Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

A CAD-based on biological method for designing optimal fatigue life

This paper presents an innovative approach to shape optimisation of three-dimensional, damage-tolerant structures. In this approach, a new and simple method, which we termed Failure Analysis of Structures (FAST), is used to estimate the stress-intensity factor for cracks at a notch. The methodology and software used to automate damage-tolerance calculations are developed using computer-aided design and FAST codes. The worst crack locations are found by modeling many cracks along fractured critical edges of the structure by using FAST. This software is then used to evaluate damage-tolerance objective functions for optimisation algorithms. A particular stress-based biological growth method is employed to study the problem of optimisation with fatigue life as the design objective. This work confirms that a stress-optimised structure does not necessarily give the longest fatigue life by numerical examples.     

汽轮机汽缸蠕变-疲劳耦合寿命预测

为探索汽轮机汽缸裂纹产生的原因、带裂纹汽缸的剩余寿命、汽缸延寿等问题,开展蠕变和疲劳交互作用下的汽缸寿命预测。利用有限元计算汽缸在稳态和启停工况下的应力情况。基于蠕变 疲劳耦合理论进行裂纹萌生和扩展的寿命预测,从运行方式和汽缸结构2方面开展优化。研究结果表明：该中压内缸中分面法兰的拐角处存在较大的热应力集中,其寿命损伤大导致裂纹萌生。经过结构修复,机组寿命显著延长。     

Design sensitivities of fatigue performance and structural dynamic response in an automotive application

Direct accounting for durability rarely finds its way into multidisciplinary optimization. Though reduction of loads by some means can certainly have a beneficial influence on the fatigue performance of a structure, changes in load levels are not a direct measure of the influence of design changes on fatigue performance. In this paper, an assessment is made of an approach to the calculation of design sensitivities of a fatigue performance index namely, number of damaging cycles to failure. The approach makes use of analytical sensitivities of structural dynamic response, and a standard approach to the calculation of fatigue performance. The method is demonstrated using a simple nine degree-of-freedom structural model of an automobile in a conceptual representation of the industrial practice of road testing and road simulation. Results suggest that the estimates of changes in fatigue life are of sufficient quality for typical fatigue life evaluations, and open the door for the incorporation of a direct measure of fatigue performance in formal structural optimization. Received January 27, 2000 Communicated by J. Sobieski     

Damage tolerance based design optimisation of a fuel flow vent hole in an aircraft structure

This paper investigates the design optimisation of a fuel flow vent hole (FFVH) located in the wing pivot fitting (WPF) of an F-111 aircraft assuming a damage tolerance design philosophy. The design of the vent hole shape is undertaken considering the basic durability based design objectives of stress, residual (fracture) strength, and fatigue life. Initially, a stress based optimised shape is determined. Damage tolerance based design optimisation is then undertaken to determine the shape of the cutout so as to maximise its residual strength and fatigue life. For stress optimisation, the problem is analysed using the gradient-less biological algorithm and the gradient-based nonlinear programming methods. The optimum designs predicted by the two fundamentally different optimisation algorithms agree well. The optimum shapes of the vent hole are subsequently determined considering residual strength and fatigue life as the distinct design objectives in the presence of numerous 3D cracks located along the vent hole boundary. A number of crack cases are considered to investigate how the crack size affects the optimal shapes. A semi-analytical method is employed for computation of the stress intensity factors (SIF), and an analytical crack closure model is subsequently used to evaluate the fatigue life. The 3D biological algorithm is used for designing the cutout profiles that optimise residual strength and fatigue life of the component. An improved residual strength/fatigue life (depending on the optimisation objective) is achieved for the optimal designs. The variability in SIF/fatigue life around the cutout boundary is reduced, thereby making the shape more evenly fracture/fatigue critical. The vent hole shapes optimised for stress, residual strength, and fatigue life are different from each other for a given nature and size of the flaws. This emphasises the need to consider residual strength and/or fatigue life as the explicit design objective. The durability based optimal vent hole shapes depend on the initial and final crack sizes. It is also shown that a damage tolerance optimisation additionally produces a reduced weight WPF component, which is highly desirable for aerospace industries. The design space near the ‘optimal’ region is found to be flat. This allows us to achieve a considerable enhancement in fatigue performance without precisely identifying the local/global optimum solution, and also enables us to select a reduced weight ‘near optimal’ design rather than the precise optimal shape.     

