Influence of microstructure on the cyclic crack growth in a low-alloy steel

Fatigue tests have been performed on compact type and 4-point bend specimens of a low-alloy steel BS4360-50D in air at 30 Hz and at various stress ratios to determine the influence of microstructure on the fatigue crack propagation. Region I of the crack growth showed crystallographic facets, while two classes of secondary cracks were observed in Region II. Ductile tearing occurred in Region III and some dimple formation was also observed.     

Determination of threshold stress intensities: fatigue of low alloy steel BS4360-50D

An experimental method for obtaining the effective stress intensities necessary for cyclic crack growth prediction is described. Also, it is shown that the critical threshold value, ΔK_{c, th}, can be estimated using simple energetic considerations, leading to an equation:

$\text{Δ}\text{K}{}_{\mathrm{c,th}}\text{=}\text{4π}\text{E}\text{λ}{}_{\mathrm{s}}\text{2?}\text{(θ}{}_{\mathrm{uts}}\text{?}{}_{\mathrm{f}}\text{)}\text{((1+}\text{n}\text{)θ}{}_{\mathrm{yc}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

The threshold values obtained compare well with the experimentally observed values for a structural steel BS 4360-50D and for other steels.     

Corrosion fatigue of BS 4360:50D structural steel in seawater

Research on through-thickness defects is reported for BS 4360:50D structural steel in air and in seawater; the results of experiments on the propagation of surface-breaking, semi-elliptic flaws under three-point bend loading are also presented. The mechanisms of corrosion fatigue crack growth of through-thickness and semi-elliptic cracks in seawater are considered, and the application of crack growth data to endurance tests on welded cruciform and tubular joints is discussed.     

A Dislocation barrier model for fatigue crack growth threshold

The primary mechanism of fatigue crack growth is crack-tip dislocation emission followed by the glide of the emitted dislocations. Both of these two processes are controlled by the crack-tip resolved shear stress field, which is characterized by the resolved shear stress intensity factor, . A dislocation barrier model for fatigue crack growth threshold is constructed. The model assumes that a fatigue crack stops growing when crack-tip slip bands are incapable of penetrating the primary dislocation barrier. The derived and deduced threshold behaviors agree with the observed constant threshold K_max,th in the low R region and constant threshold ΔK_th in the high R region. K_max,th is the K_max at the threshold. The constant K_max,th is related to the resistance of the primary dislocation barrier, which in most of cases is grain boundary; and the constant ΔK_th is related to the resistance of secondary barriers. Furthermore, the analysis shows that K_max,th is proportional to √d, where d is the grain size. The relation has been observed in steels. The model also helps to explain the characteristics of, and the transition from, microstructure-sensitive to microstructure-insensitive growth. This revised version was published online in July 2006 with corrections to the Cover Date.     

Prediction of threshold and ultra-low fatigue crack growth rates

A model was derived to predict the true threshold value for fatigue crack growth in the absence of crack closure. The model, based only on the tensile and cyclic properties of the material, was successfully verified against a set of experimental data on medium and high strength steels and one aluminium alloy. Good agreement with experimental results was also obtained for Region I of the $\text{d}\text{a/}\text{d}\text{N vs ΔK}$ curve using a fatigue crack growth rate equation based on the same model.Fatigue crack growth data obtained from the medium strength steel CK45 in the normalized state and two heat-treated conditions were analysed. Good data correlation was shown using a previously developed normalizing parameter, $\text{φ = (ΔK}{}^2\text{?ΔK}{}^2{}_{\mathrm{<mtext>th</mtext>}}\text{)/(K}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{?K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, in the entire range of fatigue crack growth rates and for stress ratios ranging from 0.1 to 0.8.     

A cumulative model of fatigue crack growth

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.     

A third-order state-space model for fatigue crack growth

A second‐order state‐space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1 - 4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075‐T6 and 2024‐T3 at constant‐amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third‐order state‐space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second‐order state‐space model is treated as the third state variable in this model. Through simulations, it is shown that the third‐order state‐space model gives better predictions than the second‐order state‐space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.     

Interfacial fatigue crack growth in foam core sandwich structures

This paper deals with the experimental measurement of face/core interfacial fatigue crack growth rates in foam core sandwich beams. The so-called ‘cracked sandwich beam’ specimen is used, slightly modified, which is a sandwich beam that has a simulated face/core interface crack. The specimen is precracked so that a more realistic crack front is created prior to fatigue growth measurements. The crack is then propagated along the interface, in the core material, during fatigue loading, as is assumed to occur in a real sandwich structure. The crack growth is stable even under constant amplitude testing. Stress intensity factors are obtained from the FEM which, combined with the experimental data, result in standard da/dN versus ΔK curves for which classical Paris’ law constants can be extracted. The experiments to determine stress intensity factor threshold values are performed using a manual load-shedding technique.     

A threshold fatigue crack closure model: Part I – model development

A fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out‐of‐plane cracking and multi‐axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two‐dimensional sawtooths, whose geometry induces mixed‐mode crack‐tip stresses. Continuum mechanics and crack‐tip dislocation concepts are combined to relate crack face displacements to crack‐tip loads. Geometric criteria are used to determine closure loads from crack‐face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

On the relationship between fatigue limit,threshold and microstructure of a low-carbon Cr-Ni steel

The relationship between the fatigue limit stress range, Δσ_w, the threshold stress intensity factor, ΔK_th, and microstructure of low-carbon 12CrNi3A steel has been investigated. Non-propagating microcracks were observed on the surface of smooth specimens which has been subjected to at least 5 × 10⁶ cycles at the fatigue limit stress. The size of the cracks depended on the characteristic sizes of the microstructure of the material. Scanning electron microscopy showed that the fractographic characteristics in the near-threshold region of fatigue macrocrack growth were similar to those in the fatigue microcrack initiation region. This implies that the fatigue limit and fatigue threshold of the material have a similar physical meaning, both signifying the resistance of the material to the propagation of fatigue cracks. The relationship ΔK_th = 1.12Δσ_W √πα was shown to be valid, where a is a material parameter relating to microstructure, rather than to the length of a macrocrack. The results also showed that the value of a depends on the material and microstructure, and that both Δσ_W and ΔK_th will change if the microstructural characteristics of the material change.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

A comparison of different methods to determine the threshold of fatigue crack propagation

Three different methods for determining the threshold value for fatigue crack growth — the load-shedding technique, the stepwise increase of load amplitude on specimens precracked in cyclic compression, and decrease of stress intensity range at a constant maximum stress intensity — were applied to a high-strength aluminium alloy. The load-shedding technique tended to lead to higher values of the threshold, especially at low R-ratios. The threshold determined with decreasing stress intensity range at a constant maximum stress intensity was larger than the effective threshold determined with stepwise increasing of load amplitude on specimens precracked in cyclic compression.     

A threshold fatigue crack closure model: Part II – experimental verification

Predictions from an analytical model that considers contributions and interactions between plasticity, roughness, and oxide induced crack closure are presented and compared with experimental data. The analytical model is shown to correctly predict the combined influences of crack roughness, oxide debris, and plasticity in the near‐threshold regime. Furthermore, analytical results indicate closure mechanisms interact in a non‐linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.     

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

Fatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.