The theory of critical distances: a review of its applications in fatigue

This paper attempts to review the most interesting findings in the use of the theory of critical distances (TCD) to predict fatigue strength of notched mechanical components. Initially, the most modern formalisations of the TCD are considered, showing their peculiarities and differences. An ad-hoc section is then focused on the multiaxial high-cycle fatigue problem, considering all the open questions arising in the presence of complex stress fields damaging the fatigue process zone in the vicinity of the stress concentrator apex. Subsequently, the physical idea on the structural volume concept is briefly investigated showing some peculiar results generated in the high-cycle fatigue regime under both uniaxial and biaxial fatigue loading. Finally, our idea to extend the use of the TCD down to the low-medium cycle fatigue regime is briefly explained.Working in collaboration with Prof. David Taylor, we have spent the last five years investigating this theory both to better understand its physical meaning and to systematically check its accuracy in predicting notch fatigue strength under different loading conditions. After so much work done in this area we feel so confident to proudly and loudly say that the TCD is a powerful engineering tool suitable for assessing real mechanical components in situations of practical interest. Finally, it can be highlighted also that the best TCD formalisations were seen to be those based on the use of linear-elastic stresses. This suggests that such a theory can successfully be used to post-process simple linear-elastic finite element (FE) models reducing time and costs of the design process.     

Notch geometry effects in fatigue: A conservative design approach

The understanding of stress concentrators (notches) is an important element in the prevention of failure in components and in the analysis of failures when they occur. This paper examines critically the methods currently used to predict the fatigue strength of components containing notches, with particular attention to the need for a conservative design approach. Current methods, if correctly applied, are shown to give conservative predictions of fatigue limit and high-cycle fatigue strength, and it is shown that the same philosophy can be extended to cover very small notches, including surface roughness. The presentation of these predictions in the form of a “mechanism map” for notch fatigue is advocated as a useful tool for designers. The problems of extending the approach to other types of stress concentrator, such as fillet radii, are discussed.     

On the prediction of high-cycle fretting fatigue strength: Theory of critical distances vs. hot-spot approach

This paper summarises the results we obtained when applying both the theory of critical distances (TCD) and the hot-spot approach to predict high-cycle fretting fatigue strength. In particular, the accuracy of such approaches was checked considering some experimental results taken from the literature and ad hoc generated to explicitly investigate the size effect in fretting fatigue. According to the well-known experimental outcome that initiation and initial growth of fretting fatigue cracks is mainly mixed-mode dominated, both the TCD and the hot-spot approach were used in conjunction with two different multiaxial fatigue criteria: the so-called modified Wöhler curve method (MWCM), that is, a conventional critical plane approach, and the well-known mesoscopic criterion due to Dang Van. Considering cylindrical-on-flat contacts tested under partial slip conditions, it was seen that the TCD is successful in predicting the size effect in fretting fatigue, resulting in more accurate predictions than those obtained by applying the classical hot-spot approach. Moreover, the present study revealed that the overall best accuracy is obtained when applying the TCD along with the MWCM. This result is very promising, especially in light of the fact that such a design methodology can be employed by simply post processing linear-elastic FE results, making it suitable for being used to assess real mechanical assemblies without the need for carrying out time-consuming elasto-plastic analyses.     

Survey of fatigue failures in helicopter components and some lessons learnt

The paper presents a comprehensive review of the failure investigations carried out within AgustaWestland Limited (AWL) over the last 30 years. The results of this survey show that fatigue accounts for approximately 55% of all failures in helicopter components. Although fatigue failures can occur in a wide range of components the types of factors responsible for initiation differ depending on the application of the part. This paper identifies the most common fatigue prone areas in the helicopter, how design considerations and certain key factors such as fretting can influence fatigue life. The importance of aircraft maintenance and quality control in the supply chain will also be discussed. Based on the survey, the paper will also illustrate several instances where fatigue failures have been eliminated through the application of novel surface engineering techniques, improvements in material & processes and modifications to the original design.     

