Local criteria for ductile fracture

Strain distributions in specimens suitable for studying the initiation of fracture are reviewed, and distributions are developed for the steady-state propagation of cracks in plane strain lension of fully plastic materials. The functional forms of local fracture criteria are discussed for different metallurgical mechanisms. It is concluded that:

1. pure Mode I (normal) fracture is unlikely to exist except in cleavage.
2. there is both theoretical and experimental evidence for the development of both: sharp and flat-bottomed cracks.
3. simultaneous diffuse and concentrated (Dugdale-Muskhelishvili) flow fields can occur in torsion of longitudinally grooved bars if the stress-strain curve has a maximum which causes band formation, so that a displacement criterion becomes appropriate for final fracture.

     

On energy balance criteria in ductile fracture

This paper is concerned with a formulation and statement of energy balance criteria during slow crack growth and at inception of catastrophic rupture in relatively high strength ductile metals. The phenomena of necking in a tensile test and slow crack growth in a uniaxially loaded, transversely cracked sheet are taken as models for a general, conceptual analysis. The various mechanistic criteria of crack instability that have been suggested are critically evaluated, in light of recent experimental data, through simple mathematical-physical examples. A more general energy balance criterion for ductile fracture is proposed which is consistant with experimental observations and which reduces to the classical Griffith theory (both conceptually and mathematically) in the case of purely elastic, brittle fracture.

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Zusammenfassung Diese Abhandlung bezicht sich auf die Formulierung and Erklaerung von Energie-Gleichgewichts — Kriteria waehrend des langsamen Wachsens von Rissen und beim ploetzlichen Reissen relativ hoch belastbarer Metalle grosser Ducktilitaet. Die Erscheinungen, dass sich eine Einschnuerung waehrend einer Zerreissproble bildet und dass eine Bruchstelle langsam in einem einachsig beanspruchten Blech mit querlaufendem Riss waechst, werden als Ausgangspunkte fuer eine grundsaetzlich allgemeine Analyse verwendet. Die verschiedenen mechanistischen, bereits vorgeschlagenen Kriteria der Riss-Instabilitaet werden kritisch im Lichte experimentell gewonnener Daten an Hand einfacher mathematisch-physikalischer Beispiele gewertet. Ein allgemeineres Energie-Gleichgewichts-Kriterium fuer Ducktilitaetsrisse wind vorgeschlagen, das mit experimentellen Beobachtungen uebereinstimmt und das sich (sowohl begrifflich wie auch mathematisch) in den Faellen rein elastisch, sproeder Rissibildung auf die klassische Griffith Theorie reduzieren laesst.

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Résumé Cette étude traite d' une formulation et constatation du critére d' équilibre d' énergie pendant la croissance lente d'une fissure et le commencement d' une rupture catastrophique dans les métaux ductiles de grande resistance. Les phénomènes d'étroitement dans un essai de traction et croissance lente d'une fissure dans une feuille soumise á une tension uniaxiale et fissurée transversalement, sont utilisés comme modéles pour une analyse conceptuelle et générals. Les différents critères mécaniques de l'ínstabilités d'une fissure qui ont été jusque ici recommendés, sont critiquement evalués dans la lumière de récentes données expérimentales par de simples exemples physico-mathématic. Un critère plus général pour l'équilibre d' énergie d'une fissure ductile est recommendé qui se conforme avec les observations expérimentales et qui se réduit á la théorie classique de Griffith (tant en conception que mathématiquement) dans le cas d'une rupture par fragilité, purement élastique.

     

A micromechanical constitutive model for dynamic damage and fracture of ductile materials

This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624–1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Grüneisen equation of state. This later aspect allows us to consider high impact velocities. All model parameters are directly assessed by experimental measurements to the exception of the nucleation law which is characterized by the way of an inverse identification method using three free-surface velocity profiles (at low, intermediate and high impact velocities). It is shown that the nucleation law can be consistently determined in the range of operating pressures. The nucleation law being identified, the development of internal damage happens to be a natural outcome of the modelling. The model is applied to predict damage development and free-surface velocity profiles for various test conditions. The variety and the quality of results support the physical basis (in particular micro-inertia effects) upon which the proposed model of dynamic damage is based.     

Study of slant fracture in ductile materials

Slant fracture is widely observed during crack growth in thin sheet specimens made of ductile materials, providing a good case for investigating three-dimensional criteria for mixed-mode ductile fracture. To gain an understanding of slant fracture events and to provide insight for establishing a slant fracture criterion, stable tearing fracture experiments on combined tension-torsion (nominal mixed-mode I/III) specimens and nominal Mode I Arcan specimens made of Al 2024-T3 are analyzed using the finite element method under three-dimensional conditions. Two types of finite element models are considered for the study of slant fracture: (a) combined tension-torsion specimens containing stationary, flat and slant cracks subject to loads corresponding to the onset of crack growth, and (b) stable tearing crack growth with slanting in a nominal Mode I Arcan specimen. Analysis results reveal that there exists a strong correlation between certain features of the crack-front effective plastic strain field and the orientation of the slant fracture surface. In particular, it is observed that (a) at the onset of crack growth in the combined tension-torsion experiments, the angular position of the maximum effective plastic strain around the crack front serves as a good indicator for the slant fracture surface orientation during subsequent crack growth; and (b) during stable tearing crack growth in the Mode I Arcan specimen, which experiences a flat-to-slant fracture surface transition, the crack growth path on each section plane through the thickness of the specimen coincides with the angular position of the maximum effective plastic strain around the crack front.     