Design study of hole positions and hole shapes for crack tip stress releasing

The method of hole drilling near or at the crack tip is often used in fatigue damage repair. From a design optimization point of view, two questions are posed: Where should the hole(s) be drilled? And is there a better shape of the hole than a circular one? For the first question, we extend earlier results for isotropic material and in general study the influence of having orthotropic material. Optimal shapes are by no means circular, and we focus on the shape of a single hole centered at (or in front of) the crack tip. It is shown that the stress field at the crack boundary can be significantly improved by noncircular shapes. As a byproduct, an alternative method for extracting the stress intensity factor from a finite element analysis is presented.     

Axisymmetric shell optimization under fracture mechanics and geometric constraint

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The shell is made from quasi-brittle materials, and through crack arising is admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by Paris fatigue law. The problem of finding the meridian shape and the thickness distribution (geometric design variables) of the shell having the smallest mass subject to constraints on the cyclic number for fatigue cracks and geometrical constraint on the shell volume is investigated. Special attention is devoted to different possibilities of problem transformation and analytical methods of their solution. Using minimax approach, optimal shapes of the shells and their thickness distributions have been found analytically.     

Optimal design of aircraft structures with damage tolerance requirements

Damage tolerance analysis (DTA) was considered in the global design optimization of an aircraft wing structure. Residual strength and fatigue life requirements, based on the damage tolerance philosophy, were investigated as new design constraints. The global/local finite element approach allowed local fatigue requirements to be considered in the global design optimization. AFGROW fatigue crack growth analysis provided a new strength criterion for satisfying damage tolerance requirements within a global optimization environment. Initial research with the ASTROS program used this damage tolerance constraint to optimize cracked skin panels on the lower wing of a fighter/attack aircraft. For an aerodynamic and structural model of this type of aircraft, ASTROS simulated symmetric and asymmetric maneuvers during the optimization. Symmetric maneuvers, without underwing stores, produced the highest stresses and drove the optimization of the inboard lower wing skin. Asymmetric maneuvers, with underwing stores, affected the optimum thickness of the outboard hard points. Subsequent design optimizations included DTA and von Mises stress constraints simultaneously. In the configuration with no stores, the optimization was driven by the DTA constraint and, therefore, DTA requirements can have an active role to play in preliminary aircraft design.     

An automated procedure for fatigue crack growth analysis

An automated procedure is developed to determine the influence of a crack detected in a structural element subjected to cyclic combined axial and bending loadings with constant amplitude. A theoretical formulation for fatigue crack growth analysis is presented and the results obtained are compared with the experimental data of the Wöhler curves. The critical crack configurations for which the fatigue failure occurs after a given number of loading cycles can be obtained from the above-mentioned comparison. Finally, an example is shown in order to illustrate the use of a computer program, which translates the proposed procedure.     

多晶硅双端固支梁高周循环下疲劳特性的分析

多晶硅固支梁是MEMS器件中较常见的可动部件,通过静电激励的方式对其进行疲劳振动加载;所用结构为面外运动结构,为了测试样品的加速疲劳特性,通过在固支梁面内引入缺陷的方式来增大应力水平值;器件在经历了1.72×1011次循环之后,微梁的谐振频率、振动幅度发生了较大偏移,其谐振频率的偏移量达到14.531 kHz,器件性能发生了严重的退化.研究结果表明,利用谐振频率的改变来表征材料性能的退化是一种准确、可行的方法,同时本文进一步分析指出,器件上引入凹槽缺陷的方法确实可起到加速疲劳的作用;可利用此方法制作不同应力水平幅度的结构进行振动载荷疲劳加载实验,从而得到固支梁结构疲劳加速因子.     

