Evaluation of fracture behavior of iron aluminides

Transcription

1 Theoretical and Applied Fracture Mechanics 45 (2006) Evaluation of fracture behavior of iron aluminides B.S.J. Kang *, R. Cisloiu Mechanical and Aerospace Engineering Department, West Virginia University, Morgantown, WV 26506, USA Available online 27 December 2005 Abstract Comparative fracture tests of three Fe-28%Al iron aluminides showed that alloys with Zr and C addition (FA-187) or with B, Zr, and C addition (FA-189) are extrinsically more susceptible to environmental embrittlement than the base ternary alloy (FA-186) under constant tensile loading condition. This may be caused by the variations of grain boundary morphology (i.e. changes of grain size and grain boundary cohesive strength) caused by the alloy addition. The effect of grain boundary size and cohesive strength are further investigated with reference to the susceptibility of hydrogen embrittlement. Finite element simulation of initial intergranular fracture of two iron aluminides (FA-186 and FA-189) are made. The computational scheme involves coupling the stress and mass diffusion analyses to determine crack-tip stress state and the crack tip hydrogen diffusion. Maximum strain failure criteria was adopted to simulate intergranular fracture. The numerical modeling results correlated well with the experimental data. The result further confirmed that the grain boundary morphology is important as it appears to control the intrinsic and extrinsic fracture behavior of iron aluminides. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Iron aluminides; Stress-assisted hydrogen diffusion; Finite element simulation; Intergranular fracture 1. Introduction Iron aluminides are of great potential use in fossil energy technology, because of their excellent corrosion resistance in the oxidzing-sulfidizing environment under high temperature, in addition to being cost effective and other advantages. However, there are concerns of environmental embrittlement when they are used at room and intermediate temperature and when exposed to moisture or hydrogen environment [1]. Comparative fracture behavior of three iron aluminides (designated as FA-186, FA-187, and FA-189) were investigated [2] to study the effect * Corresponding author. address: bruce.kang@mail.wvu.edu (B.S.J. Kang). of alloy additives to fracture behavior. Considered was the improvement of resistance to moistureinduced hydrogen embrittlement. Crack growth tests of the iron aluminides subjected to constant tensile loading in air, oxygen or water environment were conducted. Moiré interferometry was applied to obtain full-field crack tip displacements, from which crack extension, crack growth rate, cracktip strain fields, and stress intensity factor were evaluated [2]. In what follows, the relevant experimental results were determined and discussed with reference to the intrinsic and extrinsic fracture behavior of the tested iron aluminides. The experimental results indicate that grain boundary morphology plays an important role to the susceptibility of hydrogen embrittlement of iron aluminides, at least for specimens under low strain rate loading /$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi: /j.tafmec

