Crack propagation analyses with CTOA and cohesive model: Comparison and experimental validation

Two numerical models, namely an R-curve approach based on the crack tip opening angle (CTOA) and a cohesive model, are compared regarding their ability to predict ductile crack extension in thin aluminium sheets, which can be simulated under the assumption of plane stress. The experimental database is presented, the measuring techniques for the various quantities (optically and with clip gauges) are shown and the identification and validation of the respective model parameters are explained. A general concept for their identification is then derived for the case of thin walled structures under Mode I conditions.In order to investigate the performance of the models under different constraint conditions and the transferability of their parameters, C(T) specimens are used for parameter identification and M(T) specimens for validation. It is shown that for both models a single set of parameters describes the mechanical behaviour of both types of specimens. Cross-checking the two models, the crack tip opening angle is determined from the cohesive model calculations and compared with the experimental values.     

Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.     

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

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

Brittle and ductile crack propagation using automatic finite element crack box technique

In this paper, a numerical automatic crack box technique (CBT) is developed to perform fine fracture mechanics calculations in various structures without complete re-meshing. This technique aims to simulate the fatigue crack growth under mixed mode loading in 2D medium and shell structures calculated with the ABAQUS code, for elastic and for elastic-plastic materials. Using this method, series of numerical calculations by FEM of the mixed mode crack growth are carried out and compared with experimental tests such as a special cracked specimen subjected to different mixed mode loads. The crack growth paths are determined by using different elastic and elastic-plastic crack extension criteria. It is shown that the proposed technique is an efficient tool to simulate the crack extension angle in elastic and elastic-plastic materials. Nevertheless further experiments are needed to confirm conclusions deduced from elastic-plastic calculations.Using this technique, several phenomena influencing the crack extension are analyzed: the overload during fatigue, the fracture toughness of the material in relation with its critical J integral and its behaviour law.     

Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

Characteristics of fatigue crack propagation behaviour as identified by hysteresis loop at the crack tip

Fatigue crack propagation tests have been carried out under various load conditions. Hysteresis loops denoting the relationship between load and strain at the crack tip are obtained by using local compliance measurement. Crack growth acceleration, delayed retardation and non‐propagation phenomena are investigated by considering the variation of hysteresis loop expansion and hysteresis loop tail. Based on the physical meaning of hysteresis loops, two types of crack closure are ascertained and the effect of crack closure on fatigue crack propagation is studied. Results show that change of the effective amplitude of the stress intensity factor at the crack tip is the reason that crack propagation rates vary.     

Effect of load ratio and hydrogen concentration on the crack growth rate in Zr–2.5Nb tubes

Crack growth rates (CGR's) were determined under sustained and cyclic loads using 17 mm compact tension and cantilever beam specimens taken from Zr–2.5Nb tubes charged to 6–100 ppm H. The cyclic load effect on the CGR was investigated at 250 °C where load ratios, R were varied from 0.13 to 1 with a constant K_max. Under sustained loads, the CGR of the Zr–2.5Nb tube increased with supersaturation of hydrogen, ΔC and leveled off above 20–35 ppm H of the ΔC. Under cyclic loads with 1 cycle/min, the CGR at 250 °C decreased with decreasing R: 3.2 × 10⁻⁸ m/s at R = 1 and 4.8 × 10⁻⁹ m/s at R = 0.13. The striation spacing, corresponding to the critical hydride length, decreased with decreasing R, indicating easier cracking of the hydrides under cyclic loads. The decreased CGR under cyclic loads and its dependence on the ΔC are discussed using Kim's delayed hydride cracking model.     

Fiducial marks as measures of thin film crack arrest toughness

Carbon fiducial marks are formed during thin film local delamination processes induced either by indentation, forming circular blisters, or by residual stress relief through telephone cord blister formations. Hydrocarbons are sucked into the crack tip during the delamination processes, outlining the crack tip opening angle, which can be used to back calculate thin film adhesion using elastic or plastic analyses presented in the paper.     

