- Email: [email protected]
An optimization criterion for fatigue strength of metallic materials
Author’s Accepted Manuscript An optimization criterion for fatigue strength of metallic materials B. Wang, P. Zhang, R. Liu, Q.Q. Duan, Z.J. Zhang, X.W. Li, Z.F. Zhang www.elsevier.com/locate/msea
PII: DOI: Reference:
S0921-5093(18)31161-4 https://doi.org/10.1016/j.msea.2018.08.085 MSA36856
To appear in: Materials Science & Engineering A Received date: 13 July 2018 Revised date: 23 August 2018 Accepted date: 24 August 2018 Cite this article as: B. Wang, P. Zhang, R. Liu, Q.Q. Duan, Z.J. Zhang, X.W. Li and Z.F. Zhang, An optimization criterion for fatigue strength of metallic m a t e r i a l s , Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.08.085 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
An optimization criterion for fatigue strength of metallic materials
B. Wanga,b, P. Zhanga*, R. Liua, Q.Q. Duana, Z.J. Zhanga, X.W. Lib, Z.F. Zhanga,b*
a
Materials Fatigue and Fracture Division, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China.
b
Department of Materials Physics and Chemistry, School of Materials Science and Engineering, and Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University, Shenyang 110819, China.
[email protected] [email protected]
*
Corresponding author. Tel.: + 86 24 83978226.
*
Corresponding author. Tel.: + 86 24 23971043.
Abstract In this study, a criterion for optimizing the fatigue strength of metallic materials is proposed, and verified by many experimental results. The strategy for optimizing the fatigue strength is to continuously increase the ultimate tensile strength (UTS) under the condition of keeping certain work-hardening abilities. It is found that the 1
relationship between the true UTS and true uniform elongation can be described by two straight lines, and the optimal fatigue strength can be obtained at the point where the two straight lines intersect with each other. This study has great guiding significance for economizing time and money to optimize the fatigue strength of metallic materials.
Keywords: Ultimate tensile strength; Work-hardening ability; Uniform elongation; Fatigue strength.
1. Introduction It is estimated that the failures of metallic components mainly result from fatigue1; nowadays, the fatigue strength has become an important index of structural materials selection. As is well known, measuring the fatigue strength of materials would consume a lot of time and money. Thus, many efforts have been spent on relating the fatigue strength to basic mechanical properties (such as ultimate tensile strength (UTS) and hardness [1-6]), because the basic mechanical properties are much easier to get. In the 19th century, Wöhler firstly found that there was a linear relation between the fatigue strength (σw) and UTS (σb) for the ferrous metals [5]. In the following decades, numerous data of fatigue strength and UTS for steels, copper and aluminum alloys [2, 4] were obtained; and a more general relation between the fatigue strength and UTS was summarized as below [1],
w m b ,
(1)
where m is the fatigue ratio. However, the development of high-strength materials brought new challenges to this theory. It has been found that, as the UTS of materials reaches a critical value (about 1400 MPa for steels [1, 4], and about 480 MPa for wrought copper alloy [1, 2]), the corresponding fatigue strength may no longer 2
increase with further strengthening. Recently, Pang et al. [1, 7] found that the fatigue strength of high-strength steels and copper alloys would initially improve as the UTS enhances, and then become decreasing with further strengthening. Moreover, a parabolic relation between the fatigue strength and UTS was proposed as follows,
w C P b b ,
(2)
where C and P are two constants. Based on the statements above, there is a non-monotonic relation between the UTS and fatigue strength; it becomes difficult to improve the fatigue strength through continuous strengthening. Then one may raise an open question: under what strength level can the optimal fatigue strength be obtained? Therefore, further investigations on how to optimize the fatigue strength of materials will be of great importance and necessity.
2. Basic principle for fatigue strength optimization As is well known, the fatigue damage is predominantly caused by localized plastic deformation [8]. The plastic deformation of metallic materials should be mainly affected by two factors [9]. One is the tensile strength, which is the ability to resist the overall plastic deformation; the larger the tensile strength, the more difficult the plastic deformation becomes. The other is the work-hardening ability [5, 9]. During the tensile process, increasing the work-hardening ability can improve the deformation uniformity, and then inhibit the localized plastic deformation and delay the necking [10]. During the fatigue process, it is well recognized that the dislocations may pile-up at the grain boundaries or hard phases, leading to the stress localization; increasing the work-hardening ability of metallic material can promote the potential to endure the continuous accumulation of localized plastic deformation at the stress localization region, and restrain the localized fatigue damage. Therefore, increasing tensile strength and work-hardening ability of metallic materials can restrain localized plastic deformation and promote fatigue damage resistance. It has been confirmed that the elongation can reflect the work-hardening ability to some extent [10]. Usually, there is a trade-off relationship between the strength and elongation [10-12], as shown in Fig. 1. Thus, increasing the strength would sacrifice the work-hardening ability. In 3
the past decades, it was proved that, in the low-strength region, enhancing the strength could effectively improve the fatigue strength [2, 4, 5]. When the strength increased to a certain extent, the fatigue strength would decrease because of the intense deformation localization and loss of work-hardening ability [13, 14]. Therefore, an initial idea on how to optimize the fatigue strength is: increasing the strength to resist the overall plastic deformation and damage, and keeping certain work-hardening abilities to endure the localized deformation and damage. In this way, high strength combined with certain work-hardening ability may ensure that the materials obtain the optimal fatigue strength, as schematically illustrated in Fig. 1.
