Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

A modelling technique for calculating stress intensity factors for structures reinforced by bonded straps. Part I: Mechanisms and formulation

This paper describes a 2D FE modelling technique for predicting fatigue crack growth life of integral structures reinforced by bonded straps. This kind of design offers a solution to the intrinsic lack of damage tolerance of integral structures. Due to the multiple and complex failure mechanisms of bonded structures, a comprehensive modelling technique is needed to evaluate important design parameters. In this Part I of a two-part paper, the actions and mechanisms involved in a bonded structure are discussed first, followed by presenting the modelling approaches to simulate each mechanism. Delamination or disbond of the strap from the substrate is modelled by computing the strain energy release rate on the disbond front and applying a fracture mechanics criterion. Thermal residual stresses arising from the adhesive curing process and their redistribution with the substrate crack growth are calculated and taken into account in the crack growth analysis. Secondary bending effect caused by the un-symmetric geometry of one-sided strap is also modelled. In the classic linear elastic fracture mechanics, a non-dimensional stress intensity factor, i.e. the geometry factor β, depends only on the sample’s geometry. This β factor cannot be found for this kind of bonded structures, since the magnitude of disbond is related to the applied stress and the disbond size modifies the geometry of the structure. Moreover, secondary bending effect is geometric nonlinear thus the stress intensity factor cannot be normalised by the applied stress. For these reasons an alternative technique has been developed, which requires calculating the stress intensity factors at both the maximum and minimum applied stresses for each crack length. This analysis technique is implemented in a computer program that interfaces with the NASTRAN commercial code to compute the fatigue crack growth life of strap reinforced structures.     

Dependence of spectral shape of bremsstrahlung spectra on atomic number of target materials in the photon energy range of 5-30 keV

Dependence of spectral shape of total bremsstrahlung spectra i.e. the sum of ordinary bremsstrahlung (OB) and polarization bremsstrahlung (PB), on the atomic number (Z) of target materials (Al, Ti, Sn and Pb), produced by continuous beta particles of ⁹⁰Sr and ²⁰⁴Tl, has been investigated in the photon energy region of 5-30 keV. It has been found that the spectral shape of total bremsstrahlung spectra, in terms of S (k, Z) i.e. the number of photons of energy k per m_oc² per beta disintegration, is not linearly dependent on the atomic number (Z) of the target material and rather it is proportional to Zⁿ. At lower photon energies, the index values ‘n’ of Z-dependence are much higher than unity, which is due to the larger contribution of PB into OB. The decrease in ‘n’ values with increase of photon energy is due to the decrease in contribution of PB into OB. It is clear that the index ‘n’ values obtained from the modified Elwert factor (relativistic) Bethe-Heitler theory, which include the contribution PB into OB, are in agreement with the experimentally measured results using X-PIPS Si(Li) detector. Hence the contribution of PB into the formation of a spectral shape of total bremsstrahlung spectra plays a vital role.     

Numerical simulation of fatigue crack propagation in friction stir welded joint made of Al 2024-T351 alloy

In this work, fatigue crack propagation in thin-walled aluminium alloy structure with two friction stir welded T joints has been simulated numerically. Crack propagation in stiffened part of the structure between two friction stir welded T joints is analysed by using the eXtended Finite Element Method (XFEM), including software ABAQUS, as well as MORFEO, for modelling and results display. Tensile fatigue loading is applied, with stress ratio R = 0, and maximum stress σ_max = 10 MPa. Material properties (Al 2024-T351, as used in aeronautical industry) in different welded joints zones are adopted from available literature data. Following results are obtained by numerical analysis: stress–strain and displacement state in the structure, position of the crack tip and value of stress intensity factor for every crack propagation step, as well as the structural life estimation, i.e. number of load cycles, N, also for each crack propagation step. Using these results the number of cycles at which the crack starts to propagate in an unstable manner is predicted.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

Crack initiation strength of an interface between a submicron-thick film and a substrate

The focus of this study was to evaluate the fracture initiation criteria of the interface between a thin film and a substrate by Bogy’s, Kitamura’s and Griffth’s methods. The critical stress intensity parameter K_ijC in Bogy’s method and the concentrated stress parameter σ_ijC in Kitamura’s method were calculated based on the singular stress field near the interface edge. The work of separation per unit area Γ_ο in Griffth’s method was calculated based on the work of fracture process. The results obtained show that in comparison among interface strengths, the fracture toughness K_θθC and the concentrated stress parameter σ_θθC were respectively applied to material combinations with specific edge geometry and with weak stress singularity, while the work of separation per unit area Γ_ο was applied in all cases.     

