On nonlinear effects in fracture mechanics

Linear elastic treatment of fracture is considered applicable for net section stress up to about 0.8 the uniaxial tensile yield stress. Crack front plastic yield is still small enough to be viewed and treated as a small perturbation to the local crack front elastic stress field.     

The influence of notch depth on the fracture mechanics properties of polymer concrete

This research deals with unreinforced and fiber-reinforced Polymer Concrete (PC). Polymer Concrete is usually composed of natural aggregates such as silica sand, binded together with a thermoset resin, such as unsaturated polyester. In this paper it is reported the use of a direct method to calculate two size independent fracture parameters, the critical stress intensity factor, K _Ic, and the critical crack tip opening displacement, CTOD_C, from experimental results of two different size single edge notched beams, 10 and 20 mm, subjected to three point bending under quasi-static loading condition. This method is called the Two Parameter Fracture Model (TPFM). Also the Fracture Energy, G _f, of the specimens were measured to verify its size dependency. Epoxy and polyester resin specimens were studied and epoxy resin specimens reinforced specimens with short carbon and glass fibers were considered.     

Fracture mechanics and notch sensitivity

A diagram valid for the analysis of the fatigue limit of cracks and notches centred in an infinite plate was recently proposed by the authors of the present work with the aim to make explicit the bridging at the fatigue limit between defect sensitivity (correlated to the length parameter a₀, according to El Haddad–Topper–Smith's definition) and notch sensitivity (correlated to a*, where a* is a particular notch depth corresponding to the intersection between the ΔK_th and Δσ₀/K_t curves). The expression being valid, defect sensitivity and notch sensitivity were seen as two sides of the same medal. Such a diagram is now extended to finite size components by simply introducing the shape factor α commonly used in fracture mechanics. The obtained critical defect size is termed a_D, which is a material and geometry dependent parameter, in order to distinguish it from a₀, which is a material parameter. As a consequence the critical notch depth a_N is introduced, such that . This results in the proposal of a ‘universal’ diagram able to summarize experimental data related to different materials, geometry and loading conditions. The diagram, the validity of which is checked by means of several results available in the literature, is applied both to the interpretation of the scale effect and to the surface finishing effect.     

On fracture mechanics under complex stress

The majority of linear elastic fracture mechanics investigations since the pioneering work of Irwin and Paris have been carried out under tension-tension loading conditions in sheet metal. However, built up structures have generally been under complex stress conditions and to date very scanty information is available on fracture mechanics parameters under complex stress conditions. The current stale of the art for mixed mode crack tips deformation is reviewed.In order to use linear elastic fracture mechanics methodology to predict crack growth rate in shear webs, an experimental program was initiated. Initial tests on 7075-T6 Aluminum alloy sheet, using a picture frame type specimen, were conducted. The critical stress intensity factors and the rate of crack growth under aforementioned condition are established.     

On the small crack fracture mechanics

The limit of validity of linear fracture mechanics is specified by the minimum allowable crack length through an ASTM convention. Extension into the non-linear region ought to imply an extension towards smaller allowable cracks. In order to elucidate the question “How short is the smallest crack that fits the methods of fracture mechanics, and how do shorter cracks than that behave?” a pilot investigation is carried out. The process region is modelled as a Barenblatt line region and plastic flow off-side the process region is neglected. Results show that instability occurs before the process region is fully developed (as at large cracks) if the crack is short. This implies large deviations from the large crack fracture mechanics if the crack is very small. Even cracks of infinitesimal length are included in the study.     

On configurational forces at boundaries in fracture mechanics

Configurational forces invariably appear at the external boundaries of cracked bodies (including the crack faces), but it is unclear whether they influence crack growth. Also, it is unclear how such boundary configurational forces are related to the J-integrals calculated in the body. In this brief note, we (i) derive expressions for the surface configurational forces and determine their values on regions of the external boundaries with prescribed tractions or displacements, (ii) determine the relation between the far-field J-integral and the surface configurational forces, and (iii) show that surface configurational forces on the crack faces do not alter the relation between the near-tip and far-field J-integrals.     

