Grain refinement mechanisms and strength-hardness correlation of ultra-fine grained grade 91 steel processed by equal channel angular extrusion

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

Contents lists available at ScienceDirect

International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp

Grain refinement mechanisms and strength-hardness correlation of ultrafine grained grade 91 steel processed by equal channel angular extrusion

T

Miao Songa,b,∗, Cheng Sunc, Youxing Chend, Zhongxia Shange, Jin Lie, Zhe Fanf, Karl T. Hartwiga, Xinghang Zhange,∗∗ a

Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843-3003, USA Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48105, USA c Materials and Fuels Complex, Idaho National Laboratory, Idaho Falls, ID 83415, USA d Mechancial Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA e School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA f Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Grade 91 (T91 or P91) Microstructure Ferritic/martensitic steel Yield strength and hardness Grain refinement

Ferritic/martensitic grade 91 steel (T91 or P91) is one of the candidate materials for primary and secondary loops in sodium cooled fast reactor. Recently, studies show that equal channel angular extrusion (ECAE) and heat treatment can enhance the strength of T91 from 480 MPa to 1600 MPa. However, a detailed refinement mechanism is yet to be clarified. Furthermore, there is a need to correlate the hardness measurement to tensile test results in T91 steels for nuclear application. Here, we report the grain refinement mechanisms in T91 after extensive microstructural analysis. Packet (a group of martensite with the same habit plane) is identified as an elementary unit for grain refinement. The Vickers hardness correlates well with the ultimate tensile strength, with a fitting ratio of ∼3.24. However, the ratio of Vickers hardness to yield strength is a function of ductility in T91 steels.

1. Introduction Grade 91 (modified 9Cr-1Mo or P91 or T91) steel was originally designed for the steam generators of liquid metal reactors [1]. Because of its excellent mechanical and physical properties and a low fabrication cost, T91 is widely applied in pressure vessel and piping systems in fossil power and petrochemical industries [2–5]. Recently, T91 steel has received renewed interest to extend its applications in other reactor concepts. For example, T91 and other ferritic/martensitic (F/M) steels show good resistance to irradiation damage [6,7], stress corrosion cracking [8], and irradiation-assisted stress corrosion cracking [9], and are appealing candidates for core internals of light water reactors for life extension. The superb swelling resistance of F/M steels makes these steels attractive for fuel cladding in several fast reactor concepts [10], and structural materials in traveling-wave reactors [11], in which materials are expected to receive irradiation damage of hundreds of displacement-per-atom (dpa) at elevated temperatures [12]. T91 steel is typically used after a normalization and tempering process [13]. The normalization temperature is typically 1040–1080 °C,

∗

at which a fully austenitic (face-centered cubic or fcc) structure is achieved and all carbides including NbC are dissolved. After water quenching or air cooling, the material forms a martensite (body-centered tetragonal or bct) dominated microstructure. However, several carbides such as transition carbides ε- and η-carbides (M2.4C or M2C), and cementite (M3C) [14] may form during the cooling as a consequence of auto-tempering process. Tempering of T91 is usually performed at 730–800 °C. During tempering, both residual austenite and martensite decompose, and thicker martensitic laths (typically around 0.5 μm) are formed by consuming thinner laths [14]. The transformed martensitic structure is preserved with prior austenite grain boundaries (PAGBs), packets, and blocks. The packet is referred to a group of martensite with the same habit plane that can be subdivided into blocks. Blocks are typically defined as a group of martensite with similar orientation or a combination of two variants with slightly different orientation [15]. Therefore, the resulting decomposed material with preserved transformation features is often referred to as ferritic/ martensitic (F/M) steel. However, T91 is ferritic phase (body-centered cubic or bcc) with preserved transformation features if fully tempered.

Corresponding author. Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48105, USA. Corresponding author. E-mail addresses: [email protected] (M. Song), [email protected] (X. Zhang).

∗∗

https://doi.org/10.1016/j.ijpvp.2019.03.025 Received 6 February 2019; Received in revised form 3 March 2019; Accepted 20 March 2019 Available online 23 March 2019 0308-0161/ © 2019 Elsevier Ltd. All rights reserved.

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Continuing efforts are made to enhance the mechanical strength of T91. Severe plastic deformation (SPD) is widely applied for strength enhancement by refining the microstructure [16–19]. The strength of T91 can be enhanced up to two times that of its original value by equal channel angular extrusion (ECAE) [20–23] or dynamic plastic deformation (DPD) [24] or cold-swaging [25], all of which are SPD techniques. But the yield strength (0.2% proof stress) is generally below 1200 MPa. Recently, a ductile martensite with high strength and good ductility was obtained by water quenching. The yield strength of T91 has been further enhanced by a combination of ECAE and phase transformation to an unprecedented level about ∼1600 MPa, or three times of its strength measured in fully tempered condition [14], enabling a weight reduction of ∼66% for a same load. The processed T91 materials not only exhibit an excellent combination of strength and ductility, but also show enhanced irradiation tolerance when the refined microstructure is maintained [26], but may become unstable at higher dose level when recrystallization occurs [27]. Enhanced strength usually derives from a refined microstructure. The refinement mechanism of T91 steel with hierarchical microstructure (PAGBs, packets, and blocks) is still not clear, but can be gleaned from the previous studies on grain refinement by SPD techniques. Hughes and Hansen proposed a grain subdivision mechanism for cold-worked metal with large strain, in which grain refinement occurs as a consequence of coevolution of dislocation cell structures and texture [28]. Tao et al. proposed a similar mechanism for the grain refinement of surface mechanical attrition treated Fe, in which the dense dislocation walls and dislocation tangles form subboundaries that later transform to high angle grain boundaries [29]. Grain refinement by ECAE was proposed as a direct consequence of shear plane interaction with crystal structure and texture [30]. However, the proposed mechanism agrees well with results in fcc metals rather than bcc metals. Shin et al. investigated a low carbon steel (bcc structure) subjected to ECAE, and found that low angle grain boundaries form after an initial pass as a consequence of slip systems interaction, and these grain boundaries rotate to form high angle grain boundary after further extrusion [31]. Although several refinement mechanisms have been proposed for SPD materials, their effectiveness remains unproved in T91, which shows a hierarchical microstructure compared with other simple metals. The simplified microstructural process of T91 is summarized in Fig. 1, based on previous observation [14,23]. The detailed terminology is listed in Table 1. Meanwhile, T91 steels are increasingly tested in neutron [32–34] and ion irradiated [26,35–37] conditions. The mechanical properties of T91 steel or its kind are of significant interest [38–44]. Radiation often leads to significant degradation of mechanical properties, manifested by

