Assessment of Thermo-Mechanical Fatigue Behaviors of Cast Al-Si Alloys by Experiments and Multi-Step Numerical Simulation* 1

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1 Materials Transactions, Vol. 46, No. 1 (25) pp. 111 to 117 #25 Japan Foundary Engineering Society Assessent of Thero-Mechanical Fatigue Behaviors of Cast Al-Si Alloys by Experients and Multi-Step Nuerical Siulation* 1 Hiroyuki Toda, Jun Katano* 2, Toshiro Kobayashi, Toshikazu Akahori and Mitsuo Niinoi Departent of Production Systes Engineering, Toyohashi University of Technology, Toyohashi , Japan Out-of-phase type thero-echanical fatigue tests have been perfored for Al-Si cast alloys with the teperature range of K and the applied echanical strain range of.5 1.5%. Thero-echanical fatigue lives and stress-strain hysteresis loops are investigated by the experients. In general, the thero-echanical fatigue is affected by various factors such as theral expansion/contraction, elasto-plastic/ creep deforation, softening by overaging, dynaic recovery, daaging and cracking. Multi-step finite eleent siulation techniques have provided an effective way of assessing the local daaging behavior of silicon particles, along with extracting the contribution fro creep. Although the size and shape of the silicon particles in the aterial with a higher solidification rate are siilar to those of a slowly cooled aterial, it exhibits superior thero-echanical fatigue property together with a saller secondary dendrite ar spacing (SDAS, hereinafter). Since the difference in the stress-strain hysteresis loops between the two aterials has vanished when the softening by overaging is alost finished, the observed difference in the thero-echanical properties is attributed to age-hardenability rather than the SDAS. The effects of daaging at the silicon particles to this difference are also suggested. In fact, daaged silicon particles have been observed extensively fro an early stage of the thero-echanical loading, then foring fatigue cracks by the linkage of the daages. It has been clarified by the siulation that interfacial debonding is likely to occur rather than particle cracking in the aterials used. The siulation provides valuable insights into the understanding of the spatial distribution of daage in the eutectic region. The siulation has also enabled to assess the contribution of the creep deforation, indicating that ediu to high cycle fatigues are significantly affected by it. (Received July 12, 24; Accepted October 21, 24) Keywords: aluiniu-silicon alloy, thero-echanical fatigue, daage, ulti-step siulation, creep, interfacial debondong, particle cracking 1. Introduction * 1 This Paper was partly presented at the Spring Meeting of the Japan Foundry Engineering Society, held in Tokyo on May 31, 23. * 2 Graduate Student, Toyohashi University of Technology Structural coponents in cobustion engines typically experience coplicated stress states under non-isotheral condition fields such as those induced by theral transients during start-up and stop of the transportation equipents. In order to assess the durability of various coponents, one ust characterize the fatigue behavior of the aterials used under theral and echanical loading conditions. Although experiental approaches are coplicated, they provide a reasonable approxiation of the cobined theral and echanical loads that will be experienced by the aterials in service. Also, the understanding of deforation, daage initiation and growth would be ore iportant aspects for aterials scientists conducting basic research. However, due to the loss of fractographic inforation by high teperature exposure and rubbing between fracture surfaces, these are hardly approached by the conventional post-failure analyses such as fracture surface observation. In such cases, it would appear that a cobination with echanical analyses such as phenoenological constitutive odeling and finite eleent odeling provides a possibility to assess fundaental echaniss. By the way, Al-Si cast alloys are widely used for autootive cobustion engines because they exhibit superior theral resistance due to the existence of rigid silicon particles. In ters of weight saving of autoobiles, the optiu design of these cast aluinu alloys ay be clearly valuable. To this end, the understanding of basic deforation and daage behaviors is indispensable as well as acroscopic investigation of thero-echanical