The retardation phenomenon of fatigue crack growth in HT80 steel

The fatigue crack growth behavior resulting from single and multiple applications of overload was investigated for HT80 steel. A peak load was found to cause retardation of the crack growth rate, which becomes stronger with increasing the peak/baseline stress ratio or with decreasing baseline stress intensity. Multiple overloads resulted in additional retardation. These experimental data were explained according to a new model based on crack closure conception, being correlated with the residual plastic zone size ahead of crack tip induced by the peak overload(s). The proposed formulation of retardation was expressed simply as a function of peak/baseline stress ratio, $\text{r}$, and two material parameters, $\text{m}$ and β. $\text{m}$ the exponent parameter in Paris equation and β is the ratio of crack distance at the maximum retardation to the residual plastic zone size. The retardation was predicted to increase with increasing $\text{r}$ and $\text{m}$ and with decreasing β. It was suggested that the parameter, β, reflects the change in the morphology of crack tip resulted from the application of overload, which determines the shape of the curve for retarded crack growth rate vs crack distance.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

Cyclic analysis of a propagating crack and its correlation with fatigue crack growth

Stress and strain field of a propagating fatigue crack and the resulting crack opening and closing behavior were analysed. It was found that a propagating fatigue crack was closed at tensile external loads due to the cyclically induced residual stresses. Strain range value $\text{Δ?}{}_{\mathrm{y}}$ in the vicinity of the crack tip was found to be closely related with the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$ which was determined on the basts of the analytical crack opening and closing behavior at its tip. Application of this analysis to the non-propagating fatigue crack problem and the fatigue crack propagation problems under variable stress amplitude conditions revealed that both $\text{Δ?}{}_{\mathrm{y}}$ and $\text{ΔK}{}_{\mathrm{eff}}$ were essential parameters governing fatigue crack growth rate.     

Using local out-of-plane compression (LOPC) to study the effects of residual stress on apparent fracture toughness

To study and understand the effects of residual stresses on fracture behaviour, it is necessary to introduce well characterised and reproducible residual stresses into laboratory fracture specimens. One technique capable of providing such residual stresses is local compression, where the local compression is applied to the sides of a test specimen. In this paper, the technique is used to create a residual stress field in compact tension, C(T), specimens. The specimens are used subsequently to study the effects of residual stress on fracture. Finite element studies show that significant changes to the distribution of the residual stresses occur when the position of the compression tools is changed relative to the crack tip. It is also revealed that both a single and double pair of compression tools can generate both tensile and compressive residual stresses in the vicinity of the crack tip depending upon the location of the tools relative to the crack tip. The impact of local compression is illustrated by experimental results from room temperature fracture tests performed on two aluminium alloys, Al2650 and Al2024. Tensile residual stresses, created by the application of a single pair of compression tools, reduced the initiation fracture toughness of Al2650 by about one half. The ductile tearing resistance of Al2024 decreases when a double pair of tools introduces tensile residual stresses. Conversely, the tearing resistance increases when compressive residual stresses are created through local compression.     

Effect of specimen thickness on the crack propagation and crack branching in delayed failure

The crack propagation and crack branching behaviors in delayed failure have been investigated on the specimens with various thickness ($\text{B = 1.5–10}\text{mm}$).The crack propagation velocity reveals a maximum value at a medium specimen thickness ($\text{B = 5}\text{mm}$). This fact can be understood by assuming the compound effect of two factors that the triaxiality of stress at crack tip as a driving force for hydrogen diffusion increases with increase of specimen thickness $\text{B}$, and that the invasion of hydrogen atoms from specimen surface increases with decrease of $\text{B}$.The stress intensity factor at crack branching, $\text{K}{}_{\mathrm{IB}}$, increases with decrease of specimen thickness $\text{B}$, and when B is 1.5 mm, the specimen fractures without showing the crack branching. The latter fact can be explained by connecting the necessary and sufficient conditions for crack branching with the decrease in height of plastic region at the crack tip in thin specimens.     

