Plasticity-induced Fatigue Crack Closure Research Articles

Experimental investigation of crack opening loads in an aircraft load spectrum

The concept of plasticity-induced fatigue crack closure is indispensable in explaining many fatigue crack growth phenomena; and it is now widely applied in advanced fatigue life evaluation procedures. This concept has been extensively investigated experimentally over the past sixty years using different methods. However, most of these investigations are related to constant amplitude loading or simple load cases such as single or multiple overloads or block loading. In contrast, there are currently no experimental studies investigating crack closure under variable amplitude loading or load spectra, which are more realistic scenarios. This can be attributed to the many difficulties associated with the evaluation of crack opening loads for large numbers of fatigue cycles, including sensor sensitivity, signal noise, data limits, etc. Recently, the authors proposed an advanced piezoelectric sensor for cycle-by-cycle crack opening load measurements, which addresses the above limitations. In this work, the piezoelectric sensor is utilised to investigate crack closure under a typical transport aircraft load spectrum. In particular, it is demonstrated that crack opening load levels can change significantly from cycle-to-cycle, and these levels are typically larger than for constant amplitude loading at the same R-ratio. The relative density plot of crack opening load levels reveals three distinct regions, which can be associated with certain load sequences. The outcomes of this research are important for the development and validation of spectrum compression algorithms as well as advanced fatigue life evaluation procedures.

Residual opening of fatigue cracks due to the wake of plasticity

The concept of a breathing crack and the clapping mechanism, when a crack periodically opens and closes subject to a cyclic or harmonic excitation, are widely utilised in studies concerning contact acoustic nonlinearity (CAN) and nonlinear phenomena. The investigation of these phenomena is particularly important for the development of reliable non-destructive fatigue crack detection techniques. The aim of the current contribution is to demonstrate the characteristic behaviour of a fatigue crack under excitation loading using a simple analytical model that accounts for the wake of plasticity behind the crack tip, which leads to the plasticity-induced fatigue crack closure phenomenon. It is believed that incorporation of these features and more realistic behaviour of fatigue cracks can help to improve the methods for the detection of nonlinear phenomena associated with CAN. The results of the present work indicate that ultrasonic inspections based on the CAN using a bilinear stiffness model may underestimate the length of the detected crack(s) due to the plasticity-induced crack closure phenomenon. Despite many modelling assumptions, the present work can serve as a starting point for the development of accurate models for different crack geometries and load histories. The latter may help to develop effective nondestructive techniques for detection and identification of fatigue cracks and prevention of fatigue failures.

The influence of bending loading on surface fatigue crack growth life

Engineering structures often serve under complex fatigue loading and the most common of which are tension and bending loading, or their combination. Fatigue cracks always initiate as surface and other three dimensional (3D) cracks and most of the fatigue life of structures spends on 3D crack growth, but fatigue crack propagation curves of materials are widely obtained using through-the-thickness specimens. In this work, a 3D fracture mechanics based method is developed to evaluate surface crack propagation life under combined tension and bending loadings by considering the plasticity induced fatigue crack closure. The method is validated firstly against available experimental data of surface fatigue cracked plates under the combined loadings, and then applied to predict fatigue crack propagation life of surface cracked railway axles under rotating bending. It is shown that the method can make prediction of life within 0.80 to 1.08 of the test life, and the predicted shape evolution of surface crack agrees well with experimental observation. With a modification of short crack closure being made and an equivalent initial crack being assumed, the proposed method can be extended to fatigue life prediction. It is found that the influence of bending loading on fatigue life increasing for larger initial cracks, especially in the submillimeter range. This fracture mechanics based method can serve as a unified way to calculate fatigue crack growth life as well as fatigue life of practical structures under both tension and bending loadings by use of the material crack growth curves obtained with straight-through cracked standard specimens.

A finite element study on the influence of the hardening behavior on plasticity-induced fatigue crack closure

In this paper, the influence of the material hardening behavior on plasticity-induced fatigue crack closure is investigated for strain-controlled loading and fully plastic, large-scale yielding conditions by means of the finite element method. The strain amplitude and the strain ratio are varied for given Ramberg–Osgood material properties representing materials with different hardening behavior. The results show a pronounced influence of the hardening behavior on crack closure, while no significant effect is found from the considered strain amplitude and strain ratio. The effect of the hardening behavior on the crack opening stress cannot be described by existing crack opening stress equations.

Effect of Specimen Thickness and Stress Intensity Factor Range on Plasticity-Induced Fatigue Crack Closure in A7075-T6 Alloy.

