FATIGUE CRACK PROPAGATION IN BIAXIAL STRESS FIELDS

Abstract Biaxial tension-compression fatigue tests were conducted with cruciform shaped specimens in a closed-loop servo hydraulic testing machine. The effects of static and cyclic non-singular stresses acting parallel to the crack plane on the crack growth rate are discussed based on the experimental observations of crack opening behaviour and fractography. Those non-singular stresses did affect the growth rate significantly under certain conditions. The range of crack-tip opening displacement was found to be a better parameter in correlating the growth rate than the stress intensity range or its effective range. The rate tended to increase with increasing non-singular stress which is correlated to the opening displacement range. This tendency was explained by the shift of fracture mechanisms to a more brittle type due to a higher elevation of hydrostatic stress near the crack tip for the case of a larger non-singular stress term.     

Effect of stress ratio on near-threshold propagation of delimination fatigue cracks in unidirectional CFRP

The effect of the stress ratio on near-threshold growth of delamination fatigue cracks was investigated with unidirectional laminates made from Ciba Geigy 914C prepegs (T300/914) and from Toray P305 prepegs (T300/#2500). Tests of delamination fatigue crack propagation were carried out under mode I opening loading by using double cantilever beam specimens. The normalized gradient of energy release range was controlled in load-shedding tests. In the region of crack growth rates above about 5 × 10⁻¹⁰ m/cycle, the growth rate was expressed as a power function of fracture mechanics parameters. Below this region, there existed a growth threshold. The influence of the stress ratio became smaller when the rate was correlated to the energy release rate range than when the rate was correlated to the stress intensity range or the maximum energy release rate. A controlling fracture mechanics parameter is discussed on the basis of fractographic observation and mechanism consideration. A new phenomenological law of fatigue crack propagation is derived.     

ESTIMATION OF TORSIONAL FATIGUE STRENGTH OF MEDIUM CARBON STEEL BARS WITH A CIRCUMFERENTIAL CRACK BY THE CYCLIC RESISTANCE-CURVE METHOD

Near-threshold fatigue crack propagation tests were performed on circumferentially precracked round bars of a medium carbon steel under torsional loading. The crack propagation rate decreased with crack extension, because of the shear contact of crack faces. The crack propagation rate without the influence of crack-surface contact was determined by extrapolating to zero crack extension the relationship between the crack propagation rate and crack extension. The applied stress intensity factor range was divided into two parts: one was the effective value responsible for crack growth and the other was the value corresponding to crack-tip shielding. The resistance-curve method was used to predict the fatigue limit for crack initiation and fracture. The R -curve was constructed using the experimentally determined threshold value of the stress intensity range, which was the sum of the threshold effective stress intensity range and the threshold shielding stress intensity range. The threshold effective stress intensity range was constant. The R -curve was independent of the precrack length and specimen dimensions. The predicted values agreed well with the experimental results.     

Effect of strain rate on stepwise fatigue and creep slow crack growth in high density polyethylene

The effects of frequency and R-ratio (the ratio of minimum to maximum stress in the fatigue loading cycle) on the kinetics of step-wise crack propagation in fatigue and creep of high density polyethylene (HDPE) was characterized. Stepwise crack growth was observed over the entire range of frequency and R-ratio examined. A model relating crack growth rate to stress intensity factor parameters and applied strain rate was proposed by considering the total crack growth rate to consist of contributions from creep and fatigue loading components. The creep contribution in a fatigue test was calculated from the sinusoidal loading curve and the known dependence of creep crack growth on stress intensity factor in polyethylene. At a very low frequency of 0.01 Hz, fatigue crack growth rate was found to be completely controlled by creep processes. Comparison of the frequency and R-ratio tests revealed that the fatigue loading component depended on strain rate. Therefore, crack growth rate could be modeled with a creep contribution that depended only on the stress intensity factor parameters and a fatigue contribution that depended on strain rate.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

Manifestation of Hydrogen and Low-Temperature Brittleness in Near-Threshold Cyclic Crack Resistance of Materials

We experimentally show that the realization of conditions of plane deformation at the tip of a fatigue crack is not sufficient for guaranteeing the unique dependence of the crack growth rate on the range of the stress intensity factor, which is explained by the effect of crack closure. We describe advantages and disadvantages of the effective range of the stress intensity factor as a parameter that determines the mechanical conditions for the propagation of a fatigue crack. We analyze the phenomenon of positive influence of strengthening factors (a decrease in the temperature of testing and hydrogenation) on the cyclic crack resistance of materials in a low-amplitude range of loading determined with regard for the effect of crack closure. The decrease in the crack growth rate and the increase in fatigue thresholds are intensified as the level of loading decreases and the ductility of materials increases. Differences in the influence of strengthening factors in low- and high-amplitude ranges of loading are explained by different mechanisms of fracture controlled by the shearing strength and the tensile strength, respectively. We give several examples of the mechanical behavior of materials that show the inversion of the influence of hydrogen on the resistance to fracture: fatigue fracture of smooth steel specimens in gaseous hydrogen, high-temperature corrosion fatigue of preliminary hydrogenated titanium alloys, and the influence of hydrogenation on the wear resistance of structural steels in the process of friction and cavitation and on the parameters of cutting of a tool steel.     