An implicit gradient application to fatigue of complex structures

This paper presents a procedure to evaluate the stress gradient effect on the fatigue strength of steel welded joints and notched components. An effective stress is calculated by solving a second-order differential equation over all the component (the implicit gradient approach) independently of its geometric shape. The solution is obtained by assuming the isotropic linear elastic constitutive law for the material and the maximum principal stress as equivalent stress. The fatigue behaviour of geometrically complex steel welded joints is analysed and compared with previous fatigue scatter bands obtained for two-dimensional joints. In complex details, the actual critical point is derived from the analysis and is not assumed a priori. Implicit gradient analysis is also used to investigate high-cycle fatigue behaviour in the case of notches.In addition, it is shown that critical distance approaches can be obtained from the non-local theory by proper choice of the weight function.     

Thermo-mechanical fatigue damage and failure of modern high performance diesel pistons

This study resulted from an engineering failure investigation related to diesel engine piston failures which occurred during a bench dynamometer engine durability test programme. The test programme aimed at evaluating the effects of various fuel types on the durability of fuel system components in passenger car diesel engines. A number of unexpected cylinder head, turbocharger and piston failures were experienced during the course of the test programme. This study focused on the cause of the piston failures experienced during these tests.Analyses of the fractured pistons revealed that thermo-mechanical fatigue initiation occurred as a result of primary silicon phase cracking and subsequent micro-crack formation due to excessive thermo-mechanical loading. Progressive formations of such micro-cracks lead to flaws that were of sufficient magnitude to initiate propagation by high cycle fatigue mechanisms.The investigation also revealed that the excessive thermo-mechanical piston loading was caused by over-fuelling and a combination of elevated and poorly controlled post intercooler air temperature. There was no evidence to suggest that the failures were related to the test fuel formulations.     

Fatigue failure of a bar of a twin-screw extruder for plastics

The paper deals with the analysis of the failures regarding one of the bars of a twin screw extruder for plastics and reinforced plastics. The extruder was equipped with an 50 kW electric motor and very soon showed failure problems, always on the same bar, that was substituted many times. The analysis of the material, tensile tests and fractographical observations of some broken bars helped to understand that failures were due to fatigue and to define some design improvements of the bar. In-service strain gauge measurements were executed to assess the actual load acting on the bars and the data were elaborated by using the spectral analysis approach and were used to assess the fatigue strength of the bars.     

Course of SN-curves especially in the high-cycle fatigue regime with regard to component design and safety

Conventional design codes base their recommendations still on the common prejudice that an “endurance limit” exists. However, several investigations prove clearly that in the high-cycle regime a decrease of fatigue strength with increased number of cycles still occurs, even if corrosion or temperature effects are excluded. Therefore, the fatigue design of components submitted to loadings below the knee point of the SN-curve must consider this fact in order to avoid failures. With regard to the course of the SN-curve in the very high-cycle area, material and manufacturing dependent recommendations are given.     

Torsion fatigue failure of bus drive shafts

The mystery surrounding high failure rates in the drive shafts of a large municipal transit agency's fleet of 40 newly acquired articulated buses is investigated. The drive shafts were fabricated from a low-carbon (0.45%) steel such as AISI 5046. An examination of the drive shafts on all 40 buses is conducted, and 6 different drive shaft designs are identified among the fleet, but all of the failures, 14 in all, are limited to just one of the identified designs. Microscopic examination of the fracture surface of one of the failed drive shafts under a scanning electron microscope is conducted to determine the failure mode. Evidence of high-cycle fatigue is found, and a finite-element analysis is conducted to compare the maximum stress of the design exhibiting failures with the most common of the other designs that exhibits no failures. A fatigue life prediction is performed to determine just how much longer the expected fatigue life of the surviving design is compared to the design that suffered the early failures.     

