Crack Tip Plastic Strain Research Articles

Effect of L‐T and S‐T orientations on fatigue crack growth in an aluminum 7050‐T7451 plate

AbstractThis study is focused on the anisotropic fatigue crack growth (FCG) behavior of an aluminum AA7050‐T7451 plate. L‐T and S‐T orientations were studied in M(T) samples with W = 50 mm, in mode I loading, with R‐ratio of +0.05. A numerical approach was used, assuming that crack tip plastic strain is the crack driving force. A purely kinematic elastic–plastic model was calibrated using experimental data from low cycle fatigue tests of smooth specimens in L and S orientations. The predicted FCG rates agree well with experimental trends in the Paris' regime, suggesting that cyclic plastic deformation is the main damage mechanism. The numerical model was used to estimate the stress ratio effect for both orientations, which was found to be linked with crack closure variations. However, the closure free predicted trends for both microstructural orientations at R = 0.05 are not overlapped, suggesting an effect of microstructure not linked to crack closure.

Effects of material properties and mismatch on unified constraint parameter

In order to develop unified constraint-based fracture assessment method, it needs to investigate the effects of material properties and mismatches on the unified constraint parameter and develop the parameter solutions for cracked structures. In this work, the effects of material properties (yield strength and hardening exponent) and strength mismatch on the in-plane and out-of-plane unified constraint parameter Ad* of semi-elliptical surface cracks in homogeneous and welded plates have been investigated. The results show that the parameter Ad* does not essentially change with yield strength and hardening exponent of materials for cracks in homogeneous plates under bending and tension loads. The parameter Ad* of weld centerline cracks in welded plates under bending and tension loads is essentially independent on the strength mismatch. These advantages of Ad* are conducive to the development of its solutions for homogeneous and welded structures containing cracks. The effect of weld width on Ad* is related to loading mode, mismatch (undermatch or overmatch) and crack size. The mechanism of the influence of material properties, strength mismatch and weld width on Ad* has been explained by its definition and the crack-tip plastic strain distribution. The development and application of Ad* solutions for homogeneous and welded structures also have been discussed.

Mechanisms of fatigue crack growth in Ti-6Al-4V alloy subjected to single overloads

The relative importance of crack closure and residual stresses on fatigue crack growth (FCG), which is controversial, is studied here. FCG is predicted numerically in CT specimens of Ti-6Al-4V alloy submitted to single overloads, assuming that crack tip plastic strain is the driving force. The numerical procedure, which includes the effects of crack tip blunting, material hardening, crack closure and partial crack closure, was found to be very robust and to give correct trends. The high strength material studied showed relatively small overload affected zones (<0.5 mm), which is even more pronounced under plane strain conditions. The comparison of numerical results with and without contact of crack flanks showed that crack closure is responsible for the effect of overloads on FCG rate behaviour, while the effect of residual stresses is not relevant for the material studied. The transient behaviour obtained after an overload is unattainable without considering the contact of the crack flanks.

Revisiting Classical Issues of Fatigue Crack Growth Using a Non-Linear Approach.

Fatigue crack growth (FCG) has been studied for decades; however, several aspects are still objects of controversy. The objective here is to discuss different issues, using a numerical approach based on crack tip plastic strain, assuming that FCG is driven by crack tip deformation. ΔK was found to control cyclic plastic deformation at the crack tip, while Kmax has no effect. Therefore, alternative mechanisms are required to justify models based on ΔK and Kmax. The analysis of crack tip plastic deformation also showed that there is crack tip damage below crack closure. Therefore, the definition of an effective load range ΔKeff = Kmax − Kopen is not correct, because the portion of load range below opening also contributes to FCG. Below crack closure, damage occurs during unloading while during loading the crack tip deformation is elastic. However, if the maximum load is decreased below the elastic limit, which corresponds to the transition between elastic and elasto–plastic regimes, there is no crack tip damage. Additionally, a significant effect of the crack ligament on crack closure was found in tests with different crack lengths and the same ΔK. Finally, the analysis of FCG after an overload with and without contact of crack flanks showed that the typical variation of da/dN observed is linked to crack closure variations, while the residual stresses ahead of crack tip are not affected by the contact of crack flanks.

