Computational dynamic fracture mechanics

This paper provides a review on the state of the art in computational dynamic fracture mechanics. The following important essential ingredients in computational dynamic fracture mechanics are included: (i) fundamental aspects of dynamic fracture mechanics, (ii) types of fracture simulation, (iii) computational models of dynamic crack propagation, and (iv) use of dynamic J-integral in computational models. In the item (i), a special attention is focused on the asymptotic eigen fields for various states of dynamic crack tips, which provide the foundation of dynamic fracture mechanics as Williams' asymptotic eigen solutions provided the foundation of static linear fracture mechanics. In the item (ii), a new concept of mixed-phase simulation is presented for general nonself-similar crack propagation, in addition to the generation-phase and application-phase simulations. A comprehensive summary of computational models for dynamic crack propagation is given in the item (iii). Finally, in the item (iv) several attractive features of the dynamic J-integral are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Review of new formats for fracture mechanics parameters

New methods to formulate fracture mechanics parameters are presented. These include the common format that relates the deformation behavior of a cracked structure or specimen to the deformation behavior of a tensile test and the concise format that suggests a shortened form of common fracture mechanics parameters to replace the usual polynomial formulations. These forms may give an easier way to use the fracture mechanics parameters in analytical calculations. __________ Translated from Problemy Prochnosti, No. 4, pp. 39–45, July–August, 2006.     

Numerical studies in dynamic fracture mechanics

This paper provides a summary of recent studies concerning numerical modeling of dynamic crack-propagation, Both stationary mesh as well as moving mesh finite-element procedures are examined. Simple procedures, using a moving mesh of conventional isoparametric elements in conjunction with certain path-independent integrals for the evaluation of stress-intensity factors for a dynamically propagating crack are presented.

---

Résumé Le mémoire fournit des synthèses des études récentes relatives à la modélisation numérique de la propagation de fissures dynamiques. On examine, à la fois, le maillage stationaire et le maillage mobile utilisés dans les procédures d'éléments finis. On présente des procédures simples utilisant un maillage mobile d'éléments conventionnels isoparamétriques utilisé avec certaines intégrales indépendantes du parcours, en vue d'évaluer les facteurs d'intensité de contrainte dans le cas d'une fissure en cours de propagation dynamique.

     

Calculation of fracture mechanics parameters for a general corner

The Reciprocal Work Contour Integral Method of Stern, et al. is extended so that computation can be made of fracture mechanics parameters at the corner formed by arbitrarily oriented stress free surfaces. Two numerical examples are given. In one, results are compared to those obtained using an overdetermined collocation technique.

---

Résumé On procède à une extension de la méthode d'étude par intégrale de contour du travail réciproque, proposée par Stern et Al, en vue de calculer les paramètres de mécanique de rupture correspondant à l'angle formé par deux surfaces d'orientation arbitraire et libres de contrainte. Deux exemples numériques sont fournis, avec, pour l'un, une comparaison des résultats avec ceux que fournit une technique de collocation redondante.

     

Evaluation of elastic fracture mechanics parameters for bend specimens

Existing solutions for stress intensity factor and mouth opening displacement of three-point bend specimens are shown to overestimate these quantities for shallow cracks by up to ±4.5 percent, because they do not account for the disturbance of the bending stress distribution by the concentrated force at the loading point. This error is far larger than the accuracy claimed by these solutions (0.2 to 0.5 percent).New expressions are therefore developed for stress intensity, crack mouth opening displacement and crack mouth open angle of single edge notched bend specimens loaded in three-point bending. As a reference, and to show the accuracy of the solutions, also the pure bending situation is treated. Rigorously derived asymptotic solutions are used for the shallow and deep crack limits, in order to prescribe both the proper limit values and gradients to the interpolation functions, of which the intermediate values are derived from refined finite element analyses.The crack mouth opening angle solutions are primarily intended to facilitate crack mouth opening measurement at other locations then the specimen surface, i.e. at an offset from the specimen surface as is the case when removable knife edges are applied. No solutions of the crack mouth opening angle of three-point bend specimens were available until now. For use with unloading compliance crack length measurement, also an inverse crack mouth opening relation is developed. This also includes crack mouth opening measurement at an offset from the specimen surface, which is lacking in presently available expressions of this kind.     

