PSI - Issue 47

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Procedia Structural Integrity 47 (2023) 1–2

27th International Conference on Fracture and Structural Integrity (IGF27) Preface Filippo Berto a , Vittorio Di Cocco b , Giuseppe Andrea Ferro c , Francesco Iacoviello b *, Stefano Natali a , Daniela Pilone a , Sabrina Vantadori d

a "Sapienza" Università di Roma, Dipartimento di Ingegneria Chimica, Materiali, Ambiente, Italy b Università di Cassino e del Lazio Meridionale, Dipartimento di Ingegneria Civile e Meccanica, Italy c Politecnico di Torino, Dipartimento di Ingegneria Strutturale, Edile e Geotecnica, Italy d Università di Parma, Dipartimento di Ingegneria e Architettura, Italy

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons

Keywords: Preface, Fracture, Structural Integrity.

1. Preface The Italian Group of Fracture (IGF) is a cultural association devoted to: (i) spreading and promoting works and researches about fracture phenomena, even forming workgroups; (ii) promoting all the activities concerning the development of materials and structure testing standards; (iii) cooperating with foreign associations with the same intents; (iv) organizing meetings, workshops, conferences, debates and courses about fracture phenomena and (v) publishing meetings proceedings, news, journals. In the first months after the Covid-19 pandemia, we organized the IGF26 in Turin (May 2021) with a hybrid approach. The event was a success with 163 presentations from 28 different countries, but many presentation were held in remote and only some participants joined the event in presence. The IGF27 was held in February 2023 always with a hybrid approach, both in Rome, at the Engineering Faculty in via Eudossiana, and on-line. The participants number was even higher than IGF26 (more than 200), with a high

* Corresponding author. Tel.: +39.07723993681 E-mail address: iacoviello@unicas.it

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2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons 10.1016/j.prostr.2023.06.033

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participation in presence (more than 50%) and 187 presentations. The presentations were scheduled in 13 sessions, covering a wide range of topics related to theory, modelling and experiments of fracture and structural integrity phenomena. Two plenary lectures were carried out by Aleksandar Sedmak (University of Belgrade, Serbia) with the title “Numerical simulation of fatigue crack growth”, and by Stavros Kourkoulis (National Technical University of Athens, Greece), with the title “Quantifying elastic contact stresses on the lips of “mathematical” cracks”. During the event, Aleksandar Sedmak was awarded with the “2023 Manson-Coffin IGF medal” and Stavros Kourkoulis was awarded with the “2023 Paolo Lazzarin IGF Medal”. In addition, Francesco Iacoviello was awarded with the “2023 IGF Award of Merit”. According to the IGF tradition, all the presentations were video-recorded and they are now available in the IGF YouTube channel (https://www.youtube.com/playlist?list=PLT1-2PyZ6QrKcn6cpE_CJwxGiTviYuFgo). This special issue of Procedia Structural Integrity collects more than one hundred and ten papers related to the presentations given during the IGF27 conference. The number and the quality of the papers are an important sign of

the of the good health of the fracture and structural integrity community. We hope to meet you soon in presence in the upcoming IGF events!

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Procedia Structural Integrity 47 (2023) 908–914

27th International Conference on Fracture and Structural Integrity (IGF27) 27th International Conference on Fracture and Structural Integrity (IGF27)

Additively manufactured CuCrZr alloy: improvement of mechanical properties by heat treatment Additively manufactured CuCrZr alloy: improvement of mechanical properties by heat treatment

D.Cortis a , E.Mancini b , D.Orlandi a , D.Pilone c * and M.Sasso d a Gran Sasso National Laboratory, National Institute for Nuclear Physics, 67100 L’Aquila, Italy b Università degli Studi dell'Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, 67100 L'Aquila, Italy c Dipartimento ICMA, Sapienza Università di Roma, 00184 Roma, Italy d Università Politecnica delle Marche, DIISM, Via Brecce Bianche, Ancona, 60121, Italy D.Cortis a , E.Mancini b , D.Orlandi a , D.Pilone c * and M.Sasso d a Gran Sasso National Laboratory, National Institute for Nuclear Physics, 67100 L’Aquila, Italy b Università degli Studi dell'Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, 67100 L'Aquila, Italy c Dipartimento ICMA, Sapienza Università di Roma, 00184 Roma, Italy d Università Politecnica delle Marche, DIISM, Via Brecce Bianche, Ancona, 60121, Italy

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Abstract CuCrZr alloy plays a fundamental role for the production of critical components because it is characterized by good thermal and electrical conductivity and by high mechanical strength after precipitation hardening treatment. In the framework of a wider research on the mechanical behaviour of additively manufactured CuCrZr alloy, this study focuses on the effects of heat treatment parameters on the alloy strength. The additive manufacturing process, characterized by very high cooling rates, determines the formation, in the as-built condition, of a supersaturated solid solution. The results obtained reveal that aging temperature and time are critical parameters for improving the mechanical behaviour of CuCrZr alloy which behaves differently than the alloy produced through the use of traditional techniques. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Abstract CuCrZr alloy plays a fundamental role for the production of critical components because it is characterized by good thermal and electrical conductivity and by high mechanical strength after precipitation hardening treatment. In the framework of a wider research on the mechanical behaviour of additively manufactured CuCrZr alloy, this study focuses on the effects of heat treatment parameters on the alloy strength. The additive manufacturing process, characterized by very high cooling rates, determines the formation, in the as-built condition, of a supersaturated solid solution. The results obtained reveal that aging temperature and time are critical parameters for improving the mechanical behaviour of CuCrZr alloy which behaves differently than the alloy produced through the use of traditional techniques.

