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Session Chairpersons: Professor James A. Joyce, Department of Mechanical Engineering, U.S. Naval Academy, 590 Holloway Road, Annapolis, MD 21402; Professor Ronald W. Armstrong, Department of Mechanical Engineering, University of Maryland, College Park, MD 20742
DETERMINING THE J-CRACK GROWTH RESISTANCE BEHAVIOUR OF A DUCTILE MATERIAL: Edward Smith, Manchester Materials Science Center, Manchester University and UMIST, Grosnover Street, Manchester M1 7HS, UK
Ductile fracture has been the major theme of Frank McClintock's research career. This paper is concerned with the determination of a ductile material's crack growth resistance behaviour when it is expressed in terms of the deformation J-integral JD. Attention is focussed on the determination of the crack growth resistance curve from load, load-point displacement and crack extension measurements using single loaboratory test specimen. A commonly used procedure is based on the separation of JD into an elastic component JE and a plastic component JDP, and the ability to express JDP for a non-growing crack in terms of the plastic energy integrals via eta factors that are independent of the applied loadings. The paper highlights the conditions which must be satisfied for JDP to be expressed in this way, and the limitations of some currently used practices based on this JDP formulation are indicated. Against this background, the author reviews his "two extremes" procedure, whereby the appropriate eta factors are obtained by ensuring that JDP assumes the correct form at the two extreme levels of deformation: small-scale yielding and extensive deformation at limit load conditions. Determination of the eta factors requires only a knowledge of the stress intensity factor and the limit load solutions, and not the material flow properties. The "two extremes" procedure is validated by comparing its predictions with well documented results for specific geometrical configurations. However, the procedure can be applied to any geometrical configuration, and the paper provides some examples.
2:25 pm INVITED
PREDICTING THE DUCTILE-TO-BRITTLE TRANSITION IN NUCLEAR PRESSURE VESSEL STEELS FROM CHARPY SURVEILLANCE SPECIMENS: James A. Joyce, Department of Mechanical Engineering, U.S. Naval Academy, 590 Holloway Road, Annapolis, MD 21402
One important application of elastic-plastic fracture mechanics has been to assure the structural integrity of nuclear reactor pressure vessels. Present toughness requirements are based on the postulation of a large defect size, the use of dynamic test data to give lower bound toughness values, and the use of safety factors on the allowable stresses. As vessels have aged the material toughness has degraded and the ductile-to-brittle transition has shifted toward the vessel operating temperature. Extrapolating this process means that many existing vessels will not meet the present toughness requirements well before the end of their design lives. The need to superimpose multiple safety factors, as is presently done has thus been questioned, and much recent research has been directed toward lessening the toughness requirements while maintaining a high level of structural integrity. The situation remains difficult, however, at least in part because only Charpy specimens are available as surveillance specimens for many commercial reactor vessels, and these specimens are too small to obtain any type of "valid" fracture toughness information using standard ASTM methods. Presently a lower bound KIR toughness curve is shifted relative to reference temperature RTNDT and used to define the ductile-to brittle transition. The RTNDT is thus a very critical value, and difficulties have arisen because of the wide variability that can result in its estimation. Recent work by ASTM Committee E08 has proposed a method to obtain a new reference temperature and a method to define using a probabilistic approach, a median ductile-to-brittle transition curve from a set of six properly tested small samples which would in many cases be precracked Charpy specimens. This method seems to be very robust, predicting a reference temperature with small variability. From the results of these specimens a "master curve" can be developed defining the median ductile-to-brittle transition curve as well as statistical confidence bounds. This curve is plant specific and could be used to assure that the pressure vessel had adequate toughness for continued operation. This paper presents a large data set on two pressure vessel steels, A515 and A533B, obtained to investigate the newly proposed ASTM test method. Data is available on a large number of precracked Charpy specimens, as well as data on standard IT C(T) and SE (B) specimens. Additional data is also available on large specimens, specimens with shallow cracks (a/W = 0.1), and surface cracked geometries tested in tension, bending, and combined tension and bending. Most specimens demonstrated cleavage failure - in some instances after significant amounts of ductile crack extension. Since the data sets are not presently complete, how well the new procedure fares cannot be determined. The applicability of constraint quantification and correction techniques that are presently being developed separately by this project will be included in the final analysis. The comparison of the large and small specimens, the surface cracked and through cracked specimens, and the predominantly bend and tensile loadings should allow a clear determination of the value of the new proposed ASTM "master curve" approach.