3. Fatigue strength optimization criterion For the metals with the same chemical compositions, the conventional strengthening methods involve plastic deformation [15-18] and heat treatment [19, 20]. As for the high-strength metals produced by severe plastic deformation, with further strengthening (grain refinement), the deformation mechanism would transform from the dislocation mechanism or dislocation and deformation twinning mechanism to the localized shear band (SB) deformation mechanism [18, 21, 22]. For the coarse-grained (CG) metals in the low-strength region, the mechanism dominating plastic deformation is the nucleation and motion of dislocations, and may be accompanied by deformation twinning under some conditions [18, 23-25]. Due to the larger grain size, the CG metals can store more dislocations and suppress softening during plastic deformation, which means the higher work-hardening ability [25]. As for the fine-grained (FG) metals in the high-strength region, it was detected that micro SBs would generate in these materials [18, 22, 26]; because the deformation is localized in the SBs, their tensile stress-strain curves reach the UTS at small plastic strains and then plunge down rapidly, which implies the poor work-hardening ability [17, 21]. Furthermore, it was found that, when the deformation was localized in the SBs, the fatigue resistance would reduce [14]. Besides, there was other localized deformation mechanism for the high-strength metals, namely: localized grain boundary (GB) deformation [24, 27], which may cause the loss of work-hardening 4
ability. Moreover, it has been proved that the fatigue strength of such kind of high-strength metal is relatively lower [13, 28]. Similarly, the high-strength steels produced by heat treatments would exhibit intense deformation inhomogeneities at GBs, intergranular fracture and poor work-hardening ability [20]. The fatigue strength of specimen in the high-strength region exhibiting intergranular fracture was lower than that of specimen in the low-strength region displaying transgranular fracture [20]. Based on the statements above, as the strength increases, the deformation mechanism would transit from dislocation motion or dislocation motion and deformation twinning to localized SBs or GBs deformation, and at this point the work-hardening ability would disappear. The fatigue damage of metallic materials is mainly caused by localized plastic deformation. As the deformation mechanism changed into localized deformation (localized SBs or GBs deformation), the degree of localized deformation in the fatigue process would aggravate. In addition, due to the loss of work-hardening ability, the potential of metallic materials to absorb localized deformation would drop sharply. Therefore, the localized deformation mechanism and poor work-hardening ability would lead to serious localized fatigue damage, and further lower the fatigue resistance [13, 14, 20, 28]. To sum up, it can be deduced that, before the transition of deformation mechanism, the fatigue strength would augment as the UTS enhances; and the optimal fatigue strength can be obtained in the high-strength region where the deformation mechanism begins to change. However, it is still tedious to look for the mechanism transition point on the trade-off curve by performing many tensile tests and deformation mechanism observations. Generally, the trade-off curve of strength and elongation can be described by a down convex curve [10-12], as illustrated in Fig. 1. It has been reported that there is the plastic instability for irradiated specimens in the low-strength region, and the dislocation pinning, multiplication and flow are closely related to the plastic instability behavior [29, 30, 31]. Moreover, the relation between the true UTS (σtu) converted from Eq. (3) and the true UE (εtu) converted from Eq. (4) for specimens in 5
the low-strength region can be described by a straight line [29, 30, 31],
tu b 1 eu ,
(3)
tu l n1 eu ,
(4)
where σb is the UTS, eu is the uniform elongation (UE). Besides, Dong [18] has observed that, in the low-strength region of pre-deformed austenitic steels, there is a good linear relationship between the εtu and σtu, and that the plastic deformation mechanisms for the low-strength austenitic steels are the dislocation motion or the dislocation motion and deformation twinning, which is consistent with the previous studies [29, 30, 31]. As the line represents the plastic instability behaviors of specimens in the low-strength region, we may define the line as the instability strength line. While in the high-strength region of pre-deformed austenitic steels, the plastic deformation mechanism is the localized SBs deformation mechanism, and the relationship between the εtu and σtu cannot be described by the instability strength line [18]. Interestingly, it is noticed that there is another linear relationship between the εtu and σtu for specimens in the high-strength region [18]. As the line represents the localized deformation behaviors of specimens in the high-strength region, we may define the line as the localized strength line. Thus, the trade-off relationship between the σtu and εtu can be described by instability strength and localized strength lines (see Fig. 2). There is a deformation mechanism transition between the instability strength and localized strength lines. On the instability strength line, the plastic deformation mechanisms are the dislocation motion or the dislocation motion and deformation twinning (see Fig. 2). While on the localized strength line, the localized deformation mechanisms (such as localized SBs or GBs deformation) may dominate the plastic deformation behavior (see Fig. 2). The intersection point of the instability strength and localized strength lines would be the deformation mechanism transition point. Based on the analyses above, it is concluded that increasing the UTS on the instability strength line can improve the fatigue strength, while increasing the UTS on the localized strength line would lead to the reduction of fatigue strength. In this case, the optimal fatigue strength can be obtained at the point where the 6
instability strength and the localized strength lines intersect with each other (as the red point illustrated in Fig. 2).
4. Experimental data validation In order to verify the hypothesis above, some experimental data (as given in Table 1) of high-strength steels [20, 32] and Cu-Al alloys [9, 22, 28, 33] are used, and the corresponding deformation mechanisms will also be compared in the present study. For the different pre-strained Fe-30Mn-0.9C TWIP steel [32], it is found that the relationship between the true UE and true UTS can be described by the instability strength line (see Fig. 3(a)), and that their plastic deformation mechanisms are the same, namely, deformation twinning and dislocation motion [32] (see Fig. 3(a)). Also, it can be seen from Fig. 3 that, on the instability strength line, the fatigue strength would be improved as the UTS increases, which is consistent with the assumption mentioned above. As for the 18Ni maraging steel under different ageing treatments [20], as the UTS augments, the fracture mode changes from transgranular to intergranular fracture (see Fig. 3(c)) [20]. The intergranular fracture implies intense deformation inhomogeneities occurring at GBs, which would cause the decrease of the fatigue resistance [20]. This is also demonstrated by the relationship between the UTS and fatigue strength (see Fig. 3(d)). As proposed above, it is considered that the optimal fatigue strength can be obtained at the point where the instability strength and localized strength lines intersect with each other. It can be obtained from Fig. 3(c) and Eq. (4) that the engineering UTS for the intersection point is about 1793 MPa. Additionally, it can be found from the experimental results (Fig. 3(d)) that the specimen with a UTS of about 1830 MPa possesses the optimal fatigue strength [20]. Apparently, the error between the experimental and assumed results is estimated to be only about 2%. For the plastically deformed Cu-5Al [9, 22, 33] and Cu-15Al [9, 22, 28] alloys, it can be observed that the plastic deformation mechanism changes from deformation twinning and dislocation motion to the localized SBs deformation (see Figs. 4(a) and 7
(c)). Before the appearance of deformation mechanism transformation, the fatigue strength becomes increasing as the UTS improves; and as the deformation mechanism changes into the localized SBs deformation, the fatigue strength reduces with further strengthening (see Figs. 4(b) and (d)). Furthermore, according to the experimental results [9, 22, 33], it can be calculated through the parabolic relation [1, 7] that the optimal fatigue strength of Cu-5Al alloy can be obtained at the point that the UTS is about 540 MPa (see Figs. 4(b)). In contrast, according to the assumption proposed above, the optimal fatigue strength of Cu-5Al alloy may be gained at the intersection point in Fig. 4(a), and the engineering UTS for the intersection point is about 496 MPa. Finally, it can be calculated that the error between the results obtained by experiments and assumption is about 8%.