2 26 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) condition. Further investigation involved conducting computational simulations of hydrogen-assisted intergranular fracture of two of the iron aluminides (FA-186 and FA-189). The assessment showed further that grain boundary morphology is important to controlling the intrinsic and extrinsic fracture behavior of iron aluminides. 2. Experimental results Table 1 shows the alloy composition of FA-186, FA-187 and FA-189 and specimen geometry in Fig. 1. The typical microstructure of these alloys is shown in Fig. 2 and the average grain sizes are estimated to be 193, 72 and 75 lm, respectively. Table 2 shows the test matrix. A total of sixteen comparative crack growth tests under air, oxygen or water environment were conducted. Each test specimen was subjected to constant tensile loading condition and moiré interferometry was applied to obtain the crack-tip displacement fields at discrete time intervals. Except for those specimens tested in water environment (which failed in seconds), most of the Table 1 Materials Alloy Fe Al Cr Zr C B FA-186 Balance 28 5 FA-187 Balance FA-189 Balance mm 2.7 mm 5 mm 25.4 mm Fig. 1. Uniaxial test specimen. 115 mm test specimens showed initial stable crack growth followed by rapid catastrophic failure. Fig. 3 shows measured crack growth rate versus applied stress intensity factor. Figs. 4 and 5 show representative moiré fringe patterns of alloys FA-186 and FA- 189 tested in air. Also, shown in the figures are sequences of maximum principal strain distributions ahead of the crack-tip with crack growth. Note that the moiré fringes were thinned at first and discrete (or sparse) strain data were obtained. Lagrangian interpretation scheme was then applied to map these sparse strain data into fine mesh points ahead of the crack tip. This gives the detailed cracktip strain and stress fields. The maximum principal strain distributions shown in Figs. 3 and 4 correlated well with actual fracture paths. For alloy FA-186 tested in air or oxygen condition, multiple cracks were formed as soon as the initial crack started to grow (e.g. Fig. 4). The extension of these multiple microcracks formed an expanding damage zone that resulted in a crack-tip blunting effect [2] which caused initially slow crack growth rate (Fig. 3) and then final catastrophic failure. This feature of extensive multiple microcracking was not found in alloys FA-187 and FA-189; instead, clear single crack growth pattern was observed (Fig. 5). Test results in Table 2 also shows that with the same applied stress intensity factor, specimens tested in oxygen environment (with an estimated residual moisture and hydrogen of and 0.06 times the atmospheric air, respectively [2]) lasted three to nine times longer than those tested in air, indicating the effect of moisture embrittlement for all three iron aluminides. Fig. 6 shows the failure characteristics of the tested alloys in air. The fractured surface can be roughly divided into three areas corresponding to the change of failure mode. Note that stress-assisted hydrogen embrittlement at the crack tip region showed failure initiation accompanied by intergranular fracture for all the three tested specimens (i.e. area 1 in Fig. 6). For alloys FA-187 and FA-189, initial crack growth always started with intergranular mode then shifted to mixed intergranular/transgranular cleavage mode and finally to transgranular failure. As the moisture content is increased in the test environment (i.e. from oxygen to air to water), we observe an increased intergranular failure pattern in area 2. For ternary alloy FA-186, except for the sample tested in water which showed substantial intergranular mode in areas 1 and 2, the initial intergranular

3 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 2. Microstructure of FA-186, FA-187, and FA-189. region (area 1) ahead of the crack tip is very small relative to alloys FA-187 and FA-189, and transgranular cleavage is the dominate failure mode. As mentioned earlier, the sample tested in air had a very short intergranular failure initiation and then quickly changed to an expanding damage zone with multiple microcracks ahead of the notch tip leading to transgranular cleavage failure. Overall, our test results indicate that among the three alloys, the ternary alloy FA-186 has the best fracture resistance, highest fracture toughness and least sensitivity to hydrogen embrittlement (Table 2). The purpose of adding small amount of boron in FA-189 was to improve the grain boundary cohesive strength such that intergranular failure can be minimized. However, with micro-alloying of B and/or Zr, FA-187 and FA-189 have much smaller grains (Fig. 1), thus, intrinsically FA-187 and FA- 189 should have higher fracture toughness than that of FA-186. However, as shown in the above experimental results, because of their smaller grain size,

