Life Estimation and Creep Damage Quantification of Service Exposed Reformer Tube

Microstructure evaluation

Scanning Electron Micrographs in secondary electron mode Figure 1(a)–(d) of as received service exposed tubes did not exhibit any sign of degradation including voids or creep cavitation and decarburization. Both the top and bottom portions of the reformer tube revealed a columnar type of microstructure (Figure 1(a) and (d)). Basically two types of carbides are revealed in the EDX analysis – (a) Cr₂₃C₆ and (b) niobium-rich carbides as intra-dendritic carbides (light grey ones), with presence of some nickel and silicon in it (Figure 1). They are primary carbides. Nb-rich carbides appear to be coarsened and coagulated. Thus, one could see various morphology of the precipitates in the intra-dendritic region.

Figure 1:

SEM micrograph revealing microstructure of as received top and bottom portions of the reformer tube with EDAX analysis of Cr- and Nb-rich precipitates.

Formation of coarse carbides at dendritic boundaries in the bottom region of the tube was mainly due to overheating with gradual disappearance of fine intra-dendritic precipitates as well [9] (Figure 1). Due to ageing, these carbides would coarsen and gradually shape themselves as worm [9].

Hot tensile and conventional creep tests of service exposed reformer tubes

From the hot tensile strength data, creep loads at 870°C were selected in the range of 50–68 MPa. Hardness [8] and ultimate tensile strength results (Figure 2(a) and (b)), particularly for the bottom portion of the tube when compared with the standard NRIM data of similar grade of steel [10], have clearly indicated that the material has become softened due to prolong ageing. This observation could be correlated with formation of coarse carbides at dendritic boundaries with gradual disappearance of fine intra-dendritic precipitates as well at the bottom portion of the tube (Figure 1). Room temperature as well as high temperature ductility of both the bottom and top portions of the service exposed reformer tubes were in any case lower (Figure 2(a) and (b)) than that of the standard NRIM data of similar grade of steel (i.e. vigin material) [10], which is normally expected for prolong service-exposed materials.

Figure 2:

Graphical representation of tensile data of the top and bottom portions of service exposed primary reformer tube as compared with the NRIM virgin data: variation of (a) yield strength, (b) ultimate tensile strength, (c) % elongation and (d) % reduction in area with test temperature.

Conventional creep curves of the service exposed reformer tubes at stress levels 50–68 MPa/870°C (Figure 3(a)–(h)) and as well as their corresponding creep strain rate curves (Figure 3(i)–(p)) clearly exhibit substantial amount of scatter in creep deformation and absence of the primary creep (stage I) region in the scatter creep curves. It should be noted that no valid service history records were available for the individual tubes; thus, it is possible that the current test samples were machined from tubing which was replaced during an earlier shut-down of the refinery, i.e. 5 years ago.

Figure 3:

(a–d) Scatter creep curves at 870°C and at various stress levels of 11 years service exposed primary reformer tubes (top region); (e–h) Scatter creep curves at 870°C and at various stress levels of 11 years service exposed primary reformer tubes (bottom region); (i–l) Creep strain rate curves at 870°C and at various stress levels of 11 years service exposed primary reformer tubes (top region); (m–p) Creep strain rate curves at 870°C and at various stress levels of 11 years service exposed primary reformer tubes (bottom region).

An atlas of fractograph of the crept specimens (service exposed top as well as bottom portion) of the reformer tubes is exhibited in Figure 4. It is clearly seen that even though samples were crept under identical stress-temperature condition, mode of rupture appears to be different. Similar kind of observation was found by Garofalo et al. [4] and Roy et al. [11]. The creep ruptured surfaces as shown in (Figure 4(c), (e), (g), (k), (p)) had undergone considerable amount of oxidation. Detailed fractographic analysis indicated that whatever variation in the mode of fracture one observes, it could be only due to the influence or effect of oxide scale formation (Figure 4(e), (i), (g), (k)) because all creep tests were conducted in oxidizing atmosphere, i.e. in air. Due to considerable amount of oxidation, the effective cross-section area required for load bearing capacity of the crept specimen actually decreases, and this leads to catastrophic rupture with shear mode. Crept samples of top portion of the tube ruptured in a relatively brittle manner with 16.4% elongation. Bottom portion of the tube ruptured showed a quasi cleavage fracture with 17% elongation (see Figure 4(c), (d), (g), (k), (o), (p)) and it also shows brittle failure with cleavage facets (see Figure 4(g), (o), (p)) respectively. On the other hand, it is noteworthy that in the top section (Figure 4(a),(b),(f),(i),(j),(n)) and the bottom section (Figure 4(d),(h),(l)) of the tube, ductile dimples were also seen.

