Discussions of three-dimensional models for mixed-mode fatigue crack growth

This technical note discusses several three-dimensional models for mixed-mode fatigue crack growth that were developed recently by Bian and coauthors [1], [2], [3], [4] and [5]. However, these models are found being formulated from a generally incorrect three-dimensional crack-front stress field for embedded elastic elliptical cracks. The corresponding correct crack-front stress field for the elliptical cracks is thus presented, and then the three-dimensional fatigue crack growth models are corrected and expressed in much simpler functions.     

Microstructure Dependent Fatigue Cracking Resistance of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si Alloy

Fatigue cracking behavior from a notch was investigated at room temperature for Ti-6.5Al-3.5Mo-1.5Zr-0.3Si(TC11) alloys with four different microstructures obtained at different cooling rates from the β transus temperature.It was found that the alloy with lamellar structures consisting of α/β lamellae or acicular α’ martensite laths had a higher fatigue crack initiation threshold from the notch,while the bimodal structure with coarse α grain had a lower fatigue cracking resistance.The alloy with α/β lamellar structure showed a higher fatigue crack growth resistance.The length scales of the microstructures were characterized to correlate with fatigue cracking behavior.Fatigue cracking mechanism related to microstructures was discussed.     

A multifractal analysis of fatigue crack growth and its application to concrete

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structure size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.     

Extension of the Tanaka-Mura model for fatigue crack initiation in thermally cut martensitic steels

A multi scale numerical approach for evaluation of crack initiation and propagation in thermally cut structural elements made of martensitic steel is presented. A numerical simulation of micro-crack initiation is based on the Tanaka-Mura micro-crack nucleation model, where individual grains of synthetic microstructure are simulated using the Voronoi tessellation. Three improvements are added to this model (multiple slip bands, micro-crack coalescence and segmented micro-crack generation). Crack propagation is then solved on a macro scale model using linear elastic fracture mechanics approach. Some experimental tests have also been performed to check the accuracy of the numerical model. The results of the proposed computational model show a reasonable correlation with the experimental results.     

Influence of grain size on the small fatigue crack initiation and propagation behaviors of a nickel-based superalloy at 650 °C

GH4169 at 650 °C in atmosphere was investigated by using single edge notch tensile specimens. The number of main cracks and crack initiation mechanisms at the notch surface strongly depended on the grain size. The crack initiation life accounted for more percentages of the total fatigue life for the alloy with smaller grain size. The fatigue life generally increased with increasing crack initiation life. The small crack transited to long crack when its length reached ˜10 times the grain size.     

A general model to estimate life in notches and fretting fatigue

Fatigue in notched specimens and fretting fatigue are two different phenomena but they have in common the existence of a stress gradient. In these cases fatigue life estimation is usually considered as a superposition of an initiation and propagation phase. One of the main problems to estimate the fatigue life is to define the crack length where one phase finishes and the other begins. The model employed in this paper combines both phases without defining a priori the separation between them. The proposed model is applied to uniaxial and multiaxial fatigue in specimens with stress gradient: a group of fretting fatigue tests with spherical and cylindrical contact and another group of tests with notched specimens. The comparison between life estimations and experimental results allows checking the validity of the model in different conditions.     

Fatigue cracks nucleation on steel, acoustic emission and fractal analysis

In this paper, a new acoustic emission (AE) diagnostic technique, for the study of fatigue cracks nucleation and propagation on steel, was investigated. Using the fractal analysis, and the box-counting method (BCM) in particular, it is possible to characterize the spatial distribution of the prime AE sources through the fractal dimension (D) that evolve with the number of fatigue cycles (N) of the specimen. D–N curves were found useful to identify the condition of incipient collapse due to the nucleation and propagation of fatigue cracks on steel. It is possible to use the fractal dimension as a damage parameter. In all tested specimens, the crisis occurs within the same range of values of fractal dimension. The results suggest that it is possible to anticipate the detection of crack beginning relating to the other theoretical or experimental techniques.     

Numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under Gaussian excitation

The stationary vibrations of a beam excited by Gaussian noise are strongly affected by the presence of a fatigue crack. Indeed, as soon as the crack arises the system response becomes non-linear due to crack breathing and a non-Gaussian behaviour is encountered. The paper presents both numerical and experimental investigations in order to assess the capability of the non-Gaussianity measures to detect crack presence and position. Monte Carlo method is applied to evaluate in time domain the higher order statistics of a cantilever beam modelled by finite elements. The skewness coefficient of the rotational degrees of freedom appears the most suitable quantity for identification purpose being very sensitive to the non-linear behaviour of the cracked beam.     

Effect of magnetic treatment on fatigue life of AISI 4140 steel

The effect of magnetic field with different intensities on fatigue life of AISI 4140 steel has been investigated. For this purpose, unnotched and notched specimens were prepared from AISI 4140 steel. It was obtained that when the magnetic field especially was applied to the specimens at the stage of fatigue crack initiation, the fatigue life improved by reason of delaying formation time of slip bands due to regular direction and distribution of magnetic domains. And, it was observed that magnetic field was applied from the beginning of fatigue test up to occur the fatigue fracture, it was detrimental on the fatigue life because of over heating of the specimens.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Fatigue damage of high performance concrete through a 2D mesoscopic lattice model

Based on high-resolution digital images of High Performance Concrete (HPC) microstructures, a two-dimensional mesoscopic lattice model which accounts for fatigue damage is proposed. Fatigue damage is introduced by considering the coupled effects of loading cycles and tensile strain on stiffness degradation of microstructural lattice elements under fatigue loading. The ultimate tensile strain is defined as the failure threshold value for microstructural lattice elements. Further, the effects of the lattice element properties (i.e. size and finite element type) and fatigue loading parameters (i.e. stress levels) on the damage mechanisms of the HPC microstructure are investigated and discussed. It is found that lattice truss elements 1 mm long are satisfactory, giving also their smaller computational requirements in comparison to beam counterparts, to investigate fatigue damage in the HPC microstructure. The numerical results of the present model are consistent with experimental observations.     

Fatigue crack initiation and crystallographic crack growth in an austenitic stainless steel

The lifetime of a specimen under cyclic loading is usually limited by the initiation and growth of microcracks. Experimental results for the austenitic stainless steel X6 CrNiNb 18-10 are given and a model for crack initiation and crack growth in the first grains of a polycrystalline aggregate is proposed.     

Role of microstructure on initiation and propagation of fatigue cracks in precipitate strengthened Cu–Ni–Si alloy

Fatigue tests were conducted on round-bar specimens to understand the fatigue behavior of precipitate-strengthened Cu–6Ni–1.5Si alloy. Aging at 500 °C for 0.5 h produced δ-Ni₂Si precipitates in the matrix, homogeneously and heterogeneously precipitated δ-Ni₂Si particles, and a precipitate-free zone around the grain boundaries. The cracks were initiated at the grain boundaries, followed by growth along the crystallographic slip planes in the adjacent grains. Crack propagation from the crack origin along the grain boundaries was occasionally observed. The physical background of fatigue damage is discussed in light of the role of microstructure on the behavior of fatigue cracks.     

Fatigue behaviour of bare and pre-corroded magnesium alloy AZ31

Constant amplitude fatigue tests have been performed using smooth specimens of a rolled AZ31 magnesium alloy in order to assess the fatigue behaviour of the material. The tests were periodically interrupted and replicas were taken from the surface of the specimens in order to reveal crack initiation and early crack propagation. Based on the derived S–N curve a very high stress sensitivity of the fatigue life can be concluded; it may be attributed to the inability of the material to accumulate fatigue damage in terms of cyclic plasticity at the early stage of fatigue. Fatigue cracks initiate already after few fatigue cycles between strain incompatibility points (e.g. grain boundaries) due to difficulties in satisfying the von Mises criterion. The initiation and propagation mechanisms of the fatigue cracks are characterized as cleavage. Furthermore, the corrosion susceptibility of the material has been investigated in a salt spray environment. It becomes evident that the presence of corrosion damage, in terms of corrosion pitting, results in the development of stress concentration, facilitating essentially the initiation and propagation of fatigue cracks. Thus, the fatigue limit is reduced to 50% of the respective value of the un-corroded material.