MIXED MODE SMALL CRACK GROWTH

Abstract— The fatigue crack growth behavior of small part-through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated. Experiments were performed on thin-wall tubular specimens loaded in tension, torsion and combined tension torsion. Crack sizes analyzed ranged from 20 μm to 1 mm and growth rates ranged from 10^-7 to 10^-4 mm/cycle for 1045 steel and from 10^-5 to 10^-2 mm/cycle for Inconel. Nucleation and the early growth of cracks occurs on planes of maximum shear strain amplitude for both of these materials even in tensile loading. An equivalent strain based intensity factor was employed to correlate the crack growth rate under mixed mode loading conditions In loading conditions other than torsion, a transition from mode II to mode I was observed for 1045 steel. Principal strains were used to analyze mode I cracks. Cracks in Inconel 718 grow in mode II for the majority of the fatigue life. The maximum shear strain amplitude and the tensile strain normal to the maximum shear strain amplitude plane were used to calculate the strain based intensity factor for mixed mode loading.     

Kurzrisswachstum bei mehrachsig nichtproportionaler Beanspruchung

Short fatigue crack growth under multiaxial nonproportional loading Initiation and short fatigue crack growth have been investigated under nonproportional cyclic loading. A critical plane approach based on fracture mechanics is used for modelling the fatigue process. A Paris‐type crack growth law, formulated using the effective cyclic J‐integral as crack driving force parameter, is integrated to give crack growth curves. Crack opening stresses and strains are calculated with approximation equations. Jiang's plasticity model is used to predict the stress‐strain path. The good agreement between model and real damage evolution is shown comparing experimentally determined crack growth curves, crack orientations, and life curves.     

Crack path and fracture analysis in FSW of small diameter 6082-T6 aluminium tubes under tension–torsion loading

This paper reports part of the work done in a research project aimed at developing an optimised process to join 38 mm diameter tubes of 6082-T6 aluminium alloy using friction stir welding (FSW), and then to determine the fatigue performance under tension, torsion and tension–torsion loading conditions. The final outcome of the project is intended to be guidance for fatigue design of small diameter aluminium tubes joined by FSW, and this paper presents information on crack path and defects under the various loading conditions. Crack path analysis was performed using both low magnification stereo microscopy and scanning electron microscopy, in order to identify crack initiation sites, the direction of crack propagation and the interrelated influence of microstructure and weld geometry on the crack initiation path.     

Growth of tensile and fatigue cracks in metal foils

The extension of cracks in thin foils of copper, brass, and tantalum has been investigated for both monotonic and cyclic loading using optical microscopy and scanning electron microscopy. Crack growth in both tension and fatigue is found to occur primarily by a void coalescence mechanism, as previously reported for aluminum foils. The particular morphology of void formation exhibited by a given material is determined by its purity level and stacking fault energy, the latter being important as it affects the slip character—varying from planar to wavy—of the metal.Fatigue crack growth without void formation has also been observed in brass and tantalum. The resulting fracture surfaces are flat; a different growth mechanism, attributed to plane strain conditions at the crack tip rather than plane stress, accounts for this mode of propagation.     

Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone

As a composite material, cortical bone accumulates fatigue microdamage through the repetitive loading of everyday activity (e.g. walking). The accumulation of fatigue microdamage is thought to contribute to the occurrence of fragility fractures in older people. Therefore it is beneficial to understand the relationship between microcrack accumulation and the fracture resistance of cortical bone. Twenty longitudinally orientated compact tension fracture specimens were machined from a single bovine femur, ten specimens were assigned to both the control and fatigue damaged groups. The damaged group underwent a fatigue loading protocol to induce microdamage which was assessed via fluorescent microscopy. Following fatigue loading, non-linear fracture resistance tests were undertaken on both the control and damaged groups using the J-integral method. The interaction of the crack path with the fatigue induced damage and inherent toughening mechanisms were then observed using fluorescent microscopy. The results of this study show that fatigue induced damage reduces the initiation toughness of cortical bone and the growth toughness within the damage zone by three distinct mechanisms of fatigue–fracture interaction. Further analysis of the J-integral fracture resistance showed both the elastic and plastic component were reduced in the damaged group. For the elastic component this was attributed to a decreased number of ligament bridges in the crack wake while for the plastic component this was attributed to the presence of pre-existing fatigue microcracks preventing energy absorption by the formation of new microcracks.     

