EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.

Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.

Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young＇s modulus are given in the numerical analysis.

Interface crack problems for mode Ⅱ of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.

Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Fatigue Crack Propagation Analysis of Orthotropic Steel Bridge with Crack Tip Elastoplastic Consideration

Due to the complex structure and dense weld of the orthotropic steel bridge deck(OSBD),fatigue cracks are prone to occur in the typical welding details.Welding residual stress(WRS)will cause a plastic zone at the crack tip.In this paper,an elastoplastic constitutive model based on the Chaboche kinematic hardening model was introduced,and the extended finite element method(XFEM)was used to study the influence of material elastoplasticity and crack tip plastic zone on the law of fatigue crack propagation.By judging the stress state of the residual stress field at the crack tip and selecting different crack propagation rate models to investigate the crack propagation law when plastic deformation was considered,the propagation path and propagation rate of fatigue crack of the OSBD were obtained.The results show that,whether the residual stress field is considered or not,the plastic deformation at the crack tip will not cause the obvious closure of the fatigue crack at the U-rib toe during the crack propagation process,but will significantly affect the crack propagation path.When material plasticity is considered,the propagation angle of fatigue crack at the U-rib toe basically remains unchanged along the short-axis direction of the initial crack,but is going up along the long-axis direction,and the crack tip plastic zone inhibits the propagation of the crack tip on one side.Compared with linear elastic materials,the crack propagation law considering material plasticity is more consistent with that in actual bridge engineering.In terms of the propagation rate,if the residual stress field is not considered,the fatigue crack propagation rate at U-rib toe with plasticity considered is slightly higher than that without plasticity considered,because plastic deformation will affect the amplitude of energy release rate.When considering the WRS field,the fatigue crack propagation rate at U-rib toe is increased due to the combined actions of plastic deformation and stress ratio R.

Analysis on non-oscillatory singularity behaviors of mode Ⅱ interface crack tip in orthotropic bimaterial

The fracture behaviors near the mode II interface crack tip for orthotropic bimaterial are studied. The non-oscillatory field, where the stress singularity exponent is a real number, is discussed by the complex function method and the undetermined coefficient method. From the research fracture problems, the stress functions with ten undetermined coefficients and an unknown singularity exponent are introduced when △1 〉 0 and △2 〉 0. By the existence theorem of non-trival solutions for the system of eight homogeneous linear equations, the characteristic equation, the stress singularity exponent, and the discriminating condition of the non-oscillatory singularity are found. By the uniqueness theorem of the solutions for the system of twelve non-homogeneous linear equations with ten unknowns, the ten undermined coefficients in the stress functions are uniquely determined. The definitions of the stress intensity factors are given with the help of one-sided limit, and their theoretical formulae are deduced. The analytic solutions of the stresses near the mode II interface crack tip are derived. The classical results for orthotropic material are obtained.

INVESTIGATION OF THE BEHAVIOR OF A GRIFFITH CRACK AT THE INTERFACE BETWEEN TWO DISSIMILAR ORTHOTROPIC ELASTIC HALF-PLANES FOR THE OPENING CRACK MODE

The behaviors of an interface crack between dissimilar orthotropic elastic half-planes subjected to uniform tension was reworked by use of the Schmidt method.By use of the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations,of which the unknown variables are the jumps of the displacements across the crack surfaces.Numerical examples are provided for the stress intensity factors of the cracks.Contrary to the previous solution of the interface crack,it is found that the stress singularity of the present interface crack solution is of the same nature as that for the ordinary crack in homogeneous materials.When the materials from the two half planes are the same,an exact solution can be otained.

Crack-tip field on mode Ⅱ interface crack of double dissimilar orthotropic composite materials

Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.

ON J-INTEGRALS NEAR MODELS Ⅰ,Ⅱ CRACK TIPS IN THE PLATE OF ORTHOTROPIC COMPOSITE MATERIAL

In this paper, we prove the independence of the path of the imegrals near model i II track tips in the plate of the orthotropic composite material. Then we derive the computing formulae of the J-integrals at the cases of and by using a complex variable method and redueing J-imegrals to compley farmThe J-integral computational formulae derived this paper have certain reference value for the theoretical researches and the experimental verifications in the plane fracture for composite material.