Numerical Prediction of the Fatigue Crack Growth Rate in SLM Ti-6Al-4V Based on Crack Tip Plastic Strain

This study presents a numerical model to predict the fatigue crack growth (FCG) rate in compact tension specimens under constant amplitude cyclic loadings. The material studied is the Ti-6Al-4V titanium alloy produced by selective laser melting, which was submitted to two different post-treatments: (i) hot isostatic pressing, and (ii) heat treatment. The developed finite element model uses the cumulative plastic strain at the crack tip to define the nodal release. Two different FCG criteria are presented, namely the incremental plastic strain (IPS) criterion and the total plastic strain (TPS) criterion. The calibration of the elasto-plastic constitutive model was carried out using experimental data from low cycle fatigue tests of smooth specimens. For both proposed crack growth criteria, the predicted da/dN-ΔK curve is approximately linear in log-log scale. However, the slope of the curve is higher using the TPS criterion. The numerical predictions of the crack growth rate are in good agreement with the experimental results, which indicates that cyclic plastic deformation is the main damage mechanism. The numerical results showed that increasing the stress ratio leads to a shift up of the da/dN-ΔK curve. The effect of stress ratio was dissociated from variations of cyclic plastic deformation, and an extrinsic mechanism, i.e., crack closure phenomenon, was found to be the cause.

Comparative Study of the Geometric Effects on Fracture Behaviors of Side-Grooved and Plain-Sided Compact Tension Specimens

This paper investigates the fracture response and crack-tip constraint of two typical compact tension specimens. They are pre-cracked plain-sided and side-grooved specimens. In order to clarify the significant effects of geometric parameters on the crack-tip stress fields, an extensive series of detailed 3D elastic–plastic finite element analyses have been carried out. Taking the standard ratio of geometric parameters as a basis, several non-standard geometric parameters are adopted in the calculation for comparison, including specimen thickness, width, crack length. Accordingly, the variation of local J-integral and crack-tip opening displacement have been vigorously investigated over the crack front. Most importantly, the crack-tip stress fields are analyzed in detail with the emphasis on the stress triaxiality and opening mode stress. Furthermore, the crack-tip plastic strain and deformation are compared under small-scale yielding and large-scale yielding between plain-sided and side-grooved specimens, and the constraint parameter Q is employed to explain the distribution of the near-tip plastic strain. Through the vigorous research work, the variation of fracture behavior caused by geometric parameters is reasonably explained and understood.

Ductile fracture prediction based on J-integral and unified constraint parameters for cracked pipes

In actual engineering cracked components, both in-plane and out-of-plane constraints exist simultaneously, thus it is desirable to develop fracture prediction and assessment methodology incorporating both constraints. The constraint parameters Ap based on crack-tip equivalent plastic strain and Ad based on crack-tip opening displacement (CTOD) are two new unified constraint parameters for characterizing both constraints. In this work, by extensive three-dimensional finite element analyses of the parameters Ap and Ad for cracked pipes, the crack driving force (CDF) approaches for predicting ductile fracture based on two-parameter J–Ap and J–Ad have been investigated and developed. The results show that the two approaches can produce similar prediction results for ductile fracture toughness and initiation load of cracked pipes with different crack sizes. Compared with the fracture prediction based on the conventional single parameter J-integral, the application of the two-parameter approaches can reduce conservatism degree for shallower and shorter pipe cracks with low constraint. Because the parameter Ad based on CTOD can be easily measured and determined in finite element analyses. Therefore, it is recommended that the J–Ad approach may be adopted in fracture prediction and assessment of cracked components.

