SHORT FATIGUE CRACK PATH DETERMINANTS IN POLYCRYSTALLINE Ni-BASE SUPERALLOYS

Abstract— Fifty seven short fatigue cracks in the Ni-base superalloy AP1 have been examined, to ascertain how the paths taken by growing fatigue cracks are determined. The observations were made on the surface of a smooth specimen, and on the exposed fracture surfaces. Three dimensional reconstructions of the vulnerable microstructures in the vicinity of the cracks were produced. Initiation occurred in mode II, with the lines of intersection of the initiation sites with the specimen top surface orientated at approximately 45° to the tensile axis. These initiation sites developed in slip bands which crossed a large grain and at least one other grain via a grain boundary with a low angle of misorientation. 'River markings' on one of the initiation facets, indicated that the crack first opened from the top centre of the initiation grain. Subsequent to initiation, the growth paths of these cracks are related to the misorientations of the grains and the progress of the crack front.     

SHORT AND LONG FATIGUE CRACK GROWTH IN A SiC REINFORCED ALUMINIUM ALLOY

Fatigue crack growth behaviour in a 15 wt% SiC particulate reinforced 6061 aluminium alloy has been examined using pre-cracked specimens. Crack initiation and early growth of fatigue cracks in smooth specimens has also been investigated using the technique of periodic replication. The composite contained a bimodal distribution of SiC particle sizes, and detailed attention was paid to interactions between the SiC particles and the growing fatigue-crack tip. At low stress intensity levels, the proportion of coarse SiC particles on the fatigue surfaces was much smaller than that on the metallographic sections, indicating that the fatigue crack tends to run through the matrix avoiding SiC particles. As the stress intensity level increases, the SiC particles ahead of the growing fatigue crack tip are fractured and the fatigue crack then links the fractured particles. The contribution of this monotonic fracture mode resulted in a higher growth rate for the composite than for the unreinforced alloy. An increase in the proportion of cracked, coarse SiC particles on the fatigue surface was observed for specimens tested at a higher stress ratio.     

SHORT FATIGUE CRACK GROWTH BEHAVIOUR IN WASPALOY AT ROOM AND ELEVATED TEMPERATURES

Short fatigue crack growth tests have been carried out at room and elevated temperatures using the nickel-based superalloy known as Waspaloy. A fully automated computer controlled system has been developed and employed for controlling the testing and monitoring of the growth of freely initiated surface short cracks on smooth specimens. Surface cracks as small as 10 um in length have been detected and recorded at temperatures up to 700°C. Anomalous short crack propagation behaviour was observed when comparisons were made with the corresponding long crack behaviour. Some aspects of mechanical, microstructural and environmental effects on the short fatigue crack growth behaviour of the material are discussed.     

DAMAGE ACCUMULATION DURING INITIATION AND SHORT CRACK GROWTH REGIMES

The birth and growth of short cracks is analysed from an elastic-plastic fracture mechanics viewpoint. Low to high cumulative damage tests from the low stress to high strain regime indicate that there is no crack initiation period in the metallurgical sense and that cracks grow from the first cycle, but at a slow rate. The initiation phase terminates when one crack starts to dominate and accelerates to failure, its initial size being given by for the medium carbon steel tested here, of grain size 56 μm.     

CRACK NUCLEATION AND PROPAGATION IN BLADE STEEL MATERIAL

Stress corrosion cracking and corrosion fatigue of 12 Cr steel in sodium chloride solution has been investigated. Tests have been performed in air at room temperature and in aqueous solution with 22% NaCl at 80°C. The influence of corrosion pits on crack nucleation has been investigated. On fracture surfaces tested in environment (22% NaCl solution), crack initiation was observed in correspondence with corrosion pits; in this case fatigue life can be described using a fracture mechanics approach. The ΔK value for crack nucleation from a pit in rotating bending fatigue tests is very low in air (about 3 MPa√m). The results of slow strain rate tests on smooth specimens show that there is a threshold stress intensity, K_ISCC, of about 15 MPa√m and a plateau in stress corrosion crack growth rate of about 10^-5mm/s.     

