PROPAGATION AND CLOSURE OF SHORT FATIGUE CRACKS AT NOTCHES UNDER COMPRESSIVE MEAN STRESSES

Abstract— Single-edge-notched specimens of a low-carbon steel were fatigued under cyclic in-plane bending with compressive mean stresses. The development of crack closure with crack growth was studied both experimentally and theoretically. The relation between the crack opening stress and the crack length was a function of the minimum (compressive) applied stress, irrespective of the maximum stress. The effective stress intensity range was a unique parameter in correlating the crack growth rate, even if the crack was embedded in the compressive plastic zone. Under a constant minimum stress, the length of nonpropagating cracks became longer with increasing maximum applied stress. A theoretical model was proposed for predicting the crack opening stress on the basis of the compressive stress distribution at the minimum applied stress. The predicted value agreed fairly well with the experimental result. The model gave upper bounds of the crack growth rate and the length of nonpropagating fatigue cracks within the plastic zone.     

CLOSURE BEHAVIOUR OF SURFACE CRACKS

Abstract— The fatigue crack closure response was investigated for a surface crack in BS4360 50B structural steel, subjected to (1) constant amplitude loading and (2) constant amplitude loading interrupted by a single peak overload. A variety of compliance techniques was employed to determine closure behaviour. The crack mouth gauge measured the bulk, plane strain closure load, while the near tip strain gauge indicated the surface, plane stress closure response. For constant amplitude loading it was found that the surface regions of a surface crack are closed for a greater portion of the load cycle than the maximum depth point. A single peak overload caused different closure and growth rate transients at the surface of the thumbnail crack and at the maximum depth point. For growth rates above 10^-6 mm/cycle, such behaviour agrees with the response of a through crack when subjected to constant amplitude loading, and a single peak overload.     

AN ANALYTICAL PROCEDURE FOR PREDICTING OPENING LOADS OF CRACKS AT NOTCHES

Abstract— An analytical procedure for the prediction of opening load levels for cracks growing from notches is presented, and estimates are made using experimental crack opening load data. The procedure is based on McClung's original procedure for estimating the local elastic-plastic stress—strain situation at the point of a hypothetical crack tip in a notched but uncracked body. A crack opening stress value for a crack in an urmotched body under the same stress—strain condition is then predicted. The corresponding opening load level for the crack stress-strain configuration in the notched but uncracked body is then predicted with a simple backward calculation. For the evaluation of the elastic-plastic stress distribution, simple analytical relationships, such as Neuber's rule, are used. Estimation of the crack opening stress level is performed using various crack opening stress formulae reported in the literature for cracks in unnotched specimens under a uniform stress distribution. The accuracy of all the investigated crack opening stress formulae within the scope of the presented procedure is checked, and discussed in detail using experimental data sets for opening load levels of comer cracks and through-thickness cracks in notched specimens of FeE460 and A15086. The predicted results using Newman's crack opening stress formulae, simply modified in respect to the definition of the flow stress, have been identified to be qualitatively and quantitatively consistent with the trends observed in experimental crack opening data.     

THE NUCLEATION AND GROWTH OF SHORT FATIGUE CRACKS BOTH AT PLAIN SURFACES AND NOTCHES

Abstract— The problem of the nucleation and growth of short fatigue cracks is addressed from an energetic point of view. It is explained that vanishingly small cracks can only nucleate and grow at the expense of the release of some locally stored energy during the fatigue deformation. This is necessary because an external loading system alone cannot provide a positive driving force for the growth of a crack whose length is below a critical value. The concept of the local driving force is used to explain the nucleation and growth of short fatigue cracks both at plain surfaces and at notches. With this approach a meaningful definition can be given of a "short fatigue crack" and a sound physical interpretation of the Kitagawa-Takahashi plots is provided. The conditions for the existence of non-propagating cracks are clearly established and the relationship between the stress concentration factor at the root of notches and the fatigue limit is explained. The paper sets up a physical framework for the sound understanding and treatment of short fatigue cracks and the microstructural parameters which control their growth.     

FATIGUE CRACK CLOSURE OF CORNER CRACKS LOCATED AT HOLES LOADED IN TENSION OR BENDING

Abstract— The objective of this paper is to report fatigue crack growth and closure behavior for corner cracked holes. An optical interference technique is employed with transparent polymer specimens to determine the three-dimensional crack surface displacement field. The local crack closure behavior is examined along the crack front under remote tension and pure bending conditions. It was observed that the crack opening loads along the hole and the free surface were significantly higher than the opening values at interior crack locations.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

AN EXPERIMENTAL INVESTIGATION OF THE GROWTH OF SMALL CORNER FATIGUE CRACKS IN ALUMINIUM 6061-T651

Results of an experimental investigation of the fatigue growth of small corner cracks emanating from small flaws are presented. Growth-arrest behaviour was observed, and increases in crack length during growth periods were of the order of the transverse grain size. For the test material, the corner crack front intersects, on average, only three–six grains in the small crack regime monitored, so only a small number of constrained, interior grains is encountered. It is suggested that the presence of partially constrained surface grains may contribute to the 'anomalous' growth behaviour which has been observed by a number of investigators.
The crack growth histories of the test data presented exhibit considerable scatter. It is shown that a Student's t -test can be used to estimate confidence intervals in order to provide a measure of the observed scatter. The variation in confidence intervals in the transition from small to long fatigue crack growth is discussed.     

