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.     

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.     

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.     

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.     

Effects of tensile overloads on crack closure and crack propagation rates in 7050 aluminum

It has been suggested that the crack closure concept can account for the retardation in crack growth rate following removal of tensile overloads. To test this possibility measurements of effective stress were made on center notched cracked specimens during tests in which tensile overloads were applied. A comparison of the changes in crack growth rate and in effective stress following removal of the overload indicates that the crack growth rate reaches a minimum value before the effective stress does indicating that the closure concept cannot account for the decrease in crack growth rate. Additional evidence for the inability of crack closure to account for the retardation in crack growth rate is provided by specimens run at a high mean stress and then overloaded. No crack closure is observed when there is a high mean stress present, yet the crack growth rate does decrease by an amount about the same as that observed at low mean stresses where crack closure is present. Measurements of closure stress and effective stress were obtained from load-displacement curves recorded using an extensometer mounted across the crack on the specimen centerline. This procedure also enabled us to measure the distance over which the crack faces were in contact when the stress was at its minimum value in the stress cycle. The length of crack closed reached a minimum value later than did either the crack growth rate or the effective stress. It occurred when the crack tip had propagated nearly across the plastic zone created by the application of the overload.     

The effects of overloads in fatigue crack growth

Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.     

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.     

Study of fatigue crack growth retardation due to overloads in polymethylmethacrylate

Retardation of the fatigue crack growth after overloading was investigated in conjunction with the craze deformation at the fatigue crack tip in polymethylmethacrylate. The craze deformation was measured by optical interference and analysed numerically with reference to a previously proposed craze model. In the base line loading, the craze stress concentrates at the crack tip with the applied load and, hence, the non-uniform stress distribution is attained at the maximum load. The overload alters this stress distribution. Just after overloading, the crack tip stress does not reach the previous level, even at the same maximum load. The reduced crack tip stress correlates well with the retarded duration after the overload. It is concluded, therefore, that the craze stress reduction at the crack tip is the cause of crack growth retardation.     

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.     

The effect of pre-strain on fatigue crack growth and crack closure

A single pre-strain (ε = 0.03) applied to 2024-T3 material raised the static yield strength from 428 to 480 MN/m². The growth rate of a fatigue crack in the pre-strained material was about twice as large as in the material that was not pre-strained. A pre-strain followed by 1000 high, but still elastic pre-stress cycles did not further increase the growth rate. It was shown by COD measurements that crack closure occurred to a lesser extent in the pre-strained material as compared to the original material. The significance of the increased yield strength for fatigue crack growth is briefly discussed.     

Utilization of partial crack closure for fatigue crack growth modeling

Load ratio effects are of prime concern when modeling of fatigue crack growth (FCG) rate is required as a prerequisite for a reliable life prediction. The majority of research efforts regarding the load ratio effects are based on Elber's ΔK_eff approach. However, there are intrinsic difficulties encountered with its consistent application to FCG prediction. In this paper two popular crack-growth-life prediction codes FASTRAN and AFGROW are modified utilizing the enhanced partial crack closure model. The proposed utilization aggregates apparent closure mechanisms involved and demonstrates a better correlation and a significant scatter reduction of FCG data taken from literature, especially in the near-threshold region.     

Small crack growth rates from simple sequences containing underloads in AA7050-T7451

Fatigue crack growth in materials that display confined slip show crack path changes that are dependant on the loading history. In these materials certain variable amplitude loading patterns can produce strong slip bands ahead of the crack tip. One of these patterns of loadings involving bands of high R cycles followed by one or two underloads also produce distinct features or progression marks on the fracture surface that have been used to delimit small blocks of constant amplitude cycles. The same loading pattern also produces strong slip bands ahead of the fatigue crack both in the plane of the crack and out of plane. These slip bands affect the direction and possibly the rate of propagation of the fatigue crack. Thus these loading patterns make an ideal marker to look at small crack growth rates in the presence of slip bands.This paper reports on the crack growth rates for a series of fatigue cracks grown in AA7050-T7451 coupons, from near initiation to near failure. The aim of this work was to generate constant amplitude crack growth data for use in predictions that is more useful for predicting crack growth lives than that obtained from long crack constant amplitude tests. Three simple sequences which applied small bands of constant amplitude loading were used in the fatigue tests preceded by a loading sequence to produce a progression mark to delimit the bands. The fatigue cracks in the coupon initiated from etch pits on the surface of the coupons. The width of the bands of constant amplitude growth in these sequences were measured under a microscope. The growth in these sequences was found to be faster than for long cracks under constant amplitude loading.     

Fatigue crack growth due to overloads in plain concrete using scaling laws

Scaling laws are represented in power law form and can be utilized to extract the characteristic properties of a new phenomenon with the help of self-similar solutions. In this work, an attempt has been made to propose a scaling law analytically, for plain concrete when subjected to variable amplitude loading. Due to the application of overload on concrete structures, acceleration in the crack growth process takes place. A closed form expression has been developed to capture the acceleration in crack growth rate in conjunction with the principles of dimensional analysis and self-similarity. The proposed model accounts for parameters such as, the tensile strength, fracture toughness, overload effect and the structural size. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between the different parameters involved. The predicted results are compared with experimental crack growth data for variable amplitude loading and are found to capture the overload effect with sufficient accuracy. Through a sensitivity analysis, fracture toughness is found to be the most dominant parameter in accelerating the crack length due to application of overload.     

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.     

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.     

An inelastic multiple discrete aperities model for the effects of compressive underloads in fatigue crack growth

As a common practice, the compressive (negative load ratio) excursions are ignored when analyses of fatigue crack growth in metals are conducted. However, recent experimental data on fatigue crack growth with intermittent compressive load excursions have shown that the use of this assumption leads in most cases to nonconservative predictions. This paper presents a model that is capable of explaining the observed behavior, including the saturation of the compressive overload effects, and the increase in the crack growth rate once the initial, positive load ratio profile is resumed, following a compressive excursion. The model is based on the plastic crushing of a single asperity or multiple asperities located on the crack face close to the crack tip and under dominantly plane strain conditions. A comparison of the behavior for one and for two asperities is made. Moreover, the effects of hardness and strain hardening are also examined.