Interpreting the stress ratio effect on delamination growth in composite laminates using the concept of fatigue fracture toughness

This paper provides a study on fatigue delamination growth in composite laminates using energy principles. Experimental data has been obtained from fatigue tests conducted on Double Cantilever Beam (DCB) specimens at various stress ratios. A concept of fatigue fracture toughness is proposed to interpret the stress ratio effect in crack growth. The fatigue fracture toughness is demonstrated to be interface configuration independent but significantly stress ratio dependent. An explanation for this phenomenon is given using SEM fractography. Fracture surface roughness is observed to be similar in different interfaces at the same stress ratio. But it is obviously more rough for high stress ratio in comparison with that for low stress ratio, causing the fatigue resistance increase. Therefore, the stress ratio effect in fatigue crack growth can be physically explained by a difference in resistance to crack growth.     

Statistical approach to roughness-induced shielding effects

A new theoretical concept is introduced to describe the roughness‐induced shielding effects in metallic materials. This approach is based on the statistics of the local ratio between the characteristic microstuctural distance and the plastic zone size. A general equation involving both the crack branching and the crack closure phenomena is derived in the frame of linear elastic fracture mechanics under the assumption of remote mode I loading. It enables the determination of the intrinsic values of both the fracture toughness and the fatigue crack growth threshold. Moreover, the roughness‐induced component can be separated from other closure components, such as the plasticity or oxide‐induced closure. In order to estimate the total roughness‐induced shielding effect only standard materials data such as the yield stress, the mean grain size, the surface roughness and the fracture mode are necessary. Examples of applications concerning static fracture and fatigue are presented for selected metallic materials.     

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.     

A TEST METHOD FOR MODE II FATIGUE CRACK GROWTH RELATING TO A MODEL FOR ROLLING CONTACT FATIGUE

Abstract— From fractographic observations of specimens that have failed due to rolling contact fatigue, it has been concluded that the first stage of damage is the formation of mode II fatigue cracks parallel to the contact surface due to the cyclic shear stress component of the contact stress. Although these initial subsurface cracks, in both metals and ceramics, are produced in a direction parallel to the cyclic shear stress, cracks eventually grow in a direction close to the plane of the maximum tensile stress if we apply a simple mode II loading to them. The difference between crack growth in simple mode II loading and crack growth due to rolling contact fatigue is, we suppose, whether or not there is a superimposed compressive stress. Based on this hypothesis, we developed an apparatus to obtain the intrinsic characteristics of mode II fatigue crack growth, and developed a simplified model of subsurface crack growth due to rolling contact fatigue.
Some results in terms of da/dN versus ΔK_II relations have been obtained using this apparatus on specimens of steel and aluminum alloys. Fractographs of the mode II fatigue fracture surfaces of the various materials are also provided.     

A mixed mode crack growth model taking account of fracture surface contact and friction

Fracture surface interactions, of whatever origin, can significantly affect the stress intensity factor, and consequently, can also be relevant to fatigue crack propagation. In the occurrence of interaction between fracture surfaces, the effective loading cycle experienced by material near the crack tip may be very different from that evaluated on the basis of the external loadings only. The purpose of the work described in this paper is to obtain the effective mode II stress intensity factor, k _IIeff, in a surface cracked elasto-plastic plate with a factory roof fracture surface subjected to an in-plane shear (mode II) loading. A new model estimating the magnitude of the frictional mode II stress intensity factor, k _f, arising from the mismatch of the fracture surface roughness during in-plane shear, is developed. Furthermore, the results of this study are employed in modeling the fatigue response of the surface cracked plates subjected to mixed mode loading.     

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.     

7050铝合金Ⅰ-Ⅱ复合型疲劳裂纹研究

为研究7050铝合金在Ⅰ-Ⅱ型复合加载下疲劳裂纹扩展规律,在Amsler HFP5000高频试验机上利用Richard加载装置,完成紧凑拉剪(CTS)试样疲劳裂纹扩展试验,利用有限元对Ⅰ-Ⅱ复合型裂纹进行数值模拟,采用APDL命令流计算不同裂纹长度的应力强度因子,并引入最大周向应力准则计算裂纹扩展角,用有限元计算等效应...     

Experimental evidence of a common local mode II growth mechanism of fatigue cracks loaded in modes II,III and II + III in niobium and titanium

The paper is focused on an identification of the local mode II mechanism of fatigue cracks loaded under the remote mode III and the mixed mode II + III and presents a convincing experimental evidence of such a mechanism in materials with a nearly coplanar crack growth. Closure-free data were obtained by applying fatigue experiments in modes II, III and II + III in commercially pure titanium and niobium. The results revealed that the micromechanism of propagation of all kinds of shear-mode cracks can be described by a common model of advances of local mode II crack segments nearly in the direction of applied shear stress. These segments nucleated at spatial geometrical irregularities of the precrack front generating fibrous patterns at fracture surfaces.     

