Plasticity-induced Crack Closure Research Articles

Fatigue crack propagation analyses based on plastic energy approach

Plasticity effects at the crack tip had been recognized as “motor” of crack propagation. The growth of cracks is related to the existence of a crack tip plastic zone, whose formation and intensification is accompanied by energy dissipation. In the actual state of knowledge, fatigue crack propagation is modeled using crack closure concept. Recent studies demonstrated that closure effects and the role of plasticity-induced crack closure are more pronounced at the early stage of the crack growth at low stress ratio R. In this paper, an analysis of fatigue crack propagation based on energetic approach is proposed. A model describing the material behavior is also proposed. It is expressed by a unique linear relation between the crack growth rate and the hysteretic energy per cycle by including an energetic correction factor ζ M which takes into account the over evaluations obtained by hysteresis loops and shows the different effects of plasticity, crack closure and opening mode.

Fatigue Crack Growth of Ultrafine Grained Pure Ti after Severe Plastic Deformation

Fatigue crack growth behavior of the ultrafine-grained pure Ti produced by ECAP was investigated. The ECAPed sample with a total strain of 4.6 showed nearly equiaxed grains with an average size of about 0.3 μm. After ECAP, the ultimate tensile strength was increased by 60%, while the tensile elongation was decreased by 31%. The ECAPed Ti showed much higher resistance in fatigue crack growth by about a factor of 4 over the whole +K due to plasticity-induced crack closure.

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.

The effect of material model in describing mechanism of plasticity-induced crack closure under variable cyclic loading

Three-dimensional finite element method is utilized to analyze the plasticity-induced crack closure (PICC) phenomenon in a cracked plate under variable amplitude loading conditions: the effect of a single spike tensile overload, and also the case of a single compressive overload (underload). To accurately capture the PICC process the choice of material model employed is of significant importance, therefore this paper considers a relatively new model, the Ellyin-Xia model, and the more widely employed kinematic hardening model. The study shows significant difference in the results obtained while employing the two models.

Effects of crack closure on fatigue crack-growth predictions for 2024-T351 aluminum alloy panels under spectrum loading

Effects of plasticity induced crack closure on the calculated fatigue crack-growth behaviour of middle-crack tension specimens made of 2024-T351 alloy subjected to variable amplitude fatigue loading were examined. The specified loadings were four distinct aircraft spectra: (1) “modified” center-wing spectrum performed as part of this study; (2) fighter aircraft maneuver spectrum; (3) lateral gust spectrum; and (4) pressurized fuselage gust and maneuver spectrum. The experimentally observed crack-growth lives were compared with crack-growth predictions obtained using the crack closure concept in FASTRAN. Fatigue crack-growth material data extracted from the NASGRO materials database and the literature follows two distinct paths possibly due to different transitions from flat-to-slant (single or double shear) fracture. The material baselines for the FASTRAN code were selected to fit the two different paths. The two baseline curves were used to predict crack-growth life under four spectra to assess how the observed differences in the crack-growth rate trajectories affect the results. Using the lower bound baseline curve, which is suspected to be characterized by the double shear fracture mode, the FASTRAN model was able to predict crack- growth behaviour within ±25% of the test data for all four spectra.

On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems

The accurate calculation of the opening and closing stresses is an important issue in fatigue crack closure problems, since the effective driving force for crack growth is dependent on accurate calculation of the opening stresses. Often numerical methods such as finite element analysis are used to model plasticity-induced fatigue crack closure problems. There are many difficulties associated with this modelling work, since the results may depend on a wide range of parameters such as mesh refinement, node release scheme and modelling of the contact between the crack faces etc. Even after a great deal of modelling work some arbitrariness is evident in the technique used for assessing the opening and closing stresses. A number of techniques have been proposed in the literature and the current work will assess and compare these approaches. The node displacement method, the change in stresses at the crack tip, and the weight function technique will each be applied to a finite element model of a plane stress crack for a range of stress levels. In addition, an analytical model for plasticity-induced crack closure under plane stress conditions will be used to discuss the accuracy of these techniques. The investigation shows that all these techniques are equivalent provided that the displacement and stress at the crack tip are assessed accurately. However, it will be shown that use of the tensile tip stress method, proposed by some authors for assessing the closing stress, is erroneous.

Roughness- and plasticity-induced fatigue crack closure under single overloads: Analytical modelling

A simple micromechanical model for the competitive influences of roughness-induced crack closure (RICC) and plasticity-induced crack closure (PICC) on fatigue during single peak overloads has been developed following the approach of Kamp et al. [Kamp N, Parry MR, Singh KD, Sinclair I. Acta Mater 2004;52:343]. This is seen to be functionally comparable to the finite element results of the accompanying paper [Singh KD, Khor KH, Sinclair I. Acta Mater 2006;54:4393], and consistent with a range of experimental data. Competitive influences of PICC and RICC effects during overload transients are particularly identified here.

