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Session Chairpersons: Professor John W. Hancock, Department of Mechanical Engineering, University of Glasgow, Scotland G12 8QQ, UK; Dr. Peter Matic, Naval Research Laboratory, Code 6380, 4555 Overlook Drive SW, Washington DC 20375
2:00 pm INVITED
MODELING OF DUCTILE FRACTURE: Alan Needleman, Division of Engineering, Brown University, Providence, RI 02912
Analyses of fracture are discussed where the initial-boundary value problem formulation allows for the possibility of a complete loss of stress carrying capacity, with the associated creation of new free surface. Hence, fracture arises as a natural outcome of the deformation process without any ad hoc failure criterion being employed. The failure mechanisms modeled are plastic void growth and coalescence, and cleavage cracking (so that the ductile-brittle transition can be analyzed). The role of porosity induced weakening in precipitating shear band failures will be illustrated. However, the main emphasis will be on recent predictions of crack growth, including ductile-brittle transitions and three dimensional effects such as shear-lips.
2:25 pm INVITED
NON-LOCAL EFFECTS IN DUCTILE FRACTURE PREDICTIONS: Viggo Tvergaard, Department of Solid Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark
Continuum studies of ductile fracture have been based on local constitutive relations, which do not represent a material length scale. The resulting numerical predictions show inherent mesh sensitivity, since the softening material behaviour near final failure will tend to give localized damage in regions as narrow as possible within the mesh resolution. Nonlocal constitutive relations, with the delocalization related to the damage mechanism, have been proposed for ductile fracture where damage involves the nucleation and growth of voids to coalescence. The effect of using this nonlocal material model will be illustrated by a number of analyses, including studies of shear band failure, ductile matrix failure in metal matrix composites, and failure involving two size - scales of voids. Based on recent comparisons with cell - model predictions of localization in a void - sheet the relevant material length scale for a ductile fracture model are discussed.
2:50 pm INVITED
NUMERICAL SIMULATION OF DUCTILE RUPTURE: ANALYSIS OF EXPERIMENTAL SCATTER AND SIZE EFFECT: Jacques Besson, A. Pineau, Ecole des Mines de Paris, Centre des Matériaux, CNRS URA 866, 91003, BP 87 Evry Cedex, France
Ductile rupture behavior is usually characterized with specimens of various types including smooth and notched bars, compact tension specimens, bending bars. In addition, similar specimens geometries of different sizes are also used. Using different specimen geometries allows to investigate the effect of mechanical parameters such as stress triaxility and amount of plastic deformation on ductile rupture. Changing specimen sizes allows to evaluate experimental dispersion and size effects. Considering these effects is of primary importance for the transferability of laboratory tests carried out on relatively small samples to assess the resistance of relatively large industrial components. Both dispersion and size effect are caused by material heterogeneities which have to be accounted for by modeling. This work presents both experimental data and numerical simulation relative to dispersion and size effects on two very different materials. The first one is a plane carbon steel containing MnS inclusions which easily debond from the matrix so that rupture is essentially controlled by void growth. The second material is a cast ferrite - austenite duplex stainless stainless steel. Microcracks are continuously nucleated in the embrittled ferrite so that final rupture is essentially controlled by void nucleation. Both materials were tested using axisymmetric smooth and notched bars and Charpy specimens of different sizes. In order to obtain microstructural data, relevant to modeling, both materials were carefully examined. In the first case, initial local void densities (MnS inclusion content) were measured using image analysis. In the second case, local crack nucleation rates were determined by carrying out interrupted tensile tests and determining crack locations. These examinations are needed to get physically based data to be used in the modeling thus reducing the number of "fitting parameters". Modeling of rupture, dispersion and size effects can be done using two different approaches both based on finite element analysis. The first one (uncoupled) consists in carrying out simulations of the mechanical response of structures assuming that the material is undamaged. Subsequently, a local rupture criterion is applied to the structure to determine that the material remains unchanged. Subsequently, a local rupture criterion is applied to the structure to determine its failure probability. It is therefore assumed that damage is small enough not to affect the stress strain distribution in the part. In addition the material is supposed to break according to the weakest link theory. The second approach (coupled) is based on continuum damage mechanics using models for ductile metals such as those proposed by Gurson and Rousselier. In this case, the effect of damage evolution on stress distribution in the parts can be fully accounted for. In addition the effect of defect spatial distribution can also be investigated. No specific assumption has to be made on the onset of rupture. Finite element calculations were carried out for both materials using the Gurson-Tvergaard/Rousslier constitutive equations. Initial void volume fractions (first material) or microcrack nucleation rates (second material) were randomly distributed in the structures. Dispersion can be modeled by carrying a Monte Carlo type simulation using the same mesh and different random drawings. Size effect is modeled by keeping the element size constant, thus increasing the number of elements for larger structures. The uncoupled approach was also used for the first approach. Results show that size effect and dispersion can be successfully modeled using both approaches. The fully coupled approach, although more time consuming, is thought to be the most promising since: (1) it is based on fewer assumptions, (2) it can be applied to any geometry (e.g. cracked components); in particular it gives much better results on smooth tensile specimens, (3) it can model the interaction between neighboring heterogeneities clusters.