2:50 pm INVITED
A COMMON FORMAT APPROACH FOR APPLYING DUCTILE FRACTURE MECHANICS: John D. Landes+ and J. R. B. Cruz*, +Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996; IPEN, *São Paulo, Brazil (on leave to the University of Tennessee)
Applications of ductile fracture mechanics methods to prediction of structural behavior can be done using numerical or analytical methods. Numerical methods can be more accurate but are often beyond the capability of ordinary engineering organizations. Also the result may have relevance only to the specific structure being analyzed. Analytical methods have often used a failure diagram approach in which the failure load of a structure can be estimated. A ductile fracture methodology proposed by Landes, et. al. took the load versus displacement for a laboratory specimen and through a series of analytical steps predicted the load versus displacement behavior for a structural component. The prediction could be made for any geometry where the information on limit load, and the calibration of fracture parameters was available. This prediction gave a more complete information in that both the maximum load could be determined as well as the stability of the structure after maximum load. The prediction of the loading behavior during ductile fracture depends on the deformation behavior of the structure and the cracking behavior, usually the former is the more important. The ductile fracture methodology uses a principal of load separation proposed by Ernst in which the loading of a cracked body can be specified by separate but multiplicative functions, one of geometry, that is cracking behavior, and one of deformation. The load versus displacement for the specimen is separated into two functional behaviors, a transfer is made for these functions from the specimen geometry to the structural component geometry and two functions are combined to predict load versus displacement of the structural component. The entire procedure could be completed with a hand calculator. Since the first proposal of this ductile fracture methodology, additional work has been done on the determination of the deformation behavior for the structural component. Donoso, et. al. showed that deformation behavior of any structural component, including test specimens geometries, can be derived from the basic stress-strain behavior of the material. With this the deformation behavior of the component can be determined from that of the specimen using common functional expressions with similar constants, ones that be determined from the stress-strain behavior and transferred to any common geometry with a set calibration factors that pertain to that geometry. This approach was labeled, the "common format" approach. Using this "common format" approach the ductile fracture methodology was revisited to see if the procedure could be simplified using the calibration factors to transfer from one geometry to another, namely from test specimen to structural component. This paper describes the result of that study. What was found was that the 'common format' calibration factors can be used to transfer the load factors based on material stress. However, a difficulty rose with the transfer of strain factors. The relation of the structural displacement to strain behavior is sensitive to the type of displacement being measured, that is placement of the gage, and gage length. In order to complete an easy transfer of specimen deformation characteristics to the structural component, strain calibration factors need to be determined. With the development of these, the procedure in the ductile fracture methodology can be made easier and application of ductile fracture mechanics greatly facilitated.
3:15 pm BREAK
A NEW MODEL TO CALCULATE THE CRACK EXTENSION: Inhoy Gu, Department of Mechanical Engineering, Chung-Ang University, Seoul 156-756, South Korea
A fracture analysis method is proposed on the criterion that the resistance to crack extension can be characterized in the critical CTOA, an instantaneous ratio of CTOD increment to stepwise crack extension. The CTOD of finite element analysis is written in a function of crack length and applied stress for the load range up to near the limit load. The normalized CTOD function for the compact specimen is independent of crack length ratio with some conditions, under which the function can be used in the crack-extension analysis. After crack initiation, the CTOD increments due to a load increment and a crack increment are successively calculated to determine another crack extension, with their integrations during the stable crack growth. The calculations are made to fit to the tests of effective crack lengths by appropriate fracture constants. The cleavage fracture mode is characterized in the crack growth without crack opening. The total CTOD for the cleavage fracture of Al 7075-T651 increases a little as the specimen size increases greatly. Thus the cleavage fracture may occur with a rising load in big specimens and with a falling load in small specimens. The critical CTOA for the ductile fracture of Al 2024-T351 decreases with an increasing specimen size. The size-corrected fracture constants are applied to calculate the failure loads on other compact and center-cracked specimens, in good agreement with the available test loads. The fracture-predicting capability of the proposed method seems promising from cleavage to ductile fracture modes regardless of crack extension, probably, except the limit-load fracture. Therefore, the fracture constants may account for specimen property as well as material property, and they are transferred between specimens.