Keywords: Additive manufacturing; Cu alloys; CuCrZr alloy; Selective laser melting; Thermal treatment. Keywords: Additive manufacturing; Cu alloys; CuCrZr alloy; Selective laser melting; Thermal treatment.

* Corresponding author. Tel.: +39 06 44585879. E-mail address: daniela.pilone@uniroma1.it * Corresponding author. Tel.: +39 06 44585879. E-mail address: daniela.pilone@uniroma1.it

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons 2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons 10.1016/j.prostr.2023.07.021

D. Cortis et al. / Procedia Structural Integrity 47 (2023) 908–914 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Age-hardenable CuCrZr alloys have many industrial applications. Due to a favorable combination of high strength, high electrical and thermal conductivity, CuCrZr alloy can be used in the production of high heat flux components of ITER, in the manufacturing of contact wire in railways and of resistance welding electrodes (Ostachowski et al.(2019), Barabash et al. (2011)). Many works available in literature highlighted thermal and thermomechanical treatments able to increase mechanical properties of the these types of alloys. Considering that CuCrZr alloy is also considered an interesting candidate for high temperature applications such as combustion chamber liner of rocket engines, many studies have been performed to analyse mechanical performances at high temperatures, creep and fatigue resistance (Mishnev et al.(2015), Zhang et al. (2016), Xia et al. (2012), Vinogradov et al. (2002), Peng et al. (2014)). It has been also studied because it is considered a suitable material for the construction of passive satellites (Brotzu et al (2019), Brotzu et al. (2020)). In the last few years many studies have been carried out on CuCrZr alloy production by means of additive manufacturing. Many difficulties arise in the additive manufacturing process of CuCrZr alloy due to its high thermal conductivity and high optical reflectivity at 1070 nm (Popovich et al. (2016)). Several recent studies showed the ability to create dense CuCrZr parts in particular by using laser power over about 300 W. Many papers available in literature reported the relationship among process parameters, heat treatment and mechanical properties of CuCrZr alloy (Salvan et al. (2021), Kuai et al. (2022), Wallis et al. (2019), Hu et al. (2022), Sun et al.(2020), Guan et al. (2019), Tang et al. (2022)). Some authors highlighted that cooling rates of about 10 6 K/s allow to obtain microstructures that can be directly aged (Salvan et al. (2021)) with a consequent considerable increase of the hardness and thus of the mechanical strength. By comparing the hardness and yield strength data it is possible to see that they are not always in accordance. Some authors explained the strength increase of these alloys by attributing the formation of Cr – Zr – Cu nano precipitates, formed in the specimen, to the effect of intrinsic heat treatment during the SLM process (Hu et al. (2022)). Other authors attributed the increase in strength to the precipitation of Cr-enriched phases and to the high dislocation density, while the increased electrical conductivity was attributed to the decomposition of the supersaturated solid solution (Tang et al. (2022), Zhou et al. (2022)). Aim of this paper is to evaluate the effect of heat treatment on the mechanical behaviour of CuCrZr alloy. The effect of the solution annealing treatment and of the aging time and temperature are investigated. 2. Experimental Specimens were manufactured by means Laser Powder Bed Fusion (L-PBF) technology, in particular using the Selective Laser Melting (SLM) technique. The used machine (SISMA MySint100 PM/RM ) is equipped with a InfraRed (IR) laser source with a focus of 30 µm and a nominal power up to 175 W. The building volume is 100 mm x 100 mm and the layer thickness is adjustable between 20 and 100 µm. The volumetric energy density (VED) applied to the CuCrZr powder bed is ~260 J/mm 3 and it was obtained with a Laser Power (P) of 175 W, a Layer Thickness (L) of 20 µm, a Laser Scanning Speed (S) of 850 mm/s and an Hatch Distance(H) of 40 µm. The printing process was performed under a Nitrogen (N 2 ) atmosphere and a gas speed of 2.5 m/s. As it is well-known, copper has high thermal conductivity and poor adsorption coefficient at the wavelengths of the IR laser. This reduces the energy density available for the melting process, generating defects such as cavities and lack of fusion. These characteristics did not make possible to achieve material density close to 100%. The CuCrZr is an ASTM C18400 alloy with chemical composition: 0.5 – 1.5 wt% Cr, 0.03 – 0.3 wt% Zr. For the production of the specimens, a Hovadur® CCZ powder (15-45 µm) produced by Schmelzmetall has been used. The powder nominal composition is reported in Table 1. The geometry of the specimens have been designed considering the ASTM E-9 standard and the requirement of the Hopkinson bar machine used for the dynamic tests. A part of the specimens were also heat-treated (HT) with an ageing process carried out at 580 °C and at 450 °C under Nitrogen (N 2 ) atmosphere, followed by cooling in air. Figure 1 shows the produced specimens.

3

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Table 1. Hovadur® CCZ Schmelzmetall powder chemical composition (wt%).

Cu

Cr

Zr

Fe

Si

Others

98.1 - 99.4

0.5 – 1.2

0.03 – 0.3

0.08

0.1

0.2

(a)

(b)

(c)

Fig. 1. Specimens produced for quasi-static and dynamic tests before (a and b) and after (c) aging treatment.