SURFACE CRACKS AND THE FATIGUE LIMIT OF METALS

Abstract— A technique based on indenting a sphere into a material has been developed for measuring the yield strength of metals at various depths from the surface. Proceeding from the experimentally established reduction in the yield strength of the metal surface layer and cyclic crack growth resistance characteristics, the authors suggest a model simulating fatigue fracture based on the continuum mechanics assumptions which allows the fatigue limit to be estimated on the basis of a critical non-propagating fatigue crack size for components of various thickness in tension-compression or in bending; considering stress concentrations under both alternating and oscillating loads in the presence of near-surface stresses. Theoretical predictions using the model for three martensitic stainless steels and a titanium alloy showed a fair agreement with experimental data.     

AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH-THICKNESS AND SURFACE FATIGUE CRACKS

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–^12–10–⁶m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.     

THE EFFECT OF SPECIMEN SIZE ON THE BEHAVIOUR OF PENETRATING FATIGUE CRACKS

Fatigue life and penetration behaviour of cracks in HT80 steel plates were examined experimentally at room temperature for both large and small specimens containing a surface crack. Application of stress intensity factor solutions from small specimens, as proposed by the present authors, to large specimens was investigated. Crack growth behaviour, crack shape and crack opening displacement after penetration can be satisfactorily determined using the K solutions proposed by the authors.     

A CRACK CLOSURE STUDY TO PREDICT THE THRESHOLD BEHAVIOUR OF SMALL CRACKS

Abstract— The small crack problem is addressed within the applicability of Linear Elastic Fracture Mechanics as the result of crack closure phenomenon. The variation of crack closure stress intensity factory K _op as a function of crack length, a , was determined in two materials, namely a A508 steel and a 2024A1 alloy. These results were obtained on two-dimensional small cracks ( a ≫ 0.1 mm) which were machined from long fatigue cracks. These measurements of K _op in addition to data published in the literature on a nodular cast iron and a 9Cr–1Mo steel yield to a unique characteristic function: K _op/ K _o= 1 –exp(– ka ) in which k is the only parameter to characterize the small crack effect. A prediction of the threshold behaviour of small and long cracks on A508 steel is made using the results of crack closure measurements.     

SCATTER CHARACTERISTICS OF FATIGUE LIFE AND THE BEHAVIOUR OF SMALL CRACKS

Usually, there is large scatter in fatigue data and this should be evaluated quantitatively when fatigue data are applied to the design of machines and structures. Consequently it is important to clarify the physical basis of scatter in fatigue life. In this present study, rotary bending fatigue tests were performed on an annealed 0.21% carbon steel. At least sixteen smooth specimens were fatigued at each of three stress ranges and successive observations of the surface were studied for all the specimens using the plastic replica method. By examining the initiation and propagation behaviour of cracks the physical basis of scatter in fatigue life is analysed and discussed. To estimate the scatter characteristics quantitatively, the distributions of crack initiation life, propagation life, fatigue life and crack length were individually studied by assuming a Weibull distribution for each set of data.     

FINITE ELEMENT ANALYSIS OF CLOSURE BEHAVIOUR OF FATIGUE CRACKS IN RESIDUAL STRESS FIELDS

An elastic-plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8-node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field.     

THE STRESS INTENSITY FACTOR OF SMALL CRACKS AT NOTCHES

Abstract— It was found in a previous publication that stress fields around notches are quantitatively very similar, if the peak stress at the notch root (σ_peak) and the notch root radius ( ρ ) are the same. As a consequence, small cracks (length l ) should have the same stress intensity factor, if σ_peak and ρ are similar. This implies that the geometry factor C in
should primarily depend on l/ρ only, and not on other dimensions. Available data on calculated K values was analysed, which confirmed the similarity concept. An equation for C as a function of l/ρ was obtained. It was shown that K -values calculated with this equation are an accurate approximation for the stress intensity factor of small cracks at notches.     

FATIGUE LIFE AND SURFACE CRACK PENETRATION BEHAVIOUR OF AN ALUMINIUM ALLOY

Fatigue life and crack retardation behaviour after penetration were examined experimentally using CT specimens and surface pre-cracked specimens of aluminium alloy 5083-0. The fatigue crack shape before penetration is almost semicircular, and the measured aspect ratio is larger than the value obtained by calculation using K values proposed by Newman-Raju. It was found that crack growth behaviour on the back side after penetration is unique, and can be divided into three stages. The Wheeler model retardation parameter was used successfully to predict crack growth behaviour after penetration. By using a crack propagation rule, the change in crack shape after penetration can be evaluated quantitatively.