Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

The preferred fatigue crack propagation mode in a M250 maraging steel loaded in shear

Macroscopic torsional fatigue cracks are shown to propagate in shear, in plain tubular specimens, in the M250 maraging steel, for stress ranges from 90% down to 40% of the yield stress. This cannot be explained in terms of microcrack coalescence for the smallest stress range, for which microcracks are scarce. The kinetics and mechanisms of mode II fatigue crack growth are thus investigated, using precracked CTS or tubular specimens. For a high Δ K _II , slowly decelerating mode II propagation takes place for a distance that increases with Δ K _II before branching occurs. Friction stresses along the crack flanks shield the applied load and explain this deceleration. An inverse analytical procedure is used to derive the effective stress intensity factor, allowance being made for friction effects, from displacement profiles measured from microgrids using a scanning electron microscope. The measured crack growth rates correlate much better with the effective stress intensity factor than with the nominal Δ K _II value. The crack paths observed in torsion are discussed in terms of maximum crack velocity.     

Shear mode fatigue crack growth in 1050 aluminium

The shear mode crack growth mechanism in 1050 aluminium was investigated using pre‐cracked specimens. A small blind hole was drilled in the centre section of the specimens in order to predetermine the crack initiation position, and a push–pull fatigue test was used to make a pre‐crack. Crack propagation tests were carried out using both push–pull and cyclic torsion with a static axial load. With push–pull testing, the main crack grew by a mixed mode. It is thus apparent that shear deformation affects the fatigue crack growth in pure aluminium. In tests using cyclic torsion, the fatigue crack grew by a shear mode. The micro‐cracks initiated perpendicular and parallel to the main crack's growth direction during the cyclic torsion tests. However, the growth direction of the main crack was not changed by the coalescence of the main crack and the micro‐cracks. Shear mode crack growth tends to occur in aluminium. The crack growth behaviour is related to a material's slip systems. The number of slip planes in aluminium is smaller than that of steel and the friction stress during edge dislocation motion of aluminium is lower than many other materials. Correlation between the crack propagation rate and the stress intensity factor range was almost the same in both push–pull and cyclic torsion with tension in this study.     

Fatigue strength of spring steel with small scratches

In compression coil springs subjected to cyclic load, fatigue cracks can sometimes initiate and propagate from scratch‐like small defects produced during the manufacturing process and degrade the fatigue strength. In this study, torsional and rotating bending fatigue tests were conducted to examine the fatigue behavior of a high‐strength spring steel (JIS G 3561, SWOSC‐V) in the presence of small scratches. The sensitivity of the HCF and VHCF strength to small scratches was evaluated based on the parameter model.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

Microstructural effects on the short crack behaviour of a stainless steel weld metal during low-cycle fatigue

An experimental study into microstructural effects on short fatigue crack behaviour of 19 stainless steel weld metal smooth specimens during low-cycle fatigue is performed by a so-called ‘effective short fatigue crack criterion’. This material has a mixed microstructure in which it is difficult to distinguish the grains and measure the grain diameter. The columnar grain structure is made up of matrix-rich δ ferrite bands, and the distance between the neighbouring rich δ ferrite bands is an appropriate measurement for characterizing this structure. Particularly, the effective short fatigue cracks (ESFCs) always initiate from the bands of δ ferrite in the matrix in the weakest zone on one of the specimen surface zones which is orientated in accordance with the inner or outer surface of welded pipe from which the specimens were machined. These cracks exhibit characteristics of the microstructural short crack (MSC) and the physically small crack (PSC) stages. The average length of the ESFCs at the transition between MSC and PSC behaviour is ≈40 μm, while the corresponding fatigue life fraction is ≈0.3 at this transition. Different from previous test observations, the growth rate of the dominant effective short fatigue crack in the MSC stage still shows a decrease with fatigue cycling under the present low-cycle fatigue loading levels. A statistical evolution analysis of the growth rates reveals that the short fatigue crack growth is a damage process that gradually evolves from a non-ordered (chaotic) to a perfectly independent stochastic process, and then to an ordered (history-dependent) stochastic state. Correspondingly, the microstructural effects gradually evolve from a weak effect to a strong one in the MSC stage, which maximizes at the transition point. In the PSC stage, the effects gradually evolve from a strong to weak state. This improves our understanding that the short crack behaviour in the PSC stage is mainly related to the loading levels rather than microstructural effects.     