A multilayer hybrid-stress finite element analysis of a through-thickness edge crack in A ± 45° laminate

A solution is given for the three-dimensional stress field near a through-thickness edge crack in a thin ± 45° laminate having elastic ply moduli typical of graphite/epoxy. The stress distribution was obtained by a three-dimensional multilayer finite element analysis based on the hybrid stress model, formulated through the minimum complementary energy principle. The results indicate that the in-plane stresses of each individual ply follow the classical $\text{1}\text{√r}$ stress singularity, but that the shape of isostress contours in the crack tip region is strongly distorted from predictions based on two-dimensional anisotropic fracture mechanics theory. The interlaminar shear stresses increase rapidly as the crack tip is approached, but are restricted to a local region around the crack tip and flanks. The interlaminar normal stress is assumed to be negligible in the formulation of the analysis.     

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.     

Fatigue crack propagation into the residual stress field along and perpendicular to laser beam butt‐weld in aluminium alloy AA6056

Laser beam butt welds in Al‐alloys are very narrow and are accompanied by steep residual stress gradients. In such a case, how the initial crack orientation and the distance of the notch tip relative to the weld affect fatigue crack propagation has not been investigated. Therefore, this investigation was undertaken with two different crack orientations: along the mid‐weld and perpendicular to the weld. Fatigue crack propagation ‘along the mid‐weld’ was found to be faster in middle crack tension specimens than in compact tension specimens. For the crack orientation ‘perpendicular to the weld’, the relative distance between the notch tip and the weld was varied using compact tension specimens to generate either tensile or compressive residual stresses near the notch tip. When tensile residual stresses were generated near the notch tip, fatigue crack propagation was found to be faster than that in the base material, irrespective of the difference in the initial residual stress level and whether the crack propagated along the mid‐weld or perpendicular to the weld. In contrast, when compressive weld residual stresses were generated near the notch tip, fatigue crack arrest, slow crack propagation, multiple crack branching and out of plane deviation occurred. The results are discussed by considering the superposition principle and possible practical implications are mentioned.     

RESIDUAL STRESS FIELDS DURING FATIGUE CRACK GROWTH

This study outlines the distinction between (1) residual stresses at an ideal crack tip, undergoing reversed deformation in the absence of crack closure, and (2) additional residual stresses generated due to plasticity induced closure upon fatigue crack growth. Residual stresses resulting from reversed deformation in plane strain were higher compared to the plane stress case, while residual stresses generated behind the crack tip were more significant in plane stress compared to plane strain. The origin of these residual stresses was studied for two specimen geometries over a wide range of loading conditions. We define a new crack tip parameter, S_tt as the applied stress level that corresponds to the development of tensile stresses immediately ahead of crack tips. The S_tt levels were significantly higher for a fatigue crack than for an ideal crack. We attribute the difference in S_tt levels between these two cases to plasticity induced closure. The results demonstrate the importance of the S_tt parameter, since the stresses ahead of crack tips could remain compressive even when the crack surfaces are open. Moreover, the study emphasizes the need, when describing fatigue crack growth, to incorporate both the closure concept and residual stress field ahead of a crack tip.     

On a numerical simulation for stable crack extension process and a nonlinear fracture criterion

In this note a numerical simulation for a stable crack extension process has been worked out by an incremental finite element method. Utlizing the critical opening angle at the crack tip and accounting for the effect of stress history, we have visualized the stable crack extension process from initiation to instability. Several field variables including $\text{J-}\text{integrals}$, stresses and strains, have been computed for every incremental load step. It appears that the critical opening angle at the crack tip may serve as an important parameter in these fracture phenomena including the stable crack extension process. Based on the numerical results an idea for a nonlinear fracture criterion is proposed.     