Acoustic emission and fracture of ductile materials

Acoustic emission, radius of the contraction zone on the side of the specimen and load-load point displacement were measured during fracture of single edge notched specimens containing fatigue cracks of different lengths. It was found that there exists a three-fold correlation between formation of a contraction zone, noticeable acoustic emission and deviation from linearity on the load-load point displacement curves. The stress intensity factor K was evaluated from the extent of contraction on the specimen surface and related to the acoustic emission total count. A correction for K was made to account for the considerable plasticity at the crack tip. Finally, a model for the formation and development of the plastic and contraction zones is formulated.     

The measurements of fracture toughness of ductile materials

Near tip strain is proposed as a ductile fracture criterion. This criterion was used to study the onset of slow growth of surface crack. The data from two batches, B and C, of fully annealed 2024-0 aluminum alloy and HY-80 steel substantiated the proposed criterion. The measured fracture toughness at the onset of surface crack growth are 280, 110 and 800 ksi √in. for these three materials respectively. It was demonstrated that the measurement can be made easily with a small foil resistance strain gage. The near tip strain criterion was compared with both crack surface opening displacement and J-integral criteria.     

Conditions for shear localization in the ductile fracture of void-containing materials

This paper investigates the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth. The ductility predicted for a macroscopically homogeneous sample of a voided material is shown to be unrealistically large and hence an initial inhomogeneity of properties is considered, in the sense of an analysis by Marciniak and Kuczynski in the related problem of local necking in sheet metals. General conditions for a localization bifurcation with an initial inhomogeneity (imperfection), concentrating deformation to allow localization within it, are derived. The initial imperfection is taken in the form of a void-containing, thin slice of a material and is assumed to have a void volume fraction slightly larger than the outside of the imperfection. Elastic-plastic constitutive rate relations for void-containing materials proposed by Gurson are adopted to the conditions for the localization bifurcation. The critical conditions are analyzed numerically to discuss the sensitivity of localization conditions to an initial imperfection, in consideration of the implications for the theory of ductile fracture. The results suggest that the existence of an initial imperfection makes it possible for localization to occur at a reasonable strain, and the predictions from this analysis seem broadly consistent with reported experimental observations.

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Résumé Le mémoire étudie la possibilité que les ruptures ductiles se produisent par un mécanisme de Mc Clintock-Berg afférant à la localisation d'une déformation dans une bande de cisaillement étroite et ce en raison d'un adoucissement progressif du matériau par un accroissement de la densité de porosité associée à la croissance de lacunes. On montre que la ductilité prévue pour une éprouvette macroscopiquement homogène d'un matériau comportant des lacunes est irréellement grande et que dès lors, il y a lieu de considérer une inhomogénéité des propriétés dans le sens d'une analyse par Marciniak et Kuczynski effectuée dans le problème connexe du rétrécissement local des tôles minces. Les conditions générales pour une bifurcation de cette localisation en fonction d'une inhomogénéité initiale (imperfection) ainsi que pour une déformation concentrée qui permette une telle localisation dans cette inhomogénéité, sont déduites de cette analyse. L'imperfection initale est considérée sous la forme d'une mince couche de matériau comportant des lacunes, et est supposée présenter une fraction d'un volume lacunaire légèrement plus grande qu'en déhors de l'imperfection. Pour les conditions de la bifurcation de la localisation, on adopte les relations constitutives élastoplastiques proposées par Gurson dans le cas de matériaux comportant des lacunes. Les conditions critiques sont analysées par voie numérique afin de discuter la sensibilité aux conditions de localisation pour une imperfection initiale, considérant les implications que cela peut avoir pour la théorie de la rupture ductile. Les résultats suggèrent que l'existence d'une imperfection initiale rend possible une localisation sous une déformation raisonnable et les prédictions pour cette analyse paraissent largement consistantes avec les observations expérimentales publiées.

     

金属韧性断裂准则的数值模拟和试验研究

对不同外形的45钢试件进行了拉伸、压缩和扭转等材料试验,对工程中常用的5个韧性断裂准则的适用范围进行了对比研究,并采用Gurson-Tvergaard(GT)多孔材料本构模型对试验过程进行了数值模拟.指出目前使用的断裂准则都不可能对材料在多种变形条件下给出一个固定临界值.根据金属成形工艺特点,综合考虑拉伸型和剪切型2种不同韧性断裂机制,提出一个统一的韧性断裂准则形式.试验和数值计算结果证明了该准则的有效性和普适性,进而利用单向拉伸和扭转试验确定的材料常数合理地预测压缩过程中的韧性断裂现象.     

