Fatigue crack growth model for assessing reliability of box-girders for cable-stayed bridge combining SHMS with strain data

Enhancement of the computer algorithm developed for the Runyang cable-stayed bridge (RYCB) in China is made by incorporating the fatigue crack growth analysis in contrast to the SN curve approach. Strain data obtained from the structural health monitoring system (SHMS) and finite element calculations are used. This provides the application of a deterministic method in addition to the probabilistic approach with the added feature of crack growth. The choice of selecting the two-parameter fatigue crack growth criterion was based on the definition of reliability index β such that the new results can be compared with those using the SN curves. A gradual drop of the reliability index β with time with an upper limit was obtained for the crack growth model in contrast to the linear time relation for the SN curve model that had no upper limit. This difference is significant and reveals the importance for selecting the fatigue failure criterion. Deterministic and probabilistic crack growth models are used to assess the differences. The results are based on the box-girder component strain history data of the Runyang Cable-stayed Bridge (RYCB) in China, stress history recorded by structural health monitoring system (SHMS) is analyzed using the monitored stress amplitude, mean stress and stress ratio. Finite element calculations are used to supplement data at locations not accessible for measurements. Additional improvement with reference to damage accumulation and the physical meaning of the reliability index will be studies in relation to the fatigue damage of box-girder of long cable-stayed bridges.     

Accumulative damage near crack tip for welded bridge members: fatigue life determination

The behavior of crack growth for the fatigue damage accumulation near tip where damage is most severe is analyzed. Fatigue life is assessed for the welded members of bridges under traffic loading. Two parts are considered. They consist of the development of a fatigue damage accumulation model for welded bridge members and a method for calculating the stress intensity factor that is needed for evaluating the fatigue life of welded bridge members with cracks. Based on the concept of continuum damage accumulation and fatigue and fatigue crack growth relations, results are obtained to describe the relationship between the cracking count rate and the effective stress intensity factor. Crack growth and fatigue life are found for two types of welded members assisted by using fatigue experimental results. The stress intensity factors are modified by correcting for the geometric shape of the welded members in order to reflect the influence of the weldment and geometry. This is accomplished via the stress intensity factor. The calculated and measured fatigue lives were generally in good agreement for the initial cracking conditions of two types of welded members widely used in steel bridges.     

Infrared Image Processing for the Calorimetric Analysis of Fatigue Phenomena

This paper presents an infrared image processing procedure that was developed to study calorific effects accompanying material fatigue. This method enables us to separately estimate patterns of thermoelastic and dissipative sources. Heat sources were estimated on the basis of partial derivative operators present in a local form of the heat equation by using a set of approximation functions that locally fits the temperature field and takes the spectral properties of the sought sources into account. Numerical examples were used to check the validity of the method and to highlight its capabilities along with its limits. The paper concludes with examples of thermal image processing extracted from fatigue tests performed on a dual-phase steel. The coupling sources were compared to the theoretical predictions induced by a basic thermoelastic model, while the heterogeneous character of the fatigue development was highlighted in terms of dissipation sources.     

Three-dimensional structure optimal design for extending fatigue life by using biological algorithm

This paper presents some applications of a new structural shape optimization procedure for maximizing fatigue life or inspection intervals for damage tolerant structures. In this approach, a new and simple method, which we termed FAST (Failure Analysis of Structures), for estimating the stress intensity factor for cracks at a notch, as well as an extension of the biological algorithm was employed to study the problem of optimization with fatigue life as the design objective. Research by the authors has demonstrated that the optimum shape for minimizing stress is not necessarily the optimum shape for static strength or fatigue life of a damage tolerant structure. The examples are presented that highlight this difference. The optimal shapes for stress are compared with optimized shapes found for static strength with different crack lengths. These are also compared with optimized shapes found for maximum fatigue life. The choice of initial crack size was found to have a significant effect on the optimal shapes for the structures presented.     

A micromechanical explanation of the mean stress effect in high cycle fatigue

A micro–macro approach of multiaxial fatigue in unlimited endurance is presented in this study, as an extension of a previous model recently proposed by the authors [Monchiet, V., Charkaluk, E., Kondo, D., 2006. A plasticity–damage based micromechanical modelling in high cycle fatigue. C.R. Mécanique 334 (2), 129–136]. It allows to take into account coupling between polycrystalline plasticity and damage mechanisms which occur at the scale of persistent slip bands (PSB) during cyclic deformation. The plasticity–damage coupled model is obtained by adapting the Gurson [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I – yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15] limit analysis to polycrystalline materials to take into account microvoids growth along PSBs. The macroscopic fatigue criterion corresponds to microcracks nucleation at the PSB–matrix interface. It is shown that this criterion accounts for the effect of the mean stress and of the hydrostatic pressure in high cycle fatigue. Such features of HCF are related to the damage micro-mechanisms. Finally, some illustrations concerning the particular case of cyclic affine loadings are presented and comparisons of the predictions of the fatigue criterion with experimental data show the relevance of this new approach.     

