A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.     

Measurement of crack closure after the application of an overload cycle, using moiré interferometry

The crack closure behaviour on the application of a single overload cycle was studied in a Ti-6Al-4V specimen. Moiré interferometry with photoresist gratings was used to measure crack displacements. During the overload cycle a large crack opening displacement was observed at the maximum load. This was similar to predictions from a Dugdale-type crack closure model. When the load was taken back to zero, the crack was open at the crack tip due to the high levels of plastic deformation during the overload cycle. As the crack was grown there was some evidence of the deformed material on the crack faces.Moiré interferometry provided displacement data close to the crack faces, even when the crack had grown to over two-and-a-half times the overload crack length. When the overload was applied the crack bifurcated, and the Dugdale-type model under-predicted the crack opening.     

CORRELATION OF FATIGUE CRACK GROWTH BY CRACK TIP DEFORMATION BEHAVIOUR

Growth of a long mode I crack under variable fatigue loading was experimentally investigated on mild steel specimens. A dynamic elastic-plastic two-dimensional finite element program, purposely developed for the simulation of cyclic crack tip deformation, was utilised to model the transient effects on crack tip advance. The model accommodated crack tip opening displacement and both crack tip and crack edge closure. Fifty one different cycle patterns were analysed to include the application of a single overload, a single underload, a single cycle having a combined overload and underload and finally loading blocks of different sequences. Correlations of experimental fatigue crack growth rates were made from knowledge of crack tip deformation behaviour, including the use of data found in the literature. Specimens of eight materials and different geometries were analysed to determine the validity of the present approach.     

FATIGUE CRACK GROWTH DUE TO TWO SUCCESSIVE SINGLE OVERLOADS

The behaviour of fatigue growth and cyclic tip deformation of long cracks due to two successive single overloads was investigated both experimentally and numerically. The results show the effect of the ratio of the second and first overloads, and the crack increment between the two overloads. The contributions of both crack tip blunting and residual stress fields were separated and accommodated in a previously developed crack tip deformation parameter, which was utilized to predict the resulting fatigue crack growth behaviour. The following trends were experimentally observed. Should the ratio of the second and first overloads not be less than one, fatigue crack growth rates followed the predictions based on the second overload. Otherwise, either of the following two situations resulted: (1) when the two overloads were closely applied, the second overload caused an initial acceleration in growth rates followed by a behaviour controlled by the first overload; (2) when the second overload was applied after the crack growth had reached its minimum rate due to the first overload, more retardation in growth rate was observed. Based on the model developed in the paper, it is possible to enhance the retardation effect of an overload if this overload is preceded by another overload. This enhancement depends on the ratio of the two overloads and the crack increment between them.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Experimental evaluation of shielding effect on growing fatigue cracks under overloads using ESPI

The effect of single cycle overloads, ranging in size from 10% to 50%, on fatigue crack growth behaviour in compact tension specimens subject to constant amplitude loading with an R-ratio of 0.6 has been investigated using electronic speckle pattern interferometry. The resultant displacement fields have been used to evaluate crack opening and closing loads and effective stress intensity factors using the Christopher–James–Patterson model that takes explicit account of the effect of crack tip and wake plasticity on the singularity-dominated elastic fields surrounding the crack. The results show that the crack opening loads and effective stress intensity factors at the overload event are proportional to the magnitude of the overload and that period of post-overload retardation of crack growth is also proportional to the magnitude of the overload. These findings demonstrate the usefulness of the CJP model and should help enhance understanding of plasticity-induce closure phenomena.     

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 life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

Critical crack size that causes retardation of short fatigue crack by single overload

The effect of crack length on the retardation of fatigue crack propagation caused by single overload was investigated using carbon steels S25C and S45C. The retardation and crack arrest occurred even in short cracks ranging from 50 to several hundred microns. In case retardation occurs, it is caused by the increase of crack closure stress as in a long crack. The occurrence of retardation, however, showed a complex dependency on crack length, yield strength of material and the value of baseline stress ratio  R . At stress ratio  R  =−1, retardation did not occur for very short crack as short as 50 μm in the case of low yield strength material. This was because the increase of crack closure stress was prevented by the compressive stress component of baseline load. The plastically deformed layer near the crack tip was collapsed by the compressive stress of baseline load, which prevented the development of crack closure. In the case of high yield strength material, however, retardation occurred even in 50 μm crack. On the contrary at  R  = 0, retardation in the low yield strength material occurred even in 50 μm crack. The prevention of increase of crack closure did not occur in the case of  R  = 0. As a consequence, retardation basically occurs even in short crack as short as 50 μm unless the development of crack closure is impeded.     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.     

Effects of surface deformation and crack closure on fatigue crack propagation after overloading and underloading

In the case of a negative baseline stress ratio, the fatigue crack growth rate can actually accelerate after a tensile overload. This crack propagation behavior is related to the local bulging of the specimen in the thickness direction during compression and the resultant tensile residual stress distribution at the crack tip. In the present investigation, the effects of a single tensile overload as well as the effects of a tensile overload followed immediately by a compressive underload on subsequent fatigue crack growth were investigated. The extent of crack opening displacement influences the magnitude of residual stress as well as the crack-tip opening level, and consequently, the subsequent rate of fatigue crack propagation.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

Determination of displacements around fatigue cracks using image analysis of in‐situ scanning electron microscope images

A technique to in‐situ measure the displacements in the vicinity of the crack tip during fatigue crack propagation has been developed. High‐resolution images of the crack tip were taken continuously throughout the fatigue load cycles with a scanning electron microscope (SEM), and an image analysis program was used to determine the displacements at different positions with respect to the crack tip. The displacements were then used to determine crack shapes and compliance curves. The measured crack shapes show a general √r dependence versus the distance to the crack tip. However, close to the crack tip the crack shape is clearly affected by plastic deformation, even in cases when small scale yielding prevails. The compliance curve measurements close to the crack tip can be used to determine the global stress level when the crack surfaces are separated, so that the exact opening and closure stresses can be determined.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

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.     

Corrosion fatigue performance of pre-split steel wires for high strength bridge cables

The first parametric investigation about corrosion fatigue (CF) behaviour of pre-split high-strength galvanized steel wires was conducted for perfecting the design and maintenance of modern bridge cable structures. Counting the cycle number to failure presents that lower fatigue endurance always correlates with higher stress amplitude, while decrease in load ratio and/or increase in cyclic load frequency significantly prolongs the CF life. Electron fractography indicates that the fatigue crack growth rate of the steel wires is lower in air with the presence of tyre tracks on the fracture surface, and faster in aggressive media resulting from anodic dissolution and crack opening displacement at the crack tips. Longer CF endurance of bridge cable steel wires can be expected through ideal thermo-mechanical treatment after the successive cold drawing, for a significant benefit on corrosion resistance and microstructure improvement.     

Consideration of the mechanical behaviour of small fatigue cracks

The mechanical behaviour of small fatigue cracks is investigated for a low, medium and high strength material. At first an elastic consideration is performed which give a good impression how the stress fields change with crack size. In part 2 a full elastic-plastic analysis of short cracks is performed using a new numerical scheme to simulate the growth of shear bands emanating from the crack tip. The influence of material and loading paramters as well as of the crack size on the plastic crack tip opening displacement is discussed. It is also investigated how it is possible to get a conservative estimate of the crack tip deformation at small cracks.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.