The kinking behaviour of a bimaterial interface crack under indentation loading

The aims of this paper are twofold. The first is to evaluate the applicability of the formula for the crack kink angle—based on the maximum principle stress criterion—for predicting the interface kink angle in a bimaterial sample undergoing indentation loading. This formula was developed for cracks in homogenous materials but in this paper, it is used to predict the kink angle using the mode mixity at the tip of a crack lying on a bimaterial interface. The second aim is to examine the behaviour of the system, in terms of the crack kink angle and contact radius, for various coating thickness', crack lengths and combinations of properties of the coating and substrate. The system that is analysed consists of a planar bimaterial sample undergoing indentation with a tungsten-carbide spherical indenter. Two-dimensional, axisymmetric models are created to represent the system, with subdomains used for modelling the cracks. In order to determine the applicability of the kink angle formula, the angle predicted is compared to the angle that is directly calculated using boundary element method models that establish the angle of the kink which yields the maximum mechanical energy release rate. The second aim of the paper is achieved by varying the material property combinations and coating thickness of the bimaterial sample and observing the effect on the kink angle of the interface crack and the contact radius. The methodologies employed are initially verified on homogenous samples with known solutions.     

Crack kinking under nonsymmetric loading

This paper considers an asymmetrically kinked, semi-infinite crack in a two-dimensional solid under mixed-mode loading and a stress acting parallel to the main crack, the latter providing the non-singular stress term, T, in the Irwin-Williams expansion of the crack tip field. The aim of the study is twofold: First, to obtain an almost closed-form solution for the stress intensity factors at the tip of the kink with a view to explaining a curious result observed by many authors that under predominantly Mode I loading the first order solution in small kink angle is accurate for considerably large kink angles and, second, to study the effect of the in-plane tensile stress on the stability of crack growth. Where possible, the results are compared with those available in the literature.     

Time-dependent fracture criteria for 6061-T6 aluminum under stress-wave loading in uniaxial strain

New spallation threshold data for 6061-T6 aluminum were obtained under stress-wave loading conditions in uniaxial strain, covering the range of tensile pulse durations of 60 to 200 nsec. This range of pulse duration was achieved by using exploding-foil techniques to accelerate thin Mylar plates against thin aluninum specimens. A comparison was made between exploding-foil spallation tests on 6061-T6 aluminum in air and vacuum. The data indicate that the spallation threshold of 6061-T6 aluminum is sensitive to the tensile pulse duration, amplitude, and impulse at the spall location. The exploding-foil impact conditions were reduced to stress-pulse loading parameters by using a one-dimensional elastic-plastic hydrodynamic computer code. The time-dependent aspects of the spallation threshold of 6061-T6 aluminum were found to obey failure theories which were rate process oriented, and which combine the effects of tensile-pulse duration, peak tensile stress, tensile impulse, and tensile-pulse shape. The present data have been used to quantitatively establish failure relationships for 6061:T6 aluminum. Where applicable, supplemental information in the literature concerning dynamic fracture of 6061-T6 aluminum was utilized.     

On crack kinking and curving

This paper attempts to provide a comprehensive summary of results on the following topics relating to crack kinking and curving: (a) Stress intensity factors for kinked cracks under combined loading; (b) applicability of Irwin's energy-release rate formula to kinked cracks; and (c) reasons behind crack kinking and curving. It is assumed throughout that the surfaces of the cracks do not come into contact.     

Flat crack under shear loading

Summary A solution is called complete when the explicit expressions are derived for the field of displacements as well as stresses in an elastic body. A new method is proposed here which allows us to obtain exact and complete solutions to various crack problems in elementary functions; no integral transforms or special function expansions are involved. The method is based on the new results in potential theory obtained earlier by the author. The method is applied to the case of a concentrated tangential loading of a penny-shaped crack. The main potential function and the relevant Green's functions are derived. An approximate analytical solution is obtained for a flat crack of general shape. A new set of asymptotic expressions is presented for the field of stresses and displacements near the crack tip in a transversely isotropic space. The use of the method is illustrated by examples.     

Two practical applications of crack kinking

This paper illustrates on two examples of practical significance the usefulness of the crack kinking analysis pioneered by Sia Nemat-Nasser and his colleagues. The first example deals with the calculation of the pull-out force of axisymmetric headed anchors embedded deep in concrete blocks and the second with the interaction between the crack deflection and phase transformation mechanisms of toughening in ceramics containing dispersed tetragonal zirconia precipitates.     

Creep crack growth under history-dependent loading

We discuss the influence of loading history on creep crack growth. Our attention is mainly focused on the following three aspects of this problem: (i) principal laws of history-dependent creep strain of materials; (ii) creep behavior of cracks, including the choice of suitable fracture parameters that may help to predict cracking; (iii) the importance of taking the history-dependent response of the material into account. We performed numerical calculations based on the use of an appropriate constitutive model and fracture theory for (1) and (2), respectively, to analyze results of tests for (3).Battelle, Columbus, Ohio. UES Incorporated, Dayton, Ohio. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 37–45, July – Augus, 1994.     

Fatigue crack propagation under variable-amplitude loading

A finite-element analysis has been performed to investigate quantitatively the level at which fatigue crack surfaces come into contact during fatigue cycles. The results agreed well with experimental observations and suggest that quantitative design rules may be developed, based upon the crack-closure hypothesis.A summary of remarks made during a seminar held at the Institute for Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev, October 21, 1976.NASA-Langley Research Center, Hampton, Virginia 23665. Published in Problemy Prochnosti, No. 10, pp. 26–29, October, 1977.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

A probabilistic model for fatigue crack growth under random loading

A model for predicting fatigue crack growth rate and life probabilistically under random load history is presented. It allows for random growth per cycle, and is based on experimental results of constant amplitude cyclic loads. Predictions of the model are on the conservative side at the same time avoiding overdesigning. The reliability is included in the model thereby avoiding the need for using a factor of safety or ignorance in estimating a fatigue life or a crack length after N cycles of load application. The model is computer-oriented.     

System for automated fatigue crack growth testing under random loading

Procedures have been developed for computer-controlled crack propagation testing under random load sequences. They include certain features which are not available in conventional systems, but which appear essential for random load testing. These include the capability to simulate any desired K-function on standard laboratory specimens and continuous on-line rainflow analysis of the test load sequence to exclude cycles falling below given values of threshold stress intensity, stress level or range. The system also includes a procedure for automated crack-opening displacement based crack opening/closing load level measurement. Experimental studies on AlCu alloy sheet material point to a requirement for development of standards for spectrum loading crack growth testing.     

About the Dugdale crack under mixed mode loading

The plane problem of a Dugdale crack under mixed mode loading is investigated. An exact closed form solution is given and the corresponding crack displacements are discussed.

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Résumé On étudie le problème plan d'une fissure de Dugdale soumise à une sollicitation selcn un mode mixte. Une solution exacte de forme fermée est fournie et les déplacementsde fissure correspondants sont discutés.