Evaluation of overload-induced fatigue crack growth retardation parameters using an exponential model

In this study, fatigue crack growth rate in mixed-mode overload (modes I and II) induced retardation zone has been predicted by using an “Exponential model”. The important parameter of this model is the specific growth rate. This has been correlated with various crack driving parameters such as stress intensity factor range, maximum stress intensity factor, equivalent stress intensity factor, and mode mixity, as well as material properties such as modulus of elasticity and yield stress. An equation has been formulated for specific growth rate which has been used to calculate crack growth rate under mixed-mode loading conditions. It has been observed that the crack growth rate predicted by the model is in good agreement with experimental results.     

Self-similarity and crack growth instability in the correlation between the Paris’ constants

In this note the question about the existence of a correlation between the parameters C and m of the Paris’ law is re-examined. According to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter C to m and to the governing variables of fatigue is derived. Then, from the observation that the Griffith-Irwin instability must coincide with the Paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. A fair good agreement is found between the proposed theory and extensive experimental data.     

Fatigue life prediction based on crack closure for 6156 Al-alloy laser welded joints under variable amplitude loading

A fatigue prediction approach is proposed using fracture mechanics for laser beam welded Al-alloy joints under stationary variable amplitude loading. The proposed approach was based on the constant crack open stress intensity factor in each loading block for stationary variable amplitude loading. The influence of welding residual stress on fatigue life under stationary variable amplitude was taken into account by the change of crack open stress intensity factor in each loading block. The residual stress relaxation coefficient β = 0.5 was proposed to consider the residual stress relaxation for the laser beam welded Al-alloy joints during the fatigue crack growth process. Fatigue life prediction results showed that a very good agreement between experimental and estimated results was obtained.     

Interaction of residual stress with mechanical loading in a ferritic steel

A well-defined residual stress field was introduced into modified single edge notched bend, SEN(B), specimens by the ‘in-plane compression’ procedure in order to investigate the interaction between residual stress and applied mechanical loading. Numerical predictions of the residual stress field arising from the in-plane compression procedure are given along with details of the numerical fracture modelling and experimental fracture test results made on A533B ferritic steel specimens in the lower transition region at −150 °C. Use was made of a recently developed finite element post-processor capable of determining path-independent J-integral values in the presence of residual stress fields. The paper compares the experimental results to predictions made using a probabilistic ‘global approach’ based on the conventional crack-tip parameters K and J and predictions made using a well-known structural integrity assessment code, R6 (Revision 4). It is shown that obtaining more accurate estimates of the crack driving force created by residual stresses leads to better correlation between experiments and predictions, and less conservatism in the assessment code.     

Optimum blade configurations for the cutting of soft solids

For the same amount of work in separating surfaces of soft solids, the forces normal and tangential to an element of a cutting blade are determined by the local velocities of the material past the cutting edge, in particular by the ratio ξ of ‘slice’ to ‘push’ velocities. The greater the ξ, the lower the forces and hence reduced damage to the cut surfaces (i.e., better surface finish). Different examples are considered of flat blades of variable curvature (such spiral-profiled blades in food cutting machinery, scythes, sickles, sabres, etc.) where the local forces vary along the edge of the blade as the curvature changes. How to maximise ξ is discussed along with questions of whether the material to be cut is restrained or not. The mechanics of cutting by a cylinder lawn mower is also investigated. Here the blades are arranged on helices around the cylinder and ξ is determined by the helix angle and by N = (rω/f) which is the ‘gearing’ of the cylinder with respect to the forward speed of the machine. There is a compromise between low cutting forces and flatness of cut surface that has to be adopted in design of practical machines.     