5. Summary In the present study, a criterion for obtaining the optimal fatigue strength of smooth specimens for metallic materials is proposed, and the experimental data of high-strength steels and Cu-Al alloys are used to verify the criterion. The basic strategy for optimizing the fatigue strength is to continuously increase the UTS under the condition of keeping certain work-hardening abilities. It is found that the relationship between the σtu and εtu can be described by two straight lines, which are defined as the instability strength and localized strength lines, respectively. Increasing the UTS on the instability strength line can improve the fatigue strength, while increasing the UTS on the localized strength line would lead to the decrement of fatigue strength. Additionally, it is suggested that the optimal fatigue strength can be obtained at the intersection point of the instability strength and localized strength lines. The error between the results obtained by experiments and assumption is less than 10%. Finally, it should be pointed out that this criterion would not be applicable for the materials, for which the fatigue crack initiations are caused by the microstructure inhomogeneity (see Fig. 4(a) and the experimental data of partially recrystallized Cu-5Al alloy [33] in Table 1) and inclusions, since the tensile properties cannot reflect the influences of the microstructure inhomogeneity and inclusions. 8
Acknowledgement This work was financially supported by the National Natural Science Foundation of China (NSFC) under grant Nos. 51771208, 51571058, 51331007 and U1664253, and the National Key R&D Program of China under grant No. 2017YFB0703002.
References [1] J.C. Pang, S.X. Li, Z.G. Wang, Z.F. Zhang, General relation between tensile strength and fatigue strength of metallic materials, Mater. Sci. Eng. A 564 (2013) 331-341. [2] P.G. Frorrest, Fatigue of Metals, Pergamon Press, Oxford, 1962. [3] Y. Murakami, Metal Fatigue, Elsevier Science Ltd., Oxford, 2002. [4] Y.L. Lee, J. Pan, R.B. Hathaway, Fatigue Testing and Analysis (Theory and Practice), Elsevier Butter-worth Heinemann, Amsterdam, Boston, Heidelberg, 2005. [5] L. Tóth, S.Y. Yarema, Formation of the science of fatigue of metals. Part 1. 1825– 1870, Mater. Sci. 42 (2006) 673-680. [6] J.C. Pang, S.X. Li, Z.G. Wang, Z.F. Zhang, Relations between fatigue strength and other mechanical properties of metallic materials, Fatigue Fract. Eng. Mater. Struct. 37 (2014) 958-976. [7] J.C. Pang, Investigation on Fatigue and Fracture of High-Strength Metallic Materials (Doctor thesis), Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 2013. [8] S. Suresh, Fatigue of materials, Cambridge University Press, Cambridge, 1991. [9] R. Liu, P. Zhang, B. Wang, Y.Z. Tian, Z.J. Zhang and Z.F. Zhang, Conservation relation between tensile and fatigue strengths, Acta Mater. to be submitted. 9
[10] R. Liu, Z.J. Zhang, L.L. Li, X.H. An, Z.F. Zhang, Microscopic mechanisms contributing to the synchronous improvement of strength and plasticity (SISP) for TWIP copper alloys, Sci. Rep. 5 (2015) 9550. [11] Y.Z. Tian, L.J. Zhao, N. Park, R. Liu, P. Zhang, Z.J. Zhang, A. Shibata, Z.F. Zhang, N. Tsuji, Revealing the deformation mechanisms of Cu-Al alloys with high strength and good ductility, Acta Mater. 110 (2016) 61-72. [12] F.Y. Dong, J.C. Pang, P. Zhang, Q.Q. Duan, Z.F. Zhang, Mechanical properties and tensile fracture mechanisms of Fe-Mn-(Al, Si) TRIP/TWIP steels with different ferrite volume fractions, Adv. Eng. Mater. 17 (2015) 1675-1682. [13] X.H. An, S.D. Wu, Z.G. Wang, Z.F. Zhang, Enhanced cyclic deformation responses of ultrafine-grained Cu and nanocrystalline Cu-Al alloys, Acta Mater. 74 (2014) 200-214. [14] Z.J. Zhang, P. Zhang, Z.F. Zhang, Cyclic softening behaviors of ultra-fine grained Cu-Zn alloys, Acta Mater. 121 (2016) 331-342. [15] F.Y. Dong, P. Zhang, J.C. Pang, Y.B. Ren, K. Yang, Z.F. Zhang, Strength, damage and fracture behaviors of high-nitrogen austenitic stainless steel processed by high-pressure torsion, Scr. Mater. 96 (2015) 5-8. [16] X.H. An, S. Qu, S.D. Wu, Z.F. Zhang, Effects of stacking fault energy on the thermal stability and mechanical properties of nanostructured Cu-Al alloys during thermal annealing, J. Mater. Res. 26 (2011) 407-415. [17] Y.M. Wang, E. Ma, Strain hardening, strain rate sensitivity, and ductility of nanostructured metals, Mater. Sci. Eng. A 375-377 (2004) 46-52. [18] F.Y. dong, Investigations on Strength-Ductility Optimization, Fracture and Damage Behaviors of High Strength Austenitic Steels (Doctor thesis), Institute of Metal Research, Chinese Academy of Science, Shenyang, 2015. [19] E.V. Pereloma, A. Shekhter, M.K. Miller, S.P. Ringer, Ageing behaviour of an 10