The micro-statistical fracture mechanics approach to dynamic fracture problems

Continuum fracture mechanics concepts should be applied to solve dynamic fracture problems wherever a continuum approach can provide sufficient answers. Many dynamic fracture problems, however, involve multiple cracks or voids and are not well-suited to the relatively simple continuum approach. This paper describes a statistical fracture mechanics concept on a microscopi scale and illustrates its use for the case of shock-wave-induced ductile spall fracture. The paper further shows how micro-statistical fracture mechanics (MSFM) merges with continuum fracture mechanics by treating a macrocrack propagating in a DCB specimen using MSFM and the MSFM parameters deduced from the spall work.Thus, the two approaches are consistent. Although significantly more complicated, the MSFM approach promises to be helpful in improving our understanding of the influences of microstructure on toughness and in extending continuum approaches to more ductile materials and to smaller specimens.

---

Résumé Les concepts de fracture mécanique d'un continuum devraient être appliqués à la solution des problèmes de fracture de rupture dynamique dès lors qu'une approche par continuum peut fournir des réponses suffisantes. Cependant, plusieurs problèmes de rupture dynamique comportent des fissures ou des cavités multiples et ne sont pas bien adaptés à une approche par continuum relativement simple. Le mémoire décrit un concept de mécanique de la rupture statistique à une échelle microscopique et illustre son utilisation au cas d'une rupture par décollement ductile sous l'effet d'une onde de choc. On montre en outre qu'une mécanique de rupture micro-statistique peut être envisagée dans le mécanisme de rupture d'un continuum en traitant la propagation d'une macro-fissure dans une éprouvette Cantilever et en utilisant ce concept et les paramètres qui y sont liés, déduits du travail relatif à l'écaillage.Ainsi, les deux approches se révèlent applicables. Bien que considérablement compliquées, l'approche de mécanique de rupture micro-statistique se révèle prometteuse pour améliorer notre compréhension des influences de la microstructure sur la ténacité et pour une extension de l'approche du continuum de milieu continu à des matériaux plus ductiles ou à des éprouvettes plus petites.

     

Dual boundary element method for anisotropic dynamic fracture mechanics

In this work, the dual boundary element method formulation is developed for effective modelling of dynamic crack problems. The static fundamental solutions are used and the domain integral, which comes from the inertial term, is transformed into boundary integrals using the dual reciprocity technique. Dynamic stress intensity factors are computed from crack opening displacements. Comparisons are made with quasi‐isotropic as well as anisotropic results, using the sub‐region technique. Several examples are presented to assess the accuracy and efficiency of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

Fracture mechanics parameters for cracks on a slightly undulating interface

Typical bimaterial interfaces are non-planar due to surface facets or roughness. Crack-tip stress fields of an interface crack must be influenced by non-planarity of the interface. Consequently, interface toughness is affected. In this paper, the crack-tip fields of a finite crack on an elastic/rigid interface with periodic undulation are studied. Particular emphasis is given to the fracture mechanics parameters, such as the stress intensity factors, crack-tip energy release rate, and crack-tip mode mixity. When the amplitude of interface undulation is very small relative to the crack length (which is the case for rough interfaces), asymptotic analysis is used to convert the non-planarity effects into distributed dislocations located on the planar interface. Then, the resulting stress fields near the crack tip are obtained by using the Fourier integral transform method. It is found that the stress fields at the crack tip are strongly influenced by non-planarity of the interface. Generally speaking, non-planarity of the interface tends to shield the crack tip by reducing the crack-tip stress concentration.     

