On the fundamental basis of fracture mechanics

Based on the crack tip stress and strain fields, the linear and the non-linear fracture mechanics have been developed. Their applications to the studies of fracture initiation and stable crack growth may differ because of the difference in the basic postulates of various fracture theories. The correct postulates will help to develop non-linear fracture mechanics for valid fracture toughness measurements and to extend fracture mechanics beyond the realms of K and J.The basic postulates of the linear elastic fracture mechanics are examined. The theory of global energy balance, the theory of sharp notch, and the theory of the characterization of crack tip stress and strain fields by K are analyzed. Fracture initiation and stable crack growth are local fracture phenomena. Therefore the global energy balance theory for crack initiation and stable crack growth without the study of the detailed fracture processes is fortuitous. The capability of the stress intensity factor to characterize the crack tip stress and strain fields for the localized fracture process is the basis for the validity of the linear elastic fracture mechanics.The concept of the characteristic crack tip field can be directly extended to the non-linear fracture mechanics. The fracture toughness and the tearing modulus of a tough material are measures of the fracture ductility of the material. The possibility to extend fracture mechanics beyond the realms of K and J are discussed.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

A MODEL FOR THE FATIGUE LIMIT AND SHORT CRACK BEHAVIOUR RELATED TO SURFACE STRAIN REDISTRIBUTION

A model based on surface strain redistribution and the reduced closure stress of short cracks is shown to successfully predict the fatigue limit and short crack growth behaviour for aluminium alloy 2024-T351. Using this approach, the length of non-propagating cracks can be anticipated. The local stress intensity range may be resolved into two components (first the linear elastic fracture mechanics component and the second is due to surface strain concentration). Consequently, the local stress intensity range of aluminium alloy 2024-T351 is a maximum at a depth of approximately half a grain diameter and a minimum at a depth slightly in excess of three grain diameters. The reduced closure stress for short cracks coupled with the increased applied stress intensity caused by surface strain redistribution accounts for the variation of the effective stress intensity parameter as a function of crack depth. This parameter is a maximum for the smallest possible crack (3 μm) and decreases as crack length increases.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

On the relationship and the short fatigue crack threshold

Murakami and Endo have used the parameter to successfully predict the endurance limits and the threshold levels for components, which contain small defects or cracks. The present paper uses a modified linear–elastic fracture mechanics (LEFM) approach to examine the mechanistic basis for these correlations. The modifications include consideration of the endurance limit rather than the threshold level as a factor controlling fatigue crack growth in the very short crack growth range, consideration of elastic–plastic behaviour, and consideration of the role of crack closure in the wake of a newly formed crack. Predictions based upon the modified LEFM behaviour are found to be consistent with the earlier predictions of Murakami and Endo.     

PROPAGATION BEHAVIOUR OF SHORT FATIGUE CRACKS IN Q2N STEEL

Abstract— The work described in this paper characterizes short fatigue crack growth behaviour of Q2N steel having a complex microstructure and designated for pressure vessel and offshore structure applications. Short and long fatigue crack growth tests for this steel were conducted under three point bend loading conditions. It was found that, in the initial stages of growth, short cracks propagate much faster than those of long cracks when correlated with the linear elastic fracture mechanics (LEFM) parameter Δ K. A period of crack growth retardation was observed at crack lengths of approx 50 μm. The theory of the interaction between short cracks and grain boundaries fails to predict the occurrence of this deceleration minima. A new short crack deceleration mechanism is proposed based on experimental observation. Observation of the characteristic behaviour of short cracks allowed the development of a short crack growth model based on microstructural fracture mechanics analyses.     

Brittle fracture initiation from a blunting crack

Brittle fracture initiation under increasing load occurs from a blunting crack. The present paper proposes as a criterion for the transition from blunting to fast crack growth that the available elastic energy divided by a volume which depends on the fracture mechanism and the crack tip opening displacement reaches a critical value. This criterion is shown to be applicable for initiation from initially sharp cracks, initially rounded notches and from ductile growing cracks. The model allows a quantitative discussion on the size, temperature and notch root radius requirements for fracture mechanics testing.     