Fe-20Ni-1.8Mn-1.6Ti-0.59Al (wt%) maraging alloy: clustering, precipitation and hardening, Acta Mater. 52 (2004) 5589-5602. [20] B. Wang, P. Zhang, Q.Q. Duan, Z.J. Zhang, H.J. Yang, X.W. Li, Z.F. Zhang, Optimizing the fatigue strength of 18Ni maraging steel through ageing treatment, Mater. Sci. Eng. A 707 (2017) 674-688. [21] E. Ma, Instabilities and ductility of nanocrystalline and ultrafine-grained metals, Scr. Mater. 49 (2003) 663-668. [22] X.H. An, Investigations on Microstructure Evolution and Mechanical Properties of Pure Cu and Cu-Al Alloys During Severe Plastic Deformation (Doctor thesis), Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 2012. [23] L. Lu, Z.S. You, K. Lu, Work hardening of polycrystalline Cu with nanoscale twins, Scr. Mater. 66 (2012) 837-842. [24] Z.W. Shan, E.A. Stach, J.M.K. Wiezorek, J.A. Knapp, D.M. Follstaedt, S.X. Mao, Grain boundary-mediated plasticity in nanocrystalline nickel, Science, 305 (2004) 654-657. [25] X.H. Chen, L. Lu, K. Lu, Grain size dependence of tensile properties in ultrafine-grained Cu with nanoscale twins, Scr. Mater. 64 (2011) 311-314. [26] X.H. An, Q.Y. Lin, S.D. Wu, Z.F. Zhang, Microstructural evolution and shear fracture of Cu-16at.% Al alloy induced by equal channel angular pressing, Mater. Sci. Eng. A 527 (2010) 4510-4514. [27] H.V. Swygenhoven, J.R. Weertman, Deformation in nanocrystalline metals, Mater. Today 9 (2006) 24-31. [28] R. Liu, Y.Z. Tian, Z.J. Zhang, X.H. An, P. Zhang, Z.F. Zhang, Exceptional high fatigue strength in Cu-15at.% Al alloy with moderate grain size, Sci. Rep. 6 (2016) 27433. [29] X. Pan, X. Wu, M. Li, J.F. Stubbins, Modeling tensile response and flow 11
localization effects in selected copper alloys, J. Nucl. Mater. 329-333 (2004) 1088-1092. [30] T.S. Byun, K. Farrell, Plastic instability in polycrystalline metals after low temperature irradiation, Acta Mater. 52 (2004) 1597-1608. [31] T.S. Byun, K. Farrell, E.H. Lee, J.D. Hunn, L.K. Mansur, Strain hardening and plastic instability properties of austenitic stainless steels after proton and neutron irradiation, J. Nucl. Mater. 298 (2001) 269-279. [32] B. Wang, P. Zhang, Q.Q. Duan, Z.J. Zhang, H.J. Yang, J.C. Pang, Y.Z. Tian, X.W. Li, Z.F. Zhang, High-cycle fatigue properties and damage mechanisms of pre-strained Fe-30Mn-0.9C twinning-induced plasticity steel, Mater. Sci. Eng. A 679 (2017) 258-271. [33] R. Liu, Y.Z. Tian, Z.J. Zhang, P. Zhang, Z.F. Zhang, Fatigue strength plateau induced by microstructure inhomogeneity, Mater. Sci. Eng. A 702 (2017) 259-264.
Fig. 1 Schematic illustration of trade-off relation between UTS and elongation. Fig. 2 The schematic illustration of instability strength and localized strength lines, and the insert images show the dominant mechanisms of plastic deformation. Fig. 3 (a) The true UTS-UE diagram of pre-strained Fe-30Mn-0.9C TWIP steel [32]; (b) the relation between the fatigue strength and UTS of pre-strained Fe-30Mn-0.9C TWIP steel [32]; (c) the true UTS-UE diagram of 18Ni maraging steel [20]; (d) the relation between the fatigue strength and UTS of 18Ni maraging steel [20]. Fig. 4 (a) The true UTS-UE diagram of Cu-5Al alloy [9, 22, 33]; (b) the relation between the fatigue strength and UTS of Cu-5Al alloy [9, 22, 33]; (c) the true UTS-UE diagram of Cu-15Al alloy [9, 22, 28]; (d) the relation between the fatigue strength and UTS of Cu-15Al alloy [9, 22, 28]. (It should be noticed that, 12
for the Cu-5Al alloy with the highest strength in Fig. (a), the tensile tests were perfomed without strain gauge, and the UE is much larger than the actual value. Thus, the point has not been used to determine the localized strength line.)
Fig. 1
13
Fig. 2
14
Fig. 3
Fig. 4 15
Table 1 The tensile and fatigue strength data of high-strength steels [20, 32] and Cu-Al alloys [9, 22, 28, 33].
True
Ultimate Materials
Process
tensile
Uniform
condition
strength,
elongation
MPa
ultimate
True
tensile
uniform
strength,
elongation
MPa
Conditional fatigue strength (107, R = -1), MPa
As-received
960
0.875
1800
0.629
250
Fe-30Mn-0.9C
30% pre-strained
1200
0.463
1755
0.380
350
TWIP steel [32]
60% pre-strained
1460
0.249
1824
0.222
360
70% pre-strained
1610
0.136
1830
0.128
380
Aged at 500 °C
1953
0.019
1991
0.019
for 5h
1925
0.019
1962
0.019
1852
0.020
1888
0.019
1824
0.021
1862
0.020
1799
0.021
1836
0.020
Aged at 600 °C
1517
0.060
1608
0.058
for 5h
1514
0.071
1622
0.069
1583
0.054
1668
0.052
Aged at 600 °C
1551
0.044
1619
0.043
for 3h
1545
0.059
1637
0.058
1562
0.053
1644
0.051
Aged at 630 °C
1353
0.083
1465
0.080
for 3h
1364
0.085
1480
0.081
760
0.03
783
0.03
170
675
0.015
685
0.015
210
596
0.015
605
0.015
170
418
0.110
464
0.105
160
361
0.188
429
0.172
160
Aged at 550 °C for 5h
18Ni maraging steel [20]
High-pressure torsion Cold rolled
595
685
－
638
588
Cold rolled + 300 °C annealed Cu-5Al alloy [9, 22, 33]
(Partially recrystallized) Cold rolled + 325 °C annealed (Partially recrystallized) Cold rolled + 350 °C annealed
16
(Partially recrystallized) Cold rolled + 425 °C annealed (Fully
321
0.263
405
0.233
155
297
0.298
386
0.261
120
257
0.396
359
0.333
75
942
0.034
974
0.033
200
592
0.272
753
0.240
280
547
0.308
715
0.268
250
396
0.790
709
0.582
110
recrystallized) Cold rolled + 500 °C annealed (Fully recrystallized) As-received High-pressure torsion Cold rolled + 400 °C annealed Cu-15Al alloy [9, 22, 28]
(Fully recrystallized) Cold rolled + 500 °C annealed (Fully recrystallized) As-received
17
PII: DOI: Reference:
S0921-5093(18)31161-4 https://doi.org/10.1016/j.msea.2018.08.085 MSA36856
To appear in: Materials Science & Engineering A Received date: 13 July 2018 Revised date: 23 August 2018 Accepted date: 24 August 2018 Cite this article as: B. Wang, P. Zhang, R. Liu, Q.Q. Duan, Z.J. Zhang, X.W. Li and Z.F. Zhang, An optimization criterion for fatigue strength of metallic m a t e r i a l s , Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.08.085 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
An optimization criterion for fatigue strength of metallic materials
B. Wanga,b, P. Zhanga*, R. Liua, Q.Q. Duana, Z.J. Zhanga, X.W. Lib, Z.F. Zhanga,b*
a
Materials Fatigue and Fracture Division, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China.