fatigue properties. The hypo-eutectic Al-Si alloys, which are extensively used for the purpose, have a unique dual phase structure coprising an isolated -aluinu phase which often exhibits dendritic orphology and a three-diensionally networking Al-Si eutectic phase. Iportant icrostructural factors which deterine the thero-echanical fatigue properties would be precipitation and solution strengthening conditions of the aluinu atrix, size and shape of the silicon particles and a spatial distribution pattern of the Al-Si eutectic phase. Both inhoogeneous strain distribution induced by the dual phase structure and icroscopic daage behavior of the silicon particles should be considered to fully understand the resultant acroscopic thero-echanical fatigue resistance. Nevertheless, only a liited nuber of efforts are available in the current literature in which the authors are devoted to obtaining the effects of various factors on the acroscopic thero-echanical fatigue resistance; such as SDAS, 1,2) porosity, 2,3) cheical coposition, 2) heat treatent 2,3) and applied thero-echanical conditions. 5) It has been clarified in ters of theral stress hysteresis and fatigue lives that the thero-echanical fatigue resistance is iproved with the decrease in porosity 2,4) and silicon odification. 2) The effects of SDAS are not as great in certain conditions, but do exert significant influences in soe cases. 1,2) It has been deonstrated that phenoenological constitutive odeling was applicable to siulate the theroechanical responses of the cast aluinu alloys initially with tie-independent 6) and later with tie-dependent assuptions. 1) Even tie-dependent aterial characteristics such as aging and recovery during high teperature exposure were considered in soe odels. 1) The phenoenological odels provide only the predictions of acroscopic aterial responses such as theral stress hysteresis. In order to fully

2 112 H. Toda, J. Katano, T. Kobayashi, T. Akahori and M. Niinoi exploit the thero-echanical resistance of the Al-Si alloys, ore icroscopic aspects would be required by which local daage initiation and evolution are assessed without using internal variables such as daage paraeters. It is an objective of this study to investigate the theroechanical responses of the cast Al-Si alloys both by experiental and odeling approaches with special attention to the daage at the silicon particles. For the sake of drastic reduction in odel size, the finite eleent analysis was perfored in two steps; a sall region consisting of both the aluinu atrix and the silicon particle had been analyzed under the thero-echanical conditions with the output then being used for the calculation of a ore acroscopic odel as an input data. Calculated local variations in stress and strain in the dendritic structure were then utilized again as input data for the forer icroscopic odel. Such a ultistep analysis readily enables the siulation of acroscopic behaviors providing a unique possibility to assess the local daaging behaviors. This sees to be clearly advantageous copared to the above-entioned phenoenological constitutive odeling. 2. Procedure 2.1 Fatigue test Material tested A cast aluinu alloy, designated as AC4CH in the JIS, was used for the investigation. The alloy is equivalent to A356 in the ASTM standard. The alloy used had a cheical coposition of 7.12Si,.341Mg,.116Ti,.17Fe,.8Cu,.6Zr,.23Sr, and balance Al in ass pct. The elt was odified by the addition of 142 pp Sr to refine eutectic silicon particles. The Sr concentration had been deterined after a preliinary investigation in which the effects of Sr addition were tested. The alloy was poured into a steel ingot old of about which was preheated at two different old teperatures. Hereafter, the saples cast into olds held at 38 and 573 K are specified as WC (after water cooling) and NC (after no cooling), respectively. Measured cooling rates during solidification were 5 and 15 K/sec for the saples NC and WC, respectively. The saples were then tepered to provide the standard T6 condition (813 K 14.4 ks and 428 K 1.8 ks). The icrostructural details of each aterial are listed in Table 1. The icrostructural observation revealed that SDAS was larger by about 4% in the aterial NC than that of the Table 1 Microstructural features of the aterials used. Material WC Material NC Density (1 3 kg/ 3 ) Porosity (%) Dendrite secondary ar spacing () Diaeter () Si