Fatigue voids and their significance

ABSTRACT Fractures from tests on 2014‐T6511 and 2024‐T3 test coupons under specially designed programmed loading reveal voids with distinct fatigue markings. These ‘fatigue voids’ appear to form as a consequence of the separation of noncoherent secondary particulates from the matrix in early fatigue. The process of their formation is through the initiation, growth and coalescence of multiple interfacial cracks around the particulate. Such voids become visible on the fatigue fracture surface if and when the crack front advances through them. In vacuum, each fatigue void is the potential initiator of an embedded penny‐shaped crack. The one closest to the specimen surface is likely to become the dominant crack, indicating that fatigue voids appear to be the likely origins of the dominant crack in vacuum. In air, the dominant crack forms at the notch surface and grows much faster, giving less opportunity for multiple internal cracks to spawn off from the innumerable internal fatigue‐voids. Thus in air, fatigue voids do not appear to affect the fatigue process at low and intermediate growth rates. At high crack growth rates involving considerable crack tip shear, slip planes with particulate concentration offer the path of least resistance. This explains the increasing density of fatigue voids with growth rate. Very high growth rates signal the onset of a quasi‐static crack growth component that manifests itself through growing clusters of microvoid coalescence associated with static fracture. Fatigue voids are likely to form in other Al‐alloys with secondary noncoherent particulates. They have nothing in common with microvoids associated with ductile fracture.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234     

FATIGUE DAMAGE IN 1045 STEEL UNDER CONSTANT AMPLITUDE BIAXIAL LOADING

The progressive nature of fatigue damage under multiaxial stress states has been investigated. Experiments were performed on thin-wall tubular specimens of 1045 steel in tension, torsion and combined tension-torsion loading. Two equivalent strain amplitudes, one in the high cycle fatigue (HCF) region and one in low cycle fatigue (LCF) region were employed in this study. Four recently proposed damage theories were evaluated. Crack depth was used as a damage parameter in comparing damage curves under different loading modes.
Different types of crack systems were observed in the HCF and LCF regions. The damage curve obtained in tension loading can be used to evaluate the damage behavior under combined tension—torsion loading. The results of torsion loading show that torsional damage behavior is different from the above two loading modes.     

Crack extension by alternating shear

A comparison of the slip line flow field at the tip of a sharp crack and of a blunted crack shows that a sharp crack can be extended by alternating shear until it becomes blunted. Crack tip blunting is associated with high strain concentration and fracture by hole growth and coalescence. Crack extension by alternating shear has been obtained in fully plastic, plane strain sharply notched, singly and doubly grooved tensile specimens. Electron fractography shows crack extension by alternating shear at the tip of cleavage and fatigue cracks. It is shown that fatigue crack propagation is the result of repeated cyclic crack extension by alternating shear.     

THE EFFECTS OF FREQUENCY AND R-RATIO ON FATIGUE CRACK GROWTH BEHAVIOUR IN Al-Li-Cu-Mg ALLOY (8090) PLATE

Abstract— The effects of frequency and R -ratio on the fatigue crack growth rate of the Al-Li-Cu-Mg alloy 8090 have been assessed in air. Compact tension test pieces ( B = 25 mm) were tested at constant P _max using a triangular waveform (CA) and the crack length was monitored by a four-wire pulsed potential drop technique. Crack closure measurements were made during the test by a front face compliance technique.
The crack growth rate was found to be dominated by the high level of crack closure and the fatigue fracture morphology. Two fracture types were identified; a highly deviated "shear" fracture mode which was in competition with a macroscopically flat "tensile" fracture mode. The tensile fracture mode was predominant at low test frequency, high R -ratio and short crack lengths whereas the shear mode was predominant at high frequency, low R -ratio and long crack lengths. The transition from tensile to shear mode was primarily controlled by the effective stress intensity factor range, Δ K _eff.
The effect of loading variables on the transition was explained in terms of the diffusion distance of hydrogen relative to the effective cyclic plastic zone diameter. Test piece thickness had a secondary effect on the transition and this was explained in terms of gas transport considerations.     

On the interactions between strain accumulation, microstructure, and fatigue crack behavior

Fatigue crack growth is a complex process that involves interactions between many elements ranging across several length scales. This work provides an in-depth, experimental study of fatigue crack growth and the relationships between four of these elements: strain field, microstructure, crack path, and crack growth rate. Multiple data sets were acquired for fatigue crack growth in a nickel-based superalloy, Hastelloy X. Electron backscatter diffraction was used to acquire microstructural information, scanning electron microscopy was used to identify locations of slip bands and crack path, and optical microscopy was used to measure crack growth rates and to acquire images for multiscale digital image correlation (DIC). Plastic strain accumulation associated with fatigue crack growth was measured at the grain level using DIC. An ex situ technique provided sub-grain level resolution to measure strain variations within individual grains while an in situ technique over the same regions showed the evolution of strain with crack propagation. All of these data sets were spatially aligned to allow direct, full-field comparisons among the variables. This in-depth analysis of fatigue crack behavior elucidates several relationships among the four elements mentioned above. Near the crack tip, lobes of elevated strain propagated with the crack tip plastic zone. Behind the crack tip, in the plastic wake, significant inhomogeneities were observed and related to grain geometry and orientation. Grain structure was shown to affect the crack path and the crack growth rate locally, although the global crack growth rate was relatively constant as predicted by the Paris law for loading with a constant stress intensity factor. Some dependency of crack growth rate on local strain and crack path was also found. The experimental comparisons of grain structure, strain field, and crack growth behavior shown in this work provide insight into the fatigue crack growth process at the sub-grain and multi-grain scale.     