Figure 4:

Fractograph of crept service exposed specimens (both top and bottom portion of the tube) tested at 870°C in the stress range of 52–68 MPa.

Quantification of creep cavities after rupture of service exposed reformer tubes

Population of voids (appearing grey) at various stresses and strains is shown in Figure 5. The population of void cavity on the creep ruptured surface was found to be nucleated either at grain boundary (GB) or at grain boundary triple point (GBTP) predominantly and also in the vicinity of other carbide particles. A similar kind of metallographic technique was employed to measure the extent of martensite at various strain reported elsewhere [12], which is already well established.

Figure 5:

Extent of creep cavity at various stresses and strains (a, c, e, g, i, k) – 50 MPa and (b, d, f, h, j, l) – 68 MPa for the top tube. True strain at (a) 1.187, (c) 0.897, (e) 0.626, (g) 0.525, (i) 0.398 and (k) 0.359. (b) 0.781, (d) 0.652, (f) 0.565, (h) 0.40, (j) 0.244 and (l) 0.149 [8].

It was found that the probability of GBTP cavitations [8] was almost three times that of GB voids (Figure 6) where the initial inclusion volume fraction in all the specimens remained unaltered. Void distribution at GB and GBTP was inhomogeneous in the deformed austenite dendrites. After nucleation of the voids, the voids would align themselves and grow under the influence of favourable tensile stress and plastic strain. Eventually the voids would join up leading to final rupture in the tertiary region of the creep curve.

Figure 6:

(a) Number of creep cavity formation at GB and at (b) GBTP as a function of strain for all stress levels for both the top and bottom tubes together [8].

Prediction of remnant life of the service exposed reformer tubes

It was clearly revealed in Figure 1 that creep cavitation or voids in the as received (uncrept) tubes were not present and so it is realistic to obtain a residual life of 10 years (Table 1, Figure 7) for both the top and bottom portions of the reformer tubes only if there is no deterioration or localised damage in any form in the material due to prolong service exposure. NRIM stress rupture data of similar grade of steel [10] have been super imposed on the stress rupture plots (Figure 7) for the sake of comparison with the accelerated creep rupture or stress rupture data and for estimation of residual life of the tubes in the present scope of work. Nevertheless, it was evaluated from Figure 7 that, at the design temperature of 920°C/13.46 MPa, a balance life of 7 years and 6 years for the top and bottom portions of the 11 years service exposed primary reformer tubes respectively would be possible (Table 1). This is true only when there is no localised damage of any form in the material, as revealed from non-destructive evaluation method of testing. Similar health check for safety and economical reasons of the operating tubes, in terms of residual life is required after a period of about two and a half years of further service life.

Figure 7:

Stress vs LMP Plot for 11 years service exposed Reformer tube materials (a) top and (b) bottom for comparison with –20% NRIM standard data line.

Statistical analysis of creep cavity area for service exposed reformer tubes

Nucleation and growth of voids or creep cavities are responsible for creep damage. Nucleation is a random process and is deterministic, whereas growth of voids is probabilistic. The type and distribution of cavities during various stages of creep strain in a high temperature component is schematically represented in Figure 8. Most of the creep data reported for steels have focused only on experimental research with a view to examining the effect of microstructure on void formation. Void nucleation is strongly dependent upon the local stress-state and strain-state. It has been observed that over various test conditions, for the both top and bottom portions of tube, the normalised void area fraction (vf/ε) follows the Weibull distribution. In terms of true strain (ε) and cumulative probability of failure P_f, void area fraction (v_f) can be probabilistically estimated as [13]:

where a and b are Weibull parameter.

