Growth of three-dimensional cracks in finite-thickness plates

The stress field in a finite-thickness plate weakened by a three-dimensional crack and subjected to tension in a direction perpendicular to the crack plane is studied. The cases of an embedded elliptical, semi-elliptical and quarter-elliptical surface crack are considered. The stress analysis takes place by a finite element computer program which uses twenty-node isoparametric and fifteen-node enriched elements. The stress intensity factor variations along the periphery of the elliptical cracks are given for various plate thicknesses. The results of the stress analysis are used in conjunction with the strain energy density theory to study the growth characteristics of the cracks. The history of non-self-similar crack growth from initiation to final instability through the intermediate stage of stable growth is analyzed. The increments of crack growth from each point of its front are determined on the basis that the critical element in the direction of crack growth absorbs a critical amount of strain energy density. Crack growth becomes unstable when the last increment from the critical point of the crack front takes a limiting value. Results for the crack growth characteristics are given for the three types of cracks considered and various plate thicknesses.     

Fracture phenomena in a cracked plate subjected to a concentrated load

The critical load for crack extension and the corresponding angle which the fracture path forms with the initial crack propagation direction of a cracked plate subjected to a concentrated load at an arbitrary point are determined. The strain energy density theory developed by Sih is used. Two different directions of the load parallel and perpendicular to the crack axis are considered. From the whole study useful results concerning the dependence of the above two quantities on the direction and location of the applied load are derived.     

Criteria for brittle fracture in biaxial tension

The criteria of maximum tangential stress, maximum tangential principal stress, maximum tangential strain and strain energy density are applied to the problems of slit and elliptical cracks under remote uniform biaxial tension. The predicted direction of crack extension and the critical load are compared with experimental results reported by other investigators. The unstable crack paths are determined. The four criteria differ in the case of unequal tension; the strain energy density criterion is the least satisfactory. The criteria of maximum tangential strain and strain energy density can be modified to give a good prediction of critical load.     

Crack curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

Fractography of unfilled and particulate-filled epoxy resins

The objective of this work was to analyse and understand the types of fracture surface morphology found in unfilled and particulate-filled epoxy resins in the light of the thermomechanical history of the specimen (loading rate or duration of loading, temperature, strain at break). Short-term tensile tests and long-term creep tests were conducted at four different temperatures. The fracture surface features were analysed using the scanning electron and optical microscopes and, where suitable, an image analyser. In order to correlate these morphologies with certain regimes of crack velocity, fracture mechanics tests were also conducted, varying the crack speed between 10^–7 and 10² m sec^–1. In the case of the filled resin, the lifetime under static loading is governed by a phase of slow, sub-critical crack growth which is manifested by resin-particle debonding. Thereafter, the crack accelerates and finally may reach terminal velocities depending on the amount of stored elastic energy available at the moment of fracture.     

Brittle fracture considerations of two external notches under combined loading

The interaction behavior of two external notches, modeled by plane hyperbolas, is analyzed using the strain energy density failure criterion[1,2]. It is shown that the pure shear and normal loadings may be combined to the case of inclined or off-axis loading of this double-notch geometry. The crack trajectory emanating from the notch surface is assumed for most cases to follow a path along which the material elements experience more volume change than shape change. This is determined by taking the minimum values of the strain energy density function. The failure loads are obtained by holding the critical strain energy density function constant and are shown to vary with the angle between the inclined load and the major axis of the notch. The variations will depend on the aspect ratios of the notches. Graphical plots of the crack trajectories for different loading angles are displayed. The double-notch geometry is such that only local trajectory information can be gleaned from the initial state. Numerical results of failure load, fracture angle, etc. are given for notches with different degrees of bluntness.     

On crack path evolution rules

The models of crack growth in mixed mode conditions are reviewed for the plane and three-dimensional (3D) states of stress. Both critical load value and crack path or surface growth are predicted by different criteria in terms of elastic singular stress states and T-stress component. Monotonic and cyclic loading induced crack growth is considered. The energy and critical plane criteria based on local or non-local measure of stress and strain are most useful in developing predictive crack growth simulation. The finite critical distance from the crack tip should be specified to provide averaged or local stress and strain states. The application of MK-criterion of crack growth expressed in terms of volumetric and deviatoric strain energies is presented for several specific cases of monotonic and cyclic loading. The concepts of smooth and rough crack surface are discussed with application to 3D crack surface growth.     