Prediction of damage-growth based fatigue life of polycrystalline materials using a microstructural modeling approach

A new finite element-based mesoscale model is developed to simulate the localization of deformation and the growth of microstructurally short fatigue cracks in crystalline materials by considering the anisotropic behavior of the individual grains. The inelastic hysteresis energy is used as a criterion to predict the fatigue crack initiation and propagation. This criterion in conjunction with continuum damage modeling provides a strong tool for studying the behavior of materials under cyclic loading at the level of the microstructure. The model predictions are validated against an austenitic stainless steel alloy experimental data. The results show that a combined microstructural and continuum damage modeling approach is able to express the overall fatigue behavior of crystalline materials at the macroscale based on the microstructural features. It correctly predicts the crack initiation on slip bands and at inclusions in low-cycle and high-cycle fatigue, respectively, in agreement with experimental observations reported in the literature.     

A methodology for the fatigue design of notched castings in gray cast iron

Fatigue failures of machine components remain a topic of relevant importance in the industrial world. They usually occur from geometrical features such as holes, notches, corners and grooves, whose actual influence is not well estimated in the design phase. Cast parts made in gray cast iron are typical examples of components difficult to design in fatigue because they are simultaneously characterized by complex geometries and microstructure. In this contribution the issue is discussed starting from the failure analysis of a cyclically pressurized hydraulic component. The work consists of an experimental procedure, i.e. the fatigue characterization of the material on specimens extracted from cast parts, and of a numerical design activity, i.e. the prediction of life time according to the critical distance method [Taylor D. Crack modelling: a technique for the fatigue design of components. Engng Fail Anal 1996;3(2):129-36]. The implication is that cracks and localized damage begin to appear in the microstructure of gray cast iron at sharp notches from the first cycles of loading. In order to obtain a correct prediction, the fatigue design should adopt fracture mechanics arguments to determine non-propagating conditions.     

Fatigue in bamboo

This paper describes the results of an experimental programme to determine the fatigue behaviour of bamboo. Bamboo is subjected to cyclic loading, both in the plant itself and subsequently when the material is used in load-bearing applications in the construction industry. However, there is currently no data in the literature describing fatigue in this material. We found that sections of bamboo culm loaded parallel to the culm axis did not undergo fatigue failure: samples either failed on the first loading cycle, or not at all. By contrast, fatigue was readily apparent in samples loaded in compression across the diameter of the culm. The number of cycles to failure increased as the cyclic load range decreased in a manner similar to that found in many engineering materials: fatigue occurred at applied loads as small as 40% of the ultimate strength. Two different species of bamboo were tested and found to have different ultimate strengths but similar high-cycle fatigue strengths. Finite element analysis was used to help understand the progression of fatigue damage and the effect of stress concentration features. Some tentative design rules are proposed to define stress levels for the safe use of bamboo, taking fatigue into account.     

THE INFLUENCE OF AGEING AT INTERMEDIATE TEMPERATURES ON THE MECHANICAL BEHAVIOUR OF A DUPLEX STAINLESS STEEL: Part II. FATIGUE LIFE AND FATIGUE CRACK GROWTH

Abstract— The mechanical behaviour of AISI 329 steel has been investigated for ageing times up to 20,000 h at temperatures of 475, 425, 375, 325 and 275°C. The study has concentrated on the changes in the response to cyclic strains, in the low-and the high-cycle fatigue regimes, and in the resistance to fatigue crack propagation as a function of temperature and time of ageing.
It is shown that ageing increases the fatigue resistance in the high-cycle fatigue regime, but the opposite occurs in the low-cycle fatigue regime. Ageing increases the LEFM threshold stress intensity factor range for fatigue crack propagation which reaches high values in these alloys, and is influenced by the fatigue load ratio. Crack closure contributes to the LEFM threshold stress intensity factor range for crack propagation only in the annealed condition of the AISI 329 steel.     

Long life fatigue under multiaxial loading

A life prediction model in the field of high-cycle (i.e. long-life) fatigue is presented in this paper. The proposed model applies in the case of constant amplitude multiaxial proportional and non-proportional loading. The problems of the fatigue limit criterion and of the fatigue life prediction are both addressed and comparisons with experimental data are shown. Some limited discussion of the stress gradient effect is also offered. Although the particular model developed here is better suited for ferritic steels, it is explained in the paper that the methodology used to obtain this model can be adequately adapted to derive mathematically consistent models for other classes of metallic materials.     