A New Characterization Parameter of out-of-plane Constraint for C(T) Specimens

As the resistance of structures against the crack-tip plastic deformation, constraints has attracted much attention in the research of material fracture behaviour. In order to increase the accuracy of structural integrity assessment, many characterization parameters of in-plane and out-of-plane constraints have been considered and proposed in the last few decades. Three-dimensional finite element analyses have been conducted for five C(T)50 specimens with different out-of-plane constraint. The distributions of four constraint parameters (σ22/σ0, Tz, h and Dp) along crack fronts were calculated. To characterize the out-of-plane constraint, the capability of constraint parameters such as σ22/σ0, Tz, h and Dp were analyzed and compared. Results show that, compared with the three constraint parameters (σ22/σ0, Tz and h) based on crack-tip stress fields, the parameter Dp based on crack-tip equivalent plastic strain is more sensitive to out-of-plane constraint, and may effectively characterize the out-of-plane constraint.

Linear matching method for design limits in plasticity

In this paper a state-of-the-art numerical method is discussed for the evaluation of the shakedown and ratchet limits for an elastic-perfectly plastic body subjected to cyclic thermal and mechanical load history. The limit load or collapse load, i.e. the load carrying capacity, is also determined as a special case of shakedown analysis. These design limits in plasticity have been solved by characterizing the steady cyclic state using a general cyclic minimum theorem. For a prescribed class of kinematically admissible inelastic strain rate histories, the minimum of the functional for these design limits are found by a programming method, the Linear Matching Method (LMM), which converges to the least upper bound. By ensuring that both equilibrium and compatibility are satisfied at each stage, a direct algorithm has also been derived to determine the lower bound of shakedown and ratchet limit using the best residual stress calculated during the LMM procedure. Three practical examples of the LMM are provided to confirm the efficiency and effectiveness of the method: the behaviour of a complex 3D tubeplate in a typical AGR superheater header, the behaviour of a fiber reinforced metal matrix composite under loading and thermal cycling conditions, and effects of drilling holes on the ratchet limit and crack tip plastic strain range fora centre cracked plate subjected to constant tensile loading and cyclic bending moment.

Effect of compressive loads on plasticity induced crack closure

Compressive stresses play an important role on tension–compression fatigue which can be attributed to plasticity induced crack closure (PICC). The objective here is to study numerically the effect of compressive stresses on PICC and to discuss the applicability of PICC to explain the effect of negative stress ratios on fatigue crack growth rate. The compression produces reversed plastic deformation at the crack tip, reducing linearly the crack opening level. The incursion to negative stress ratios did not produce sudden changes in the behavior of PICC and no saturation with the decrease of minimum load was observed for ΔKeff. Crack closure was able to collapse da/dN–ΔK curves with negative stress ratios, indicating the applicability of the crack closure concept to explain the effect of negative R. The analysis of crack tip plastic strain range with and without contact of crack flanks confirmed the validity of crack closure concept.

Effects of hydrogen-altered yielding and work hardening on plastic-zone evolution: A finite-element analysis

In the present paper, finite-element analysis of a cracked specimen was conducted using a unified model for the elastic–plastic deformation and hydrogen diffusion. We considered the effects of the hydrogen-reduced yielding strength and work-hardening coefficient and used a comparison parameter in the simulation of the hydrogen-localized plastic zone near a crack tip. We realized two important facts: (1) the normal component of the plastic strain in the direction of remote stress near the crack tip is significantly increased by the reduced work-hardening coefficient at the same stress-intensity factor; (2) the reduced work-hardening coefficient enhances the localization of the plastic zone when compared to the case using the normal component of the crack-tip plastic strain in the direction of remote stress, which probably determines the ductile–brittle transition of the fatigue-crack propagation mode under a hydrogen atmosphere. These results indicate that the reduction in work-hardening coefficient and the utilization of the crack-tip plastic strain as a parameter to organize the data play important roles in the prediction of the transition condition of hydrogen-accelerated fatigue-crack propagation.

