Behavior Of Small Cracks Research Articles

Growth of small cracks and prediction of lifetime in high-temperature alloys

The lifetime to initiate an engineering crack is usually predicted from S–N curves in high cycle fatigue or Coffin–Manson curves in low-cycle fatigue. This paper investigates how to predict the engineering life to initiate an engineering crack from the growth of small cracks. Small cracks can nucleate from defects and especially ceramic inclusions in superalloys produced by powder metallurgy. The behavior of short cracks nucleated from artificial defects was investigated under small scale yielding. A deterministic prediction of the life of smooth specimens was made using the growth law measured in air or in vacuum. The distribution of real defects was then used in a probabilistic life prediction model. The growth of small cracks under large scale yielding was investigated in stainless steels. A modified Tomkins equation can account for the behavior of small cracks and provide an estimate of the lifetime under low-cycle fatigue or thermal fatigue. A damage model based on the propagation of micro-cracks originating at casting defects has been developed for single crystal turbine blades, operating under thermo-mechanical creep–fatigue conditions. The model used the process zone concept introduced by Mc Clintock. Weakening of material due to localized oxidation embrittlement is shown to account for oxidation–creep–fatigue interactions. The model gives satisfactory life predictions under various thermo-mechanical loading conditions. A local approach to fracture is proposed for fatigue crack growth using a fracture criterion as a post-processor of a finite element model, for two-dimensional long cracks.

P-19 Fatigue crack initiation and small fatigue crack propagation behavior in high vacuum on Ti- and Al alloys

In this study, we investigated initiation and propagation behavior of small fatigue crack on A7075 and Ti-6Al-4V in vacuum environment. As well as the ambient air environment, so-called small fatigue crack behavior were observed in vacuum. In both materials, the fatigue crack initiation life and failure life in vacuum environment are always longer than that of ambient air environment. In case of A7075, effect of the air on small fatigue crack propagation rate is less than that of obtained on Ti-6Al-4V.

114 S35C焼なまし材のねじり疲労限度近傍における微小き裂の挙動(OS 材料利用・改質に関する実験・数値解析(その3))

114 S35C焼なまし材のねじり疲労限度近傍における微小き裂の挙動(OS 材料利用・改質に関する実験・数値解析(その3))

Fatigue crack growth from foreign object damage under combined low and high cycle loading. Part II: A two-parameter predictive approach

An approach based on a two-parameter fatigue theory has been developed to predict FOD-induced small crack growth under combined low and high cycle fatigue loading conditions. In this approach, both ΔK and Kmax are recognized as being important to the fatigue crack growth process and therefore included in a crack growth formulation. An elastic stress intensity factor is not appropriate for the small cracks studied here, particularly due to the influences of residual stresses and stress concentration produced at FOD indentations. The El Haddad approach was used as a correction factor, providing a modified stress intensity range ΔKmod and maximum stress intensity Kmod,max. The levels of stress concentration and residual stresses were calculated by a general finite element code ABAQUS. The results show that small crack growth data compare well with those of long cracks when correlated with a new two-parameter crack driving force (ΔKmod)n′(Kmod,max)p′(1-ΔKmod,th/ΔKmod)0.25, where n′ and p′ are material constants derived from long-crack fatigue tests. This means that FOD-induced small crack behaviour may be predicted using long-crack experimental results.

Prediction of the behavior of small fatigue cracks

A modified linear-elastic fracture mechanics approach has been proposed and developed by McEvily and co-workers, with which the fatigue crack growth rates of both small cracks and large cracks can be quantitatively evaluated. This paper reviews the recent results of applications of this approach to the following fatigue problems involving the prediction of the behavior of small fatigue cracks: (1) in an examination of the use of Miner's rule in fatigue life estimation under variable amplitude loading, (2) in the verification of the a r e a parameter model, and (3) in the prediction of the fatigue life and strength of defect-containing components subjected to multiaxial stress.

Low-cycle fatigue small crack initiation and propagation behaviour of cast magnesium alloys based on in-situ SEM observations

In-situ observations on the initiation and propagation behaviour of low-cycle fatigue small cracks in cast magnesium–aluminium alloys (AM50 and AM60B) were carried out with scanning electron microscopy (SEM) to elucidate the resistance to fatigue cracking and to evaluate the fatigue small crack growth rate accurately and quantitatively. The results indicate that the fatigue small cracks formed preferentially on β-phase (Mg17Al12) boundaries at room temperature. In addition, the effects of the parameters of stress levels in low-cycle fatigue and temperatures as well as microstructure on fatigue small crack propagation behaviour are revealed. The variation of crack open displacement (COD) with stress levels and cycles at elevated temperature shows that it is unsuitable to estimate the fatigue small crack growth rate of cast magnesium alloys using conventional measurement methods such as the plastic-replica technique due to the obvious difference between microscopic cracks in the open and closed states. Stabilized crack propagation behaviour is limited to cases where the physical crack length is less than 1 mm in low-cycle fatigue.