COMPARISON OF SHORT AND LONG FATIGUE CRACK GROWTH IN 7075-T6 ALUMINUM

The fatigue crack growth rates of physically-short cracks (0.5 ≤a≤ 1.0 mm), intermediate cracks (1 < a≤ 2 mm) and long cracks (7 < a < 25 mm) were compared using SEN type tensile specimens in 7075-T6 aluminum alloy with load ratios, R, of 0.05, ? 1 and 0.5 under constant amplitude testing at room temperature. It was found that the short cracks grew much faster than long cracks based on applied δK with da/dN≤ 10^?7 m/cycle. Even the intermediate cracks grew faster than the long cracks below 10^?7 m/cycle. The transition crack lengths where similitude with δK existed was between 1 and 2 mm. Mean stress effects were similar for R= 0.05 and ? t, but R= 0.5 caused increased crack growth rates. The above differences are partially attributed to crack closure effects. Based upon plastic zone sizes, LEFM was justifiable with all the experiments.     

EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic-plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through-thickness crack emanating from a notch root under elastic—plastic loading conditions.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

SHORT FATIGUE CRACK GROWTH IN PLAIN AND NOTCHED SPECIMENS OF AN 8090 Al-Li ALLOY

Abstract— Fatigue tests on notched and plain specimens were carried out under a combined acoustic and optical microscope. Crack initiation in plain specimens occurs invariably at inclusions which act as sites of stress concentration. Short crack propagation behaviour shows the usual pattern of accelerations and retardations associated with microstructural variations. Growth can only be sustained if the applied stress is sufficiently high to overcome the microstructural barriers. For the notched specimens the extent of the notch tip and crack tip plastic zone sizes control crack propagation. A short crack will continue to propagate only if its own plastic zone can sustain growth as the crack tip extends beyond the notch zone, otherwise it becomes non-propagating. Notch plastic zones are calculated using both approximate and accurate solutions. Some microstructural effects are discussed.     

THE NUCLEATION AND GROWTH OF SHORT FATIGUE CRACKS BOTH AT PLAIN SURFACES AND NOTCHES

Abstract— The problem of the nucleation and growth of short fatigue cracks is addressed from an energetic point of view. It is explained that vanishingly small cracks can only nucleate and grow at the expense of the release of some locally stored energy during the fatigue deformation. This is necessary because an external loading system alone cannot provide a positive driving force for the growth of a crack whose length is below a critical value. The concept of the local driving force is used to explain the nucleation and growth of short fatigue cracks both at plain surfaces and at notches. With this approach a meaningful definition can be given of a "short fatigue crack" and a sound physical interpretation of the Kitagawa-Takahashi plots is provided. The conditions for the existence of non-propagating cracks are clearly established and the relationship between the stress concentration factor at the root of notches and the fatigue limit is explained. The paper sets up a physical framework for the sound understanding and treatment of short fatigue cracks and the microstructural parameters which control their growth.     

SHORT CRACK COALESCENCE AND GROWTH IN 316 STAINLESS STEEL SUBJECTED TO CYCLIC AND TIME DEPENDENT DEFORMATION

Abstract— A study has been undertaken into short crack growth behaviour of AISI type 316 stainless steel under creep-fatigue conditions at 550°C within the high strain range of 0.9 to 2.5% and including a 60 min hold-time. During the high-temperature, reverse-bending tests, surface crack initiation and growth on both the tensile-hold and the compressive-hold sides of circular-section specimens were monitored by means of a plastic replication technique. Detailed analysis revealed that under creep-fatigue conditions, the initiation and growth behaviour of many individual cracks and their subsequent coalescence to form a major Stage II (tensile) crack was the dominant feature in the failure process. A life prediction model is proposed which incorporates the process of short crack coalescence. Satisfactory predictions of creep-fatigue lifetimes are derived from the model.     

ANALYSIS AND MODELISATION OF SHORT CRACK GROWTH BY DUCTILE FRACTURE MICROMECHANISMS

Abstract— A ductile medium strength steel has been modelled by means of the Gurson model, and been used to investigate the effect of crack tip constraint in several fracture mechanics specimens. Both numerical and experimental results have been obtained, in the course of the crack extension process, for single edge notch bending specimens with different crack length-to-width ratios. The geometries with the shorter cracks always exhibited higher J values at initiation and steeper J crack growth resistance curves, and these results have been explained in terms of the stress and strain fields and damage development in the region ahead of the crack tip.     