Table 1 Microstructural symbols and nomenclature used for different phases [14]. Symbol

Nomenclature

αP αA α′M α′T α′AT αB M/A δ γ PAGB ε-C η-C θ

polygonal ferrite in grain interiors allotriomorphic ferrite/grain boundary ferrite martensite tempered martensite auto-tempered martensite bainitic ferrite martensite/austenite constituent delta ferrite retained austenite prior austenite grain boundary epsilon carbide eta carbide cementite

radiation hardening and embrittlement [45]. The dimensions of heavy ion irradiated T91 steels may be small, making it difficult to perform conventional tension tests. Despite small punch methods has been widely used to investigate mechanical properties of small volume materials [46–48], there is still a need to probe evolution of mechanical properties by using indentation experiments, with the hope to infer yield strength or tensile strength from hardness measurements. Busby et al. have investigated the correlation between yield strength and hardness of austenitic stainless steels and ferritic steels [49]. However, the relation between hardness and yield strength for ferritic/martensitic T91 steel is largely unknown. Here, we present microstructural characterizations of T91 steels processed via different ECAE enabled thermo-mechanical treatments with special attention to the grain refinement mechanisms. A strengthhardness correlation is established for T91 steels. Such a correlation may provide the much needed correlation between hardness and flow stress in T91 steels for their nuclear reactor applications, and may have general implications for other ferritic/martensitic steels. 2. Experimental procedure The nominal chemical composition (in wt.%) of T91 steel is 9.38Cr, 0.91Mo, 0.19 V, 0.38Mn, 0.085C, 0.34Si, 0.08Cu, 0.097Ni, 0.032Al, 0.080Nb, 0.042N, 0.019P, 0.0008S, balance Fe. As-annealed (AA) T91 steel was prepared by annealing of the as-received (AR) T91 material at 800 °C for 1 h, followed by furnace cooling. This additional treatment (800 °C annealing and furnace cooling) ensures that the AA T91 is fully tempered. Billets with size 25.4 × 25.4 × 127 mm3 were cut for further processing. The extrusion process was detailed previously [14,23]. The Fig. 1. Microstructural process of T91 steel during heat treatment and equal channel angular extrusion (ECAE). (a) Single γ phase forms during normalization at 1040 °C. (b) Water quenching after normalization produces complicated microstructural including martensite, ferrite, carbides, and residual austenitic phase. Residual γ phase locates between martensitic laths. Carbides form due to the auto-tempering of martensite during the cooling process. Polygonal ferrite or bainitic ferrite forms with needle shaped martensite or ε-carbides. (c) Hierarchical microstructures of T91 steel forms after tempering. (d) Low temperature plastic deformation refines the grains and breaks the prior austenitic grain boundaries. More detailed microstructural evolution is available in Refs. [14,23].

213

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Table 2 Heat treatments and thermomechanical processing conditions of T91 samples. Identifiers

TMT processing condition

AR AA 1ART 1A300 2B300 3Bc700 1000WQ 1000ECAE WQ/T/1A300 (1A300+)

as-received material annealing of as-received material at 800 °C/1 h, followed by furnace cool one EACA pass at room temperature one ECAE pass at 300 °C two ECAE passes at 300 °C using route B (90° rotation between passes) three ECAE passes at 700 °C using route Bc (+90° rotation between passes) 1000 °C solution treatment followed by water quenching one ECAE pass at 1000 °C, followed by water quench Tempering of 1000WQ sample at 500 °C/10 h, then one ECAE pass at 300 °C

identifiers of samples with indication of their thermo-mechanical treatment history are described in Table 2. Specimens with dimensions of 15 × 10 × 6 mm3 were cut for examination. The extruded materials were cut away from both ends (left and right 1 inch) and the upper and lower surfaces of the billet to avoid potential inhomogeneous deformation. Dogbone-shaped tensile specimens with gauge dimensions of 8 × 3 × 1 mm3 were cut from the inner part of the water quenched or ECAE processed billets using electro discharged machining (EDM) technique. Tensile tests were performed with an MTS machine at a cross head speed of 0.008 mm/s, equivalent to an initial strain rate of 1 × 10−3s−1. The strain was measured by an extensometer. Two-three samples were tested for each condition. The hardness was measured by an LM 300AT micro hardness tester using a 2.9 N force for a loading time of 13s by using a pyramidal shape diamond indenter with 15 indentations per measurement. The indentation depths were on the order of a few microns and way above the size dependent range [50]. Therefore, no surface effect was expected. The samples for optical microscopy (OM) and scanning electron microscopy (SEM) studies were prepared following a standard mechanical polishing procedure, and etched in a 5 g FeCl3, 20 ml HCl and 100 ml water solution [51]. The same samples were also used for electron backscatter diffraction (EBSD) studies. EBSD specimens were prepared following a similar procedure with electro-polishing in place of etching. The electro polishing was performed at −40 °C and 20 V for 30s with 10 vol.% perchloric acid methanol solution. Electron transparent disks were prepared by mechanical grinding of 3 mm diameter disks down to around 60 microns, and then perforated in a TenuPol-5 twinjet polisher with the polishing solution at a voltage of 10–20 V and −40 °C. SEM experiments were performed on an FEI Quanta 600 microscope operated at 20 kV with a working distance of 10 mm. The working distance for EBSD experiments was 10 mm. The step sizes for data collection were 0.05 or 0.02 μm. Transmission electron microscopy (TEM) analysis was performed on an FEI Tecnai F20 analytical electron microscope operated at 200 kV.

