Effect of thermomechanical processing on the creep ...boehlert/GROUP/publications/ourphilmag2008pa… · temperature or dislocation substructure changes that occur during interrupted

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Philosophical Magazine

Vol. 88, No. 5, 11 February 2008, 641–664

Effect of thermomechanical processing on the creep

behaviour of Udimet alloy 188

C.J. Boehlert*, S.C. Longanbach and T.R. Bieler

Department of Chemical Engineering and Materials Science, Michigan State University,East Lansing, MI 48824, USA

(Received 26 June 2007; final version received 16 January 2008)

Udimet alloy 188 was subjected to grain-boundary engineering involvingthermomechanical processing in an attempt to improve the creep performanceand determine the effects on creep deformation processes. The as-receivedsheet was cold-rolled to either 10, 25 or 35% reduction per pass followed by asolution treatment at 1191�C for 1 h plus air cooling. This sequence wasrepeated four times and the resultant microstructure and grain-boundarycharacter distribution were described using electron backscatter diffraction.The fraction of general high-angle grain boundaries tended to increase withincreased cold rolling. The 10 and 25% cold-rolled materials exhibited lowercreep rates than the 35% cold-rolled material. The measured creep stressexponents and activation energies suggested that dislocation creep with latticeself-diffusion was dominant at 760�C for stresses ranging between 100 and220MPa. A transition in the creep exponent below the applied stresses of100MPa indicated that a different secondary creep mechanism was rate-controlling at low stresses. A significant amount of grain-boundary crackingwas observed both on the surface and subsurface of deformed samples,but surface cracks were greater in number and size than those within the bulk.The cracking behaviour was similar in both vacuum and air environments,indicating that grain-boundary cracking was not caused by environment.To assess the mechanisms of crack nucleation, in situ scanning electronmicroscopy was performed during elevated-temperature (T� 760�C)tensile-creep deformation. Sequential secondary electron imaging and electronbackscatter diffraction orientation mapping were performed in situ to allow theevolution of crack nucleation and linkage to be followed. Cracking occurredpreferentially along general high-angle grain boundaries and less than 15% ofthe cracks were found on low-angle grain boundaries and coincident site latticeboundaries. A fracture initiation parameter analysis was performed to identifythe role of slip system interactions at the boundaries and their impact on cracknucleation. The parameter was successful in separating the population of intactand cracked general high-angle boundaries at lower levels of strain, but notafter crack coalescence dominated the fracture process. The findings of thiswork have significant implications regarding grain-boundary engineering ofthis alloy and potentially for other alloy systems.

Keywords: microstructure; creep; electron backscatter diffraction

*Corresponding author. Email: [email protected]

ISSN 1478–6435 print/ISSN 1478–6443 online

� 2008 Taylor & Francis

DOI: 10.1080/14786430801944836

http://www.informaworld.com

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1. Introduction

The development of superior-strength materials used in high-temperature applications

is necessary for the continued improvement of turbine engine systems. Udimet

alloy 188 (also known as Haynes Alloy No. 188) is a commercially available

cobalt–nickel–chromium–tungsten alloy with good creep strength and oxidation resistance

up to 1093�C. The high chromium content produces a corrosion-resistant scale. The alloy

also has good fabricability, tensile strength and elongation-to-failure ("f), weldability,

low-cycle fatigue resistance and corrosion resistance [1–6]. Despite its use in gas turbines,

combustors, flame holders, liners and transition ducts, only a limited number of studies

have examined how processing affects the microstructure and creep behaviour of Udimet

alloy 188 [4, 5, 7, 8].Klarstrom [7] found that strongly textured recrystallized sheets gave a significant

improvement in the low-strain creep strength over baseline untextured sheets. The

thermomechanical processing (TMP) that gave optimum results consisted of 80% final

cold work followed by an anneal at 1232�C for 10min. The major components of the

texture resulting from this TMP schedule, with respect to the plane of the sheet and the

rolling direction, were identified as (110) [–110] and (112) [–110]. Typical dislocation

structures in baseline untextured sheets consisted of tangles produced by the intersection

and reaction of glide dislocations plus pileups at grain boundaries and relatively large

carbide particles. Whittenberger [4,5] stated that the measurable changes in the creep

behaviour of Udimet alloy 188 are ascribable to thermal-ageing effects rather than

corrosion in air or LiF–22CaF2 environments. From these limited studies, it is evident that

a complete understanding of the physical mechanisms responsible for the elevated-

temperature creep behaviour and associated microstructure–property relationships is

lacking. In particular, it has yet to be established if this alloy can be thermomechanically

processed to significantly alter the grain boundary character distribution (GBCD, the

fraction of each type of boundary found in a microstructure), which has proven to have a

significant influence on the mechanical deformation, creep behaviour and corrosion

resistance of other fcc-based superalloy systems [9–25]. Thus, there is the potential to

improve performance using grain-boundary engineering strategies.Grain-boundary engineering, as first described by Watanabe [26], is the process of

altering the GBCD through TMP. The types of boundaries are characterized as general

high-angle boundaries (GHAB), low-angle boundaries (LAB, less than 15� misorientation)

and coincident site lattice boundaries (CSLB or R). The GBCD is related to the spatial

configuration of these boundaries and the connectivity of the boundary network

[10,22,27]. Lehockey and Palumbo [21] have shown that a high fraction of

LABsþCSLBs (termed special boundaries) significantly enhances resistance to creep of

pure nickel at elevated temperature. In their study, they performed post-deformation

electron backscattered diffraction (EBSD) analysis on samples deformed in creep which

exhibited grain boundary voids and cavitation. They stated that the voids appeared almost

exclusively along GHABs. If the boundaries maintain the same misorientation throughout

the deformation process, e.g. when grain boundary sliding is dominant, this may be an

acceptable means to characterize the types of grain boundaries where voids have formed.

