The influence of geometry of edge-cracked plates on crack initiation

In this paper the influence of geometry of edge-cracked plates on crack propagate under mixed mode loading conditions is studied. The edge-cracked plates under tension are examined. The crack extension angle and the critical stress of fracture are determined for various values of the crack inclination angle and the ratio of the crack length to specimen's width. The Det.-criterion developed by the author is used.     

Simulation of cup-cone fracture using the cohesive model

The cohesive model is used for the prediction of the crack path during stable crack extension in ductile materials. The problem of crack-path deviation is investigated by means of simulation of crack propagation in a round tensile bar. The respective phenomenon is known as cup-cone fracture. It is shown that the model is able to predict the failure mechanism, which consists of normal fracture in the center and combined normal/shear fracture in the so-called “shear lips” at the specimen’s rim. The damage evolution and crack path predicted by the model are presented. The effect of the normal and shear failure parameters on the crack-deflection point and several aspects of the finite element mesh are discussed.     

Fracture toughness parameters and elasticplastic analysis of non-moderate fracture conditions using finite element methods

Non-moderate fracture conditions of load and geometry, in which plastic zones remain neither constant in size nor uniform in shape as load or crack progress, were simulated using two dimensional elasticplastic finite element calculations. Comparison of conventional crack extension energy rate G, as determined by elastic fracture mechanics and by a compliance method suitable for non-linear deformation, is made with Rice's ‘J integral’, with crack opening displacement, and also with plastic strain energy. The relationship of crack opening displacement to crack extension force can be linearised by selecting values of crack opening displacement at locations which nominally follow the calculated location of the elastic-plastic boundary on the crack face. The relatively large plastic zones associated with high loading are shown, and the field determined in the usual manner from incremental load increases is compared with the field resulting when only two steps are used to reach the same load. Some insight is gained into the use of finite element calculations for determining, from among the various fracture indicators, a single parameter capable of describing nonmoderate fracture conditions.     

A note on Orowan mechanism below the root of an yielding crack like notch in a strain-hardening metal

Based on Orowan's historic model, a local fracture initiation criterion is proposed for high strength strain-hardening metals. A crack like notch geometry is studied in the following Von Mises yielding materials: (a) an ideally plastic-elastic solid, and (b) a power law strain-hardening metal. Orowan mechanism is seen to be dominant below the root region of an yielding crack like notch, just before the onset of fracture. Close to the elastic-plastic interface, Orowan's Kink-band forms inside the plastic region, when a mismatch Kink-stress (in radial component only) reaches a critical value in this particular region. It is extremely important to note that, this narrow Kink-band zone, where the micro-cracks are likely to nucleate, lies at a distance approx. $\text{3}\text{4}\text{s}$, where s is the size of the plastic zone on the crack extension plane under a plane strain deformation. A reverse slip mechanism operates in this region in addition to the presence of a pure hydrostatic tension, just before the release of this critical Kink-stress. Due to this stress history, a large inhomogeneous strain-localization occurs in a narrow band, which could then interact with the free notch surface before the onset of final instability. Thus, at the onset of crack extension, (satisfying Griffith-Irwin criterion of fracture), the stress intensification at the notch tip root is directly proportional to the strength of this critical strain-localization and inversely proportional to the plastic zone size on the crack extension plane. Hence, it is concluded that: Orowan's mechanism and McClintock's criteria for critical strain-localizations should play the most important roles for predicting the local fracture behaviour of metals.     