Fig. 2. Directions of extruded billet. ND- normal direction; TD-transverse direction; ED-extrusion direction; LP-longitude plane; TP-transverse plane; and FP-flow plane.

pass at room temperature, the grain was significantly refined as shown in Fig. 3(b). The direction of elongated lamella is near 27° from the extrusion direction, and is very close to the theoretical value of ∼26.6° [52]. Packet boundaries are still visible after first pass. Fig. 3(c) shows the 3Bc700 (3 ECAE processes via route Bc at 700 °C) specimen, where dynamic recrystallization has occurred, and grains have a lower aspect ratio compared to 1ART (1 ECAE pass at room temperature) samples. No transformed features (PAGBs, packets, blocks) are observed. Fig. 3(d) shows the martensite dominated microstructure in 1000WQ (water quench from 1000 °C) T91. A similar structure is observed compared with AA materials, but with a higher grain boundary area fraction per unit volume. The consumption of thinner martensite laths during tempering reduces the grain boundary area fraction of the water quenched (WQ) materials. T91, subjected to water quenching-tempering-ECAE at 300 °C (WQ/T/1A300), contains a grain refined martensite microstructure as shown in Fig. 3(e). The elongated lamellae are dependent on the packet orientation, and show different elongation direction dependent relative to the extrusion direction. Cracks may form at the lath boundaries of the material due to the limited ductility of the marteniste. The grain boundary characterizations (misorientation and length) were summarized in Table 3. Low angle grain boundaries account for nearly 30% of the total grain boundary length (length in 2D and area in 3D). Although the grains were significantly refined by processing, the ratio of high angle grain boundary length to total grain boundary length doesn't seem to increase with processing. The refined grain size (thickness of lamellae) was reported previously [23]. Panoramic views (by combining ∼ 15 TEM images) of the grain structures are shown in Fig. 4. STEM images collected from three orthogonal processing directions in Fig. 5 show the distribution of carbides for different deformation cases. Grains with different shapes are observed in the AA material, as shown in Fig. 4(a). Carbides are observed in the AA material within laths or at lath boundaries and PAGBs as shown in Fig. 5(a). An elongated lamella structure is formed on the FP after one pass at 300 °C as shown in Fig. 4(b). The PAGBs are broken into fragments, and all grain boundary carbides are redistributed as shown in Fig. 5(b). Further refinement occurs after two passes following route B at 300 °C with further refined lamella thickness as shown in Fig. 4(c). Hence carbides are better distributed. High temperature processing produces a similar elongated lamella structure with smaller

3. Results 3.1. Microstructure of ECAE processed T91 steels Fig. 2 defines the relevant directions related to the ECAE process. For example, the flow plane (FP) is defined by the normal and extrusion direction (ND and ED). All the deformed microstructure are examined on flow plane. Fig. 3 shows orientation image microscopy (OIM) micrographs of alloy T91 for several different processing conditions. Asannealed T91 (AA T91) show in Fig. 3(a) contains packets, which are defined as a group of martensite (or tempered martensite) laths with the same habit plane. Across the packet boundary, significant orientation change is observed. Blocks, which are typically formed by martensite with similar orientation or special arrangement of two variants with different orientations, are observed within packets. PAGBs are frequently observed as shown by the arrow in Fig. 3(a). After one ECAE 214

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Fig. 4. TEM images showing significant grain refinement by ECAE. (a) AA T91 has a typical tempered martensite lath structure on all three planes. (b) The 1A300 specimen is composed of refined shear elongated lamellae. (c) 2B300 contains much more refined grains. (d) 1A625 and (e) 2B625 T91 also consist of refined grains.

Fig. 3. Orientation image microscopy (OIM) micrographs of T91 steels after various processing conditions: (a) as-annealed T91, (b) 1ART, (c) 3Bc700, (d) 1000WQ, and (e) WQ/T/1A300. ECAE specimens were examined along flow planes. The color code of grains reflects their orientation in the inverse pole figure (IPF) map inserted in the lower left corner in (a). Note Fig. 2 (a) has a different scale from Fig. 2(b)–(e). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Further processing can enhance the strength but is less significant compared with the initial pass induced strengthening. Low temperature processing produces more hardening than high temperature processing. The processed martensitic T91 (Q/T/1A300) shows a much higher hardness than any of the processed ferritic materials. Fig. 7 shows the engineering stress-strain curves for the representative conditions. Table 4 summarizes the yield strength, tensile strength, ductility, and hardness of all the samples tested. The hardness vs. yield strength is plot in Fig. 8(a). The hardness-toyield strength ratio (H/σy) is between 3.0 and 4.5. The hardness to tensile strength (ultimate tensile strength) ratio, (H/σUTS), shown in Fig. 8(b), however, is close to a single value ∼ 3.24 with a very small deviation. The ductility was examined as a potential factor to affect the ratio as shown in Fig. 9. Hence, the H/σy value increases with uniform elongation or uniform strain, which is defined by the elongation at maximum load. Meanwhile, H/σUTS increases slightly with uniform elongation, but bounded between a relative narrow range 3 and 3.5.