However, when dislocation creep mechanisms dominate, deformation within the grain

interior leads to grain rotations, so post-deformation assessment of grain boundary

misorientation only reflects the final state. Thus, effects of grain boundary misorientation

642 C.J. Boehlert et al.

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evolution on cavity formation are not known. Even slight changes in the grain orientations

across a grain boundary could change it from a special to a GHAB. Thus, it would bebeneficial to perform EBSD analysis on the microstructure before, during and after the

creep deformation.Despite the strong evidence that a high fraction of low-energy boundaries and a good

network percolation of low-energy boundaries are beneficial, the failure process does not

occur at low-energy boundaries, so it is important to examine how damage nucleates onhigh-energy GHABs that are more susceptible to cracking. In particular, it is desirable to

determine why cracks occur on some GHABs, but not others. A paradigm to examine thecause of damage nucleation in boundaries first introduced by Simkin et al. [28] and further

developed in subsequent papers [29–35] was used in this study to explore mechanisms fordamage nucleation in GHABs.

The ability to examine details of the GBCD without complications of stress,

temperature or dislocation substructure changes that occur during interrupted tests isenabled with recent progress in the development of in situ scanning electron microscopy

(SEM) techniques for understanding the deformation behaviour of materials. Use of ahigh-beam current and the stability of a hot Schottkey field emission gun (FEG), along

with the latest camera technology for rapidly obtaining high-quality electron backscatterdiffraction Kikuchi patterns (EBSPs) now enables a unique capability for imaging surface

deformation. It is possible to make unprecedented sub-micron resolved measurements ofthe local two-dimensional crystal-structure distribution in materials during high-

temperature tensile-creep deformation. This study describes the technique developed toacquire secondary electron images and EBSD orientation maps in situ during tensile-creep

deformation at temperatures as high as 760�C.

2. Experimental

Strain annealing and TMP are well established methods for altering the GBCD [9,10,27].

One approach for altering the GBCD involves imposing small strain increments on theorder of 6–8% followed by annealing to cause grain boundaries to migrate towards lower

energy configurations [36]. Another approach involves moderate strain levels (�10–30%)followed by short high-temperature anneals [10,22,27]. The latter approach was used in this

work, where the Udimet alloy 188 sheet material (composition listed in Table 1) was coldrolled to either 10, 25 or 35% reduction followed by a solution treatment at 1191�C for 1 h

followed by air cooling. It is noted that 1191�C is above the recrystallization temperature forUdimet alloy 188 based on previous findings [6]. This sequence was repeated four times. The

original thickness of the as-processed sheet was 8.4mm, while the final thicknesses of the 10,25 and 35% cold-rolled sheets were 5.5, 2.8 and 1.7mm, respectively.

Each processed sheet was sectioned and metallographically polished before spatially

resolved EBSD orientation maps were obtained using hardware and software

Table 1. Measured composition of the Udimet 188 alloy in wt%.

Co Ni Cr W Fe Mn Si C Al Mo

36.8 24.2 22.1 12.0 2.5 1.0 0.4 0.1 0.1 0.4

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manufactured by EDAX-TSL, Inc (Mahwah, NJ, USA). The specimens were ground

mechanically using 15, 6 and 1 mm diamond suspension for 20min, respectively, and then

polished using 0.06-mm colloidal silica for 60min. The step size used to obtain the EBSD

orientation maps ranged between 0.5 and 2 mm and over 500 grains were typically analyzed

per orientation map. The GBCD was assessed with LABs defined as having 2–15� of

misorientation. Brandon’s criterion [37] was used to distinguish between GHABs and

CSLBs. Measured fractions of GHABs, LABs, CSLBs and twins (R3) were averaged from

several orientation maps, performed on the cross-sections, rolling faces or longitudinal

sections of the TMP sheet materials. Tensile specimens were machined from the TMP

sheet materials using either electrical discharge machining (EDM) or conventional milling

with the tensile axis along the rolling direction.Room-temperature (RT) and 760�C tensile tests were performed at a strain rate of

10–3/ s using a servohydraulic testing machine described elsewhere [38]. Strain was

measured during the tensile tests with an extensometer attached directly to the gauge

section of the sample. In some cases, up to three experiments were performed and the

average values reported. Standard Vickers hardness measurements were obtained at RT,

where at least three measurements were made on each of the TMP microstructures and the

average values reported.Creep experiments were performed in air using constant-load vertical creep frames

(Applied Test Systems, Inc., Butler, PA, USA) with a 20:1 lever-arm ratio at temperatures

and stresses between 760–815�C and 25–220MPa, respectively. Specimen temperatures

were kept within 3�C of the target temperature in the gauge section and strain was

monitored using a linear variable differential transformer attached to a 25-mm gauge-

length high-temperature extensometer. The specimens were soaked at the creep

temperature for at least 1 h to establish thermal equilibrium prior to applying load.

After the creep strain had proceeded well into the secondary regime, either the load or

temperature was changed or the creep test was discontinued. The tested specimens were

cooled under load to minimize recovery of the dislocation substructure. Selected specimens

were taken to failure.Constant-load, in situ tensile-creep experiments were performed using a screw-driven

tensile stage built by Ernest F. Fullam, Inc. (Clifton Park, NY, USA) placed inside the

chamber of a SEM. The loading rate was 3.7N/s (50 lbs/min) and the desired load was

maintained within� 8N. Flat dog-bone-shaped samples, with gauge-section dimensions of

3mm wide by 2.5mm thick by 10mm long, were cut using EDM and the EDM recast

layers were subsequently removed by grinding. Images of the sample geometry and tensile

stage are available in [39] and details of this apparatus and testing technique can be found

elsewhere [40,41]. Polished samples were radiantly heated using a 6-mm diameter tungsten-

based heating element placed just below the gauge-section of the sample. The temperature,

monitored by a thermocouple spot-welded directly to the sample’s gauge-section, was

maintained within 7�C of the target temperature throughout the experiments. The samples

were held at temperature for 30min, prior to loading, to minimize the thermal stresses. The

load–displacement–time relationship was continuously monitored using MTESTW

version F 8.8e data acquisition and control software (Admet, Inc., Norwood, MA,

USA). The displacement values included the lag in the grip system at the beginning of the

experiments. As the pressure within the SEM chamber never exceeded 3� 10–6 Torr,

oxidation did not significantly affect the in situ secondary electron and backscatter


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electron imaging characterization. The experiments lasted up to 72 h and no phase

instability was observed during the experiments.At selected intervals during these experiments, images were obtained from the same

areas of the sample without interrupting the creep experiment. Although the samples were

not etched, grain boundaries were visible using secondary electron imaging at

temperatures above 600�C. For each processing condition, one experiment was performed

at T¼ 650�C and �¼ 300MPa, and the other experiment at T¼ 760�C and �¼ 220MPa.

