Hydrogen-assisted stress corrosion cracking simulation using the stress-modified fracture strain model

Transcription

1 Journal of Mechanical Science and Technology 26 (8) (2012) 2631~ DOI /s x Hydrogen-assisted stress corrosion cracking simulation using the stress-modified fracture strain model Nak-Hyun Kim 1, Chang-Sik Oh 3, Yun-Jae Kim 1,*, Kee-Bong Yoon 2 and Young-Wha Ma 2 1 Deartment of Mechanical Engineering, Korea University, Anam-Dong, Sungbuk-Ku, Seoul , Korea 2 Deartment of Mechanical Engineering, ChungAng University, Anam-Dong, Sungbuk-Ku, Seoul , Korea 3 Korea Institute of Nuclear Safety, 62 Gwahak-Ro, Yuseong-Gu, Daejeon , Korea (Manuscrit Received Setember 5, 2011; Revised March 6, 2012; Acceted March 12, 2012) Abstract This aer rooses a numerical method to simulate hydrogen-assisted stress corrosion cracking, via couled diffusion elastic-lastic finite element damage analyses based on henomenological stress-modified fracture strain model. For validation, simulated results using the roosed method are comared with ublished exerimental data of FeE 690T comact tension tests under air and hydrogen condition with various constant load-line dislacement rates. The simulated results agree well with exerimental data. Keywords: Hydrogen-assisted stress corrosion cracking; Finite element damage analysis; Fracture simulation Introduction Hydrogen-assisted stress corrosion cracking is a severe environmental tye of failure [1]. Tests under hydrogen environments can be dangerous and very exensive, and thus efficient (finite element hydrogen assisted stress corrosion cracking) simulations would be quite useful. To simulate hydrogen-assisted stress corrosion cracking, two issues need to be resolved: hydrogen diffusion simulation and hydrogen-induced cracking simulation. For hydrogen diffusion simulation, the hydrogen transort model, roosed by Sofronis and McMeeking [2], can be used. It has been used extensively to investigate the effect of the hydrostatic stress and traing on the hydrogen distribution [3-6]. In their model, the hydrogen transort is affected by hydrostatic stress and lastic strain, and thus couled diffusion elastic-lastic finite element (FE) analyses have to be carried out. In our revious work [7], the above hydrogen transort model was imlemented into the general urose rogram ABAQUS [8]. For rogressive cracking simulation, a henomenological stress-modified fracture strain model, recently roosed by the authors [9], is used in resent work. The model is based on the well-known fact that the fracture strain for ductile fracture strongly deends on stress triaxiality [10-13]. Under hydrogen environment, it has been also shown that a similar aroach * Corresonding author. Tel.: , Fax.: address: kimy0308@korea.ac.kr Recommended by Associate Editor Youngseog Lee KSME & Sringer 2012 can be taken [14-16]. For a given material, the stress-modified fracture strain model can be determined from smooth and notched bar tensile test results, for instance. The incremental damage is defined by ratio of lastic strain increment and fracture strain. When the accumulated damage becomes unity (at an FE gauss oint), all stress comonents (at the gauss oint) are reduced to a small value to simulate failure. The model is validated against extensive exerimental data in our revious aers [9, 17]. This aer rooses a method to simulate hydrogen-assisted stress corrosion cracking. The method is a combination of the hydrogen transort model and the henomenological stressmodified fracture strain model. To validate the roosed method, simulated results are comared with ublished exerimental results of FeE 690T comact tension tests under air and hydrogen condition [18]. 2. Summary of exerimental data In this section, test data ublished in the literature, Ref. [18], are briefly summarized. Test data include comact tension C(T) tests under air and hydrogen charging conditions, made of FeE 690T. The chemical comosition of the FeE 690T is given in Table 1. The yield and tensile strengths are σ y = 695 MPa and σ u = 850 MPa, resectively. The exerimental engineering stress-strain curve is shown in Fig. 1. A series of re-cracked comact tension secimens were tested in laboratory air and in ASTM substitute ocean water under hydrogen charging conditions. The C(T) secimens had

