Surface initiated crack growth simulation in moving lubricated contact

The paper describes a two-dimensional computational model for simulating surface initiated crack growth in the lubricated contact area that leads to surface pitting of mechanical components. The model assumes size and orientation of the initial crack which is subjected to contact loading conditions, accounting for the elasto-hydrodynamic-lubrication effects and tangential loading due to sliding. The influence of a lubricating fluid, driven into the crack by hydraulic mechanism, is also considered. The minimum strain energy density criterion is used to analyze crack propagation with the aim of the finite element analysis. The model is applied to a real pitting problem of a gear. The results for pit sizes correlate well with those observed in experimental testing.     

SGBEM modeling of fatigue crack growth in particulate composites

The symmetric-Galerkin boundary element method (SGBEM) has previously been employed to model 2-D crack growth in particulate composites under quasi-static loading conditions. In this paper, an initial attempt is made in extending the simulation technique to analyze the interaction between a growing crack and clusters of perfectly bonded particles in a brittle matrix under cyclic loading conditions. To this end, linear elastic fracture mechanics and no hysteresis are assumed. Of particular interest is the role clusters of inclusions play on the fatigue life of particulate composites. The simulations employ a fatigue crack growth prediction tool based upon the SGBEM for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors, a Paris law for fatigue crack growth rates, and the maximum principal stress criterion for crack-growth direction. The numerical results suggest that this fatigue crack growth prediction tool is as robust as the quasi-static crack growth prediction tool previously developed. The simulations also show a complex interplay between a propagating crack and an inclusion cluster of different densities when it comes to predicting the fatigue life of particulate composites with various volume fractions.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

渐开线直齿轮弹流润滑条件下的多轴疲劳寿命预估

本文中基于弹流润滑分析和次表面应力建立了渐开线直齿轮多轴疲劳寿命计算模型.相对于传统的单轴疲劳模型,考虑了齿轮固定点的应力历史和材料属性对疲劳寿命的影响,并可以得到齿轮在完整啮合过程中的寿命分布.首先建立齿轮的有限长弹流计算模型,得到齿轮啮合过程中的油膜压力和油膜厚度,再根据油膜压力计算出次表面的应力分布;通过分析齿轮计算区域随啮合过程移动的关系,得到固定点的应力历史,再根据基于应力历史的多轴疲劳寿命模型对齿轮的完整啮合过程进行寿命预估.计算分析了不同粗糙度幅值对轮齿各点寿命大小和分布的影响.研究表明:齿面粗糙度对疲劳寿命的影响显著,随着粗糙度幅值的增大,表层下最大应力向齿面移动,导致低疲劳寿命区向齿面发展且逐步扩展到整个单齿啮合区;而表面粗糙度降低到一定程度则对疲劳寿命的影响变得不明显.     

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.     

拉-拉循环荷载作用下的界面脱粘研究

应用弹性力学和断裂力学基本理论，基于剪滞模型，研究了纤维增强复合材料中纤维与基体界面在拉-拉循环荷载作用下的疲劳脱粘特性。建立了描述疲劳裂纹扩展的等效Paris公式，得到了界面疲劳脱粘扩展速率、脱粘应力以及脱粘界面的摩擦系数与循环加载次数的关系式。通过数值模拟计算，进一步分析了界面疲劳脱粘的力学机理。本文分析，考虑了疲劳加载引起的脱粘界面的损伤及损伤分布的不均匀性。同时还考虑了材料泊松比的影响。     

Fatigue crack growth induced by domain switching under electromechanical load in ferroelectrics

Reliability calls for a better understanding of the failure of ferroelectric ceramics. The fracture and fatigue of ferroelectric ceramics under an electric field or a combined electric and mechanical loading are investigated. The small-scale domain-switching model is modified to analyze failure due to fracture and fatigue. Effects of anisotropy and electromechanical load coupling are taken into account. Analytical expressions are obtained for domain-switching regions near the crack tip such that of 90° domain switching can be distinguished from 180° domain switching in addition to different initial poling directions. The crack tip stress intensity variation of ferroelectric ceramics due to the domain switching is analyzed. A positive electric field tends to enhance the propagation of an insulating crack perpendicular to the poling direction, while a negative field impedes it. Fatigue crack growth under various coupling loads and effects of the stress field and electric field on near field stress intensity variation are analyzed. Predicted crack growth versus cyclic electric field agrees well with experiment.     

