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Monday-Thursday Room: 314A
Session Chairperson: Dr. R.K. Mahidhara, Tessera Inc., 3099 Orchard Drive, San Jose, CA 95134
APPROXIMATE SOLUTIONS FOR STRAIN HARDENING SOLID WITH A CRACK: Yu G. Matvienko, Mechanical Engineering Research Institute, Russian Academy of Sciences, 4 Griboedov Street, 101830 Moscow, Russia
A working out of nonlinear fracture mechanics criteria and application of calculation methods requires the availability of solutions to elastic-plastic crack problems. Such solutions depend on details of deformation behaviour of materials. For most cases the solutions must be computed numerically and that could be connected with some difficulties. Therefore, a working out of approximate analytical solutions is an actual problem. New analytical solutions relate J-integral to applied stress, notch (crack) geometry and strain hardening. The method is based on stress concentration analysis near a notch-crack tip in strain hardening solid. Approximate analytical J-solutions are calculated in accordance with the theoretical stress concentration factor formulas of Neuber for several crack configurations: elliptical notch in infinite plate, deep grooved shaft, deep double etch notch, shallow double notch in tension. The important role of J-integral is a measure of the intensity of the near-tip stress and strain that can be written in the form of the HRR-singularity. So, to assess J-dominance for fully plastic conditions the HRR-model and the method based on an equation of equilibrium was employed. It was assumed that (i) the characteristic size of the singularity is determined by the condition of the equality of the singularity stress and the applied stress, (ii) the force, that is not transmitted by the crack, is counterbalanced by the additional force of the singularity stress field depends strongly on the crack size and weakly on hardening. To predict the behaviour of a crack in ductile materials it is necessary to use non-linear fracture mechanics criteria. One such criterion can be associated with the failure assessment diagram (FAD) which merges the two extreme brittle fracture and plastic collapse. New FAD has been obtained from the energy balance taking into account crack tip blunting and difference between the energy of surface stresses and the surface energy. The present work assumes the relation between crack blunting and J-integral.
ESTIMATION OF DUCTILE FRACTURE TOUGHNESS FROM TENSILE TESTS FOR ENGINEERING APPLICATIONS: S.K. Ray, A.K. Bhaduri and P. Rodriguez, Fracture Mechanics Section, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
An empirical method for characterizing the ductile fracture toughness using two parameter (viz., Gf and hf) that can be determined from tensile test data of smooth cylindrical specimens has been evolved for engineering applications by Ray, Bhaduri and Rodriguez (herein after referred to as the RBR method). This stipulates that the post-necking regime during tensile deformation is demonstrated by microvoid growth and coalescence processes, and therefore the energy absorbed in this regime can be used to estimate the resistance of the necked region to ductile fracture. The test procedure employed is simple, and does not require gauge-length extensometry. The test is carried out in a screw-driven machine at constant cross-head speed, with on-line deformation of the load train. The method of computing RBR parameters, Gf and hf from the tensile test data at ambient and elevated temperatures, is described.
With Wpn the energy absorbed by the specimen from necking to fracture and An the uniform cross-sectional area at the necking point, the parameters GfWpn/An estimates the average energy per unit cross-sectional area required to cause fracture. Also, with Af as the minimum cross-sectional area of the neck at fracture, ln(An/Af) measures the average longitudinal plastic strain perpendicular to the plane of the neck accumulated from the point of necking to fracture. Therefore, the parameter, ¥f=Gf/ln(An/Af) estimates the average incremental plastic energy per unit volume by the specimen per unit longitudinal plastic strain at the neck to sustain the fracture process. In the post-necking regime of tensile deformation with progressive development of the neck, the absorption of energy tends to get increasingly confined to the near-neck section, and therefore Gf and more so ¥f reflect the resistance of this region to microvoid growth. Hence, for an initially homogeneous ductile specimen, the RBR parameters estimate the toughness in a severely work-hardened condition and for a state of stress which is a combination of uniaxial tensile and hydrostatic stresses. For a specimen with gradient in toughness along its length, for example a transverse-weld specimen the neck is expected to initiate at the section least resistant to microvoid growth. For such a specimen, therefore the RBR method automatically determines the toughness of the weakest section, without a prior knowledge as to its location or the need for placing a notch or crack in the section. The advantage of the RBR method has been successfully exploited to characterize the effect of aging of three different dissimilar metal weld (DMW) joints viz. (i) an Alloy 800/2.25Cr-1Mo steel joint (at 300 K), (ii) an Alloy 800/9Cr-1Mo steel joint (at 300 K) and (iii) a type 316LN stainless steel/Alloy 800 joint (at 773 K), including determination of the optimum post-weld heat treatment (PWHT) temperature determined from the RBR toughness parameters is identical to that determined by the conventional method of correlating the microstructure with conventional tensile properties. For the Alloy 800/9Cr-1Mo steel DMW joint, the RBR toughness parameters led to unambiguous identification of the optimum PWHT temperature while the conventional structure-property method failed to do so. The efficacy and sensitivity of the two new ductile fracture toughness parameters have also been demonstrated.
