Analytical modeling of fatigue crack propagation in metals coupled with elasto-plastic deformation

In the present investigation, the G _max criterion, which is based on the elastic strain energy principle, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the plastic strain energy and, hence, a new elasto-plastic energy-based model is presented. Subsequently, the proposed model is employed to predict fatigue crack growth in rectangular steel plates under complex stress states. The results obtained using the elasto-plastic energy model proposed are compared with those obtained using the commonly used Paris law and our experimental data.     

Fatigue behaviour characterization of the fibre-matrix interface

The fracture behaviour of FRP composite materials is significantly influenced by the behaviour of the fibre-matrix interfacial bond. Thus far interfacial bond mechanical characterization has been based upon the critical strength and critical fracture energy of debonding. Characterization of the fatigue behaviour of the interfacial debonding process, however, may be more valuable for composite design and fibre-matrix selection. A fracture mechanics model of interfacial bond fatigue based on the mode II strain energy release rate (G _II) is presented. An expression forG _II is derived for a single fibre in matrix cylinder model. By fitting the model to single fibre pull-out fatigue test data, fatigue crack propagation plots for specific fibre-matrix combinations can be drawn. These should prove useful for the development of fatigue resistant FRP composite materials.     

Fracture indentation beneath flat and spherical punches

The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy , and that the critical strain energy release rateG _c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2<G<G _c. The 1971 experimental results of Mikosza and Lawn are easily interpreted by this model. Finally, experiments performed on a borosilicate glass give results that agree satisfactorily with the theory. Due to kinetic effects, an apparent surface energy of about 4.5 J m^–2 is obtained, larger than the intrinsic surface energy and slightly lower than the fracture energy derived from high-speed experiments.     

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

Influence of mode mixity and loading conditions on the fatigue crack growth behaviour of an epoxy adhesive

Adhesive joints usually experience mixed mode and mostly cyclic stresses conditions during their service life. The aim of the current research is to investigate the fatigue behaviour of a structural epoxy adhesive. Pure modes I and II and mixed mode tests were carried out to study the fracture and fatigue crack growth (FCG) behaviour of the adhesive. Compliance‐based beam method was considered for experimental fracture energy measurement. The effects of load level and load ratio on the mode I FCG behaviour and Paris law parameters were also investigated. Result showed that the effect of load level on fatigue crack propagation is more pronounced for lower R ratios. It was found that when the crack faces are closer during the unloading process, the difference between the R² and G_min/G_max is higher. Some possibilities are the crack closure phenomenon, difficulty in measuring the G_min , and the employed data reduction approach.     

Inverse method for identifying the underlying crack distribution in plates with random strengths

Summary In the current investigation we seek to identify the underlying crack number and crack length distributions in brittle plates with a known strength distribution. The inverse problem in probabilistic fracture mechanics is defined, and the numerical procedure to solve the inverse problem is constructed. The simulation process of generating simulated plates containing simulated random cracks is elaborated. The maximum strain energy release rate criterion (G _max) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the known plate strengths. The gamma, lognormal and two-parameter Weibull distributions are employed for the underlying crack length distribution, and are compared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presented as part of the demonstration of a method for using the crack distribution identified in the inverse problem to predict the strength and the probability of fracture in a practical application.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy

The micromechanisms of fatigue crack propagation in a forged, polycrystalline IN 718 nickel-based superalloy are evaluated. Fracture modes under cyclic loading were established by scanning electron microscopy analysis. The results of the fractographic analysis are presented on a fracture mechanism map that shows the dependence of fracture modes on the maximum stress intensity factor, K_max, and the stress intensity factor range, ΔK. Plastic deformation associated with fatigue crack growth was studied using transmission electron microscopy. The effects of ΔK and K_max on the mechanisms of fatigue crack growth in this alloy are discussed within the context of a two-parameter crack growth law. Possible extensions to the Paris law are also proposed for crack growth in the near-threshold and high ΔK regimes.     