particle Aspect ratio Roundness *Theoretical density: 2.67 (1 3 kg/ 3 ) Strength, σ and σ / MPa UTS Material NC Fig. 1 UTS El. Material WC aterial WC. The features of silicon particles are siilar between the two aterials. Figure 1 shows tensile properties of each alloy. The aterial WC shows slightly higher strength both in the ultiate tensile strength, UTS (by about 5%), and.2% proof stress, :2 (by about 14%), respectively. The ost significant difference is observed in elongation where that of the aterial WC is alost doubled Thero-echanical fatigue test procedure Test speciens are cylindrical easuring 12 in length with button-head shoulders. Gauge section is 1 in diaeter by 2 long. Specien surface was buffed carefully with MgO powder. Thero-echanical fatigue tests were perfored with a servo-hydraulic testing achine with a capacity of 49 kn. The speciens were heated with an induction heating coil and cooled with air fro a copressor. Firstly the speciens were heated up without loading to T in ¼ 323 K, and then out-of-phase fatigue tests were perfored in a strain control ode with the axiu and iniu teperatures of 523 and 323 K, respectively, as illustrated in Fig. 2. Strain easureent and its control were perfored using an extensoeter attached to the speciens. A triangular wavefor and a cyclic period of 4 sec were used with stress ratio, R, of.1. Applied echanical strain, ", was varied fro.5 to 1.5%. 2.2 Nuerical analysis For coputational purposes, two-diensional idealized icrostructures in which the eutectic Al-Si phase was a network and the -aluinu phase isolated like islands were analyzed using an axi-syetric forulation as scheatically shown in Fig. 3. Instead of using a ore realistic aterial odel such as a clustered three diensional array of the silicon particles in the aluinu atrix, the finite eleent analysis was perfored in two steps for the sake of drastic reduction in odel size. Firstly a sall region consisting of both the -aluinu and the single silicon particle (Fig. 3(a), hereinafter Single particle odel) had been analyzed in advance in order to obtain the theroechanical deforation behavior of the eutectic Al-Si phase. The second odel consisting of both the -aluinu and the Al-Si eutectic region shown in Fig. 3(b) (hereinafter Dual phase odel) was then analyzed using the hoogenized.2 Results of the tensile tests Elongation, El (%)

3 Assessent of Thero-Mechanical Fatigue Behaviors of Cast Al-Si Alloys 113 Teperature, T / K x t t x c t D E Eutectic region Mechanical strain, (%) Fig. 2 =.5, 1., 1.5 Out-of-phase teperature/applied echanical strain cycle adopted. P 4 P 5 P 1 P 2 Si particle P 3 P 6 y.5µ (a) Single particle odel A B C F 5µ (b)dual phase odel y Fig. 4 Axi-syetric finite eleent eshes used for the two-step finite eleent siulation. 3µ (a) Single particle odel (Eutectic region) (b) Dual phase odel (Whole alloy) Fig. 3 Explanation of the two-step calculation sequence for the finite eleent siulation adopted in the present study. The Single particle odel was used to obtain the deforation behaviors of the eutectic region in the Dual phase odel which represents the whole aterial. aterial characteristics (i.e. elasto-plastic, creep and theral expansion behaviors) calculated by the Single particle odel. This substantially eans that the Single particle odel was nested in the eutectic region of the dual phase phase. Models for regular arrays of the perfectly aligned isolated phases were considered in both of the cases. Aspect ratio was assued to be unity for both the silicon particle and the unit cell in the Single particle odel. The volue fraction of silicon was set to be 14.4% which corresponded to that in the eutectic region of the present Al-7.12%Si alloy. Aspect ratio was assued to be for both the -aluinu phase and the unit cell of the Dual phase odel. The volue fraction of the -Al phase was assued to be 49.3% which yielded overall silicon volue fraction of 7.12%. The finite eleent esh initially consisted of quadrilateral eleents having eight nodes. A quarter of each unit cell was divided into 1725 and 1721 eleents, for the Single particle odel and the Dual phase odel, respectively, as shown in Fig. 4. In several cases, the convergence of solutions was checked. Each rectangular unit cell containing one isolated phase is required to aintain a rectangle throughout deforation history to assue a regular array of the perfectly aligned isolated phases. The boundary conditions for this syetry y =@x ¼ on the vertical surface x =@y ¼ on the horizontal surface ð2þ Here, u j are coponents of displaceent vectors. A second set of boundary conditions was eployed consisting of (3) and (4) to enforce axi-syetric deforation of the unit cells about y ¼. u y ¼ on y ¼ ð3þ u x ¼ on x ¼ ð4þ Silicon was odeled as a linear elastic solid with Young s odulus, E ¼ 13:132 GPa, Poisson s ratio, ¼ :2783 7) and linear theral expansion coefficient, ¼ 2:8 1 6 K 1. 