Fatigue life predictions by integrating EVICD fatigue damage model and an advanced cyclic plasticity theory

An event independent cumulative damage (EVICD) fatigue prediction model was previously developed for the fatigue damage prediction under general multiaxial stress state and loading conditions. The model takes the plastic strain energy as the major contributor to the fatigue damage. The application of the EVICD model does not require a cycle counting method for general random loading. In the current effort, derivations were made to explicitly and directly relate the material constants in the fatigue model to the parameters in the Manson–Coffin equations and the cyclic stress–strain curve of the material. In addition, an advanced cyclic plasticity theory was implemented for the determination of the detailed stress–strain response that was required as the input for the EVICD fatigue model. Three metallic materials were used to demonstrate the capability of the modified fatigue model for the predictions of fatigue lives under different loading conditions. The results show that the fatigue model can provide fatigue life predictions in close agreement with the experimental observations.     

Effects of Environmental Degradation on Flexural Failure Strength of Fiber Reinforced Composites

Fiber-reinforced composite laminates are often used in harsh environments that may affect their long-term durability as well as residual strength. In general, environmental degradation is observed as matrix cracking and erosion that leads to deterioration of matrix-dominated properties. In this work, cross-ply laminates of carbon fiber reinforced epoxy were subjected to environmental degradation using controlled ultraviolet radiation (UV) and moisture condensation and the post-exposure mechanical properties were evaluated through elastic modulus and failure strength measurements. Additionally, both degraded and undegraded were subjected to cyclic fatigue loading to investigate possible synergistic effects between environmental degradation and mechanical fatigue. Experimental results show that the degradation results in reduced failure strength. Greater effects of degradation are observed when the materials are tested under flexural as opposed to uniaxial loading. Based on strength measurements and scanning electron microscopy, we identified various damage modes resulting from exposure to UV radiation and moisture condensation, and cyclic loading. The principal mechanisms that lead to reduction in mechanical properties are the loss of fiber confinement due to matrix erosion, due to UV radiation and moisture condensation, and weakened/cracked ply interfaces due to mechanical fatigue. An empirical relationship was established to quantify the specific influence of different damage mechanisms and to clarify the effects of various degradation conditions.     

Fatigue life enhancement of structures using shape optimisation

The paper proposes a new approach for shape optimisation with fatigue life as the design objective. Conventional designs often incorporate stress optimisation that aims at reducing stress concentrations around a structural boundary by minimising the peak stress. However, this is only an effective and sufficient measure for an ‘ideal’ or ‘flaw-less’ structure. It is a well-known fact that flaws (cracks) are inevitably present in most structures. This emphasises the need to investigate the influence of cracks on optimised shapes. Numerical modelling of cracks using the Finite Element Method requires a fine mesh to model the singularity at crack tips, which makes fracture calculations computationally expensive. Furthermore, for a damage tolerance based optimisation, numerous cracks are to be considered at various arbitrary locations in a structure, and fatigue life evaluation needs to be repeated for each crack at every iteration. This makes the optimisation process extremely computationally inefficient for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, there has been inadequate research to consider fracture parameters, such as fatigue life, in the optimisation objective. To address this, the paper presents an approach for the shape optimisation of damage tolerant structures with fatigue life as the design constraint.The damage tolerance based optimisation was performed using a number of nonlinear programming algorithms, namely the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method, the Fletcher Reeves (Conjugate Direction) method, and the Sequential Unconstrained Minimisation Technique (SUMT). These methods were extended for optimising the fatigue life in the presence of numerous surface cracks. A significant enhancement in fatigue life was achieved for various crack cases consisting of different initial and final crack sizes. It is shown that the fatigue life optimised shapes can be considerably different from the corresponding stress optimised solution. This emphasises the need to explicitly consider fatigue life as a distinct design objective when optimising damage tolerant structures. A fatigue life optimisation leads to the generation of a ‘near uniform’ fatigue critical surface. The design space near the ‘optimal’ region was found to be relatively flat. This means that the precise identification of the local/global optimum solution is not critical, because a significant structural performance enhancement can be achieved in the ‘near’ optimal region. An additional benefit of fatigue life optimisation is that the resulting optimised shapes may even be lighter than the stress optimised designs. To verify the optimal solutions obtained using the nonlinear programming algorithms, the results were compared with those obtained using a heuristic optimisation method (Biological algorithm). The solutions predicted by both the methods, employing inherently different (gradient-based and gradient-less) algorithms, were found to agree very well.     