A Strip-Yield algorithm for the analysis of closure evaluation near the crack tip

“Plasticity-induced crack closure” phenomenon is the leading mechanism of different effects (R-ratio, overload retardation, … ) acting on crack growth rate in many metallic materials. Experimental tests are carried out to quantify the physical phenomenon, while Strip-Yield analytical models have been developed for predicting life of components. In the present work, an additional module to be applied to a Strip-Yield model is proposed in order to derive the strains near the crack tip. Particularly, the module is based on the Westergaard’s elastic complex potential. The presented algorithm allowed us to obtain the correlation between “local compliance” experimental results and the corresponding Strip-Yield analyses. This method can be taken as a semi-analytical procedure for calibrating the constraint factor, i.e., the most delicate parameter for Strip-Yield models.     

On the strengthening effect of increasing cycling frequency on fatigue behavior of some polymers and their composites: Experiments and modeling

Effect of cycling frequency on fatigue behavior of neat, talc filled, and short glass fiber reinforced injection molded polymer composites was investigated by conducting load-controlled fatigue tests at several stress ratios (R = −1, 0.1, and 0.3) and at several temperatures (T = 23, 85 and 120 °C). A beneficial or strengthening effect of increasing frequency was observed for some of the studied materials, before self-heating became dominant at higher frequencies. A reduction in loss tangent (viscoelastic damping factor), width of hysteresis loop, and displacement amplitude, measured in load-controlled fatigue tests, was observed by increasing frequency for frequency sensitive materials. Reduction in loss tangent was also observed for frequency sensitive materials in DMA tests. It was concluded that the fatigue behavior is also time-dependent for frequency sensitive materials. A Larson–Miller type parameter was used to correlate experimental fatigue data and relate stress amplitude, frequency, cycles to failure, and temperature together. An analytical fatigue life estimation model was also used to consider the strengthening effect of frequency in addition to mean stress, fiber orientation, and temperature effects on fatigue life.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials under cyclic compression

For prediction of the fatigue crack growth (FCG) behavior under cyclic compression, a plasticity-corrected stress intensity factor (PC-SIF) range ΔK_pc is proposed on the basis of plastic zone toughening theory. The FCG behaviors in cyclic compression, and the effects of load ratio, preloading and mean load, are well predicted by this new mechanical driving force parameter. Comparisons with experimental data showed that the proposed PC-SIF range ΔK_pc is an effective single mechanical parameter capable of describing the FCG behavior under different cyclic compressive loading conditions.     

Fatigue behaviour and crack growth rate of cryorolled Al 7075 alloy

The effects of cryorolling (CR) on high cycle fatigue (HCF) and fatigue crack growth rate behaviour of Al 7075 alloy have been investigated in the present work. The Al 7075 alloy was rolled for different thickness reductions (40% and 70%) at cryogenic (liquid nitrogen) temperature and its tensile strength, fatigue life, and fatigue crack growth mechanism were studied by using tensile testing, constant amplitude stress controlled fatigue testing, and fatigue crack growth rate testing using load shedding (decreasing ΔK) technique. The microstructural characterization of the alloy was carried out by using Field emission scanning electron microscopy (FESEM). The cryorolled Al alloy after 70% thickness reduction exhibits ultrafine grain (ufg) structure as observed from its FESEM micrographs. The cryorolled Al 7075 alloys showed improved mechanical properties (Y.S, U.T.S, Impact energy and Fracture toughness are 430 Mpa, 530 Mpa, 21 J, 24 Mpa m^1/2 for 40CR alloy) as compared to the bulk 7075 Al alloy. It is due to suppression of dynamic recovery and accumulation of higher dislocations density in the cryorolled Al alloys. The cryorolled Al alloy investigated under HCF regime of intermediate to low plastic strain amplitudes has shown the significant enhancement in fatigue strength as compared to the coarse grained (CG) bulk alloy due to effective grain refinement. Fatigue crack growth (FCGR) resistance of the ufg Al alloy has been found be higher, especially at higher values of applied stress intensity factor ΔK The reasons behind such crack growth retardation is due to diffused crack branching mechanism, interaction between a propagating crack and the increased amount of grain boundaries (GB), and steps developed on the crack plane during crack-precipitate interaction at the GB due to ultrafine grain formation.     