Crack propagation in a glass particle-filled epoxy resin

Crack propagation in an epoxy resin reinforced with spherical glass particles has been followed using a double-torsion test. In particular the effect of strain rate, volume fraction and particle size upon the stability of propagation, the Young's modulus, the critical stress intensity factor,K _Ic and the fracture energy,G _Ic has been studied. It has been shown that the crack propagation behaviour can be explained principally in terms of crack pinning, although it has been found that propagation is also affected by blunting the breakdown of the particle—matrix interface. It has been demonstrated that crack-front pinning is consistent with a critical crack opening displacement criterion.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

CORROSION FATIGUE FRACTURE BEHAVIOUR OF A SiC WHISKERALUMINIUM MATRIX COMPOSITE UNDER COMBINED TENSIONTORSION LOADING

We describe an investigation into the fatigue fracture behaviour under combined tension–torsion loading of a SiC whisker-reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061-T6, under load-controlled conditions with a constant value of the combined stress ratio, α = τ_max /σ_max in laboratory air or in a 3.5% NaCl solution at the free corrosion potential. The corrosion fatigue strength of both the matrix and composite was less in the solution than in air. The dominating mechanical factor that determined the fatigue strength in air was either the maximum principal stress or the von Mises-type equivalent stress, depending on the combined stress ratio. However, in the 3.5% NaCl solution, the corrosion fatigue strength of both materials was determined by the maximum principal stress, irrespective of the combined stress ratio. In the case of the matrix material, crack initiation occurred by a brittle facet normal to the principal stress due to hydrogen embrittlement. However, in the composite material, the crack was initiated not at the brittle facet, but at a corrosion pit formed on the specimen surface. At the bottom of the pit, a crack normal to the principal stress was nucleated and propagated, resulting in final failure. Pitting corrosion was nucleated at an early stage of fatigue life, i.e. about 1% of total fatigue life. However, crack initiation at the bottom of a pit was close to the terminal stage, i.e. about 70% or more of total fatigue life. The dominating factor which determined crack initiation at a pit was the Mode I stress intensity factor obtained by assuming the pit to be a sharp crack. Initiation and propagation due to pitting corrosion and crack growth were closely examined, and the fatigue fracture mechanisms and influence of the 3.5% NaCl solution on fatigue strength of the composite and matrix under combined tension–torsion loading were examined in detail.     

Determination of double-Determination of double-K criterion for crack propagation in quasi-brittle fracture Part I: experimental investigation of crack propagation

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kⁱⁿⁱ, which can be directly evaluated by the initial cracking load, P_ini, and the precast crack length, a₀, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with K^un, which can be obtained inserting the maximum load, P_max, and the effective crack length, a, into the same formula of LEFM. The values of the two parameters, K _Ic ⁱⁿⁱ and K _Ic ^un , obtained from the small size three-point bending notched beams and the large size compact tension specimens show that K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent. Evaluating with the K-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the K-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.     

Investigation of crack closure in stainless steel by laser interferometry

The effect of strain-induced martensite transformed during fatigue on the fatigue crack propagation rate near ΔK _th, as well as low-cycle fatigue behaviour of three differently heat-treated stainless steels, was investigated. The heat treatments were chosen so that austenite stability during fatigue was different. The crack closure stress during fatigue crack propagation near the ΔK _th region was measured using laser interferometry. The sensitized specimen showed the highest value of closure load ratio (K _cl/K _max), which was considered to be due to the roughness-induced crack closure caused by intergranular facets. The specimen with the lowest austenite stability showing the largest amount of strain-induced martensite during fatigue, showed the highest crack growth rate. The effect of brittle fracture through the harder strain-induced martensite was larger than that of possible transformation-induced crack closure.     

FATIGUE CRACK PROPAGATION CHARACTERISTICS OF GLASS FIBRE REINFORCED POLYCARBONATE IN HOT DISTILLED WATER

The fatigue crack propagation behaviour of polycarbonate and glass fibre reinforced polycarbonate was studied in hot distilled water. The effects of temperature, distilled water and glass fibre content on fatigue crack growth rate were determined. In distilled water at 333 K, the fatigue crack growth rate decreased with increasing glass fibre content. A melting was observed of the adhesive bond between the glass fibres and the matrix. It was evident that the fracture morphology closely relates to the fatigue crack growth rate which depends on the ΔK parameter rather than the K_max parameter when the materials are tested in hot distilled water.     