8) The teperature-dependent deforation behavior of the -aluinu was siulated utilizing the aterial properties of a A611 alloy (Al-.58Mg-.5Si-.5Fe in ass %). 9) The elastic-plastic odel with a kineatic hardening was chosen as representative of the behavior of the aluinu alloys. The aluinu was assued to yield plastically obeying a von Mises surface and later the Prandtl-Reuss associated flow rule with creep deforation obeying the following power-law: _" c ¼ A n ð5þ where _" c is strain rate and is the tensile stress at a constant teperature during the steady state creep. The stress exponent, n, and the constant, A, depend on teperature, icrostructural features and the activation energy of the deforation process. For an isotropic aterial, the von Mises yield function, f, is stated as follows:

4 114 H. Toda, J. Katano, T. Kobayashi, T. Akahori and M. Niinoi f ¼ J :2 2 ¼ where the second invariant of a deviatoric tensor, ij, is expressed as J 2 ¼ 1 2 ij ij, and :2 is yield stress. In the Prandtl-Reuss associated flow rule, the total strain increent is expressed as: d" pij d ij where d" pij is plastic strain increent and is a scalar rate variable. The aterials were assued to be copletely solid throughout the deforation. For the nuerical siulation of the syste of non-linear equations a Newton-Raphson iteration algorith has been ipleented in which the applied displaceent is increased stepwise up to the final value. The analysis was perfored using the ANSYS software package with a DEC Alfa workstation. Theral and echanical disturbances which are identical to the experient were applied in the coputations. The calculations were terinated at the end of the second cycle and stress/strain variations during the second cycle were evaluated. Since there is no arked difference in the geoetrical features of icrostructure between the two Al-Si alloys used, the siulation is utilized not for interpreting the difference between the two aterials but for gaining valuable icroechanistic insight to understand the thero-echanical fatigue behavior of the cast Al-Si alloys. ð6þ Stress, / MPa Teperature, T / K WC N = 1 N = 1 N = 1 N = NC N = 1 N = 1 N = 1 N = Mechanical strain, / 1 Fig. 6 Stress strain hysteresis loops recorded between cyclic nuber, N, of 1 and 4 cycles. Applied echanical strain range was 1.%. Loading direction 3. Experiental Results Figure 5 shows theral fatigue lives, N f, at the three applied echanical strain ranges, ". The aterial WC shows longer fatigue lives for all ". At the highest ", N f is ore than seven ties longer in the aterial WC at the axiu than that of the aterial NC. Figure 6 shows easured stress-strain hysteresis loops at 1µ Fig. 7 An optical icrograph of a specien surface in the aterial WC. Applied echanical strain range was 1.% and N ¼ 2 cycles. Mechanical strain range, (%) Fig. 5 Material WC Material NC Cyclic nuber to failure, N / cycle f Results of the thero-echanical fatigue tests. 1, 1, 1 and 4 cycles when " of 1.% was applied. Teperature at corresponding applied strain, which is specified fro Fig. 2, is plotted on the upper horizontal axis for reference. Concerning the elastic loading lines in the high teperature range and the elastic unloading lines in the low teperature range, their slopes decrease with the increase in cycle. This ay be attributable to the daage evolution at silicon particles. Figure 7 shows an optical icrograph of a specien surface representing daaged silicon particles and partial linkage of the daaged silicon particles foring icrocracks. The icrograph was taken at only the 2th. cycle, iplying that the daage evolution occurs extensively fro such an early stage of the thero-echanical loading. Closer inspection of Fig. 7 reveals that icrocracking does not occur so uniforly with soe of the silicon particles left intact at this agnification. This inhoogeneous daaging behavior will be discussed later with the analytical results.