The edge crack problem for an orthotropic functionally graded strip under concentrated loads

The plane crack problem of an orthotropic functionally graded strip under concentrated loads is studied. The edge crack is perpendicular to the boundary and the elastic property of the material is assumed to vary depending on thickness. By using an integral transform method, the present problem can be reduced to a single integral equation which is solved numerically. The influences of parameters such as the nonhomogeneity constant and the geometry parameters on the stress intensity factors (SIFs) are studied. It is found that the nonhomogeneity constant has important influences on the SIFs.

Fe-SMA主动加固钢桥面横隔板弧形切口疲劳裂纹实桥应用研究

为确定铁基形状记忆合金(Fe-SMA)主动加固正交异性钢桥面板横隔板弧形切口疲劳裂纹的可行性,以某在役钢箱梁斜拉桥为背景进行实桥加固研究。根据现场横隔板弧形切口的开裂特征,在对裂纹钻孔止裂的基础上,提出利用Fe-SMA材料对横隔板弧形切口裂纹进行粘贴加固的方案,并进行加固施工。通过现场测试得到Fe-SMA板条热激活过程的应变和温度变化,分析Fe-SMA板条和钢板之间的相互作用及加固机理。结果表明:粘贴Fe-SMA板利用Fe-SMA热驱动形状记忆效应可有效便捷地为结构施加预压应力,实现对受损部位的主动加固;经过Fe-SMA联合止裂孔修复后,热驱动作用下的Fe-SMA可以产生200~240 MPa的预拉应力,并在钢板止裂孔边缘施加43~90 MPa的压应力,可有效阻止裂纹进一步扩展;加固体系在加热激活过程完好可靠,当控制一侧加热区域中部温度为200℃时,热传导作用下非加热区域中部的温度为60℃以下,而背面总体温度基本在90℃以下。

焊接残余应力对钢桥面疲劳性能的影响与处理措施

为改善正交异性钢桥面的抗疲劳性能,对钢桥面进行退火处理以降低关键焊缝的焊接残余应力。首先系统性地回顾和探讨钢桥面焊接残余应力分布模式,同时就残余应力对疲劳裂纹发展的影响进行了文献分析。随后,归纳和总结了国内外主流焊接残余应力消除方法,并开展对比分析。借鉴压力容器制造方法,建议在正交异性钢桥面制造中引入退火处理工艺以降低焊接残余应力。研究聚焦钢桥面中疲劳问题较突出的顶板与U肋连接焊缝,设计了16个(其中9个退火处理,7未作处理)局部足尺单U肋试件进行残余应力测试与疲劳试验。试验结果表明,退火处理后焊缝残余应力实测值降低约80%,疲劳强度提高约23%。可以看出,退火处理可以大幅降低焊接残余应力,从而有效提升钢桥面抗疲劳性能。

基于深度学习的正交异性钢桥面板疲劳裂纹智能识别方法研究

为提高正交异性钢桥面板疲劳裂纹的识别效果,基于深度学习方法,进行正交异性钢桥面板疲劳裂纹识别方法研究。制作疲劳裂纹试件,通过室内检测采集检测结果图像建立数据集,结合图像预处理改进数据集中图像;基于单一回归目标检测(You Only Look Once,YOLO)系列中的YOLOv5s图像识别算法,引入轻量级卷积注意力机制(Convolutional Block Attention Module,CBAM),建立疲劳裂纹超声相控阵检测图像的智能识别方法;将该方法应用于超声波相控阵检测结果判读。结果表明:结合限制性对比度直方图均衡(Contrast Limited Adaptive Histogram Equalization,CLAHE)算法与自适应中值滤波的图片预处理方法较为适合超声相控阵检测图像的图片预处理;通过引入CBAM改进图像识别算法,图像识别的精确度相较改进前提升1.28%,达到98.74%;建立的YOLOv5s-CBAM图像识别算法能够准确地框选疲劳裂纹区域,对四类常见疲劳裂纹类型的识别置信度达到0.91,对其它裂纹类型的识别置信度达到0.85,在室内环境下能够满足疲劳裂纹的智能检测需求。

正交异性钢桥面板横梁切口裂纹的Lamb波监测分析

为探究钢桥面板横梁切口裂纹的Lamb波技术监测效果,设计了2个钢桥面板足尺模型,通过循环加载使其横梁切口处发生疲劳开裂,利用Lamb波监测裂纹扩展情况,进而从波信号中提取标准化特征,用于评估裂纹扩展.建立并验证了钢桥面板有限元模型,进行了裂纹长度、传感器位置等各种参数分析,以确定最佳传感器布置.试验结果表明:当裂纹扩展长度与波传播路径垂直时,标准化特征增大;当两者路径平行时,标准化特征减小.参数化分析结果确定了切口处裂纹监测的最佳传感器位置,建议在选定横梁切口区域,预先布置1个激励器和4个接收器,激励器位于距切口50 mm处,接收器位于距离切口50 mm处或距顶板50~100 mm处.