Modeling fatigue crack and spalling for rolling die under hot milling

In hot milling process, rolling die is subjected to nonsteady conditions which can rise the combinations of fatigue and spalling damage mechanism. An understanding about the failure mechanism of the rolling die is essential under hot rolling process. Fatigue crack growth and spalling process are governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic‐plastic fracture mechanics, an analytical model are presented in this paper to determine the elliptical crack growth rate and spalling damage mechanism. The model includes new proposed constitutive equations for fatigue and spalling crack growth. To verify the models, finite element simulation and experimental data are considered. The results show good agreement with finite element simulation and experimental data.     

Some Peculiarities of Fatigue Crack Growth at Various Stages of Its Development

The author considers some peculiarities of fatigue crack growth in metals at the stages of its initiation and initial development, and stable and unstable growth that precedes final fracture. It is shown that at the stage of initial growth of fatigue cracks, the stress state, nonlocalized fatigue damage that precedes initiation of the main fatigue crack, residual surface stresses, surface manufacturing and in-service defects, and contact interactions are the factors that determine the crack paths. Stable growth of a fatigue crack is primarily determined by the stress-strain state of a structure as a whole and by the stress-strain state at the crack tip with allowance for its variation due to crack propagation, which is evaluated by the criteria of fracture mechanics. The author also studied peculiarities of fatigue crack development in compressor blades of marine gas turbines. It is shown that for embrittled steels, when fatigue cracks develop under plane strain conditions, final fracture occurs at very small crack sizes. In this case, the characteristics of fatigue fracture toughness are appreciably lower than the static values. The paper also considers peculiarities of unstable fatigue crack propagation.     

An engineering approach to fatigue analysis based on elastic‐plastic fracture mechanics

Nowadays cast iron components are widely used in highly stressed structures. Component lifetime is strongly influenced by inhomogeneities caused by the material's microstructure and the manufacturing process (graphite particles, (micro‐)shrinkage pores, inclusions). Inhomogeneities often act as a fatigue crack starter. Lifetime until failure may be divided into stages for crack initiation, short and long crack growth. Initiation of a crack of technical size (a ≈ 1mm) is often dominated by the growth of short cracks. The paper presents an approach to analyse the mechanically short fatigue crack growth based on elastic‐plastic fracture mechanics considering the closure behaviour of short cracks. The effective J‐integral range is used as a crack driving force. Finite element analysis results as well as analytical solutions to approximate the crack driving force are presented. The application of the approach is successfully demonstrated for cast iron material EN‐GJS‐400‐18‐LT using data from fatigue tests, microstructure and fracture surface analyses to assess the fatigue life.     

Measuring fatigue cracks in fillet welded joints

Accurate measurement of short (<1 mm depth) elliptical fatigue cracks that grow from the toes of fillet welds has proved to be an obstacle to the application of fracture mechanics principles to welding fatigue. This paper reports a DC potential drop technique which allows continuous measurement of the depth of such elliptical cracks. A delicate compromise between sensitivity and accuracy, combined with superior electrical stability displayed by the measurement apparatus, has allowed detection of: 1 — crack growth less than 0.01 mm and; 2 — crack growth rates less than 10^?7 mm/cycle for cracks less than 1 mm deep.Preliminary results have indicated the relative importance of stress ratio, defect size and material variation on the growth of these short elliptical cracks. When the weld toe is subject to high stress ratios the phenomenon may be considered propagation dominated whereas low stress levels increase the influence of threshold and initiation mechanisms.     

Growth behaviour of small surface fatigue cracks in AISI 304 stainless steel

A series of axial tensile fatigue tests (R = 0.1) was carried out to investigate the initiation and the growth behaviours of very small surface fatigue cracks under two different surface conditions (viz. smooth and pitted surfaces) of AISI 304 stainless steel at room temperature. This paper deals with both of the two approaches regarding the analysis of fatigue: the approach based on the concept of fracture mechanics and low cycle fatigue. In particular, both the initiation and growth of cracks and the coalescence of small cracks by fatigue in the specimen have been investigated by the methods of surface replicas and photomicrographs. Quantitative information such as the initiation period, growth and coalescence behaviours of small cracks, and crack growth properties were systematically obtained. The results show that the accurate determination of these parameters is critical for the application of fracture mechanics to fatigue life assessment.     