grain aspect ratios compared with the low temperature processing cases as shown in Fig. 4(d) and (e). But the carbides here, Fig. 5(d), are hard to observe compared with the low temperature processing condition. 3.2. Vickers hardness and stress-strain curves The hardness of the processed materials is summarized in Fig. 6 (15 indentations per measurement). Generally, the hardness measured from different planes is consistent with one another. However, the 3Bc700 shows poor consistency among the different planes, which indicates an inhomogeneous microstructure after dynamic recrystallization. Most of the strengthening occurs during the first pass of ECAE processing.

Table 3 Grain boundary characterization for different processing conditions. (Note: LAGB-low angel grain boundary; HAGB-high angle grain boundary; L-length of GB.). ID

LAGB (2°≤θ ≤ 15°) 2°≤θ ≤ 5°

AA 1ART 3Bc700 1000WQ 1A300+

HAGB (θ ≥ 15°) 5°≤θ ≤ 15°

L (μm)

Fraction (%)

L (μm)

Fraction (%)

1260 1140 787 316 3080

17.5 16.6 12.6 14.3 18.1

728 730 790 169 1386

10.2 10.6 12.6 7.7 8.1

L (μm)

Fraction (%)

5180 5010 4690 1730 12,590

72.3 72.8 74.8 78.1 73.8

215

Area (μm2)

GB length per unit area (×106/m)

2569 227 419 399 555

2.8 30.3 14.9 5.6 30.7

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Fig. 7. Engineering stress vs. strain curves for representative conditions (some data were published in Ref. [14] and included here for comparison).

Table 4 Tensile properties and hardness data of T91 steel subjected to various thermal mechanical treatments.

Fig. 5. Scanning transmission electron microscopy (STEM) micrographs showing distribution of carbides (bright particles) and deformation of the PAGBs in T91 by ECAE examined from three directions. (a) In AA T91, PAGBs are clearly visible, decorated by carbides. (b) 1A300 specimen shows refined grains and redistributed carbides; (c) 2B300 specimen shows smaller grains, and undetectable evidence for PAGBs. (d) 2B625 T91 with relatively small carbides and fine grains.

ID

Yield strength (MPa)

Tensile Strength (MPa)

Uniform strain (%)

Hardness (MPa)

AA 1ART 1A300 2B300 1A625 2B625 3Bc700 AR 800WQ 900WQ 1000WQ 1100WQ 1200WQ 1A300+ 1000ECAE

482 ± 3 900 ± 4 838 ± 3 982 ± 4 706 ± 22 681 ± 22 615 ± 4 508 ± 3 972 ± 45 1127 ± 74 1207 ± 17 1212 ± 45 1156 ± 49 1588 ± 86 1248 ± 25

646 ± 3 935 ± 3 886 ± 5 1031 ± 3 819 ± 9 805 ± 2 763 ± 15 681 ± 4 1123 ± 4 1338 ± 1 1349 ± 17 1347 ± 15 1319 ± 14 1588 ± 86 1422 ± 33

9.4 ± 0.3 1.4 ± 0.1 1.9 ± 0.3 1.6 ± 0.2 5.6 ± 0.3 4.5 ± 1.3 8.5 ± 1 7.8 ± 0.5 5.4 ± 0.2 4.7 ± 0.6 4.7 ± 0.7 4.9 ± 0.6 5.1 ± 0.6 1.5 ± 0.1 4.3 ± 0.2

2110 2910 2870 3170 2790 2810 2580 2230 3760 4440 4460 4470 4490 4820 4640

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

60 120 80 50 120 170 170 80 110 90 90 90 130 250 90

Grain refinement, on the other hands, occurs by different mechanisms, depending on processing temperature and initial microstructure (as shown in Fig. 10). For ferritic T91 as shown in Fig. 10 (a) processed at low temperature, the packet is still visible after the first pass, as shown in Fig. 10(b). Significant grain refinement within the packet occurs after one pass. The grains or blocks within these packets typically have low angle grain boundaries. Due to the grain misorientation, the grains rotate differently to accommodate the plastic deformation which may facilitate the formation of high angle grain boundaries. Meanwhile, the dislocation pile-ups against the lath boundary can help to subdivide the elongated lamellae. The elongation direction is close to the ideal shear angle of 26.6° from the extrusion direction, which indicates the neighbor grains deformed collectively. The polygonal ferrites, generally larger in size, in the as-annealed T91 were refined simultaneously with the packets. For ferritic T91 processed at high temperature as shown in Fig. 10(c), dynamic recrystallization occurs, and no packet and other transformed structures remain. The final structure is a result of competition between grain refinement and grain growth. For the martensitic T91 steel as shown in Fig. 10(d) processed at low temperature, the packet is also visible after one pass as shown in Fig. 10(e). However, due to the poor deformability of martensite, neighboring packets or blocks cannot always rotate cooperatively. Therefore, cracks with micron size in dimension may form during the extrusion process. In this case, a large deviation can occur for the elongated grain direction compared with the ideal value of 26.6°.

Fig. 6. Vickers hardness values on different planes of ECAE processed T91 steel. No significant difference is noticed in low temperature processed material (T ≤ 300 °C). A difference in hardness occurs on different planes of the high temperature (625 and 700 °C) processed T91 steel.

