FEM SIMULATION OF CRACK PROPAGATION AND OXIDATION INDUCED STRESSES IN A TBC MODEL SYSTEM 1) ¨ 1) and J. Rosler ¨ P. Seiler1∗) , M. Baker 1) ¨ Braunschweig, Langer Kamp 8, Institut fur ¨ Werkstoffe (IfW), Technische Universitat 38106 Braunschweig, Germany
ABSTRACT Plasma sprayed thermal barrier coating systems are used on top of highly stressed components e.g. on gas turbine blades to protect the underlying substrate from the high surrounding temperatures. A typical coating system consists of the bond-coat (BC) and the thermal barrier coating (TBC). The thermally grown oxide (TGO) between the BC and the TBC develops in service as a third layer which is caused by the diffusion of oxygen through the TBC. To study the behaviour of the complex failure mechanisms in thermal barrier coatings, a simplified model system is used to reduce the number of the system parameters. The artificial system consists of a bond-coat material (fast creeping Fecralloy or slow creeping MA956) as the substrate with a Y2 O3 partially stabilised plasma sprayed zirconium dioxide TBC on top and a TGO between the two layers. Alongside the experimental studies a FEM model was developed to calculate the stress distribution inside the system [1]. The simulation permits the identification of compression and tension areas which are established by the growth of the oxide layer and the stresses which occur during the heating and cooling processes. Furthermore, a 2-dimensional finite element model of crack propagation in the model system was developed in which the crack direction is calculated by using short test cracks in different directions. The direction of the crack in the coating system is defined as the crack direction with the maximum energy release rate [2, 3]. The simulated stress distributions and the obtained crack path provide an insight into the possible failure mechanisms in the coating and allow to draw conclusions for optimising real thermal barrier coating systems. KEYWORDS Plasma spraying, Thin films, Thermal barrier coating, Failure mechanism, Finite element analysis INTRODUCTION Thermal barrier coating system are used on turbine blades in gas turbines. They are used on top of the highly stressed nickel-based substrates in the combustion chamber and protect the substrates from the 1400◦ C hot gas temperature. A standard coating system consists of a nickel-based substrate and two additional layers: the metallic bond-coat (BC) and the ceramic thermal barrier coating (TBC). A third layer is formed in service between the TBC and the BC: the so called thermally grown oxide (TGO). Oxygen diffuses 1
through the TBC due to the high porosity of the TBC and the high ionic diffusivity of oxygen in zirconia [4, 5]. The coating system fails in service because of the growth of the TGO, the interfacial roughness [6], creep processes, sintering processes in the TBC, the complex load conditions [5] and stresses in the coating which are induced by the mismatch of the thermal expansion coefficient of all layers [1, 6]. A model system was developed which reduces the influence parameters of the coating system. The model system consists of a MCrAlY bulk material Fecralloy which is in this case used as the substrate. Fecralloy consists of 72.8 wt % iron, 22 wt % chromium, 5 wt % aluminium, 0.1 wt % yttrium, and 0.1 wt % zirconium. The model system allows to study the creep influence of the BC material itself by using different MCrAlY bulk material. Therefore, a second substrate was used in the model system: MA956 as a slow creeping oxide-dispersion-strengthened (ODS) material. The Y2 O3 partially stabilised plasma sprayed zirconium dioxide TBC is applied by atmospheric plasma spaying directly to the substrate. Therefore, the failure mechanisms in the BC and TBC can be studied without the influence of the nickel-based substrate. The TGO grows between the substrate and the TBC in the model system. Different FE models are developed to study the failure mechanism of the model system and to compare it with a standard nickel-based coating. The crack growth in the coating systems takes places at the end of the cooling time [7]. Therefore, cooling simulations were performed with a varied initial TGO-thickness to study the influence of the TGO. The results are compared with a standard nickel-based system shown in [1, 6]. Furthermore, a failure model was generated to examine the path of the crack inside the coating system near the TBC/TGO interface. The coating fails likely near or directly at this interface. The crack propagates without determining the crack path in advance. FEM MODEL The geometry is based on [1, 6] and is almost identical to the model described in [8]. It was calculated with the ABAQUS finite element code. Fig. 1 shows a sketch of the model. It consists of CAX8RHT elements with a quadratic approximation. The TGO influence is studied by varying the initial TGO thickness between 1 µm and 7 µm.