On crack opening stress level in fatigue by Eddy current technique

Linear elastic fracture mechanics relates fatigue crack growth with the stress intensity factor at the crack tip. Presence of residual deformations at the tip of a fatigue crack reduces the crack tip stress intensification such that effective stress intensity range $\text{ΔK}{}_{\mathrm{e}}\text{= U · ΔK}$. In this paper use of eddy current technique is exhibited to find the values of test value of effective stress range factor $\text{U}{}_{\mathrm{test}}$. A reasonable comparison between computed and experimental results of $\text{U}{}_1$ and $\text{U}{}_{\mathrm{test}}$ on two Al alloys 6061-T6 and 6063-T6 has recommended the Eddy Current Technology for finding out the values of crack opening stress level under given loading conditions.     

Initiation of stress corrosion cracking and fatigue crack under compressive stress

Macroscopic compressive stress was able to induce stress corrosion cracking (SSC) of type 304 stainless steel in a boiling 42% MgCl₂ solution and of mild steel in a boiling 60% Ca(NO₃)₂ + 3% NH₄NO₃. The incubation period of SCC under the compressive stress was ten to hundred times longer than that under the tensile stress.For ultra-high strength steel and aluminum alloy, a fatigue crack could initiate from a notch tip under a cyclic compressive load. The threshold value Δσ_th or Δ$\text{K}{}_{\mathrm{th(\rho )}}$ for fatigue crack initiation under the compressive load was four times as high as that under tensile load. The crack grew at a decreasing rate until eventually it stopped growing altogether under cyclic compressive load. The crack nucleation under compressive stress became easier and the propagation distance of the fatigue crack was longer if the minimum cyclic compressive load was near zero.     

Fatigue crack growth testing at negative stress ratios: discussion on the comparability of testing results

It is an accepted fact in fatigue community that compressive loads contribute to fatigue crack growth. Evidences range from fatigue crack growth under fully compressive loads to effects of compressive underloads to negative stress ratio loading. Because the crack closes under compression and the crack flanks transmit compressive stresses, the loading situation is completely different to those of tensile loading. The present paper addresses the comparability of crack growth testing procedures at negative stress ratios. It reveals that compressive loading at the crack tip differs in different specimens for an equal maximum stress intensity factor K_max and negative stress ratio R. Furthermore, the crack length can significantly influence the loading conditions at the crack tip for tension–compression loading. Depending on the specimen type and crack length, a negative force ratio may lead to a change of algebraic sign of the stresses at the crack tip or not. As a consequence, the comparability of available literature results for R ≤ 0 tests is not ensured. Proposals to improve the comparability of tension–compression crack growth testing will be given.     

Calculation of stress intensity factors for straight cracks in grooved and ungrooved shafts

Stress intensity factors have been calculated by finite element methods for a straight edged crack in a plane normal to the axis of rotation of a circular cylinder under tension and bending, and for a similar crack at the base of a symmetric groove in a shaft under tension and bending and under compressive stresses on the cylindrical surface. Satisfactory agreement with results of simplified approximations was found in most cases. A simple formula for determining the effect of the crack on the stiffness of the shaft in bending has also been derived.For the crack in an ungrooved cylinder, the stress intensity factor due to tensile or bending loads was highest at the centre, and lower than that due to a semi-elliptical notch in a slab of the same thickness under the same load. For bending loads on cracks of depths up to a tenth of the cylinder diameter, the stress intensity factor is approx. $\text{1}\text{1}\text{2}\text{σ√l}$ (where $\text{l}$ is the maximum crack depth and σ the maximum stress in the absence of the crack). For cracks in shallow grooves, the maximum stress intensity under tensile and bending loads is also at the centre but that for cracks in deep grooves is at the surface. The maximum stress intensity factor due to shrink fit is near the surface for both types of groove.     

A numerical investigation on the effect of an overload on fatigue crack opening and closure behaviour

The effect of a superimposed single tensile overload or a compressive overload in a block of constant-amplitude cycles on the crack opening and closing stresses is investigated using an elastic–plastic finite element analysis. The results obtained are in basic agreement with the experimental observations. Following an applied tensile overload cycle, the crack opening and closing stresses increase instantaneously, while the imposition of a compressive overload cycle results in a small decrease of the crack opening and closing stresses. A detailed discussion of the residual stress and strain patterns caused by the plastic deformation during the overload cycle and the corresponding crack profiles is included. The main governing mechanism resulting in the change of crack growth due to an overload is pointed out.     