Samples were ground using SiC papers ranging from 80 to 2400 grit, polished with 0.1 µm alumina suspension, and then etched with ferric chloride to observe the microstructure by using SEM and optical microscope. Aging curves have been obtained by using a microindenter. XRD measurements were made with a diffractometer equipped with a Philips X’PERT vertical Bragg– Brentano powder goniometer. A step – scan mode was used in the 2θ range from 30° to 100° with a step width of 0.02° and a counting time of 1 s per step. The radiation used was the monochromatic Cu Kα radiation. 3. Results and discussion As a first step of this investigation the powders used for producing the specimens were analysed by SEM/EDS. Figure 2 shows the morphology of the powders. They have a size varying between 15 and 45 µm and a spherical shape. The micrographs in Figure 2 show the presence of satellites justified by the fact that powders are partially recycled during the production process. EDS analyses reported in Table 2 show that the powder composition is the nominal one. The additive manufactured specimens have been analysed to investigate the alloy microstructure. As it can be observed in Figure 3 the microstructure is constituted by irregular grains having a variable size and, in particular, it is possible to observe grains elongated in the direction of heat removal. Moreover the high thermal conductivity and the high reflectivity of this alloy determine the formation of lack of fusion (indicated by arrows) and of cavities that sometimes contain frozen metallic droplets or unmolten particles. This inhomogeneous microstructure depends on the very high cooling rates and on the process parameters that affect the material local thermal cycle. EDS analyses of the additively manufactured alloy (Table 3) reveal that Zr is below the detectability limit and that Cr concentration is about 60% of that of the powders. The high localized temperatures reached during the production process determine the evaporation of part of the alloying elements. This is an important finding because the use of different values of VED could produce different alloying element concentrations in the manufactured part and thus different mechanical properties. By comparing the microstructure of additive manufactured alloys with the one of alloys produced by using traditional techniques it is evident that in the latter case (Fig. 4) the grains are quite regular and characterized by the presence of twins. Moreover Fig. 4b highlights the presence of Zr and Cr rich precipitates (small grey phases). They form during solidification because both Cr and Zr have a very low solubility in copper. These precipitates are not visible in the microstructure of additively

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manufactured specimens because, as suggested by other authors (Salvan et al.(2021)), the high cooling rates involved in the additive manufacturing process of copper alloys, produce the formation of a supersaturated solid solution, whose presence influences not only the mechanical properties of the alloy, but also the type of thermal treatment necessary to increase the alloy mechanical strength.

Fig 2. SEM micrographs showing the CuCrZr powder morphology.

Table 2. EDS analyses of CuCrZr powders. Element

Weight (%)

Atom (%)

Cr Cu

0.97

1.18

98.93

98.75

Zr

0.10

0.07

Fig. 3. Optical micrographs the alloy microstructure after etching with ferric chloride and a detail of cavities (micrograph on the left).

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Table 3. EDS analyses of the additively manufactured specimens. Element Weight (%)

Atom (%)

Cr Cu

0.58

0.71

99.42

99.29

Zr

nd

nd

Fig. 4. Optical micrograph showing the microstructure (a,b) of a CuCrZr alloy produced by using traditional techniques after forging and aging and Cr-rich precipitates (b).

In order to study the aging treatment a thermal treatment at 580 °C has been performed on the as-built specimens and on the specimens previously subjected to solution annealing at 980 °C for 1 h. The aging curves reported in Fig. 5 show that both types of specimens reach the hardness peak after a very short time interval and that after solution annealing the alloy hardness is much lower. XRD patterns of the CuCrZr specimens in the as-built conditions and after annealing (Fig. 6) show that in the as-built conditions (Fig.6a) only copper peaks are visible, while, after solution annealing, a small peak characterizing a Zr-rich phase appears (Fig.6b). This suggests that the heat treatment at 980 °C determines the formation of Zr-rich phases that are not coherent with the metallic matrix and that in the aging stage limit the formation of coherent particles that would be able to increase the alloy hardness and strength.

Fig. 5. Aging curves obtained by treating at 580 °C solution annealed (green line) and as-built (blue line) samples.

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Considering that the temperature affects the aging treatment, we evaluated the effect of aging temperature on mechanical properties. Figure 7 highlights that the aging treatment temperature has a strong effect on the mechanical performances of the alloy. By aging as-built specimens at 580 °C the hardness peak is reached after only 30 minutes, but due to overaging, hardness quicky decreases. Aging performed at 450 °C allows to attain higher hardness values, even after the peak. This could be explained considering that a lower temperature treatment requires more time to reach the hardness peak because the diffusivity value is lower, but probably in these conditions is possible to form nanometric particles that are more effective in hindering dislocation movement with consequent strength increase.

Fig. 6. XRD pattern of an as-built sample (a) and of a solution annealed sample (b).

Fig. 7. Aging curves obtained by aging as-built specimens at 450 °C (red line) and at 580 °C (blue line).

4. Conclusions The research reported in this paper highlights that CuCrZr alloys produced by means of additive manufacturing are very different from the traditional ones. Metallurgical defects like lack of fusion and cavities are difficult to avoid because of the high thermal conductivity and reflectivity of copper. The alloy microstructure is strongly affected by the extremely high cooling rates involved in the additive manufacturing process. These high cooling rates determine also the formation of a supersaturated solid solution in the as-built samples that can be subjected to a direct aging process. The experimental results highlighted also that aging temperature and time considerably affect the mechanical

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behaviour of CuCrZr alloy. In order to tailor the alloy for a specific application it is essential to carefully select both additive manufacturing parameters and aging temperature and time.

