Simulation of three-dimensional fatigue crack propagation using enriched finite elements

A three-dimensional methodology for simulation of fatigue crack propagation is presented. The method is leveraged by the use of enriched crack tip elements to compute the mixed-mode stress intensity factors. The crack growth model used and the crack propagation life calculation are also described. As examples, fatigue crack propagation of a mode-I surface crack and crack advancements of mixed-mode surface cracks are simulated. The predicted results showed excellent agreement with experimental data from the literature. Thus, it is concluded that the crack propagation method developed allows efficient and accurate simulation of three-dimensional fatigue crack propagation problems.     

滚动接触疲劳载荷对铁轨表面接触疲劳裂纹应力强度因子的影响

为研究轮轨滚动接触疲劳（Rolling Contact Fatigue,RCF）载荷对铁轨表面裂纹应力强度因子的影响,以UIC60铁轨轮廓尺寸为依据建立轮轨接触的三维有限元模型,通过改变RCF载荷大小、轮轨表面摩擦因数和接触中心位置等轮轨接触的输入参数,计算铁轨表面接触裂纹尖端的应力强度因子,分析RCF载荷对铁轨表面接触疲劳裂纹的影响. 结果表明RCF载荷作为控制铁轨表面接触裂纹的重要因素,其变化直接导致裂纹尖端应力强度因子的变化,从而改变裂纹的扩展状况;为减缓铁轨表面裂纹的扩展,可以针对载荷采取均匀分布载重量、使用润滑剂降低轮轨摩擦因数等相应措施.     

A solution method for static and dynamic analysis of three-dimensional contact problems with friction

A solution method is presented for the analysis of contact between two (or more) three-dimensional bodies. The surfaces of the contacting bodies are discretized using quadrilateral surface segments. A Lagrange multiplier technique is employed to impose that, in the contact area, the surface displacements of the contacting bodies are compatible with each other. Distributed contact tractions over the surface segments are calculated from the externally applied forces, inertia forces and internal element stresses. Using the segment tractions, Coulomb's law of friction is enforced in a global sense over each surface segment. The time integration of dynamic response is performed using the Newmark method with parameters and . Using these parameters the energy and momentum balance criteria for the contacting bodies are satisfied accurately when a reasonably small time step is used.

The applicability of the algorithm is illustrated by selected sample numerical solutions to static and dynamic contact problems.     

Computerized design of modified helical gears finished by plunge shaving

Among the several types of gear shaving operations, plunge shaving is used for finishing gears in mass-production due to the low cost and short machining time. Plunge shaving may be used to apply surface modifications with the purpose of reducing noise and vibration by the predesign of favorable functions of transmission errors, and modify gear tooth surfaces to avoid edge contacts and increase gear endurance, safety, and service life. A new geometry for helical gear tooth surfaces that combine the advantages of gear drives with lineal and localized contacts is proposed and obtained by plunge shaving. The shaver tooth surfaces are conjugated to those of an ideal helical gear with surface modifications. In this way, the to-be-shaved gear and the shaving cutter will be in line contact, and only a radial feed motion of the shaver is needed to generate the required pressure for the shaver to cut the excess of material on the gear tooth surfaces. A numerical example of design illustrates the advantages of the proposed geometry.     

聚氨酯橡胶摩擦轮有限元及疲劳寿命分析

针对汽车滑板输送机聚氨酯橡胶摩擦轮的开裂问题,对摩擦轮与滑板之间的相互作用进行预压紧力和接触摩擦驱动有限元分析,获得摩擦轮的应力和变形分布等结果. 在获得摩擦轮周向应力分布的基础上,根据疲劳裂纹扩展公式对聚氨酯橡胶部分进行疲劳寿命分析,验证是否满足设计要求. 分析过程和结果能为聚氨酯橡胶摩擦轮的详细设计提供参考.     