2 2630 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~2638 Table 1. Chemical comositions of the FeE 690T (wt.%). C S P Si Mn Cr Mo [19]), δ 5, were monitored. Crack growth resistance curves in terms of δ 5 are shown Fig Stress corrosion cracking simulation-v-overview 3.1 Damage model for air condition The damage model used in this aer is a henomenological one based on the concet of the stress-modified fracture strain model; the (true) fracture strain ε f for dimle fracture strongly deends on the stress triaxiality, σ h /σ e [10-13]. σh σ1+ σ2 + σ = 3 (1) σe 3σe Fig. 1. Smooth bar tensile test result. where σ i (i = 1-3) denotes the rincial stress comonent; and the von Mises equivalent stress σ e is given by 2 {( 1 2) ( 1 3) ( 3 2) } σe = 1 σ σ + σ σ 2 + σ σ 2. (2) 2 Although detailed exressions differ slightly, it is known that the deendence of ε f on the stress triaxiality can be modeled using an exonential function. In this work, the following form of ε f is assumed: f εa σ Aex B h = + C σ e (3) Fig. 2. Schematic of a comact tension secimen (unit: mm). where ε a f is the true fracture strain in air condition; and Α, B and C are material constants. For a given material, these constants can be determined from notched bar tensile test results (see for instance Ref. [9]). However, for the resent work, notched bar tensile test results are not available, and accordingly they are determined in a different way, which will be described later in Section Damage model for hydrogen condition Fig. 3. Exerimental CTOD (δ 5 ) R-curves tested under air and hydrogen charging conditions with various loading rates. width W = 40 mm, thickness t = 19 mm and an initial crack length to width ratio of a o / W = 0.55, as shown in Fig. 2. A cathodic otential of -900 mv vs. Ag/AgCl electrode was alied to the secimens during the test to romote hydrogen charging. The secimens were loaded at various load-line dislacement rates. The crack growth increment, Δa, and the crack ti oening dislacement (measured at hardness indentations located ± 2.5 mm above and below the ti of the fatigue re-crack by using a secially designed cli-on gage Under hydrogen condition, material ductility can decrease due to hydrogen embrittlement. This imlies that the fracture strain deends not only on the stress triaxiality but also on hydrogen concentration. Dietzel and co-workers [14-16] roosed that reduction in fracture strain due to hydrogen concentration can be modeled simly using the following function: ε f f C 1 L h ε a μ = C env where ε h f is fracture strain under hydrogen; C L is the hydrogen concentration er unit volume in normal interstitial lattice (NIL) sites; C env is environmental hydrogen concentration; and μ ( 0 μ 1) is fracture strain reduction arameter, which deends on material and environmental condition. (4)

3 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~ Hydrogen diffusion model Hydrogen is assumed to reside either at normal interstitial lattice sites (NILS) or reversible traing sites generated by lastic straining. Oriani s theory assumes local equilibrium between the two oulations [20]. θ T θ L ex W B = 1-θT 1-θ L RT where θ L is the occuancy of the interstitial sites, θ T is the occuancy of the traing sites, W B is the tra binding energy, R(= 8.31 J/mol) is gas constant, and T (in Kelvin) is the absolute temerature. The hydrogen concentration er unit volume in traing sites, C T, can be exressed as CT = αθtnt (6) where α is the number of sites er tra and N T = N T (ε ) denotes the tra. The hydrogen concentrations are related to the number of sites, C L, can be exressed as CL = βθlnl (7) where β is the number of NILS er solvent atom and N L = N A /V M denotes the number of lattice sites er unit volume where N A = atoms/mol is Avogadro s number and V M is the molar volume of the host lattice. The governing equation for transient hydrogen diffusion accounting for traing and hydrostatic drift as C L D 2 L CL + t D C V N L L H T ε σkk αθt 0 3RT + = ε t where tis the time derivative, V H is the artial molar volume of hydrogen in solid solution, σ is the Cauchy stress, D L is the hydrogen diffusion constant through NILS, Deff = DL ( 1+ CT CL ) is an effective diffusion constant. It is known that the resence of hydrogen affects the elasticlastic constitutive law. To