4 28 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Table 2 Test matrix Iron aluminide Specimen a Structure condition Initial crack b Environment Initial K (MPa p ffiffiffiffi m ) Lasting time b FA B2 FP Air min 86-5 B2 FP Dry oxygen min DO 3 EDM Air min c min 86-9 DO 3 EDM Dry oxygen h d min 86-w1 DO 3 EDM Water h d s FA B2 EDM Air min 87-5 B2 EDM Dry oxygen min 87-8 DO 3 EDM Air 25 2 min 87-7 DO 3 EDM Dry oxygen min 87-w1 DO 3 EDM Water s FA B2 EDM Air min 89-1 B2 EDM Dry oxygen min 89-7 DO 3 EDM Air min 89-6 DO 3 EDM Dry oxygen min 89-w1 DO 3 EDM Water s 89-w2 DO 3 EDM Water s a All tests were conducted at room temperature. b FP: Fatigue pre-cracked; EDM: Electron-discharge machining. c Slow crack growth. d Almost no crack growth. FA-187 and FA-189 are extrinsically more susceptible to environmental embrittlement than FA-186 under low strain rate loading condition. To further investigate the effect of grain boundary morphology as related to the susceptibility of hydrogen embrittlement, finite element modeling simulations are made of the initial intergranular fracture of two iron aluminides (FA-186 and FA- 189) under either air or vacuum conditions. The objective of the numerical modeling analyses is to correlate with the experimental results as well as to further validate our assertion that grain boundary morphology plays an important role on the intrinsic and extrinsic fracture behavior of iron aluminides. 3. Computational modeling A finite element model coupled with a hydrogen diffusion model is developed to simulate the intergranular crack growth due to hydrogen embrittlement. The numerical analyses were carried out using the commercial finite element code ABA- QUS TM. A submodeling technique was implemented to obtain detailed near-tip stress and strain fields by using a refined mesh for the area ahead of the crack tip. The crack-tip submodel is designed to represent qualitatively the grain sizes of FA-186 or FA-189. The concept of submodeling consists of performing two independent analyses, one on the global model with a coarse mesh, and the other on a locally refined mesh (submodel), with the only link being the transfer of interfacial boundary displacements. The nodal displacements of the global model are interpolated onto the boundary of the submodel providing a detailed solution in the area of interest. Due to the symmetry of loading, only half of the specimen size was modeled in the global model. This model consists of 1744 plane stress elements with a fine mesh in the region around the crack tip, as shown in Fig. 7. Near the crack tip region, two submodels were designed to represent qualitatively the grain size of FA-186 and FA-189, respectively. A multi-grain crack tip cell was used in the local finite element mesh composed of a periodic array of regular hexagonal grains. As shown in Fig. 8, the hexagon used in the submodel for FA-186 represents the typical grain size of 193 lm and the submodel contains a total of 8448 elements. The hexagon used for FA-189 represents the typical grain size of 75 lm and the submodel contains a total of 22,528 elements.

5 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 3. Environmental crack growth rate for (a) FA-186, (b) FA-187 and (c) FA Finite element sub-modeling The first assumption made in modeling the grains and grain boundaries was that the grain boundary is weaker than the matrix. Also, due to the addition of small amount of B in FA-189, the grain boundary cohesive strength of FA-189 is stronger than that of FA-186. According to this assumption, we chose the following Young s modulus values: E GBðFA-186Þ ¼ 40%E matrix ¼ 40% 1:41E þ 5 ¼ 0:564E þ 5 MPa; ð1þ E GBðFA-189Þ ¼ 70%E matrix ¼ 70% 1:41E þ 5 ¼ 0:987E þ 5 MPa. ð2þ The next assumption was needed to ensure that the submodeling approach will satisfy the (deformation) compatibility condition. A homogenization procedure based on the rule of mixture (ROM) was adopted in this study. In this approach, the heterogeneous material in the submodel (with two different Young s modulus values for matrix and grain boundaries) is replaced with an equivalent homogeneous one having the same Young s modulus values as that of the global model. The ROM formula was written in terms of area fractions, i.e. E submodel ¼ E matrix A matrix þ E GB A GB ; ð3þ