Characterization of stable crack extension in aluminium sheet material using the crack tip opening angle determined optically and by the δ5 clip gauge technique

Tests standards aimed at deriving fracture toughness data and crack resistance curves under low constraint condition have recently been finished by ASTM and ISO. These standards cover various experimental methods for determining critical crack tip opening angles, CTOA, for characterising stable crack extension in sheet material. In this paper, some key items of these standard methods are validated, namely the experimental determination of the crack tip opening angle by optical observation and using the δ₅ clip gauge method. When applying such standard methods to material characterization it is of particular interest to know how CTOA-data derived by different methods compare with each other. This paper compares CTOA-data as derived by the optical method with those derived by using the δ₅ clip gauge method. In order to study possible specimen size and geometry effects the methods have been applied to a wide range of specimen geometries. The results demonstrate that CTOA-data derived by the optical method are well suited to provide a specimen size and geometry independent characterization of stable crack extension where the thus obtained CTOA-data are constant over a large amount of stable crack extension. In contrast to this result, CTOA-data obtained from the δ₅ clip gauge method revealed a complex pattern of size and geometry effects, and only in case of compact specimens with a selected size the two CTOA-methods provide nearly identical CTOA-data over a large amount of crack extension.     

Strain localization below the root of an yielding notch

Prandtl-Orowan mechanism for plastic crack extension is discussed. A method of calculating strain localization below an yield notch in Prager's elastic-plastic material is described. Firstly, a boundary value problem is solved for an elastic notch under the combined loadings of normal and shear stresses acting on its flank faces. Secondly, the stresses and strains in the compressibility gradient are calculated on the crack extension plane assuming a forward slip. Thirdly, taking a sticking plastic friction on the flank faces, it is found that a large transverse strain localizes at the plastic incompressibility-compressibility gradient ahead of an yielding notch. Finally, it is suggested that Rayleigh-Lin type fluid mechanics instability criterion may help to understand such plastic flow localization problem.     

Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growth—II. finite element analysis

Finite element studies are presented on both mode I and mixed mode stable crack growth under static loadings through an aluminium (D16AT) alloy. A COD based criterion has been used to predict the load-displacement diagram from initiation to instability. The theoretical predictions are compared with experimental results presented in Part I. Results on computed crack profiles, stress-strain distribution ahead of the crack tip, J integrals, J resistance curves, plastic zones, etc., are included. The study indicates that the load-displacement diagram associated with a mixed mode stable crack growth in a compact tension type of specimen geometry can be predicted reasonably accurately using the criterion of a fixed crack opening displacement at a finite distance behind the crack tip provided the crack is allowed to grow in the direction of initial growth in the finite element analysis. The crack assumes a more blunted profile in a mixed mode than in the mode I at all the stages of stable extension. The distributions of normal stress and strain in the direction perpendicular to the crack extension line, ahead of the current crack tip, have similarities between the mode I and mixed mode, irrespective of loading angle. Both the stress and strain levels increase as the crack extension proceeds. In a mixed mode, the J integral at the onset of crack extension is the lowest compared with the values at the later stages of the extension. Further, the tearing modulus associated with initial kinking is very small; it becomes close to the mode I values at the later stages. The tearing modulus remained approximately constant during the whole mode I stable growth and it had a similar trend subsequent to kinking in a mixed mode. The specific work of crack extension is zero as Δa → 0 and it increases gradually with Δa irrespective of the mode of loading; the actual variation depends on the loading angle. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line.     

FATIGUE CRACK GROWTH UNDER MIXED MODE LOADING

Abstract —Mixed mode fatigue crack growth is analysed using Sih's strain energy density approach. A centre crack panel geometry loaded under uniaxial cyclic tension is considered. The crack angle is varied from 30° to 90°. A procedure for the determination of crack propagation life is outlined. The crack trajectory due to cyclic loading is predicted. The crack growth rate, the cyclic life and the cyclic life ratio are discussed, for an aluminium alloy and a steel, as a function of initial crack angle, crack length, stress amplitude, and the strain energy density factor.     

Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growth—I. Experimental

Experimental results on mode I and mixed mode stable crack growth under static loadings through an aluminium alloy (D16AT) are presented. The compact tension type of geometry was employed for both the sets of tests. Data pertaining to load-deflection diagrams, crack opening displacements, crack front geometry, etc., are included. There is a greater spurt of crack growth at the initiation stage in a mixed mode than in mode I. The crack opening angle (COA) remained nearly constant during the whole stable growth. There is a substantial tunneling, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as the ratio a₀/W increases. Because of this tunneling, the COD at a point finite distance behind the crack tip and on the specimen surface is much more than expected. At the maximum load the tunneling is 2 to 3.5 mm in the case of mode I. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum to initiation load ratio varied in the range 1.50 to 1.75 for the whole range of tests.     