On fracture mechanics in lifting an ice sheet

The penetration of a wedge-like tool into an ice sheet at the interface with its substrate may develop a semi-elliptic interfacial crack. The Griffith energy-balance concept is employed to determine the critical conditions for interfacial crack propagation. The results show that an interfacial crack of any semi-elliptic shape tends to propagate in a stable manner and change the shape to a critical shape at which the propagation becomes unstable. The interfacial crack propagation may be interrupted by transverse fractures in the ice sheet.

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Résumé En faisant pénétrer un outil en forme de coin à l'interface entre un film de glace et le substrat sur lequel il est déposé sur une épaisseur uniforme, il peut se développer dans cet interface une fissure semi-elliptique.On fait appel au concept d'équilibre énergétique de Griffith afin de déterminer les conditions critiques pour que se propage la fissure.Les résultats démontrent que, quelle que soit sa forme, une fissure interfaciale semi-elliptique tend à se propager de manière stable, et à atteindre une forme critique pour laquelle la propagation devient instable.Des ruptures transversales dans le film de glace peuvent avoir pour effet d'interrompre la propagation de la fissure.

     

On the fundamental basis of fracture mechanics

Based on the crack tip stress and strain fields, the linear and the non-linear fracture mechanics have been developed. Their applications to the studies of fracture initiation and stable crack growth may differ because of the difference in the basic postulates of various fracture theories. The correct postulates will help to develop non-linear fracture mechanics for valid fracture toughness measurements and to extend fracture mechanics beyond the realms of K and J.The basic postulates of the linear elastic fracture mechanics are examined. The theory of global energy balance, the theory of sharp notch, and the theory of the characterization of crack tip stress and strain fields by K are analyzed. Fracture initiation and stable crack growth are local fracture phenomena. Therefore the global energy balance theory for crack initiation and stable crack growth without the study of the detailed fracture processes is fortuitous. The capability of the stress intensity factor to characterize the crack tip stress and strain fields for the localized fracture process is the basis for the validity of the linear elastic fracture mechanics.The concept of the characteristic crack tip field can be directly extended to the non-linear fracture mechanics. The fracture toughness and the tearing modulus of a tough material are measures of the fracture ductility of the material. The possibility to extend fracture mechanics beyond the realms of K and J are discussed.     

On curved crack paths in finite strain fracture mechanics

A criterion is derived to predict crack trajectories in two dimensional components, which is valid for finite strain fracture mechanics. First a relation between the curvature in mixed-mode crack propagation and the corresponding configurational forces is derived, based on the principle of maximum dissipation. With the help of this, a numerical scheme is presented which is based on a predictor-corrector method using the configurational forces acting on the crack together with their derivatives along real and test paths. With the help of this scheme it is possible to take bigger than usual propagation steps, represented by splines. Essential for this approach is the correct numerical determination of the configurational forces acting on the crack tip. The methods used by other authors are shortly reviewed and an approach valid for arbitrary non-homogenous and non-linear materials with mixed-mode cracks is presented. Numerical examples show, that the method is able to predict the crack paths in components with holes, stiffeners etc. with good accuracy.     

On the finite element method in linear fracture mechanics

The usefulness of the finite element method for the computation of crack tip stress intensity factors is established. Although ordinary finite element methods lack the ability to represent crack tip stress singularity, meaningful values for crack tip stress intensity factors can be obtained by a simple process. The results are compared not only to the results of other analytical solutions, but additional correlation is made of two different fracture test specimen types.     