3:15 pm BREAK
3:25 pm INVITED
MICROSTRUCTURE MECHANICS DESCRIPTION OF DUCTILE FRACTURING IN POLYCRYSTALS: Ronald W. Armstrong, C.C. Chen, G.R. Irwin, M.E. Natishan, F.J. Zerilli*, X.J. Zhang, Department of Mechanical Engineering, University of Maryland, College Park, MD 20742; *Permanent address: Research and Technology Depth Naval Surface Warfare Center, Silver Spring, MD 20903-5000
Evidence is reviewed of particle size aspects of hole formation and growth, texture effects and grain size influences, for example, as revealed in stereosection fractographs of titanium and steel alloy ductile failure surfaces, in the latter case, near to the condition of cleavage fracturing. The results are related to model considerations of particle debonding and local region strain rate enhancement and plastic instability properties (see e.g. J.P. Gudas, G.R. Irwin et al., in "Defect Assessment in Components - Fundamentals and Applications", Mechanical Engineering Publications Ltd. London, 1991, pp. 549-568), as well as to constitutive equation aspects of plasticity and fracturing.
3:40 pm INVITED
MACROCRACK NUCLEATION IN DUCTILE MATERIALS: Owen Richmond, Aluminum Company of America, Alcoa Technical Center, 100 Technical Drive, Alcoa Center, PA 15069
In ductile materials, it is typical of many microcracks and pores to nucleate and grow before some of these coalesce to form dominant macrocrack which leads to ultimate failure. This paper is concerned with quantitative identification of the microstructural regions in which this macrocrack nucleation occurs, and the development of constitutive relations for these regions. These microstructure-based constitutive relations can then be used in macromechanical analyses to evaluate potential improvement in macroscopic behavior due to alterations in microstructure.
4:05 pm INVITED
MICROSTRUCTURAL EFFECTS IN DUCTILE FRACTURE: Anthony W. Thompson, Lawrence Berkeley National Laboratory, MS 62-203, One Cyclotron Road, Berkeley, CA 94720
Microvoid coalescence or MVC fracture depends strongly on microstructure. This applies to each of the constituent processes of MVC, namely nucleation, growth and coalescence of voids, and is true for both transgranular and intergranular MVC. Experimental as well as analytical evidence on this point reveals both needs for further experiments, and gaps in analytical understanding. Methods to vary the behavior of MVC processes, such as variations in temperature, or introduction of hydrogen, convey further information (provided MVC fracture is maintained) and have proven valuable in understanding these processes; of particular value are the notch bend tests, in which stress state can readily be varied to identify control of stress, strain, or a combination of the two.
A MODEL FOR CRACK INITIATION AND CRACK GROWTH IN DUCTILE MATERIALS: Xi Zhang and Yiu-Wing Mai, University of Sidney, Centre for Advanced Materials Technology, Department of Mechanical and Mechatronic Engineering, Sydney, New South Wales 2006, Australia
A refined mathematical model is presented in this paper to account for the effects of void nucleation, growth and coalescence on fracture initiation and subsequent quasi-static, slow and little crack growth in ductile materials under plane strain and mode I condition. A chain of larger voids uniformly-distributed ahead of the crack tip is used to model the discontinuous fracture process and discontinuous nucleation of small voids at second-phase particles is the main cause for crack initiation in high strength and ductility steels. A cumulative damage criterion, which is the ratio of uncracked length between the crack tip and the first large void to characterize size, is employed. Effects of crack-tip constraint and material parameters on ductile fracture are discussed in terms of the gradient of the variation of crack-tip constraint within the damage zone. Estimation of upper-bound fracture toughness is established and numerical results show that, with the exception of crack growth there is no obvious constraint effect on ductile crack initiation.