SIMPLE STOCHASTIC MODELS OF FRACTURE WITH HEALING: M. Ausloos, R. D'Hulst, N. Vandewalle, SUPRAS, Institut de Physique B5, Université de Liège, B-4000 Liège, Belgium
There are several ways of approaching the problems of fracture. One of them is through algorithmic modelisation. We follow the ideas of a stochastic process, i.e. the most extreme situation, in order to find whether general behaviors of fracture phenomena can be quantified and if so through which ingredients. We use the numerical power of coarse grain cases allowing for easy access to asymptotic time regimes. Atoms on sites in a two dimensional plane are supposed to be ejected inside or outside an initial boundary. Several "percolation/fracture-like" path were found as a function of size. The concentration of the various crack thresholds, the distribution of clusters, the fractal dimension of the cracks were obtained. Power law features were indicative of essential processes. It will be shown that the rules give sometimes rise to "healing processes".
ATOMISTIC STUDIES OF CRACK PROPAGATION: Diana Farkas, Vijay Shastri, Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219
We will present the results of atomistic studies of fracture in ordered intermetallic alloys using the embedded atom method. The propagations of cracks is studied through atomistic computer simulation with particular emphasis on the competition between crack propagation and dislocation emission processes at the crack tip. The boundary conditions for these simulations are obtained from continuum elasticity theory and the region close to the crack is allowed to relax in order to achieve the minimum energy configuration. The atomistic simulations enable the study of the local atomic configuration at the crack tip in a realistic crystal structure and its importance for crack propagation. The studies include the simulation of crack structure and propagation in the presence of dislocations, in an effort to contribute to the modeling of ductile fracture processes.
COMPARISION OF LOCALIZED NECKING CRITERIA USED IN FINITE ELEMENT ANALYSIS OF SHEET METAL FORMING OPERATIONS: Sriram Sadagopan, Robert H. Wagoner, Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210
Localized necking is one of the most common failure modes limiting formability in technological sheet metal forming operations. Prediction of localized necking for general three dimensional components using finite element simulations can be very useful in die/process design. Different failure criteria, based on macroscopic quantities, are used to predict localized necking. This presentation will compare the results from these different failure criteria for some standard geometries. The effect of applied boundary conditions on these results will also be discussed.
POSTER SESSION: Mechanisms of Fracture
MICROPLASTICITY AND DUCTILE FRACTURE IN A METASTABLE BETA TITANIUM ALLOY: Wally O. Soboyejo+, B. Rabeeh* and S. Rokhlin*, +Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus OH 43210-1179; *Department of Industrial, Welding and Systems Engineering, The Ohio State University, 190W. l9th Ave. Columbus OH 43210
Micromechanisms of tensile deformation and fracture in a metastable beta Ti-15V-3Cr-3Al-3Sn alloy are elucidated in this paper. Tensile deformation is shown to be associated with significant levels of microplasticity at stress levels above ~10% of the tensile yield strength. Microplasticity in the so-called elastic regime is shown to occur via shear localization and concomitant slip band formation; grain boundary sliding; subgrain formation; stress induced a phase precipitation; and atomic flow mechanisms that are not fully understood at present. Ductile fracture is also shown to initiate by decohesion around a precipitates produced largely via stress-induced precipitation. Catastrophic failure in the metastable beta Ti-15V-3Cr-3Al-3Sn alloy is shown to occur by the coalescence of microvoids produced via decohesion around a precipitates. Attempts are made to model the ductile fracture processes using classical ductile fracture theories. The implications of the microplasticity phenomena are also discussed within the context of elasticity and plasticity theories.