At the least, EBSD orientation maps were acquired prior to and after the tensile-creep

deformation for the same areas of the sample. For selected samples, EBSD orientation

maps were acquired in situ at several intervals during the creep deformation for identical

areas of the sample without interrupting the creep experiment. This was accomplished

using a FEI XL-30 FEG SEM and tilting the SEM stage to approximately 66� with respect

to the incident beam. The working distance for this configuration was 29mm and a tilt-

correction feature was used to account for the foreshortening in the SEM images. The

EBSD detector was inserted to a distance of approximately 21mm from the centre of the

electron beam. The in situ EBSD orientation maps were acquired over a 200� 200-mm area

using a step size of 0.5-mm in 20min (approximately 140,000 points acquired with a speed

of approximately 150 points per second). The amount of displacement measured by the

testing assembly during this 20-min period was typically 7 mm; this small drift did not

significantly disturb the EBSD orientation mapping accuracy. The confidence of correctly

indexing the EBSPs was initially high (495% of the pixels confidently indexed) but, with

increased time and displacement, the EBSP quality decreased mainly due to development

of surface topography.

3. Results and discussion

This section describes how the TMP affected the microstructure and resulting tensile and

tensile-creep behaviour. After the creep properties are presented, a means to analyze and

model the grain-boundary cracking behaviour is presented.

3.1. Microstructure

The average equiaxed fcc grain size, which excluded twins, ranged from 25 to 50 mm

(10–23 mm including twins) depending on the amount of cold rolling (Table 2).

All microstructures exhibited a small amount (less than 5 vol%) of homogeneously

distributed fine spherical precipitates, believed to be M6C or M23C6 carbide precipitates

based on previous literature [6]. Figure 1 illustrates EBSD data for a 10% cold-rolled

Table 2. GBCD parameters and FCC grain size of the TMP sheets averaged from more than sixEBSD maps.

Cold rolling (%) GHABs CSLBs (R3) LABsGS excludingtwins (mm)

GS includingtwins (mm)

10 0.30 0.50 (0.39) 0.20 25 1325 0.35 0.53 (0.45) 0.12 50 2335 0.39 0.57 (0.45) 0.04 25 10


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microstructure. The orientation map (Figure 1a) shows that the alloy exhibited an

equiaxed microstructure and the orientations were distributed fairly evenly. Table 2 lists

the fractions of LABs, GHABs, CSLBs and R3 boundaries for each TMP

microstructure. Pole figure analysis (Figure 1b) indicated that the microstructures

were not strongly textured (approximately 2� random for all cases). The strongest

preferred orientation has a (111) pole close to the normal direction illustrated

in Figure 1b. A significant volume fraction of annealing twins was observed in

this microstructure, as evident in the orientation map (Figure 1a) and in the

misorientation histogram (Figure 1c). The fraction of twins, GHABs and CSLBs

tended to increase slightly with increased cold-rolling reduction while the fraction of

LABs tended to decrease. The maximum fraction of twins, which constituted the vast

majority of the CSLBs, was 0.45 in the 25 and 35% cold-rolled microstructures. If we

consider that the combination of the LAB and CSLB fractions constitute the overall

fraction of special boundaries, then the 10, 25 and 35% cold-rolled microstructures

exhibited special boundary fractions of 0.70, 0.65 and 0.61, respectively. The 10 and

25% cold-rolled microstructures also exhibited a slightly larger grain size than the 35%

cold-rolled microstructure. From the statistical percolation physics of 3-D grain-

boundary engineering, percolation along weak boundaries is possible if the special

boundary fraction is less than 0.78 [42]. Thus, the ability of a weak boundary to

percolate would be expected to diminish as the special boundary fraction approaches

this threshold.

Figure 1. (a) EBSD normal direction inverse pole figure orientation map from 10% cold-rolledmicrostructure. (b) Pole figures and (c) grain-boundary misorientation angle histogram for a 10%cold-rolled microstructure.


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3.2. Tensile behaviour

The RT tensile properties were similar for the 10 and 25% cold-rolled materials, while the

35% cold-rolled material exhibited the greatest yield strength, ultimate tensile strength and

hardness (Table 3). At 760�C, the 25% cold-rolled material exhibited the greatest strength

(Table 4). All samples exhibited elongations greater than 14% and ductile fracture

characteristics (Figure 2). No cracking was observed during the tensile experiments until

the samples achieved strains greater than 10%.

3.3. Creep behaviour

The creep experiments were used to analyze and identify the likely rate-limiting

deformation mechanisms and to identify how different cold rolling and annealing cycles

affect the performance. As failure was strongly affected by grain-boundary cracking,

the cause of this was examined using a slip system-based analytical crack nucleation

model.

3.3.1. Conventional creep experiments

The creep strain-time history was typical for metals, exhibiting primary, secondary and

tertiary stages of creep [43,44]. Figure 3 illustrates strain versus time plots for the TMP

materials at �¼ 220MPa and T¼ 760�C. The 10 and 25% cold-rolled materials exhibited

lower secondary strains and strain rates than the 35% cold-rolled material, and the 25%

cold-rolled sample was the most creep-resistant. The minimum creep strain rate–applied

stress–temperature relationship suggested that two different secondary creep deformation

mechanisms were active based on the different creep exponent (n) and apparent activation

energy (Qapp) values (Table 5). These parameters suggested that dislocation

creep controlled by lattice self-diffusion is the rate-controlling creep mechanism between

100 and 220MPa. Below 100MPa, the low-stress exponent suggests that grain-boundary

sliding may control the creep rate, based on creep theory for pure metals [43,45,46].

