MICROSCOPIC ANALYSIS OF POLYCRYSTALLINE MATERIAL AT HIGH TEMPERATURE

ACTA METALLURGICA SINICA (ENGLISH LETTERS)Vol. 17 No. 4 pp 350 354 August 2004MICROSCOPIC ANALYSIS OF POLYCRYSTALLINE MATERIAL ATHIGH TEMPERATURES. Imatani, R. Kawakami and Y. KawanoKyoto University, Sakyo-Ku, Kyoto 606 -8501, JapanManuscript received 31 May 2004The microscopic analyses of polycrystalline material at high temperature were carriedout. The crystal plasticity model proposed by Asaro and Needleman was applied to apolycrystal model in the finite element simulation and the crystal slip system was ran-domly provided for each crystal. The grain boundary sliding, which was characteristicat high temperature, was also taken into account. It was shown that the inhomo-geneous deformation develops over the polycrystal and that the strain concentrationappears around the triple point of crystal grain boundary.KEY WORDScrystal plasticity, finite element method, grain boundary, inho-mogeneity1. IntroductionPolycrystalline materials are composed of great amount of crystal grains, each of whichis jointed with neighboring grains via grain boundary. Since the slip systems are distributedin each grain at random, the materials are essentially inhomogeneous. Furthermore thegrain boundary has a significant variation in mechanical property at high temperature.Such a mechanical and geometrical inhomogeneity is supposed to infuence not only thedeformation behavior but also the damage evolution. And so it is necessary to evaluatethe mechanical behavior of the materials from the viewpoint of microscopic level of crystalgrain size.The theory of crystal plasticity comes back from the critical discussions by TaylorI!],and several single crystal models have been developed. Among them a concise theory byAsaro and Needleman2] is highly appreciated since the model describes the explicit depen-dence of the slip system on the macroscopic strain accompanying the latent hardening. Incontrast the grain boundary sliding is somewhat phenomenological because of its dissipatedsystem. Tvergaad and van der Giessen3 deal with the grain boundary sliding and theyare sucessful in simulating a polycrystal model involving the void growth.The microscopic inhomogeneity of polycrystalline material from both experimental andnumerical points of view is discussed in this paper. Microscopic strain distribution wasmeasured on a heat affected zone (HAZ) of Mod. 9Cr- 1Mo steel4 at high temperature.The strain concentration is observed around the triple point of grain boundary, and thedevelopment of surface roughness is also discussed during a tensile loading. A numericalsimulation model based on the crystal plasticity combining the grain boundary sliding[5]is presented in the second part. The variation of strain concentration with regards to thecombination of slip system in crystal grain and the geometrical condition of grain boundarywere discussed.中国煤化工MYHCNMHG3512. ExperimentalA Mod.9Cr- 1Mo weld joint material is used for the experiment. As shown in Fig.1,the specimen is cut out from the weld joint material. The central part of the specimen isshaped slightly thinner in order to enhance the deformation and it covers the heat affectzone (HAZ). The experiment is carried out at high temperature of 650°C. The crystalproperties and micro-hardness at room temperature are shown in Fig.2 where we foundthat coarse grains are developed near the weld metal, and then the grain size significantlydecreases and fine grains of about 5 through 6μm are generated near the base material. Thehardness is almost proportional to the grain size within the HAZ range for this weld jointmaterial, while most other materials show the opposite tendency due to the well-knownHall-Petch effect. A tensile loading is imposed on the specimen.The microscopic strain is identifed from the photo images taken by a scanning electronmicroscope (SEM) and an atomic force microscope (AFM). The measurement of strainstarts from the identification of the specific crystal grain before and after the deformation.Characteristic points such as triple points are tracked through the deformation. Assuminga crystal as a polygon, whose corners and specific points in the grain are regarded asnodes in finite element technique, three dimensional variation of the nodes implies thedisplacement. After the deformation, the strain is converted from the simple calculationthrough the strain-displacement matrix. Then we can specify the distribution of straincomponents on the surface at microscopic level.Fig.3 stands for the surface state of the specimen, in which the upper figures show theAFM images while the lower figures mean the principal strain distribution together withthe principal direction at the same location. An example is taken from the surface state ina fine grain region. The scale of the images in z-direction is magnified, compared with theother directions, in order to emphasize the surface roughness. The strain in the fine regionis in general larger than that in the coarse region corresponding to the hardness distributionshown in Fig.2. The scatter of the variation in strain is observed and forms a sort of bandor wavy distribution over the domain. Larger strain is localized and concentrated aroundthe particular region marked with the circles. Such a tendency suggests that mechanicaland geometrical inhomogeneity has a predominant infuence on the strain concentration inthe microscopic level.L。Vickers hardness2tL ●grain size ]280密1 Weld joinyt 260240.HAZt 222018Distance from weld bound x,mmFig.1 Specimen from weld joint.