Crack growth in elastically damaged materials

Brittle, polycrystalline and polyphase materials such as ceramics and fibre-reinforced brittle composites contain residual thermo-mechanical stresses from manufacturing. These stresses are concentrated at sites of microstructural inhomogeneities such as grain and phase boundaries. The nucleation and growth of microcracks can minimize the local micro-strain energy density; thus, the local, residual stresses can act as nuclei for microcracks. The density of nuclei, statistically distributed within the material, depends on grain size, i.e. the distance between nuclei, with defined values of micro-strain energy density, is material specific. Stress-induced microcracking can act as an attractor for elastic damage at the local scale to produce a process zone that acts as a sink of strain-energy release on a larger scale, for example, the process zone at a crack front. It can be shown that the stress-rate dependent growth of local damage follows a power law which quantifies strengthening and softening during slow crack growth, prior to catastrophic crack extension. The damage-induced zone, produced by the release of strain energy on the local scale, can shield the macrocrack and grow to a critical value at the failure load. The influence of the microstructure on damage will be quantified and related to sub-critical and critical crack extension in brittle materials.A sudden heart attack ended the life and work of my father, on Friday 27 August 1993. This paper was found almost finished on his computer. The last corrections were done just a few hours before his death. It is dedicated as a farewell paper and legacy to all friends and colleagues, in his memory. Dr Isabell Buresch. Wieland Werke AG, Ulm, Germany 27 September 1993     

Modelling of Surface Crack Growth under Lubricated Rolling–Sliding Contact Loading

The paper describes modelling approach to computational simulation of surface crack growth subjected to lubricated rolling–sliding contact conditions. The model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact and the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The motion of the contact sliding load is simulated with different load cases. The strain energy density (SED) and maximum tangential stress (MTS) crack propagation criteria are modified to account for the influence of internal pressure along the crack surfaces due to trapped fluid. The developed model is used to simulate surface crack growth on a gear tooth flank, which has been also experimentally tested. It is shown that the crack growth path, determined with modified crack propagation criteria, is more accurately predicted than by using the criteria in its classical form.     

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field Part I: Slit and elliptical cracks under uniaxial tensile loading

Predictions for the angle of crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential strain (MTSN) and strain energy density (SED) for angled slit and elliptical cracks under uniaxial tensile loading are compared. The tangential stress associated with the MTS criterion need not be a principal stress and a new approach to this criterion is suggested. A criterion based on maximum tangential principal stress (MTPS) is proposed. Predictions by these two criteria are compared. Some difficulties associated with the application of the SED criterion are indicated. A new basis, which permits a unification of all the criteria in respect of prediction of critical load, is suggested. Some of the results have been compared with data available in the literature.     

Bruchmechanische Untersuchungen an niedriglegierten Baustählen mit Hilfe des COD-Konzepts

COD Investigations on Low Alloy Steels Fracture toughness tests were performed at low alloy steels using the COD concept. Especially have been investigated the effect of evaluation methods, determination of stable crack initation and the effect of specimen geometry on the critical crack tip opening displacement: The evaluation methods in use today yield different δ_c-values, therefore a standard procedure method may be desirable. The potential method seems to give the best results for characterizing stable crack growth. A control by unloading and marking the crack extension by additional fatigue loading or other methods might be necessary. An effect of specimen thickness on the critical crack opening displacement was only found at thin specimens, in which no plane strain appeared or only arised in a small region within the center of the specimen. The crack opening displacement at the moment of first crack propagation (stable or instable) proved to be independent of specimen thickness if the amount of plane strain exceeded 50%. For this condition also was found no influence of crack length within the range for a/W = 0,2 to 0,65.     

Fatigue as a process of cyclic brittle microfracture

While fatigue crack growth in vacuum may occur by slip alone, environmental fatigue including crack growth in air is strongly influenced by crack‐tip surface chemistry that adversely affects ductility. Cumulative diffusion, combined with adsorption and chemisorption in the loading half‐cycle may promote instantaneous crack extension by brittle microfracture (BMF). Unlike slip, the BMF component will be sensitive to parameters that affect near‐tip stresses, such as load history and constraint. BMF dominates near‐threshold environmental fatigue. Being a surface phenomenon, it loses its significance with increasing growth rate, as slip‐driven crack extension gains momentum and growth becomes less sensitive to environment. The BMF model provides for the first time, a scientific rationale for the residual stress effect as well as the related connection between stress–strain hysteresis and load‐sequence sensitivity of metal fatigue including notch response. Experimental evidence obtained on a variety of materials under different loading conditions in air and vacuum appears to support the proposed model and its implications.     

