SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Effect of steady torsion on fatigue crack initiation and propagation under rotating bending: Multiaxial fatigue and mixed-mode cracking

Axles and shafts are of prime importance concerning safety in transportation industry and railway in particular. Knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is therefore essential for design and maintenance purposes. The effect of a steady torsion on both small and long crack growth under rotating bending is focused in this paper. For small crack growth, a modified effective strain-based intensity factor range is proposed as the parameter that correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. Results show that this parameter is appropriate for determining fatigue crack growth of small cracks on rotating bending with an imposed steady torsion.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

Effects of the transient Mode II on the steady state crack growth in Mode I

Turbo-generator shafts in power plant systems are often subjected to transient torques due to electric faults and high-speed reclosures. These transient torques cause the initiation and growth of cracks in Modes II and III. However, these cracks are further subjected to cyclic bending (Mode I crack growth) due to the turbine shaft weight or possible misalignments. Such load histories are also very common in railroad tracks. An existing crack may be subjected to a sudden Mode II, followed by a steady state Mode I. In order to predict the fatigue life, the effect of the transient Mode II on a subsequent Mode I crack growth must be understood. In this paper the effects of the Modes I and II overloads on a subsequent Mode I crack growth are studied on the AISI 4340 and spherodized AISI 1090 steels using three- and four-point bending specimens. The results show that in contrast to Mode I overloads, where the crack is either arrested or retarded for a distance of the order of magnitude of the transient plastic zone size, Mode II overloads give rise to the crack growth acceleration (for a very short distance, much smaller than the Mode II transient plastic zone size with no retardation afterwards). The three known mechanisms of the crack closure in Mode I (plasticity-, roughness- and oxide-induced crack closures) were examined for the Mode II overloads and were found not to be applicable for that Mode.

Fractography analysis of 1090 steel at the point of Mode II overload showed a significant amount of shear cracks and cavities. Such cavities could contribute to the crack growth acceleration in the subsequent Mode I crack growth.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

Mode III fatigue crack propagation rates in 6061-T6 aluminium

Fatigue crack growth rates were studied in type 6061-T6 aluminium alloy. Unlike the preponderance of previous studies, the present observations were carried out on cracks driven by a Mode III, or antiplane shear, type of loading. The observed crack growth rates were precisely correlated with the Mode III stress intensity factor range, ΔK_III. A simple power growth rate law, similar to that which predicts the growth rates of the more common Mode I driven crack, relates the incremental extension of the fatigue crack per cycle of loading to the stress intensity factor range. Fractographic examination of the fatigue crack surfaces indicated that the cracks propagated transgranularly, and did not seek out principal tensile stress planes, or Mode I growth habits.     

Calculation of mode III stress intensity factor by BEM for cracked axisymmetric bodies

This paper is concerned with the numerical calculation of Mode III stress intensity factor by BEM for cracked axisymmetric bodies, under torsion. Mode III stress intensity factors K _III are obtained using the asymptotic displacement field in the vicinity of the crack border. The asymptotic field is derived by integration along the boundary of the meridian of the cylinder. For traction free cracks no discretization of the crack surface was found necessary. Numerical results proving the efficiency of the proposed method are presented and compared with results given in the literature and with those obtained by FEM.     

Non‐planar mixed‐mode growth of initially straight‐fronted surface cracks,in cylindrical bars under tension,torsion and bending,using the symmetric Galerkin boundary element method‐finite element method alternating method