References

Barabash, V.R., Kalinin, G.M., Fabritsiev, S.A. et al., 2011. Specification of CuCrZr alloy properties after various thermo-mechanical treatments and design allowables including neutron irradiation effects, Journal of Nuclear Materials 417, 904-907. Brotzu, A., Felli, F., Pilone, D. et al. 2019. Study of CuCrZr alloy for the production of a passive satellite, Procedia Structural Integrity 18, 742 748. Brotzu, A, Felli, F, Pilone, D, et al., 2020. Study of the fracture behavior of a CuCrZr alloy. Mat Design Process Comm. 2:e113. Guan, P., Chen, X., Liu, P. et al., 2019. Effect of selective laser melting process parameters and aging heat treatment on properties of CuCrZr alloy. Materials Research Express 6 , 1165c1. Hu, Z., Du, Z., Yang, Z. et al., 2022. Preparation of Cu–Cr–Zr alloy by selective laser melting: Role of scanning parameters on densification, microstructure and mechanical properties, Materials Science and Engineering: A836, 142740. Kuai, Z., Li, Z., Liu, B. et al., 2022, Selective laser melting of CuCrZr alloy: processing optimisation, microstructure and mechanical properties, Journal of Materials Research and Technology 19, 4915-4931. Mishnev, R., Shakhoba, I., Belyakov, A. et al., 2015. Deformation microstructures, strengthening mechanisms, and electrical conductivity in a CuCr–Zr alloy. Mater. Sci. Eng., A 629, 29–40. Ostachowski, P., Bochniak, W., Łagoda, M. et al. , 2019. Strength properties and structure of CuCrZr alloy subjected to low-temperature KOBO extrusion and heat treatment. Int J Adv Manuf Technol 105, 5023–5044. Peng, L., Xie, H., Huang, G. et al., 2014. Dynamic of phase transformation in Cu–Cr–Zr alloy. Adv. Mater. Res. 887–888, 333–337. Popovich, A., Sufiiarov, V., Polozov, I. et al. 2016. Microstructure and mechanical properties of additive manufactured copper alloy, Mater. Lett. 179, 38–41. Salvan, C., Briottet, L., Baffie, T. et al., 2021. CuCrZr alloy produced by laser powder bed fusion: Microstructure, nanoscale strengthening mechanisms, electrical and mechanical properties, Materials Science and Engineering: A826, 141915. Sun, F., Liu, P., Chen, X., Zhou, H., Guan, P., & Zhu, B. (2020). Mechanical Properties of High-Strength Cu–Cr–Zr Alloy Fabricated by Selective Laser Melting. Materials 13, 5028. Tang, X., Chen, X., Sun, F. et al., 2022. A Study on the Mechanical and Electrical Properties of High-strength CuCrZr Alloy Fabricated Using Laser Powder Bed Fusion. Journal of Alloys and Compounds 924, 166627. Vinogradov, A., Patlan, V., Suzuki, Y. et al., 2002. Structure and properties of ultra-fine grain Cu–Cr–Zr alloy produced by equal-channel angular pressing. Acta Mater. 50, 1639–1651. Wallis C., Buchmayr B., 2019. Effect of heat treatments on microstructure and properties of CuCrZr produced by laser-powder bed fusion, Materials Science and Engineering A744, 215 – 223. Xia, C., Jia, Y., Zhang, W. et al., 2012. Study of deformation and aging behaviors of a hot rolled– quenched Cu–Cr–Zr–Mg–Si alloy during thermomechanical treatments. Mater. Des. 39, 404–409. Zhang, Y., Volinsky, A., Tran, H., et al., 2016. Aging behavior and precipitates analysis of the Cu–Cr–Zr–Ce alloy. Mater. Sci. Eng., A 650, 248– 253. Zhou, J., Huang, Y., Li, Z. et al, 2022. Effect of heat treatments on microstructure, mechanical and electrical properties of Cu–Cr–Zr alloy manufactured by laser powder bed fusion. Materials Chemistry and Physics 296, 127249.

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© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Abstract Warm prestressing (WPS) is a phenomenon where cracked ferritic–martensitic steels get a higher fracture resistance in the lower shelf region after first being deformed in the upper-shelf region. In the current study, a predictive model for the WPS e ff ect was developed based on a fracture mechanics based strip-yield approach. The strip yield-model was modified to account for strain hardening during plastic deformation. It was found that a suitable fracture criterion was to assume failure at the point where the lower-shelf crack tip plastic zone reached the same size as the plastic zone introduced during deformation in the upper-shelf. The model predicted the WPS e ff ect with acceptable accuracy for several temperature–load cycles. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the IGF27 chairpersons. Keywords: warm prestressing; fracture mechanics; strip-yield model; prediction; turbine steel; fracture toughness 27th International Conference on Fracture and Structural Integrity (IGF27) A modified strip yield model to predict warm prestressing e ff ects in turbine steel Robert Eriksson a, ∗ , Ahmed Azeez a a Department of Management and Engineering, Linko¨ping University, Linko¨pings universitet, Linko¨ping 58183, Sweden Abstract Warm prestressing (WPS) is a phenomenon where cracked ferritic–martensitic steels get a higher fracture resistance in the lower shelf region after first being deformed in the upper-shelf region. In the current study, a predictive model for the WPS e ff ect was developed based on a fracture mechanics based strip-yield approach. The strip yield-model was modified to account for strain hardening during plastic deformation. It was found that a suitable fracture criterion was to assume failure at the point where the lower-shelf crack tip plastic zone reached the same size as the plastic zone introduced during deformation in the upper-shelf. The model predicted the WPS e ff ect with acceptable accuracy for several temperature–load cycles. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the IGF27 chairpersons. Keywords: warm prestressing; fracture mechanics; strip-yield model; prediction; turbine steel; fracture toughness 27th International Conference on Fracture and Structural Integrity (IGF27) A modified strip yield model to predict warm prestressing e ff ects in turbine steel Robert Eriksson a, ∗ , Ahmed Azeez a a Department of Management and Engineering, Linko¨ping University, Linko¨pings universitet, Linko¨ping 58183, Sweden