Fatigue crack growth mechanisms at the microstructure scale in Al–Si–Mg cast alloys: Mechanisms in the near-threshold regime

The near-threshold crack growth behavior (Δ K th/Region I) of hypoeutectic and eutectic Al–Si–Mg cast alloys was investigated for both long and short cracks. To isolate and establish the mechanistic contributions of microstructural features (dendritic α-Al matrix/eutectic phases/Mg–Si strengthening precipitates), alloys with various Si content/morphology, grain size level, and matrix strength were studied; the effect of secondary dendrite arm spacing was also assessed. The mechanisms in Paris-Region II and Region III will be presented in a subsequent publication. The long-crack threshold behavior of the materials is attributed to combined effects of microstructure/roughness-induced and residual stress (introduced during heat treatment)-induced closure mechanisms. The threshold behavior of small cracks is explained through closure-unrelated mechanisms and barrier effects of the characteristic microstructural features of each alloy. The fatigue crack growth tests were conducted on compact tension and corner crack tension specimens under constant stress ratio, R = 0.1, in ambient conditions.

Initiation and Growth Behavior of Small Fatigue Cracks in Ultra-fine Grained P/M Aluminum Alloy at Elevated Temperatures

Small fatigue crack initiation and growth behavior at elevated temperatures were investigated using ultra-fine grained P/M (Powder Metallurgy) aluminum alloy of which grain size was from 200 to 500nm. Reversed plane bending fatigue tests were conducted at three different temperatures of room temperature (R.T.), 200°C (473K) and 250°C (523K), and crack initiation and small crack growth were studied in detail by means of replication technique. The fatigue strength decreased as test temperature increased. The cracks initiated at the boundary between powders regardless of test temperatures, and total fatigue life was dominated by crack initiation life. The fatigue crack initiation and growth behavior was almost irrelevant to the test temperatures. Fatigue crack growth rates, da/dn, were slightly accelerated at a fixed Kmax with increasing test temperature, while da/dn evaluated in terms of Kmax/E (E : Elastic modulus) agreed well. The dependence of fatigue strength and crack growth rate on test temperature was much smaller than that of conventional aluminum alloys, indicating the high heat resistance of ultra-fine grained P/M aluminum alloy.

Influence of Microstructure on Small Crack Behavior

Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic property of each crystal influences on the local stress field ahead of a crack tip if the crack size is not large enough in comparison with the grain diameter. This brings about the change in the crack driving force (CDF) such as stress intensity factors. In the present study, in order to investigate the cause and magnitude of the change in the CDF, the finite element analysis is performed. The calculations are carried out for a single crystal model, a bi-crystal model, and a polycrystal model containing a transgranular or an intergranular semi-circular crack. The results implied that the magnitude of CDF is dependent not only on the crystal orientation but also on the deformation-constraint caused by the difference in elastic modulus of grains near the crack tip. The statistical scatter of CDF due to the random crystal orientation in a polycrystal is examined by a Monte Carlo simulation. The variation in the SIF becomes small as the crack size increases.

Small crack behavior and fracture of nickel-based superalloy under ultrasonic fatigue

Fracture and small crack behavior in the very high cycle domain of 10 9 cycles were investigated with a nickel-based superalloy under ultrasonic fatigue in ambient air at room temperature. The influence of ultrasonic frequency is examined by comparing the results with those in conventional low frequency fatigue. It is found that fatigue strength increases as frequency is raised up to 19.5 kHz and the most of fatigue life is consumed in nucleating and propagating small cracks up to 100 μm. Transition of fracture mode from transgranular ductile fracture to cleavage-dominated fracture occurs beyond a critical stress intensity factor range of approximately 21 MPa m , leading to the catastrophic failure under ultrasonic fatigue.

Closure mechanisms in Al–Si–Mg cast alloys and long-crack to small-crack corrections

Crack growth behavior of small and long cracks has been a subject of much research; the differences observed in the growth response were largely attributed to crack closure. In this study, cast Al–Si–Mg alloys of various residual stress levels and Si content/morphology were investigated, and the dominant closure mechanisms were identified. The near-threshold fatigue crack growth behavior of the alloys is controlled by two types of closure: residual stress-induced (due to residual stresses introduced during heat treatment) and microstructure/roughness-induced (due to variations in Si content/morphology). These closure mechanisms were individually discussed and closure corrective techniques were applied to long crack growth results. The near-threshold closure corrected long crack growth data compare favorably with small crack growth data.