Fatigue crack growth experiments are performed using A7075-T6 compact tension (CT) specimens with various thicknesses t (1–21 mm). The stress intensity factor at the crack opening level Kop is measured, and the effects of t and the stress intensity factor range ΔK on Kop are investigated. In addition, the change in Kop value due to specimen surface removal is investigated. Furthermore, we clarify that the radius of curvature of the leading edge of the fatigue crack decreases as t becomes thinner. Using the three-dimensional elastoplastic finite element method, the amount of plastic lateral contraction (depression depth d) at the crack tip after fatigue loading is calculated quantitatively. The following main experimental results are obtained: In the region where ΔK is 5 MPam1/2 or higher, the rate of fatigue crack growth da/dN at a constant ΔK value increases as t increases from 1 to 11 mm. The da/dN between t = 11 and 21 mm is the same. Meanwhile, in the region where ΔK is less than 5 MPam1/2, the effect of t on da/dN is not observed. The effects of t and ΔK on the da/dN–ΔK relationship are considered physically and quantitatively based on d.

Surface fatigue crack growth under variable amplitude loading

Plasticity-induced fatigue crack closure plays an important role in fatigue crack growth. Under fatigue loading with variable amplitude, however, the influence of fatigue crack closure along the crack front in three-dimensional cracked bodies is difficult to analyze. Here we develop a three-dimensional strip yield model to calculate crack opening stresses of surface fatigue cracks under variable amplitude loading. An equivalent thickness concept is incorporated to quantify the thickness effect for points on the surface crack front with a series of straight-through cracks. Using this equivalent thickness based strip yield model and fatigue crack growth rate curves obtained with standard through the thickness cracked specimen under constant amplitude loading, fatigue growth of surface cracks under variable amplitude loading are able to be predicted. We used this method to calculate fatigue crack growth of five semi-elliptical surface cracks and found that the ratios of the predicted life to the experimental life ranged from 0.86 to 1.01. The average value of the results was 0.93 and the standard deviation was 0.055. Good agreements are found between the predicted and experimental life for semi-elliptical surface cracks under variable amplitude loading. This method paves an avenue for fatigue crack growth life prediction of practical structures using materials properties obtained in laboratory according to material test standards.

Equivalent thickness-based three dimensional stress fields and fatigue growth of part-through cracks emanating from a circular hole

Accurate characterization of stress states is essential to assess structural integrity and predict fatigue crack growth life. Strong three dimensional constraints always raise at cracks and holes, but have never been investigated in the frame of three dimensional fracture theory for part-through cracks emanating from a hole. Here the three dimensional constraint and its effect on crack tip fields of corner and surface cracks emanating from a circular hole in tensile plates are comprehensively analyzed using finite element method. Distributions of the out-of-plane constraint factor Tz are strongly dependent on relative circular hole size and relative thickness parameters, but the K-Tz description of the stress field remains efficient with the present of circular hole. The equivalent thickness conception based on Tz distributions is applied to crack tip stress field description. Based on the equivalent thickness conception and plasticity-induced fatigue crack closure model, evaluation of fatigue growth of corner crack emanating from a circular hole is demonstrated and validated against test data in the literature.

Experimental evaluation of CTOD in constant amplitude fatigue crack growth from crack tip displacement fields

In the current work an experimental study of the crack tip opening displacement (CTOD) is performed to evaluate the ability of this parameter to characterise fatigue crack growth. A methodology is developed to measure and to analyse the CTOD from experimental data. The vertical displacements measured by implementing Digital Image Correlation on growing fatigue cracks are used to measure the CTOD. Fatigue tests at R ratios of 0.1 and 0.6 were conducted on compact-tension specimens manufactured from commercially pure titanium. A sensitivity analysis was performed to explore the effect of the position selected behind the crack tip for the CTOD measurement. The analysis of a full loading cycle allowed identifying the elastic and plastic components of the CTOD. The plastic CTOD was found to be directly related to the plastic deformation at the crack tip. Moreover, a linear relationship between da/dN and the plastic CTOD for both tests was observed. Results show that the CTOD can be used as a viable alternative to ?K in characterising fatigue crack propagation because the parameter considers fatigue threshold and crack shielding in an intrinsic way. This work is intended to contribute to a better understanding of the different mechanisms driving fatigue crack growth and the address the outstanding controversy associated with plasticity-induced fatigue crack closure.

