发生。

INTERACTION OF ELASTIC WAVES WITH A PERIODIC ARRAY OF COLLINEAR INPLANE CRACKS

A boundary integral equation method is applied to the study of the interaction of plane elastic waves with a periodic array of collinear inplane cracks.Numerical results are presented for the dynamic stress in- tensity factors.The effects of the wave type,wave frequency,wave incidence angle,and crack spacing on the dynamic stress intensity factors are analyzed in detail.

柱面SH波作用下管道的动力响应

在地下空间开发建设过程中,钻爆法开挖诱发的爆破地震波对地下管道安全至关重要。当爆源距离管道较近时,波阵面的曲率会对管道的爆破动力响应特性产生显著影响。采用波函数展开法研究了柱面SH波爆破作用下管道的动应力集中问题,首先讨论了混凝土管道和PVC管道的动应力集中系数分布规律,进而探讨了一般情况下波源到管道轴线距离、入射波频率以及管道与土层剪切模量比η对管道内壁动应力集中系数的影响。结果表明:相较于PVC管道,混凝土管道内壁的动应力集中系数分布形状对柱面SH波频率较敏感;η是影响管道动应力集中系数的重要指标,当入射波频率一定时,随着η的增大,管道最大动应力集中系数也逐渐增大;η一定时,随着入射波频率增大,管道最大动应力集中系数逐渐减小;波源到管道轴线距离会因波阵面曲率对管道破坏位置产生影响,而其对最大动应力集中系数的影响较小。

SH波入射下正交各向异性双相介质界面附近圆孔的动应力集中

基于复变函数和格林函数的方法,探讨了SH波在具有圆孔的正交各向异性两相介质中的散射,分析了圆孔周围的动态响应规律。首先建立问题的二维解析模型,将全空间分为两个部分:均匀各向同性上半空间以及含圆柱形孔洞的正交各向异性下半空间。采用格林函数法推导出了两半空间界面处各点的格林函数表达式,并引入复变量,构造出了SH波入射下求解区域内位移和应力的表达式。考虑界面的连续性条件,将未定反平面力加载到两个半空间的水平界面上,推导出Fredholm定解积分方程组,用弱奇异积分方程的直接离散方法求解。最终通过算例分析,发现介质的正交各向异性参数、入射波波数、角度以及孔洞埋深等对下半空间圆孔周边的动应力集中系数(DSCF)影响显著。

应力损伤下玄武岩纤维混凝土内部孔隙结构及能量耗散试验研究

基于试验研究不同应力水平损伤作用下玄武岩纤维混凝土损伤度、孔隙结构及能量耗散规律,采用非金属超声波检测仪测量0σm、0.15σm、0.3σm、0.45σm、0.6σm五种不同应力水平损伤作用下试件纵波波速及损伤因子变化规律,利用核磁共振(NMR)试验方法研究不同应力水平损伤作用下试件T_(2)谱分布、孔径分布及孔隙率变化规律,并结合万能压力机对试件进行单轴压缩试验,分析其应力-应变曲线、峰值应力及能量耗散变化规律。结果表明:应力作用下,玄武岩纤维混凝土试件会发生损伤,试件高度随作用应力水平的增大而减小,纵波波速先小幅度增大后降低,低应力水平作用对试件整体性有增强效果,高应力水平作用对试件造成损伤,且应力越大,损伤程度越高;0.3σm应力水平作用下试件T_(2)图谱峰值最低,0.6σm应力水平作用下试件T2图谱峰值最高,试件孔隙率随应力水平的增大先减小后增加;试件内部孔隙主要以微孔、中孔形式存在,低应力水平作用下试件内部原生裂纹被压缩,试件内部中孔向微孔转化,总孔隙率降低,高应力水平作用时试件在应力作用下发生损伤变形,试件内部裂纹孔径增大,孔隙率增加;玄武岩纤维的掺入增加了混凝土的塑性变形能力,试件峰值应力随作用应力水平的增大而降低,且降幅显著增加;试件单位体积耗散能会随应力水平的增大而减小,机械损伤度S随应力水平的增大存在小幅度增加,应力损伤下试件弹性变形能力减小,能量耗散率增加。

多次冲击荷载下GFRP管约束混凝土劈裂拉伸力学性能试验研究

为探究冲击荷载作用下GFRP管对混凝土结构的约束保护作用,采用非金属超声波分析仪测量不同冲击次数下GFRP约束混凝土试件纵波波速,利用直径为74 mm分离式霍普金森压杆装置(SHPB)对试件开展动态单轴劈裂拉伸试验,分析试件纵波波速、损伤因子、应力应变曲线、峰值应力与GFRP管壁厚度及冲击次数间的关系。结果表明:冲击次数的增加使得试件纵波波速降低,损伤因子增大,在第4次冲击荷载作用后管壁厚度1、1.5、2 mm试件损伤因子分别为29.56%、22.33%、17.77%,管壁厚度的增加,增加了对混凝土的径向约束,改善了混凝土内部的应力状态,降低了其在冲击荷载作用下的损伤度。素混凝土试件的动态拉伸应力应变曲线呈单峰曲线,GFRP约束混凝土试件的动态拉伸应力应变曲线呈双峰曲线,管壁与混凝土接触面处使得应力波产生透反射从而改变波的传播路径。相较于管壁厚度为0.5 mm试件,管壁厚度为1、1.5、2 mm在第1次冲击荷载作用下试件应力增幅为12.03%、24.97%、51.11%,2.0 mm管壁厚度时相较于第1次冲击荷载作用,第2、3、4次冲击作用下能量吸收率降幅为6.72%、12.75%、15.92%,试件峰值应力及破碎耗能密度随管壁厚度增加而增大,随冲击次数的增加而降低。

多次冲击荷载下玄武岩纤维高强混凝土孔隙结构及力学特性试验研究

为探究玄武岩纤维高强混凝土在多次冲击荷载作用下的安全性,采用非金属超声波分析仪及核磁共振试验装置测量不同应变率及冲击次数下试件纵波波速及内部孔隙结构,利用直径为74 mm分离式霍普金森压杆装置对试件开展动态压缩试验,分析试件纵波波速、损伤因子、T_2图谱、孔隙结构及应力应变随冲击气压及冲击次数间的变化规律。试验结果表明:试件纵波波速随冲击次数增加而降低,损伤因子随冲击次数的增加而增大,两者间呈良好的二次线性正相关;试件T_2图谱主要呈三峰型,冲击次数的增大会使图谱向右偏移且峰值增加;冲击次数的增加使孔隙直径增大且孔隙数目增多,试件孔隙率增大,且后续冲击作用更有利于裂隙的扩展;试件内部微孔、中孔含量占试件总孔隙率的95%以上,冲击荷载作用使试件内部微孔、中孔占比减小,大孔、裂隙占比增加;多次冲击荷载作用会使试件峰值应力降低,应变量增大,冲击次数与峰值应力间呈良好的二次函数负相关。

直角域中角点凹陷与浅埋孔洞对SH波的散射

为得到直角域中角点凹陷与浅埋孔洞的动态响应解析解,基于波函数展开法结合“镜像”思想构造角点凹陷和浅埋孔洞处的散射波场,采用傅里叶积分变换和坐标移动技术求解散射波场中的未知系数。通过参数化分析讨论入射波角度、频率及孔洞位置变化时,直角域中角点凹陷与浅埋孔洞对水平剪切(SH)波散射的影响。结果表明:SH波高频入射时,角点凹陷与浅埋孔洞之间的距离越近,孔洞处动应力的集中现象越明显,且要特别关注垂直和水平入射的情况,此时孔洞处动应力集中系数(DSCF)最大。