b
Department of Materials Physics and Chemistry, School of Materials Science and Engineering, and Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University, Shenyang 110819, China.
[email protected] [email protected]
*
Corresponding author. Tel.: + 86 24 83978226.
*
Corresponding author. Tel.: + 86 24 23971043.
Abstract In this study, a criterion for optimizing the fatigue strength of metallic materials is proposed, and verified by many experimental results. The strategy for optimizing the fatigue strength is to continuously increase the ultimate tensile strength (UTS) under the condition of keeping certain work-hardening abilities. It is found that the 1
relationship between the true UTS and true uniform elongation can be described by two straight lines, and the optimal fatigue strength can be obtained at the point where the two straight lines intersect with each other. This study has great guiding significance for economizing time and money to optimize the fatigue strength of metallic materials.
Keywords: Ultimate tensile strength; Work-hardening ability; Uniform elongation; Fatigue strength.
1. Introduction It is estimated that the failures of metallic components mainly result from fatigue1; nowadays, the fatigue strength has become an important index of structural materials selection. As is well known, measuring the fatigue strength of materials would consume a lot of time and money. Thus, many efforts have been spent on relating the fatigue strength to basic mechanical properties (such as ultimate tensile strength (UTS) and hardness [1-6]), because the basic mechanical properties are much easier to get. In the 19th century, Wöhler firstly found that there was a linear relation between the fatigue strength (σw) and UTS (σb) for the ferrous metals [5]. In the following decades, numerous data of fatigue strength and UTS for steels, copper and aluminum alloys [2, 4] were obtained; and a more general relation between the fatigue strength and UTS was summarized as below [1],
w m b ,
(1)
where m is the fatigue ratio. However, the development of high-strength materials brought new challenges to this theory. It has been found that, as the UTS of materials reaches a critical value (about 1400 MPa for steels [1, 4], and about 480 MPa for wrought copper alloy [1, 2]), the corresponding fatigue strength may no longer 2
increase with further strengthening. Recently, Pang et al. [1, 7] found that the fatigue strength of high-strength steels and copper alloys would initially improve as the UTS enhances, and then become decreasing with further strengthening. Moreover, a parabolic relation between the fatigue strength and UTS was proposed as follows,
w C P b b ,
(2)
where C and P are two constants. Based on the statements above, there is a non-monotonic relation between the UTS and fatigue strength; it becomes difficult to improve the fatigue strength through continuous strengthening. Then one may raise an open question: under what strength level can the optimal fatigue strength be obtained? Therefore, further investigations on how to optimize the fatigue strength of materials will be of great importance and necessity.
2. Basic principle for fatigue strength optimization As is well known, the fatigue damage is predominantly caused by localized plastic deformation [8]. The plastic deformation of metallic materials should be mainly affected by two factors [9]. One is the tensile strength, which is the ability to resist the overall plastic deformation; the larger the tensile strength, the more difficult the plastic deformation becomes. The other is the work-hardening ability [5, 9]. During the tensile process, increasing the work-hardening ability can improve the deformation uniformity, and then inhibit the localized plastic deformation and delay the necking [10]. During the fatigue process, it is well recognized that the dislocations may pile-up at the grain boundaries or hard phases, leading to the stress localization; increasing the work-hardening ability of metallic material can promote the potential to endure the continuous accumulation of localized plastic deformation at the stress localization region, and restrain the localized fatigue damage. Therefore, increasing tensile strength and work-hardening ability of metallic materials can restrain localized plastic deformation and promote fatigue damage resistance. It has been confirmed that the elongation can reflect the work-hardening ability to some extent [10]. Usually, there is a trade-off relationship between the strength and elongation [10-12], as shown in Fig. 1. Thus, increasing the strength would sacrifice the work-hardening ability. In 3
the past decades, it was proved that, in the low-strength region, enhancing the strength could effectively improve the fatigue strength [2, 4, 5]. When the strength increased to a certain extent, the fatigue strength would decrease because of the intense deformation localization and loss of work-hardening ability [13, 14]. Therefore, an initial idea on how to optimize the fatigue strength is: increasing the strength to resist the overall plastic deformation and damage, and keeping certain work-hardening abilities to endure the localized deformation and damage. In this way, high strength combined with certain work-hardening ability may ensure that the materials obtain the optimal fatigue strength, as schematically illustrated in Fig. 1.