拉压循环载荷下正交异性钢桥面板肋-面板焊缝裂纹扩展分析

采用四步法计算了考虑循环载荷中压应力影响的正交异性钢桥面板的肋-面板焊缝表面裂纹扩展。第一步是基于正交异性钢桥面板的疲劳分析模型,计算肋-面板焊缝处的应力,第二步是通过肋-面板焊缝的三维局部模型,用Schwartz-Neumann交替法计算焊缝表面裂纹的应力强度因子分布,第三步是用二维断裂力学模型和增量塑性损伤模型,计算循环载荷中的压应力对裂纹扩展的影响,第四步是用第二步中的三维裂纹分析结果和第三步中的二维断裂力学模型得到的裂纹扩展公式,计算钢桥面板的肋-面板焊缝表面裂纹扩展。计算结果表明,对应于正交异性钢桥面板肋-面板焊缝处的循环应力,本文所用模型的裂纹尖端反向塑性区导致裂纹扩展率增加50%以上。研究结果为正交异性钢桥面板肋-面板焊缝裂纹的疲劳寿命分析提供了研究基础。     

A cyclic steady-state method for fatigue crack propagation: Evaluation of plasticity-induced crack closure in 3D

The numerical study of plasticity-induced crack closure using the node-release technique presents many difficulties widely studied in literature. For instance various rules, proposed for overcoming mesh sensitivity, are challenged by more recent studies. This paper intends to propose and evaluate a numerical method for the investigation of crack propagation under fatigue loading, and particularly for the assessment of plasticity-induced crack closure in three-dimension. The method is an extension of the “steady-state method” to cyclic loadings. The steady-state method allows a direct computation (on a fixed mesh, without releasing nodes) of stress and strain fields around the crack tip and in the wake for a steady crack growth. The method is extended to simulate crack propagation under fatigue loading. Therefore it constitutes a valuable numerical tool for gaining insight into the physics of crack propagation, as it provides accurate mechanical fields around the crack tip and their relation with crack growth rate, various loading modes and parameters. The proposed method is also compared with the classical node-release technique. A very good agreement between the two methods is found. However the steady-state method needs much less mesh refinement and computational time. Following an analysis of some features of the fatigue crack, a discussion on a crack closure criterion is opened, and a reliable criterion for the determination of local crack closure is proposed.     

An investigation of partial cone cracks in silicon nitride balls

Hybrid silicon nitride ball/steel raceway bearings are used in advanced aircraft engines and space propulsion systems. Silicon nitride is a brittle material and partial cone cracks, or c-cracks, originate from contact interactions during manufacturing. These cracks limit the Rolling Contact Fatigue (RCF) life of the balls. Here the authors examine subsurface Hertzian stresses between contacting spheres, using an analytical stress solution, to investigate their applicability to predicting and characterizing crack size and shape. The authors also incrementally develop these cracks through an iterative crack growth procedure using a 3D finite element analysis. Comparisons are then made to experimental images of the flaws in silicon nitride. By varying the initial conditions during the contact interaction of the balls we demonstrate that a wide range of cone and partial cone cracks, observed in practice, can be generated using both the analytical and numerical fracture mechanics approaches. Furthermore, an expression is presented for the impact velocity that induces a cone crack from a maximum radial stress criterion at the contact periphery.     