4. Discussion 4.1. Grain refinement mechanism Carbide refinement mechanisms have been proposed previously for both low and high temperature processed ferritic T91 [23]. At a lower processing temperature, the large carbides remain at the boundary, and are topologically and chemically conserved during processing. Therefore, no significant refinement of these carbides occurs. At high temperature, large carbides may dissolve especially under high internal stress, and later precipitate in-situ during the subsequent processing.

216

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Fig. 9. (a) Hardness to yield strength ratio increases monotonically with the increasing uniform elongation. (b) Hardness to tensile strength ratio increases slightly with uniform elongation, and varies between 3 and 3.5.

Fig. 8. (a) Vickers hardness (TP) vs. yield strength (0.2% proof stress) correlation for as-received and processed T91 steels. The lower and upper limit of the correlated ratios is between 3.1 and 4.5. (b) The Vickers hardness vs. ultimate tensile strength data follows a tight linear fit with a slope value of 3.24.

change in hardness is close to three times that of yield strength. Zhang et al. proposal a general guideline for the strength and hardness correlation for various materials [55]. A more recent treatment of the relationship between stress and hardness is summarized in Ref. [56]. Because strain hardening usually occurs during the indentation process, the correlation of hardness with tensile strength or yield strength has to include plastic strain effects for ductile metals (typically assumed to be 8–10%). If the material follows power law work hardening behavior, the relationship between Vickers hardness and ultimate tensile strength can be expressed as [53]:

Meanwhile, the blocks within the packets can be directly sheared into small grains, indicating a localized deformation within the blocks or lath. 4.2. The correlation of microhardness and strength The possible strengthening mechanisms were discussed previously [14,23]. This parts focus on the correlation of microhardness and strength. Hardness is an important parameter for evaluating mechanical properties, and the hardness measurement technique is especially helpful when the samples are too small to be tested in tension. Tensile test results and hardness both reflect the materials' response to an external load. However, the correlation of hardness to yield strength or to tensile strength is empirical. If a material is incapable of appreciable further work-hardening, the hardness and yield stress follow the classic Tabor relationship [53]:

HV = 3σy,

HV = 2.9σuts

1 1−n n ⎛ ⎞ , 1 − n ⎝ 12.5n ⎠

(2)

where σuts is the ultimate tensile strength (MPa), and n is the work hardening coefficient. Based on Considѐre criterion of necking [57], n = e if power law work hardening is assumed. e is the true strain at necking, which is equal to ln (1+ εu), and can be typically approximated as the uniform elongation (εu) of the alloy. The value 12.5 results from the assumption that Vickers indentation produces 8% plastic strain. Pavlina et al. derived another relationship based on the linear regression of hardness and tensile strength for multiple steels [58]:

(1)

where HV is the value of Vickers hardness (MPa), and σy is the yield stress (MPa). Meyers interpreted this equation based on a geometric analysis under a flat punch [54]. This relationship is frequently verified by experimental results. Busby et al. summarized data from irradiated austenitic stainless steels and ferritic steels [49]. In both case, the

HV = 2.624σuts + 262,

(3)

where the unit is in MPa. The current study shows that the correlation of hardness and tensile 217

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

Table 5 Hardness of T91 steels (all units in MPa) by experiment and calculation from experimentally measured yield strength or UTS based on different models. Measured hardness

Tabor's σy Model

Tabor's σuts Model

Pavlina linear regression σuts

Cahoon's σy model

Gao's σy model

AA 1ART 1A300 2B300 1A625 2B625 3Bc700 AR 800WQ 900WQ 1000WQ 1100WQ 1200WQ 1A300+ 1000ECAE

2110 2910 2870 3170 2790 2810 2580 2230 3760 4440 4460 4470 4490 4820 4640

1450 2700 2510 2950 2120 2040 1850 1520 2920 3380 3620 3640 3470 4760 3740

2020 2820 2690 3120 2560 2500 2390 2130 3510 4170 4200 4200 4110 4790 4420

1960 2720 2590 2970 2410 2370 2260 2050 3210 3770 3800 3800 3720 4430 3990

1800 2790 2630 3060 2410 2270 2440 1820 3300 3770 4030 4070 3900 4930 4130

2270 3190 3040 3430 2830 2700 2690 2280 3630 4020 4240 4270 4230 5000 4320

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

60 120 80 50 120 170 170 80 110 90 90 90 130 250 90

value is slightly underestimated by Cahoon's model (σy) and Tabor's model using σuts, but is overestimated by Gao's model using σy. A similarity of the three effective models is that they all involve the work hardening coefficient to predict hardness. The work hardening coefficient is an indicator of ductility. On the other hand, because more than one parameter are involved in these models, it is difficult to predict the yield strength (based on Gao's model σy, or Cahoon's model σy) or tensile strength (Tabor's model σuts) from a Vickers hardness measurement, which is important for practical applications. Despite the complex correlation, the yield strength of T91 can be reasonably estimated with care by using Tabor's model (σy). But the ultimate tensile strength of T91 can be much better estimated by the regression coefficient, 3.24, established in the current study.

Fig. 10. Schematic of ECAE induced grain refinement mechanisms derived from EBSD analyses (a) The as-annealed T91 comprises ferrite with residual transformation features, such as PAGBs and packet boundaries. (b) The packet boundaries are preserved after low temperature processing in 1ART specimen, but significant grain refinement occurs within the packets. (c) No packet can be identified after high temperature processing (such as 3Bc700) due to dynamic recrystallization. (d) Water quenched T91 (1000WQ) is dominated by the martensitic phase. (e) In WQ/T/1A300 specimen, grain refinement of martensite is not as effective as that of ferrite. In addition, for this case, cracks may form due to the plastic incompatibility between different packets or blocks. See text for more details.