Figure 8:

A schematic representation of the nature of damage evolution in material subjected to creep loading and the phases used to represent the same.

The probability of failure due to void area at various strain is calculated using eq. (7). From statistical point of view, the pattern of Weibull distribution (Figure 9) followed for analysing probability of rupture due to cavity or void area shifts with increase in true strain towards the higher population of void.

Figure 9:

Probability distribution of void area fraction at 870°C/56 MPa: (a) top and (b) bottom portion of service exposed reformer tube, at various true strain.

Deterministic approach: CDM model for creep damage of service exposed reformer tubes

Kachanav [14] CDM model (K-model) has been used to estimate creep damage. The model is well established and has been applied to analysis of accumulation of creep strain data for 11 years service exposed reformer tube (both top and bottom portions) for different stresses at 870°C in the present investigation. Nucleation of voids/cavities being deterministic, the scatter band in damage estimation under identical test conditions can be easily estimated by carrying out a Monte Carlo Simulation. Similar simulation study was carried out on service exposed P22 grade of steel [15] and austenitic stainless steel [16].

According to Cane [17], a creep damage (ω) relationship can be established for estimating the creep life fraction already utilized with respect to time, t and at constant stress conditions:

where λ is creep damage tolerance factor (l=εr/ε˙mtr) [18–20].

Strain rate accumulation can be estimated [14–16] during the entire tenure of creep life by introducing ω. Estimation of damage (ω) from eq. (5) is then made at the limiting conditions, (i.e. at ω = 0;t = 0 and ω = 1; t = t_r) from the following equation [14–16]:

A and n are material constants. The value of ω can be calculated from eq. (9), as experimentally calculated (Exp) data as shown in Figure 10. Similar predictions on a recent work pertaining to service exposed P22 grade of steel [15] were made.

Figure 10:

Comparison of the experimental and predicted values of mean time to reach a specified damage state by CDM (K-model) and B-model approach with relative confidence interval (CI) at 870°C/56 MPa: (a) top and (b) bottom portion of service exposed reformer tube.

Experimental data for estimating ω, agrees well with simulation-based CDM model for estimation of damage with scatter associated with it. This pertains to the sudden changes in creep damage in the tertiary region as well (Figure 10).

Stochastic approach: Markov process for creep damage of service exposed reformer tubes

Growth of voids/cracks is probabilistic. Cumulative damage process is the accumulation of voids and microcracks inside the material. Figure 8 gives a schematic representation of the various stages of nucleation and joining of voids/cavities leading to rupture at different levels of accumulation of strain. During creep, a virgin material goes through each of the stages represented in Figure 8, before rupture occurs. The process of accumulation of damage during creep depends only on its current state. Therefore, it was possible to simulate this by a Markov chain process [16, 21] which is defined as a stochastic process satisfying the following condition:

Similar study was carried out for an austenitic stainless steel and is reported and discussed in details in [16]. S_n represents nth event and the indices i, j, k, etc. represent the state number. The process of void growth is irreversible. In other words, if it is in state S_i it cannot move to S_j where j < i. State 1 indicates the initial state with no damage and state b indicating the final damage state (rupture or failure state) or the absorbing state. Leckie and Hayhurst [20] have defined the initial distribution of the different damage levels at time t = 0, by a (1 × b) row vector p_o:

Probability of moving to state 3 and beyond is zero. Accumulation of creep damage in a material is represented by a transition matrix P [21, 22], (refer to Appendix for details).

All states in the transition matrix P are transient, except for state b (absorbing state). Bogdanoff and Krieger [22] had suggested a simple procedure for estimating these elements to simulate fatigue damage evolution. The same procedure [22] had been used in this work as B-model to predict creep damage evolution as a function of time.

Comparison of the experimental and predicted values of mean time to reach a specified damage state by CDM (K-model) as well as B-model approach with relative confidence interval (CI) of 99% at 870°C/56 MPa: (a) top and (b) bottom portion of service exposed reformer tube is revealed in Figure 10. This indicates or depicts that both the predictions are in close agreement with that of experimental data and can describe the sudden changes of damage associated with creep in the tertiary region as well.