DUCTILE CAVITY GROWTH IN NORMALLY BRITTLE MATERIALS: Donald R. Curran, R.E. Tokheim, and T. Cooper, SRI International, 333 Ravenswood Avenue, Menlo Park, CA 94025
The term "ductile fracture" can be interpreted in a number of ways, but to a materials scientist who focuses on microscopic mechanisms the meaning is clear: "ductile fracture" means that failure occurs by the nucleation, growth, and coalescence of approximately ellipsoidal microscopic voids in plastically deforming material. To be sure, extremely ductile materials stretched under plane or uniaxial stress conditions may fail in the absence of voids by simple plastic necking. Nonetheless, in most practical engineering applications of failure in ductile materials, microscopic "ductile fracture" play a central role in the failure process. Frank McClintock was one of the pioneers in this area (as well as many others), and his 1968 paper [J. Appl. Mech., 35, p.363], along with papers by C.A. Berg [Proc. Fourth U.S. National Congress Appl. Mech. 2 (1962) 885], J.R. Rice and D.M. Tracy [J. Mech. & Phys. Solids, 17 (1969) 202], A.L. Gurson [Trans. ASME, J. Eng. Mater. & Technol. (1977) 2], and M.Y. He and J.W. Hutchinson [J. Appl. Mech. 48 (1981) 830], stimulated much further work. The above papers discussed the conditions for cavity growth in a viscous or plastically deforming material under tension and shear. In the present paper, we take a similar approach, but consider cases in which the cavity growth is driven not only by the externally applied stresses, but also by internal cavity pressure. Such conditions arise when a material is exposed to penetrating radiation from lasers or x-ray sources of sufficient fluence to cause local heterogeneities to vaporize while leaving the matrix material relatively cool. Under such loading conditions, microscopic cavity pressures of several tens of GPa may be produced, sufficient to cause the surrounding matrix material to flow plastically, even when the matrix material is a normally brittle material like a ceramic. Under some boundary conditions, the expanding cavities may drive the matrix material into tension, producing brittle tensile fractures between cavities. We present a computer model of the above processes, and illustrate the model with several example calculations.
5:10 pm INVITED
HYDROGEN EFFECTS ON THE DUCTILE FRACTURE ON IRON-BASED SUPERALLOYS: Neville R. Moody*, I. Baskes*, J.E. Angelo,* and T. Tsuji**; *Sandia National Laboratories, P.O. Box 969, Mail Stop 9403, Livermore, CA 94551; **Shizuoka University, Hamamatsu, Japan
Austenitic superalloys can exhibit dramatic reductions in ductility and crack growth resistance when hydrogen triggers a change in failure mode. All failures begin by void growth at fractured matrix carbides. However, void growth is prematurely terminated terminated in hydrogen by second generation void formation at slip band intersections and separation of interconnecting slip band segments. As a first approximation to understanding hydrogen effects on the fracture process, we have combined the Embedded Atom Method with Monte Carlo simulations to model the segregation of hydrogen to dislocation in slip bands and slip band intersections. We will present these results and draw a direct correlation between the segregation of hydrogen to slip band intersections, void formation, and crack growth susceptibility.
5:30 pm INVITED
NEAR-TIP FRACTURE PROCESSES IN DUCTILE MATERIALS: Kwai S. Chan, Southwest Research Institute, San Antonio, TX 78238
Ductile fracture is generally considered to occur via void nucleation, growth, and coalescence mechanisms that result in a dimpled fracture appearance. For many materials, void initiation and growth take place at hard particles or inclusions. However, ductile fracture involving void formation has been observed in materials that contain neither hard particles nor inclusions. In this paper, the near-tip fracture processes in several structural alloys, including Al-, Ti-, and Nb-base alloys, that exhibit ductile fracture in a variety of microstructures with and without hard particles are summarized. Possible mecha nisms for the formation of dimpled fracture in these materials are identified. These fracture mechanisms are correlated with the microstructures and the fracture resistance curve to provide a basic understanding of the role of microstructure in the crack-tip fracture process, the transition from ductile to brittle fracture, and the source of fracture resistance.
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