Table 4. 760�C tensile properties.

Cold rolling (%) YS (MPa) UTS (MPa) "f (%)

10 276 485 14.025 353 578 17.935 328 510 14.0

Table 3. Room temperature properties.

CR (%) YS (MPa) UTS (MPa) RT("f,%) Hardness (Hv)

10 1167 1435 20.7 43425 1193 1433 22.5 43235 1346 1496 17.0 460


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Figure 3. Creep strain versus time plots for the TMP specimens at T¼ 760�C and an applied stressesof �¼ 220MPa.

Figure 2. Secondary electron SEM image of the fracture surface for a 35% cold-rolled tensilesample, which exhibited ductile dimpling, tested at T¼ 760�C.

Table 5. Creep exponents and apparent activation energies.

CR (%) �/T(MPa/�C) n �/T (MPa/�C) Qapp (kJ/mol)

10 100–220/760 6.8 165/760–815 40225 100–220/760 6.5 165/760–815 45035 100–220/760 6.4 165/760–815 43235 25–100/760 2.5


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The 35% cold-rolled condition exhibited greater creep rates than the other TMP materials

at all the stresses and temperatures evaluated. The lower creep resistance of the 35% cold-

rolled microstructures is correlated with a smaller grain size and a lower fraction of special

boundaries, both of which could account for its lesser creep resistance [21].Creep rupture experiments were performed at T¼ 815�C and �¼ 165MPa and each

sample ruptured within 7 h of the other samples, as indicated in Table 6. There did not

appear to be a significant effect of TMP on the creep-rupture lives under this creep stress

and temperature combination. Grain-boundary cracking was observed on the faces of the

ruptured samples both near and away from the fracture surfaces, and these cracks

appeared at strains as low as 2% (Figures 4 and 5). There were no visible flaws or cracks

along the grain boundaries after TMP or at such low strains in hot tensile deformation, so

the cracks developed due to creep deformation. As the surface oxidized in air and similar

surface cracking was also observed in vacuum, as illustrated in Figures 4 and 5. This

implies that grain-boundary cracking was not due to environmental effects. As the cracks

surrounded shapes that were comparable to the grain shapes in Figure 1, it is clear that the

particles were not the primary cause of crack nucleation. Each of the ruptured samples

exhibited at least 20% elongation-to-failure and mixed-mode fracture features were

observed on the fracture surfaces (Figures 6a and b). A lesser extent of ductile dimpling

was observed compared to the 760�C tensile fracture surfaces (Figure 2) and there were

localized regions showing grain boundary facet fracture amidst the rather rough fracture

surface. EBSD orientation mapping, performed on the side of a creep rupture sample near

the fracture but beneath the surface due to grinding polishing (Figure 7), indicated

obvious grain-boundary cracking, but it occurred to a lesser extent than on the surface.

All of the grain boundaries that exhibited cracks were GHABs. However, as this

microstructure did not represent the pretest condition and because significant grain

rotations probably occurred (this was observed in the in situ experiments described next), it

was not clear whether these cracks developed in boundaries that were initially GHABs or

whether a special boundary became a GHAB with deformation. To gain a better

understanding of how crack nucleation and growth evolved, in situ tensile-creep

experiments were performed and the results of these experiments are described next.

3.3.2. In situ creep experiments

Grain-boundary cracking was observed for samples tested in both conventional creep and

in situ creep experiments, as evident in the SEM images in Figures 4, 5 and 6a, and in the

EBSD orientation maps in Figures 7 and 8. Figure 4 illustrates backscatter electron SEM

micrographs taken from the surface of in situ creep specimens tested at T¼ 650�C and

Table 6. Creep rupture time at T¼ 815�C,�¼ 165MPa.

Cold-rollingdeformation (%) Tr (h)

10 8825 9035 95


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Figure 5. Backscatter electron SEM EBSD orientation map of the surface, adjacent to the fracturesurface, of an in situ creep-tested 35% cold-rolled sample tested at 650�C and 300MPa. Comparingthis with the subsurface image of another creep ruptured sample (Figure 7), which exhibited a similarstrain-to-rupture (�20%), it is evident that the extent of cracking at the surface is greater than thatwithin the subsurface bulk. The loading axis was horizontal.

Figure 4. Backscatter electron SEM images of surface sections from in situ creep-tested samplesat 650�C and 300MPa: (a) 10%, (b) 25% and (c) 35% cold rolled. The loading direction washorizontal and each sample was taken to failure. Each sample had exhibited approximately 10%creep strain.


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�¼ 300MPa at strains near 10%, and Figures 5 and 6a show the surface near theruptured end of an in situ experiment. The grain-boundary cracks propagated bothperpendicular and parallel to the loading direction, though the widest cracks were onboundaries perpendicular to the loading direction. From these observations, it is clear thatgrain-boundary cracking is an important deformation and failure mode for this alloy.Figures 8a and b show EBSD orientation maps of identical areas before and after creepdeformation for a 35% cold-rolled specimen. Of the more than 20 boundaries thatappeared to be cracked, only one was a special boundary. This observation was confirmedon other samples. Figure 8c indicates an area imaged from another sample and again the

Figure 7. EBSD orientation map of a 25% cold-rolled sample creep tested to rupture at T¼ 815�Cand �¼ 165MPa. The specimen exhibited over 20% strain to failure. This area was from asubsurface polished section near the fracture surface. Substantial lattice curvature is evident in thecolour gradients within most grains. The loading axis was horizontal.