5. Conclusions In this study, microstructural characterization was performed, and the hardness and strength correlations were investigated in thermomechanically treated T91 steels. The results were summarized as follows:

strength in the T91 steels can be expressed as: (4)

HV = 3.24σuts.

1. Grain refinement in T91 steel is sensitive to the characteristic of the starting microstructure and processing temperature. The packet, which is referred to a group of tempered martensite evolving from a group of martensite with the same habit plane, serves as the fundamental unit for grain refinement in T91 steels. Grain refinement by severe plastic deformation in martensitic T91 steel is not as effective as that in ferritic T91 steel. The packet is preserved at low processing temperatures but is not preserved when dynamic recrystallization occurs at high processing temperatures. 2. The hardness for ferritic/martensitic T91 steels correlates well with ultimate tensile strength by a coefficient of 3.24, while its correlation with yield strength is dependent on the work hardening coefficient or ductility. A reliable prediction of yield strength from Vickers hardness is, therefore, challenging, but can be reasonably established with care.

Cahoon et al. derived an empirical relationship between hardness and yield strength [59]:

HV = 3 × 10nσy.

(5)

Gao considered the strain hardening and indentation size effects based on an expanding cavity model. The relationship between hardness and yield strength he derived is [60]: n

H=

ID

n

2 ⎧ 3 1 E 1⎡ 1 E ⎤⎫ σy 1 + ⎜⎛ cot α ⎟⎞ + ⎢ ⎜⎛ cot α ⎟⎞ − 1⎥ , ⎬ 3 ⎨ 4 ⎝ 3 σy n 3 σ y ⎠ ⎠ ⎣⎝ ⎦⎭ ⎩

(6)

where E is the elastic modulus, which is around 210 GPa for T91 steel (achieved from tensile curve), and α is the half angle for the indentation tip is around 68° for a Vickers indenter. The experimentally measured and the calculated hardness based on the five models are calculated and compared in Table 5. All five models show the right trend for the hardness. The Tabor model based on yield strength (σy) shows the largest deviation from the measured hardness values. The Pavlina linear regression (σuts) approach also has a large hardness difference with the measured values for T91 steels. The large departure of these two models from experimental measurement suggests a single coefficient may not be appropriate for all materials. The other three models give a better estimation of hardnesses. The hardness

Acknowledgements We acknowledge financial support from NSF-DMR 1611380. This work was partially supported by the Idaho National Laboratory Directed Research&Development (LDRD) Program under Department of Energy (DOE) Idaho Operations Office Contract DE-AC07-051D14517. Technical assistance on ECAE processing from Mr. Robert Barber is 218

International Journal of Pressure Vessels and Piping 172 (2019) 212–219

M. Song, et al.

greatly appreciated. We also acknowledge the use of microscopes at the Microscopy and Imaging Center (MIC) at Texas A&M University and Purdue University.

[27]

[28]

Appendix A. Supplementary data

[29]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpvp.2019.03.025.

[30]

References

[31]