STUDY ON THE SURFACE CRACK GROWTH BEHAVIOR IN 14MnNbq BRIDGE STEEL

Three-dimensional crack closure correction methods are investigated in this paper.The fatigue crack growth tests of surface cracks in 14MnNbq steel for bridge plate subjected to tensile and bending loadings are systematically conducted.The experimentally measured fatigue crack growth rates of surface cracks are compared with those of through-thickness cracks in detail.It is found that the crack growth rates of surface cracks are lower than those of through-thickness cracks.In order to correct their differences in fatigue crack growth rates, a dimensionless crack closure correction model is proposed.Although this correction model is determined only by the experimental data of surface cracks under tensile loading with a constant ratio R=0.05, it can correlate the surface crack growth rates with reasonable accuracy under tensile and bending loadings with various stress ratios ranging from 0 to 0.5.Furthermore, predictions of fatigue life and crack aspect ratio for surface cracks are discussed, and the predicted results are also compared with those obtained from other prediction approaches.Comparison results show that the proposed crack closure correction model gives better prediction of fatigue life than other models.     

裂纹闭合和循环塑性预应变及循环载荷压缩部分对裂纹扩展速率的影响

本文针对三种国产材料 Ｌｙ１１ｃｚ、 Ｌｙ１２ｃｚ 铝合金和 １８ Ｍｎ Ｈ Ｐ钢,通过实验初步考察了循环塑性预应变和循环载荷压缩部分对疲劳裂纹扩展的影响;采用电测法,测定了两种铝合金材料疲劳裂纹扩展的张开应力和有效应力强度因子幅值比 Ｕ。结果表明：（１）材料循环塑性预应变和循环载荷压缩部分,都使疲劳裂纹扩展速率提高;（２）常幅载荷下,在疲劳裂纹稳定扩展阶段,有效应力强度因子幅值比 Ｕ 与应力比 Ｒ 有关,与裂纹长度ａ 无关,并依赖于材料的力学性能。     

Fatigue life evaluation by weight functions for orthotropic bridge decks

This paper is concerned with the prediction of fatigue crack propagation in welded orthotropic decks for road and railway steel bridges. The analysis makes use of a weight function (WF), that provides effective evaluation of the stress intensity factor (SIF) for any crack length and loading condition. The WF was determined by a hybrid (numerical/analytical) technique and verified with numerical results. The fatigue life were estimated for different initial crack lengths and loading cycles. Endurance limits were obtained to establish in-service inspection schedule of the structure. The effect of weldment residual stress on the fatigue life was also analyzed. It was shown that the WF technique provides an expedient evaluation of these effects, also accounting for non-linear (contact) phenomena.     

循环加载条件下混凝土Ⅰ型裂缝扩展模拟的接触算法

沿裂缝可能开展路径设置接触点对,把求解接触问题的有限元混合法进行扩展,以实现循环加载条件下混凝土Ⅰ型裂缝扩展的数值模拟.根据荷载过程状态和缝面接触状态的不同,将循环荷载作用下的混凝土本构关系抽象为力学模型中的六种不同接触状态,不同的接触状态对应着不同的位移-应力曲线关系.以缝面张开位移和接触应力作为接触状态转变的判断参量,并给出了各状态的转变关系和数值判断条件,以接触算法实现了循环加载条件下混凝土Ⅰ型断裂扩展的数值模拟.首先给出了有限元混合法求解接触问题的基本思路,然后引入循环荷载下的混凝土本构关系,再对Ⅰ型裂缝扩展的数值实现方法进行了阐述,最后通过数值算例说明了数值实现方法的正确性和有效性.     

On dissolution driven crack growth

The formation and growth of a crack in a body subjected to stress driven material dissolution is studied. The rate of material dissolution is proportional to strain energy and curvature of the body surface. The formation of a crack from a plane surface is preceded by an evolving surface roughness. The continued dissolution enhances roughness amplitude resulting in pit formation. As the pit grows deeper into the material, it assumes the shape of a crack. The sharpness of the crack reaches its maximum during this transition from a pit to a crack. As the crack grows, a self-similar state is gradually assumed. During this phase characteristic lengths of the crack shape scale with the crack length. In line with this the crack progressively becomes blunt. The widest part of the crack when unloaded is in the vicinity of the crack tip. A consequence of the model is that no criterion is needed for crack growth. Neither is a criterion needed for determination of the crack path. It also follows that the crack growth rate is almost independent of the remote load. Further, spontaneous crack branching is anticipated. A motivation for this is given.     