6 30 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 4. Maximum principal strain distribution ahead of crack tip. FA-186 SENT specimen, room temp, air. where A matrix (= area of grain elements/total area) is the area fraction of grains, and A GB (= area of grain boundaries/total area) is the area fraction of grain boundaries. The results of the E matrix and E GB values obtained for FA-186 and FA-189 are shown in Table 3. The validity of the proposed homogenization procedure and submodeling technique can be verified by examining the contour plots of principal strains near the interfacial boundaries of the submodeled region. As shown in Fig. 9, the superimposed contour plots of principal strains of the global model and submodel showed good interfacial deformation compatibility Hydrogen diffusion model The hydrogen diffusion model is based on the concept of an elastic interaction between the hydrostatic pressure (or the volumetric component of a crack tip stress tensor) and the dilatation associated with an interstitial hydrogen atom [3]. The localization of hydrogen atoms can be explained by the effect of hydrostatic stress on the chemical potential of hydrogen atoms. For the simple case of spherical hydrogen, the enhanced hydrogen concentration by r ii /3 in the region has been shown to follow Boltzman statistics. The governing equations for hydrogen diffusion used in ABAQUS TM are an extension of Fick s equation. That allow for nonuniform solubility of the diffusing substance in the base material and for hydrogen diffusion driven by the gradient of pressure [4]. A more general treatment of the subject can be found in [5]: C H ¼ C 0 exp r iiv H ; ð4þ 3RT

7 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 5. Maximum principal strain distribution ahead of crack tip, FA-189 SENT specimen, room temp, air. where C 0 is the initial concentration and V H is the partial molar volume of hydrogen. The flux of concentration of the hydrogen gas is J ¼ D oc ox þ SK op p. ð5þ ox Here, D is the diffusivity, S is the solubility of the hydrogen gas, K p is the pressure stress factor and p is the pressure stress. The basic solution variable (used as the degree of freedom at the nodes of the mesh) is the normalized concentration (often also referred to as the activity of the diffusing material) defined by / ¼ C=S; ð6þ where C is the mass concentration of the diffusing hydrogen and S its solubility. This variable was chosen because the mesh includes dissimilar materials (i.e. different Young s modulus values for grains and grain boundaries) and in this case the normalized concentration is continuous across the interface between the grain and grain boundary. Stress-assisted diffusion of hydrogen is specified by defining the pressure stress factor, K p, using the analytical solution presented in [6], as K p ¼ V H/ Rðh h z Þ ; ð7þ where R = J/mol K is the universal gas constant, V H = mm 3 /mol is the partial molar volume of hydrogen in iron-based metals.

8 32 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 6. Representative fractographies for FA-186, FA-187 and FA-189 in Air. Finally, the following material properties are selected for the computational calculations [4]. pffiffiffi Solubility: S ¼ 1: kj mol 1 P exp ; RT Diffusivity: D ¼ 2: m 2 s exp kj mol 1 6:88 RT ð8þ ; ð9þ where S is the solubility expressed in atoms of H 2 gas per m 3 of iron, P is the partial pressure of hydrogen gas and T the is temperature. For this research, we set P = 1 atm and T = 300 K. Note that the initial concentration is dictated by Sievart s law: C = P 1/2 S. The crack surface is assumed to be open and to allow equilibration with the hydrogen gas, such that the dominant process will be the transport of hydrogen from the crack tip. A

9 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) steady-state hydrogen diffusion analysis is conducted and the rate of change of concentration with respect to time is omitted from the governing equations Steps simulating intergranular fracture due to hydrogen embrittlement Fig. 7. Global model. Fig. 8. Fine mesh at crack tip region (submodels). (1) Finite element stress/strain analysis of the global model. (2) Finite element stress/strain analysis of the submodel at the crack-tip region. (3) Steady-state hydrogen diffusion analysis based on the hydrogen diffusion model coupled with the results from step (2). (4) Degrade the material properties in the high hydrogen concentration zone in submodel. (5) Finite element stress/strain analysis of the updated specimen configuration (similar to steps (1) and (2)). (6) Apply maximum principal strain failure criterion and simulate intergranular crack growth. (7) Go to step (1) and repeat the cycle. For this simulation, it is proposed that a material degradation will occur at the stress-assisted hydrogen concentration region. To the best knowledge of the authors, no similar modeling work or actual experimental material property degradation measurement has been done to substantiate this assertion. Nevertheless, we believe that this is a reasonable assumption that the probable cause of the initial intergranular crack growth is due to material property degradation at the crack-tip stressassisted hydrogen concentration zone. Accordingly, the material property (Young s modulus in this analysis) is reduced both at the matrix and grain boundary region. The reductions are indicated in Table 4. After degrading the material properties, a new static analysis of the submodel is carried out to determine the updated crack tip stress/strain state; and, based on the selected failure strains for FA- 186 and FA-189, the possibility of intergranular Table 3 Material properties Alloy Total area of submodel (mm 2 ) Area of grain boundaries (mm 2 ) Area fraction of GB E GB (MPa) E Global (MPa) E matrix new (MPa) FA % 0.564E E E+5 FA % 0.987E E E+5