Time and Temperature Dependent Fatigue Strengths for Three Directions of Unidirectional CFRP

This paper is concerned with the characterization of time and temperature dependent fatigue strengths for three loading directions of unidirectional CFRP, that is, the longitudinal tensile and compressive directions as parallel to the fiber direction and the transverse tensile direction as transverse to the fiber direction, within the plane of the unidirectional ply, which are the most basic directions for fiber composites. These three kinds of fatigue strengths were measured at various frequencies and temperatures. The master curves of these fatigue strengths were constructed using measured data based on the time-temperature superposition principle. As results, it was cleared that each of three kinds of fatigue strength shows characteristic time and temperature dependent behavior. The tensile fatigue strength for the longitudinal direction of unidirectional CFRP moderately depends on time and temperature as well as the number of cycles to failure. The compressive fatigue strength for the longitudinal direction strongly depends on time and temperature, however this strength scarcely depends on the number of cycles to failure. The tensile fatigue strength for the transverse direction strongly depends on time and temperature as well as the number of cycles to failure.     

疲劳裂纹闭合研究的进展

本文阐述了疲劳裂纹闭合的四种诱发机制,介绍了疲劳裂纹闭合现象测量的几种方法并结合作者的工作进行了评述.文中详细地介绍和探讨了材料、应力比、试样几何尺寸、环境及载荷谱等因素对裂纹闭合现象的影响,指出了目前研究工作中存在的问题.并对今后开展研究工作的方向提出了看法.     

Rapid evaluation of the fatigue limit in composites using infrared lock-in thermography and acoustic emission

Fatigue limit determination via the conventional Wöhler-curve method is associated with extended experimental times as it requires testing of a large number of specimens. The current paper introduces a methodology for fast, reliable and experimentally economic determination of the fatigue limit in monolithic and composite materials by means of combined usage of two nondestructive inspection methods, namely infrared (IR) lock-in thermography and acoustic emission (AE). IR thermography, as a real-time and non-contact technique, allowed the detection of heat waves generated due to thermo-mechanical coupling as well as of the energy dissipated intrinsically during dynamic loading of the material. AE, on the other hand, was employed to record the transient waves resulting from crack propagation events. Aluminum grade 1050 H16 and cross-ply SiC/BMAS ceramic matrix composites were subjected to fatigue loading at various stress levels and were monitored by an IR camera and AE sensors. The fatigue limit of the monolithic material, obtained by the lock-in infrared thermography technique and supported by acoustic emission was found to be in agreement with measurements obtained by the conventional S–N curve method. The fatigue limit of the ceramic matrix composite was validated with acoustic emission data.     

A boundary element modeling of fatigue crack growth in a plane elastic plate

This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given.     

An Experimental Rig to Investigate Fatigue Crack Growth Under Dynamic Loading

A novel experimental rig capable of generating a versatile dynamic loading has been designed and tested to overcome the shortcomings of conventional fatigue testing machines such as the difficulty in providing zero crossing aperiodic loading. The main principle of this new design is based on two, single degree of freedom based excited oscillators, where inertial forces act on a specially designed specimen. By changing the natural frequency of the oscillator, the extent of the preloads and pattern of the excitation signal on the shaker, the rig provides a new and robust means of fatigue testing, particularly for aperiodic loading.     

Surface hardness increase of 2024 aluminum alloy subjected to cyclic loading

Constant amplitude fatigue tests at R = 0.1, conducted on the aircraft aluminum alloy 2024 T3, have revealed an appreciable surface hardness increase of the alloy at the nano- and meso-scale during fatigue. The observed surface hardness changes could be monitored with confidence by means of nanoindentations. The degree of hardening increases with increasing number of fatigue cycles following exponential relations. With increasing fatigue stress level degree of hardening increases as well. The observed results provide a basis for developing concepts to early detect and also monitor fatigue damage accumulation in aluminum aircraft structures based on measurements of the material’s hardness changes by means of nanoindentations.     