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

The paper presents a review of multiaxial fatigue failure criteria based on the critical plane concept. The criteria have been divided into three groups, according to the fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the critical plane orientation. Multiaxial fatigue criteria based on the critical plane concept usually apply different loading parameters in the critical plane whose orientation is determined by (a) only shear loading parameters (crack Mode II or III), (b) only normal loading parameters (crack Mode I) or sometimes (c) mixed loading parameters (mixed crack Mode). There are also criteria based on few critical plane orientations and criteria based on critical plane orientations determined by a weighted averaging process of rotating principal stress axes.     

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.     

Fatigue of engineering structures under combined nonproportional loads: An overview

Nonproportionality in fatigue is a matter of loading sequences acting on structures. In such loading cases, a life assessment‐based search of the initiation site is required. This means that for a variety of potential sites, their stress‐strain sequences must be determined and the corresponding fatigue lives have to be calculated. For the determination of local stress‐strain sequences, a superposition of the action of loads at all times for all potential sites must be performed. The superposition has not only to be performed at a particular time of a load reversal but also for a sufficiently large number of intermediate points in time. For the assessment of crack initiation under local nonproportional stress‐strain sequences, a multiaxial fatigue damage hypothesis must be specified. Due to the superiority with respect to accuracy, critical plane approaches are the favourite ones when dealing with nonproportional fatigue of ductile metals. For describing fatigue crack growth, the time sequences for the stress intensity factors corresponding to the 3 opening modes must be obtained by superposition. A mixed‐mode hypothesis must be applied to predict both the direction and the increment of crack growth at each crack front point. A first prediction trial should be based on an appropriate extension of the maximum tangential stress hypothesis. An application of a variant of the maximum shear stress hypothesis might be an amendment. Especially in the case of crack turning, the consideration of crack face contact is mandatory.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.     

Crack growth in an orthotropic medium

Abstract

The elastostatic problem of an orthotropic body having a central inclined crack and subjected at infinity to a uniform biaxial load is considered. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. The problem must be considered as one of general orthotropy, due in particular to the fact that the elastic coefficients of the material change with rotation of the reference system. The stress fields at the crack tip are reported and the presence of the non‐singular terms underlined. The Strain Energy Density Theory is extended to orthotropic materials. It is assumed that the Critical Strain Energy Density Factor has a polar variation. The crack initiation is determined via minimization of the ratio of the strain energy density over the material critical strain energy density, pointing out the effects of orthotropy and load biaxiality. The effects of the non‐singular terms on crack growth for different orthotropic materials is also studied, underling the relation between orthotropy and non‐singular terms.     

Determination of Critical Tearing Energy of Tyre Rubber

Abstract:  An experimental investigation was conducted to determine the crack growth characteristics and critical tearing energy of pure tyre rubber under mode-I and -III loading. Constrained tension and trousers specimens were used, respectively. In the trousers test it was observed that the crack does not propagate at a steady rate, but in a stick–slip way, i.e., it is arrested and re-initiated at fairly regular intervals. Thus, the force necessary to propagate the crack varies widely from a maximum value at crack initiation to a minimum value at crack arrest. In the constrained tension tests, no stable crack growth was observed and crack initiation coincides with catastrophic fracture. The critical tearing energies corresponding to crack initiation and arrest under mode-III and to unstable crack growth under mode-I loading were determined from the load–displacement records by an approximate analysis of the trousers and the constrained tension tests.     

Delamination vs matrix cracking in layered composites subjected to transverse loading

An algorithm is presented to compute the distribution of the strain energy release rate along the crack front of a penny-shaped delamination in a layered orthotropic body. The method applies a finite element recently proposed for three-dimensional analysis of layered orthotropic circular plates. The algorithm is economical even though it treats a full three-dimensional state of stress. The method requires only a single virtual crack extension to accurately compute the strain energy release rate at a point along the crack front. The method is applied to the study of delamination crack growth in a nine layer cross-ply laminate. The variation of strain energy release rate, G, along the crack front, is determined. The significance of the plate aspect ratio, as well as length scale, on the fracture process is studied. The establishment of a loading case where a distributed transverse compressive loading causes delamination growth is given.     

Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.