Fatigue crack growth retardation inconel 600

The effect of single-cycle overloads on the subsequent fatigue crack growth behavior of Inconel 600 is studied. Overloads ranging from 10 to 50% are applied to a sample undergoing baseline fatigue crack growth at constant Δ$\text{K}$. In all cases, the crack growth rate increases slightly immediately after the overload and then decreases rapidly to a minimum value before later returning to the pre-overload value. The plastic zone size, affected crack length and the crack growth increment at minimum crack growth rate, $\text{a}\text{?}$, are measured for each overload.The affected crack length is considerably larger than the overload plastic zone size for overloads greater than 20%. Consequently, although the minimum crack growth rate occurs within the plane stress overload plastic zone, the effect of the overload extends well beyond the overload region.Within the overload plastic zone, contact occurs between the crack faces due to the excessive deformation produced during the overload cycle. The size of the contact region agrees very well with the overload plastic zone size. Beyond the overload region, Δ$\text{K}{}_{\mathrm{eff}}$ remains less than the applied Δ$\text{K}$ for some time due to the wedge action of the plastically deformed overload region, delaying recovery of the pre-overload crack growth rate. The crack growth rate recovers only after the crack grows out of the region of influence of the wedge.     

An examination of mixed fatigue-tensile surface crack growth in rails

The fracture instability associated with alternating periods of fatigue and tensile growth of surface cracks was investigated in steel rails. Three different steels were tested. The instabilities commenced when the maximum stress intensity factor $\text{K}$ exceeded the fracture toughness $\text{K}{}_{\mathrm{IC}}$ and resulted in crack jump or total rail failure. The conditions for the establishment of fatigue-tensile crack jump and arrest are described. The load level, residual stresses, crack geometry and fracture toughness effects are analysed. The fatigue surface cracks were penetrated in both stress relieved and stress unrelieved rails. The effective stress intensity factors including the contribution of the applied load and residual stresses were calculated. For both the fatigue-tensile and tensile-fatigue transitions the stress intensity factors were almost the same with the value for the tensile-fatigue transition being slightly lower. Both calculated stress intensity factors were close to the fracture toughness $\text{K}{}_{\mathrm{IC}}$.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

Elastodynamic near-tip fields for a rapidly propagating interface crack

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar isotropic elastic solids is investigated. Both anti-plane and in-plane motions are considered. The anti-plane displacements and the in-plane displacement potentials are sought in the separated forms $\text{r}{}^{\mathrm{q}}\text{F(θ)}$, $\text{r}$ and θ being polar coordinates centered at the moving tip. The mathematical statement of the problem reduces to a second-order linear ordinary differential equation in θ, which can be solved analytically. Formulation of the boundary and interface conditions leads to an eigenvalue problem for the singularity exponent $\text{q}$. For the in-plane problem, root $\text{q}$ is found to be complex. Thus, the stresses exhibit violent oscillations within a small region around the crack tip, and the solutions have physical significance only outside this region. The angular stress distributions are plotted for various crack speeds, and it is found that at a high enough speeds the direction θ of maximum stress moves out of the interface. This result indicates that a running interface crack may move into one of the adjoining materials.     

Near-tip behavior of a crack in a plane anisotropic elastic body

The asymptotic form of the stress and displacement components near the tip of a straight crack in a generally rectilinear anisotropic plane elastic body are resolved. As in the isotropic analysis, the solutions for the stresses display a $\text{r}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ dependence, where r is the distance from the tip, while the angular dependence depends upon the anisotropy in a complicated way. The effect of some special anisotropies upon these solutions is fully explored. Finally, these solutions are used to solve the problem of a finite length straight crack in an anisotropic elastic plane when uniform stresses are applied far from the crack. This solution includes obtaining the stress intensity factors, and the nature and magnitude of the crack face displacements.