聚氨酯橡胶摩擦轮有限元及疲劳寿命分析

针对汽车滑板输送机聚氨酯橡胶摩擦轮的开裂问题,对摩擦轮与滑板之间的相互作用进行预压紧力和接触摩擦驱动有限元分析,获得摩擦轮的应力和变形分布等结果.在获得摩擦轮周向应力分布的基础上,根据疲劳裂纹扩展公式对聚氨酯橡胶部分进行疲劳寿命分析,验证是否满足设计要求.分析过程和结果能为聚氨酯橡胶摩擦轮的详细设计提供参考.     

Study of TBM cutterhead fatigue crack propagation life based on multi-degree of freedom coupling system dynamics

Cutterhead is the core component of TBM tunneling equipment, which endures strong, multi-point distributed impact loads when the TBM tunnels, owing to the extreme surrounding rock environment of high hardness, high temperature and high quartz content. For this reason, the cutterhead works in an extremely severe vibration environment, which leads to engineering fault by a large area crack damage before the service life. Hence, the study on life prediction of TBM cutterhead under the impact loads is a core part of cutterhead design. This paper combines with the technology of system dynamics, linear elastic fracture mechanics and cumulative theory of fatigue damage, for the first time, proposes a method of fatigue crack propagation life prediction for the large and complex structures. In this paper, the TBM cutterhead of an actual project is taken as an example, to predict the fatigue crack propagation life of cutterhead piece and analyze the influences of plate thicknesses on fatigue life, then a new improved scheme of cutterhead structure is presented. The results show that the fatigue crack propagation life of actual cutterhead is 26.6 km, which is able to meet the requirement of 20 km service life. Moreover, the upper cover plate thickness has the greatest influence on cutterhead fatigue crack propagation life, with the thickness increasing 10%, the life increases nearly by 1.24 times. Then, the other influencing factors are as follows: thickness of the main support plate, thickness of the annular support plate and thickness of the support plate, whereas the influence of the lower cover plate thickness on fatigue life is minimal. Furthermore, the plate thickness limit sizes meeting the life requirement are obtained, and a new structure modified scheme of cutterhead is proposed. Compared with the original scheme, the new cutterhead scheme meets the requirements of structural strength and service life with 8.08% weight decrease, which achieves life determination design and lightweight design. The proposed method of fatigue crack propagation life prediction is feasible in the design and application stage of TBM cutterhead, besides, it is flexible enough and can also be applied in damage strength assessment, dynamic parameters optimization and establishment of nondestructive inspection cycle for the other large and complex structure, and takes on stronger project value and generality.     

Prediction of constant amplitude fatigue crack growth life of 2024 T3 Al alloy with R-ratio effect by GP

The objective of this study is to develop a genetic programming (GP) based model to predict constant amplitude fatigue crack propagation life of 2024 T3 aluminum alloys under load ratio effect based on experimental data and to compare the results with earlier proposed ANN model. It is proved that genetic programming can effectively interpret fatigue crack growth rate data and can efficiently model fatigue life of the material system under investigation in comparison to ANN model.     

Non-linear MSD crack growth by DBEM for a riveted aeronautic reinforcement

A special specimen is created cutting a rectangular notched area from the surrounding of the upper left corner of a wide body aircraft door. Then a constant amplitude fatigue traction load is applied by a special servo-hydraulic machine, in order to induce a Multi Site Damage (MSD) scenario.The Dual Boundary Element method (DBEM), as implemented in a commercial code, is adopted for a three-dimensional MSD crack growth simulation of such multi-layer and multi-material component. To this aim, the cracked part of a pre-existing global two-dimensional model is extracted and “extruded” in order to generate a three-dimensional submodel, whose boundary conditions are imposed displacements, calculated by the two-dimensional model, along a virtual line corresponding to the submodel boundary. Non-linear contact conditions are applied between the mating plate surfaces in the area surrounding the cracks, in order to precisely model the plate interactions in the area of interest.The three-dimensional approach is aimed to improve, with respect to the two-dimensional approach, the correlation between numerical and experimental results (e.g. by an accurate assessment of the secondary bending effects). The obtained improvements on crack growth rates, in the initial part of the crack propagation, justify the increased computational effort that a three-dimensional non-linear approach involves.The proposed numerical procedure, based on DBEM, is successfully validated for the virtual testing of a complex aeronautic reinforcement.     