Modelling of small fatigue crack growth interacting with grain boundary

The slip band at the tip of a small fatigue crack interacting with grain boundaries is modelled for four cases: a slip band not reaching the grain boundary, a slip band blocked by the grain boundary, a slip band propagated into an adjacent grain, and a slip band propagated through one and then blocked by a second grain boundary. The theory for continuously distributed dislocations is used to calculate the crack-tip sliding or opening displacement and the microscopic stress intensity factor under tensile and shear loading. Assuming that the range of the tip displacement directly determines the propagation rate of both Stage I and II cracks, prediction of the propagation behavior of a small crack is made as a function of the distance between the crack tip and the grain boundary, and of the difficulty to propagate slip into adjacent grains, as well as a function of crack length and stress level. The directions for further development of modelling are discussed.     

Near-threshold fatigue propagation of physically through-thickness short and long cracks in a low alloy steel

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.     

Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium

The mechanism of mixed‐mode fatigue crack propagation was investigated in pure aluminum. Push‐pull fatigue tests were performed using two types of specimens. One was a round bar specimen having a blind hole, one was a plate specimen having a slit. The slit direction cut in the specimen was perpendicular or inclined 45 degrees relative to the centre of the specimen axis. In both cases, cracks propagated by mode I or by the mixed mode combining mode I and shear mode, depending on the testing conditions. In these cases the crack propagation rate was evaluated with a modified effective stress intensity factor range. Crack propagation retardation was observed in some specimens. However, it was found that the crack propagation rate could also be evaluated by the effective stress intensity factor range independent of the crack propagation mode.     

LOW CYCLE FATIGUE CRACK PROPAGATION AT A NOTCH UNDER PULSATING LOAD

Abstract Fatigue crack propagation tests were carried out under pulsating stress, partly alternating stress and alternating plastic fatigue for Cr- Mo-V steel and mild steel. Although stress and strain intensity factors do not effectively correlate the fatigue crack growth rate over a wide range of stress and strain conditions, a normalized fatigue crack growth rate [(d a /d N )/ a ] is related to the strain range. The fatigue crack propagation behavior at a notch under pulsating load is analyzed with the above relation by considering the cyclic elastic- plastic condition at the notch.     

On the Presence of the Out–of–Plane Singular Mode Induced by Plane Loading With K<Subscript>II</Subscript> = K<Subscript>I</Subscript> = 0

Previous studies by a number of researchers demonstrated that in the case of a plane crack subjected to shear loading conditions characterized by a remote stress intensity factor, K_II, a three-dimensional singular mode (called mode O or out-of-plane mode) develops at the crack tip. This singular mode occurs due to the primary shear loading and Poisson’s effect. Similar to mode III, the O-mode is associated with the transverse shear stress components. Recent theoretical and numerical studies have also demonstrated a strong presence of this singular mode in plates weakened by pointed V-notches. Therefore, it was suggested that O-mode can play an important role in fracture initiation, particularly at large opening angles (above 102.6°) when the applied mode II is non-singular.     

加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟

采用不同应力比条件下的16MnR钢紧凑拉伸试样,设计了三种有限元分析模型,即不考虑加载历史效应的静态裂纹扩展模型,同时考虑加载历史和裂纹闭合的动态裂纹扩展模型以及仅考虑加载历史的伪动态裂纹扩展模型,对疲劳裂纹闭合过程、裂纹尖端的应力-应变迟滞环、疲劳损伤和裂纹扩展速率进行了数值模拟与分析,进而着重探讨了加载历史和裂纹闭合影响疲劳裂纹扩展行为的交互作用机制。结果表明:对于同类分析模型,应力比越大越不容易产生裂纹闭合;而在应力比相同的情况下,加载历史引起的残余压应力对裂纹闭合有明显的促进作用。裂纹闭合效应阻碍了平均应力的松弛,减小了裂纹尖端附近的应力-应变场强度、疲劳损伤和裂纹扩展速率,而加载历史引起的残余压应力则加快了平均应力的松弛和抑制了棘轮效应。与实验结果比较发现,只有同时考虑了裂纹闭合效应和加载历史影响的动态裂纹扩展模型,才能对疲劳裂纹扩展行为进行准确、定量的模拟。     

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.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

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.     