Roughness- and plasticity-induced fatigue crack closure under single overloads: Finite element modelling

Results from finite element modelling of plasticity-induced crack closure (PICC) and roughness-induced crack closure (RICC) of fatigue cracks subjected to single overloads are presented. Effects of L/ r p ratios on RICC, where L and r p represent crack asperity length and plastic zone size, respectively, are seen to be functionally similar to results presented previously for constant amplitude fatigue loading [Kamp N, Parry MR, Singh KD, Sinclair I. Acta Mater 2004;52:343–53], particularly in the saturation of the influence of RICC for L/ r p(OL) ⩾ 1, where r p(OL) is the overload plastic zone size. The present work is seen to map out overload regimes where RICC and PICC effects may be expected to influence crack growth transients. Comparisons of modelled and experimental closure levels, and growth rate studies are presented, with the accompanying paper [Singh KD, Khor KH, Sinclair I. Acta Mater (in press)] considering a simplified analytical representation of the effects presented here.

Strain-gauge compliance measurements near the crack tip for crack closure evaluation: Applicability and accuracy

The “plasticity-induced crack closure” phenomenon is the leading mechanism which controls the main effects on fatigue crack growth (e.g. stress ratio and load interaction effects) in metallic materials. Experimental tests, consisting mainly in global and/or local compliance measurements of the considered specimen, are usually carried out to quantify the physical phenomenon, but some aspects concerning the elaboration of acquired local compliance signals are not yet clear. From the analytical point of view, the so-called “Strip-Yield” model has proven to be the most versatile and powerful tool for estimating crack closure levels, but its application to structural steels is not yet straightforward due to the delicate calibration process. The present work tries to add some new ideas on the elaboration of local compliance experimental data, obtained from a M( T) specimen, simulating the measurements by means of an optimised Strip-Yield model implementation enriched by a novel module based on the Westergaard’s elastic complex potentials. The application of the method to the calibration of the Strip-Yield model has been already successfully faced elsewhere, so here the analytical results gave the possibility, together with dedicated FEM analyses, to investigate some of the different parameters and to state some conclusions about the reliability and applicability of local compliance measurements.

3-D modelling of cyclically loaded composite patch repair of a cracked plate

A three-dimensional finite element model is utilized to capture the effects of plasticity-induced crack closure (PICC) on an adhesively bonded patch repair of a cracked plate. To accurately capture the PICC process the choice of material model employed is of significant importance, therefore this paper considers a relatively new model, the Ellyin–Xia model. The paper shows that the PICC phenomenon is beneficial to the repair.

Three dimensional finite element prediction of crack closure and fatigue crack growth rate for a corner crack

The effect of plasticity induced crack closure on fatigue crack growth rate has been examined for the case of a 2024 aluminium alloy plate with two lateral corner cracks emanating from a central hole. The plate was subjected to constant amplitude loading and a combination of constant amplitude and single overload loading prior to the measurement of the opening load. The opening load was measured by comparing the strain ahead of the crack tips with the far field strain as the load on the specimen was cycled. Measurements were also made of the growth rate of the crack in fatigue. A three-dimensional finite element quarter model was developed of the plate with a central hole and corner cracks. The geometry of the model forced the crack to assume a constant aspect ratio of bore length to surface length as the crack grew. Two different aspect ratios of 1:1 and 1.5:1 were considered. The load on the model was cycled and the crack extended by releasing nodes so as to predict the development of a plastic wake behind the advancing crack. The opening load was predicted from the finite element displacement versus load results. These opening load predictions agreed favourably with the experimental measurements. The finite element model was also used to predict the fatigue crack growth rate. This was achieved by first evaluating the effective stress intensity factor range from the stress distribution ahead of the crack tip. A Paris law fit to high R-ratio test data was then made to allow the corresponding growth rate to be calculated. Encouraging comparisons of the finite element predictions of fatigue crack growth rate with experimental measurement were obtained.

Surface crack and cracks networks in biaxial fatigue

Semi-elliptical fatigue crack growth in 304 L stainless steel, under biaxial loading, was investigated. Compared to those of through-cracks under uniaxial loading, the growth rate of surface cracks is increased by a non-singular compressive stress and reduced by a tensile stress, when R = 0. Plasticity-induced crack closure under biaxial loading was investigated through 3D finite element simulations with node release. Roughness and phase-transformation-induced closure effects were also discussed. The interactions in two-directional crack networks under biaxial tension were investigated numerically. It appears that the presence of orthogonal cracks should not be ignored. The beneficial influence of interaction-induced mode-mixities was highlighted.

Crack retardation equations for the propagation of branched fatigue cracks

The stress intensity factors (SIF) associated with branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest. This crack branching mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in some plane strain controlled fatigue crack growth problems. Analytical solutions have been obtained for the SIF of branched cracks, however, numerical methods such as Finite Elements (FE) or Boundary Elements (BE) are the only means to predict the subsequent curved propagation behavior. In this work, a FE program is developed to calculate the path and associated SIF of branched cracks, validated through experiments on 4340 steel ESE(T) specimens. From these results, semi-empirical crack retardation equations are proposed to model the retardation factor along the crack path. The model also considers the possible interaction between crack branching and other retardation mechanisms.