In this paper, the stress intensity factor (SIF) variations along an arbitrarily developing crack front, the non‐planar fatigue‐crack growth patterns, and the fatigue life of a round bar with an initially straight‐fronted surface crack, are studied by employing the 3D symmetric Galerkin boundary element method‐finite element method (SGBEM‐FEM) alternating method. Different loading cases, involving tension, bending and torsion of the bar, with different initial crack depths and different stress ratios in fatigue, are considered. By using the SGBEM‐FEM alternating method, the SIF variations along the evolving crack front are computed; the fatigue growth rates and directions of the non‐planar growths of the crack surface are predicted; the evolving fatigue‐crack growth patterns are simulated, and thus, the fatigue life estimations of the cracked round bar are made. The accuracy and reliability of the SGBEM‐FEM alternating method are verified by comparing the presently computed results to the empirical solutions of SIFs, as well as experimental data of fatigue crack growth, available in the open literature. It is shown that the current approach gives very accurate solutions of SIFs and simulations of fatigue crack growth during the entire crack propagation, with very little computational burden and human–labour cost. The characteristics of fatigue growth patterns of initially simple‐shaped cracks in the cylindrical bar under different Modes I, III and mixed‐mode types of loads are also discussed in detail.     

Fatigue crack growth of a welded tube–flange connection under bending and torsional loading

In this contribution the results of an experimental investigation into the fatigue crack growth of welded tube-to-plate specimens of steel StE 460 under bending, torsion, and combined in-phase and out-of-phase bending/torsion loading are presented. The tests were performed at stress ratios of R = −1 and R = 0. The residual stresses were reduced by thermal stress relief. The fatigue crack development is compared with the prediction on the crack growth rates of Paris. Individual stress intensity factors for the semielliptical surface cracks in the tube-flange specimens are approximated on a weight function analogy using the published solutions of other workers.     

TORSIONAL FATIGUE OF A MEDIUM CARBON STEEL CONTAINING AN INITIAL SMALL SURFACE CRACK INTRODUCED BY TENSION–COMPRESSION FATIGUE: CRACK BRANCHING,NON-PROPAGATION AND FATIGUE LIMIT

In order to examine the threshold condition for the fatigue limit of materials containing a small crack under cyclic torsion, reversed torsional fatigue tests were carried out on 0.47% C steel specimens containing an initial small crack. Initial small semi-elliptical cracks ranging from 200 to 1000 μm in length were introduced by the preliminary tension–compression fatigue tests using specimens containing holes of 40 μm diameter. The threshold condition for the fatigue limit of the specimens containing artificial small defects under rotating bending and cyclic torsion are also reviewed. Crack growth behaviour from an initial crack was investigated. The torsional fatigue limit for a semi-elliptical small crack is determined by the threshold condition for non-propagation of Mode I branched cracks. The torsional fatigue limit of specimens containing an initial small crack can be successfully predicted by the extended application of the √area parameter model in combination with the σ_θmax criterion.     

Surface flaws behavior under tension,bending and biaxial cyclic loading

Fatigue surface crack growth and in-plane and out-of-plane constraint effects are studied through experiments and computations for the aluminum alloy D16T. A tension/bending central notched plate and cruciform specimens under different biaxial loadings with external semi-elliptical surface cracks are studied. The variation of the fatigue crack growth rate and surface crack paths is studied under cyclic tension, bending and biaxial tension–compression loading. For the experimental surface crack paths in the tested specimens, the T-stress, out-of-plane T_z factor, local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of the I_n-integral are calculated as a function of the aspect ratio by finite element analysis to characterize the constraint effects along the semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface, as well as at the deepest point of the semi-elliptical surface crack front, of the tested tension/bending plate and cruciform specimens. From the results, characteristics of the fatigue surface crack growth rate as a function of the loading conditions are established.     

Statistischer Größeneinfluß unter mehrachsiger Wechselbelastung

Statistical Size Effect Under Alternating Load The results of 41 series of tests with smooth cylindrical and notched specimens, subjected to uni- and multiaxial alternating loads (tensioncompression, torsion, rotating bending and combined torsion and bending), are compared with theoretically predicted data. The prediction are based on the ?Weakest-Link-Concept”?. Multiaxial stresses are included either by means of suitable strength criteria, or by a fracturemechanical consideration of a crack in a multidimensional stress field. For the evaluation of the experimental data the 2-parametric Weibull's equation was used. The experimental and theoretical results may deviate by less than 20%, when the ratio between the strength at cyclic torsion and cyclic bending ist taken into account in the function of survival probability [eqns. (2), (7)].     

