On the mixed Mode II/III fatigue threshold behaviour for aluminium alloys 2014‐T6 and 7075‐T6

This paper describes an investigation into the fatigue threshold behaviour of two structural aluminium aerospace alloys, Al 2014‐T6 and Al 7075‐T6, when subjected to Mode II, Mode III and mixed Mode II/III loading. A unique four‐point shear loading test rig was employed to cyclically load sharply edge‐notched square bar specimens using an increasing load technique. The main aim of the work has been to generate Mode II–Mode III interaction diagrams for the fatigue threshold in each case, in order to facilitate improved design procedures for components fabricated from these alloys, which are susceptible to fatigue cracking under predominantly shear type loading. Aircraft are subjected to structural loads consisting of: pressurization, tension/compression, bending, shear and torsion, both on the ground and in flight. Representative fatigue fracture surfaces have been examined using scanning electron microscopy.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

Acoustic emission source characterization in concrete under biaxial loading

The results are reported of a mode identification study on cracks produced during mixed mode loading of concrete. The locations of cracks were found to agree very well with the surface crack patterns for a variety of loading paths. The classification of cracks into mode I and mode II were conducted using a simplified moment tensor analysis. The results indicated that, in general, cracking occurs in mode I, even when the loading is pure shear. Mode II deformations generally follow the mode I cracks, as the crack interface is subjected to shear.     

Mixed mode fracture behaviour of steel fibre reinforced concrete

In this paper, results are reported for a series of discrete end hooked and straight fibre pullout tests subjected to mixed mode action with the results compared to that of discrete fibres pulled out in Mode I (tensile) and Mode II (shear) fracture. As has been previously observed from Modes I and II fracture tests, the snubbing effect dominates the behaviour of fibres at large fibre bending angles. At large fibre bending angles, considerable slip and crack separation occurred prior to the fibres being engaged in taking load and fibres that are inclined close to the cracked surface are ineffective in carrying load. The results of the test were compared with the fibre engagement and bond stress models in the Unified Variable Engagement Model (UVEM). A good correlation is observed for the UVEM model with the test data and provides further confirmation of the validity of the UVEM model to predict the mix mode fracture of steel fibre reinforced concrete.     

MODE I AND MIXED MODE I/II FATIGUE CRACKING IN Ni3Al(CrB) SINGLE CRYSTALS

Abstract— Nominal mode I and mixed mode I/II fatigue tests were carried out using the intermetallic compound Ni₃Al(CrB) in the form of single crystal specimens. The effects of crystal orientation and load mode on fatigue crack initiation and growth were studied. The fracture surfaces of the single crystals were characterized by a cleavage-like appearance and cracking occurred either on a single {111} plane or on multiple {111} planes irrespective of whether mode I or mixed mode I/II loadings were applied. It was found that the crack initiation and growth behaviour are dependent on both crystal orientation and applied loading mode. The cracking behaviour predicted by three mixed mode fracture criteria (MTS, SED and G criteria) in polycrystalline materials under mixed mode loading can be understood from the present results on single crystals.     

Fracture and fatigue performance of textile commingled yarn composites

The response to mechanical loads of unidirectional commingled warp knitted and woven glass fibre reinforced polyethylene terephthalate laminates has been characterized. The mechanical properties of the two materials were determined under tension, in-plane shear and flexure. The flexural fatigue properties were determined for the woven laminates by means of three-point bending tests with a loading ratio of R=0.1 at stress levels of 50–90% of the ultimate static strength. The Mode I, Mode II and mixed mode (Mode I : II ratios 4 : 1, 1 : 1 and 1 : 4) interlaminar fracture toughnesses of the laminates were determined by means of the double cantilever beam and mixed mode bending tests, respectively. The main fractographic features, as determined by a scanning electron microscopy examination, of the Mode I dominated failures were a brittle matrix failure and larger amounts of fibre pull-out. As the Mode II loading component increased, the amount of fibre pull-out was reduced and the features of the matrix appeared to be more sheared. Cusps were found on the fracture surfaces of specimens tested in pure Mode II and mixed mode I : II=1 : 4. Cusps are normally not found in thermoplastic matrix composites. © 1998 Kluwer Academic Publishers     