Figure 6. (a) Secondary electron SEM image of the fracture surface (left side) and cracked edgeadjacent to the fracture surface of an in situ creep tested 35% cold-rolled sample creep tested atT¼ 650�C and �¼ 300MPa. The loading axis was horizontal. (b) Secondary electron SEM image ofthe fracture surface of a creep ruptured 25% cold-rolled sample tested at T¼ 815�C and�¼ 165MPa, which exhibited a strain-to-rupture of approximately 20%. From a stereo image,flat terraces are clearly observed at tips of white arrows, indicating grain boundary decohesionperpendicular to the tensile axis (out of page). A grain boundary facet nearly perpendicular to thefracture surface is marked by the black arrow.


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vast majority of the cracked boundaries were GHABs. For the 35% cold-rolled condition,the original grain-boundary misorientation angles were measured for over 100 grainboundaries. Only five of the cracked grain boundaries were CSLBs or LABs, while all theother cracked grain boundaries were GHABs. This implies that twin boundaries, CSLBsand LABs are less susceptible to grain-boundary cracking than GHABs during creepdeformation of this alloy.

Figures 9–11 show images from a region in the centre of Figure 1 for a 10% cold-rolledsample tensile-creep tested in situ at T¼ 760�C and �¼ 220MPa. Figure 9 shows the areamonitored at two displacements, indicated in the lower right hand side of the images.Figure 10 shows an EBSD map prior to deformation from the same area, and the outlineof this scan is visible in the secondary electron image in Figure 9a. Figure 11 comparessecondary electron photomicrographs and EBSD image quality maps from the middle ofthe area shown in Figure 9. The strains noted in Figure 11 are based on the displacementsof surface features.

The image quality maps in Figure 11 suggest locations of cracked boundaries, butwhen compared to the secondary electron images, it is clear that the image quality mapswere not reliable indicators of cracks. The black boundaries in the image quality mapswere regions where the EBSPs had low quality or were not indexable, but this did notimply that cracks existed at such locations. The criteria used to decide if a crack or a cavitywas present in a boundary are illustrated in Figure 11. The overlaid black lines inFigure 10 indicate cracked boundaries. Surface grain-boundary microcracks were

Figure 8. EBSD orientation map of the same section of a 35% cold-rolled sample (a) before creepand (b) after a creep displacement of approximately 500 mm at T¼ 760�C and �¼ 220MPa. (c) AnEBSP orientation map of a different 35% cold-rolled sample with a slightly lower creep displacement(400 mm) under the same creep conditions. The majority of the grain boundaries that had crackedwere GHABs, indicated by R. The arrow in (b) marks the only special boundary that cracked. Theloading axis was horizontal.


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observed at displacement levels as low as 370 mm ("�5%), where voids or cavitiesdeveloped in boundaries that developed ledges where grain-boundary sliding occurred.

In situ SEM and EBSD data for a 25% cold-rolled specimen deformed under identicalconditions as the 10% cold-rolled specimen just presented is shown in Figures 12 and 13.

Figure 9. Secondary electron photomicrographs of the area in the middle of Figure 1 of a 10% cold-rolled specimen, while it was crept in situ at T¼ 760�C and �¼ 220MPa at displacements of (a)0.264 and (b) 0.592mm (loading axis was horizontal). From corresponding surface marks in bothimages, the linear strain was in the range 5.5–7.5% in this region.

Figure 10. EBSD inverse pole figure orientation map for the creep-tested 10% cold-rolled specimenshown in Figure 9, indicating the boundaries that cracked during the experiment (overlaid blacklines). Several of the grain boundaries are labelled (R¼GHAB, R3¼ twin, L¼LAB, RX¼CSLB),showing that cracks tended to form on the GHABs. The loading axis was horizontal.


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The boxed region in Figure 12 was EBSD mapped prior to the experiment and theboundary characteristics are labelled in Figure 13. About half of the GHABs cracked andabout 10% of the CSLBs cracked.

In both in situ tensile-creep specimens, cavities linked up with increasing strain tobecome microcracks, which coalesced into larger grain boundary cracks. No intragranular

Figure 11. Secondary electron SEM images (left side) and image quality EBSD maps (right side)at different displacements (indicated, as d below each image) for the creep-tested 10% cold-rolledsample shown in Figures 9 and 10, showing how grain-boundary sliding (ledges) and cracknucleation features have a different appearance. What appear to be cracks in image quality maps areoften ledges that developed by grain-boundary sliding. Cracks have a characteristic bright halo alongboth sides of the dark crevice, while ledges do not.

Figure 12. Secondary electron SEM micrographs for a 25% cold-rolled specimen creep deformed atT¼ 760 �C and �¼ 220MPa after (a) 116.8 mm displacement, (b) more than 1.039mm displacement.The area within the boxes was characterized using EBSD mapping in figure 13. The loading axis washorizontal.


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cracks were observed. The cracks propagated along grain boundaries oriented at various

angles with respect to the tensile axis including those parallel to the loading direction.

In general, there were more cracks and greater crack openings in boundaries with a higher

tensile normal stress. Combining the observations for all the samples examined (including

well over 500 boundaries with approximately 200 cracked boundaries), over 85% of the

cracked boundaries were initially GHABs. This further verifies that CSLBs and LABs are

less susceptible to grain-boundary cracking than GHABs during creep deformation of this

alloy. Although grain-boundary sliding can occur even within the dislocation-creep

dominated regime, it was impractical to perform in situ creep experiments within the low-

stress regime, which may have been controlled by grain boundary sliding, due to the fact

that this SEM was not available for continued single use for such a long period of time.

3.3.3. Slip system interactions leading to damage nucleation at GHABs

A parameter developed to evaluate mechanical twin-induced grain boundary cracking

at grain boundaries in an equiaxed (duplex) TiAl alloy [29–33] was modified for the

Udimet alloy 188, because mechanical twinning does not occur during creep. In a TiAl

four-point bend specimen deformed to a surface strain of about 1.5% at ambient

temperature, this parameter was able to distinguish between cracked and intact

boundaries, which provides some degree of predictive capability. When mechanical

twinning occurs, an intense local shear is imposed on the grain boundary, which could

occur similarly by a dislocation slip band, as illustrated schematically in Figure 14a.