Elastodynamic near-tip fields for a rapidly propagating interface crack

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar isotropic elastic solids is investigated. Both anti-plane and in-plane motions are considered. The anti-plane displacements and the in-plane displacement potentials are sought in the separated forms $\text{r}{}^{\mathrm{q}}\text{F(θ)}$, $\text{r}$ and θ being polar coordinates centered at the moving tip. The mathematical statement of the problem reduces to a second-order linear ordinary differential equation in θ, which can be solved analytically. Formulation of the boundary and interface conditions leads to an eigenvalue problem for the singularity exponent $\text{q}$. For the in-plane problem, root $\text{q}$ is found to be complex. Thus, the stresses exhibit violent oscillations within a small region around the crack tip, and the solutions have physical significance only outside this region. The angular stress distributions are plotted for various crack speeds, and it is found that at a high enough speeds the direction θ of maximum stress moves out of the interface. This result indicates that a running interface crack may move into one of the adjoining materials.     

Computation of fracture mechanics parameters for structures with residual stresses

Most manufacturing processes induce residual stresses in metallic parts, which will influence the in-service behaviour of the part with respect to fatigue and damage tolerance resistance, corrosion resistance and strength. In the particular case of a compressive residual stress field, the fatigue and damage tolerance behaviour is actually improved. The objective of this work is to develop a numerical method, based on the boundary element method and the principle of superposition, to assess the influence of residual stresses on fracture mechanics parameters. The numerical procedures are detailed and applied on an actual toughness test specimen, for which failure loads with and without residual stresses where measured. In spite on the complexity of the failure process with internal stresses, the method captures well the magnitude of the toughness variation.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

A review of dynamic fracture mechanics in China

This paper summarizes the recent development of dynamic fracture in China. The review covers analytical and numerical results on elastodynamic crack fields in 3D and layered media; experimental and theoretical research on dynamic mechanical properties of rocks and advanced materials; transient effects on ideally plastic crack-tip fields when the inertia forces are not negligible.     

A collocation procedure for determining fracture mechanics parameters at a corner

An overdetermined collocation procedure is presented for determining fracture mechanics parameters. The use of more than one eigenvector coupled with the overdetermined collocation procedure circumvents many of the problems normally found with the collocation procedure. Results are compared with those of other methods on two test problems.

---

Résumé Pour déterminer les paramètres de mécanique de rupture d'un coin, on fait appel à une procédure de collocation surabondante. L'emploi de plus d'un eigenvecteur, couplé à cette procédure de collocation permet de circonvenir plusieurs des problèmes que l'on rencontre normalement avec une procédure de collocation classique. On compare, sur deux problèmes test, les résultats obtenus avec d'autres méthodes.

     

Pre-cracking technique for fracture mechanics experiments along interface between thin film and substrate

Utilizing the difference in interface strength due to fabrication process, a technique for producing a sharp pre-crack between a thin film and a substrate is proposed. A cracked specimen for examining fracture toughness of interface between a sputtered copper (Cu) thin film and silicon (Si) is made by the method. A vacuum-evaporated Cu thin film, which has poor adhesion to Si, is inserted between the sputtered Cu thin film and the Si substrate as a release layer. The release layer debonds from the Si substrate at very low load, and the sharp pre-crack is successfully introduced along the interface. Using the pre-cracked specimen, the interface fracture toughness test is conducted and the critical J-integral, J_C, is evaluated as about 1 J/m² for the sputtered Cu/Si interface.     