Figure 1: Sketch of the FEM model with the valley and the peak positions.
The substrate/TGO interface and the TGO/TBC interface, respectively, are approximated with a sinusoidal shape. The thickness of the TGO is constant at every point normal to this interface. The FEM model is axially symmetric and contains symmetric boundary conditions to generate a fully periodic sinus interface. 2
The analysis of the stresses was performed at prominent positions at the interface (valley and peak positions in Fig. 1). The discussed stress values at this positions are the mean values of the radial stresses σ11 in the selected elements at the integration points. The measured parameters of the substrate materials Fecralloy and MA956 are shown in Tab. 1. The material parameters of the TGO and the TBC can be found in [6]. It was not possible to measure the creep properties at 1000◦ C of thin layers like the TBC and TGO. Therefore, a parameter variation was performed. The slow and fast creep parameters of these layers can also be found in [6]. 20◦ C
Young’s modulus E, [GPa] Young’s modulus E, 1000◦ C [GPa] ν, 20◦ C ν, 1000◦ C α, 20◦ C [K−1 ] α, 1000◦ C [K−1 ] density ρ [kg/m3 ] creep activation energy Q [kJ/mol] creep exponent n [-] creep prefactor A0 [MPa−n s−1 ] creep factor a [K−1 ]
nickel-based 184 145 0.30 0.30 1.2 × 10−5 1.6 × 10−5 7.65 × 103 -
Fecralloy 148.6 81.7 0.30 0.33 1.11 × 10−5 1.46 × 10−5 7.1 × 103 486 5.29 1.72 × 10−10 -0.012
MA956 148.6 81.7 0.30 0.33 1.11 × 10−5 1.46 × 10−5 7.1 × 103 depends on σ (∗) depends on σ (∗) depends on σ (∗) depends on σ (∗)
Table 1: Material parameters of the nickel-based alloy Fecralloy and MA956. (∗) The creep parameters of MA956 depend on the current stress (see Tab. 2).
σ < σts1 σts1 < σ < σts2 σ > σts2
A0 [MPa−n s−1 ] 78.978 3.466 × 10−124 8.68 × 1016
n [-] 4.9827 41.0 5.2911
Q [kJ/mol] 453 453 486
a [K−1 ] 0.0 0.1 −0.0122
Table 2: Creep parameters of MA956, eq. (1). The creep rate in the TBC and in the TGO was calculated with a Norton creep law ε˙ = Aσ n . The creep rate of Fecralloy and MA956 is calculated by Q ·σ n (1) ε˙ = A0 · exp(aT ) · exp − RT {z } | A
with the activation energy Q, the creep exponent n and an additional factor a (Tab. 1). The creep parameters Q, A0 , n, and a are fitted values obtained from experimental creep tests. The creep behaviour of MA956 is characterised by two temperature dependent threshold stresses σts1 and σts2 . They divide the validity of the creep parameters in three ranges (Tab. 2). The different threshold stresses are due to the dispersed Y2 O3 particles which form obstacles to the dislocation movement. Dislocation can detach from the obstacles at the threshold stress. This complex behaviour was approximated by fitting different creep parameters [9]. The threshold stresses are calculated 3
(a) Fecralloy model.
(b) Nickel-based model.