10 34 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 9. Superposed contour plots of principal strains of global model and submodel (left) FA-186 and (right) FA-189. Table 4 Reduction of Young s Modulus Normalized concentration ratio % of reduction of Young s modulus E new submodel Current crack tip Initial crack tip E global Current crack tip Initial crack tip Fig. 10. Submodel and corresponding adjusted global model. Table 5 Finite element simulation matrix Stress intensity factor, K Failure strain Environment Fracture behavior FA-186 K = 17.3 MPa p m 4% Vacuum Slow and straight, stopped after 0.6 mm Air Very slow and straight, stopped after 0.63 mm 6% Vacuum (5%) Slow and straight, stopped after mm Fracture behavior FA-189 Very slow, blunting effect, stopped after 0.51 mm Straight crack growth, after 0.4 mm it changed to multiple cracking Stopped immediately after mm, almost no crack growth Air No growth Straight slow crack extension to failure K = 36. MPa p m 4% Vacuum Wide spread micro-cracks; relatively fast and stopped after 1.08 mm Air Wide spread initial micro-cracks, more pronounced blunting effect, expanding damage zone growth 6% Vacuum Slow and straight, blunting effect, stopped after 0.89 mm Straight crack growth, stopped after 0.56 mm Air Less initial micro cracks (comparing to 4%) and less initial crack tip blunting

11 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) cracking is evaluated and proper boundary conditions in the crack tip submodel region are then adjusted. A failure strain of 4% for FA-186 and a failure strain of 6% for FA-189 are selected in this numerical analysis. Because both the geometric configuration and material properties in the submodel were changed with the updated crack growth, it is necessary to satisfy the displacements compatibility requirement at the interfacial boundary region. This was accomplished by updating the crack length in the global model together with modifying the elastic modulus of the elements in the global model corresponding to the submodel area, as shown schematically in Fig. 10. This updating procedure was done at every three to four simulation steps at which the new Young s modulus of the submodel was determined based on the rule of mixture approach and material properties of Fig. 11. Hydrogen diffusion zones and principal strain distributions for FA-186, air, K I = MPa p m.

12 36 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) the matrix and grain boundary were then modified accordingly. 4. Results and discussion Table 5 shows the finite element simulation matrix. As shown, a total of 12 comparative finite element simulations were carried out under either air or vacuum condition and at two different stress intensity factors. Figs. 11 and 12 show examples of intergranular crack growth due to hydrogen embrittlement for FA-186 under applied stress intensity factors of and 36.9 MPa p m, respectively. Fig. 13 shows the intergranular crack growth due to hydrogen embrittlement of FA-189 under applied stress intensity factor of MPa p m. As shown, the results indicate small maximum principal strain distribution at the crack tip region for FA-186 (all are below 6%) and thus small amount of crack growth is predicted compared to FA-189 which shows a continuous crack growth up to failure. However, if the applied stress intensity factor is increased to K I = 36.9 MPa p m, a much larger Fig. 12. Hydrogen diffusion zones and principal strain distributions for FA-186, air, K I = 36.9 MPa p m.