Failure investigation of blade and disk in first stage compressor

A matched blade tenon and disk mortise of the first stage compressor in an aeroengine fractured simultaneously. Apparently, both had fatigue features on the fracture surfaces. Macro observations showed the cracking sites were roughly at the central region of the matched tenon and mortise. Contact surfaces examination revealed there were important marks, showing abnormal contact of the tenon and mortise in service. Material qualities were inspected and the stresses in the tenon and in the mortise were calculated under normal conditions. These demonstrate that the failures were not due to the insufficiency of failure resistance but the deviation from expected conditions. Conclusively, the bad contact of the tenon and the mortise is responsible for the failures. Field non-destructive inspection was performed on other aeroengines of the same type, and some cracks, which were very similar to those in the fractured tenon and mortise, were found. Further investigation revealed that the design shortcoming resulted in over-compensation of centrifugal bend moment and bad contact condition.     

A probabilistic approach to fatigue risk assessment in aerospace components

This paper describes a new possible approach to fatigue design of aerospace components founded on probabilistic bases compared with safe life and damage tolerance that are founded on deterministic bases.

A numerical tool has been introduced and explained together with the experimental activity for its validation analyses.

For a typical aerospace component, such as a lap-joint panel, an acceptable maximum risk level has been established and the maintenance program has been planned to ensure operating life without catastrophic failures.

The analysis has shown that this new approach introduces several benefits in fatigue design.     

Failure analysis of rolling mill stand coupling

The failure analysis of two slipper couplings showed that both couplings fractured as a result of fatigue. In both cases, the fracture started in the corner between the paddle and the coupling body and propagated around the corner. Both fractures are caused by deficient design of the fillet between the paddle and the coupling body with high stress concentration. In order to extend actual service life, three design modifications have been considered. Numerical analysis showed that redesign of coupling by stiffener between the paddle and the coupling body reduces maximum local and actual service life of couplings can be improved from finite to infinite.     

An unusual failure of a nickel-aluminium bronze (NAB) hydraulic valve

Investigation of a hydraulic leak from a nickel-aluminium bronze (NAB) valve in a naval vessel revealed that two corners of a square flange had fractured in a macroscopically brittle fashion such that the valve was in three pieces – an unusual occurrence for a ductile material. Moreover, fracture surfaces were almost entirely intergranular, and there were no signs of dimpled fracture surfaces or shear lips typical of fast fracture in NAB. A few macroscopic progression markings were evident and, at high magnifications, intergranular facets exhibited slip lines and (probably) fatigue striations. Fracture surfaces produced by fatigue of specimens cut from the valve were similar to the in-service fractures for fatigue at very low (near-threshold) crack-growth rates, but not for fatigue at higher crack-growth rates. Data in the literature for NAB, especially in regard to previous failure analyses of NAB hydraulic couplings, indicated that environmentally assisted cracking modes such as stress-corrosion cracking were not involved. All the above (and other) observations indicated that failure of the valve occurred entirely by high-cycle fatigue, probably in the gigacycle regime, at very low stress amplitudes. The cyclic stresses are most probably associated with high-frequency vibration/resonance, but the source of the excitation causing this problem was not identified. High mean stresses, due to torquing bolts to specified levels on the square flange (which is free to deflect) probably facilitated fatigue crack initiation from machining grooves. Various recommendations were made in regard to preventing further failures.     

High cycle fatigue of welded structures: Design guidelines validated by case studies

Experience with fatigue failures, of both welded and non-welded details, has demonstrated that the design guidelines in many fatigue codes are inadequate for fabricated equipment that requires a life exceeding 10⁷ cycles. Stress ranges from strain gauge testing and finite element analysis of vibrating screens, combined with the actual life results, have been used to establish design criteria applicable to machinery operating in the giga-cycle range. Case studies from recent investigations are used to illustrate the validity of the design criteria.     

叉车货叉断裂分析

通过对断裂叉车货叉进行了化学成分分析，宏微观检验以及用疲劳强度设计方法对货叉安全系数进行验算，认为，货叉断裂的主要原因是由于表层脱碳使疲劳强度下降和安全系数小于所推荐的许用安全系数[n]=1.3-1.75引起的。