拉杆疲劳裂纹导致的组合转子性能退化研究

 组合转子作为燃气轮机等的核心部件,其性能退化机理并不明确,揭示其性能退化机理并有效地进行性能退化评估对燃气轮机等长期安全运行具有重要意义.为此,从结构损伤导致性能退化的角度出发,分析拉杆裂纹引起的组合转子性能退化特性.分别建立了组合转子有限元模型和弯曲、扭转刚度模型,利用有限元模型对拉杆上含初始裂纹的组合转子进行裂纹扩展分析,得到拉杆裂纹扩展速率;利用弯曲和扭转刚度模型分析了不同深度的裂纹对组合转子振动的影响,得到组合转子固有频率随裂纹尺寸的变化规律;并提出了衡量由微裂纹导致的组合转子性能退化的度量指标,实现了拉杆裂纹引起的组合转子性能退化的定量评估.研究表明：随着拉杆裂纹尺寸的增大,裂纹的扩展速率变快;拉杆裂纹的存在对组合转子的弯振影响较大,对扭振影响相对较小.     

Cyclic fatigue crack growth behaviour in β-(Si–Al–O–N) at ambient and elevated temperatures

Four-point bending fatigue tests on a hot-pressed sintered Sm–-(Si–Al–O–N) ceramic were conducted at room temperature, 900 °C and 1000 °C in air under different load ratios and cyclic frequencies. The growth of indentation cracks was measured during the fatigue tests. The results indicate that the cyclic fatigue crack growth threshold is lower and crack growth rates are higher, for given values of K_max, at 1000 °C than those at room temperature. The cyclic fatigue crack growth behaviour at 900 °C is similar to that at room temperature. It was found that the crack growth retardation due to cyclic fatigue loading is much more pronounced at higher frequencies. An increase in cyclic frequency from 1 to 10 Hz cause a reduction of up to two orders of magnitude in crack propagation rates. High-temperature cyclic fatigue crack growth rates increased and threshold stress intensity factor ranges decreased with increasing load ratio. Possible mechanisms for cyclic crack growth are discussed.     

ON THE CALIBRATION, OPTIMIZATION AND USE OF d.c. ELECTRICAL POTENTIAL METHODS FOR MONITORING MODE III CRACK GROWTH IN TORSIONALLY-LOADED SAMPLES

Abstract— The use of d.c. electrical potential methods is described for the monitoring of Mode III (anti-plane shear) fatigue cracks in circumferentially-notched cylindrical specimens subjected to cyclic torsion. Calibration of potential change with crack depth and optimization of current input and potential measurement probe locations are achieved using simple finite element procedures, and are verified experimentally. The use of the method for Mode III crack growth studies is described in the light of crack face electrical shorting problems associated with torsional crack closure.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.     

FINITE ELEMENT ANALYSIS OF DELAMINATION CRACKS IN BENDING OF CROSS-PLY LAMINATES

SUMMARY

A study of delamination crack growth due to bending in cross-ply laminates is presented. For the understanding of interlaminar fracture behaviour of laminated composites the modelling of delamination crack growth induced by bending and shear cracks in three point bending specimens is carried out. A plane strain two-dimensional (2-D) finite element analysis is used to determine the strain energy release rates during delamination of the laminated beam. Contact elements were used to prevent the material interpenetration on the crack surfaces. The solution of the contact problem taking into account friction along crack surfaces is obtained. Energy release rates G_I and G_II for Mode I and Mode II fracture are calculated by virtual crack closure integral (VCCI) methods. Comparison of total energy release rates, obtained by local energy methods, with an analytical solution based on the beam theory and a global energy method have been carried out. Good agreement of the results obtained by various methods have been observed. Comparison of the results obtained by the solution of the contact problem and without contact elements have been performed. Significant differences between the values of energy release rates obtained with and without using contact elements have been observed. The influence of the coefficient of friction on the energy release rates is insignificant.