Evaluation of stress corrosion resistance and corrosion fatigue fracture behavior of ultra-high-strength P/M Al–Zn–Mg alloy

Quasi-static tensile tests in air and slow strain rate tests (SSRTs) in a 3.5% NaCl solution were conducted in an ultra-high-strength P/M Al–Zn–Mg alloy fabricated through powder metallurgy. Attention is also paid to fatigue strength and fatigue crack growth behavior in laboratory air and in a 3.5% NaCl solution. The alloy has extremely high strength of about 800 MPa. However, elongation at break remains small, at about 1.3%. The final fracture occurs by a macroscopically flat crack normal to the tensile axis, with little reduction in area and little shear lip on the periphery of a smooth sample. However, it fails microscopically in a ductile manner, with dimples. Dimple size is less than 1 μm, because the grain size of the alloy is extremely small. Strengthening mechanisms operating in the alloy are: small grains, sufficient metastable η′ phase in a matrix, and intermetallic compound acting as a fiber reinforcement. The SSRT strength in a 3.5% NaCl solution decreases slightly at a very low strain rate, that is smaller than those observed in aluminum alloys sensitive to stress corrosion. This means that the crack initiation resistance to stress corrosion is superior. However, under cyclic loading, the corrosion fatigue strength becomes lower than that conducted in air, because pitting corrosion on a sample surface acts as a stress concentrator. Crack initiation site of quasi-static and fatigue failure of the alloy is at inclusions, and hence, it is essential to decrease inclusions in the alloy for the improvement of the mechanical properties. Fatigue crack resistance of the alloy is inferior to conventional Al–Zn–Mg alloys fabricated by ingot metallurgy, because the fatigue fracture toughness, or ductility, of the alloy is inferior to other Al alloys, and intergranular cracking promotes crack growth. However, no influence of 3.5% NaCl solution on corrosion fatigue crack growth is observed, although an investigation is required into whether stress corrosion crack growth occurs or not, and at the same time, and of corrosion fatigue crack growth behavior at lower stress intensity. The fracture surface and crack initiation sites are closely examined using a high-resolution field emission type scanning electron microscope, and the fracture mechanisms of the alloy are discussed.     

Environment effects and surface roughness on fatigue crack growth at negative R-ratios

Fatigue crack growth has been widely studied, since it plays an important role on the damage tolerance analysis of mechanical components and structures. The environment, material properties and stress ratio significantly influence the fatigue crack growth behaviour of materials. Experimental tests were performed in M(T) specimens of a normalized DIN Ck45 steel at constant load ratios for R = 0.7, 0.5, 0, −1, −2, −3, in ambient air and vacuum conditions, using a new and patented chamber of vacuum. Special emphasis is given to the study of environment effects, stress ratios and related effects of crack roughness. Fracture surface roughness and crack closure effect were systematically measured for all tests in order to compare the influence of different environment and R-ratios. Results have shown that fatigue crack growth rates are higher in air than in vacuum and the fracture surface roughness is also higher in air than in vacuum for comparable stress ratios. The effect of the environment on fatigue crack growth rates seems to be more significant than any mechanical contributions such as plasticity, oxide and roughness which can induce the so-called crack closure.     

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.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

THE EFFECTS OF MICROSTRUCTURE AND FRACTURE SURFACE ROUGHNESS ON NEAR THRESHOLD FATIGUE CRACK PROPAGATION CHARACTERISTICS OF A TWO-PHASE CAST STAINLESS STEEL

In this study, the effects of stress ratio, microstructure and fracture surface roughness on the fatigue properties of a two-phase cast stainless steel were investigated. This behaviour was examined by means of the fracture mechanics approach and fractography. The fatigue crack growth rate decreased with decreasing stress ratio. The stress ratio markedly influenced the fatigue crack growth rate as ΔK approached the ΔK_th value. The roughness of the fracture surface was greater in the as-cast material than in the heat-treated material. Analysis of the crack growth data using ΔK_eff showed that the effect of R ratio could be explained but that the effect of microstructure on crack growth rate could not.     

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.     

Crack morphology models for fracture toughness and fatigue strength analysis

Planar cracks represent an approximation, largely adopted in fracture mechanics and fatigue problems, of the physical reality, where cracks feature complex geometric morphologies related to material microstructure, residual stresses, material properties dispersions and so on. In the present paper, firstly a model to describe the influence of roughness and friction of the crack surfaces is reviewed in relation to the resulting near‐tip stress field and the fracture resistance under monotonic loading. Such a model is based on the Distributed Dislocation Technique, and considers a periodic profile of the crack. Then, some approximate theoretical models describing periodically kinked cracks are reviewed in their application to the estimation of fatigue strength of materials. In particular, the influence of crack path meandering on fatigue propagation is analysed by modelling the crack profile as a piecewise linear periodic curve in two dimensions. The same type of model is discussed within the framework of self‐similar fractal geometries. In the paper, emphasis is given to the effect of crack size on the fracture resistance and fatigue strength, where such an effect depends on the ratio between the characteristic length of the crack morphology and the nominal length of the crack itself.     