Cyclic crack opening displacement behavior during high-amplitude block loading

Load-crack opening displacement hysteresis behavior was monitored for fifty cycles of highamplitude loading which followed fatigue pre-cracking at low stress intensity factor levels. The material studied was quenched and tempered (400°C) AISI 4140 steel which showed pronounced cyclic softening. Despite this softening behavior, cycle-to-cycle decreases in load-COD hysteresis were observed during the initial cycles of high-amplitude loading. Steady state load-COD hysteresis behavior was attained by fifty loading cycles in each case and the fifty-cycle hysteresis loop widths agreed well with those for continuously cycled (non-pre-cracked) samples for equivalent loading conditions. The cycles during which the load-COD hysteresis decreased most dramatically represented fatigue crack growth distances equal to approximately 30% of the calculated plane strain monotonic plastic zone size. Greater percentage reductions in load-COD hysteresis were observed for lower stress intensity factor ranges. The observed behavior was in general agreement with that predicted by finite element fatigue crack closure models in the literature. In addition, the level of prior loading was found to have a pronounced effect on subsequently measured fracture toughness values for this material.     

Fatigue behavior characterization of laser-welded cold rolled sheet metal (SPCEN)

For the present work, the fatigue behavior of laser-welded cold-rolled sheet metal (SPCEN) was studied. Also, the thickness heterogeneity effect of weldment on the fatigue strength and crack growth behavior was studied. The sheet metals of same thickness (0.9 mm) were laser-welded (Case A), and the sheet metal of 0.9 mm thickness was laser-welded to the sheet metal of 2.0 mm thickness (Case B). For both cases, fatigue tests were conducted applying the load perpendicular or parallel to the welding line. Finite element analysis was performed to determine the form of stress intensity factor as a function of crack length for both cases. The results showed that the fatigue strength of Case A was 8.5% higher than that of Case B when the loading direction was parallel to the welding line. However, the fatigue strength of Case A was similar to that of Case B for the perpendicular fatigue loading to the welding line. At the same crack length, the stress intensity factor of Case A was greater than that of Case B. It was also found that for both cases, the crack propagation rate decreased noticeably in the front of weld bead but increased rapidly in the weld bead. The retardation of crack propagation was due to the increased hardness in the front of weld bead, and the increased crack propagation rate was due to the reduced fracture toughness in the weld bead.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

Environmental dynamic fatigue crack propagation in high density polyethylene: an empirical modelling approach

Part of a programme to study environmental dynamic fatigue crack propagation in engineering thermoplastics is presented. High density polyethylene has been studied in terms of its stress cracking properties under dynamic loading conditions in detergent. This work complements previous investigations on stress cracking in detergent under static loading. The stress cracking was found to vary according to loading conditions and in conclusion, a dependence of crack growth rate on test frequency, amplitude and level of stress intensity factor is reported. An emperical model describing environmental fatigue crack propagation is proposed which adequately represents the experimental results of high density polyethylene, Nylon 66 and which, it is suggested, may be suitable for use with other polymers.     

Fatigue behavior of aluminum alloys under biaxial loading

The biaxiality effect, especially the effect of non-singular stress cycling, on the fatigue behavior was studied, employing cruciform specimens of aluminum alloys 1100-H14 and 7075-T651. The specimens, containing a transverse or a 45^o inclined center notch, were subjected to in-phase (IP) or 100% out-of-phase (hereinafter referred to as “out-of-phase or OP”) loading of stress ratio 0.1 in air. The biaxiality ratio λ ranged from 0 to 1.5, and 3 levels of stress were applied. It was observed that: (1) at a given λ, a lower longitudinal stress induced a longer fatigue life under IP and OP loading, and the fatigue life was longer under IP loading, (2) the fatigue crack path profile was influenced by λ, phase angle (0^o or 180^o), and initial center notch (transverse or 45^o inclined); (3) the fatigue crack path profiles, predicted analytically and determined experimentally, had similar features for the specimens with a transverse center notch under IP loading; and (4) the fatigue crack growth rate was lower and the fatigue life longer for a greater λ under IP loading, whereas it changed little with change in λ under OP loading. These results demonstrate that non-singular stress cycling affects the biaxial fatigue behavior of aluminum alloys 1100-H14 and 7065-T651under IP and OP loading.