Effect on fatigue crack growth of interactions between overloads

ABSTRACT Various types of interactions between overloads were studied in a 0.38% C low carbon steel. The retarding effect due to consecutive overloads is found to increase with the number of overloads, until it reaches a maximum. Similarly, it is found that a critical distance between overloads ensures the highest retarding effect, while shorter or longer spacing are less efficient for retarding crack growth. These effects are successfully explained using FEM calculations of the effective stress intensity factor. The kinematic hardening of the alloy, which is very efficient in ferritic–pearlitic steels, is shown to be mostly responsible for those effects. Taking into account the amplitude of kinematic hardening allows qualitative explanation of the observed effects. The order of application of the cycles during variable amplitude fatigue is thus important and should be taken into account for predicting fatigue lives.     

The effect of overloads on threshold and crack closure

The effect of tensile and compressive overloads on the threshold stress intensity level and crack closure behaviour of one aluminium alloy and three steels has been investigated. A few tensile overloads significantly decreased the crack propagation rate and increased the threshold stress intensity. An initially decreased and then increased opening stress was mostly responsible for the delayed retardation and crack arrest. Intermittant compressive overloads significantly accelerated the crack propagation and decreased the threshold stress intensity which was a function of the frequency of overloading. The opening stress was decreased to below zero after a large compressive peak load, and it took >10⁵ cycles for the opening stress to return to its stable level. During this period an initially high crack propagation rate also gradually decreased to the stable value.     

The significance of fractography for investigations of fatigue crack growth under variable-amplitude loading

Fatigue crack growth tests were carried out on 2024-T3 and 7075-T6 centrally cracked specimens. Variable-amplitude (VA) load spectra were used with periodic overload (OL) cycles added to constant-amplitude (CA) cycles. The fatigue fracture surfaces were examined in the SEM to obtain more detailed information on crack growth contributions of different load cycles. The striation patterns could be related to the load histories. SEM observations were related with (i) delayed retardation, (ii) the effect of 10 or a single OL on retardation, (iii) crack growth during the OL cycles, and (iv) crack growth arrest after a high peak load. Fractographs exhibited local scatter of crack growth rates and sometimes a rather tortuous 3D geometry of the crack front. Indications of structurally sensitive crack growth under VA loading were obtained. Fractography appears to be indispensable for the evaluation of fatigue crack growth prediction models in view of similarities and dissimilarities between crack growth under VA and CA loading.     

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.     

Fatigue crack growth with overloads/underloads: Interaction effects and surface roughness

The generalization of damage tolerance to variable amplitude fatigue is of prime importance in order to maintain the reliability of structures and mechanical components subjected to severe loading conditions. Engineering spectra usually contain overloads and underloads which distribution may not be random. However for predicting the life of a structure, a simplified spectrum is usually determined from the real one, in order to reduce testing periods on prototypes. Therefore it is thus important to know which cycles can contribute to crack growth and which can be neglected. This paper presents an analysis of fatigue crack growth on M (T) specimens made of a medium carbon steel DIN Ck45. The specimens are subjected to repeated blocks of cycles made up of one or several (1, 2, 6 or 10) overloads (or underloads) separated by a variable number (10, 1000 or 10 000) of baseline cycles. The main objective of this study is to better understand the mechanisms at the origin of interactions effects due to the presence of overloads (or underloads) at different locations of each block loading. Under constant amplitude loading, single variables ΔK and K_max are required in crack growth relationships. The transferability of fatigue laws, obtained under constant amplitude loading to variable amplitude fatigue, requires at least an additional variable, whose evolution with crack length accounts for the interactions effects between cycles of different types. Results have shown that the interaction effects in fatigue crack growth are closely related to the mechanisms of crack growth: cyclic plastic behaviour of the material and fracture surface roughness. Measurements of roughness of the surface fracture were carried out in both constant amplitude and variable amplitude tests. The roughness characterization helped to determine the importance of the mechanisms on variable amplitude fatigue crack growth and determine the influence of overloads/underloads on fatigue crack growth.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Stage II fatigue crack growth

The linear part of the fatigue crack growth diagram is found to be divided into Stages IIa and IIb by the point O whose coordinates K^* and A are dependent on the physical and structural characteristics of the material. In Stage IIa K_eff remains constant as the microcrack advances in increments corresponding to the dislocation cell structure size, λ, pausing for (dN−1) cycles to accumulate the elastic energy required for the crack opening. During Stage IIb K_op remains constant and the microcrack opens during each cycle and advances irrespective of the substructure but in accordance with an increasing value of K_eff. The effects of temperature and vacuum on K^* are considered; the A values correspond to those of λ and are independent of the above effects.     

A review of some aspects of fatigue crack growth under variable amplitute loading

The literature on some aspects of the influence of variable amplitude loading on fatigue crack growth has been reviewed. In particular the importance of residual stresses, fatigue crack closure, microstruture, geometry and environment on the fatigue crack growth of long, through-thickness cracks following overloads, underloads and overload-underload combinations in Mode 1 opening have been identified. Other behaviour, including the influence of temperature, frequency and the effects of mixed-mode loading, is beyond the scope of this review. Areas of work requiring further investigation have been proposed.     