Experimental Investigation and Finite Element Analysis of Fatigue Crack Growth in Pipes Containing a Circumferential Semi-elliptical Crack Subjected to Bending

In this paper, a circumferential external surface flaw in a metallic round pipe under cyclic bending loading is considered. Because of very rapid changes in the geometrical parameters around the crack front region, the mesh generation of this region must be done with great care. This may lead to an increase in the run time which makes it difficult to reach valid results and conclusions. Because of the advantages of the sub-modeling technique in problems which need very high mesh density, this method is used. Stress intensity factors in mode I condition are determined using three-dimensional finite element modeling with 20 node iso-parametric brick elements in the ANSYS 9.0 standard code and the singular form of these finite elements at the crack front. In order to estimate the analysis error, the structural parameter error in energy norm criterion was used. Because of the advantages of non-dimensional analysis, this method is employed, and the stress intensity factors are normalized. For the analysis of the fatigue crack growth, the Paris law is used. The propagation path of the surface flaw is obtained from the diagram of aspect ratio versus relative crack depth. The fatigue crack growth analysis (the relative crack depth against loading cycles diagram) of different initial crack aspect ratio under cyclic loading is also considered. Fatigue shape development of initially semi-elliptical external surface defects is illustrated. The effect of the Paris exponent (material constant) on fatigue crack propagation is shown as well. Moreover, the fatigue crack growth of several specimens is assessed experimentally using a manually-constructed experimental set up. Finally, the experimental results obtained by cyclic bending loading tests are compared with the numerical results. The experimental results show good conformity with the finite element results.     

点蚀演化及腐蚀疲劳裂纹成核的能量原理

作为一种不可逆的热力学过程,腐蚀疲劳的点蚀演化受到体系应变能、表面能和电化学能的共同影响。基于能量学原理,对腐蚀疲劳点蚀演化过程中的能量问题进行探索性研究。引入双变量半椭球模型描述点蚀的演化过程,推导了点蚀形状参数在演化过程中的变化方程。基于应力强度因子准则建立点蚀向疲劳裂纹转化的临界条件,同时分析应力振幅对腐蚀疲劳裂纹成核寿命的影响。     

Analysis of three-dimensional edge cracks under tensile loading

Three-dimensional edge cracks are analyzed using the Self-Similar Crack Expansion (SSCE) method with a boundary integral equation technique. The boundary integral equations for surface cracks in a half space are presented based on a half space Green's function (Mindlin, 1936). By using the SSCE method, the stress intensity factors are determined by the crack-opening displacement over the crack surface. In discrete boundary integral equations, the regular and singular integrals on the crack surface elements are evaluated by an analytical method, and the closed form expressions of the integrals are given for subsurface cracks and edge crakcs. This globally numerical and locally analytical method improves the solution accuracy and computational effort. Numerical results for edge cracks under tensile loading with various geometries, such as rectangular cracks, elliptical cracks, and semi-circular cracks, are presented using the SSCE method. Results for stress intensity factors of those surface breaking cracks are in good agreement with other numerical and analytical solutions.     

Strain-induced passivity breakdown in corrosion crack initiation

Corrosion crack nucleation and growth are modelled as a moving boundary problem. The model incorporates three physical processes––dissolution, passivation and straining––into a continuum mechanical framework. The dissolution triggers surface advance; the passivation restrains the access of the environment to bare metal; the deformation causes for passivity breakdown. Plane cracks nucleating from surface pits in an elastic–plastic material body under fatigue load are considered. The problem is solved using a FEM program and a moving boundary tracking procedure. The model simulates how cracks form and grow in a single continuous course. The geometry of the developed cracks is found independent of the initial pit size. Plasticity is found to influence the curvature at the tip of the nucleated corrosion cracks. The most important evolution length parameter, the width of the corrosion crack, is found to depend on the size constraints of the tracking procedure. It is concluded that the model is deficient for determining all length scales observed in reality. Physical processes to be considered in an advanced model are proposed and discussed.     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.