Evolution of residual stresses with fatigue crack growth in integral structures with crack retarders

Bonded straps are investigated for their ability to retard a growing fatigue crack in metallic structures. The evolution of the residual stresses in the vicinity of the strap with fatigue crack growth has been studied. Cracks were grown in single edge-notched tension (SEN(T)) specimens reinforced with either a titanium or a carbon fibre reinforced plastics (CFRP) strap. The residual stress evolution has been measured in situ during crack growth using neutron diffraction, and modelled with a finite element approach. The peak residual stresses induced by the mismatch of the coefficient of thermal expansion between the strap and plate materials were seen to be fairly constant with crack growth. Good correlation between the experimental and the modelling results was found, except at very long crack lengths for a specimen that exhibited considerable fracture surface roughness at long crack lengths. The difference was attributed to wedging of the fracture surface changing the expected stress state, rather than any effect of the strap.     

The model of the residual life time estimation of tribojoint elements by formation criteria of the typical contact fatigue damages

A two-dimensional theoretical model is proposed for investigation of the fracture processes and assessing residual contact durability of solids subjected to cyclic contact. The model is based on the step-by-step calculation of fatigue crack propagation paths in the contact region which includes the criteria of local fracture of materials under complex stress–strain state, characteristics of fatigue crack growth resistance of materials and also presupposes the possible change of fracture mechanisms (transversal shear – normal opening fracture mechanisms). Within the frames of the model the peculiarities of formation of such typical contact fatigue damages like pits, spalls, squat (“dark spot”) and cracking (“checks”) in rolling bodies and edge cracks growth in the elements of fretting couples under conditions of sliding/sticking between them are investigated. Examples of assessing the life time by damages formation (pitting and spalling) in the contact region are presented.     

The effect of crack surface interaction on the stress intensity factor in Mode III crack growth in round shafts

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interaction of the mutual fracture surfaces results in a pressure and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor.The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loading by considering a pressure distribution between mating fracture surfaces. The pressure between fracture surfaces results from climbing of asperities respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the interactions diminish beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.     

Effect of Closure of a Crack Caused by the Roughness of Its Surfaces on Fatigue Fracture under the Conditions of Transverse Shear

We develop a model aimed at the prediction of propagation of mode II fatigue cracks with regard for the interaction of their lips caused by the roughness of the fracture surfaces. In this model, the relationship between normal and shear contact stresses is described by the Amonton's law of friction and the plastic yield of the material in the prefracture zone is taken into account with the help of the model of thin plastic strips. The method of singular integral equations is used to solve the corresponding boundary-value problem for a plate with cracks propagating from two semiinfinite collinear notches. The distribution of contact stresses is determined and the stress intensity factors and displacements of the crack lips are evaluated. The proposed example is used to analyze the basic specific features of the influence of contact of the crack lips on fatigue fracture under the action of shear loads. The obtained results are confirmed by the experimental data on the propagation of mode II fatigue cracks in specimens of HY-130 steel.     

THE EFFECT OF MICROSTRUCTURE AND FRACTURE SURFACE ROUGHNESS ON FATIGUE CRACK PROPAGATION IN A Ti-6A1-4V ALLOY

Characteristics of fatigue crack propagation (FCP) have been studied on materials with three different microstructures of a Ti-6A1-4V alloy, prepared with different heat treatments. The effect of microstructure on the FCP behaviour was attributed to the development of crack tip shielding, primarily resulting from the role of crack path morphology in inducing crack closure and crack deflection. Roughness-induced crack closure played an important role on the near-threshold FCP behaviour at a stress ratio of 0.05, but the FCP data plotted in terms of the effective stress intensity factor range, δK_eff (allowing for crack closure), still exhibited the effect of microstructure. Fractographic examinations were performed, using a scanning electron microscope (SEM) with the aid of image processing, which enabled a three-dimensional reconstruction of the fracture surface using a stereo pair of SEM micrographs. Fracture surface roughness was evaluated quantitatively by the ratio of the real area of the reconstructed fracture surface to its projected area. As fracture surface roughness was taken into account in evaluating the FCP data in addition to crack closure, the effect of microstructure disappeared, indicating that the intrinsic FCP resistance was the same in all the materials. Thus, it was concluded that fracture surface roughness was a dominating parameter in controlling the FCP of the Ti-6A1-4V alloy.