Measurement and Modeling of Hydrogen Environment-Assisted Cracking in Monel K-500

Hydrogen environment-assisted cracking (HEAC) of Monel K-500 is quantified using slow-rising stress intensity loading with electrical potential monitoring of small crack propagation and elastoplastic J-integral analysis. For this loading, with concurrent crack tip plastic strain and H accumulation, aged Monel K-500 is susceptible to intergranular HEAC in NaCl solution when cathodically polarized at −800 mVSCE (E A, vs saturated calomel) and lower. Intergranular cracking is eliminated by reduced cathodic polarization more positive than −750 mVSCE. Crack tip diffusible H concentration rises, from near 0 wppm at E A of −765 mVSCE, with increasing cathodic polarization. This behavior is quantified by thermal desorption spectroscopy and barnacle cell measurements of hydrogen solubility vs overpotential for planar electrodes, plus measured-local crevice potential, and pH scaled to the crack tip. Using crack tip H concentration, excellent agreement is demonstrated between measurements and decohesion-based model predictions of the E A dependencies of threshold stress intensity and Stage II growth rate. A critical level of cathodic polarization must be exceeded for HEAC to occur in aged Monel K-500. The damaging-cathodic potential regime likely shifts more negative for quasi-static loading or increasing metallurgical resistance to HEAC.

Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate

In this paper a centre cracked plate subjected to cyclic tensile loading and cyclic bending moment is considered. The effect of circular holes drilled in the region of the crack tip on the ratchet limit and crack tip plastic strain range is studied. Direct evaluation of the ratchet limit and crack tip plastic strain range is solved by employing the new Linear Matching Method (LMM). Parametric studies involving hole diameter and location are investigated. The optimum hole location for reducing the crack tip plastic strain range with the least reduction in ratchet limit is identified, and located at a distance 10% of the semi-crack length from the crack tip on the side opposite the ligament for both cyclic tensile loading and cyclic bending moment cases. It is also observed that the optimum location is independent of the hole size for both cyclic loading cases.

Study on Crack Retardation with the Consideration of Crack Surface Roughness by FEM

As one of the key factors to induce crack closure, crack surface roughness plays a dominated role in evaluating the characteristics of short fatigue cracks. The crack retardation induced by the crack surface roughness was investigated by numerical simulation in this paper. The influence of crack surface roughness on short fatigue cracks was directly applied into the numerical simulation procedure with the help of friction coefficients on the contacted crack surfaces. The driving forces of cracks represented by the two indicators such as crack tip displacement and plastic strain range were studied and used to characterize the retardation induced by crack surface roughness. It is shown that the evidence of crack surface roughness affecting on crack retardation is obvious and the influence of crack surface roughness on the characteristics of short fatigue cracks must account for in evaluating the performance of short fatigue cracks.

Effect of overload on fatigue crack retardation of aerospace Al-alloy laser welds using crack-tip plasticity analysis

Investigations on fatigue crack growth retardation due to single tensile and periodic multiple over load in strength undermatched laser beam welded 3.2 mm thick aerospace grade aluminium alloy 2139-T8 sheets are conducted. The effect of overload on the fatigue crack propagation behaviours of the homogenous base metal and welded panels (200 mm wide, centre cracked) was compared using experimental and FE analysis methods. The effective crack tip plasticity has been determined in homogeneous M( T) specimens using Irwin’s method and in both homogeneous and laser welded specimen by calculating crack tip plastic strain using FE analysis for single tensile overload. The crack retardation due to the overload in welded specimens is described by the Wheeler Model. The crack tip plastic zone size in the welded specimen was determined by FE analysis using maximum plastic zone extension at the mid sheet thickness. The results show that the Wheeler Model can be implemented to the highly heterogeneous undermatched weld to describe the crack retardation in fatigue following single tensile overload. Fatigue crack growth retardation due to single overload is found to be larger than the base metal. However, after periodic multiple overload, shorter crack retardation has occurred for undermatched welds than the base metal.