1. Introduction 1. Introduction

Warm prestressing (WPS) is the phenomenon where a (typically ferritic or ferritic–martensitic) steel experiences an increase in fracture resistance, K f , (above the fracture toughness, K Ic ) below its ductile to brittle transition temperature (DBTT) after going through a temperature–load history above its DBTT. The WPS e ff ect may give an additional margin of safety and has mainly been utilized in the nuclear sector Blumenauer and Krempe (2001); Kordisch et al. (2000); Hure et al. (2015). The WPS e ff ect is mainly attributed to three mechanisms Blumenauer and Krempe (2001); Kordisch et al. (2000): Warm prestressing (WPS) is the phenomenon where a (typically ferritic or ferritic–martensitic) steel experiences an increase in fracture resistance, K f , (above the fracture toughness, K Ic ) below its ductile to brittle transition temperature (DBTT) after going through a temperature–load history above its DBTT. The WPS e ff ect may give an additional margin of safety and has mainly been utilized in the nuclear sector Blumenauer and Krempe (2001); Kordisch et al. (2000); Hure et al. (2015). The WPS e ff ect is mainly attributed to three mechanisms Blumenauer and Krempe (2001); Kordisch et al. (2000):

• The introduction of a residual stress field at the crack tip. • Crack tip blunting. • Increased yield strength at the crack tip due to strain hardening. • The introduction of a residual stress field at the crack tip. • Crack tip blunting. • Increased yield strength at the crack tip due to strain hardening.

∗ Corresponding author. Tel.: + 46-13-281139 E-mail address: robert.eriksson@liu.se ∗ Corresponding author. Tel.: + 46-13-281139 E-mail address: robert.eriksson@liu.se

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228

2

a)

K

b)

K

Fracture toughness

Fracture toughness

K 1

K 1 = K 2 K f

K f

K 2

T 2

T 1

T 2

T 1

T

T

Fig. 1. Schematic illustrations of a (a) LUCF cycle and (b) LCF cycle.

All mechanisms have in common that they are the result of plastic deformation at the crack tip. In general, most researchers seems to favor residual stresses as the main contributing mechanism since stress relief heat treatments after WPS load have been shown to reduce the WPS e ff ect Reed and Knott (1996); Blumenauer and Krempe (2001); Chen et al. (2002). There are many possible temperature–load histories, but two cases have become particularly common when char acterizing WPS: the load–cool–fracture (LCF) cycle and the load–unload–cool–fracture (LUCF) cycle, both are illus trated in Fig. 1. The LCF cycle is generally considered to give a larger increase in K f than LUCF Reed and Knott (1996). The following terminology is used to describe the temperature–load cycle • The temperature where the WPS load is applied is denoted T 1 and the applied load is denoted either P 1 (force) or K 1 (stress intensity). • For LUCF, the value of the lowest load at T 1 is denoted P 2 (force) or K 2 (stress intensity). For LCF, P 2 = P 1 , K 2 = K 1 . • At low temperature, T 2 , the load at fracture is denoted P f with the corresponding fracture resistance K f (stress intensity). The WPS load, P 2 , needed to give rise to a WPS e ff ect have been variously described as K 1 > K Ic Reed and Knott (1996) or P 1 P GY ≥ 0 . 5where P GY is the load causing general yield Wang et al. (2002). Models describing the WPS e ff ects include “global” approaches such as that of Wallin (2003, 2004) which do not require the stresses in front of the crack to be known and “local” approaches such as the Beremin Beremin (1983) and modified Beremin models Lefevre et al. (2002); Kordisch et al. (2000) which are based on a weakest link assumption and require that stresses are known. The crack tip plastic zone created during WPS load forms, what Chell (1986) refers to as, a “residual zone” which will not deform further when the crack is loaded to fracture at low temperature. As pointed out by several authors Reed and Knott (1996); Smith et al. (2010), plasticity is necessary for cleavage to occur, meaning that failure will occur at the onset of plasticity outside of the residual zone. In the present work, a physically based analytical model was developed based on fracture mechanics. As most suggested mechanisms of the WPS e ff ect could be, at least, indirectly related to plastic zone size, a strip-yield model was taken as a basis for the developed model. WPS tests were performed in an electromechanical tensile test rig, Alwetron TCT 100, and a 3-zone furnace. Tem perature was controlled by three thermocouples; two mounted on each grip and one mounted on the specimen. Load line displacement was measured using a high temperature extensometer, Epsilon Tech. Corp. The studied material was a wrought, creep resistant 9 % Cr steel for turbine applications with a DBTT around ∼ 50 ◦ C. The tests were performed using standard compact tension specimens with thickness 25 mm (CT25); side grooves where used. The specimen was heated during a small preload of 0.5 kN to avoid going into compression during heating. Once the desired temperature was reached, the specimen was left to dwell for 30 min to reach a homogeneous temperature prior to loading. For the LCF cycle, the furnace was turned o ff immediately after reaching maximum load (except for specimen no. 8, see Table 1, which was left to dwell 60 min prior to cooling). For the LUCF cycle, 2. Experiments