Figure 13. EBSD inverse pole figure orientation map for a 25% cold-rolled specimen prior to creeptesting at T¼ 760�C and �¼ 220MPa. The GHABs and CSLBs that were analyzed are marked. Theloading axis was horizontal.


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If the slip that occurs in dislocation creep is planar (which is likely in low stacking

fault energy materials such as this cobalt-based alloy), the mechanisms that lead to

crack nucleation during RT deformation in the tetragonal TiAl alloy system and during

creep of this fcc-based superalloy may be similar.An interaction between a twin or a shear band and a grain boundary imposes a

highly concentrated shear discontinuity along the grain boundary plane. To maintain

compatibility with the neighbouring grain, appropriate slip systems must be activated in

the neighbouring grain, as illustrated in Figure 14a. If a dislocation in the initiating

grain is able to penetrate through a grain boundary, as illustrated in the slip transfer

process in Figure 14b, residual dislocation content must be left in the boundary plane,

which may increase the energy of the boundary and reduce its cohesive bonding force.

Slip transfer has been observed in RT deformation when the angles illustrated in

Figure 14b are small. However, at elevated temperature, slip transfer may be facilitated

by diffusion to assist the climb of dislocations in the grain boundary. If this does not

occur efficiently, then the grain boundary may accumulate defects that increase its

energy. Opening a crack requires energy to create two new surfaces (Griffith criterion),

so if the interfacial energy is higher, less additional energy is required to open the

crack. Thus, the details of slip interactions in the boundary could alter the boundary

energy locally.The fracture initiation parameter (fip), used for twin induced microcracking in TiAl

(Equation (1)) is computed from the Burgers vector, b, slip plane normal, n, and tensile

direction, t. The fip is analogous to a multiplicative probability statement based on several

geometrical factors that could enhance crack nucleation due to a local shear strain

concentration at the boundary [29–35]. These factors include the likelihood of having a slip

system that imposes a local mode I opening displacement on a boundary and the effect of

imperfect slip transfer on raising the grain-boundary energy (i.e. decreasing the cohesive

energy). The fip was modified for creep in a cubic fcc metal in equation (3), and further

modified based upon prior experience in equation (4) to incorporate the apparent grain

boundary normal direction: [29]

F1 ¼ mtwjb̂tw � t̂j�ordjb̂tw � b̂ordj ð1Þ

Figure 14. Mode I opening crack at grain boundary (dashed line) due to slip band or twin (a) and(b) geometry of slip transfer, where the angles refer to changes in the slip system in the neighbouringgrain.


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m ¼ jb̂m � t̂jjn̂m � t̂j ð2Þ

Fc1 ¼ mjb̂m � t̂j �neighbor

jb̂m � b̂neighborj ð3Þ

Fc2 ¼ mjb̂m � t̂jjn̂gb � t̂j �neighbor

jb̂m � b̂neighborj ð4Þ

The fip Fc1 is the slip analogue of the twin-based equation (1). All the fip values are theproduct of several terms involving unit vectors (denoted by ^) in crystallographicdirections, but expressed in the sample coordinate system, as illustrated schematically inFigure 14a. The first term, m, is the Schmid factor (Equation (2)) of a highly-stressed slipsystem in a grain pair. This slip system could cause a large shear discontinuity at a grainboundary. The second term of the fip is part of the Schmid factor. This scalar product (i.e.b̂m � t̂) quantifies the strength of a mode I opening component on the boundary. The lastterm of the fip is the sum of the scalar products between the Burgers vector of a highly-stressed slip system in the initiating grain (with Schmid factor m) and the Burgers vectorsof slip systems in the neighbouring grain. These scalar products quantify how well the localshear direction at the boundary can be accommodated by dislocation activity in theneighbouring grain (� in Figure 14b). Fc2 is the same as Fc1, but it includes jn̂gb � t̂j, whichidentifies the magnitude of the mode I opening force on the boundary. This is an upperbound since the inclination of the boundary with the surface is not known. Finally, theintentional lack of slip plane orientation information in these fip values is based upon priorexperience, where slip plane information carried no correlations with crack nucleation[34,35].

The value of a fip is large for orientations of a shear direction that impose the greatestopening force due to mass being transferred by shear away from the boundary; this isquantitatively expressed in the first two terms. The sum is largest when there is the greatestpotential for imperfect slip transfer, i.e. when two or more neighbouring grain systems thatare somewhat well aligned with the initiating slip system, but not closely aligned (if theinitiating and neighbouring slip directions were closely aligned then only one directionwould give a high scalar product and all other terms would be significantly smaller). Whentwo or more neighbouring grain slip systems help accommodate the shear imposed by theinitiating grain, the amount of imperfect slip transfer is great, leading to more residualdislocation content left in the grain boundary, which raises its energy and lowers theresistance to crack formation.

Similar to the TiAl analysis [29–35], fip values were larger for the cracked boundarypopulations than the intact boundary populations for the 10% cold-rolled Udimet alloy188, as evident in the results for Fc1 in Figure 15 (details of such a computation areprovided in [33]). The box plots in Figure 15 show the mean fip values� one standarddeviation for several variations of the fip, indicating overlap between the cracked andintact boundary populations. Appendix A provides details regarding the relativesignificance of each of the terms in the fip. The fact that various methods of evaluationgive effectively the same outcome indicates that the fip may be a fairly robust way toevaluate the likelihood for grain-boundary fracture.

A statistical analysis based upon the Student’s t-test shows that the cracked andintact populations are distinct. The results of these calculations are reported as t-test


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�-values in Table 7 for several different approaches to calculating the fip (see AppendixA). The �-value quantifies the probability that the null hypothesis is false, i.e. that themeans of the cracked and intact populations are the same. Thus, the �-value is usefulas a figure of merit for identifying fip values that are better or worse in predictingwhich boundaries are most likely to crack. From the �-values in Table 7, it is clearthat Fc2, which includes the effect of the apparent grain boundary normal direction,is the most effective predictor of boundaries that are most susceptible to cracking.