3:50 pm INVITED
DUCTILE FRACTURE OF HIGH TOUGHNESS STEELS UNDER MULTIAXIAL TENSION: D. M. Goto, J.P. Bandstra, D. A. Koss, Department of Materials Science and Engineering, Penn State University, University Park, PA 16802; Concurrent Technologies Corporation, 1450 Scalp Avenue, Johnstown, PA 15904
The influence of stress state on ductile fracture is examined on the basis of both experiments and computational modeling. Using HY-100 steel as a model material, we examine the failure of notched tensile specimens in terms of the void initiation, growth, and linking process. Particular attention is given to the issue of void linking as a result of either global coalescence, which occurs at high stress triaxilities, or a localized void-sheet process, as is observed at high stress triaxilities. The void-sheet mode of linking is modeled on the basis of microstructural conditions present in the HY-100 steel with the result that the predicted influence of stress state agrees well with experimental observations. The transition to global void coalescence, and a much greater sensitivity of failure stress to stress state, is also addressed. This research was supported by the Office of Naval Research, the Naval Surface Warfare Center, and Concurrent Technologies Corporation.
4:15 pm INVITED
MIXED-MODE NON-LINEAR FRACTURE ALONG INTERFACES: John L. Bassani, N.J.-J. Fang, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
Recently, problems in interfacial fracture have led to a general interest in planar crack growth under mixed-mode loading. Of particular interest is the relationship between the applied stress intensity/mode-mix and the corresponding quantities near the crack tip. We have developed mixed-mode solutions of the HRR type and of the Hui-Riedel type for stationary and propagating interface cracks. In contrast, asymptotic and small-scale yielding solutions for the crack growth in a time-independent elastic-plastic material predict that the mode mix (tension versus shear) in the vicinity of the crack tip can only take on discrete values rather than varying continuously with the mode mix of the remotely applied elastic fields. In the case of a stationary interface crack or a growing creep crack in either homogeneous materials or along interfaces we have found crack-tip solutions which admit a continuous variation of mode mix within certain limits. Slip line solutions for stationary interface cracks have also been developed. These asymptotic solutions are in good agreement with small-scale-yielding finite element calculations that include the transient growth period.
RECENT ADVANCES IN THE APPLICATION OF THE GURSON MODEL TO THE EVALUATION OF DUCTILE FRACTURE TOUGHNESS: Winfried Schmitt, D. -Z. Sun, J. G. Blauel, Fraunhofer Institut Werkstoffmechanik, Fraunhofer IWM Wöhlerstraße 11, D-79108 Freiburg, Germany
For many metallic materials the Gurson model modified by Needleman and Tvergaard describes the ductile rupture process characterized by nucleation, growth and coalescence of voids. Since these local processes are similar in smooth specimens and in cracked specimens, a material dependent critical volume fraction of voids, fc, may be determined from numerical analyses of tensile tests. However, because of the strong gradient in the stress-strain field at the crack tip an additional length parameter, lc, is required to model the coalescence process in cracked specimens. Since the effects of triaxiality are adequately taken into account in the model, fc and lc may be transferred to specimens with different shapes and sizes. Hence, it is possible to evaluate ductile fracture resistance curves for different geometries and loading conditions with the same set of micromechanical parameters. The authors have applied this local approach to ductile fracture for a series of ferritic and austenitic steels including weld materials even after neutron embrittlement. Besides notched and smooth tensile specimens of standard sizes also miniature specimens with diameter down to 2 mm have been used for the determination of fc. Dynamic effects have been taken into account based on dynamic tensile tests and visco-plastic formulation to model the strain-rate sensitivity of the stress-strain curves. The characteristic length is usually determined for small SENB-specimens. As examples, instrumented impact tests with SENB and Charpy specimens have been simulated using three-dimensional models.