3. Fatigue strength optimization criterion For the metals with the same chemical compositions, the conventional strengthening methods involve plastic deformation [15-18] and heat treatment [19, 20]. As for the high-strength metals produced by severe plastic deformation, with further strengthening (grain refinement), the deformation mechanism would transform from the dislocation mechanism or dislocation and deformation twinning mechanism to the localized shear band (SB) deformation mechanism [18, 21, 22]. For the coarse-grained (CG) metals in the low-strength region, the mechanism dominating plastic deformation is the nucleation and motion of dislocations, and may be accompanied by deformation twinning under some conditions [18, 23-25]. Due to the larger grain size, the CG metals can store more dislocations and suppress softening during plastic deformation, which means the higher work-hardening ability [25]. As for the fine-grained (FG) metals in the high-strength region, it was detected that micro SBs would generate in these materials [18, 22, 26]; because the deformation is localized in the SBs, their tensile stress-strain curves reach the UTS at small plastic strains and then plunge down rapidly, which implies the poor work-hardening ability [17, 21]. Furthermore, it was found that, when the deformation was localized in the SBs, the fatigue resistance would reduce [14]. Besides, there was other localized deformation mechanism for the high-strength metals, namely: localized grain boundary (GB) deformation [24, 27], which may cause the loss of work-hardening 4
ability. Moreover, it has been proved that the fatigue strength of such kind of high-strength metal is relatively lower [13, 28]. Similarly, the high-strength steels produced by heat treatments would exhibit intense deformation inhomogeneities at GBs, intergranular fracture and poor work-hardening ability [20]. The fatigue strength of specimen in the high-strength region exhibiting intergranular fracture was lower than that of specimen in the low-strength region displaying transgranular fracture [20]. Based on the statements above, as the strength increases, the deformation mechanism would transit from dislocation motion or dislocation motion and deformation twinning to localized SBs or GBs deformation, and at this point the work-hardening ability would disappear. The fatigue damage of metallic materials is mainly caused by localized plastic deformation. As the deformation mechanism changed into localized deformation (localized SBs or GBs deformation), the degree of localized deformation in the fatigue process would aggravate. In addition, due to the loss of work-hardening ability, the potential of metallic materials to absorb localized deformation would drop sharply. Therefore, the localized deformation mechanism and poor work-hardening ability would lead to serious localized fatigue damage, and further lower the fatigue resistance [13, 14, 20, 28]. To sum up, it can be deduced that, before the transition of deformation mechanism, the fatigue strength would augment as the UTS enhances; and the optimal fatigue strength can be obtained in the high-strength region where the deformation mechanism begins to change. However, it is still tedious to look for the mechanism transition point on the trade-off curve by performing many tensile tests and deformation mechanism observations. Generally, the trade-off curve of strength and elongation can be described by a down convex curve [10-12], as illustrated in Fig. 1. It has been reported that there is the plastic instability for irradiated specimens in the low-strength region, and the dislocation pinning, multiplication and flow are closely related to the plastic instability behavior [29, 30, 31]. Moreover, the relation between the true UTS (σtu) converted from Eq. (3) and the true UE (εtu) converted from Eq. (4) for specimens in 5
the low-strength region can be described by a straight line [29, 30, 31],
tu b 1 eu ,
(3)
tu l n1 eu ,
(4)
where σb is the UTS, eu is the uniform elongation (UE). Besides, Dong [18] has observed that, in the low-strength region of pre-deformed austenitic steels, there is a good linear relationship between the εtu and σtu, and that the plastic deformation mechanisms for the low-strength austenitic steels are the dislocation motion or the dislocation motion and deformation twinning, which is consistent with the previous studies [29, 30, 31]. As the line represents the plastic instability behaviors of specimens in the low-strength region, we may define the line as the instability strength line. While in the high-strength region of pre-deformed austenitic steels, the plastic deformation mechanism is the localized SBs deformation mechanism, and the relationship between the εtu and σtu cannot be described by the instability strength line [18]. Interestingly, it is noticed that there is another linear relationship between the εtu and σtu for specimens in the high-strength region [18]. As the line represents the localized deformation behaviors of specimens in the high-strength region, we may define the line as the localized strength line. Thus, the trade-off relationship between the σtu and εtu can be described by instability strength and localized strength lines (see Fig. 2). There is a deformation mechanism transition between the instability strength and localized strength lines. On the instability strength line, the plastic deformation mechanisms are the dislocation motion or the dislocation motion and deformation twinning (see Fig. 2). While on the localized strength line, the localized deformation mechanisms (such as localized SBs or GBs deformation) may dominate the plastic deformation behavior (see Fig. 2). The intersection point of the instability strength and localized strength lines would be the deformation mechanism transition point. Based on the analyses above, it is concluded that increasing the UTS on the instability strength line can improve the fatigue strength, while increasing the UTS on the localized strength line would lead to the reduction of fatigue strength. In this case, the optimal fatigue strength can be obtained at the point where the 6
instability strength and the localized strength lines intersect with each other (as the red point illustrated in Fig. 2).
4. Experimental data validation In order to verify the hypothesis above, some experimental data (as given in Table 1) of high-strength steels [20, 32] and Cu-Al alloys [9, 22, 28, 33] are used, and the corresponding deformation mechanisms will also be compared in the present study. For the different pre-strained Fe-30Mn-0.9C TWIP steel [32], it is found that the relationship between the true UE and true UTS can be described by the instability strength line (see Fig. 3(a)), and that their plastic deformation mechanisms are the same, namely, deformation twinning and dislocation motion [32] (see Fig. 3(a)). Also, it can be seen from Fig. 3 that, on the instability strength line, the fatigue strength would be improved as the UTS increases, which is consistent with the assumption mentioned above. As for the 18Ni maraging steel under different ageing treatments [20], as the UTS augments, the fracture mode changes from transgranular to intergranular fracture (see Fig. 3(c)) [20]. The intergranular fracture implies intense deformation inhomogeneities occurring at GBs, which would cause the decrease of the fatigue resistance [20]. This is also demonstrated by the relationship between the UTS and fatigue strength (see Fig. 3(d)). As proposed above, it is considered that the optimal fatigue strength can be obtained at the point where the instability strength and localized strength lines intersect with each other. It can be obtained from Fig. 3(c) and Eq. (4) that the engineering UTS for the intersection point is about 1793 MPa. Additionally, it can be found from the experimental results (Fig. 3(d)) that the specimen with a UTS of about 1830 MPa possesses the optimal fatigue strength [20]. Apparently, the error between the experimental and assumed results is estimated to be only about 2%. For the plastically deformed Cu-5Al [9, 22, 33] and Cu-15Al [9, 22, 28] alloys, it can be observed that the plastic deformation mechanism changes from deformation twinning and dislocation motion to the localized SBs deformation (see Figs. 4(a) and 7
(c)). Before the appearance of deformation mechanism transformation, the fatigue strength becomes increasing as the UTS improves; and as the deformation mechanism changes into the localized SBs deformation, the fatigue strength reduces with further strengthening (see Figs. 4(b) and (d)). Furthermore, according to the experimental results [9, 22, 33], it can be calculated through the parabolic relation [1, 7] that the optimal fatigue strength of Cu-5Al alloy can be obtained at the point that the UTS is about 540 MPa (see Figs. 4(b)). In contrast, according to the assumption proposed above, the optimal fatigue strength of Cu-5Al alloy may be gained at the intersection point in Fig. 4(a), and the engineering UTS for the intersection point is about 496 MPa. Finally, it can be calculated that the error between the results obtained by experiments and assumption is about 8%.