Fatigue and damage tolerance behaviour of corroded 2024 T351 aircraft aluminum alloy

The fatigue and damage tolerance behaviour of pre-corroded 2024 T351 aluminum alloy specimens has been investigated and compared to the behaviour of the uncorroded material. The experimental investigation was performed on specimens pre-corroded in exfoliation corrosion environment and included the derivation of S–N and fatigue crack growth curves as well as measurements of fracture toughness. The fatigue crack growth tests were performed for different stress ratios R. To obtain reference material behaviour all mechanical tests were repeated under the same conditions for uncorroded specimens. For the corroded material an appreciable decrease in fatigue resistance and damage tolerance was obtained. The results of the experimental investigation were discussed under the viewpoint of corrosion and corrosion-induced hydrogen embrittlement of the 2024 aluminum alloy. The need to account for the influence of pre-existing corrosion on the material’s properties in fatigue and damage tolerance analyses of components involving corroded areas was demonstrated.     

Plasticity-damage based micromechanical modelling in high cycle fatigueUne modélisation micromécanique couplant plasticité et endommagement en fatigue polycyclique

A micro-macro approach of multiaxial fatigue in unlimited endurance is proposed. It allows one to take into account plasticity and damage mechanisms which occur at the scale of Persistent Slip Bands (PSB). The proposed macroscopic fatigue criterion, which corresponds to microcracks nucleation at the PSB-matrix interface, is derived for different homogenization schemes (Sachs, Lin-Taylor and Kröner). The role of a mean stress and of the hydrostatic pressure in high cycle fatigue is shown; in particular, in the case of Lin-Taylor scheme and linear isotropic hardening rule at microscale, one recovers the linear dependance in pressure postulated by K. Dang Van for the macroscopic fatigue criterion. This dependence is related here to the damage micro-mechanism. Finally, the particular case of affine loading is presented as an illustration. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006).     

Crystal plasticity finite element modelling of low cycle fatigue in fcc metals

A new dislocation-based model for low cycle fatigue in fcc metals at a length scale smaller than the feature size of the dislocation structures is presented. It uses the crystal plasticity finite element method and dislocation densities as internal variables. Equations for the dipole distance distribution, for the double cross slip mechanism and a new dislocation multiplication law are introduced, which can predict the emergence of vein and channel structures starting from a randomly perturbed dislocation distribution. The characteristics of these structures in copper and aluminium, as well as the mechanical properties, are compared with experiments. Compared with existing density-based theories, the capability to reproduce dislocation patterning is a significant step forward.     

Surface finish of open holes on fatigue life

In this paper, the effect of surface finish of open holes on the fatigue life has been studied. Four defects of the surface finish are simulated. They are scratch, void, inclusion and roundness. Firstly, the effect of the four defects on the stress distributions around the holes has been studied by the finite element method (FEM). The fatigue lives are determined based on the stress distributions by the method of nominal stress approach. The results show that the fatigue lives are dependent on the quantity of the surface finished. There are the critical defect values of scratch, void and inclusion, smaller than which there is no effect of the surface finish on the fatigue life. For these three defects, the fatigue lives decrease with the increasing of the values of the defects. It is the same to the defect of roundness, e.g. the bigger roundness tolerance is, the shorter the life is. Further, an approximate quadratic curve has been found for the relationship between the roundness tolerances and their logarithmic fatigue lives.     

Affected depth approach to determine the fatigue strength of materials containing surface defects

This paper explains a novel methodology to determine the High Cycle Fatigue (HCF) reliability of materials with defects. A defect was represented by a semi-spherical void situated at a specimen surface subjected to periodic loading. Then, the Finite Element (FE) method was carried out to find out the stress distribution near the defects for diverse sizes and diverse loadings. The Crossland stress change is studied and interpolated by a mathematical function depending on fatigue limits, defect radius, and profundity from the defect tip. The HCF strength of defect material is computed by the “stress strength” approach via the Monte Carlo sampling. This approach leads to determine Kitagawa–Takahashi diagrams, for a definite reliability, of materials with defects. The calculated HCF reliabilities agree well with fatigue tests. Obtaining Kitagawa–Takahashi diagrams with reliability level permits the engineer to be engaged in an endurance problem to compute the defective fatigue lives in safe and efficient process. As a final point, we discuss the sensitivity effects of defect size, defect free fatigue limits, affected depth, and load amplitude to envisage the fatigue reliability of materials with defects.