考虑残余应力的钢桥面板-肋双面焊裂纹应力强度因子计算方法

建立焊接分析有限元模型,对顶板-纵肋双面焊构造的焊接过程进行数值模拟,拟合得到顶板焊趾细节沿板厚方向分布的横向残余应力分布经验公式;建立钢桥面板断裂力学数值模型,结合统一的权函数表达式,推导适用于顶板焊趾处裂纹最深点和表面点应力强度因子的新权函数,并将权函数计算的应力强度因子与有限元计算的应力强度因子进行对比。研究结果表明:顶板-纵肋双面焊顶板焊趾处残余应力沿板厚方向处于拉—压—拉状态,呈正弦函数分布;在二次应力分布下,权函数法与有限元法计算所得顶板焊趾处裂纹最深点应力强度因子最大相对误差为7.4%,表面点应力强度因子最大相对误差为4.1%;在焊接残余应力场下,权函数法与有限元法计算所得顶板焊趾处裂纹最深点应力强度因子最大相对误差为7.6%,表面点应力强度因子最大相对误差为8.6%;权函数法能有效计算钢桥面板-肋双面焊顶板焊趾处疲劳裂纹应力强度因子。

钢桥面横隔板弧形切口维修加固与寿命评估

正交异性钢桥面板弧形切口在使用中经常发生开裂,不合理的弧形切口设计导致的应力集中是产生疲劳开裂的主要原因。热切割改进弧形切口能有效地降低横隔板所受车载应力,但过程中会产生高水平的残余应力影响疲劳寿命。为此,提出了热维护+冷维护的疲劳维护方案,以热切割优化改进切口,并在纵肋与横隔板连接处粘贴钢板加固。采用ABAQUS软件建立钢箱梁节段模型计算维护前后车载应力,开展热切割残余应力测试试验,并通过数值模拟分析热切割弧形切口切向残余应力分布规律,基于钢材的本构模型对车载应力与热切割残余应力进行耦合,结合实测交通数据、采用线疲劳累计损伤理论计算了考虑热切割残余应力影响的弧形切口疲劳寿命,并对比分析了不同维护方案的效果。结果表明:采用热切割改进弧形切口后可明显改善应力集中问题,车辆荷载作用下的压应力峰值降低50%;但改进弧形切口会产生高水平的残余应力,显著影响其疲劳性能,疲劳寿命仅为67.75年,低于桥梁设计使用寿命;在改进切口上粘贴钢板进行冷维护,可进一步减小弧形切口的车载应力峰值,双面粘贴10mm钢板应力峰值降低79%,并显著增加其疲劳寿命;当采用相同厚度的补强钢板时,单面粘贴的疲劳维护效果优于双面粘贴。本文提出的热维护+冷维护方案可以降低热切割残余应力的影响,获得更优的疲劳维护效果,为钢桥面板弧形切口疲劳维护提供了新的技术选择。

基于扩展有限元法的钢桥面横隔板弧形切口疲劳裂纹扩展特性研究

为了解正变异性钢桥面板横隔板弧形切口疲劳开裂的规律,以某跨径350 m的独塔单跨钢箱梁自锚式悬索桥为背景,基于扩展有限元法建立纵肋-横隔板弧形切口多尺度裂纹扩展数值模型,求解弧形切口在轮载作用下的应力强度因子,分析轮载-热残余应力耦合作用下的疲劳裂纹扩展形态和特性。结果表明:当顺桥向车轮作用于弧形切口正上方时,应力强度因子急剧增大,基于该响应曲线可以识别疲劳荷载模型的轴组,但无法识别轴组内的单轴。弧形切口切向热残余拉应力峰值达到341.1 MPa,使得轮载作用下的压应力幅转换为拉应力幅,裂纹扩展方向与实桥疲劳裂纹的扩展形态基本吻合。由于弧形切口处于复杂的三维变形状态,以面内变形为主,因而弧形切口为Ⅰ型断裂主导的Ⅰ-Ⅱ-Ⅲ型复合裂纹扩展模式,裂纹扩展速率与应力强度因子幅均随着裂纹扩展呈现出先增大后减小的趋势。