Figure 2: Radial stresses σ11 in the TBC after cooling from 1000◦ C to room temperature of Fecralloy and nickel-based model. Initial TGO thickness: 3 µm. during the simulation by equating two equations (1) with the different creep parameters, e.g. the first threshold stress is defined by 1 A1 n2 −n1 . (2) σts1 = A2 A1 (A0 , Q, a, R, T ) and n1 are the parameters in the range σ < σts1 , A2 (A0 , Q, a, R, T ) and n2 are the parameter in the range σts1 < σ < σts2 , respectively (Tab. 2). SIMULATED COOLING STRESSES The model is isothermal in all layers of the coating system from 1000◦ C to room temperature (24◦ C). It is supposed that the whole model is in a stress free state at 1000◦ C because all stresses are relaxed at high temperature, which is an appropriate assumption [7]. The cooling time from 1000◦ C to 24◦ C is 60 s (cooling rate: ∼16 Ks−1 ). The model was simulated with different creep properties: An elastic simulation without creep and a simulation with creep in all layers. A standard nickel-based system, including a MCrAlY BC, was compared with the Fecralloy and MA956 model system. Elastic simulation In order to study the cooling process systematically, initially all layers were modelled with elastic material behaviour. The cooling stresses of a standard nickel-based substrate and the simplified Fecralloy model system were simulated with varying initial TGO thicknesses which are constant for the whole simulation. MA956 was not taken into account in the elastic simulation, because the elastic properties are equal to Fecralloy 1. Fig. 2 shows the distribution of stresses for the simulated coating systems with a TGO thickness of 3 µm. The distribution of stress is similar in both simulations. There are compressive stresses in the peak and tensile stresses in the valley. However, the maximum tensile stress is not in the valley position in the nickel-based model, but in the middle of the sinusoidal interface. 4
(a) BC or substrate stresses, respectively
(b) TBC stresses
Figure 3: Radial stresses against the TGO thickness at prominent positions (Fig. 1). This difference can be explained by plotting the stresses at prominent positions (Fig. 1) against the TGO thickness (Fig. 3). Every data point represents an independent simulation in which the geometry was created for every initial TGO thickness. The stresses inside the BC of the nickelbased model are significantly higher than the stresses inside the Fecralloy substrate. This can be explained as follows: the Young’s modulus of MCrAlY is significantly larger than the Young’s modulus of Fecralloy. An elastic simulation is strain controlled and for this reason larger stresses are expected. On the other hand, the thermal expansion coefficient of Fecralloy is lower, which results in lower thermally induced stresses. The larger stresses inside the TBC in the Fecralloy model in Fig. 2 are caused as follows: in absence of the TGO, the thermal contraction of Fecralloy causes tensile stresses in the peak and compressive stresses in the valley. The thermal contraction of the TGO on the other hand leads to compressive stresses in the peak and tensile stresses in the valley. If the stresses caused by the BC or by the substrate respectively decrease, the TGO induced stresses will dominate the coating system, even at low TGO thicknesses [6]. The TBC stresses in both models converge with increasing TGO thickness, because the influence of the TGO overlays that of the substrate. Hence, the influence of a growing TGO affects and dominates the distribution of stresses in the TBC. The shift in the stress state (from compression to tension and vice versa) at lower TGO thicknesses and larger cooling stresses in Fecralloy point to a lower critical TGO thickness and an earlier failure of Fecralloy samples compared to a standard nickel-based coating system. This matches experimental results, in which a spallation occurs at a TGO thickness of 5 µm in the Fecralloy model system. A nickel-based system fails at a TGO thickness of approximately 10 µm. Creep in TBC, TGO and the substrate As a second step, the influence of creep in all layers of the coating system was taken into account. Furthermore, creep was activated in the substrate of the model system. Creep in the nickel-based substrate was neglected, because an influence would only occur at the substrate/BC interface. 5
(a) slow/slow creep in TBC/TGO.
(b) fast/fast creep in TBC/TGO.
Figure 4: Creep in TBC, TGO, MCrAlY BC in the nickel-based model and the substrate in the model system. Fig. 4 shows the stresses at the TBC/TGO interface of the Fecralloy, the MA956 and the nickelbased model. The creep properties were chosen as combinations of slow/slow creep and fast/fast creep in the TBC/TGO [6]. The creep in the substrate of the model system can be neglected at high TGO thickness, because the TGO dominates the stresses. The shift in the stress state from tension to compression in the valley occurs in MA956 and Fecralloy at lower TGO thicknesses compared with the nickel-based model. This result could also be found in the elastic simulation. This confirms the thesis that there is a smaller critical TGO thickness in MA956 and Fecralloy compared to the nickel-based substrate. CRACK PROPAGATION The model with a iterative crack propagation in the TBC is based on the simulations in [2, 3, 10]. The new crack angle of every iteration is calculated by choosing the direction of the maximum energy release rate by using trial cracks in different directions. The crack can only propagate if the energy release rate exceeds a critical value (Gc = 75 J/m2 ). If the released energy falls below that critical value, the crack will stop and a full thermal cycle is simulated (heating 1 min; dwelling 160 min, 1000◦ C; cooling 1 min) while the TGO grows which leads to different stresses caused by the growing influence of the TGO [8]. The model is in a stress free state at room temperature before the first thermal cycle starts. The initial TGO thickness is 0.5 µm. The TGO growth was simulated by anisotropic swelling of the whole TGO with a 10 times larger growth rate normal to the interface compared with the direction parallel to the interface [1]. A Tammann law was used to calculate the growth rate [11]: s˙ =
1 kp0 · 2 s2
(3)
with the current TGO thickness s, the parabolic oxidation constant kp0 and the growth rate s. ˙ The 6
parabolic oxidation constant of this simulation is kp0 = 1.5 × 10−17 m2 /s which describes the oxidation kinetics of α-Al2 O3 at 1000◦ C. The growth rate was calculated once at the beginning of every thermal cycle and is constant for this cycle. The following creep parameter of the TGO and the TBC are used: the creep exponent is n = 1.0 and the creep prefactor is A0 = 10−16 MPa−1 s−1 in both materials with a creep activation energy of QT GO = 408 kJ/mol and QT BC = 244 kJ/mol. The initial crack starts at the peak position 0.2 µm above the TGO/TBC interface (Fig. 1). Gc = 75 J/m2 . The trial crack length is l = 0.75 µm in every step.