Computer prediction of misaligned welded joints

Experimental tests have shown that misalignment can reduce the fatigue strength of welded joints significantly. Further theoretical investigations are also required to understand the behavior of these joints. In the present study, boundary element technique together with the hypersingular boundary integral equation are employed to estimate the notch stress concentration factors at the surface. These are then used to predict the fatigue life. The addressed variable is the root crack length, or partial penetration depth, which can be accurately modeled by boundary element method. It is shown that there is a good correlation between the previous experimental results and the present theoretical results.     

Robust shape optimization of notches for fatigue-life extension

An iterative 2D finite-element-based optimization procedure has been developed which incorporates robust design philosophies. This has been used to determine precise free-form shapes for a hole in a plate example, with the aim of maximizing its fatigue-life when exposed to varying load orientations. Past methods have typically considered only a single nominal load orientation, with empirical approaches to deal with the orientation variability, thus resulting in suboptimal solutions. Here a robust stress method is developed that produces a notch shape that minimizes the peak stress and renders it constant for a range of load orientations. Furthermore, a more sophisticated robust fatigue-damage optimization method is then developed to minimize the peak fatigue damage for a given stochastic distribution of load orientations. Fatigue calculations for an example problem with significant load orientation variation show that the robust optimization methods provide fatigue-life extensions 2 to 8 times better than past methods. It is anticipated that the implementation of robust optimal shapes in metallic components would result in greater fatigue-life extension.     

Design of maintenance schedules for fatigue-prone metallic components using reliability-based optimization

This contribution focuses on the design of optimal maintenance schedules for metallic structures prone to develop fatigue cracks. The crack propagation phenomenon is addressed using a fracture mechanics approach. The problem of maintenance scheduling is addressed within the framework of reliability-based optimization (RBO). Thus, it is possible to minimize the costs associated with maintenance and eventual failure while explicitly considering uncertainties in the crack propagation phenomenon and inspection activities. The underlying RBO problem is solved using an efficient method recently developed by the authors. A numerical example demonstrating the application of the proposed approach is presented.     

Shape optimization for 2-D mixed-mode fracture using Extended FEM (XFEM) and Level Set Method (LSM)

Weight and service life are often the two most important considerations in design of structural components. This research incorporates a novel crack propagation analysis technique into shape optimization framework to support design of 2-D structural components under mixed-mode fracture for: (1) maximum service life, subject to an upper limit on volume, and (2) minimum weight subject to specified minimum service life. In both cases, structural performance measures are selected as constraints and CAD dimensions are employed as shape design variables. Fracture parameters, such as crack growth rate and crack growth direction are computed using extended finite element method (XFEM) and level set method (LSM). XFEM employs special enrichment functions to incorporate the discontinuity of structural responses caused by the crack surfaces and crack tip fields into finite element approximation. The LSM utilizes level set functions to track the crack during the crack propagation analysis. As a result, this method does not require highly refined mesh around the crack tip nor re-mesh to conform to the geometric shape of the crack when it propagates, which makes the method extremely attractive for crack propagation analysis. An accurate and efficient semi-analytical design sensitivity analysis (DSA) method is developed for calculating gradients of fracture parameters. Two different approaches—a batch-mode, gradient-based, nonlinear algorithm and an interactive what-if analysis—are used for optimization. An engine connecting rod example is used to demonstrate the feasibility of the proposed method.     