Numerical investigation of through crack behaviour under welding residual stresses

Numerous engineering structures operate under the presence of residual stresses resulting from welding or other manufacturing processes. In the present work, the effect of typical residual stress fields on stress intensity factors and crack propagation angle of cracks developing into the residual stress field under mixed mode loading conditions is studied. For the calculations a numerical methodology based on linear elastic finite element analysis is used. The presented results provide a useful tool for an efficient assessment of the influence of residual stress field on the crack evolution behaviour.     

An analysis of crack growth in thin-sheet metal via a cohesive zone model

A cohesive zone model (CZM) is applied to crack growth in thin sheet metal. CZM parameters are determined from results of global measurements and micromechanical damage models. Crack propagation in constrained center-cracked panels is analyzed to verify the choice of CZM parameters. Special attention is paid to the interaction between buckling and crack growth and to crack link-up in multi-site damaged specimens. The good agreement found between the predicted and experimental data demonstrates that the approach is attractive in investigation of structural integrity of thin-walled structures and does not require assumptions regarding the geometry and size dependence of crack growth parameters.     

Influence of nano-inclusions’ grain boundaries on crack propagation modes in materials

The effect of nano-inclusions on materials’ strength and toughness has attracted great interest in recent years. It has been shown that tuning the morphological and microstructural features of materials can tailor their fracture modes. The existence of a characteristic size of inclusions that favours the fracture mode (i.e. transgranular or intergranular) has been experimentally observed but also predicted by a 2D model based on energetic arguments which relates the crack propagation mode to the ratio of the interface area between the crystalline inclusion and the matrix with the area of the crystallite inclusion in a previous work. In the present work, a 3D model is proposed in order to extend the 2D model and take into account the influence of the size of grain boundary zone on the toughening/hardening behavior of the material as it was observed experimentally in the literature. The model relates crack propagation mode to the ratio of the volume of the grain boundary zone between the crystalline inclusion and the matrix with the volume of the nano-inclusion. For a ratio below a critical value, transgranular propagation is favoured while for larger values, intergranular propagation is favoured. We also demonstrate that the extent of the grain boundary region also can significantly affect this critical value. The results of the model are in agreement with the literature experimental observations related to the toughening/hardening behavior as a function of the size of crystalline inclusions as well as the width of the grain boundary regions.     

Simulation of ductile crack propagation and determination of CTOAs in pipeline steels using cohesive zone modelling

This paper presents recent results of numerical studies on stable crack extension of high toughness steels typical of those in modern gas pipelines using cohesive zone modelling (CZM). The main focus of the work is on the determination of crack‐tip opening angles (CTOAs) of these steels from CZM. Two sets of materials are modelled. The first material set models a typical structural steel, with variable toughness described by four traction–separation (TS) laws. The second set models an X70 pipe steel, with three different TS laws. For each TS law, there are three defining parameters: the maximum cohesive strength, the final separation and the work of separation. The specimens analysed include a crack in an infinite plate (small‐scale yielding, SSY) and a standard drop‐weight tear test (DWTT). Fracture propagation characteristics and values of CTOA are obtained from these two types of specimens. It is shown that cohesive zone models can be successfully used to simulate ductile crack propagation and to numerically measure CTOAs. The ductile crack propagation characteristics and CTOAs obtained from SSY and DWTT specimens are compared for each set of steels. In addition, the CTOA results from numerical CZM of DWTT specimens of X70 steel are compared with those from laboratory tests.     

Crack tip opening displacement of a Dugdale crack in a three-phase cylindrical model composite material

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.     

Modelling the softening within the fracture process zone associated with the fissuring mode of crack growth in Zr-2.5Nb CANDU pressure tube material

The fissuring mode of fracture in CANDU pressure tube material, and in particular Stage 1 crack growth (essentially flat J _R curve) as observed in some irradiated compact toughness specimens has been investigated. Models are presented of the fracture process zone associated with a crack that tunnels at the specimen mid-section, which extends preliminary work reported earlier. Various types of process zone behaviour are analysed, and based on an appropriate value for J _c, the J value associated with the cumulative mode of crack propagation in irradiated material, together with an estimate of the tensile stress at the leading edge of the process zone, the known failure mechanism (formation, growth and coalescence of voids) of the ligaments between the fissures is shown to be reasonably consistent with the experimental measurements of the fissure spacing and fissure length.     