Propagation of surface fatigue cracks in human cortical bone

An understanding of how fatigue cracks grow in bone is of importance as fatigue is thought to be the main cause of clinical stress fractures. This study presents new results on the fatigue-crack growth behavior of small surface cracks (∼75–1000 μm in size) in human cortical bone, and compares their growth rates with data from other published studies on the behavior of both surface cracks and many millimeter, through-thickness large cracks. Results are obtained with a cyclically loaded cantilever-beam geometry using optical microscopy to examine for crack growth after every 100–500 cycles. Based on the current and previous results, small fatigue cracks appear to become more resistant to fatigue-crack growth with crack extension, analogous to the way the fracture resistance of cortical bone increases with crack growth. Mechanistically, a theory attributing such behavior to the development of bridges in the wake of the crack with crack growth is presented. The existence of such bridges is directly confirmed using optical microscopy.

Mode I solution for micron-sized crack

The feature size of micro-electronic, optoelectronic and biomedical devices is in the sub-micron scale and is pushing toward the nanometer scale. Defects in these small structures are correspondingly smaller such that small crack behavior is becoming an important design consideration for reliability and performance of such devices. Analyses of small cracks are complicated by the rapid variation in the deformation in the crack tip zone. Strain gradients in the near tip zone, which can be ignored in large cracks, will influence the small crack behavior when the crack tip zone is in the order of the crack size. In this paper, we consider two-dimensional crack deformations with strain gradient effect and establish the dual formulations in terms of potentials. The formulations reduce to the conventional linear elastic fracture theory, when the material length scale parameters for the higher order deformation measures are zero. One of the formulations is in terms of two complex stress functions and two pseudo potentials. The complex stress functions are harmonic and the governing equations for the pseudo-potentials are two uncoupled second order partial differential equations. The solutions for these equations are coupled through the boundary conditions. A perturbation method is used to construct the solution for mode I cracks under a K-field when only the effect of the rotational gradient is included. The perturbation solution has 1 / r induced singularity for the stresses. The induced deformation decays exponentially away from the crack tip. The induced stresses become insignificant beyond 3 ε, the typical characteristics of a boundary layer type. To a first order approximation, the induced deformation energy normalized by that of the classical solution under constant applied crack opening load is linearly proportional to ε. This implies that the induced energy release rate is linearly proportional to the length scale parameter. The induced energy release rate under a fixed crack opening load is negative indicating that the rotational gradient shields the crack and lowers the total deformation energy release rate for small crack.

Effect of Atmospheric Humidity on the Fatigue Crack Propagation Behavior of Short Cracks in Silicon Nitride

The effect of the environment on crack-growth processes in silicon nitride was studied by investigating the static and fatigue crack-growth behavior of small surface cracks, as influenced by testing (i) in the ambient environment, (ii) in distilled water, (iii) under vacuum, and (iv) in toluene. A principal finding was that testing under cyclic conditions led to crack-growth rates that were much higher in air than in toluene, whereas testing under static conditions in air or toluene led to minor differences in the rate of static fatigue crack growth. This difference in sensitivity to the environment under static and cyclic loading conditions was attributed, in part, to a much-greater extent of microcracking at the surface ahead of the main crack in air under cyclic conditions, in comparison to that in other environments. This propensity for microcracking at the surface in air under cyclic conditions also was reflected in the aspect ratios of the crack shapes that developed.

Application of a threshold curve model to high-cycle fatigue behavior of small cracks induced by foreign-object damage in Ti–6Al–4V

A threshold curve method previously developed was applied to analyze the high-cycle fatigue behavior of small cracks induced by foreign-object damage (FOD) in a Ti–6Al–4V alloy for which experimental results can be obtained from recent publications. Foreign object damage represents the impact by small hard objects such as stones or pieces of metal and is a major cause of fatigue failure in gas turbine engines. Experimental results found in the literature showed that the small cracks induced by FOD in Ti–6Al–4V alloys could propagate at an applied Δ K as small as 1 MPa m 1/2, i.e. well below the ‘worst-case’ Δ K thR threshold of 1.9 MPa m 1/2 for long cracks in this alloy (load ratio R=0.95). According to the results obtained in the present work, the threshold for propagation of small cracks (≧20 μm) can be as small as 0.8 MPa m 1/2 considering a stress ratio R=0.8, for which the threshold for long cracks is about 2.3 MPa m 1/2. Further, the minimum stress ratio R at which the analyzed cracks can propagate seems to be about 0.6, for which the threshold for large cracks is about 2.7 MPa m 1/2. These results show that for microstructurally small cracks, the absence of crack closure effect is not the only reason for the observed faster propagation rates and lower propagation thresholds when compared with long cracks.