DAMAGE EVOLUTION IN HYPO- AND PSEUDO-EUTECTIC Al-Si ALLOYS: Tz. Kamenova, R. Doglione, J.L. Douziech, C. Berdin and Dominique François, École Centrale Paris, Laboratoire De Méchanique, Grande Voie des Vignes, F-92295 Châtenay-Malabry Cedex, France
The evolution of fracture processes in an hypoeutectic and in an eutectic Al-Si cast alloys has been studied by means of in situ tensile tests SEM observations. Chilled and cast alloys were investigated. It has been established that the damage initiates at low strains (of the order of 0.5%) by fracture of the largest Si particles, situated at the periphery of eutectic colonies. When the strain increases, finer and finer particles break within the colonies. In the hypereutectic alloys further straining induces a concentration of the damage along the fine interdentritic particles alignments. This leads to the formation of intensive slip bands in these regions followed by microcracks coalescence. The cracks thus created stop at the eutectic colonies, until final fracture by their propagation. The validity of the Weibull statistics to describe the number of cracked Si particles as a function of the applied load was proven. It was also observed that the volume increase of the microcracks was very small. These observations allowed to build a model of damage evolution based on micromechanics of inclusions at two different scales, that of eutectic colony and that of the whole specimen, yielding the fracture probability in the various zones.
EFFECTS OF INCLUSION DISTRIBUTION ON THE FRACTURE TOUGHNESS OF STRUCTURAL STEELS: Warren M. Garrison, Jr., Department of Materials Science and Engineering, Carnegie Mellon University, 3301 Wean Hall, Pittsburgh, PA 15213; Andrzej L. Wojcieszynski, Crucible Research Center, Campbells Run Road, Pittsburgh, PA 15205; Luena E. Iorio, Department of Materials Science and Engineering, Carnegie Mellon University, 3301 wean Hall, Pittsburgh, PA 15213
When fracture occurs by micro-void coalescence the fracture toughnesses of structural steels are controlled by both the inclusion distribution and the fine-scale microstructure. The characteristics of the inclusion distributions which influence toughness include volume fraction, spacing and void nucleation resistance. The effects of inclusion distributions on toughness are, however, not independent of the fine-scale microstructure and the extent to which varying characteristics of the inclusion distributions influences toughness can depend on the fine-scale microstructure. This talk will focus on three areas. First the effects of inclusion spacing and void nucleation resistance of inclusion particles will be discussed. Second, the degree to which such effects are influenced by fine-scale microstructure, in particular austenite grain size, will be considered. It has been found that the most effective way of minimizing the detrimental effect of inclusions on fracture toughness is to getter sulfide as titanium carbo-sulfide as particles of titanium carbo-sulfide are more resistant to void nucleation than particles of other sulfides such as MnS. Therefore, the third topic to be considered will be the effect of alloy composition on the formation of as titanium carbo-sulfide. This work was funded by the National Science Foundation, The Army Research Office, Teledyne Allvac and the Ben Franklin Program of Pennsylvania.
FRACTURE TOUGHNESS OF WC-Co CERAMIC-METAL COMPOSITES: James M. Densley, Carolyn E. Graves, John P. Hirth, Department of Materials and Mechanical Engineering, Washington State University, Pullman, WA 99164
The fracture toughness of a normal and nanoscale grain size WC-Co ceramic-metal composite with same compositions are compared. The fracture behavior is discussed as a mechanism of localized plastic deformation. Analysis of the cermets is done by both pure mode I and mixed-mode I/III fracture toughness methods.