Optimal design of interference fit assemblies subjected to fatigue loads

This paper presents a methodology for an optimal design of interference fit subjected to fatigue loads. Optimization consists in finding a trade-off between mass and competing safety factors at hub and shaft contact zone as well as in shaft fillet. Developing an effective calculation method for fatigue strength of an interference fitted assembly using the finite element method is one of the main steps of the procedure. Meanwhile, coupling the finite elements model of interference fit with an optimization algorithm is not adequate considering the computing time and the significant number of calculations necessary to portrait the assembly behavior. Therefore, a sequential approximate multi-objective optimization algorithm (SAMOO) is presented. The method involves Design Of Experiments (DOE), interpolation with kriging functions, and multi-objective optimization. Preliminary study of parameter variance, and advanced post-processing of multi-objective optimization, provide engineers with valuable information for identifying an optimal design of interference fit assembly using fewer finite element calculations.     

An integrated CAE environment for simulation-based durability and reliability design

This paper introduces a flexible, general purpose, integrated Computer-Aided Engineering (CAE) system, called Durability and Reliability Analysis Workspace. It carries out the simulation-based spectral fatigue damage and failure probability analysis of mechanical components. In this environment, a hybrid quasi-static method for computing dynamic stress time history has been introduced, a critical plane method for predicting multiaxial fatigue crack initiation life have been used. Also, a new methodology for assessing component reliability based on fatigue failure mode has been proposed. The corresponding CAE tools for the purpose of aiding engineers in the durability and reliability analysis have been developed and implemented in the system. The system also provides a graphical, menu-driven user interface for quick and easy interaction with these tools. Advanced Computer Integrated Technology is utilized to integrate CAE tools bound into a system with automatic control, coordinate, and communicate. This paper explains the methodologies and treatment in the implementation of the CAE system. The objective of this research is to provide a layer of network computational services for reliable remote computations and data transfers between an engineering workstation and a computation server on a high-speed computer. It incorporates methods of both engineering and computer science to allow the engineer to solve engineering problems through automation and reliability, utilizing high-speed procedures.     

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.     

Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading

Microstructure based mechanistic calculations, coupled with physically motivated crack initiation criterion, can provide effective means to predict fatigue cracking in polycrystalline materials. However the accommodation of large number of cycles to failure, as observed in the experiments, could be computationally exhaustive to simulate using conventional single time scale finite element analysis. To meet this challenging requirement, a novel wavelet transformation based multi-time scaling algorithm is proposed for accelerated crystal plasticity finite element simulations in this paper. An advantage over other conventional methods that fail because of assumptions of periodicity etc., is that no assumption of scale separation is needed with this method. The wavelet decomposition naturally retains the high frequency response through the wavelet basis functions and transforms the low frequency material response into a “cycle scale” problem with monotonic evolution. The method significantly enhances the computational efficiency in comparison with conventional single time scale integration methods. Adaptivity conditions are also developed for this algorithm to improve accuracy and efficiency. Numerical examples for validating the multi-scaling algorithm are executed for a one dimensional viscoplastic problem and a 3D crystal plasticity model of polycrystalline Ti alloy under the cyclic loading conditions.     

Elastoplastic analysis of tubular joints of offshore platforms

The subject of this paper is the analysis and design of complex tubular joints, eventually including internal and external gussets and stiffener rings, corresponding to fixed and mobile offshore structures.Two different joints are analysed. In the first case an X joint is studied for elastic and elastoplastic behaviour, loading up to collapse in order to determine ultimate strength and safety factor. Finite elements which can reproduce the elastic and plastic singularities of the stress and the strain fields in the crack tip, are then used for the analysis of a T joint. Both direction and rate are considered in the crack propagation, and an elastoplastic analysis is carried out, to determine the crack opening displacement (COD).Finally, the consideration of fatigue effects in tubular joints is discussed, and techniques for evaluating fatigue life are outlined.     

Simplified analysis of plastic and stable crack growth

A simplified analysis model for the initiation of stable growth and the propagation of a surface crack is proposed. Surface crack growth behavior can be analyzed by two-dimensional flnite element analysis using the simplified model. This model is applied for the estimation of the penetration load on Type 304 stainless steel plate with a part-through notch.