Plastic strain-controlled short crack growth and fatigue life

Constant plastic strain-controlled and constant stress-controlled tests were performed on smooth and lightly notched specimens machined from a massive forging of 42CrMo4 steel. Comparison of the fatigue life curves plotted as function of the plastic strain amplitude and stress amplitude shows a decisive role of plastic strain amplitude. Crack initiation and the kinetics of short crack growth were studied in constant plastic strain amplitude loading and the relation between the crack growth coefficient and plastic strain amplitude was established. This is equivalent to the Coffin–Manson law and shows that the Coffin–Manson law can be interpreted in terms of short crack growth.     

Deformation behaviour,short crack growth and fatigue livesunder multiaxial nonproportional loading

Experimental results of a research project on short crack growth under multiaxial nonproportional loading are presented. Fatigue lives, crack growth curves and the deformation behaviour of hollow tube specimens and notched specimens were investigated under combined tension and torsion loading. The results served as basis for the development of a cyclic plasticity model [Döring R, Hoffmeyer J, Vormwald M, Seeger T. A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading. In: Comput Mater Sci. 28(3–4);2003:587–96; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Constitutive modelling of nonproportional hardening, cyclic hardening and ratchetting. In: Proceedings of the seventh international conference on biaxial/multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 291–6; Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004.] and a short crack model [Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Fatigue lifetime prediction based on a short crack growth model for multiaxial nonproportional loading. In: Proceedings of the seventh international conference on biaxial and multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 253–8].Stress–strain paths including nonproportional hardening and experimental fatigue lives of the unnotched specimens under different loading cases are discussed and compared with calculations. Load-time-sequences were in-phase, 45° and 90° out-of-phase loading with constant and variable amplitudes, torsion without and with superimposed static normal stress, and strain paths like box, butterfly, diamond and cross path. For the notched specimens fatigue lives under 0° and 90° out-of-phase loading are compared with calculations based on finite element results and the short crack model. During some tests the initiation, growth and orientation of short cracks was studied using the plastic replica technique.     

Creep-fatigue crack propagation in lead-free solder under cyclic loading with various waveforms

Crack propagation tests of lead-free solder were conducted using center-notched plate specimens under cyclic tension-compression of three load waveforms: pp waveform having fast loading and unloading, cp-h waveform having a hold time under tension, and cc-h waveform having a hold time under tension and compression. In the case of fatigue loading, i.e. pp waveform, the path of crack propagation was macroscopically straight and perpendicular to the maximum principal stress direction, showing tensile-mode crack propagation. The introduction of the creep components by hold time in cc-h and cp-h waveforms promoted shear-mode crack propagation. For fatigue loading of pp wave, the crack propagation rate was expressed as a power function of the fatigue J integral and the relation was identical for load-controlled and displacement-controlled conditions. The creep component due to the hold time greatly accelerates the crack propagation rate when compared at the same values of the fatigue J integral or the total J integral (the sum of fatigue J and creep J integrals). The creep crack propagation rate was expressed as a power function of the creep J integral for each case of cp-h and cc-h waveforms. The crack propagation rate for cp-h waveform is higher than that for cc-h waveform. The predominant feature of fracture surfaces was striations for pp waveform and grain boundary fracture for cp-h waveform. Grain fragmentation was abundantly observed on the fracture surface made under cc-h waveform.     

Analysis of Acoustic Emissions from a Steel Bridge Hanger

A steel bridge hanger with three fatigue cracks was monitored for acoustic emission (AE) using combined source location, strain gauge monitoring, and waveform analysis. AE activities from all three cracks were clearly identified and classified as crack growth or noise signals using location, strain magnitude, position on strain cycle, and uniqueness of waveforms as the primary criteria. A vast majority of AE from the cracks was found to be due to crack face rubbing and the crushing of corrosion products between the crack faces while limited crack growth emissions were detected. Results from laboratory tests on A588 compact tension specimens under variable-amplitude tension-tension fatigue loading were used to aid in interpreting AE data from the hanger. Crack growth AEs from these tests were detected only on overload cycles mostly above 92% of the maximum load while AE due to crack face rubbing occurred throughout the load cycle.     

