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.     

The fatigue crack growth rate and crack opening displacement in 18G2A-steel under tension

In the paper, the results of crack tip opening displacement (CTOD) and crack opening displacement (COD) in place of crack initiation as well as the fatigue crack growth rate in higher strength steel are presented. The investigation were carried out on flat specimens with central notch under constant amplitude tensile fatigue loading at stress ratio R = 0.2 and different value of the stress σ_max. The test results showed that with growth of crack length l grew values of the CTOD and COD. In the work, it was proposed calculation of the CTOD value on basis various dependence of plastic zone radius on crack tip.     

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.     

Some recent fatigue and fracture mechanics research in BIAM

The paper presents a brief review of some of the major research activities on fatigue and fracture mechanics in recent years at the Beijing Institute of Aeronautical Materials. Attention is mainly given to the studies on weight function methods for analyses of two- and three-dimensional crack problems, fatigue crack growth under variable amplitude loading, small crack effects and a fracture-mechanics-based total fatigue life prediction method.Abbreviations 2(3)D two- (three-) dimensional - BIAM Institute of Aeronautical Materials, Beijing - CCT center cracked tension - COD crack opening displacement - CTOD crack tip opening displacement - FEM finite element method - LEFM linear elastic fracture mechanics - SENT single edge notched tension - SIF stress intensity factor - WFM weight function method     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading

A generalized Irwin model is proposed to investigate elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under combined tension and shear loading. The dependence of the stress intensity factors, the plastic zone size, the effective stress intensity factor and the crack tip opening displacement on the crack depth h, the Dundurs’ parameters and the phase angle θ is discussed in detail. Numerical results show that in most cases, if the crack is embedded in a stiffer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will increase. On the contrary, if the crack is embedded in a softer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will decrease.     

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.     

Effect of overload on crack closure in thick and thin specimens via digital image correlation

The displacement field of compact tension (CT) specimens have been mapped by digital image correlation (DIC) local to growing fatigue cracks to study overload effects for plane stress and plane strain. We have extracted crack opening displacement (ΔCOD) and stress intensity (K) determined by a Muskhelishvili fit to the crack tip displacement field to infer the closure load. In both cases a classical knee was observed upon unloading consistent with closure which disappeared during the accelerated growth following OL, before increasing during retardation. In both cases following OL the crack growth rate is perturbed for a distance similar to the plastic zone.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Plastic zone correction on a Zener–Stroh crack interacting with a circular inclusion in ductile materials

Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with a circular inclusion (fibre) in fibre‐reinforced composites has been carried out. The Zener–Stroh crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a crack–inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed‐mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic–plastic fracture behaviour of the crack. In our study, the plastic zone size (PZS), crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, crack–inclusion distance and the crack sharp tip position on the fracture behaviour of the crack is discussed. It is found that the shear modulus ratio and the crack–inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the crack sharp tip position.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.     

Towards a new model of crack tip stress fields

This work introduces a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of plasticity through an analysis of their shielding effects on the applied elastic field. The ability of the model to characterize plasticity-induced effects of cyclic loading on the elastic stress fields is assessed and demonstrated using full-field photoelasticity. The focus is on determining the form of the shielding stress components (induced by compatibility requirements at the elastic–plastic interface along the crack flank and via the crack tip plastic zone) and how they influence the crack tip elastic stress fields during a load cycle. The model is successfully applied to the analysis of a fatigue crack growing in a polycarbonate CT specimen.     

Numerical investigation of crack tip strain localization under cyclic loading in FCC single crystals

In this work, the crack tip strain localization in a face centered cubic single crystal subject to both monotonic and cyclic loading was investigated. The effect of constraint was implemented using T-stress and strain accumulation was studied for both isotropic and anisotropic elastic cases with the appropriate application of remote displacement fields in plane strain. Modified boundary layer simulations were performed using the crystal plasticity finite element framework. The consideration of elastic anisotropy amplified the effect of constraint level on stress and plastic strain fields near the crack tip indicating the importance of its use in fracture simulations. In addition, to understand the cyclic stress and strain behavior in the vicinity of the crack tip, combined isotropic and kinematic hardening laws were incorporated, and their effect on the evolution of yield curves and plastic strain accumulation were investigated. With zero-tension cyclic load, the evolution of plastic strain and Kirchhoff stress components showed differences in magnitudes between isotropic and anisotropic elastic cases. Furthermore, under cyclic loading, ratcheting was observed along the localized slip bands, which was shown to be affected by T-stress as well as elastic anisotropy. Negative T-stress increased the accumulation of plastic strain with number of cycles, which was further amplified in the case of elastic anisotropy. Finally, in all the cyclic loading simulations, the plastic strain accumulation was higher near the \(55^0 \) slip band.     

Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS

A predictive method for remaining component lifetime evaluation consists in integrating the crack growth law of the material considered in a finite element step-by-step process. So, as part of a linear elastic fracture mechanics analysis, the determination of the stress intensity factor distribution is a crucial point. The aim of the present work is to test several existing numerical techniques reported in the literature. Both the crack opening displacement extrapolation method and the J-integral approach are applied in 2D and 3D ABAQUS finite element models. The results obtained by these various means on CT specimens and cracked round bars are in good agreement with those found in the literature. Nevertheless, since the knowledge of the field near the crack tip is not required in the energetic method, the J-integral calculations seem to be a good technique to deal with the fatigue growth of general cracks.     

Deformation behaviour at the tip of a physically short fatigue crack due to a single overload

A two-dimensional elastic–plastic finite element analysis was utilized to investigate the transition behaviour of a physically short fatigue crack following the application of a single overload cycle. The deformation accommodated at the tip of a crack artificially advancing with a fully reversed load was considered. The development of the cyclic crack tip opening displacement was computed and then modelled to include the effects of the stress level of the base cycles, overload pattern and crack length at which the transient cycle was applied. The cyclic crack tip opening displacement was initially of a relatively high value. It decreased and then increased to match the behaviour under the base load cycles. The extent and location of both the minimum and matching points were dependent on the overload crack length and the stress compared with the material’s yield stress. In the case of the yield stress being exceeded by the overload, the minimum and the-return-to-normality points are identical. A previously developed crack tip deformation parameter was invoked to predict relevant experimental fatigue growth rates of short cracks reported in the literature.     

Cyclic crack tip deformation and its relation to fatigue crack growth

Characteristics and mechanism of fatigue crack growth in mild steel have been investigated taking account of crack tip deformations: crack tip opening displacement δt and the size of highly deformed zone ahead of crack tip Rx0.2 (the size of the zone with accumulated strain above 0.2). δt was measured directly at midsection of the specimen with a profile projector. Rx0.2 was obtained from strain distribution ahead of crack tip determined by the use of the recrystallizalion phenomenon.It is revealed that crack growth rates ranging from 0.02 μm/cycle to 200 μm/cycle are expressed well by a second power function of both δt and Rx0.2. Abrupt increases in μt and Rx0.2 occured at a growth rate of about 1 μm/cycle. At this growth rate, fracture appearance changed from striation to dimple. These transitions are due to the transition of stress state. It is also shown that fatigue fracture strain is constant independently of crack growth rate and is equal to the ductile fracture strain in monotonic loading. The constant fracture strain is the criterion for fatigue failure of ductile steels.