Finite element crack closure analysis of a compact tension specimen

Crack closure behaviour of a compact tension (CT) specimen subjected to a constant amplitude cyclic mechanical load, with load ratio R = −2 and the maximum load approaching and exceeding the yield strength based limit load of the specimen, has been examined by performing large strain elastic–plastic finite element (FE) crack growth analyses assuming kinematic hardening. Results from static analyses show that the near crack tip stress and plastic strain fields do not change significantly with further loading after crack closure takes place. Results from crack growth analyses show that the crack closure type depends on the maximum stress intensity factor (SIF) and the crack tip constraint conditions, and that the crack opening/closing loads can be correlated by the maximum SIF, for given crack tip constraint conditions (plane stress/strain). The equation given in the R5 procedure for the crack closure factor, q 0, is conservative compared with the results obtained from the FE simulation.

Elastic–plastic finite element analysis and experimental study of short and long fatigue crack growth

A detailed elastic–plastic finite element analysis of cracks under mode I loading is presented under both small- and large-scale yielding conditions. Five centre-cracked panel specimens with different crack lengths are analysed. The size of the crack tip plastic zone, the crack opening profile and the plastic strain distribution in front of the crack tip for short (0.1 mm) and for longer cracks (0.2, 0.4, 1 and 2 mm) have been studied. The analysis shows that the crack tip plastic zone size, crack tip plastic strain and crack tip opening displacements are larger for a short crack than for longer cracks at the same nominal stress intensity factor. Experimental study of both the short and long fatigue crack growths for an ultra-fine grain aluminium alloy IN9052 has also been performed. The experimental results show that the short fatigue cracks propagate faster than the long fatigue cracks under the same stress intensity factor ranges. However, if the short and long fatigue crack growth rates are correlated by the plastic zone size, the short and long fatigue crack growth rates fall in the same band.

The tip plastic strain energy applied to ductile fracture initiation under mixed-mode loading

Crack tip plastic strain energy is considered for characterizing a mixed-mode crack initiation. It is postulated that mixed-mode cracking for a strain hardening material begins as the crack tip plastic strain energy approaches a critical plastic strain energy. The corresponding crack tip plastic strain energy at a pure mode I initiation is considered as the crack initiation criterion. The crack initiation loads for various mixed-mode crack specimens made of D16AT aluminum alloy are then predicted. The predicted crack initiation loads correlate well with the experimental data available.

THE ROLE OF CYCLIC PLASTICITY IN CRYSTALLOGRAPHIC CRACK GROWTH RETARDATION

This paper presents a review of the effect of crack tip cyclic plasticity on retarded crystallographic (stage I) crack growth in metal single crystals, bicrystals, engineering polycrystals and particulate-reinforced metal matrix composites (PMMC). The cyclic plastic deformation at the tip of a crystallographic crack, is shown to be affected by tortuous crack wake, adjacent grain boundary, or by the surrounding particles in a PMMC. Evidence gathered shows that change in the crack growth direction results from the redistribution of crack tip plastic strain. Similarly, the crack growth rate deceleration is related to the reduction of the cyclic plastic strain range due to the crack tip shielding. The role of the cyclic plasticity as a driving force in the shielded crystallographic crack growth, is demonstrated. The threshold for both the short and long crack growth corresponds to a critical loading condition which produces a persistent slip band of the characteristic microstructural size.

Measurement of the temperature field induced by dynamic crack growth in Beta-C titanium

The temperature increase at the tip of a dynamically propagating crack may have a significant effect on a material's mechanical properties, and hence on its dynamic fracture toughness. In order to start to understand this phenomena, measurements of the temperature field at the tip of a dynamically growing crack in Beta-C titanium alloy were performed using a linear array of high speed infrared detectors. The results show that a maximum temperature of 450°C is reached at the crack tip. In addition, the dynamic fracture toughness was measured for crack speeds from 0 to 500 m/s. In this speed range, the toughness appears to be constant. Estimates of the crack tip energy release rate and plastic strain rate are made using analysis of the experimental data.