Interaction effect of adjacent small defects on the fatigue limit of a medium carbon steel

Structural steels contain various material irregularities and natural defects which cause local stress concentrations from which fatigue cracks tend to initiate. Two defects in close proximity to each other may affect local stress distributions, and thus, begin to interact. In this paper, the effect of interacting small cracks on the fatigue limit is systematically investigated in a medium carbon steel. The growth of interacting cracks, as well as the characteristics of non-propagating cracks and microstructural aspects, was closely examined via the plastic replica method. It was found that although the fatigue limit is essentially controlled by the mechanics of interacting cracks, based on their configuration, the local microstructure comprised ferrite and pearlite has a statistical scatter effect on the behaviour of interacting cracks and non-propagating thresholds. With respect to the fatigue limit, when two defects were in close proximity, they behaved as a larger single defect. However, with greater spacing between defects, rather than mechanical factors, it is the local microstructure which determines the location and characteristics of non-propagating cracks.     

Statistical analysis on rolling contact fatigue in railroad axle bearing steel

High‐strength steels are widely used in high‐performance bearings utilized in most mechanical systems. However, there has been little statistical analysis regarding the fatigue failure behaviour of the material, where surface peeling resulted from contact fatigue during rolling is a significant life‐limiting mechanism. In this study, we examine the statistical behaviour of surface‐crack nucleation, propagation, and peeling in a high‐speed train axle bearing made of GCr15 steel by using a laboratory rolling‐contact equipment. We reveal that cyclic rolling‐contact leads to the formation of a hardness gradient in the outer ring of the bearing. The gradient layer is of several millimetres. The peeling rate could be as high as 28 μm per million cycles when the contact pressure is close to that applied in real service. Peeling‐induced cracking is dominantly transgranular. The incipient angle is about 23.2°, and its depth could be hundreds of micrometres. The findings reported here could be employed to assess the lifetime of bearings made of GCr15 steel and possible other engineering metals.     

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.     

Elastic correction of fatigue crack growth laws

Fatigue crack growth (FCG) is usually studied assuming that ΔK is the driving parameter. An effective ΔK is considered in the presence of crack closure. However, after crack opening, there is an elastic regime that does not contribute to FCG. The objective here is to quantify this elastic range of ΔK, ΔK_el, for different loading conditions and material properties. The yield stress was found to be the most important material parameter, followed by the hardening exponent. A linear decrease of ΔK_el with ΔK was found for the 7050‐T6, 6082‐T6, and 6016‐T4 aluminium alloys, while the 304L stainless steel presented a slight increase. On the other hand, the increase of K_max was found to increase the elastic fatigue range. Relatively high values of elastic range were obtained for the plane strain state, compared with the plane stress state.     

Short fatigue crack propagation during low-cycle,high cycle and very-high-cycle fatigue of duplex steel – An unified approach

The present paper reviews experimental results on the fatigue damage of austenitic–ferritic duplex steel under various load levels ranging from LCF to VHCF, placing the focus towards the relationship between the crystallographic orientation of individual grains and grain patches that exhibit slip band formation, fatigue crack initiation and growth. A combination between fatigue testing of electropolished specimens and analytical electron microscopy (SEM/EBSD, TEM) revealed that under LCF loading conditions almost all the ferrite and the austenite grains showed plasticity, while under HCF and VHCF loading conditions, slip band formation was limited to the softer austenite grains and a low plastic activity is observed in the ferrite. Once being formed, the bands generate high stress concentrations, where they impinge the α–γ phase boundaries, eventually, leading to the crack initiation. This is discussed by applying a numerical simulation approach based on the finite-element (FEM) and the boundary-element (BEM) method.     