Out-of-plane stretching and tearing fracture in ductile sheet materials

Pre-cracked ductile steel sheets are fractured by combined in-plane streching and bending. The deformation mimics the mode of fracture when plating is dented and torn as in ship grounding. Fracture toughness is determined for this mode of tearing. Values are greater than those obtained with DENT testpieces on the same material because of the different mode of crack opening. This revised version was published online in August 2006 with corrections to the Cover Date.     

A fracture model for surface flaws and certain types of weld defects in ductile materials

A model is proposed for prediction of fracture initiation from surface flaws, bands of slag inclusions and zones with low yield strength in thin-walled structures. The model applies to cases where the whole ligament or defect zone is plasticized. Application of the model to design cases requires information from stress and elongation measurements on tensile specimens cut perpendicular to defect regions of the actual type. Predictions by the model of critical stresses are compared to results from burst tests on pipes with surface flaws. The correlation is found to be good and existing deviations between experiment and theory can be given a rational explanation within the framework of the model. This suggests that bulging and out of plane loading effects which are not taken into account in the model are not significant in these problems. The model thus makes a “limit” analysis possible for “two-dimensional” structures containing defects of the types mentioned above.     

A note on fracture criteria for interface fracture

Several criteria for interface fracture are examined and compared to test results obtained from glass/epoxy specimens. These include two energy release rate criteria, a critical hoop stress criterion and a critical shear stress criterion. In addition, approximate plastic zone size and shape within the epoxy are determined for these tests.     

Continuous-discontinuous formulation for ductile fracture

In this contribution, a continuum-discontinuum model for ductile failure is presented. The degradation of material properties through deformation is described by a Continuum Damage Mechanics model, which uses a non-local integral formulation to avoid mesh dependence. In the final stage of failure, the damaged zone is replaced by a macro crack for a more realistic representation of the phenomenon. The inclusion of the discontinuity surfaces is performed by the XFEM and Level Set Method to avoid the spurious damage growth typical of this class of models.     

A study on an effect of geometric singularities on ductile fracture

This paper describes the appearance of fractures in the vicinity of geometric singularities in cold upsetting of three series of slightly different samples between flat and spherical dies. The main goal of the research is to understand an effect of geometric singularities on ductile fracture. To this end, the series of tests are designed such that the site of fracture initiation moves to the geometric singularity, as compared to conventional tests, independently of its effect on the ductile fracture process. The paper concerns with a qualitative effect of geometric singularities on ductile fracture initiation rather than with quantitative values of parameters controlling the ductile fracture process.     

A study on the ductile fracture of Al-alloys 7075 and 2017

The mechanism of the ductile fracture is studied experimentally for the Al-alloys 7075-T6 and 2017-T4 specimen.The experiments are conducted for the 1CT specimen and they are analyzed by using the acoustic emission and FRASTA (Fracture Surface Topographic Analysis) technique and the process of the fracture is investigated in real time.By the frequency analysis there are 3 kinds of AE patterns of the AE occurrence.By using the FRASTA technique, the details of voids nucleation and growth and the coalescence of voids and crack and the crack propagation process is clarified visually.AE with small amplitude corresponds to the cracking and decohesion of the inclusions and the AE of the large energy with eminent low cycle components corresponds to the high speed coalescence of cracks and voids nearby and this energy corresponds to the propagation area of the crack.

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Résumé On étudie expérimentalement le mécanisme de la rupture ductile sur des échantillons d'alliages d'aluminium 7075-T6 et 2017-T4. Les essais sont effectués sur des éprouvettes ICT, analysées par émission acoustique et par examen topographique de la surface de rupture, le processus de la rupture étant étudié en temps réel.Trois types d'émissions acoustiques ressortent d'une analyse de fréquences. Le détail de la nucléation de cavités, puis de la croissance et de la coalescence des cavités en une fissure, puis du processus de la propagation de la fissure apparaissent clairement grâce à l'examen topographique.Une émission acoustique à forte énergie avec des composantes à basse fréquence correspond à une coalescence à grande vitesse de fissures et de cavités dans le voisinage, et cette énergie est en relation avec la surface de propagation de la fissure.

     

Effect of hardening models on different ductile fracture criteria in sheet metal forming

Prediction of the fracture is one of the challenging issues which gains attention in sheet metal forming as numerical analyses are being extensively used to simulate the process. To have better results in predicting the sheet metal fracture, appropriate ductile fracture criterion (DFC), yield criterion and hardening rule should be chosen. In this study, the effects of different hardening models namely isotropic, kinematic and combined hardening rules on the various uncoupled ductile fracture criteria are investigated using experimental and numerical methods. Five different ductile fracture criteria are implemented to a finite element code by the user subroutines. The criterion constants of DFCs are obtained by the related experimental tests. The in-plane principle strains obtained by the finite element analyses for different DFCs are compared with the experimental results. Also, the experimental results are used to evaluate the principle strain values calculated by the finite element analysis for different combinations of DFCs and hardening rules. It is shown that some DFCs give better predictions if the appropriate hardening model is employed.