EFFECT OF LOADING MODE ON FRACTURE PROPERTIES OF A VANADIUM ALLOY: H.-X (Huaxin) Li, R.J. Kurtz, R.H. Jones, Pacific Northwest National Laboratory, P. O. Box 999, Mail Stop IN P8-15, Richland, WA 99352
The effect of mode I and mixed-mode I/III loading on the fracture behavior of a vanadium alloy containing 4 wt% Cr and 4 wt% Ti (V4Cr4Ti) was investigated at room temperature. The V4Cr4Ti alloy was annealed at 1000°C for 1 hour in vacuum. Compact tension (CT) specimens were used to study mode I properties and modified compact tension (MCT) specimens were used for mixed-mode I/III. A MCT specimen is the same as a CT specimen except the principal axis of the crack plane is slanted at an angle of 25 and 45 degrees from the load line. When the crack angle is equal to zero, a MCT specimen becomes a CT specimen. With the MCT specimen, an applied load can be resolved to mode I load (Pi) and mode III load (Piii) at the crack tip. The mixities [Piii/Piii+Pi] used were 0, 0.32 and 0.5 for crack angles 0, 25 and 45 degrees, respectively. It was found that the introduction of Piii dramatically lowered fracture toughness of V4Cr4Ti alloy. The mechanism how mixed-mode I/III loading affects fracture behavior of the V4Cr4Ti alloy is discussed.
DYNAMICALLY GENERATED DISLOCATIONS SUB-STRUCTURE AHEAD OF A CRACK TIP: N. Zacharopoulos*, D.J. Srolovitz* and R. A. LeSar**, *Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109; **Center for Materials Science, Los Alamos National Laboratory, NM 87545
We investigate the propagation of a semi-infinite, mode III crack at constant KIII. At each time step, crack can grow and/or screw dislocations can be emitted from the crack tip. This model incorporates dislocation interactions with the crack, other dislocations, and all image dislocations. The emitted dislocations can significantly shield the crack. Dislocation-dislocation and dislocation-crack interactions are calculated using the fast multipole method applied within a stress-function framework. Dislocation-crack interactions are described using a conformal mapping procedure. Dislocation microstructures, generated from the crack tip, are shown over a wide range of loading rates. With increasing loading rate, a transition is observed from ductile-to-brittle behavior. However, even when the crack propagates in a brittle manner, significant dislocation emission occurs first. The dislocation microstructures observed are very complex and highly organized. As the load continues to increase, several distinct transitions in dislocation microstructure are observed. The effects of pre-existing dislocation network within the material are also examined. The dislocation network is strongly modified by the crack, decreases dislocation emission from the crack tip and, after evolution in the crack tip field, provides some crack tip blunting.
MECHANISMS OF DUCTILE FRACTURE IN PURE SILVER UNDER HIGH-TRIAXIAL STATES: Michael E. Kassner, Department of Mechanical Engineering and The Center for Advanced Materials Research, Oregon State University, Corvallis, OR 97331
Experimental and finite element method (FEM) analyses were used to study the mechanisms of ductile fracture of constrained, high purity, silver interlayers under high triaxial stress states. Interlayer bonds loaded in simple tension develop a principal stress state that is large and axisymmetric. Ductile, plastic-strain failure was observed in these bonds when the maximum mean stress to yield ratio () approached approximately four, in agreement with recent numerical analyses by other investigators, who postulated unstable growth of a cavity subjected to a far-field axisymmetric stress state at this ratio, without significant far-field plastic strain. Ambient temperature delayed-failure (creep) tests of constrained silver interlayers, at relatively low applied loads, also appear to be due to unstable cavity growth. The mechanism of ductile fracture was further studied by biaxially loading these interlayers through the application of various combinations of tension and torsion loads. Low macroscopic-strain ductile fractures are again observed, but the axisymmetric and non-axisymmetric failure-stress values and FEM analysis of the stress levels required for cavity instability do not directly support an unstable growth model, even when considerations for plastic incompatibilities across grain boundaries are considered. Other ductile fracture theories such as cavity nucleation and interlinkage warrant consideration.
THE EFFECTS OF STERILIZATION AND OXIDATION ON THE FRACTURE OF 'ARTIFICIAL CARTILAGE' (ULTRA-HIGH MOLECULAR WEIGHT POLYETHYLENE): Thomas J. Mackin and Jeff Windau, Department of Mechanical and Industrial Engineering, The University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801
Ultra-high molecular weight polyethylene (UHMWPE; 4x103 g/mole) is commonly used as artificial cartilage in orthopedic implants. Several processing methods are used to fabricate the stock material, followed by machining, and gamma-irradiation sterilization prior to final implantation. Over the 15 year anticipated lifetime, cyclic and tribological loading change the properties of the material. The need for improved implant lifetimes motivated a detailed investigation of the relationships between processing/sterilization and properties in UHMWPE. Gamma irradiation changes the mechanical properties by promoting enhanced crystallization, while lifetime aging results in the formation of carbon-oxygen groups that change the subsequent properties. Both effects improved the ductility of the materials and led to overall improvements in yield strength, tensile strengths elastic modulus. These results are in sharp contrast to previous studies where any increase in crystallinity decreased the ductility of the UHMWPE. A broad array of experimental techniques were utilized to verify the measured changes in microstructure and properties. We will report on these changes in mechanical properties coupled with a fractographic analysis of failed specimens to relate the mechanisms of ductile failure in UHMWPE to the microstructural changes brought about by production, fabrication, sterilization and aging of these implant materials.