incororate the hydrogen-induced lattice deformation, the total deformation rate tensor can be calculated by e D D D D h = + + (9) where D e, D and D h denote, resectively, the elastic, lastic and hydrogen arts. The hydrogen induced deformation rate D h is urely dilatational and isotroic [2]. h d ( 0) D ln 1 c c Δ v = + σ dt 3Ω (5) (8) (10) where ( ) c= CL + CT NL is the total hydrogen concentration in NILS and traing sites measured in H atoms er solvent atom, c 0 is the initial hydrogen concentration in the absence of any straining, Δ ν = VH NA is the volume change er hydrogen atom introduced into solution, and Ω is the mean atomic volume of the host metal atom. The effective lastic strain ε can be calculated by ε = 2 D D /3. (11) The above equations show that calculation of hydrogen diffusion is fully couled to the field of the hydrostatic stress and effective lastic strain, as calculation of lastic strains requires determination of hydrogen concentration. 3.4 Progressive failure simulation Once the form of ε f is determined as a function of the stress triaxiality, incremental damage due to lastic deformation, Δω, is calculated (at each gauss oint within finite elements) using Δε Δ ω = (12) ε f where Δε is the equivalent lastic strain increment, calculated from FE analysis. When the accumulated damage becomes unity, ω = ΣΔω = 1, failure is assumed locally and incremental crack growth is simulated simly by reducing all stress comonents at the gauss oint sharly to a small lateau value (tyically less than 10MPa). 3.5 Imlementation to ABAQUS To imlement constitutive equations for hydrogen diffusion (in Section 3.3), two user subroutines within ABAQUS are develoed [7]. The first one is UMATHT for the hydrogen diffusion analysis, and the second one is UMAT to define a material s mechanical behavior to incororate deformation rate induced due to lattice straining by the solute hydrogen. Detailed information is given in Ref. [7]. To imlement damage model and rogressive failure simulation, described in Sections 3.2 and 3.4, the user subroutine UMAT is also used. The information on hydrogen concentration at gauss oints, which is calculated in UMATHT, is assed into the UMAT. The user subroutine UMAT calculates damage accumulation, according to Eq. (12). When the accumulated damage becomes critical (unity), stresses are relaxed simly by changing the yield surface. Note that in our revious study [9], the user subroutine UHARD was used. However, for the resent work, the UHARD subroutine cannot be used due to couled diffusion and elastic-lastic analysis, and

4 2632 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~2638 (a) (a) (b) Fig. 4. (a) FE mesh to simulate tensile test of the smooth bar; (b) comarison of exerimental engineering stress-strain data [18] with FE result. accordingly the user subroutine UMAT is used by adding the hydrogen effect on fracture strain. 4. Fracture simulation under air condition 4.1 Determination of damage model and element size To determine the stress-modified fracture strain model for FeE 690T, conventional elastic-lastic 3-D FE analyses (w/o damage) were first erformed to simulate tensile tests of smooth bar. FE mesh for smooth bar is shown in Fig. 4(a). The number of elements is 6,258. Simulated result for smooth tensile test is comared with exerimental tensile data in Fig. 4(b). The cross symbol in Fig. 4(b) indicates the failure initiation oint in tests. The FE results can simulate deformation behavior well even after necking, but deviate from exerimental results after failure initiation oints, as they cannot simulate failure. In Fig. 5(a), variation of the stress triaxiality with the equivalent lastic strain for the smooth tensile bar is shown. Both the stress triaxiality and equivalent lastic strain are extracted in the center of the secimens, where failure initiation is exected to occur. Initially, the stress triaxiality in the center of the secimen is almost constant, but once necking develos, it increases with increasing equivalent lastic strain. As a failure criterion should include the history of stress and strain, an average stress triaxiality is introduced, defined by ε f σh 1 σh d ε σ = e (13) σ ave ε 0 e f where ε f denotes the equivalent lastic strain to failure initiation. Resulting equivalent lastic strain to failure initiation (called the fracture strain) for the smooth bar is shown in Fig. (b) Fig. 5. (a) Variations of the stress triaxiality with the equivalent lastic strain for smooth bar tensile tests; (b) assumed fracture strain as a function of the stress triaxiality. Fig. 6. FE mesh of the C(T) secimen for damage analysis. 