On basic definitions of unified fracture mechanics terminology

The adoption of unified fracture mechanics terminology (UFMT) will promote efficient communication between specialists in different fields of fracture research, harmonization of national and international standards relating to fracture mechanics, and last but not least improvement of the existing methodology for teaching and education in fatigue and fracture. In this paper the definitions of some basic and related terms included in different standards on fracture mechanics terminology are confronted with one another. Alternative definitions of the same terms are offered. By this strategy the author tries to show that the definitions of basic and related terms appropriate for the UFMT should emerge as a consequence of harmonizing a crack model with an actual crack and then both taken together with a fracture model, laboratory test methods, and failure assessment codes.Published in Problemy Prochonsti, No. 1, pp. 17–29, January, 1996.This paper is published as a matter of discussion.     

On the use of strain gages in dynamic fracture mechanics

An experimental study is conducted to show the application of strain gages in studies of dynamic fracture. In particular, strain gages have been used to evaluate the dynamic stress intensity factors in different specimen geometries in a variety of materials. A direct comparison of the results obtained from strain gages is made with those obtained using dynamic photoelasticity. A detailed evaluation of the effect of the position and orientation of the strain gage on the determination of the fracture parameters is also presented.     

On quarter-point three-dimensional finite elements in linear elastic fracture mechanics

Use of the finite element method for calculating stress intensity factors of two-dimensional cracked bodies has become commonplace. In this study, the more difficult task of applying finite elements to three-dimensional cracked bodies is investigated. Since linear elastic material is considered, square root singular stresses exist along the edge of an embedded crack. To deal with this numerical difficulty, twenty noded, isoparametric, serendipity, quarter-point, singular, solid elements are employed. Examination of these elements is carried out in order to determine the extent of the singular behavior.In addition, the stiffness derivative technique is explored, together with quarter-point elements, to determine an accurate procedure for computing stress intensity factors in three-dimensions. The problem of chosing a proper virtual crack extension is addressed. To this end, the disturbance in the square root singular stresses is examined and compared with a similar disturbance which occurs in two-dimensions. As a numerical example, a pennyshaped crack in a finite height cylinder is considered with various meshes. It is found that stress intensity factors can be calculated to an accuracy within 1 percent when quarter-point cylindrical elements are employed with the stiffness derivative technique such that the crack extension is one in which one corner node is not moved, the other corner node is moved a small distance, and the midside node is moved one-half that distance. This crack extension is analogous to that of a straight crack advance for a brick element. Both of these crack advances disturb the square root singular stresses in a manner similar to that which occurs with the two-dimensional eight noded element in which the crack has been advanced a small distance.     

A notch multiaxial-fatigue approach based on damage mechanics

The fatigue assessment of structural components under complex multiaxial stresses (cyclic or random stress histories) can be conveniently tackled by means of damage mechanics concepts. In the present paper, a model for notch fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which quantifies the damage accumulation in the material up to the final failure. The material collapse can be assumed to occur when the damage is complete, that is, when the parameter D reaches the unity. In the case of notched structural components, such a damage parameter D must be evaluated by taking into account the stress value as well as the gradient effect at the notch root. The proposed model, which also employs the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, is calibrated through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some uniaxial or complex stress histories. The model presents the advantages to be mechanically based and to not require any evaluation of a critical plane and any loading cycle counting algorithm to determine the fatigue life.     

Quantum fracture mechanics

Quantum fracture mechanics (QFM) is proposed by the author as a purely theoretical alternative of the generally accepted experimental-theoretical approach to fracture physics. The main concepts of theory and formulation of several main problems are examined. Using QFM to solve a problem of the initiation of cracks and dislocations makes it possible to predict the brittle-plastic nature of a specific crystal. Analytical and numerical results of calculations carried out using this theory are represented, including subcritical crack growth in a homogeneous lattice and intergranular layers: in loading and unloading, under stationary loading in creep conditions and in cyclic loading in fatigue conditions.Translated from Problemy Prochnosti, No. 2, pp. 3–9, February, 1990.The author is grateful to Jim Rice for reading the document and for useful comments.