中国煤化rbardneYHCNMHG352.The surface roughness is detected for the specimen by use of the AFM data. Thespectrum intensity is obtained through the fast Fourier transformation (FFT) analysis.Before the tensile loading, the surface of the specimen is almost flat, and no difference isobtained between the fine grain region and the coarse grain region. The surface roughnessdevelops during the deformation process and it is proportional to the imposed strain. Therelation of spectrum intensity is plotted in Fig.4 where we find a significant difference. Thespace length at the high intensity shows two or three times of the average grain size. Thismeans that a wavy form appears with the period of several grains. This confirms the strain” pattern observed in Fig.3.fine graincoarse grain |0.01 tSpnt另0.001Lcedhg dirocicnotiropal etmoh, %0.00010)b)Wave length, μmFig.3 Strain analysis of local region: (a) AFMFig.4 Surface roughness.image; (b) strain distribution.3. Numerical SimulationA crystal plasticity model proposed by Asaro and et al.!3 and a nonlinear grain bound-ary model originally proposed by Beerl5l are applied to the finite element method. Whena crystal has a shear strain ya) with a slip direction g(a) and a slip plane m(a), the rateof macroscopic strain e is expressed bye= 2 i{a)sym(a(a) 8 mla)(1)while the resolved shear stress r(a) acting on the slip system (a) is given byτ(a) = g(a) . (oTm()(2)The development of (plastic) shear strain is related to the resolved shear stress withthe relationship|(a)(/m)-1(3)(=)in which g(a) stands for the hardening variable. The latent hardening can be describedby introducing the coefficient dependent on other slips in the evolution of g(a). The grainboundary sliding is modeled by a contact/slip element whose thickness is zero. The relativedisplacement at the upper/ lower sides on the boun中国煤化工fness, and anYHCNMHG353elastic-viscous sliding is availablebased on the Mohr-Coulomb yieldcondition for the contact force. Thefinite element equation is obtainedthrough the virtual work principle,and the three dimensional code isdeveloped.Fig.5 demonstrates the defor-mation of a three dimensional block(blsubject to a simple tension. Herein this simulation the grain bound-ary sliding is not taken into accountbut the effect of statistical properties in crystal slip is examined.1x1x1 in Fig.5a means that each el-ement is assigned to a crystal grainsuch that the slip system is ran-domly installed for every element,(c)2x2x2 in Fig.5b implies that each 8element block is assigned to a crys-tal grain, and 4x4x4 in Fig.5c indi-cates that each 64 element block isassigned to a crystal grain. Even inthe tension, the variation of strainis evolved because of the inhomo-geneity of slip system, and the vari-ation is controlled due to the ac-Strain, %celerating/decelerating effects withneighboring crystal. When a sim-ilar slip system is set in neighbor-ing crystals, the deformation is en-Fig.5 Deformed shape and strain distribution ofhanced and forms a wavy pattern infinite element mesh under monotonic load-strain distribution. Such an effecting: (a) 1x1x1; (b) 2x2x2; (c) 4x4x4.confirms the experimental observa-tion in Figs. 3 and 4.The effect of crystal grain sliding is shown in Fig.6 where a simplified block with 4crystal grains is stretched. Here the effect of stiffiness of grain boundary is checked. Thestrain level in crystals is relaxed due to the grain boundary sliding. This loose contact isable to predict a gap between the crystals, and it lead to the nucleation of small cracks alongthe grain boundary. The discontinuity of displacement over the crystals also produces thesurface roughness. When harder stiffness is installed in the contact element, the variation ofstrain is enhanced while the strain concentration is observed around the triple point cornerof crystal grains. The strain concentration is observed regardless of the slip systems in thecrystal grain, and so the effect of grain boundary is supposed to be predominant at hightemperature regime although it seems dificult to中国煤化工experimentalTHCNMHG354例51suin,%Fig.6 Bird'seye-view of polycrystal aggregate: (a) small stifness in contact;(b) larger sifness in contact.point of view. Not only the stifness but also the geometrical condition affect the strainconcentration at the microscopic level, and so further development of crystal plasticityanalysis is required for understanding the mechanical behavior of polycrystal aggregatesfrom microscopic viewpoint.4. ConclusionsThe microscopic analysis is carried out for a polycrystalline material at high tempera-ture. The surface state is detected by SEM/AFM and the microscopic strain is identifiedat crystal grain level. The strain concentration is observed around the corner of crystaland it forms a wavy pattern in strain distribution. The surface roughness is proportionalto the crystal grain size, and so polycrystals with larger grain size may have a significantinhomogeneity. The second part deals with numerical evaluation for such a behavior. Acrystal plasticity model is introduced into FEM code with grain boundary sliding. Thecompeting effect in slip system affects the inhomogeneity in strain distribution while thegrain boundary sliding is dominant on a localized strain around grain boundary. The nu-merical results suggest that the geometrical conditions such as slip system configurationand grain boundary, rather than the mechanical properties in each crystal grain, have asignificant infuence on the microscopic inhomogeneity. This may be a key point to evaluatethe strength of polycrystalline materials at high temperature. Further development with anumber of crystal grains will enable us to simulate more realistic behavior of inhomogeneousmaterials.Acknowledgements- -This work was supported by the Ministry of Education, Japan, as 21st Century COEprogram on Sustainable Energy System (E-3) and as grant-in-aid for scientific re-search (No.15360053). The test material was provided by Ishikawajima- Harima HeavyIndustry LTD, which is also acknowledged.REFERENCES1 G.I. Taylor, J. Inst. Metals 62 (1938) 307.2 R.J. Asaro, Adu. Appl. Mech. 23 (1983) 1.3 E. van der Giessen and V. Tvergaard, Int. J. Fracture 48 (1991) 153.4 M. Tabuchi, T. Watanabe, K. Kubo, M. Matsui, J. Kinugawa and F. Abe, J. Soc. Mat. Sci, Japan50 (2001) 116.5 G. Beer, Int. J. Num. Methods Eng. 21 (1985) 585.中国煤化工MHCNMHG