A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter "D" which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: (1) randomness in the microstructure due to random shapes and sizes of the material grains; (2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and (3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.     

Fatigue life prediction under cyclic thermal loads using the boundary elements method for two-dimensional problems

This study describes a sub-domain boundary element procedure for predicting the fatigue life of elastic media under cyclic transient thermal loads. The procedure assumes an initial crack in a two-dimensional medium, and evaluates the crack extension along a path defined by the maximum circumferential stress criterion. Partial closure may occur on the growing crack faces due to thermal loading. Appropriate thermal and mechanical boundary conditions are imposed on the numerical model to account for the contact state. The analysis requires solutions to the equations of quasi-static thermo-elasticity, and uses an iterative procedure to detect the contact region. We investigate cases of pure opening or mixed mode fracture, demonstrating the effects of crack closure on the predicted fatigue life. We compare the obtained results with those of other publications.     

A two-scale extended finite element method for modelling 3D crack growth with interfacial contact

3D fatigue crack growth problems are nowadays handled using X-FEM coupled with level set techniques. It is also well established that such an approach allows mesh-independent crack modelling and no remeshing during crack propagation. However, when contact and friction occur along the crack faces, a discretization of the internal variables linked to the interface law is necessary. The interface discretization is generally constructed from the finite elements cut by the crack. As a consequence, a mesh dependency between the bulk discretization and the interface discretization is introduced. However, the dimension of the possible non-linearities arising at the crack interface (like confined plasticity or unilateral contact with friction) may be several orders of magnitude finer than the crack size. A finer discretization is thus required to accurately capture these non-linearities. The aim of the present paper is to develop a method considering the 3D cracked structure and the crack interface as two independent global and local problems characterized by different length scales and different behaviors. Here, the interface is seen as an autonomous entity with its own discretization, variables and constitutive law. A formulation involving three-fields is used. The interface is linked to the global problem in a weak sense in order to avoid instabilities in the contact solution. Two iterative strategies are considered to solve the contact problem. Two-dimensional and three-dimensional numerical examples are presented to demonstrate the ability of the model to solve the contact at the crack interface with or without propagation at a given level of accuracy.     

正交异性钢桥肋-桥面板焊缝裂纹的三维断裂力学分析

正交异性钢桥的肋-桥面板焊缝处的疲劳裂纹是典型的三维裂纹问题,但是现在普遍采用平面应变二维裂纹模型对其进行断裂力学分析.基于Schwartz-Neuman交替法建立正交异性钢桥肋-桥面板焊缝裂纹的局部三维断裂力学分析模型;评估焊缝处表面裂纹的形状和深度对应力强度因子的影响;采用Paris公式估算等应力幅下焊缝的疲劳寿命.计算结果表明:用平面应变二维裂纹模型进行正交异性钢桥的肋-面板焊缝的断裂力学分析会严重低估其疲劳寿命;采用三维断裂力学模型进行肋-桥面板焊缝裂纹的疲劳寿命分析十分必要.     

Multi-fidelity design of stiffened composite panel with a crack

Crack propagation is an important concern in the design of aircraft composite fuselage and wing panels. However, numerical simulation of crack propagation is computationally expensive. This work proposes combining high-fidelity analysis model with low-fidelity model to calculate the crack propagation constraint in the design optimization process. Correction response surfaces are employed to relate the high-fidelity models to the low-fidelity models. Four different forms of correction response surface methods are explored and their prediction capabilities are compared. The multi-fidelity approach is found to be more accurate than single-fidelity response surface method at the same computational cost.     

Numerical simulation of rapid crack propagation in viscoplastic materials

A finite element model for the simulation of fast crack propagation under dynamic Mode I load conditions is developed. The principal tools are an enhanced strain formulation and a quasi-contact algorithm. Crack propagation is controlled by the implemented fracture criterion. The model accounts for viscoplastic material behavior, dynamic effects and contact in the crack zone. The numerical results demonstrate that these physical effects are of major importance when load speed is increased to a high level and therefore they cannot be neglected.     