Stress intensity factor equations for branched crack growth

Overload-induced fatigue crack branching is a well-known crack growth retardation or arrest mechanism, which can quantitatively explain such effects even when arguments based on plasticity induced crack closure cannot be applied, e.g. in high R-ratio or in plane strain controlled fatigue crack growth. However, the few results available for branched cracks cannot be used to predict the subsequent crack growth nor account for the delays observed in practice. In this work, specialized finite element (FE) and fatigue life assessment software are used to solve this problem. The crack path and associated stress intensity factors (SIF) of kinked and bifurcated cracks are numerically obtained by the FE program for several angles and branch lengths, and the companion life assessment program is used to estimate the number of delay cycles associated with them. From these results, crack retardation equations are proposed to model the number of delay cycles and the retardation factor along the crack path, allowing for a better understanding of the influence of crack deflection in the propagation life of structural components.

Fatigue crack growth in thin aluminium alloy sheets under loading sequences with periodic overloads

This study analyses the fatigue crack growth behaviour in thin AlMgSi1-T6 aluminium alloy sheets under several loading sequences containing periodic overloads. The observed fatigue crack growth behaviour is compared to constant amplitude loading and discussed in terms of type of loading sequence, intermediate baseline cycles and stress ratio. The crack closure parameter U was obtained for periodic single overload tests and compared with the crack growth transients. Crack retardation increases with overload periodicity and decreases with stress ratio increase. Higher crack growth retardation was observed under loading sequences with decreasing load levels in comparison to increasing ones as well as under loading sequences with extended periodicity. In spite of some discrepancy, attributed to the quick change of the closure levels, it is clear that plasticity-induced crack closure plays an important role on the load interaction effects observed in this aluminium alloy.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth at elevated temperature has been simulated using the finite element method for sustained and cyclic loading conditions, representative of time-dependent and time-independent crack growth. Elastic-creep (EC) and elastic-plastic-creep (EPC) models have been used to simulate the crack growth under sustained loads at 650 and 725°C. Crack mouth opening displacements as well as the evolution of the inelastic zones due to creep and plasticity have been obtained. Elastic-plastic finite element analysis has been carried out to simulate the crack growth under cyclic load using a constitutive model. Fatigue crack growth was simulated for plane stress, plane strain and generalized plane strain loading conditions. The influence of plasticity on the effective crack driving force was also examined. Creep damage was found to be very limited at both temperatures for this alloy. Plasticity-induced crack closure was found to be absent in plane strain or generalized plane strain conditions, overestimated in plane stress loading conditions by the conventional compliance method.

超微細結晶粒Ｐ／Ｍアルミニウム合金の２段繰返し変動下における疲労き裂進展特性

Fatigue crack growth tests were carried out using CT specimens of ultra-fine grained P/M (Powder Metallurgy) aluminum alloy of which grain size was from 200 to 500nm. Fatigue crack growth behavior was investigated under constant amplitude and repeated two-step variable amplitude load sequences. It was found that roughness induced crack closure played an important role in closure behavior of this material. Although the roughness of fracture surface was smaller than the other conventional aluminum alloys, the roughness induced crack closure was dominant because of the small crack tip opening displacement (CTOD) with respect to the roughness level. Under repeated two-step loading, crack opening load was lower than that under constant amplitude loading with the same K value as the high level load, and the crack growth retardation caused by load history was not prominent comparing with other aluminum alloys. It is considered that the crack opening load under variable amplitude loading was dominated by the roughness induced crack closure. The small contribution of the plasticity induced crack closure was due to the constraint of plastic strain by the grain boundaries of ultra-fine grains.

A Strip-Yield algorithm for the analysis of closure evaluation near the crack tip

“Plasticity-induced crack closure” phenomenon is the leading mechanism of different effects ( R-ratio, overload retardation, … ) acting on crack growth rate in many metallic materials. Experimental tests are carried out to quantify the physical phenomenon, while Strip-Yield analytical models have been developed for predicting life of components. In the present work, an additional module to be applied to a Strip-Yield model is proposed in order to derive the strains near the crack tip. Particularly, the module is based on the Westergaard’s elastic complex potential. The presented algorithm allowed us to obtain the correlation between “local compliance” experimental results and the corresponding Strip-Yield analyses. This method can be taken as a semi-analytical procedure for calibrating the constraint factor, i.e., the most delicate parameter for Strip-Yield models.

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.

Numerical analysis for prediction of fatigue crack opening level

Finite element analysis (FEA) is the most popular numerical method to simulate plasticity-induced fatigue crack closure and can predict fatigue crack closure behavior. Finite element analysis under plane stress state using 4-node isoparametric elements is performed to investigate the detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The mesh of constant size elements on the crack surface can not correctly predict the opening level for fatigue crack as shown in the previous works. The crack opening behavior for the size mesh with a linear change shows almost flat stress level after a crack tip has passed by the monotonic plastic zone. The prediction of crack opening level presents a good agreement with published experimental data regardless of stress ratios, which are using the mesh of the elements that are in proportion to the reversed plastic zone size considering the opening stress intensity factors. Numerical interpolation results of finite element analysis can precisely predict the crack opening level. This method shows a good agreement with the experimental data regardless of the stress ratios and kinds of materials.