Dynamic problem of expanding crack under concentrated load

An analysis is presented on a dynamic problem of two-dimensional crack which is subjected to a time-increasing concentrated load on the surface and expands at both ends at a constant velocity. The dynamic stress intensity factor and the dynamic energy release rate are calculated for a linear elastic solid. A further extension of elastic analysis with simulated plasticity is made by the strip yield model, the Dugdale's model. It is shown that the plastic zone length, the COD and the energy release rate are expressed by functions decreasing with the crack velocity.     

The green's function for a slant edge crack

The Green's functions are determined for plane edge cracks which meet the free surface at an arbitrary angle. Modes I and II stress intensification factors are found for both normal and shear loading of the crack, since coupling is found to occur between each type of loading and the two possible modes of crack-tip response.     

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.     

Fatigue crack propagation simulation in an aircraft engine fan blade attachment

This paper discusses the computation of three-dimensional fatigue crack growth rates in a typical military aircraft engine fan blade attachment under centrifugal and aerodynamic loads. The three-dimensional crack growth simulations utilize FRANC3D, a state-of-the-art crack propagation software developed at Cornell University, which uses boundary elements and linear elastic fracture mechanics. With an existing three-dimensional finite element contact stress analysis with a prescribed coefficient of friction (COF) along the contact surface, the displacements and stress intensity factors are calculated on the crack leading edge to yield crack propagation trajectories and growth rates. Due to complex geometry of the fan blade attachment and loading conditions, all three-fracture modes are considered and the associated stress intensity factors (SIF) are calculated using the Crack Opening Displacement (COD) approach. Crack propagation trajectories under mixed-mode conditions are obtained using the planar and maximum tangential stress crack-extension criteria. The fatigue crack in the blade attachment is subjected to an over speed mission cycle that includes high cycle frequencies (i.e., spectrum load) and the crack growth rate is predicted utilizing the Forman–Newman–de Koning (FNK) model. Scanning Electron Microscope (SEM) images of a cracked component from an engine ASMET (Accelerated Simulated Mission Endurance Test) are used to evaluate and compare the simulation results. The calculated SIF's from the simulations indicate a strong Mode-I (K_I) and Mode-III (K_III) interaction at the edge of contact (EOC). However, on the free surface it is primarily a crack opening (K_I) condition only. The crack growth rates are determined using the planar extension criterion which correlates better with the test data than the maximum tangential stress extension criteria.     

Plastic zones in fatigue

This paper presents a model to evaluate the plastic zone size at the crack tip using mechanical properties of the material and loading conditions (Mode I). The parameter U controlling the effects of residual deformations has been incorporated. The model was found to compare well with Antolovich's model with crack growth extension data for 2024-T3 aluminum alloy.     

A crack in a linear-elastic material under mode II loading, revisited

A sharp crack in a two-dimensional infinite linear-elastic material, under pure shear (mode II) loading is re-examined. Several criteria have been proposed for the prediction of the onset and direction of crack extension along a path emanating from the tip of the initial crack. These criteria date back some three decades and are well documented in the literature. All the predictions from the different criteria are close and indicate that the crack extension takes a direction at an angle of ≈ −70° measured counterclockwise from the positive x -axis, in the case of a remotely applied positive shear stress. However, the possibility seems to have been overlooked that the crack extension may initiate not from the crack tip itself, but instead may initiate on the free surface at an infinitesimal distance behind the crack tip. The effect of crack tip plasticity on the relevant stresses in the region of the crack tip is investigated by the application of an elastic–plastic finite element program.     