In contrast, the Fc1 �-values for the 25% cold-rolled specimen (Figures 12 and 13)indicated that there was no significant difference between the cracked and intactboundary populations. Although the estimated strain ("�2%) where fracturedboundaries were evaluated for the 25% cold-rolled specimen (Figure 12a) was smallerthan the strain ("�10%) used for the 10% cold-rolled specimen (Figure 9b), the extentof crack coalescence was much more developed in the 25% cold-rolled specimen(Figure 9). As the cracks propagated further in the 25% cold-rolled specimen beforethey were first analyzed, it was not clear where cracks nucleated, so this key in situobservation was missed in this specimen. Consequently, the analysis on the 25% cold-rolled specimen may represent crack propagation more than the crack nucleationevents.

While t-test values are valuable to identify the statistical significance of the fip, thehistograms in Figures 16–18 also provide some mechanistic insights. Two cases areillustrated in the histograms in Figure 16, which shows a nearly Gaussian distributionfor the maximum F6

c1 value (Figure 16a) and a skewed distribution for the F12c1 (max m)

values (Figure 16b) (note further details in Appendix A). For a given type of fip, theshape of the histogram is similar for both the 10 and 25% cold-rolled specimens (notshown). The mean fip values for the cracked and intact boundaries are also indicatedon the histograms in Figure 16 with a *. When the apparent boundary normaldirections presented in Figure 17 are included in the fip, i.e. variations of Fc2, the t-teststatistics improve dramatically and the histograms, such as those in Figure 18, becomemuch more uniform in their message; the intact boundaries have a nearly flat

Figure 15. The statistics for several fip values and their components are provided for the GHABs inthe 10 and 25% cold-rolled data sets (Figures 10 and 13); the 10% data are transparent and shiftedto the right to allow for ease in comparing. Statistics of the cracked and intact boundaries inFigures 10 and 13 are illustrated with box plots. The mean is the centre of each box, which extendsone standard deviation above and below the mean. Extreme values are identified with lines extendingabove and below the boxes (the sum terms are scaled by 1/4 and 1/2 for plotting purposes). Theseparation between the cracked and intact populations is greater for the 10% cold-rolled data set.


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Table

7.�-V

alues

from

t-testsin%

(two-tailed,unequalvariance,evaluatedin

ExcelT

M)forelem

ents

ofandvariants

ofthefip.

Types

ofboundaries

*

Cracked

Intact

Max(m

)b̂m�t̂

� � ��

n̂m�t̂

� ��

n̂gb�t̂

� ��

P12i¼

1

P6 i¼

1F12c1ðm

ÞF6 c1ðm

ÞmaxðF

12c1Þ

maxðF

6 c1Þ

F12c8ðm

ÞF6 c8ðm

ÞmaxðF

12c8Þ

maxðF

6 c8Þ

10%

cold

rolled

21GHAB

26GHAB

58.4

0.24

0.19

0.92

0.22

0.75

2.47

2.57

3.83

0.77

1.05

0.67

1.91

0.95

25GHABþ

CSLB

26GHAB

91.2

1.23

2.01

5.28

1.07

0.77

2.05

1.37

1.31

0.32

0.85

0.39

1.31

0.68

25GHABþ

CSLB

72GHABþ

CSLB

90.2

1.22

2.02

0.23

37.05

27.36

1.57

3.08

0.16

0.13

0.055

0.072

0.063

0.032

4CSLB

46CSLB

33.2

79.61

93.94

13.93

72.34

56.13

46.70

39.28

0.19

9.76

9.9

12.3

10.2

6.1

25%

cold

rolled

84GHAB

84GHAB

35.4

19.4

11.4

0.06

8.7

56.4

74.0

82.8

70.5

72.51

0.1

0.3

0.1

0.05

95GHABþ

CSLB

84GHAB

25.4

23.8

18.3

0.1

6.2

43.8

72.4

71.2

71.0

73.80

0.4

0.9

0.3

0.1

95GHABþ

CSLB

154GHABþ

CSLB

13.5

33.9

45.5

0.0005

12.4

94.4

90.0

63.2

37.2

22.45

0.0009

0.004

0.0005

0.0004

11CSLB

70CSLB

20.8

70.9

30.8

42.05

56.6

79.7

79.8

88.4

36.5

37.92

46.23

57.95

37.82

33.05

Bold

implies

495%

probabilitythatthecracked

andintact

boundaries

are

from

differentpopulations.


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distribution at low fip values that decreases toward zero with high values, whilecracked boundaries tend to have a more Gaussian histogram centered on high fip

values. Boundaries having fip values above the cracked mean fip value have a higherprobability of cracking, and correspondingly boundaries having fip values below theintact mean fip are not likely to crack.

The above analysis was made using a combination of EBSD data and highquality secondary electron images of the same regions to decipher which boundarieswere cracked. Use of only image quality maps was inadequate for obtaining statisticallysignificant separation of the cracked and intact populations (t-test �-values �5%). Thisemphasizes the importance of reliably identifying nucleated cracks prior to crackpropagation before performing a fip analysis. This implies that a qualitatively assessedhigh defect density in material adjacent to a grain boundary (which lowers the imagequality value) cannot be directly correlated to cracking. This is consistent withobservations and detailed analysis on TiAl in [34,35].

Figure 16. Histogram of fip values from GHABs for (a) 10% cold-rolled specimen maxðF 6c1Þ,

and (b) 25% cold-rolled specimen F12c1(m). See Appendix A for further details.

Figure 17. Histogram of n̂gb � t̂��

�� of GHABs for (a) 10% and (b) 25% cold-rolled specimen.


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4. Summary and conclusions

This work has resulted in several findings and observations that have direct implications

on the microstructure and creep behaviour of TMP Udimet alloy 188. For high applied

stresses, the measured creep parameters (n and QApp) suggested that dislocation creep was

the dominant creep deformation mechanism. In the low applied stress regime, the

measured stress exponents suggested that grain-boundary sliding was a possible rate-

controlling mechanism. Through strain-annealing processing, it is possible to alter the

GBCD in Udimet alloy 188 while maintaining a near-random texture. The fraction of

Figure 18. Histogram of fip values from GHABs for (a) 10% cold-rolled specimen F6c2ðmÞ, and

(b) 25% cold-rolled specimen maxðF12c2 Þ.