5. Summary In the present study, a criterion for obtaining the optimal fatigue strength of smooth specimens for metallic materials is proposed, and the experimental data of high-strength steels and Cu-Al alloys are used to verify the criterion. The basic strategy for optimizing the fatigue strength is to continuously increase the UTS under the condition of keeping certain work-hardening abilities. It is found that the relationship between the σtu and εtu can be described by two straight lines, which are defined as the instability strength and localized strength lines, respectively. Increasing the UTS on the instability strength line can improve the fatigue strength, while increasing the UTS on the localized strength line would lead to the decrement of fatigue strength. Additionally, it is suggested that the optimal fatigue strength can be obtained at the intersection point of the instability strength and localized strength lines. The error between the results obtained by experiments and assumption is less than 10%. Finally, it should be pointed out that this criterion would not be applicable for the materials, for which the fatigue crack initiations are caused by the microstructure inhomogeneity (see Fig. 4(a) and the experimental data of partially recrystallized Cu-5Al alloy [33] in Table 1) and inclusions, since the tensile properties cannot reflect the influences of the microstructure inhomogeneity and inclusions. 8
Acknowledgement This work was financially supported by the National Natural Science Foundation of China (NSFC) under grant Nos. 51771208, 51571058, 51331007 and U1664253, and the National Key R&D Program of China under grant No. 2017YFB0703002.
References [1] J.C. Pang, S.X. Li, Z.G. Wang, Z.F. Zhang, General relation between tensile strength and fatigue strength of metallic materials, Mater. Sci. Eng. A 564 (2013) 331-341. [2] P.G. Frorrest, Fatigue of Metals, Pergamon Press, Oxford, 1962. [3] Y. Murakami, Metal Fatigue, Elsevier Science Ltd., Oxford, 2002. [4] Y.L. Lee, J. Pan, R.B. Hathaway, Fatigue Testing and Analysis (Theory and Practice), Elsevier Butter-worth Heinemann, Amsterdam, Boston, Heidelberg, 2005. [5] L. Tóth, S.Y. Yarema, Formation of the science of fatigue of metals. Part 1. 1825– 1870, Mater. Sci. 42 (2006) 673-680. [6] J.C. Pang, S.X. Li, Z.G. Wang, Z.F. Zhang, Relations between fatigue strength and other mechanical properties of metallic materials, Fatigue Fract. Eng. Mater. Struct. 37 (2014) 958-976. [7] J.C. Pang, Investigation on Fatigue and Fracture of High-Strength Metallic Materials (Doctor thesis), Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 2013. [8] S. Suresh, Fatigue of materials, Cambridge University Press, Cambridge, 1991. [9] R. Liu, P. Zhang, B. Wang, Y.Z. Tian, Z.J. Zhang and Z.F. Zhang, Conservation relation between tensile and fatigue strengths, Acta Mater. to be submitted. 9
[10] R. Liu, Z.J. Zhang, L.L. Li, X.H. An, Z.F. Zhang, Microscopic mechanisms contributing to the synchronous improvement of strength and plasticity (SISP) for TWIP copper alloys, Sci. Rep. 5 (2015) 9550. [11] Y.Z. Tian, L.J. Zhao, N. Park, R. Liu, P. Zhang, Z.J. Zhang, A. Shibata, Z.F. Zhang, N. Tsuji, Revealing the deformation mechanisms of Cu-Al alloys with high strength and good ductility, Acta Mater. 110 (2016) 61-72. [12] F.Y. Dong, J.C. Pang, P. Zhang, Q.Q. Duan, Z.F. Zhang, Mechanical properties and tensile fracture mechanisms of Fe-Mn-(Al, Si) TRIP/TWIP steels with different ferrite volume fractions, Adv. Eng. Mater. 17 (2015) 1675-1682. [13] X.H. An, S.D. Wu, Z.G. Wang, Z.F. Zhang, Enhanced cyclic deformation responses of ultrafine-grained Cu and nanocrystalline Cu-Al alloys, Acta Mater. 74 (2014) 200-214. [14] Z.J. Zhang, P. Zhang, Z.F. Zhang, Cyclic softening behaviors of ultra-fine grained Cu-Zn alloys, Acta Mater. 121 (2016) 331-342. [15] F.Y. Dong, P. Zhang, J.C. Pang, Y.B. Ren, K. Yang, Z.F. Zhang, Strength, damage and fracture behaviors of high-nitrogen austenitic stainless steel processed by high-pressure torsion, Scr. Mater. 96 (2015) 5-8. [16] X.H. An, S. Qu, S.D. Wu, Z.F. Zhang, Effects of stacking fault energy on the thermal stability and mechanical properties of nanostructured Cu-Al alloys during thermal annealing, J. Mater. Res. 26 (2011) 407-415. [17] Y.M. Wang, E. Ma, Strain hardening, strain rate sensitivity, and ductility of nanostructured metals, Mater. Sci. Eng. A 375-377 (2004) 46-52. [18] F.Y. dong, Investigations on Strength-Ductility Optimization, Fracture and Damage Behaviors of High Strength Austenitic Steels (Doctor thesis), Institute of Metal Research, Chinese Academy of Science, Shenyang, 2015. [19] E.V. Pereloma, A. Shekhter, M.K. Miller, S.P. Ringer, Ageing behaviour of an 10