A MIXED-MODE FRACTURE MECHANISM MAP: M. Manoharan, Division of Materials Engineering, School of Applied Science, Nanyang Technological University, Singapore-639798, Singapore
As fracture mechanics has developed as a discipline, many parameters have been developed to characterize the instability condition. However, a majority of this work has been confined to the investigation of mode I fracture. Thus, we have standardized methods for experimentally determining KIC, JIC and J-resistance curves for mode I crack propagation. However, cracks in real materials can be subjected not just to tensile stresses but to complex stress states so that the development of suitable parameters to characterize mixed-mode crack initiation and propagation is important in the evolution of suitable design criteria. Further, observations indicate that initially flat cracks in some tough materials tend to reorient themselves to oblique planes during growth. For these materials, crack propagation can be said to occur under combined mode conditions. A considerable amount of work on mixed mode I/III fracture toughness of materials is available. The superposition of mode III loading results in drastic reduction in fracture toughness in some materials whereas in other materials it has little effect or even results in an increase in the fracture toughness. Fracture mechanism maps delineating regions of susceptibility to tensile and shear loads have been proposed. In this paper, data on a wider range of materials, including steels, aluminum alloys, metal matrix composites, ceramics and polymers will be used to extend and reinforce the fracture mechanism map concept.
EFFECTS OF STRESS STATE ON DEFORMATION AND FRACTURE OF STRUCTURAL MATERIALS: John J. Lewandowski, Dept. of Materials Science and Eng., Case Western Reserve University, Cleveland, OH 44106
The deformation and fracture of structural materials is significantly affected by changes in the microstructure and imposed stress state. Such changes in stress state may affect the micro-mechanisms of failure whereby a material which normally fails in a ductile manner may undergo a ductile-to brittle transition. In other cases, the imposition of a more severe stress state may accelerate the stages of ductile fracture to such an extent that very low ductility is obtained. The imposed stress state may be easily changed via testing notched specimens or via testing with confining pressure in monolithic materials. The presentation will review previous and ongoing work investigating the effects of stress state on the fracture of a variety of metallic materials, including more recent work on metallic composites.
THE ROLE OF DISLOCATION NUCLEATION IN THE BRITTLE-TO DUCTILE TRANSITION IN SILICON SINGLE CRYSTALS: K. Jimmy Hsia, Department of Theoretical and Applied Mechanics, University of Illinois, 216 Talbot Laboratory, 104 South Wright Street, Urbana-Champaign, IL 61801
EFFECT OF HYDROGEN ON THE MECHANICAL PROPERTIES OF LOW CARBON STEEL: B. Sarkar, D. Mukerjee, R&D Centre for Iron and Steel, Steel Authority of India Limited, Ranchi-834002, India
The effect of hydrogen on the mechanical properties of a low carbon steel has been investigated. In-situ tensile and hardness tests have been carried out while charging hydrogen. It has been observed that there is a substantial reduction in ductility as a result of hydrogen charging while there is no change in hardness. The strain hardening exponent (n) value decreased from 0.26 to 0.22 ( a decrease of about 15%) whereas, the total elongation decreased from a value of 44.2% to 33.8% (a fall of about 24%) as a result of hydrogen charging. This is suggestive of the fact that hydrogen charging affects all the stages of ductile fracture. Hydrogen charging has been found to increase the number of dimple nucleating sites. Consequently there was a decrease in the average dimple size. It is believed that the effect of hydrogen on the reduction of ductility is more prominent in the post necking region. It has been concluded that hydrogen charging enhances the number of dimple nucleating sites which promotes the process of ductile fracture.
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