The effect of bi‐modal and lamellar microstructures of Ti‐6Al‐4V on the behaviour of fatigue cracks emanating from edge‐notches

ABSTRACTThis paper is aimed at evaluating the influence of bi‐modal and lamellar microstructures on the behaviour of small cracks emanating from notches in α+β titanium Ti‐6Al‐4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on double‐edge‐notched specimens. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 88 and 58% of the 0.2% material yield stress. Crack closure effects were measured by an extensometric technique and discussed. Variations in crack aspect ratio were determined and considered in the ΔK calculation. Corresponding results were discussed by considering the effect of the yielded region at the notch tip calculated by elastic–plastic finite element modelling of the fatigue tests. The importance of the bi‐modal and lamellar microstructures on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. The crack growth rate data obtained were compared with those measured using standard C(T) specimens (long crack).

Fatigue limit estimation for WC-Co cemented carbides on the basis of linear elastic fracture mechanics

The fracture and fatigue behavior of two microstructurally different hardmetals (WC-Co cemented carbides) is investigated. Mechanical characterization includes flexural strength and fracture toughness as well as fatigue limit and fatigue crack growth (FCG) behavior under monotonic and cyclic loads respectively. Considering that fatigue lifetime of cemented carbides is given by subcritical crack growth of preexisting defects, a linear elastic fracture mechanics approach is attempted to assess fatigue life - FCG relationships for these materials. It concentrates on addressing the fatigue limit - FCG threshold correlation under infinite fatigue life conditions. Thus, the fatigue limit associated with natural flaws is estimated from FCG threshold experimentally determined for large cracks under the assumptions that (1) similitude on the FCG behavior of small and large cracks applies for cemented carbides, and (2) critical flaws are the same, in terms of nature, geometry and size, under monotonic and cyclic loading. The reliability of this fatigue mechanics approach is sustained through the satisfactory agreement observed between estimated and experimentally determined values for the fatigue limit under the different load ratios investigated.

Behaviour of fatigue cracks emanating from circular notches in Ti‐6Al‐4V under bending

ABSTRACTThis paper is aimed at evaluating the behaviour of small cracks emanating from notches in the Ti‐6Al‐4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on prismatic specimens with a central hole. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 56.6 and 100% of the 0.2% yield stress of the material. Microstructural effects were discussed. To this purpose a specific device based on the ‘in situ’ detection of cracks by photomicroscopy was developed. Corresponding results were analysed quantitatively considering the effect of the yielded region at the notch tip by elastic–plastic finite element modelling. Furthermore, information regarding the sites of fatigue crack initiation and propagation path were discussed on the basis of careful fractographic analysis of the specimens. The importance of the two phase α, β microstructure on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. Mechanically and microstructurally long cracks were correlated by linear‐elastic fracture mechanics.

マグネシウム合金ＡＺ６１押出材の疲労挙動と破壊機構

This paper presents the fatigue crack propagation (FCP) characteristics and the fatigue behaviour of smooth specimens in an extruded AZ61 magnesium alloy. FCP tests and axial fatigue tests have been performed at the stress ratio of 0.05 and -1 respectively, in laboratory air at ambient temperature. Fatigue properties were evaluated and compared with those of a rolled AZ31 alloy in a previous report, and fracture mechanisms were discussed on the basis of crack initiation, small crack growth and fracture surface analysis. The relationship between FCP rate and stress intensity factor for large cracks consisted of two parts with different slopes, which became much more remarkable when FCP rates were characterized in terms of the effective stress intensity factor. This was attributed to a fracture mechanism transition because the fracture surface appearance was clearly different above and below the stress intensity factor where the slopes changed. The fatigue strength of the AZ61 alloy was higher than that of the AZ31 alloy and the fatigue strengths at 107 cycles were 60MPa and 50MPa respectively. However, the fatigue strengths characterized in terms of fatigue ratio were similar with a considerably low fatigue ratio of 0.22. Regardless of stress level, fatigue cracks initiated at the specimen surface in intergranular or transgranular mode due to cyclic slip deformation at a very early stage of fatigue cycling. The growth behaviour of small cracks was consistent with the FCP characteristic after allowing for crack closure for large cracks, but the operative micromechanisms were different between small and large cracks. Except for subsurface fracture occurred in the AZ31 alloy, the fatigue properties described above were basically the same as observed in the AZ31 alloy.

Characterizing small fatigue cracks in metallic alloys

Small fatigue cracks grow faster than large fatigue cracks and below the large-crack threshold, and it is necessary to include these characteristics in many life-prediction models. Numerous micromechanics experimental measurements have been made to determine the origin of this anomalous small-crack behavior and to unify and predict small- and large-crack growth-rate behavior. Micromechanics showed that a stress-intensity factor described the crack-opening displacement (COD). Four methods for characterizing small-fatigue-crack behavior are reviewed: three based on fracture mechanics and one empirical. The three fracture mechanics-based methods are essentially complementary to each other and allow prediction of small-crack growth-rate behavior.