Approximate formulae for estimating the j-integral of a circumferentially cracked round bar under tension or torsion

The approximate formulae for estimating the J contour integral by the use of a single load-displacement curve were newly derived for the circumferentially cracked round bar subjected to tensile (Mode I) or torsional (Mode II) loading, by paying attention to the elastic-plastic deformation behavior which is characterized by full yielding (net section of specimen is in yield) or general yielding (gross section of specimen is in yield). As application examples, elastic-plastic fracture toughness tests were performed at room temperature on Ni-Cr-Mo-V forged steel. The ductile crack growth resistance curves under the Mode I or the Mode III loading were measured with the multi-specimen method, and the fracture behaviors of each mode were examined.     

Deformation and tearing of blast-loaded stiffened square plates

Experimental and numerical results for fully built-in stiffened square plates subjected to blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation) and mode II (tensile tearing) failure as the load intensity increases. The numerical analysis is carried out using a finite element formulation which incorporates non-linear geometry and material effects as well as strain rate sensitivity. Mode I is predicted well for both maximum deflection and deformation shape. Initiation of mode II failure is predicted by a maximum strain criterion, but the limited mode II data is insufficient for conformation.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

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.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Experimental and numerical investigations on the influence of the loading direction on the fatigue crack growth

During a service loading fatigue cracks can be subjected to a mixed mode loading if, due to the alteration of the loading direction, the basic crack modes (Modes I, II and III) are combined. An alteration of the loading direction, e.g. can occur either occasionally paired with an overload (mixed mode overload) or permanently in terms of a mixed mode block loading as a combination of normal and shear stresses.Within the scope of this paper, experimental investigations on both mixed mode overloads, which are interspersed into a Mode I baseline level loading, and mixed mode block loadings are presented. The experimental investigations show that the retardation effect decreases with an increasing amount of Mode II of the overload. Due to the block loading, the fatigue crack growth rate is retarded as well, and the crack is also deflected. The kinking angle depends on the fraction of shear stresses. Furthermore, a detailed elastic–plastic finite element analysis of the fatigue crack growth after mixed mode overloads is presented in order to understand the mechanism of the load interaction effects. By such numerical simulations, it can be shown that, due to mixed mode overloads, plastic deformations occur, which on the one hand reduce the near-tip closure and on the other hand cause a far-field closure. Also the stress distribution before and after the crack tip changes. A mixed mode overload causes lower closure and the crack tip deformations become asymmetrical, which is a reason for the smaller retardation effect of a mixed mode overload.     

Experimental fracture investigation of CNT/epoxy nanocomposite under mixed mode II/III loading conditions

For the first time, the brittle fracture of epoxy‐based nanocomposite reinforced with MWCNTs (multi‐walled carbon nanotubes) and subjected to mixed mode II/III loading conditions is investigated. This experimental investigation is carried out using a newly developed test configuration. Araldite LY 5052 epoxy, which is a resin frequently used in aerospace industry, is utilized to fabricate pure epoxy and nanocomposite test specimens with two different MWCNTs contents of 0.1 and 0.5 wt%. The obtained experimental results reveal that adding MWCNTs to epoxy resin up to 0.5 wt% improves the fracture toughness under pure mode II and pure mode III loading with an increasing trend. This is while the improvement under mixed mode II/III loading is reduced by adding nanotubes more than 0.1 wt%. To justify the variations of fracture toughness in terms of nanoparticles content, SEM (scanning electron microscopy) photographs of the fracture surfaces of the specimens in the vicinity of the initial crack front are prepared. Additional fracture mechanisms caused by adding carbon nanotubes are discussed in detail based on the provided SEM images.     

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

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.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

An improved semi-circular bend specimen for investigating mixed mode brittle fracture

An edge cracked semi-circular specimen subjected to asymmetric three-point bend loading was suggested for investigating mixed mode fracture in brittle materials. Using finite element analysis, the crack parameters were obtained for various crack lengths and different locations of loading points. It was shown that by selecting appropriate positions for the loading points, full mode mixities from pure mode I to pure mode II could be achieved. Then, a series of fracture tests were conducted on PMMA using the proposed specimen. Very good agreement was found between the experimental results and those predicted from the generalized maximum tangential stress criterion.     

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

A novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.