Experimental and Numerical Simulation Study of Plasticity-Induced and Roughness-Induced Fatigue Crack Closure

In this study, fatigue crack closure behavior was investigated in the aluminum alloy 6061-T6 and the carbon steel JIS. S25C. It was found that crack closure in the aluminum alloy 6061-T6 showed the characteristics of plasticity-induced fatigue crack closure (PIFCC), whereas the carbon steel JIS. S25C showed the characteristics of roughness-induced fatigue crack closure (RIFCC). The experiments included the determination of the crack-opening levels Kop as a function of stress intensity factor range ΔK and the effect of surface removal on the crack-opening level. In order to simulate the behaviors of the plasticity-and the roughness-induced fatigue crack closure, the finite element method was adopted. The results of FEM were in good agreement with the experimental results. It was cconcluded that at a given yield strength level , a low Youngs modulus and a low work-hardening coefficient will favor PIFCC, whereas a high Youngs modulus and a high work-hardening coefficient will favor RIFCC.

Finite element modeling of plasticity-induced crack closure due to occasional mode II loading on mode I fatigue crack growth

Plasticity-induced fatigue crack closure associated with occasional mode II loading was simulated for two-dimensional middle-crack tension geometry by using the finite element method. When a single mode II cycle was superposed onto the steady-state mode I crack growth, the range of crack tip opening displacement, ΔCTOD, exhibited the initial drop and subsequent recovery under plane strain condition. On the other hand, under plane stress condition, ΔCTOD exhibited the initial jump and drop right after the single mode II loading, and then it showed the recovery. The present results indicate that occasional mode II loading can cause a small retardation for mode I crack growth due to the enhanced plasticity-induced closure.

Effet de l’équilibre glycémique sur le statut antioxydant d’une population de diabétiques de la ville de Constantine

Plasticity-induced fatigue crack closure associated with occasional mode II loading was simulated for two-dimensional middle-crack tension geometry by using the finite element method. When a single mode II cycle was superposed onto the steady-state mode I crack growth, the range of crack tip opening displacement, ΔCTOD, exhibited the initial drop and subsequent recovery under plane strain condition. On the other hand, under plane stress condition, ΔCTOD exhibited the initial jump and drop right after the single mode II loading, and then it showed the recovery. The present results indicate that occasional mode II loading can cause a small retardation for mode I crack growth due to the enhanced plasticity-induced closure.

Syndrome d’interruption de la tige pituitaire de révélation tardive

Plasticity-induced fatigue crack closure associated with occasional mode II loading was simulated for two-dimensional middle-crack tension geometry by using the finite element method. When a single mode II cycle was superposed onto the steady-state mode I crack growth, the range of crack tip opening displacement, ΔCTOD, exhibited the initial drop and subsequent recovery under plane strain condition. On the other hand, under plane stress condition, ΔCTOD exhibited the initial jump and drop right after the single mode II loading, and then it showed the recovery. The present results indicate that occasional mode II loading can cause a small retardation for mode I crack growth due to the enhanced plasticity-induced closure.

A macrostructural model for simulating the combined effects of roughness and plasticity induced fatigue crack closure

We adapt a weight function based modified strip-yield model to geometrically include the mode I effects of roughness induced crack closure. A rough crack geometry is simulated as a sine wave fitted to a sawtooth defined by an asperity angle and period. Additional crack closure due to the sliding of crack faces is incorporated into the strip-yield model by lengthening and shortening the crack face elements, creating a sawtooth-like crack wake. We study combined roughness and plasticity induced crack closure by varying the crack face asperity angle and period. The addition of rough crack face geometry effects causes the amount of crack closure to oscillate above and below an average value influenced primarily by the asperity angle. The periodicity of the rough crack has little or no effect on closure.

Recent Advances in Fatigue Crack Growth

Many of the recent advances in the understanding of the fatigue crack growth process have resulted from an improved realization of the importance of fatigue crack closure in the crack growth process. Two basic crack closure processes have been identified. One of which is known as plasticity-induced fatigue crack closure (PIFCC), and the other is roughness-induced fatigue crack closure (RIFCC). Both forms occur in all alloys, but PIFCC is a surface-related process which is dominant in aluminum alloys such as 2024-T3, whereas RIFCC is dominant in most steels and titanium alloys. A proposed basic equation governing fatigue crack growth is (1) where where Kmax is the maximum stress intensity factor in a loading cycle and Kop is the stress intensity factor at the crack opening level. is the range of the stress intensity factor at the threshold level which is taken to correspond to a crack growth rate of 10-11 m/cycle. The material constant A has units of (MPa)-2, and therefore Eq. 1 is dimensionally correct. Eq.1 has been successfully used in the analysis of both long and short cracks, but in the latter case modification is needed to account for elastic-plastic behavior, the development of crack closure, and the Kitagawa effect which shows that the fatigue strength rather than the threshold level is the controlling factor determining the rate of fatigue crack growth in the very short fatigue crack growth range. Eq. 1 is used to show that The non-propagating cracks observed by Frost and Dugdale resulted from crack closure. The behavior of cracks as short as 10 microns in length can be predicted. Fatigue notch sensitivity is related to crack closure. Very high cycle fatigue (VHCF) behavior is also associated with fatigue crack closure.