Fe-20Ni-1.8Mn-1.6Ti-0.59Al (wt%) maraging alloy: clustering, precipitation and hardening, Acta Mater. 52 (2004) 5589-5602. [20] B. Wang, P. Zhang, Q.Q. Duan, Z.J. Zhang, H.J. Yang, X.W. Li, Z.F. Zhang, Optimizing the fatigue strength of 18Ni maraging steel through ageing treatment, Mater. Sci. Eng. A 707 (2017) 674-688. [21] E. Ma, Instabilities and ductility of nanocrystalline and ultrafine-grained metals, Scr. Mater. 49 (2003) 663-668. [22] X.H. An, Investigations on Microstructure Evolution and Mechanical Properties of Pure Cu and Cu-Al Alloys During Severe Plastic Deformation (Doctor thesis), Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 2012. [23] L. Lu, Z.S. You, K. Lu, Work hardening of polycrystalline Cu with nanoscale twins, Scr. Mater. 66 (2012) 837-842. [24] Z.W. Shan, E.A. Stach, J.M.K. Wiezorek, J.A. Knapp, D.M. Follstaedt, S.X. Mao, Grain boundary-mediated plasticity in nanocrystalline nickel, Science, 305 (2004) 654-657. [25] X.H. Chen, L. Lu, K. Lu, Grain size dependence of tensile properties in ultrafine-grained Cu with nanoscale twins, Scr. Mater. 64 (2011) 311-314. [26] X.H. An, Q.Y. Lin, S.D. Wu, Z.F. Zhang, Microstructural evolution and shear fracture of Cu-16at.% Al alloy induced by equal channel angular pressing, Mater. Sci. Eng. A 527 (2010) 4510-4514. [27] H.V. Swygenhoven, J.R. Weertman, Deformation in nanocrystalline metals, Mater. Today 9 (2006) 24-31. [28] R. Liu, Y.Z. Tian, Z.J. Zhang, X.H. An, P. Zhang, Z.F. Zhang, Exceptional high fatigue strength in Cu-15at.% Al alloy with moderate grain size, Sci. Rep. 6 (2016) 27433. [29] X. Pan, X. Wu, M. Li, J.F. Stubbins, Modeling tensile response and flow 11
localization effects in selected copper alloys, J. Nucl. Mater. 329-333 (2004) 1088-1092. [30] T.S. Byun, K. Farrell, Plastic instability in polycrystalline metals after low temperature irradiation, Acta Mater. 52 (2004) 1597-1608. [31] T.S. Byun, K. Farrell, E.H. Lee, J.D. Hunn, L.K. Mansur, Strain hardening and plastic instability properties of austenitic stainless steels after proton and neutron irradiation, J. Nucl. Mater. 298 (2001) 269-279. [32] B. Wang, P. Zhang, Q.Q. Duan, Z.J. Zhang, H.J. Yang, J.C. Pang, Y.Z. Tian, X.W. Li, Z.F. Zhang, High-cycle fatigue properties and damage mechanisms of pre-strained Fe-30Mn-0.9C twinning-induced plasticity steel, Mater. Sci. Eng. A 679 (2017) 258-271. [33] R. Liu, Y.Z. Tian, Z.J. Zhang, P. Zhang, Z.F. Zhang, Fatigue strength plateau induced by microstructure inhomogeneity, Mater. Sci. Eng. A 702 (2017) 259-264.
Fig. 1 Schematic illustration of trade-off relation between UTS and elongation. Fig. 2 The schematic illustration of instability strength and localized strength lines, and the insert images show the dominant mechanisms of plastic deformation. Fig. 3 (a) The true UTS-UE diagram of pre-strained Fe-30Mn-0.9C TWIP steel [32]; (b) the relation between the fatigue strength and UTS of pre-strained Fe-30Mn-0.9C TWIP steel [32]; (c) the true UTS-UE diagram of 18Ni maraging steel [20]; (d) the relation between the fatigue strength and UTS of 18Ni maraging steel [20]. Fig. 4 (a) The true UTS-UE diagram of Cu-5Al alloy [9, 22, 33]; (b) the relation between the fatigue strength and UTS of Cu-5Al alloy [9, 22, 33]; (c) the true UTS-UE diagram of Cu-15Al alloy [9, 22, 28]; (d) the relation between the fatigue strength and UTS of Cu-15Al alloy [9, 22, 28]. (It should be noticed that, 12
for the Cu-5Al alloy with the highest strength in Fig. (a), the tensile tests were perfomed without strain gauge, and the UE is much larger than the actual value. Thus, the point has not been used to determine the localized strength line.)
Fig. 1
13
Fig. 2
14
Fig. 3
Fig. 4 15
Table 1 The tensile and fatigue strength data of high-strength steels [20, 32] and Cu-Al alloys [9, 22, 28, 33].
True
Ultimate Materials
Process
tensile
Uniform
condition
strength,
elongation
MPa
ultimate
True
tensile
uniform
strength,
elongation
MPa
Conditional fatigue strength (107, R = -1), MPa
As-received
960
0.875
1800
0.629
250
Fe-30Mn-0.9C
30% pre-strained
1200
0.463
1755
0.380
350
TWIP steel [32]
60% pre-strained
1460
0.249
1824
0.222
360
70% pre-strained
1610
0.136
1830
0.128
380
Aged at 500 °C
1953
0.019
1991
0.019
for 5h
1925
0.019
1962
0.019
1852
0.020
1888
0.019
1824
0.021
1862
0.020
1799
0.021
1836
0.020
Aged at 600 °C
1517
0.060
1608
0.058
for 5h
1514
0.071
1622
0.069
1583
0.054
1668
0.052
Aged at 600 °C
1551
0.044
1619
0.043
for 3h
1545
0.059
1637
0.058
1562
0.053
1644
0.051
Aged at 630 °C
1353
0.083
1465
0.080
for 3h
1364
0.085
1480
0.081
760
0.03
783
0.03
170
675
0.015
685
0.015
210
596
0.015
605
0.015
170
418
0.110
464
0.105
160
361
0.188
429
0.172
160
Aged at 550 °C for 5h
18Ni maraging steel [20]
High-pressure torsion Cold rolled
595
685
－
638
588
Cold rolled + 300 °C annealed Cu-5Al alloy [9, 22, 33]
(Partially recrystallized) Cold rolled + 325 °C annealed (Partially recrystallized) Cold rolled + 350 °C annealed
16
(Partially recrystallized) Cold rolled + 425 °C annealed (Fully
321
0.263
405
0.233
155
297
0.298
386
0.261
120
257
0.396
359
0.333
75
942
0.034
974
0.033
200
592
0.272
753
0.240
280
547
0.308
715
0.268
250
396
0.790
709
0.582
110
recrystallized) Cold rolled + 500 °C annealed (Fully recrystallized) As-received High-pressure torsion Cold rolled + 400 °C annealed Cu-15Al alloy [9, 22, 28]
(Fully recrystallized) Cold rolled + 500 °C annealed (Fully recrystallized) As-received
17