Load interaction effects on fatigue crack propagation in 2024-T3 aluminum alloy

Variable amplitude fatigue studies have been conducted within a linear-elastic fracture mechanics framework in order to systematically examine the effect of complex loading on fatigue crack retardation in 2024-T3 aluminum alloy. Complex loading conditions were simulated by introducing a second tensile or compressive peak load after the crack had extended various distances, a', into the region affected by a previously applied high load excursion.

Maximum interaction between single peak overloads resulted when the two peak load cycles were separated by a small distance, a' _min, where the fatigue crack propagation rate resulting from a single overload reached a minimum. This behavior was attributed in part to interference of tensile displacements produced during the first peak load cycle which was verified from fractographic observations. Crack growth rate retardation was related also to the development of a favorable compressive residual stress at the crack tip. Peak loads were found to act as completely isolated events only when they were separated by a distance approximately three times the plastic zone size resulting from a single overload. Comparable findings resulted when 10 cycle block overloads were employed in place of single peak excursions.

When a single peak overload was followed by a compressive cycle, retardation was found to decrease to a minimum; however, when the loading sequence was reversed, the effect was less damaging. In addition, as the distance between positive and negative peak loads was increased, the number of delay cycles quickly approached that associated with a single high load excursion.     

The effect of anelasticity and phase transformation on crack growth in Y-TZP ceramics

Crack growth behavior has been investigated under monotonic and cyclic loadings for Y-TZP that produces remarkable anelastic strain. Monotonic loading testing was carried out under the condition of various stress rates (8 × 10², 8 × 10^–1 and 8 × 10^–4 MPa/s) and temperatures (RT and 373 K). Resistance of crack propagation was observed at the lowest stress rate at elevated temperature. Cyclic fatigue crack growth rate was examined under the condition of different frequencies and stress waveforms. Crack growth rate clearly depended on stress waveform, which was explicable by exhaustion and restoration of anelasticity at the crack tip region. Experimental results make it clear that anelasticity works as strong resistance against crack growth. In this study, the effect of environment-induced tetragonal to monoclinic phase transformation on fracture strength was also investigated for pre-cracked sample. Aged (transformed) samples have shown extreme crack closure and considerable improvement in strength.     

The effect of mode ratio and bond interface on the fatigue behavior of a highly-toughened epoxy

The fatigue threshold and the cyclic crack growth of a highly-toughened epoxy adhesive were studied under mode I and several mixed-mode loading cases and compared with the quasi-static critical fracture energies. Four different adhesive systems were examined using steel and aluminum substrates having different surface roughness, and surface treatment. The effect of increasing the amount of mode II (increasing the phase angle) on the fatigue threshold strain energy release rate and the cyclic crack growth rate was found to be insignificant at low phase angles. However, a significant increase in the fatigue threshold and decrease in the cyclic crack growth rate was observed at higher phase angles. These trends were similar to that seen in adhesive joint fracture. Adherend surface roughness and surface preparation affected the fatigue behavior significantly, particularly at low crack speeds and high phase angles. The fatigue properties were essentially the same for both steel and aluminum adherends provided that the crack paths were cohesive. A general observation was that the fatigue crack path moved progressively closer to the more highly strained adherend under mixed-mode loading as the applied strain energy release rate and hence the crack speed, decreased. This caused mixed-mode cracks to be nearly interfacial in the threshold region.     

Numerical simulation of prestrain history effect on ductile crack growth in mismatched welded joints

Pipe reeling may lead to plastic pre‐deformation (prestrain) around existing cracks in components; therefore, investigating whether this process accelerates or counteracts ductile crack growth, especially for strength mismatched welded joints, is warranted. This study focused on the effect of prestrain history on ductile crack growth in mismatched welded joints. A single‐edge‐notched tension specimen was selected for numerical study, and the crack was assumed to have existed before a prestrain history was applied. Crack growth resistance curves for plane strain and mode I crack growth under large‐scale yielding conditions have been computed using the complete Gurson model. Meanwhile, symmetrical and non‐symmetrical prestrain cycle modes with different loading levels were applied to the overmatched specimens. The outcome demonstrated that the mismatch ratio (the ratio between the yield stress of the weld metal and base metal) showed a significant effect on fracture resistance regardless of the stage at which the prestrain cycle loading was located. By contrast, the processing of the crack growth was weakened by the increase of prestrain values, and the symmetrical prestrain cycle resulted in greater plastic damage than the non‐symmetrical prestrain cycle did. However, the initial crack length had a non‐significant effect on the ductile fracture considering the prestrain and mismatch effects.