Fatigue crack propagation in rocker and roller-rocker bearings of railway steel bridges

In this work, a method is proposed for rolling contact fatigue crack propagation analysis using contact and fracture theories in conjunction with fatigue laws. The proposed method is used in the fatigue analysis of rocker and roller-rocker bearings of a railway open web girder bridge which is instrumented with strain gages. Using a contact algorithm based on the minimum energy principle for bodies in rolling contact with dry friction, the normal and tangential pressure distribution are computed. It is seen that the most critical location of a crack in bearings is at a point very close to the contact region, as expected.     

Consideration of the mechanical behaviour of small fatigue cracks

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

Crack Tip Opening Angle Measurement Methods and Crack Tunnelling in 2024‐T351 Aluminium Alloy

Abstract: The crack tip opening angle (CTOA) fracture criterion is one of the most promising fracture criterion used to characterise the stable tearing process in metallic materials. Traditional methods used for the experimental characterisation of the CTOA involve accurate identification of the crack tip at each tearing event. Recently alternative methods have been proposed that reduce the necessity of accurately defining the current crack and rely more on the shape of the crack flanks to define the CTOA. In addition, these methods define an ‘apparent crack tip’, which may be different from the actual surface crack tip and may provide insight into the amount of crack‐front tunnelling that is occurring. In the current research, compact tension specimens fabricated from 6.35 mm thick 2024‐T351 aluminium alloy plate were evaluated to investigate different CTOA measurement methods and their potential for estimating crack‐front tunnelling. In addition to characterizing the CTOA, fatigue marker bands were employed to map the evolution of crack‐front tunnelling. The experimental critical CTOA values obtained from the alternative methods were noticeably lower than that obtained from the traditional approach and showed noticeably more scatter. When compared to the experimentally obtained marker bands, the alternative methods indicated limited potential for predicting crack‐front tunnelling.     

Prediction of crack propagation paths in the unit cell of SOFC stacks

Planar Solid Oxide Fuel Cells (SOFC) stacks are multi-material layered systems with different thermo-mechanical properties. Due to their severe thermal loading, these layers have to meet high demands to preserve their mechanical integrity without any cracks initiation and propagation. In this paper, cracks propagation in a typical unit cell of the stack which consists of positive electrode–electrolyte–negative electrode (PEN) is modeled. Based on the mechanical properties of each layer and their interfaces, an energy criterion as a function of crack length is used for the prediction of possible crack extensions in the PEN. An analysis of the competition between crack deflections in the interfaces and crack penetration in layers is presented.     

On the mechanism of crack propagation resistance of fully lamellar TiAl alloy

The study was done using notched two-colony thick tensile specimens of a directionally solidified cast fully lamellar TiAl alloy. In-situ observations of fracture processes in scanning electron microscope (SEM) were combined with section-to-section related observations of fracture surfaces to investigate the crack growth process. Finite element method (FEM) calculations are carried out to evaluate the stresses for propagating cracks. The results reveal that: (1) the reason why enhancement of applied load is required to propagate the main crack, was attributed to that the main crack observed at the surface did not extend all the way through the specimen's thickness thus the stress field was still controlled by the notch, in which a definite stress required for extending a crack tip should be kept by increasing the applied load. (2) Crack propagation resistance is enhanced at colony boundaries, only when a change occurs from an inter-lamellar propagation to a trans-lamellar propagation (3) Ligament bridging toughening phenomena can be integrated into aforementioned mechanism. As a whole the processes of new crack nucleation with bridging ligament formation decreases the crack propagation resistance rather than increasing it. (4) In case the majority of microcracks are surface cracks, the effect of microcrack shielding is not obvious.