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the specimen was unloaded to P 2 = 0 . 5 kN and then the furnace was turned o ff . For both cycles, the specimens were left to cool in the furnace overnight. Two minimum temperatures were tested: 20 ◦ C and 50 ◦ C. Once the specimens had properly cooled, they were pulled to fracture in crosshead displacement control at 1 mm / min. The maximum temperatures used were 100–400 ◦ C and the applied loads were 40–60 kN. The tests are summarized in Table 1

Table 1. Performed WPS tests. No. Cycle

T 1 , ◦ C

T 2 , ◦ C

P 1 , kN

P 2 , kN

1 2 3 4 5 6 7 8 9

LCF LCF LCF LCF LCF LCF LCF LCF LCF LCF LCF

100 200 200 300 300 300 300 300 300 400 400 200 300 300 300 400

50 50 50 40 50 50 50 50 60 50 50 50 40 50 60 50

20 20 50 20 20 20 50 20 20 20 50 20 20 20 20 20

50 50 50 40 50 50 50 50 60 50 50

10 11 12 13 14 15 16

LUCF LUCF LUCF LUCF LUCF

0.5 0.5 0.5 0.5 0.5

3. Model description

Most mechanisms contributing to the WPS e ff ect (i.e. residual stresses, crack tip blunting and increase in yield strength) depend on the amount of plastic deformation at the crack tip. It seems reasonable that a parameter that de scribes the amount of plastic deformation at the crack tip should quantify, at least indirectly, all relevant mechanisms causing the WPS e ff ect. The crack tip plastic zone size should work as such a parameter. A convenient way of estimat ing the plastic zone size is the fracture mechanics based strip-yield model. Therefore, a modified strip-yield approach was used to develop a model that describes the WPS e ff ect. The following sections outline the model.

3.1. Solutions for the stress intensity factor

Stress intensity factor solutions for a standard CT specimen are readily available in various handbooks; it is

3 2

4

13 . 32

a W

a W

a W

+ 14 . 72

− 5 . 6

a W

2 +

2

3

a W −

P √ BB N W

K I =

0 . 886 + 4 . 64

(1)

1 − a

W

with the specimen width, W , and the crack length, a , as defined in Fig. 2. B is the specimen thickness and B N is the thickness at the side grooves (if present). The stress intensity factor can also be obtained by integrating the weight function, h ( x ), and the crack face pressure, p ( x ), over the crack length

a 0

5 2

1 √ 2 π a

x a

x a

x a

x a

β 1 1 −

+ β 2 1 −

+ β 3 1 −

+ β 4 1 −

− 1 2

1 2

3 2

K I =

h ( x ) p ( x ) dx , h ( x ) =

(2)

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Fig. 2. Standard CT25 specimen.

The weight function used here is by Eder and Chen (2021) where x is defined as in Fig. 2 and the coe ffi cients, β , are given in Table 2.

Table 2. Coe ffi cients for the weight function. a / W β 1

β 2

β 3

β 4

0.2 0.3 0.4 0.5 0.6 0.7 0.8

2.00 2.00 2.00 2.00 2.00 2.00 2.00

3.3270 4.9886 7.2610 10.4356 15.1033 22.6834 37.2393

1.4351 1.7280 2.7054 5.2943 11.3700 26.0237 69.1970

-0.4652 -0.4130 -0.4570 -0.7632 -1.6671 -4.0924 -11.7568

In the strip-yield approach, the crack surface pressure is set constant to the negative of the yield strength, p ( x ) = − σ ys , and is only applied over a virtual extension of the crack, ρ . The solution then becomes

a + ρ  a

h ( x ) dx

K ρ = − σ ys

7 2  

π  

= − σ ys 

a a + ρ 

3 

a a + ρ 

5 

a a + ρ 

7 

a a + ρ 

 β 1  1 −

1 2

3 2

5 2

2( a + ρ )

β 2

β 3

β 4

+  (3) where the notation K ρ has been introduced for a stress intensity factor calculated from the crack face pressure on the virtual crack extension ρ (which will later be taken as equal to the plastic zone size). 1 − + 1 − + 1 −

3.2. Material model

In the strip-yield approach, the material is assumed ideally plastic. In the current work, however, a “quasi-ideal plastic” model is used by which is meant:

1. When the material is loaded, the average plastic zone strain, ϵ pz , is estimated from displacements determined from the stress intensity factor (further explained below). 2. Based on estimated plastic zone strain, the flow stress, σ flow , is calculated from a simple one dimensional com bined linear isotropic / kinematic hardening model (described in Appendix A). 3. The so determined σ flow is taken as the yield stress, σ ys , in an ideal plastic model and used in the strip yield model, i.e. σ ys = σ flow ( ϵ pz ). The procedure is illustrated in Fig. 3.