13 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 13. Hydrogen Diffusion zones and principal strain distributions for FA-189, air, K I = MPa p m. diffusion zone with higher hydrogen concentrations is noted for the case of FA-186, and, thus, multiple cracks can be initiated from the very beginning, which will further lead to an expanding damage zone as observed in the experimental results. This feature of extensive multiple cracks is also observed in the vacuum simulations (see Fig. 14), leading to the suggestion that extrinsically FA-186 is less sensitive to hydrogen embrittlement than FA-189. As for the case of FA-189, the hydrogen diffusion zone is larger with three times higher hydrogen concentrations than those of FA-186, as shown in Fig. 13. This leads to much faster crack growth rate as observed in the experiment. Figs. 15 and 16 show the intergranular crack growth of FA-189 in vacuum under applied stress intensity factors of and 36.9 MPa p m, respectively. As shown, the simulation results for FA-189 indicate minimal crack growth ( mm crack growth under K I = MPa p m and 0.56 mm crack growth under K I = 36.9 MPa p m) which shows that, intrinsically, FA- 189 has better fracture resistance than FA-186 (0.63 mm crack growth under K I = MPa p m and a widespread micro-cracking under K I = 36.9 MPa p m).

14 38 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 14. Principal strain distribution for FA-186, K I = 36.9 MPa p m, Vacuum. 5. Conclusion Experimental results showed that, because of their smaller grain size, FA-187 and FA-189 are extrinsically more susceptible to environmental embrittlement than FA-186 under low strain loading condition. To further investigate the effect of grain boundary morphology as related to the susceptibility of hydrogen embrittlement, comparative finite element modeling simulations of initial intergranular fracture of two iron aluminides (FA-186 and FA- 189) subjected to stress-assisted hydrogen embrittlement were carried out. Summarized numerical results are as follows: (1) Under the same applied load and in vacuum condition, FA-189 showed a better fracture resistance than FA-186. (2) Under the same applied load and moisture environment, FA-189 has a higher hydrogen

15 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) Fig. 15. Principal strain distribution for FA-189, K I = MPa p m, Vacuum. Fig. 16. Principal strain distribution for FA-189, K I = 36.9 MPa p m, Vacuum. concentration in front of the crack tip than that of FA-186, which leads to much faster crack growth rate. (3) Grain boundary size plays an important role to the extrinsic environmental fracture behavior of iron aluminides. (4) The numerical simulation results agree well with the experimental results. Both results indicated that intrinsically FA-189, which has stronger grain boundary cohesive strength but smaller grain size, has better fracture resistance than that of FA-186, however, extrinsically it is more susceptible to hydrogen embrittlement under low strain loading conditions. Acknowledgements This research is supported by the Office of Fossil Energy, AR&TD Materials Program, US Department

16 40 B.S.J. Kang, R. Cisloiu / Theoretical and Applied Fracture Mechanics 45 (2006) of Energy, under Contract No. SUB-19X-ST547C with UT-Battelle, LLC. Technical assistance from Dr. C.T. Liu at ORNL is greatly appreciated. References [1] N.S. Stoloff, C.T. Liu, Environmental embrittlement of iron aluminides review, Intermetallics 2 (1994) [2] B.S.-J. Kang, Q. Yao, Z. Li, C.T. Liu, Investigation on environmental assisted fracture behavior of iron aluminides using moire interferometry, Mater. Sci. Eng. A (1997) [3] H.H. Johnson, Hydrogen embrittlement and stress corrosion cracking, in: R. Gibala, R.F. Hehemann (Eds.), Proceedings of the Troiano Festschrift Symposium, Case Western Reserve University, June 1 3, 1980, ASM, Ohio, 1984, p. 3. [4] P. Sofronis, R.M. McMeeking, Numerical analysis of hydrogen transport near a blunting crack tip, J. Mech. Phys. Solids 37 (3) (1989) [5] G.C. Sih, J.G. Michopoulos, S.C. Chou, Hygrothermoelasticity, Martinu Nijhoff Publishers, Boston, [6] H.W. Liu, Stress-corrosion cracking and the interaction between crack-tip stress field and solute atoms, J. Basic Eng. Trans. ASME 92 (1970)