滚动接触疲劳载荷对铁轨表面接触疲劳裂纹应力强度系数的影响

为研究轮轨滚动接触疲劳(Rolling Contact Fatigue,RCF)载荷对铁轨表面裂纹应力强度系数的影响,以UIC60铁轨轮廓尺寸为依据建立轮轨接触的三维有限元模型,通过改变RCF载荷大小、轮轨表面摩擦因数和接触中心位置等轮轨接触的输入参数,计算铁轨表面接触裂纹尖端的应力强度系数,分析RCF载荷对铁轨表面接触疲劳裂纹的影响.结果表明RCF载荷作为控制铁轨表面接触裂纹的重要因素,其变化直接导致裂纹尖端应力强度系数的变化,从而改变裂纹的扩展状况.为减缓铁轨表面裂纹的扩展,可以针对载荷采取均匀分布载重量、使用润滑剂降低轮轨摩擦因数等相应措施.     

Surface Smoothing Procedures in Computational Contact Mechanics

This work addresses the problems arising in the finite element simulation of contact problems undergoing large deformation. The frictional contact problem is formulated in the continuum framework, introducing the interface laws for the normal and tangential stress components in the contact area. The variational formulation is presented, considering different methods to enforce the contact constraints. The spatial discretization within the finite element method is applied, as well as the temporal discretization required to solve the three sources of nonlinearities: geometric, material and frictional contact. The discretization of contact surfaces is discussed in detail, including different surface smoothing procedures. This numerical strategy allows to solve the difficulties associated with the discontinuities in the contact surface geometry introduced by finite element discretization, which leads to nonphysical oscillations of the contact force for large sliding problems. The geometrical accuracy of different interpolation methods is evaluated, paying particular attention to the Nagata patch interpolation recently proposed. In this framework, the Node-to-Nagata contact elements are developed using the augmented Lagrangian method to regularize the variational frictional contact problem. The techniques used to search for contact in case of large deformations are discussed, including self-contact phenomena. Several numerical examples are presented, comprising both the contact between deformable and rigid obstacles and the contact between deformable bodies. The results show that the accuracy and robustness of the numerical simulations is improved when the contact surface is smoothed with Nagata patches.     

基于倍频双晶复合传感器的构件疲劳微裂纹非线性超声检测

通过对固体中非线性超声传播模型的研究,分析了裂纹静态压力与超声波作用力对裂纹超声非线性响应的影响,在此基础上,建立了反映裂纹区应力-应变非线性关系的弹性接触机制超声非线性响应模型;以及反映裂纹闭合状态转换的碰撞接触机制超声非线性响应模型。基于上述理论,通过实验研究发现裂纹尖端区的二次谐波激发效率与裂纹的开口区和闭合区及裂纹最终扩展的极限长度有关。因此,可使用二次谐波激发效率作为定量表征金属试件疲劳微裂纹缺陷的特征参数,实验中使用了自主研制倍频双晶复合换能器,这种倍频双晶复合换能器在工程实际应用中作在线检测更为方便、实用。     

Numerical–experimental crack growth analysis in AA2024-T3 FSWed butt joints

This paper deals with a numerical and experimental investigation on the influence of residual stresses on fatigue crack growth in AA2024-T3 friction stir welded butt joints. The computational approach is based on the sequential usage of the Finite Element Method (FEM) and the Dual Boundary Element Method (DBEM). Linear elastic FE simulations are performed to evaluate the process induced residual stresses, by means of the contour method. The computed stress field is transferred to a DBEM environment and superimposed to the stress field produced by a remote fatigue traction load applied on a friction stir welded cracked specimen; the crack propagation is then simulated according to a two-parameter growth model. Numerical results have been compared with experimental data showing good agreement and evidencing the predictive capability of the proposed method. The obtained results highlight the influence of the residual stress distribution on crack growth.