Analysis of the fracture behaviour of a stitched single-lap joint

The effect of stitching on the fracture response of single-lap composite joints was studied by a combined experimental and numerical analysis. Unstitched and Kevlar stitched joints were tested under static and fatigue loading to characterize damage progression and failure modes; a three-dimensional finite element analysis was carried out to evaluate the influence of stitches on strain energy release rates as a function of damage and to identify the role of various stitching parameters on the fracture behaviour of joints.It was observed that the failure of the joints occurs as a consequence of the propagation of delamination at the interface between the adherends; the propagation is stable under fatigue loads and unstable under static loads. Stitching does not improve the static strength of joints but significantly prolongs the duration of the crack propagation phase under fatigue loading.The results of finite element modelling indicate that the incorporation of stitches reduce G_I to zero after the delamination front passes the stitch line, but it is not effective in reducing mode II energy release rate. They also show that strain energy release rates are not greatly affected by the length of stitch-laminate debonding, which, conversely, does influence stitch tensioning. Moreover, 3D analysis reveals that stitches become less efficient in reducing the crack driving force with increasing stitching steps.     

A MODEL FOR THE EFFECT OF A GASEOUS ENVIRONMENT ON THE LEFM FATIGUE THRESHOLD CONDITION OF STEELS

Using a different approach to those methods involving hydrogen-embrittlement and crack-closure mechanisms a previously developed model is extended to predict the commonly observed effects of yield strength and a gaseous environment on the long-crack fatigue crack growth threshold. The model assumes the existence of two intrinsic thresholds namely an upper bound value and a lower bound value related to, respectively, K_max-controlled cleavage and δK-controlled reversed shear mechanisms of crack growth in a critically stressed volume at the crack tip. This new development assumes that nascent hydrogen atoms, liberated from moisture in the environment, assist in reducing dislocation mobility thereby rationalizing experimental observations on low strength materials in moist laboratory air when compared to a dry inert environment. Quantitative predictions of fatigue thresholds in laboratory air and inert environments show good agreement with experimental data for several low and high strength steels. This alternative procedure may be found to be useful in practical design applications when reasonably fast and accurate estimates are required.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Crack growth simulation for arbitrarily shaped cracks based on the virtual crack closure technique

In this paper, crack growth simulation for arbitrarily shaped cracks was investigated based on the virtual crack closure technique. During simulations, the crack front was represented by an approximated zigzag line which had the same general shape as the given crack. For this approximated zigzag crack front, a modified approach was developed to determine the required nodal forces, virtually closed area and displacement opening. After the strain energy release rate G was calculated, crack growth was governed by the fracture criterion G/G _C = 1 at all the crack tip nodes. The important features of the proposed approach are that (i) a simple stationary finite element mesh can be used for arbitrarily shaped cracks and (ii) adaptive re-meshing technique is avoided in studying crack growth. Three cases having different initial crack shapes are presented to assess the validity of this approach and to evaluate the ease of use in tracking crack growth. Reasonable agreement between the present study and other approaches are obtained. The shape changes during crack propagation can also be tracked with ease.     

Energy rates and crack stability in small scale yielding

Crack stability in small scale yielding is traditionally analysed using the R-curve approach with toughness indexed by either of the linear elastic fracture mechanics parameters K or G. In ductile materials stable tearing commences well before crack instability and progresses under increasing G_R. This is often assumed to mean that toughness is increasing with crack growth. It is shown in this paper that a rising G_R curve is generated even when a crack propagates with constant toughness (constant energy dissipation rate). The paper demonstrates that this apparent anomaly occurs because G does not represent the energy input rate for a crack advancing under increasing load in an elastic-plastic material. The constant energy dissipation rate model is consistent with a size independent G_R curve; also crack instability predictions are identical with both theories. The G_R curve approach has practical advantages, but use of energy dissipation rate offers better physical insight and greater versatility when analysing tough materials.