ANALYSIS OF A CRACK IN A FUNCTIONALLY GRADED STRIP WITH A POWER FORM SHEAR MODULUS

The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.

SCATTERING OF ANTI-PLANE SHEAR WAVES IN A FUNCTIONALLY GRADED MATERIAL STRIP WITH AN OFF-CENTER VERTICAL CRACK

The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.

SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

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.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

TORSIONAL IMPACT RESPONSE OF A PENNY-SHAPED CRACK IN A FUNCTIONAL GRADED STRIP

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.

THERMAL FRACTURE OF FUNCTIONALLY GRADED PLATE WITH PARALLEL SURFACE CRACKS

This work examines the fracture behavior of a functionally graded material （FGM） plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors （TSIFs） at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.

Analytical solution of multiple moving cracks in functionally graded piezoelectric strip

The dynamic behaviors of several moving cracks in a functionally graded piezoelectric （FGP） strip subjected to anti-plane mechanical loading and in-plane elec- trical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.

Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips

The dynamic interaction of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips subjected to the anti-plane shear harmonic stress waves was investigated. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is jump of displacement across the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter, the circular frequency of the incident waves and the thickness of the strip upon stress, electric displacement and magnetic flux intensity factors of cracks.

Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli's gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.

Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

The crack tip fields are investigated for a cracked functionally graded material （FGM） plate by Reissner＇s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson＇s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner＇s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner＇s effect when the in-homogeneity parameter approaches zero.

P110S钢级油管管体断裂原因

某油井P110S钢级油管接箍下方8 m位置处发生断裂,采用宏观观察、化学成分分析、金相检验、扫描电镜和能谱分析、X射线衍射分析等方法对油管断裂原因进行分析。结果表明:该批油管力学性能不稳定,油管断口上的腐蚀产物主要为FeS;油管的强度较高、使用温度较低且质量较大,导致油管内部形成硫化物应力腐蚀开裂。

含裂纹缺陷的预扭壳结构非线性振动特性研究

基于扩展等几何方法和一阶壳体剪切变形理论建立了含裂纹缺陷的功能梯度预扭壳结构的非线性振动控制方程。控制方程中考虑了预扭壳结构的预扭角度及几何非线性,应用扩展等几何方法,采用反映位移变化的富集函数来描述裂纹的位置及长度,一方面可以提高计算精度,另一方面可以避免在裂纹处的网格加密,提高计算效率。采用了直接迭代法求解非线性振动控制方程。通过与现有文献结果对比,证明了本文方法的正确性和稳定性。在此基础上,探究裂纹对功能梯度预扭壳结构非线性振动频率的影响,研究了预扭角度、裂纹位置及长度和材料的功能梯度指数等参数对预扭壳非线性振动特性的影响规律。

中厚板探伤缺陷分析及质量改进

针对鞍钢Q460E中厚板钢板存在的探伤缺陷问题,采取扫描电镜成分分析、夹渣物检验、酸蚀低倍检验等方法,分析了连铸和模铸钢板中夹渣和裂纹缺陷的产生原因,并制定了改进措施。通过对比、归类国内外中厚板产品主要探伤标准,将探伤缺陷分为八个质量等级。统计改进前后各质量等级钢板占比,得出最优质量等级钢板占比显著上升,钢板内部质量明显提高。

辽宁省高速公路灌缝率对PCI检测结果的影响分析及裂缝封闭方案建议

道路破损状况是影响道路行车安全性与舒适性的重要指标,通常情况下,裂缝病害对道路破损状况指标(PCI)的负面影响最为严重。文章基于2021~2022年辽宁省高速公路沥青路面2车道技术状况评价结果,分析了灌缝率对PCI检测结果的影响。结果表明:提高灌缝率对道路PCI指标评价有一定程度的提升,且通过提高灌缝率来提升路面技术状况评价结果,在短期内有着较高的经济效益。研究同时提出了裂缝等级四级划分标准,结合辽宁省高速公路沥青路面常用养护方案,评估了各养护方案在文章所设裂缝等级下的适用性。

气缸体铸件裂纹缺陷的改善措施

分析了气缸体裂纹产生的原因。针对易产生裂纹的位置,在相应的型板位置增加防裂纹片后,低牌号件号的铸件裂纹情况改善效果明显,而高牌号件号的裂纹改善效果并不显著,有待进一步的研究。

分级循环荷载下裂隙岩石疲劳破坏特性与能量演化机制

分级循环荷载下裂隙岩石裂隙扩展模式、疲劳变形特性以及能量演化规律对地下工程安全施工和运营有着重要意义。考虑裂隙角度、裂隙数量和裂隙分布开展常规劈裂试验、分级循环荷载试验和非接触变形测量试验,对破坏特征、动弹性模量进行分析,研究轴向不可逆变形与疲劳寿命之间的关系。从能量角度出发,计算破坏过程中的总吸收能量、可释放应变能及耗散能,分析能量演化与裂隙扩展模式响应关系。研究结果表明:1)岩石疲劳变形可分为初始变形阶段、稳定阶段和加速破坏阶段,滞回环曲线呈现出“疏—密—疏”的特性,对每200个循环的动弹性模量进行分析,加载第2阶段动弹性模量有强化特征,进入第3阶段后动弹性模量减小;2)总吸收能、耗散能和弹性能都呈上升趋势,总吸收能增长缓慢,增长速度随着循环次数增加逐渐变缓,耗散能在进入破坏阶段后迅速上升,弹性应变能变化趋势不明显,中等倾角的耗散能较多;3)在破坏过程中均会产生翼裂纹和倾斜次生裂纹,裂纹相互作用和合并,产生连续塑性应变累积,形成压碎的小颗粒碎屑,这与静荷载作用下脆性破坏机制不同。

预制裂纹对X70管线钢冲击韧性和断裂机制的影响

随着管线钢应用逐渐增加,预防裂纹的扩展研究作为管线钢结构性能的研究重点而备受学者关注。本试验采用疲劳方法预制裂纹缺口,利用示波冲击试验,测试其与常规V型缺口在不同温度下对X70管线钢韧性的影响。结果表明,相较于常规V型缺口冲击试验,预制裂纹缺口的韧脆转变温度提高了约44℃,更贴近GB/T 20801.2—2020《压力管道规范工业管道第2部分:材料》规定的最低使用温度,在温度值的确定上提供了科学参考。通过对预制裂纹扩展过程中特征参数和宏微观断口形貌的分析研究,结果表明,裂纹扩展随着温度降低表现出一定的规律性,为基于示波冲击试验预测断裂机制提供了一定的参考依据。