Figure 5: Propagated crack in the TBC with the released energy.
The crack growth can be divided into two regions: an increasing energy release rate from the beginning of the crack growth up to l = 5 µm, and a range starting with a decreasing energy release rate from l = 5 µm to the end (Fig. 5). The energy release of the first crack iteration (Fig. 5, l = 0.75 µm) is lower than the critical energy release rate. This incipient crack was introduced in the model as the crack seed. The energy release is bigger than the critical energy release after the TGO grows to 1 µm (after 4 thermal cycles). The crack propagates after 4 cycles and does not stop. It may stop at l = 7 µm if Gc is larger than 100 J/m2 . The crack propagates in mode II in region 1 (Fig. 5). Therefore, tension areas in the stress state are not necessary to drive the crack. On the other hand, the crack opens in region 2 by normal stresses. Friction was not taken into account in this simulation and may be the next step to refine the simulation. Dissipating energy at the crack face may stop the crack. If the crack stops, than it can propagate again if the TGO grows and therefore higher TGO induced stresses can be found near the TBC/TGO interface.
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CONCLUSION A model system of a TBC was presented in which the creep parameters of the BC material can be easily adjusted. Simulations were performed to compare this system to a standard nickel-based thermal barrier system. It was shown that the stresses in the model system are in the same order of magnitude as in nickel-based standard thermal barrier coatings, but the model system may fail at a lower critical TGO thickness. Varying the creep parameters show that creep plays only a minor role in the cooling process. The growth stresses of the TGO and the stress relaxation plays an important role if the temperature was held at 1000◦ C, which was examined in the model system in [8]. A method of calculating crack propagation using trial cracks has been presented for the model system. The crack propagates partially in mode II and cannot stop in the system. This contradicts the considerations of Freborg et al. [12] in which cracks stop in regions of compression. This may change if the energy can dissipate at the crack face. REFERENCES ¨ ¨ [1] Rosler J, Baker M and Aufzug K 2004 Acta Materialia 52 4809–4817 ¨ [2] Baker M 2008 Computational Materials Science 43 179–183 ¨ [3] Baker M 2009 Proceedings of Crack Propagation 2009, Vicenza [4] Fox A C and Clyne T W 2004 Surface and Coatings Technology 184 311–321 [5] Padture N P, Gell M and Jordan E H 2002 Science 296 280 – 284 ¨ ¨ [6] Baker M, Rosler J and Heinze G 2005 Acta Materialia 53 469–476 [7] Trunova O, Bednarza P, Herzog R, Beck T and Singheiser L 2008 International Journal of Materials Research (formerly Zeitschrift fuer Metallkunde) 99 1129 ¨ ¨ [8] Seiler P, Baker M, Beck T, Schweda M and Rosler J 2009 Fem simulation of tbc failure in a model system proceedings 15th International Conference on the Strength of Materials (ICSMA-15), submitted [9] Herzog R, Schuster H, Schubert F and Nickel H 1994 Mikrostruktur und mechanische Eigenschaften der Eisenbasis-ODS-Legierung PM2000 Tech. rep. ¨ [10] Baker M 2009 Computational Materials Science 45 680–683 [11] Burgel R 2001 Handbuch Hochtemperatur- Werkstofftechnik 2nd ed (Braunschweig/ Wies¨ baden: Vieweg) [12] Freborg A M, Ferguson B L, Petrus G J and Brindley W J 1998 Material Science and Engineering A245 182–190 ∗ Corresponding
author:
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