[1] V. Sikka, C. Ward, K. Thomas, Ferritic Steels for High Temperature Applications, Ed. By AK Khare, ASM, Metals Park, OH, 1983, p. 65. [2] R. Swindeman, M. Santella, P. Maziasz, B. Roberts, K. Coleman, Issues in replacing Cr–Mo steels and stainless steels with 9Cr–1Mo–V steel, Int. J. Press. Vessel. Pip. 81 (6) (2004) 507–512. [3] M.J. Cohn, J.F. Henry, D. Nass, Fabrication, construction, and operation problems for grade 91 fossil power components, J. Press. Vessel Technol. 127 (2) (2005) 197–203. [4] A. Tonti, D. Lega, A. Antonini, M. Romitelli, A. Alvino, Damage characterization of an ASTM A 213 grade 91 tube after 116.000 h of service in a reforming plant, Int. J. Press. Vessel. Pip. 132 (2015) 87–96. [5] N. Saini, R.S. Mulik, M.M. Mahapatra, Influence of filler metals and PWHT regime on the microstructure and mechanical property relationships of CSEF steels dissimilar welded joints, Int. J. Press. Vessel. Pip. 170 (2019) 1–9. [6] M. Song, C.R. Lear, C.M. Parish, M. Wang, G.S. Was, Radiation tolerance of commercial and advanced alloys for core internals: a comprehensive microstructural characterization, J. Nucl. Mater. 510 (2018) 396–413. [7] C. Lear, M. Song, M. Wang, G. Was, Dual ion irradiation of commercial and advanced alloys: evaluating microstructural resistance for high dose core internals, J. Nucl. Mater. 516 (2019) 125–134. [8] G. Was, P. Ampornrat, G. Gupta, S. Teysseyre, E. West, T. Allen, K. Sridharan, L. Tan, Y. Chen, X. Ren, Corrosion and stress corrosion cracking in supercritical water, J. Nucl. Mater. 371 (1) (2007) 176–201. [9] M. Wang, M. Song, C.R. Lear, G.S. Was, Irradiation assisted stress corrosion cracking of commercial and advanced alloys for light water reactor core internals, J. Nucl. Mater. 515 (2019) 52–70. [10] C. Azevedo, Selection of fuel cladding material for nuclear fission reactors, Eng. Fail. Anal. 18 (8) (2011) 1943–1962. [11] T. Ellis, R. Petroski, P. Hejzlar, G. Zimmerman, D. McAlees, C. Whitemer, N. Touran, Traveling-wave Reactors: a Truly Sustainable and Full-Scale Resource for Global Energy Needs, Proceeding of ICAPP, 2010. [12] G. Was, Z. Jiao, E. Getto, K. Sun, A. Monterrosa, S. Maloy, O. Anderoglu, B. Sencer, M. Hackett, Emulation of reactor irradiation damage using ion beams, Scripta Mater. 88 (2014) 33–36. [13] ASTM, A., 1992. 213-Standard Specification for Seamless Ferritic and Austenitic Alloy-Steel Boiler, Superheater, and Heat-Exchanger Tubes. [14] M. Song, C. Sun, Z. Fan, Y. Chen, R. Zhu, K. Yu, K. Hartwig, H. Wang, X. Zhang, A roadmap for tailoring the strength and ductility of ferritic/martensitic T91 steel via thermo-mechanical treatment, Acta Mater. 112 (2016) 361–377. [15] S. Morito, H. Tanaka, R. Konishi, T. Furuhara, Maki, The morphology and crystallography of lath martensite in Fe-C alloys, Acta Mater. 51 (6) (2003) 1789–1799. [16] W. Han, Z. Zhang, S. Wu, S. Li, Influences of crystallographic orientations on deformation mechanism and grain refinement of Al single crystals subjected to onepass equal-channel angular pressing, Acta Mater. 55 (17) (2007) 5889–5900. [17] M. Song, C. Sun, J. Jang, C. Han, T. Kim, K. Hartwig, X. Zhang, Microstructure refinement and strengthening mechanisms of a 12Cr ODS steel processed by equal channel angular extrusion, J. Alloys Compd. 577 (2013) 247–256. [18] W. Han, H. Yang, X. An, R. Yang, S. Li, S. Wu, Z. Zhang, Evolution of initial grain boundaries and shear bands in Cu bicrystals during one-pass equal-channel angular pressing, Acta Mater. 57 (4) (2009) 1132–1146. [19] R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov, Bulk nanostructured materials from severe plastic deformation, Prog. Mater. Sci. 45 (2) (2000) 103–189. [20] Z. Fan, T. Hao, S. Zhao, G. Luo, C. Liu, Q. Fang, The microstructure and mechanical properties of T91 steel processed by ECAP at room temperature, J. Nucl. Mater. 434 (1) (2013) 417–421. [21] D. Foley, K. Hartwig, S. Maloy, P. Hosemann, X. Zhang, Grain refinement of T91 alloy by equal channel angular pressing, J. Nucl. Mater. 389 (2) (2009) 221–224. [22] T. Hao, H. Tang, G. Luo, X. Wang, C. Liu, Q. Fang, Enhancement effect of inter-pass annealing during equal channel angular pressing on grain refinement and ductility of 9Cr1Mo steel, Mater. Sci. Eng. A 667 (2016) 454–458. [23] M. Song, R. Zhu, D. Foley, C. Sun, Y. Chen, K. Hartwig, X. Zhang, Enhancement of strength and ductility in ultrafine-grained T91 steel through thermomechanical treatments, J. Mater. Sci. 48 (21) (2013) 7360–7373. [24] Z. Zhang, O. Mishin, N. Tao, W. Pantleon, Microstructure and annealing behavior of a modified 9Cr− 1Mo steel after dynamic plastic deformation to different strains, J. Nucl. Mater. 458 (2015) 64–69. [25] X. Jin, S. Chen, L. Rong, Microstructure modification and mechanical property improvement of reduced activation ferritic/martensitic steel by severe plastic deformation, Mater. Sci. Eng. A 712 (2018) 97–107. [26] M. Song, Y. Wu, D. Chen, X. Wang, C. Sun, K. Yu, Y. Chen, L. Shao, Y. Yang, K. Hartwig, Response of equal channel angular extrusion processed ultrafine-

[32]

[33] [34] [35]

[36] [37] [38]

[39]

[40]

[41]

[42]

[43]

[44] [45] [46]

[47]

[48]

[49] [50] [51]

[52] [53] [54] [55] [56] [57] [58] [59] [60]

