C. L. Chow

A finite element analysis of continuum damage mechanics for ductile fracture

A finite element formulation of an anisotropic theory of continuum damage mechanics for ductile fracture is presented. The formulation is based on a generalized model of anisotropic continuum damage mechanics of elasticity and plasticity proposed earlier by the authors. The validity of the proposed anisotropic damage model and finite element formulation is verified by comparing the predicted fracture load of center-cracked tension specimen made of thin aluminium alloy 2024-T3 with those determined experimentally and excellent agreement is achieved. The proposed finite element analysis can thus provide an important design tool to solve practical problems of engineering significance which may have hitherto been found difficult using the conventional fracture mechanics concept.RésuméOn présente une formulation par éléments finis dune théorie anisotrope de la mécanique dendommagement dun continuum, applicable aux ruptures ductiles. Cette formulation est basées sur la généralisation dun modèle de mécanique dendommagement dun continuum anisotrope pour lélasticité et la plasticité, proposé précédemment par les auteurs. On vérifie la validité du modèle dendommagement anisotrope proposé et de sa formulation par éléments finis, en comparant aux valeurs expérimentales la charge de rupture prévue pour une éprouvette mince de traction dalliage daluminium 2024-T3 présentant une fissure centrale. On trouve un excellent accord. Lanalyse par éléments finis proposée peut ainsi constituer un outil de conception important pour résoudre des problèmes pratiques de construction que lon aurait trouvé difficiles à traiter par les concepts de la mécanique de rupture traditionnelle.

A continuum damage mechanics approach to crack tip shielding in brittle solids

This paper focuses firstly on the development of a comprehensive anisotropic theory of continuum damage mechanics for brittle solids suffering progressive deterioration. The basic concept of damage parameterization is re-examined and a new set of damage variables introduced yielding a new damage effect tensor through which the effective stress and strain tensors are defined. Constitutive equations of the damaged material are established incorporating a new hypothesis on equivalence between damaged and undamaged responses of the material. The model is completed by introduction of a general damage characteristic tensor which accounts for the experimentally observed fact that the rate of damage growth depends nonlinearly on applied external loads. The established damage model is next applied to investigate the crack-tip shielding effect due to anisotropic microcracking. The ratio of near-tip to remote stress intensity factors is obtained in closed form. A moderate but definite effect of anisotropy of microcracking is observed. The case of isotropic damage is found to be the least effective in screening remote external loads and is in accord with the results obtained by other researchers using different approaches.

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value wc. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of β=30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.The effect of varying damage coefficients on the fracture loads is examined and it is found that the crack initiation load decreases with the increase of anisotropic damage coefficient.

Fracture studies with DCB specimen

An unifying approach for the DCB specimen with or without the introduction of a groove is presented. The analysis is based on the beam-on-elastic foundation models. Equations are derived for the determination of the foundation modulus for both the groove and beam-foundation models. It is found that the choice of the foundation models used for the evaluation of the fracture toughness should be made on the specimen geometry in terms of the ratios of the specimen thickness and height.Assumptions used in the elastic foundation models are examined and observed that these can be reasonably satisfied by the DCB specimen with the groove height of 1 mm and the thickness ratio of b/B less than 0.25.RésuméOn présente une approche unifiée relative à léprouvette en poutre double cantilever comportant ou non lintroduction dune rainure. Lanalyse est basée sur un modèle de poutre sur appui élastique. Des équations sont déduites de la détermination du module de lappui par rapport à un modèle de lentaille ét un modèle de la poutre-appui. On trouve que le choix des modèles dappui utilisé pour lévaluation de la ténacité à la rupture devrait être fait en tenant compte de la géométrie de léprouvette sous la forme dun rapport de son épaisseur à sa hauteur.Les hypothèses utilisées pour les modèles dappui élastiques sont examinées et lon observe que ces modèles peuvent être raisonnablement satisfaits pour des éprouvettes en poutre double cantilever présentant une hauteur de rainure de 1 mm et un rapport dépaisseur b/B inférieur à 0,25.

Mixed mode ductile fracture using the strain energy density criterion

An investigation of extending the application of the strain energy density criterion to mixed mode ductile fracture is described. Thin plates embedded with a center crack inclined at β=30 and 60 degrees are analysed. An Euclerian finite element formulation is used for the large elastic-plastic flow problem incorporating isotropically hardening Prandtl-Reuss material and incremental deformation.An alternative criterion based on the maximum dilatational energy for determining crack initiation angle in ductile fracture is proposed. Based on this criterion, the predicted fracture loads for the cracked plates of β=30 and 60 degrees are compared satisfactorily with the measurements.