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σ

σ

Y fl ow σ

ys σ

K EH E + H

Y

K

E

ε

ε

ε pz

ε pz

Fig. 3. The “quasi-ideal plastic” material modeling where the constant σ ys in the ideal-plastic model is taken from the flow stress, σ flow , in a linear isotropic / kinematic hardening model; E and H K are the elastic and plastic moduli.

u y

u x

r= ρ

y

2 π

θ =

Crack

x Plastic zone

Fig. 4. Average strain in the plastic zone is estimated from the displacements on the boundary of the plastic zone, u y , and its size, ρ .

3.3. Estimation of crack tip average strain

In polar coordinates, ( r ,θ ), the displacement in y , u y , around the crack tip becomes

, κ =   3 − ν 1 + ν

K I 2 µ 

2  θ

sin 

θ 2 

2 

plane stress 3 − 4 ν plane strain

r 2 π

E 2(1 + ν )

u y =

κ + 1 − 2cos

(4)

, µ =

where E is the elastic modulus and ν is the Poisson’s ratio. The plastic zone is constrained by the surrounding elastic material. The strain in the plastic zone is thus determined by the displacements at the boundary of the plastic zone. An estimation of the average y -component of the strain in the plastic zone, ϵ pz , can therefore be taken as

u y  r = ρ,θ = ρ

π 2 

K κ 4 µ √ ρπ

(5)

ϵ pz =

=

where ρ is the plastic zone size as illustrated in Fig. 4. This is obviously a rough approximation but it will turn out to be accurate enough for estimating a reasonable flow stress.

3.4. Modeling of the WPS cycle

During the WPS load, P 1 at T 1 , a plastic zone will form. Based on earlier observations that cleavage fracture requires active plastic deformation, fracture is assumed to occur at T 2 when the applied load just causes plastic defor mation outside of the WPS plastic zone; i.e. failure occurs when the plastic zone at T 2 reaches the same size as of that formed during WPS load ( P 1 at T 1 ). For the LCF cycle, this is pretty straight forward:

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LCF

LUCF

a)

WPS plastic zone

WPS plastic zone

P 1

T 1

P 1

T 1

σ ys1

σ ys1

σ ys1

σ ys1

P 1

P 1

ρ

ρ

a

a

b)

WPS plastic zone

WPS plastic zone

WPS reversed plastic zone

T 1

P 2 = P 1

T 1

P 2

σ 2

σ 2 = σ ys1

σ ys1 σ ys1

σ 2 = σ ys1

σ 2

P 2 = P 1

P 2

≈ ρ

ρ

a

a

ρ

c)

WPS plastic zone

WPS plastic zone

plastic zone

plastic zone

P

T

T

P

σ ysf

2

2

σ ysf

σ res σ res

σ ysf

σ ysf

P

P

< ρ

< ρ

a

a

d)

WPS plastic zone

WPS plastic zone

plastic zone

plastic zone

T

P=P f

T 2

P=P

σ ysf

2

f

σ ysf

σ res σ res

σ ysf

σ ysf

P=P f

P=P f

= ρ

a

= ρ

a

Fig. 5. The overall procedure for establishing the plastic zone size for the LCF and LUCF cycles: a) WPS load ( P 1 ) at T 1 , b) unloading to P 2 ; for LCF P 2 = P 1 , for LUCF residual stresses are introduced, c) temperature is dropped to T 2 , the load starts to increase, d) fracture at load P f as the plastic zone reaches the same size as the plastic zone from step a).

1. A plastic zone forms at T 1 during WPS load ( P 1 ). 2. The stresses in the plastic zone is retained during cooling to T 2 as the load is kept constant. 3. At T 2 , some additional load must be added to cause plasticity just outside of the WPS plastic zone since the yield strength is higher at T 2 compared to T 1 . Fracture occurs as the plastic zone at T 2 just barely extends outside of the WPS plastic zone. Figure 5 illustrates the procedure. For the LUCF cycle the procedure is a bit more involved; the unloading to P 2 < P 1 will leave some residual stresses that needs to be accounted for. The procedure becomes: 1. A plastic zone forms at T 1 during WPS load ( P 1 ). 2. The load is dropped to P 2 < P 1 ; residual stress from P 1 remains. (How these are estimated is explained below.) 3. Stresses from P 2 as well as residual stresses in the plastic zone are retained during cooling to T 2 . 4. At T 2 , fracture occurs when the sum of residual stresses and stresses from P f causes the plastic zone at T 2 to just barely extends outside of the WPS plastic zone. Figure 5 illustrates the procedure.

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The plastic zone size, ρ , is determined through a modified strip-yield approach where the material is allowed to harden as ρ increases in size. Mathematically, the procedure involves the steps described below. Loading to P 1 at T 1 results in a WPS plastic zone of size ρ which is obtained by iteratively solving  K 1 = P 1 √ BB N W 2 + 3 2  0 . 886 + 4 . 64 a + ρ W − 13 . 32  a + ρ W  2 + 14 . 72  a + ρ W  3 − 5 . 6  a + ρ W  4 

a + ρ W  1 − a + ρ W 

     

K 1 κ 4 µ √ ρπ

ϵ pz1 = estimated strain σ ys1 = | σ flow ( ϵ pz1 ) | from constitutive model; see Appendix A K ρ 1 = − σ ys1  2( a + ρ ) π    β 1  1 − a a + ρ  1 2 + β 2 3  1 − a a + ρ  3 2 K 1 + K ρ 1 = 0 criterion for stopping iteration

(6)