A THEORETICAL AND EXPERIMENTAL STUDY OF ENVIRONMENTAL HYDROGEN-ASSISTED SHORT FATIGUE CRACK GROWTH IN AN Al-Li ALLOY

Abstract— The initiation and propagation of fatigue cracks in an Al-Li 8090 alloy in a vapour environment of 0.6 M NaCl solution was investigated. A severe degradation of the resistance to short crack growth was exhibited. Preliminary work carried out to establish the susceptibility of the material to hydrogen embrittlement demonstrated a close correlation between the deformation mode of this alloy and hydrogen absorption. The combination of highly localized slip and highly localized hydrogen fugacity creates a high susceptibility to hydrogen-assisted crack growth.
On the basis of current micro-mechanical models, it is suggested that hydrogen trapping induces a reduction of the friction stress acting in the crack tip plastic zone. Consequently, enhanced plasticity at the crack tip due to the decrease in friction stress leads to an increase in crack growth rate.
An exact solution for a surface crack in a semi-infinite plane is obtained based on a dislocation crack model. Using this solution a computer method is developed to calculate the time-dependent short crack growth rate and fatigue lifetime. Both solutions show good correspondence with the experimental results.     

岩石类材料裂隙形成和扩展的相场方法模拟

相场方法通过定义一个连续分布函数来近似表示自由不连续裂纹,在此基础上建立最小能量变分框架,从而得到描述裂纹发展的控制方程。不需要提前设定裂纹的形状、尺寸和方向,相场方法就能很好地描述裂纹的形成和扩展,为利用数值方法模拟裂纹扩展提供了一个严谨准确的理论框架。该文首次将相场方法用于模拟岩石裂隙扩展问题,预测包含不同岩桥倾角的预制双裂隙岩石类材料在单轴压缩作用下的损伤和破坏过程,并与室内试验结果进行对比。结果表明相场方法非常适合模拟岩石类材料内部复杂裂隙的萌生、扩展和连接过程,在岩体工程稳定性分析领域具有广阔的应用前景。     

A MICRO-MECHANICS ANALYSIS FOR SHORT FATIGUE CRACK GROWTH

Crack initiation and early growth of fatigue cracks in a fully annealed 0.4% carbon steel was investigated using plastic replicas and torsion loading. In a structure consisting of a 70/30 mixture of pearlite and ferrite the cracks are seen to develop and grow initially along slip bands in the ferrite phase. Energetic considerations lead to the formulation of a model which, while characterizing short crack growth rate, also considers those microstructural variables relevant to fatigue crack initiation and early crack growth. The driving force for crack growth is provided by the energy of the slip band; correspondingly crack growth per cycle is proportional to the strength of the slip band. In the short fatigue crack region, cracks grow initially at a fast rate but deceleration occurs quickly and, depending on the stress level, they either arrest or are temporarily halted at a critical length. This critical length is shown to coincide with the value of the threshold length for crack growth under LEFM conditions.     

A PROBABILISTIC MODEL OF SHORT FATIGUE CRACK GROWTH

Abstract— A probabilistic model is presented that draws a direct link between stochastic microstructure and the statistics of measured growth rates. The model is formulated as a semi-Markov process. The underlying Markov process describes the evolution of a growth control variable as an explicit function of crack length. The growth control variable is open to a variety of interpretations, depending on the mechanisms known to control growth in any given application. Elapsed fatigue cycles and the distribution of times to failure are calculated by invoking an empirical or postulated law of growth rate. This law is either a deterministic or probabilistic relationship between the growth control variable and the crack velocity. It may, and usually does, contain parameters that are evaluated by calibration against available statistical data. This process guarantees a high level of robustness of the model's predictions. The computational generality of the formulation facilitates the treatment of spectral loading.     

PREDICTING FATIGUE LIFE IN COMMERCIALLY PURE ALUMINIUM USING A SHORT CRACK GROWTH MODEL

Abstract— Advances in manufacturing techniques and improvements in non-destructive inspection procedures have reduced the size of initial defects in fatigue-critical components to the scale of the microstructure. Unfortunately, the growth of these so-called short fatigue cracks is not properly characterised by conventional linear elastic or elastic-plastic fracture mechanics. However, the Navarro-de los Rios crack growth model does account for many aspects of their growth and has proved successful in predicting fatigue life of medium carbon and C-Mn steels. In consequence, the growth of short fatigue cracks in commercially pure aluminium, under fully reversed uniaxial loading, has been studied, using a plastic replication technique and modelled, using the Navarro-de los Rios crack growth equation. The predicted lifetimes are in good agreement with the actual experimental lifetimes, and compare favourably with predictions based on two previously reported crack growth models.