Fatigue crack propagation in aluminium and PMMA

The applicability of the above fatigue law has subsequently been examined for various materials under different loading conditions. The effective mean stress has since been revealed to be a significant variable influencing the rate of crack propagation [3]~ Forman et al. [3] attributed the sensitivity of mean stress effect on Pariss law to the increased rate of crack propagation as K approached K , the fracture • . . m x ~ c toughness of the materlal. The modlfled ~aris s crack growth zormulation, proposed by Forman, is expressed as

Quasi-static cracking of several ductile materials under plane stress conditions

Quasi-static cracking of several ductile materials with large fracture toughnesses and low yield strengths was described. Laboratory size testpieces with reinforcements provided by special test rigs were used. All irreversibilities and general yielding other than at the crack tip were successfully eliminated. Plane stress fracture toughnesses for alloys of aluminum and zinc, low carbon steels and polycarbonate were thus easily obtained.RésuméOn décrit la fissuration quasi statique de divers matériaux présentant de grandes tenacités à la rupture et de faibles limites élastiques.Pour les essais de laboratoire, on utilise des éprouvettes comportant des renforcements nécessités par lemploi dun dispositif spécial dessai. Ceci a permis déliminer, avec succès, toutes les irréversibilités ainsi que toute plastification générale autres que celles qui surviennent à lextrémité de la fissure.Ces tenacités à la rupture en état plan de tension ont été aisément déterminées dans le cas dalliages daluminium et de zinc, daciers à bas carbone ainsi que de polycarbonate.

A conic-section simulation analysis of two-dimensional fracture problems using the finite element method

A conic-section simulation analysis to determine the stress intensity factors for fracture mechanics problems of practical interest using the finite element method is presented. The method makes use of elliptic displacement functions which are satisfied by the introduction of an “equivalent ellipse” obtained through first simulating the actual crack surface displacements as a part of a parabola or a hyperbola. Unlike other finite element approaches that incorporate no special crack-tip treatment, the present approach requires neither extremely small finite elements in the vicinity of the crack tip nor the computation of several strain energies. The cases examined include not only problems of the opening mode (I) or the edge-sliding mode (II), but also the combined modes of crack deformation.RésuméOn présente une analyse par simulation permettant de déterminer les facteurs dintensité de contraintes pour des problèmes de mécanique de rupture dintérêt pratique, en utilisant la méthode des éléments finis. On recourt à des fonctions de déplacement elliptique, qui sont satisfaites par lintroduction dune ellipse équivalente, obtenue en assimilant les déplacements réels en surface de la rupture à une portion de parabole ou dhyperbole. Au contraire des autres approches par éléments finis qui ne prévoient pas un traitement particulier de lextrémité de la fissure, la méthode proposée ne requiert ni de mailles extrêmement fines au voisinage de cette extrémité, ni de nombreux calculs dénergies de déformation. Les cas examinés ne se limitent pas aux problèmes douverture de mode I ou de mode II, mais couvrent aussi des modes combinés déformation de la fissure.

On the finite element method for calculating stress intensity factors with a modified elliptical model

A finite element method based on the modification of the elliptical displacement function model developed earlier by the authors is presented for the determination of stress intensity factors in cracked bodies. The modified elliptical model not only retains the simplicity of the original method in describing stress conditions at the crack tips but also extends the application of the method to cases where the elliptical shape of the crack surface is not entirely preserved. The present method avoids the need for successive computations of several strain energies in a cracked body as required by the strain energy approach and of high concentration of very fine elements at the crack tip by the conventional stress approach.RésuméOn présente une méthode par éléments finis basée sur la modification du modèle de la fonction de déplacements elliptiques développée précédemment par les auteurs, pour déterminer les facteurs dintensité des contraintes dans des solides fissurés. Le modèle modifié conserve la simplicité de la méthode originale pour décrire les conditions de contraintes aux extrémités dune fissure. En outre, il permet détudier son application à des cas où la forme de la surface de la fissure nest pas rigoureusement elliptique.La méthode proposée évite de devoir procéder à des calculs en série de plusieurs énergies de déformation dans le corps fissuré, ainsi que le requiert lapproche basée sur lénergie de déformation. Elle permet aussi de ne pas devoir calculer des concentrations importantes déléments à très petites mailles à lextrémité de la fissure, ainsi que lexige lapproche concentionnelle basée sur les contraintes.