Characterization of the elevated temperature static load crack extension behavior of type 304 stainless steel

Creep crack extension rates in Type 304 stainless steel, obtained as a function of temperature over the range 650–800°C and as a function of specimen geometry at 750°C, are empirically correlated with both the net section stress and the apparent stress intensity factor. The results indicate that the stress intensity correlation is strongly dependent on specimen geometry, whereas the net section stress correlation appears to be generally valid. A direct correspondence between crack extension and local (crack tip) displacement is noted when creep crack extension rates at 750°C are compared with COD obtained from actual castings of the crack tip. By introducing the concept of a miniature creep specimen at the crack tip, a physical model for creep crack growth is developed, based on local stress relaxation and strain accumulation, that is consistent with both experimental observation and existing theories of steady state creep.     

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as a_o/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.     

EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens

Corrosive environment causes corrosion pits at material surface and reduces the fatigue strength significantly. Fatigue crack usually initiates at and propagates from these locations. In this paper, a general methodology for fatigue life prediction for corroded specimens is proposed. The proposed methodology combines an asymptotic stress intensity factor solution and a power law corrosion pit growth function for fatigue life prediction of corroded specimens. First, a previously developed asymptotic interpolation method is proposed to calculate the stress intensity factor (SIF) for the crack at notch roots. Next, a growing semi-circular notch is assumed to exist on the specimen’s surface under corrosive environments. The notch growth rate is different under different corrosion conditions and is assumed to be a power function. Fatigue life can be predicted using the crack growth analysis assuming a crack propagating from the notch root. Plasticity correction is included into the proposed methodology for medium-to-low cycle fatigue analysis. The proposed methodology is validated using experimental fatigue life testing data of aluminum alloys and steels. Very good agreement is observed between experimental observations and model predictions.     

Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities

Crack extension paths are often irregular, producing rough fracture surfaces which have a fractal geometry. In this paper, crack tip motion along a fractal crack trace is analysed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. The ratio of the dynamic stress intensity factor to the applied stress intensity factor K(L(D, t), V)/K(L(t), 0), is a function of apparent crack velocity V_o, microstructure parameter d/a (grain size/crack increment step length), fractal dimension D, and fractal kinking angle of crack extension path . For fractal crack propagation, the apparent (or measured) crack velocity V_o, cannot approach the Rayleigh wave speed Cr. Why V_o is significantly lower than Cr in dynamic fracture experiments can be explained by the effects of fractal crack propagation. The dynamic stress intensity factor and apparent crack velocity are strongly affected by the microstructure parameter (d/a), fractal dimension D, and fractal kinking angle of crack extension path . This is in good agreement with experimental findings.     

Weight function calculations for mixedmode fracture problems with the virtual crack extension technique

An efficient finite element method is presented for calculating the stress intensity factors (K_I and K_II) and the weight functions for mixed-mode cracks with one virtual crack extension. The computational efficiency is enhanced through the use of singular elements and the application of colinear virtual crack extension (VCE) technique to symmetric mesh in cracktip neighborhood. This symmetric mesh in crack-tip vicinity permits the analytical separation of strain energy release rate into G_I for Mode I and G_II for Mode II for the mixed fracture problems with the colinear virtual crack extension.

Rice's displacement derivative representation of weight function vector for symmetric crack has been extended to the mixed fracture mode at nodal location (x_i,y_i) with crack length (a) and inclination angle (β) as h_I(II)(x_i, y_i, a, β) = (H/2K_I(II)(∂U_I(II)(x_i, y_i, a, β/∂a).

This equation permits explicit determination of weight functions for the entire structure of a given asymmetric crack geometry with colinear VCE technique. The explicit weight functions for mixed fracture mode depend strongly on the constraint conditions. The method of obtaining the required stress intensity factors of a given asymmetric crack geometry, from the weight function concept under the selected constraint conditions, which are different from constraint conditions used in the available weight functions for the same crack geometry, is also presented in this paper. This is accomplished by combining the predetermined explicit weight functions with the self-equilibrium forces at their application locations. These self-equilibrium forces include both the applied surface tractions and the reaction forces induced from the constraint conditions.