Strengthening of alloy 8090 and its fracture mechanics parameters

An investigation has been made of the tensile properties, impact-, initial fracture toughness and fracture mode of an aluminium-lithium 8090 alloy at room temperature and 77 K, depending upon the heat treatment and orientation. The peak-aged material exhibited an excellent combination of strength and toughness, equal to or exceeding that shown by the high-strength aluminium alloys of the 2000 and 7000 series. The superior strength and toughness of peak-aged plates, including that of 3% stretched material, compared to underaged material seems to be associated with the lower content of coarse insoluble precipitates, a higher density of S-precipitates in a matrix ligament (grain) which promote ductile fracture. The impact toughness of the peak-aged specimens increased at 77 K only in the L-T plate orientation, while in the T-L orientation it was somewhat lower or remained the same. The toughness increase at 77 K is discussed in terms of the role of the matrix and (sub)grain-boundary precipitates, freezing of low-melting point impurities of sodium and potassium alkaline metals at (sub)grain boundaries and the occurrence of the fine crack divider delamination toughening. The yield strength, R _o.2, increase on ageing was accompanied by a corresponding increase in initial crack divider fracture toughness, K _lc, opposite to the trends obtained for some traditional high-strength aluminium alloys. Changes of K _lc versus R _o.2 depending on orientation are discussed using models for ductile fracture toughness behaviour of aluminium alloys, based on the criterion that a critical width of the heavily strained zone at the crack tip approximates the average ligament width, d _p, i.e. the thickness of the elongated grain in the L-T and T-L plate orientations. It was also found that, for constant chemical composition and fabrication practice of the alloy, a critical plate thickness exists B 0.1 6 t _i, where _i is the initial thickness of the rolling ingot, for which the tensile strength properties in the L-T orientation are the same as that in the T-L orientation, while the plasticity (measured by elongation to failure) of the plate is a maximum. Two types of laminated cracks were observed on fracture surfaces of the specimens: large, >1 mm deep (the number of these cracks remains the same as the number of hot-rolling passes), and fine <0.4 mm (shallow laminated cracks, the number of which significantly increases with decreasing temperature, 77 K).     

Incremental path-independent integrals in inelastic and dynamic fracture mechanics

Certain incremental path-independent integrals, of relevance in the mechanics of fracture of elastic-plastic materials described by a classical flow theory of plasticity, are presented. Both quasi-static as well as dynamic fracture situations are considered. The topics discussed include: (i) incremental path-independent integrals that characterize the crack-tip fields in elastic-plastic materials; (ii) incremental integrals related to the incremental total potential energy difference; and (iii) the complementary or dual representations of these integrals. The use of these integrals is illustrated through some numerical examples. Comments are made on the utility of these integrals in postulating rational fracture criteria.     

A hybrid method to assess interface debonding by finite fracture mechanics

Adhesive connections are potentially weak locations in many kinds of engineering structures. Since adhesive joints can be regarded locally as bimaterial notches, the assessment of the hazard of crack nucleation, initiation and propagation in the vicinity of bimaterial notches and the reliability of the junctions is an important problem. An essential requirement in this context is a sufficient criterion for crack nucleation. The present contribution proposes a modified approach based on Leguillon’s hypothesis in order to provide a feasible criterion. A crack at a notch is assumed to be initiated and to grow if and only if both the released energy and the local stresses exceed critical values. Thus, simulating virtual crack growth along an interface of two dissimilar bonded materials, the integrity of the bond is revisable. The approach enables the determination of characteristic lengths for freshly nucleated cracks forming the base for any further integrity assessment. As an example, the concept is applied to the analysis of an adhesive bond of metallic and ceramic materials under severe thermal loading conditions as they occur, among other examples, in high temperature fuel cell technology. It is shown that the failure hazard of the adhesive joint can be reduced significantly by an appropriate local design.     

Some considerations on dynamic biem—I: A dynamic program for two-dimensional fracture mechanics problems

In Part I of this report, the theoretical and numerical fundamentals of BIEM techniques in real transformed dynamic are presented.Interesting remarks on how the numerical integrations have been done, are pointed out in the method.In Part II, to be published in a detailed paper, numerical results for impact problems obtained by BIE Method, through a dynamic program of general application, will be shown.     

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.