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (R_eff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved.     

Application of the substructured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures

The substructured finite element/extended finite element (S-FE/XFE) approach is used to compute stress intensity factors in large aircraft thin walled structures containing cracks. The structure is decomposed into a ‘safe’ domain modeled with classical shell elements and a ‘cracked’ domain modeled using three-dimensional extended finite elements. Two applications are presented and discussed, supported by validation test cases. First a section of stiffened panel containing a through-thickness crack is investigated. Second, small surface cracks are simulated in the case of a generic ‘pressure membrane’ with realistic crack configurations. These two semi-industrial benchmarks demonstrate the accuracy, robustness and computational efficiency of the substructured finite element/extended finite element approach to address complex three-dimensional crack problems within thin walled structures.     

Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the microstructural support factor for different failure hypotheses: Part II: Microstructural support analysis

On the basis of the comprehensive and accurate stress field equations for sharp rounded V-notches derived in Part I of this contribution, the microstructural support factor of these notches is determined which quantifies the fictitious notch radius in Neuber’s elastic microstructural support concept. By means of Filippi’s equations and considering different failure criteria (Rankine, von Mises and Beltrami) the fictitious notch radius is evaluated for different notch opening angles as a function of the actual notch radius and the microstructural support length. Plane stress and, alternatively, plane strain conditions are introduced. Once the fictitious radius has been found, the support factor s is derived from the expression: fictitious notch radius minus actual notch radius divided by microstructural support length. The support factor s is found to be very sensitive to the notch opening angle, but constant ‘plateau values’ are determined for an actual radius greater than the microstructural support length. The dependence of s on the failure criterion and the multiaxiality conditions (plane stress or plane strain) is also investigated. Various numerical analyses using the FE method have been carried out to compare the theoretical stress concentration factor to the effective stress concentration factor, the former obtained by considering fictitiously rounded notches under tension loading using the plateau values of s, the latter obtained by integrating the relevant stress over the microstructural support length along the bisector of the pointed V-notch. Finally, dealing with out-of-plane shear loading, Neuber’s corresponding solution valid for sharp rounded notches is re-evaluated and the numerical analysis described above is extended to this loading case. All the comparisons above are preceded by elementary solutions for pointed notches in general. It is shown that the plateau values of s are well suited for engineering usage in structural strength assessments.     

Influence of mixed alkali on the spectral properties of vanadyl ions doped xNa2O-(30 − x)K2O-60B2O3 glasses—an EPR and optical study

Electron paramagnetic resonance (EPR) and optical investigations have been performed in the mixed alkali borate xNa₂O-(30 − x)K₂O-60B₂O₃ (5 ≤ x ≤ 25) glasses doped with 10 mol% of vanadyl ions in order to look for the effect of ‘mixed alkalis’ on the spectral properties of the glasses. The observed EPR spectra have structures for x > 5 mol% which are characteristic of a hyperfine interaction arising from an unpaired electron with the ⁵¹V nucleus and it builds up in intensity as x increases. It is observed that the mixed alkali play a significant role in accommodating the vanadyl ions in these mixed alkali glasses and for x > 5 mol%, shows a well resolved hyperfine structure typical for isolated VO²⁺ ions. The spin-Hamiltonian parameters (g and A), the dipolar hyperfine coupling parameter (P) and Fermi contact interaction parameter (k) have been evaluated. It is observed that the spin-Hamiltonian parameters do not vary much with the change in composition. It is observed that with increase of x, an increase occurs in tetragonal distortion for VO²⁺. The number of spins (N) participating in resonance and the paramagnetic susceptibility (χ) have been calculated. It is observed that N and χ increase with x. The optical bandgap energies evaluated for these glasses slightly increase with x and reach a maximum around x = 20 and thereafter decrease showing the mixed alkali effect. Optical band gap energies obtained in the present work vary from 2.73 to 3.10 eV for both the direct and indirect transitions. The physical parameters of the glasses are also determined with respect to the composition.