219

grained T91 steel subjected to high temperature heavy ion irradiation, Acta Mater. 74 (2014) 285–295. J.G. Gigax, H. Kim, T. Chen, F. Garner, L. Shao, Radiation instability of equal channel angular extruded T91 at ultra-high damage levels, Acta Mater. 132 (2017) 395–404. D. Hughes, N. Hansen, High angle boundaries formed by grain subdivision mechanisms, Acta Mater. 45 (9) (1997) 3871–3886. N. Tao, Z. Wang, W. Tong, M. Sui, J. Lu, K. Lu, An investigation of surface nanocrystallization mechanism in Fe induced by surface mechanical attrition treatment, Acta Mater. 50 (18) (2002) 4603–4616. Y.T. Zhu, T.C. Lowe, Observations and issues on mechanisms of grain refinement during ECAP process, Mater. Sci. Eng. A 291 (1) (2000) 46–53. D.H. Shin, I. Kim, J. Kim, K.-T. Park, Grain refinement mechanism during equalchannel angular pressing of a low-carbon steel, Acta Mater. 49 (7) (2001) 1285–1292. L. Tan, B. Kim, Y. Yang, K.G. Field, S. Gray, M. Li, Microstructural evolution of neutron-irradiated T91 and NF616 to ∼ 4.3 dpa at 469°C, J. Nucl. Mater. 493 (2017) 12–20. Z. Jiao, S. Taller, K. Field, G. Yeli, M. Moody, G. Was, Microstructure evolution of T91 irradiated in the BOR60 fast reactor, J. Nucl. Mater. 504 (2018) 122–134. X. Jia, Y. Dai, Microstructure in martensitic steels T91 and F82H after irradiation in SINQ Target-3, J. Nucl. Mater. 318 (2003) 207–214. J. Gigax, T. Chen, H. Kim, J. Wang, L. Price, E. Aydogan, S.A. Maloy, D.K. Schreiber, M.B. Toloczko, F. Garner, Radiation response of alloy T91 at damage levels up to 1000 peak dpa, J. Nucl. Mater. 482 (2016) 257–265. A.M. Monterrosa, Z. Jiao, G.S. Was, The influence of helium on cavity evolution in ion-irradiated T91, J. Nucl. Mater. 509 (2018) 707–721. G. Gupta, Z. Jiao, A. Ham, J. Busby, G. Was, Microstructural evolution of proton irradiated T91, J. Nucl. Mater. 351 (1–3) (2006) 162–173. S.A. Maloy, M.B. Toloczko, K. McClellan, T. Romero, Y. Kohno, F.A. Garner, R.J. Kurtz, A. Kimura, The effects of fast reactor irradiation conditions on the tensile properties of two ferritic/martensitic steels, J. Nucl. Mater. 356 (1–3) (2006) 62–69. O. Anderoglu, T.S. Byun, M. Toloczko, S.A. Maloy, Mechanical performance of ferritic martensitic steels for high dose applications in advanced nuclear reactors, Metall. Mater. Trans. A 44 (1) (2013) 70–83. T.S. Byun, M.B. Toloczko, T.A. Saleh, S.A. Maloy, Irradiation dose and temperature dependence of fracture toughness in high dose HT9 steel from the fuel duct of FFTF, J. Nucl. Mater. 432 (1–3) (2013) 1–8. T.S. Byun, D.T. Hoelzer, J.H. Kim, S.A. Maloy, A comparative assessment of the fracture toughness behavior of ferritic-martensitic steels and nanostructured ferritic alloys, J. Nucl. Mater. 484 (2017) 157–167. A. Prasitthipayong, D. Frazer, A. Kareer, M. Abad, A. Garner, B. Joni, T. Ungar, G. Ribarik, M. Preuss, L. Balogh, Micro mechanical testing of candidate structural alloys for Gen-IV nuclear reactors, Nucl. Mater. Energy 16 (2018) 34–45. Y. Dai, J. Henry, Z. Tong, X. Averty, J. Malaplate, B. Long, Neutron/proton irradiation and He effects on the microstructure and mechanical properties of ferritic/ martensitic steels T91 and EM10, J. Nucl. Mater. 415 (3) (2011) 306–310. X. Jia, Y. Dai, Small punch tests on martensitic/ferritic steels F82H, T91 and Optimax-A irradiated in SINQ Target-3, J. Nucl. Mater. 323 (2–3) (2003) 360–367. G.S. Was, Fundamentals of Radiation Materials Science: Metals and Alloys, Springer, 2016. M. Moreno, Application of small punch testing on the mechanical and microstructural characterizations of P91 steel at room temperature, Int. J. Press. Vessel. Pip. 142 (2016) 1–9. M. Bruchhausen, S. Holmström, J.-M. Lapetite, S. Ripplinger, On the determination of the ductile to brittle transition temperature from small punch tests on Grade 91 ferritic-martensitic steel, Int. J. Press. Vessel. Pip. 155 (2017) 27–34. B. Gülçimen, A. Durmuş, S. Ülkü, R. Hurst, K. Turba, P. Hähner, Mechanical characterisation of a P91 weldment by means of small punch fracture testing, Int. J. Press. Vessel. Pip. 105 (2013) 28–35. J.T. Busby, M.C. Hash, G.S. Was, The relationship between hardness and yield stress in irradiated austenitic and ferritic steels, J. Nucl. Mater. 336 (2) (2005) 267–278. W.D. Nix, H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity, J. Mech. Phys. Solids 46 (3) (1998) 411–425. Q. Gao, Y. Liu, X. Di, L. Yu, Z. Yan, Martensite transformation in the modified high Cr ferritic heat-resistant steel during continuous cooling, J. Mater. Res. 27 (21) (2012) 2779. Y.T. Zhu, T.C. Lowe, Observations and issues on mechanisms of grain refinement during ECAP process, Mater. Sci. Eng. A 291 (1–2) (2000) 46–53. D. Tabor, The Hardness of Metals, Oxford University Press, 2000. K.K. Chawla, M. Meyers, Mechanical Behavior of Materials, Prentice Hall, 1999. P. Zhang, S. Li, Z. Zhang, General relationship between strength and hardness, Mater. Sci. Eng. A 529 (2011) 62–73. Y.-T. Cheng, C.-M. Cheng, Scaling, dimensional analysis, and indentation measurements, Mater. Sci. Eng. R: Rep. 44 (4) (2004) 91–149. M.A. Meyers, K.K. Chawla, Mechanical Behavior of Materials, Cambridge University Press Cambridge, 2009. E. Pavlina, C. Van Tyne, Correlation of yield strength and tensile strength with hardness for steels, J. Mater. Eng. Perform. 17 (6) (2008) 888–893. J. Cahoon, W. Broughton, A. Kutzak, The determination of yield strength from hardness measurements, Metall. Mater. Trans. B 2 (7) (1971) 1979–1983. X.-L. Gao, An expanding cavity model incorporating strain-hardening and indentation size effects, Int. J. Solids Struct. 43 (21) (2006) 6615–6629.