SUPERIMPOSED EFFECTS OF DSA AND NEUTRON-IRRADIATION ON MECHANICAL AND FRACTURE BEHAVIOR OF FERRITIC STEELS IN THE UPPER SHELF REGION: Rao K. Mahidhara1 and K. Linga Murty2, 1Tessera Inc., 3099 Orchard Drive, San Jose, CA 95134; 2North Carolina State University, P. O. Box 7909, Raleigh, NC 27695
It is now well established that radiation embrittlement of ferritic steels such as used for pressure boundary applications is sensitive not only to the alloying elements (Cu, Ni, P etc.) and interstitial impurities (IIAs) such as C and N, but also radiation flux and irradiation temperature. The increased strength and decreased ductility in the DSA region leads to reduced energy to fracture and this region usually lies in the upper shelf regime. This is also clearly evident in the elastic-plastic fracture toughness (JIC). While dips in the fracture energy are noted in steels, pure (Armco) showed peaks in this region apparently due to the increased rates of work-hardening. Exposure to neutron irradiation suppressed the effects of DSA leading to apparent increased energy values at temperatures where dips are noted in the unirradiated materials. Such tests on pure iron are in progress and results to-date will be reported here. Radiation effects on Hall-Petch relation are investigated in pure iron, and radiation exposure resulted in increased friction hardening and decreased source hardening which lead to interesting effects of thermal neutrons on radiation hardening of these materials.
USE OF X-RAY TOMOGRAPHIC MICROSCOPY TO STUDY DUCTILE FRACTURE: Wayne E. King, G.H. Campbell, D.L. Haupt, J.H. Kinney, R.A. Riddle, W.L. Wien, Chemistry and Materials Science Directorate, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-9900
X-Ray tomographic microscopy (XTM) is a promising technique to investigate ductile fracture because voids formed under conditions of high triaxiality can be directly observed nondestructively. In this experiment, ultra high vacuum diffusion bonding has been used to make model specimens in the Al/sapphire system. Samples were prepared in the 4-point bend geometry with notch. XTM images acquired after several loadings of the sample revealed the morphology of the growing voids. The primary finds are that (i) damage ahead of the notch initiates by interface debonding at a location coinciding with maxima in triaxiality and tensile traction at the interface, (ii) debonding occurs at the most early stages in the observation of plasticity, (iii) the debond expands for a limited distance, likely arresting due to crack tip blunting, (iv) this lenticular debond then becomes spherical with further strain, and (v) intergrowth of the spherical voids leads to the typical ductile rupture fracture surfaces observed in the system. This work performed under the auspices of U. S. Department of Energy and the Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
MICROPLASTICITY AND DUCTILE FRACTURE IN METALS: Wally O. Soboyejo, B. Rabeeh, J. Dipasquale, R. Pryor, Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus OH 43210-1179
Recent evidence of microplasticity in ductile metals is presented for a range of ductile metals with cubic and hexagonal closed packed structures deformed to failure under monotonic loading. Microplasticity is shown to occur at very low stress levels (~5 - 10%) of the bulk stress. Microscopic of microplasticity evidence is shown to include: slip band localization via shear localization; grain boundary sliding; subgrain formation; deformation-induced precipitation; and localized flow mechanisms. Ductile fracture is shown to initiate by coalescence of voids that are nucleated around stress-induced precipitates. Deformation in the so-called elastic regime is shown to be associated with the spread of localized plasticity phenomena across the gauge. Linear plasticity concepts are used to explain the initial deformation characteristics. The implications of microplasticity are also assessed for fatigue damage initiation and ductile fracture initiation.
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