A mathematical model to approach the fracture process of overconsolidated clay

Some soil and most rock masses contained defects (joints, cracks, bedding planes, fissures in clay, etc.). Beyond the peak shear strength of a mass of soil or rock, the stress falls as the strain increases. In this paper, the plane strain problem with double edge-cracks under shear loads is analysed based on linear elastic fracture mechanics but with finite stress concentration concept. We assumed that the fissured clay is a kind of strain-softening material and the growth of slip surface is along the maximum shear stress plane. The growth of slip surfaces in the progressive failure is expressed by the shear loads and slip displacement curves, which are obtained under the crack tip opening displacement criteria (CTOD_c) or the energy release rate criteria (J_c). The residual slip displacements are also taken into account by cumulating the elastic ones.     

FATIGUE MICROCRACKS IN A LOW CARBON STEEL

Abstract— The behaviour of a low carbon steel has been studied, in particular the initiation, growth and coalescence of fatigue microcracks on the surfaces of smooth specimens via surface replicas and photomicrographs. From the study, quantitative information on the initiation period, growth and coalescence of cracks, statistical distributions of crack length and crack depth, density of cracks, distribution pattern and characteristics of the major crack, were obtained. Knowledge of these parameters is critical for non-destructive inspection during service life and the application of fracture mechanics to life assessment.     

Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

An enhanced probabilistic model for cleavage fracture assessment accounting for local constraint effects

Objective of the present study is the development of an enhanced model for the probabilistic cleavage fracture assessment of ferritic materials considering the conditions for both, nucleation and propagation of micro defects. In a first step, the local load and deformation history at the cleavage initiation spot is analysed numerically for a variety of fracture mechanics specimens. The experimental data base includes experiments on standard deep and shallow crack specimens with different geometries as well as novel small scale cruciform bending specimens. These specimens enable the application of an additional stress component along the crack front. Based on the results, a two-criteria concept for cleavage initiation is proposed, assuming that the propagation of existing micro defects is controlled by the maximum principal stress whereas the nucleation of potentially critical micro defects is governed by a combination of the local plastic strain and the local stress triaxiality at the respective material point. Based on these assumption, a probabilistic cleavage fracture model is formulated and validated against the experimental data base.     

THE GROWTH OF SMALL FATIGUE CRACKS IN A LOW CARBON STEEL; THE EFFECT OF MICROSTRUCTURE AND LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS

The growth characteristics of small fatigue cracks were studied under rotary bending in a low carbon steel prepared with two ferrite grain sizes of 24 and 84 μm, and were compared with the growth characteristics of large through cracks in fracture mechanics type specimens. The effect of microstructure on crack growth rates and the interaction in growth behaviour between two neighboring small cracks were examined experimentally, and also the critical crack lengths above which linear elastic fracture mechanics (LEFM) is applicable were evaluated for small crack growth and for fatigue crack thresholds. It is found that small cracks grow much faster than large ones and also show growth rate perturbations due to grain boundaries. It is indicated that the critical crack lengths for fatigue crack thresholds are significantly shorter than those for small crack growth.     

FATIGUE MICROCRACKS IN TYPE 304 STAINLESS STEEL AT ELEVATED TEMPERATURE

Microcracking of type 304 stainless steel at 538°C has been studied, in particular, the initiation, growth and coalescence, of fatigue microcracks on smooth specimens via surface replicas and photomicrographs. Quantitative information, such as, initiation period, growth and coalescence behaviour, statistical distributions of crack length, density of cracks, distribution patterns and crack growth properties, were obtained. Knowledge of these parameters is critical for the application of fracture mechanics to fatigue life assessment and the damage evaluation of structures at elevated temperature.     

Analysis of mixed-mode cracks in a rubbery particulate composite

The mixed-mode loading of a rubbery particulate composite is studied experimentally. Linear fracture mechanics concepts are used to determine the initiation of growth, the initial growth direction, and the subsequent growth rate for a range of mode mixities. The fracture toughness locus is determined to be elliptical, with the Mode II toughness being lower than its Mode I counterpart. The initial growth directions correlate with maximum strain energy density theories. The crack growth rates can be modeled effectively using an equivalent Mode I crack.     

THE SHORT CRACK PROBLEM

Abstract— The problem associated with short crack growth, defined as situations in which the intensity of the crack tip field is underestimated by linear elastic fracture mechanics analyses, is briefly reviewed.
Two cases are identified, cracks growing in plastically strained materials, such as occurs in high strain fatigue studies and at notch roots, and small cracks growing in single grains as occurs close to the fatigue limit in plain specimens.
Important mechanical and metallurgical features of short cracks are discussed with particular reference to the upper and lower bound definition of a short crack.