5 Assessent of Thero-Mechanical Fatigue Behaviors of Cast Al-Si Alloys 115 Stress, / MPa =.5% = 1.% = 1.5% Cyclic nuber, N / cycle Fig. 8 Variations of the hysteresis-loop end stresses in the stress strain cycles of the aterial WC. More significant reduction in the slope (such as half coparing with the initial value) was seen at 3 cycles when " of.5% was applied. This ight be caused by the existence of relatively large cracks. Figure 8 is the variations of the loop-end stresses in the stress-strain hysteresis loops of the aterial WC. Abrupt drops in stress during the final stages seen on the tensile side correspond to such acroscopic crack foration and extension. Since the cracks are closed under a copressive applied strain, the copressive loop-end stresses are not affected by the existence of the cracks. Coparing the two aterials especially during the elastic unloading when the daages are open, the slopes of the unloading lines are slightly saller in the aterial NC than those of the aterial WC. Although quantitative evaluation is difficult, it ay suggest that the daaging behavior of the silicon particles is different between the two aterials, which has soe contribution to the difference in the theroechanical fatigue lives shown in Fig. 5. In addition, Fig. 6 also shows significant reductions in the yield stress, the axiu stress and the strain hardening with cycle. These are siply attributed to over-aging behavior of the aluinu atrix during holding at the high teperature range. It can readily be noted fro Fig. 8 that the strength drop due to the rapid overaging occurs particularly between 1 1 cycles. This ay explain that the obvious differences in the stressstrain hysteresis loops of Fig. 6 between the two aterials are seen only at the 1st. and 1th. cycles and subsequent hysteresis loops are alost identical between the two aterials. This ay suggest that the ajor contribution to the thero-echanical fatigue life is the aging condition of the atrix aluinu and not spatial distribution pattern of the silicon particles (i.e. SDAS, etc.). Strain softening behavior can be also seen in Fig. 6 while copressive strain is applied (i.e. during teperature rise) after teperature reaches K. These teperatures correspond to 52 59% of the elting point of this alloy, suggesting stress relaxation by creep deforation ust be involved to soe extent. The strain softening ay be, Stress, / MPa Teperature, T / K Experient -1 Prediction Mechanical strain, / 1 Fig. 9 Coparison of stress strain hysteresis loops between the experient and the finite eleent siulation. The loops for the second cycle are shown. however, caused by cobined effects of the overaging phenoenon, the creep behavior, dynaic recovery and the teperature dependency of flow stress, and not by the relaxation by the creep deforation only. The contributions fro the three factors can be hardly separated by only the experiental efforts. The contribution of each factor will be therefore extracted by the nuerical siulation to assess predoinant echaniss over the high teperature range. 4. Discussion of the Experiental Results with the Nuerical Siulations 4.1 Thero-echanical deforation behavior A siulated stress-strain hysteresis loop is copared with that obtained in the thero-echanical fatigue test shown in Fig. 9. There sees to be soe discrepancy between the experient and the siulation probably due to the inaccurate aterial properties used and other factors. Much gentle elastic loading and unloading lines in the experient can be attributed to the existence of a nuber of fatigue cracks as well as the extensively daaged silicon particles. In fact, the easured initial loading line until the stress falls into the positive side sees to be close to the siulation. It can be inferred that the elastic effects of the cracks and daages are negligibly sall when they are closed under the copressive loading. Another discrepancy to note is rearkable strain softening during the high teperature copression, suggesting the actual teperature dependency of flow stress is uch stronger than that of the A611 wrought aluinu alloy which was substituted for the atrix aluinu. However, it can be deeed that the tendency in the siulation is roughly consistent with that of the experient. Therefore, the results of the siulation are used for the further interpretation of the thero-echanical fatigue behavior. The accuulation of creep strain is extracted and shown in Fig. 1. Since the present study adopts the out-of-phase type