5(b), as a function of the (average) stress triaxiality. To determine the fracture strain ε f, Eq. (3), however, we need two more oints, as Eq. (3) includes three material constants. Although extra data oints can be obtained using notched bar tensile test results, they are not available for the resent roblem. At this oint, it is worth noting that, based on semianalytical aroach, Rice and Tracey [13] suggested that the value of B can be aroximated as B = -1.5, regardless of materials. Even when the B value is fixed to B = -1.5, a comlete form of the fracture strain cannot be determined. In the resent work, it will be comleted by comaring with the C(T) secimen test results, as described next. To determine the fracture strain as a function of the stress triaxiality, FE damage analysis of the C(T) test under air condition is erformed using various choices of the stress-

5 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~ Table 2. The diffusion roerties for FeE 690T [14]. D L (mm 2 /s) 4.00E-05 Tem (K) 298 V M 7.12E+03 N t0 8.80E+13 (mm 3 /mol) (mm -3 ) 2.00E E+15 V H W B (kj/mol) 42.1 C env (atoms/mm 3 ) 2.10E+14 N t1 (a) Fig. 8. Comarison of C(T) test result under air condition [18] with FE result with the calibrated mesh size and fracture strain. (b) Fig. 7. Effects of the element size and assumed fracture strain on resistance curves: (a) ε f = 0.1 at σ h /σ e = 2.5; (b) ε f = 0.15 at σ h /σ e = 2.5. modified fracture strain. Various choices are made by assuming a oint at the stress triaxiality of σ h /σ e = 2.5, which is the theoretical value for the Prandtl field [21] (see Fig. 5(b) for instance). Our exerience indicates that the fracture strain at σ h /σ e = 2.5 ranges roughly from 10% to 20% of the uni-axial ductility for tyical structural steels [9, 17]. Note that 10% of the uni-axial ductility corresonds to ~0.1 for the resent material. To erform FE damage analysis, an issue related to a finite element size needs to be resolved. An element size in FE damage analysis should be related to the micro-structural length scale, and thus is an imortant arameter. A tyical FE mesh for the damage analysis is shown in Fig. 7. Four-node lane strain solid elements (element tye CPE4) of the size Xmm x Xmm were uniformly saced in the cracked section. Analysis was erformed by systematically varying the element size X. To incororate the large geometry change effect, the large geometry change otion was chosen. Effects of assumed fracture strain and element size on simulated results of the C(T) test under air condition are shown in Fig. 7. For comarison, exerimental results are also shown. Results using the fracture strain of 0.1 at σ h /σ e = 2.5 are shown in Fig. 7(a), and those using 0.15 in Fig. 7(b). Results show that the fracture strain at σ h /σ e = 2.5 affects the sloe of the resistance curve, whereas the element size affects its magnitude. Based on such observations, the element size and fracture strain at σ h /σ e = 2.5 can be calibrated. Resulting (calibrated) values are the mesh size of 0.04mm and the fracture strain of 0.13 at σ h /σ e = 2.5, giving the following fracture strain: σ 2.52ex 1.5 h ε f = σ. (14) e Simulated results using these values are comared with exerimental data in Fig. 8, showing excellent agreement. 5. Fracture simulation under hydrogen charging condition 5.1 Material roerties To simulate hydrogen diffusion rocess, described in Section 3.2, diffusion roerties of FeE 690T, summarized in Table 2 [14], were used. Furthermore the tra density, N T, in Eq. (15) is related to the lastic deformation ε by [14] 0 1( ) 0.7 NT = NT + NT ε. (15) To reflect the effect of hydrogen embrittlement on the fracture strain, the fracture strain reduction arameter μ is introduced. As this arameter is also unknown, it should be calibrated. As described in the next section, it is calibrated by comaring simulated results with the C(T) test data of 0.1mm/h, and is used to redict other test data with slower loading rates.