Examination of the fatigue crack growth equations

Most of the crack growth equations proposed so far correlate the crack growth rate (da/dN or da/dt) with crack tip parameters such as the stress intensity factor (SIF) or energy release rate (ERR). In our previous works, an experimental setup was designed to examine the applicability and the boundary of the functional relationship between da/dN and the crack tip parameters, particularly, ERR. In the present paper, the variation of the ERR along the experimentally observed curvilinear crack trajectories is obtained by means of the finite element method. The analysis shows that the Paris-Erdogan type of laws are applicable until the crack tip is located outside the strong crack-defect interaction region (SI region). A functional relationship between da/dN and ERR breaks down within this region. This suggests the existence of additional crack tip parameters that are not accounted for within conventional fracture mechanics. An approach to modeling the observed phenomenon is discussed following the concept of the Crack Layer theory.     

The influence of cross-sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.     

On retardation effects during fatigue crack growth under random overloads

A stochastic approach to fatigue crack growth under random overload sequences, superimposed on a base-line cyclic load, is described. The approach consists in presentation of the delay time due to the retardation effect associated with the overload peaks as a purely discontinuous Markov process. A numerical procedure based on the Kolmogarov-Feller integrodifferential equation is developed. Application of the model is illustrated by examples.     

Restraint of fatigue crack growth by wedge effects of fine particles

This paper presents some experimental results which demonstrate restraint of fatigue crack growth in an Al–Mg alloy by wedge effects of fine particles. Fatigue test specimens were machined from a JIS A5083P‐O Al–Mg alloy plate of 5 mm thickness and an EDM starter notch was introduced to each specimen. Three kinds of fine particles were prepared as the materials to be wedged into the fatigue cracks, i.e. magnetic particles and two kinds of alumina particles having different mean particle sizes of 47.3 μm and 15.2 μm. Particles of each kind were suspended in an oil to form a paste, which was applied on the specimen surface covering the notch zone prior to the fatigue tests. In order to make some fracture mechanics approaches, in situ observations of fatigue cracks were performed for the two cases using a CCD microscope, with a magnification of ×1000. The crack length and the crack opening displacement (COD) at the notch root, δ, were measured. First it was ensured by control tests that the wedge effect of the oil itself was negligible. Then it was found that the large size alumina particles were not effective in restraining crack growth because the paste was difficult to make due to the large particle size and the particles could not enter the cracks properly. However, both of the magnetic particles and the small size alumina particles effectively restrained crack growth, especially the latter which produced 143–350% increase in the lifetime to failure. From the in situ observations, in the case of the small size alumina particles, a pronounced retardation of crack growth was observed immediately after the crack length exceeded 0.4 mm, and this is considered to be due to the range of COD value, δ_max ? δ_min , being strongly affected by the wedge effects of the particles. The crack retardation effect continues almost through the entire lifetime if the alumina paste is re‐applied at specified intervals, while the effect is apparently lost after the crack length exceeds ～2 mm when such re‐painting is not continued. After the fatigue tests, some macro‐ and microfractographic analyses were performed using a CCD microscope, a SEM and an EPMA (electron probe microanalyser), in order to examine the mechanism of fatigue crack restraint by the wedge effects of the fine particles. From those analyses, it was reasoned that the fine particles that entered a fatigue crack are subjected to cyclic pressures between the crack faces and then form a kind of wedge which causes significant levels of crack closure that restrain crack growth.     

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.     

Effect of underloads or overloads in fatigue crack growth by crack-tip blunting

Crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading is one of the basic mechanisms for fatigue crack growth in ductile metals. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using re-meshing at several stages of the plastic deformation. A compressive underload in one of the cycles tends to increase the rate of cyclic crack growth, and this effect is studied in detail for a single underload, based on the blunting re-sharpening mechanism. Subsequently, the increased rate of crack growth due to periodically occurring underloads is analysed. A single overload has the opposite effect of giving a significant delay in the subsequent fatigue crack growth. An analysis is carried out to compare the effect of a small overload to that of a larger overload.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Modelling of initial fatigue crack growth and crack branching under fretting conditions

Crack propagation during Stage I, in terms of crack initiation sites and growth directions and crack branching mechanisms under fretting conditions, is investigated using both experimental and theoretical approaches. Fretting tests were conducted on an aeronautical aluminium alloy. Two crack types are observed during Stage I corresponding, respectively, to specific mode I and II conditions. Transition from Stage I to Stage II is characterized for both crack types by a crack branching towards a new propagation direction of ≈65° to the specimen surface. Specific parameters linked to mode I and II propagation driving forces are proposed. Crack location and initial growth directions during Stage I are predicted in accordance with these parameters, and are in very good agreement with experimental observations. The conditions governing the transition from Stage I to Stage II are then identified. It is shown that under fretting conditions, cracks branch along a new direction, thereby maximizing the crack-opening amplitude.     

Micromechanisms of fatigue crack growth retardation following overloads

New mechanistic interpretations to rationalize fatigue crack growth retardation due to load excursions are presented. It is reasoned that crack closure arising from residual tensile displacements is not the primary mechanism for growth attenuation following a peak tensile overload. A new mechanism for retardation is discussed in terms of a “micro-roughness” model. Quantitative analyses are provided to estimate the extent of reductions in effective driving force in the retarded growth region due to possible crack branching and fracture face micro-roughness. It is argued that the retarded crack advance is effectively governed by the micromechanisms of Stage I growth although nominally Stage II conditions exist in the post-overload zone. The implications of the present arguments are shown to be consistent with a number of typical post-overload phenomena cited in the literature.