6 116 H. Toda, J. Katano, T. Kobayashi, T. Akahori and M. Niinoi -2 Table 2 Calculated axial stress values at points A to F which are specified in Fig. 3(b). The data were used for the further calculations of particle stresses shown later in Figs. 11 and 12. Point x (MPa) y (MPa) A B C D E F Creep strain, / = st cycle 2nd cycle Tie, t / s Fig. 1 Accuulation of creep strain, " c, calculated by the finite eleent analysis. Increent of the creep strain per cycle, " c, is shown in the figure. loading/heating synchronization, the copressive creep strain accuulated during heating is alost twice as large as the tensile creep strain during cooling fro the axiu teperature The accuulation of the copressive creep strain is only 2:7 1 5 per cycle which is less than 1/15 of the applied echanical strain range. Although the strain accuulation per cycle is negligibly sall, the accuulated strain reaches 1% after about 37 cycles have been applied. As described above, the accuracy of the siulation depends on how accurately the high teperature aterial properties are considered. However, it is clear that the effects of the creep deforation are not negligible for the ediu to high cycle thero-echanical fatigue regies. The copressive creep strain is the highest near the top of the -aluinu in the eutectic region (Point A in Fig. 4), while the lowest (roughly half) near the equator (Point C in Fig. 4). Such distribution of creep strain ay exert a significant effect on particle daaging and subsequent crack initiation/propagation processes, because local deforation of the atrix aluinu can cause the generation of larger internal stresses in a silicon particle. Concerning the differences in the thero-echanical fatigue lives shown in Fig. 5 and the stress-strain hysteresis loops shown in Fig. 6, there is little inforation available fro the siulation, because there is no arked difference in the geoetrical features of icrostructure between the two aterials except for SDAS. The effect of SDAS cannot be taken into account in the current siulation because of the assuption of continuu solid. It can be deeed that the saller SDAS gives rise to the deviation fro the continuu echanics because the nuber of the silicon particles per a band width of the eutectic region decreases, typically to one to several particles in the width direction as can be seen in the slender eutectic strips in Fig. 6. This suggests preature fracture of the silicon particles occurs due to inhoogeneous stress/strain distribution along the width direction. However, this ay result in inferior thero-echanical fatigue property for the saller SDAS, which is contrary to the experiental result shown in Fig. 5. Overall, the differences in the thero-echanical fatigue lives can be attributed to the age-hardenability, as stated earlier. 4.2 Daage behavior of the silicon particles In order to assess the particle cracking and the particle/ aluinu interfacial debonding behaviors, local stress distributions calculated for the eutectic region of the Dual phase odel, which are listed in Table 2, were once ore applied as external disturbances to the Single particle odel. This substantially eans that the single particle odel is surrounded by the ezoscopic a/eutectic region Dual phase odel in which aterial deforation is siulated using the noralized aterial properties. Such odel construction readily enables to couple between the icroscopic and ezoscopic echanical events as has been applied to various issues. 1,11) Local stress/strain distributions in and around a silicon particle have been then calculated in the sae way with the aterial properties of the teperature. Figure 11 suarizes the variations of interfacial noral stress at a silicon particle/aluinu atrix interface when the silicon particle is located at points A-F specified in Fig. 3(b). The interfacial stress is higher when the particle is located in the iddle of the eutectic region (i.e. points E and F). The interfacial stress is the highest at 45 degrees fro the top. Figure 12 suarizes the variations of the axiu Interfacial stress, / MPa Top A Equator 15 C B D E F Angle fro the y axis, / deg Fig. 11 Variations of interfacial noral stress, r,atan-aluinu/ silicon particle interface. Silicon particles located at points A-F specified in Fig. 4(b) were analyzed. The angle was defined with point P 1 in Fig. 4(a) as an origin.