6 2634 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~2638 Fig. 9. Boundary condition for the couled diffusion and elastic-lastic roblems at C(T) secimen. (a) Fig. 10. Comarison of C(T) test results under hydrogen conditions [18] with FE results. (b) Fig. 11. Relative hydrogen concentration in the ligament at crack initiation for different loading rates: (a) 0.1 mm/h; (b) mm/h. 5.2 FE analysis and boundary conditions The FE damage analysis for the C(T) secimens under hydrogen environments with different loading rates is erformed using ABAQUS. Two-dimensional FE damage analysis was erformed using four-node quadrilateral elements (CPE4 for ductile failure simulation and CPE4T for hydrogen assisted SCC simulation) to simulate the test under hydrogen conditions with different loading rates. To incororate the large geometry change effect, the large geometry change otion was chosen. The boundary condition for the couled diffusion and elastic-lastic roblems is schematically shown in Fig. 9. Along the cracked surface, the concentration boundary condition is alied; it is assumed that the cracked surface is under uniform NILS hydrogen concentration, C L = C env, at all times. On other surfaces, the no flux boundary condition is alied; it is assumed that the surface is insulated. As mentioned, to reflect the hydrogen embrittlement effect on the fracture strain, the arameter μ needs to be calibrated. In the resent work, it is calibrated by comaring with the C(T) test data of the 0.1 mm/h loading rate (the fastest loading rate). Comarison suggests the value of μ = Stress corrosion cracking simulations for the C(T) test under hydrogen condition with slower loading rates are erformed using calibrated arameters: the element size of 0.04 mm, the fracture strain under air condition using Eq. (14) and μ = Results Simulated results for three different loading rates, 0.1 mm/h, 0.01 mm/h and mm/h, are comared with exerimental data in Fig. 10. For comarison, test data under air condition are also included together with simulated ones. Results show that simulated results agree overall well with exerimental data for all loading rates. Agreements are good for the loading rate of 0.1 mm/h and 0.01mm/h. For the slowest loading rate of mm/h, redicted results are above the exerimental ones, but the effect of the loading rate on the resistance curve can be clearly reroduced. The rofiles of the relative NILS hydrogen concentration (C L /C env ) ahead of the crack ti are shown in Fig. 11 for two different loading rates, 0.1mm/h and mm/h. For a fast loading rate (0.1 mm/h), the crack initiates and grows before sufficient hydrogen is diffused into secimen where the hydrostatic stress is high. As results, there is no hydrogen eak ahead of the crack ti. When loading rate is decreased, however, there is sufficient time for hydrogen to be diffused to the hydrostatic eak location. 6. Conclusions A numerical method to simulate the hydrogen assisted stress corrosion cracking is roosed. The method is a combi-

7 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~ nation of the hydrogen transort model and the henomenological stress-modified fracture strain model. The hydrogen transort model of Sofronis and McMeeking [2] was used to simulate the effect of the hydrostatic stress and traing on the hydrogen distribution. For rogressive cracking simulation, a henomenological stress-modified fracture strain model is used, roosed by the authors [9]. The model is based on the fact that the fracture strain for ductile fracture strongly deends on stress triaxiality. The hydrogen embrittlement effect on the fracture strain is incororated in a simle form. The roosed method is validated by comaring with ublished exerimental data of stress corrosion cracking testing of FeE 690T C(T) tests under air and hydrogen condition. In hydrogen condition, the secimens were subjected to three different loading rates. The simulated results agree well with exerimental data. Acknowledgment This work is suorted by the MEST/KOSEF (Nuclear R&D Program, M M ), funded by Korea Science & Engineering Foundation. Nomenclature A, B, C : Material constants in Eq. (3) a, a o, Δa : Crack length, initial value and its increment C env : Environmental hydrogen concentration C T, C L : Hydrogen concentration er unit volume in traing sites and in NILS, resectively D L : Hydrogen diffusion constant through NILS D eff : Effective diffusion constant N A : Avogadro's number (6.0232x10 23 ) N T : Tra density measured in number of tras er unit volume N L : Number of solvent lattice atoms er