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.

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.

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.

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.

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.

Analysis on cracking of deck pavement on Jiangyin Bridge

Based on four-year field inspection and investigation on deck pavement of mastic asphalt on Jiangyin Bridge, cracking causes of mastic asphalt are studied. Cracks of deck pavement are summarized on crack length and width to get a clear view of their propagations. Traffic surveys including traffic volume, axle load and vehicle speed were also conducted to assess their influences. Samples taken on-site were tested with pulling-out test and fatigue test to benchmark their properties. According to the inspection and tests results, it is concluded that the cracks are induced by rutting and fatigue. Lack of fatigue resistance, not well bonded to the steel deck and insufficient high temperature stability are supposed to be the main reasons as well as high density of low speed, excessively overloaded trucks.

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.

混凝土铺装层开裂对正交异性钢桥面疲劳性能劣化作用研究

为合理评估混凝土铺装层开裂对正交异性钢桥面板疲劳性能劣化的影响,开展足尺模型疲劳试验并进行数值仿真分析,得到铺装层开裂后钢桥面板典型易损细节疲劳应力,并提出疲劳应力增大系数量化分析裂缝尺寸对各细节疲劳应力的影响效应。结果表明:混凝土裂缝深度不超过其厚度20%时,正交异性钢桥面典型细节疲劳应力增幅很小;混凝土层正下方的横隔板-U肋-顶板及横隔板-U肋细节疲劳应力对混凝土裂缝长度、深度变化较敏感,混凝土开裂对横隔板弧形开口处及U肋圆弧处的影响较小;纵桥向裂缝对疲劳应力的影响比横桥向裂缝显著,且多裂缝会明显增大疲劳细节处应力水平,会加速桥面结构疲劳性能劣化,因此须设钢筋网阻滞裂缝扩展。

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。

基于裂纹扩展分析的正交异性钢桥面板疲劳响应研究

轮载下正交异性钢桥面板的局部效应显著,相邻各疲劳易损细节的疲劳行为相互影响,特别是随着某个细节裂纹扩展,相邻细节疲劳应力可能增大,桥面板疲劳性能呈加速劣化趋势。疲劳应力响应及桥面板性能劣化评估已成为钢桥面板运营期面临的挑战和亟待进行的工作。为合理评估开裂正交异性钢桥面板的疲劳性能演化情况,基于既有足尺模型疲劳试验,综合采用有限元程序ANSYS和Franc3D的多尺度交互技术模拟钢桥面板典型疲劳易损细节裂纹扩展行为,探究裂纹扩展过程中各关键细节(顶板与U肋连接焊缝、U肋与横隔板连接焊缝、横隔板开孔处)的疲劳应力响应和演化情况。结果表明:裂纹扩展对正交异性钢桥面板局部变形(挠度)影响很小;不同开裂模式下,各细节处应力变化规律存在较大差异,裂纹扩展的响应呈现出局部特征,仅对最近的细节主拉应力有一定的增大效应;顶板与纵肋焊缝连接处和横隔板开孔处的裂纹扩展对相邻疲劳细节的主拉应力提升效果较显著,可能导致该处萌生裂纹。研究结果可为开裂后正交异性钢桥面板的疲劳性能评估提供参考。

钢桥面板顶板贯穿裂纹长度涡流检测及其影响因素

针对正交异性钢桥面板顶板贯穿型疲劳裂纹隐蔽性强、难以精确检测的问题,提出通过涡流检测方法对裂纹长度进行测量。首先,对试验获取的涡流检测信号进行分析,探究信号特征与裂纹长度之间的关系,据此拟合出裂纹长度的测量公式,并通过有限元模拟对其有效性进行验证;其次,研究线圈参数与扫查速度对检测效果的影响;最后,通过有限元模拟分析了水平裂纹相邻顶点间距、裂纹与线圈中心的偏移距离、裂纹与线圈扫查方向的夹角对检测结果的影响。结果表明:增加圆柱形线圈外径与内径之比并适当减小线圈内阻可提高检测灵敏度;裂纹长度的测量值随着线圈扫查速度的增大而减小;水平裂纹相邻顶点间距越大,越利于精确测量裂纹长度;随着裂纹与线圈中心偏移距离的增加,检测信号的变化幅值逐渐减小,裂纹长度测量值也随之下降;此外,线圈扫查方向与裂纹长度方向的夹角越大,越不利于检测。该钢桥面板疲劳裂纹长度涡流检测方法可实现高效、便捷、精准的无接触式检测,为钢桥的运营维护提供相关技术参考。