7 2   

5 

a a + ρ 

7 

a a + ρ 

5 2

β 3

β 4

1 −

1 −

+

+

with respect to ρ (i.e. ρ is increased in increments, starting from ρ = 0, until the condition K 1 + K ρ 1 = 0 is fulfilled). Note that σ flow is taken from the linear isotropic / kinematic hardening model (which must be updated in each iteration as ϵ pz depends on ρ ). K 1 is calculated from Eq. 1 and K ρ 1 fromEq. 3. Changing the load to P 2 results in  K 2 = P 2 √ BB N W 2 + 0 . 886 + 4 . 64 a + ρ W − a + ρ 2 a + ρ 3 a + ρ

3 2 

4 

a + ρ W  1 − a + ρ W 

W 

W 

W 

+ 14 . 72 

− 5 . 6 

13 . 32 

      

K 2 κ 4 µ √ ρπ

estimated strain

ϵ pz2 =

σ 2 =   K ρ 2 = σ 2 

(7)

σ ys2 = | σ flow ( ϵ pz2 ) | if the material plasticize | σ ( ϵ pz2 ) |

see Appendix A

if the material does not plasticize

7 2   

π  

a a + ρ 

3 

a a + ρ 

5 

a a + ρ 

7 

a a + ρ 

 β 1  1 −

1 2

3 2

5 2

2( a + ρ )

β 2

β 3

β 4

1 −

1 −

1 −

+

+

+

which does not need to be solved iteratively as ρ remains the same as in the previous step. Note that the material does not necessarily plasticize during unloading, so the stress σ 2 may take either the value σ ys2 (yield stress) or a stress, σ ( ϵ pz2 ), in the elastic region. However, unloading the crack after the creation of a plastic zone will, at least most of the time, result in some degree of reversed plasticity as the surrounding elastic material forces the plastic zone to shrink. It is here assumed that the crack face pressure introduced by P 1 , σ ys1 , remains at unloading and tries to close the crack. Therefore, after unloading, the plastic zone, ρ , becomes loaded by the positive crack face pressure σ 2 which counteracts the closing pressure σ ys1 . (Reversed plasticity may occur in a zone smaller than the plastic zone, i.e. of size <ρ , however, it should be a fair approximation to assume that σ 2 acts on the full plastic zone ρ .) This loading–unloading procedure will introduce some residual stresses in the plastic zone. The residual stress, σ res is here assumed to simply be the di ff erence between the crack face pressures introduce by P 1 and P 2 , i.e.

(8)

σ res = σ ys1 − σ 2

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In the same way, a “residual stress intensity factor”, K res , is introduced as

K res = K ρ 1 + K ρ 2

(9)

which subjects the crack to an internal load which must be added to any externally applied load. Note that K ρ 1 < 0 and K ρ 2 > 0. In summary: • For the LCF cycle, K res = 0 since P 1 = P 2 = ⇒ σ ys1 = σ 2 = ⇒ K ρ 1 = − K ρ 2 . • For the LUCF cycle, K res 0 since K ρ 1 K ρ 2 . After the load has been changed to P 2 (or in the case of the LCF cycle, have been hold constant at P 2 = P 1 ), the temperature drops to T 2 . The fracture load, P f , is calculated iteratively from  K int = P f √ BB N W 2 + 0 . 886 + 4 . 64 a + ρ W − a + ρ 2 a + ρ 3 a + ρ

3 2 

4 

a + ρ W  1 − a + ρ W 

W 

W 

W 

+ 14 . 72 

− 5 . 6 

13 . 32 

      

( K int + K res ) κ 4 µ √ ρπ

ϵ pzf = estimated strain σ ysf = | σ flow ( ϵ pzf ) | from constitutive model; see Appendix A K ρ f = − σ ysf  2( a + ρ ) π    β 1  1 − a a + ρ  1 2 + β 2 3  1 − a a + ρ  3 2 K int + K ρ f = 0 criterion for stopping iteration

(10)

7 2   

5 

a a + ρ 

7 

a a + ρ 

5 2

β 3

β 4

1 −

1 −

+

+

This must be solved iteratively since K int is unknown leading to an unknown plastic zone strain, ϵ pzf , and, consequently, an unknown yield stress, σ ysf . The variable K int is only an intermediate result used to find P f . Residual stresses can be accounted for in two ways: either they are added to the load or they modify material strength. Here, the latter approach is chosen and K res is added to the stress intensity used to calculate the average plastic zone strain, ϵ pzf . Note that, for LUCF, K res is typically K res < 0 thus reducing ϵ pzf and consequently reducing σ flow , thereby reducing σ ysf (i.e. plasticity occurs at a lower load when K res < 0). Finally, the critical stress intensity, K f , is calculated from P f at the correct crack length, a , (as oppose to at a + ρ ).

3 2 

4 

13 . 32 

a W 

a W 

a W 

+ 14 . 72 

− 5 . 6 

a W

2 +

2

3

a W −

P f √ BB N W

K f =

0 . 886 + 4 . 64

(11)

 1 − a

W 

4. Comparison to experimental data and discussion

The model was applied to the test data listed in Table 1. It turned out that the influence of the minimum temperature (i.e. T 2 = 20 ◦ Cand T 2 = 50 ◦ C) was negligible, so these were treated as a common dataset. The comparison between experimental results and the model prediction is shown in Fig. 6. For reference, Fig. 6 also includes the Wallin model which is Wallin (2003)    K f = 0 . 15 K Ic +  K Ic ( K 1 − K 2 ) + K 2 if K 2 ≥ K 1 − K Ic then set K 2 = K 1 if K f ≤ K Ic then set K f = K Ic (12)