unit lattice volume NILS : Normal interstitial lattice site R : Gas constant (= 8.31J/mol/K) T : Absolute temerature (K) V H : Partial molar volume of hydrogen in solid solution V M : Molar volume of the host lattice measured in units of volume er lattice mole W B : Tra binding energy δ 5 : Crack-ti oening dislacement measured using the 5 mm cli gage ε, Δε : Equivalent lastic strain and its increment ε f f a, ε h : Fracture strain under air and hydrogen conditions, resectively μ : Fracture strain reduction arameter, see Eq. (4) σ e, σ h : Effective stress and hydrostatic stress, resectively, see Eqs. (1) and (2) σ 1, σ 2, σ 3 : Princial stress comonents ω, Δω : Accumulated damage and incremental damage References [1] J. P. Hirth, Effect of hydrogen in the roerties of iron steel, Metallurgical and Materials Transactions A, 11 (6) (1980) [2] P. Sofronis and R. M. McMeeking, Numerical analysis of hydrogen transort near a blunting crack ti, Journal of the mechanics and Physics of Solids, 37 (3) (1989) [3] H. K. Birnbaum and P. Sofronis, Hydrogen-enhanced localized lasticity-a mechanism for hydrogen related fracture, Material Science and Engineering A, 174 (1994) [4] A. Taha and P. Sofronis, A micromechanics aroach to the study of hydrogen transort and embrittlement, Engineering Fracture Mechanics, 68 (2001) [5] J. Lufrano, P. Sofronis and H. K. Birnbaum, Elastolastically accommodated hydride formation and embrittlement, Journal of Mechanics and Physics of Solids, 46 (1998) [6] Y. Liang, P. Sofronis and R. H. Dodds Jr., Interaction of hydrogen with crack-ti lasticity: effects of constraint on void growth, Material Science and Engineering A, 366 (2004) [7] C. S. Oh, Y. J. Kim and K. B. Yoon, Couled analysis of hydrogen transort using ABAQUS, Journal of Solid Mechanics and Materials Engineering, 4 (7) (2010) [8] ABAQUS Version 6.7. User s manual, Dassault Systemes, [9] C. S. Oh, N. H. Kim, Y. J. Kim, J. H. Beak, Y. P. Kim and W. S. Kim, A finite element ductile failure simulation method using stress-modified fracture strain model, Engineering Fracture Mechanics, 78 (2011) [10] F. A. McClintock, A criterion of ductile fracture by the growth of holes, ASME J Al. Mech., 35 (1968) [11] A. C. Mackenzie, J. W. Hancock and D. K. Brown, On the influence of state of stress on ductile failure initiation in high strength steels, Engineering Fracture Mechanics, 9 (1977) [12] J. W. Hancock and M. J. Cowling, Role of state of stress in crack-ti failure rocesses, Material Science and Technology, (1980) [13] J. R. Rice and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields, Journal of the mechanics and Physics of Solids, 17 (1969) [14] M. Pfuff and W. Dietzel, Mesoscale modelling of hydrogen assisted crack growth in heterogeneous materials. In: Carinteri A, editor, Proceedings of the 11th international conference on fracture, Turin (Italy) (2005). [15] W. Dietzel, M. Pfuff and G. G. Juilfs, Hydrogen ermeation in lastically deformed stee membranes, Material science, 42 (2006) [16] W. Dietzel and M. Pfuff, The effect of deformation rates on hydrogen embrittlement. In: Thomson AW, Moody NR, editors, Hydrogen effects in materials, The minerals and Materials Society (1996) [17] N. H. Kim, C. S. Oh, Y. J. Kim, K. B. Yoon and Y. H. Ma,

8 2636 N.-H. Kim et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2631~2638 Comarison of fracture strain based ductile failure simulation with exerimental results, International Journal of Pressure Vessels and Piing, 88 (2011) [18] I. Scheider, M. Pfuff and W. Dietzel, Simulation of hydrogen assisted stress corrosion cracking using the cohesive model, Engineering Fracture Mechanics, 75 (2008) [19] D. Hellmann and K. H. Schwalbe, On the exerimental determination of CTOD based R-Curves, The crack ti oening dislacement in elastic-lastic fracture mechanics, K.-H. Schwalbe ed. Sringer Verlag, Berlin-Heidelberg- New York (1986) [20] R. A. Oriani, The diffusion and traing of hydrogen in steel, Acta Metallurgica, 18 (1970) [21] T. Anderson, Fracture Mechanics Fundamentals and Alications, 3rd edition, CRC Press (2005). Nak-Hyun Kim received a B.S. degree in Mechanical Engineering from Korea University in He is currently in the doctoral course of the Graduate School of Korea University. His research interests are in damage mechanics and hydrogen embrittlement. Yun-Jae Kim is a rofessor of the Mechanical Engineering Deartment, Korea University, Seoul, Korea. He received his Ph.D in 1993 from Massachusetts Institute of Technology, USA. His research interests are in structural integrity and reliability.