A micromechanical approach to fatigue in small notches*

The present work shows the application to small notches of a micromechanical model which describes the growth of a short crack across the steep stress gradient generated at the root of a notch. The model, based on the theory of distributed dislocations, takes into account the interaction between short cracks and material barriers such as grain boundaries. The term ‘small notches’ refers in this paper to stress raisers the size of which is of the same order as the characteristic microstructural unit of the material. Typical examples are superficial scratches, corrosion pits, inclusions or pores. Comparisons between predicted fatigue limits and experimental results reported in the literature for different materials containing small artificial defects are shown and discussed.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

S–N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel

The S – N curve obtained from cantilever-type rotary bending fatigue tests using hour-glass-shaped specimens of high carbon-chromium bearing steel clearly distinguished the fracture modes into two groups each having a different crack origin. One was governed by crystal slip on the specimen surface, which occurred in the region of short fatigue life and a high stress amplitude level. The other was governed by a non-metallic inclusion at a subsurface level which occurred in the region of long fatigue life and low stress amplitude. The inclusion developed a fish-eye fracture mode that was distributed over a wide range of stress amplitude not only below the fatigue limit defined as the threshold for fracture due to the surface slip mode but also above the fatigue limit. This remarkable shape of the S – N curve was different from the step-wise one reported in previous literature and is characterized as a duplex S – N curve composed of two different S – N curves corresponding to the respective fracture modes. From detailed observations of the fracture surface and the fatigue crack origin, the mechanisms for the internal fracture mode and the characteristics of the S – N curve are discussed.     

Mixed-mode crack opening displacement measurements for small fatigue cracks growing in Astroloy at 20 °C

Crack opening displacements were measured for small fatigue cracks in Astroloy being grown with uniaxial stress application under high-cycle fatigue conditions. Four cracks were investigated including one that grew from 27 to 74 μm in three increments. Most of the cracks grew at an angle to the loading axis and all opened bimodally. Crack opening scaled with distance from the crack tip similar to an elastic crack, which allowed the calculation of a local stress intensity factor for both mode I and mode II. The proportion of mode II stress intensity factor was relatively large, varying as 0.06 < Δ K _II /Δ K _I < 0.42, with an average of ~0.3. Thus, uniaxial loading remote to the cracks resulted in a bimodal opening response on the scale of the cracks.     

Branch crack development from the flank of a fatigue crack propagating in mode II

The propagation of fatigue cracks in mode II often leads to the development of a branch starting from a crack flank, some distance behind the tip and not to the expected bifurcation at the crack tip. This type of branch is suggested to initiate by decohesion along a secondary slip plane and to grow in mode I due to the tensile component of the mode II stress field. Finite element calculations are performed to evaluate the stress intensity factors for the main crack and the branch as a function of the position of the latter. It is shown that the branch has a substantial shielding effect on the main crack and generates contact forces along its flanks. The simultaneous and competitive growth of the main crack and the branch in fatigue is simulated step by step using kinetic data for mode II and mode I obtained for a maraging steel.     

The effect of grain size on small fatigue crack growth in pure titanium

The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = −1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range ΔK_eff (after allowing for crack closure, the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, η, of growth rate in coarse-grained material were smaller than those in fine-grained material. The η values were significantly large at a/d 3 (a = crack depth, D = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size.     

Determination of the length dependence of the threshold for fatigue crack propagation

A rising load amplitude crack growth test on specimens pre-cracked in cyclic compression is presented as a procedure to determine the length dependence of the threshold of fatigue crack propagation described by the R(resistance)-curve for the threshold of stress intensity factor range. The experimental results show that the residual stress field in front of the pre-crack can significantly influence the R-curve.In order to measure the material specific R-curve which is not affected by the pre-cracking condition it is important to use the smallest possible load amplitude. To achieve this goal, a very small notch root radius is essential. It is shown that at notches machined by razor blade polishing technique the load amplitude for pre-cracking can be reduced to values where the load history does not influence the R-curve for the threshold of stress intensity range.