On the Distinction Between Plasticity- and Roughness-Induced Fatigue Crack Closure

A series of experiments has been carried out to determine why some alloys display plasticity-induced fatigue crack closure (PIFCC), whereas other alloys display roughness-induced crack closure (RIFCC). Two alloys were studied, the aluminum alloy 6061-T6 (PIFCC) and a steel of comparable yield strength, S25C (RIFCC). The experiments included the determination of the crack-opening levels as a function of ΔK, da/dN as a function of ΔK eff – ΔK effth, removal of the specimen surface layers, removal of the crack wake, the determination of crack front shapes, crack surface roughness profiles, and the degree of lateral contraction in the plastic zone at a crack tip. Based on crack tip opening displacement (CTOD) considerations, it is concluded that PIFCC is favored in alloys of low modulus and relatively low yield strength. In addition, a low strain-hardening rate such as for the 6061 alloy will favor PIFCC. Steels with a higher modulus and a higher strain-hardening rate than 6061 will, in general, exhibit RIFCC, even at comparable yield strength levels. In ferritic steels, the fracture surface roughness and consequently the crack-opening level will increase as the coarseness of the microstructure increases.

A study of combined roughness and plasticity induced fatigue crack closure for long cracks using a modified strip-yield model

Combined roughness- and plasticity-induced crack closure for long cracks is studied using a Design and Analysis of Computer Experiments approach. A newly developed modified strip-yield model which has been adapted to incorporate the mode I effects of roughness induced crack closure is used for the study. The effects of maximum stress, load ratio, roughness asperity angle, and roughness periodicity are quantified. In addition, conditions affecting the benefit of roughness-induced crack closure are investigated.

The influence of T-stress on plasticity induced crack closure under plane strain conditions

A small scale yielding two-parameter modified boundary layer analysis is performed to study the occurrence of plasticity induced fatigue crack closure under constant amplitude plane strain conditions. A wide range of T-stress and KI levels are considered in the finite element analysis with the purpose of exploring the behavior of the crack opening stress. The influence of the T-stress on crack closure is shown. Crack closure was observed for some values of T-stress, while other values of T-stress resulted in an absence of closure under steady-state conditions.

Simulation and comparison of several crack closure assessment methodologies using three-dimensional finite element analysis

Plasticity induced fatigue crack closure simulations were performed using a three-dimensional finite element analysis of a single edge-cracked tension specimen under constant amplitude loading and load ratio R = 0. Four different methodologies were considered to assess fatigue crack closure: (a) a node displacement method monitoring the first and second nodes behind the crack tip, (b) a contact stress method, (c) the traditional compliance offset method, and (d) the adjusted compliance ratio (ACR) technique. The evolution of crack driving force was compared in terms of U = Δ K eff / Δ K , where Δ K eff and Δ K are the effective and applied stress intensity factor ranges, respectively. The node displacement method using the first node behind the crack tip and the contact stress method produced the lowest levels of U. Larger U levels were obtained from the node displacement method using the second node behind the crack tip followed by those from the compliance offset technique. The ACR methodology provided the highest U values for the range of applied loading considered in this study.

An Efficient Way to Characterize the Fatigue Crack Growth Based on Numerical Analysis

The behavior of plasticity induced fatigue crack closure (PICC) in middle tension specimen was analyzed by the elastic-plastic finite element method. For the constant-K (CK) loading cases, the opening stress intensity factor are independent of crack length. The level of increases with the maximal applied stress intensity factor for given load ratio and increases with for fixed . The in plane strain state is much smaller than that in plane stress state. The results under CK loadings can be deduced to constant amplitude cyclic loading case during which the load ratio, maximal load level, crack length and specimen thickness are all the factors affecting the crack closure effect. The phenomena revealed in the analysis are beneficial in understanding the driving force mechanism of the fatigue crack growth.

Plasticity-Induced Fatigue Crack Closure in High-Strength Steels: Is it a Real Phenomenon?

High-resolution elastoplastic simulations of a plane-strain tensile crack under cyclic loading visualised the Laird-Smith mechanism of fatigue crack growth, which manifested the effects of K and overload, but no signs of crack closure. Simulations discarded the supposed mechanism of plasticity-induced crack closure (PICC) via out-of-plane stretching of material elements filling-in the crack and coming in contact at unloading. Specimen compliance curves turned out to be nonlinear merely by virtue of plasticity with no contribution of crack closure. Thus the results manifested the ambiguity of main justifications about the phenomenon of PICC.