Figure 19. For about 2/3 of the cases the maximum value of a fip for a grain pair results from theslip system with a maximum Schmid factor.


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annealing twins and GHABs, and CSLBs increased slightly with increased cold-rolling

deformation, while the fraction of LABs decreased with increased cold-rolling deforma-

tion. The 10 and 25% cold-rolled microstructures exhibited the greatest special

boundary fractions and the lowest minimum creep rates compared to the 35% cold-

rolled material.This alloy was susceptible to grain-boundary cracking during creep deformation for all

the processing conditions examined. To quantify the types of grain boundaries that

exhibited preferential cracking, a testing methodology was developed to acquire secondary

electron SEM images and EBSD orientation maps during tensile-creep deformation

at 760�C. Cracking was more prevalent on the GHABs and less prevalent on the

LABsþCSLBs (515% of all the cracked boundaries). Thus, this methodology showed

that even though special boundaries are resistant to crack nucleation, a small fraction of

special boundaries do crack. A fracture initiation parameter (fip) analysis showed that

particular combinations of slip system activation and grain misorientations could be

identified as more or less likely to generate crack nucleation. This is the first time this

analysis has been applied to creep of a cubic metal. The grain-boundary cracking appeared

to be more highly correlated with slip vectors than slip plane geometry. The success in

using the fip analysis for an alloy, different from which it was initially developed, and in a

different deformation mode, suggests that the fip approach may be generally applicable for

predicting crack nucleation. Overall, the results of this study, which suggest the possibility

of non-destructive evaluation of the damage potential (i.e. reliability) prior to use on the

basis of strategic analysis of EBSD-mapped microstructures. Hence evaluation of the

distribution of fip values provides additional criteria for grain-boundary engineering of

this alloy.

Acknowledgements

This work was supported by the National Science Foundation through grant DMR-0533954.The authors are grateful to Nathan Eisinger (Special Metals Corporation) for performing the alloyprocessing and Adam King (formerly of Michigan State University and now at Rocketdyne)for assistance with the mechanical testing. In addition, the authors thank EDAX-TSL, Inc.(specifically Matthew Nowell, John Carpenter and Dr Stuart Wright) for allowing us to use theirSEM/EBSD facility for performing some of the in situ tensile-creep experiments and for theirtechnical assistance in this regard. Discussions regarding statistical analysis with Professor DarronMason, Albion College, are appreciated.

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Appendix A: fip calculation details

In addition to fip values, Table 7 and Figure 15 also contain statistics for the components of thefip values. It is noteworthy that the Schmid factor is not a reliable indicator of propensity tocrack, while the two components of it are. The jb̂m � t̂j and the jn̂m � t̂j terms taken separatelyindicate low �-values, but the mean of the plane normal component jn̂m � t̂j is lower for thecracked population whereas the jn̂b � t̂j is higher (shown in Figure 15). Hence, the opposite effectscause a nullifying effect that makes the Schmid factor a poor indicator for cracking. This alsosuggests that the slip-plane component of the slip transfer process may be less important thanthe slip direction, which was shown to be true in more detailed analysis in TiAl [33–35]. Also,from Figure 15, the sum terms taken separately are not particularly strong indicators forcracking either. The single component that gives the strongest indicator for fracture is theapparent grain boundary inclination jn̂gb � t̂j. This is not surprising, as the tensile opening force ishighly correlated with this term.

Calculation of fip values can be done with a number of different approaches. When a fip iscalculated with the maximum Schmid factor, this identifies the system most likely to cause thegreatest shear discontinuity in the boundary plane. This is denoted as Fc1 (m). On the other hand, ifthere are two slip systems with similar Schmid factors, the orientation of this slip system with respectto the tensile axis or the grain boundary plane could be quite different. Also, the slip transferprocesses in the neighbouring grain may also differ, leading to different values in the sum term.Thus, the slip system with the highest Schmid factor may not generate the greatest residualdislocation content in the boundary, so it may be important to consider the case where the value ofthe fip is highest, denoted as max(Fc1). Typically, the maximum fip correlates with the highest mvalue, but even the 5th highest m value can generate the highest value of the fip, as indicated inFigure 19. Also, the number of terms in the sum could be important, as slip systems with a lowSchmid factor may not be relevant [47–49]. Such a hypothesis can be tested by using a smaller sumthat considers only the more highly stressed half of the slip systems (6 of 12 with highest Schmidfactors, e.g. denoted as F6

c1), leading to fip values that are about half as large.Thus, it is possible to combine these two ideas to obtain four fip values, labelled in Table 7. The

means, standard deviations and spreads of the populations based upon these different approachesare illustrated in Figure 15. These four fip values were evaluated using different combinations of theGHAB and CSLB populations, yielding the several t-test parameters reported in Table 7. From the�-values in Table 7, it appears that using the smaller sum and the maximum value of Fc1 and all typesof boundaries provides the best statistical separation of the 10% cold-rolled populations. However,most of the other approaches also give good statistical separation of the two populations, with�97% or better confidence. This is similar to previous observations for TiAl, where there was nodramatic difference between the maximum m and maximum fip approaches [33]. While the lowest �-values were obtained when both CSLBs and GHABs were included in the analysis, �-values of thespecial boundaries alone yielded a high probability that the cracked and intact boundaries were fromthe same population. Thus, there is no obvious reason for the lower �-values in the combinedpopulations. Additionally, there was no apparent pattern regarding cracked and intact specialboundary misorientations when the deviation from the ideal (Brandon criterion) was considered.


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Effect of thermomechanical processing on the creep ...boehlert/GROUP/publications/ourphilmag2008pa… · temperature or dislocation substructure changes that occur during interrupted