7 Assessent of Thero-Mechanical Fatigue Behaviors of Cast Al-Si Alloys 117 Stress, and / MPa and average axial stresses in a silicon particle with its location. Although the difference by location is not so significant, the particle stress is seen to be the lowest at point B. The reported fracture strength of a silicon particle exceeds 78 MPa, 12) iplying that the particle daage during the thero-echanical loading in the present aterials is doinated by the interfacial debonding and not by the particle cracking. The distribution predicted by Fig. 11 sees to be in qualitative agreeent with the experiental observation in Fig. 7. Although it has not been investigated in the present study, the coparison between aterials with ore distinctly different icrostructures can give a ore definitive etallurgical and echanical insight in the icrostructure/fatigue properties relationships. It will be discussed ore fully later by a future research. 5. Suary Maxiu stress Average stress A B C D E F Location Fig. 12 Variations of the axiu axial stress, y ax and the average axial stress, y ave, in a silicon particle. The silicon particle located at points A F specified in Fig. 4(b) was analyzed. It was an objective of this study to investigate the theroechanical responses of the cast Al-Si alloys both by the experiental and odeling approaches with particular attention to the daage at the silicon particles. The ultistep finite eleent siulation techniques provided a highly effective way of assessing the local daaging behavior of silicon particles, along with extracting the contribution fro creep. This sees to be clearly advantageous copared to the traditional experiental and analytical approaches. The aterial with the higher solidification rate exhibited superior thero-echanical fatigue property. The difference in the thero-echanical properties was found to be attributable ainly to the age-hardenability of the atrix and the daage initiation at the silicon particles rather than the difference in SDAS. In fact, the daaged silicon particles were observed extensively fro an early stage of the thero-echanical loading, foring fatigue cracks by the linkage of the daages. It was clarified by the siulation that interfacial debonding was likely to occur rather than particle cracking in the aterials used. The siulation also provided valuable echanistic insights into the understandings of the spatial distribution of daage along with the contribution of the creep deforation. REFERENCES 1) H. Sehitoglu, X. Qing, T. Sith, H. Maier and J. A. Allison: Metall. Trans. A 31A (2) ) R. B. Gundlach, B. Ross, A. Hetke, S. Valtierra and J. F. Mojica: AFS Trans. 12 (1994) ) K. Moizui, H. Tezuka and T. Sato: J. Japan Inst. Light Metals 53 (23) (in Japanese) 4) H. Ikuno, S. Iwanaga and Y. Awano: Toyota Central R&D Labs Review 31 (1996) ) B. Flaig, K.-H. Lang, D. Lohe and E. Macherauch: Fatigue under Theral and Mechanical Loading, eds. J. Bressers and L. Rey, (Kluwer, Netherlands, 1996) ) D. C. Drucker and L. Palgen: ASME J. Appl. Mech. 48 (1981) ) J. J. Worian and R. A. Evans: J. Appl. Phys. 36 (1965) ) J. H. L. Pang, D.Y. R. Chong and T. H. Low: IEEE Trans. Cop. Pack. Technol. 24 (21) ) J. G. Kaufan: Properties of Aluinu Alloys (ASM International, Materials Park, Ohio, 1999) ) P. Poza and J. Llorca: Metall. Mater. Trans. 3A (1999) ) J. W. Leggoe, A. A. Maoli, M. B. Bush and X. Z. Hu: Acta Metall. 46 (1998) ) T. Kobayashi: Marer. Sci. Foru (23)