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Estimation of changes in the mechanical properties of stainless steel subjected to fatigue loading via electrical resistance monitoring
International Journal of Engineering Science 65 (2013) 40–48
Contents lists available at SciVerse ScienceDirect
International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci
Estimation of changes in the mechanical properties of stainless steel subjected to fatigue loading via electrical resistance monitoring Mohammad A. Omari, Igor Sevostianov ⇑ Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA
a r t i c l e
i n f o
Article history: Received 12 September 2012 Received in revised form 12 February 2013 Accepted 13 February 2013 Available online 22 March 2013 Keywords: Fatigue Resistivity Microcracks Dislocation cluster Elastic properties Microstructure
a b s t r a c t The paper focuses on experimental study of mechanical and electrical properties of fatigued specimens combined with the analysis of microstructural changes produced by cyclic loading. The specimens have been cut from stainless steel 304 and subjected to cyclic loading (up to 80,000 cycles) at several values of maximal stress rmax. At low values of rmax as well as at the low number of cycles no significant changes in mechanical properties and mild decrease in electrical conductivity (approximately uniform over the specimen) have been observed. The latter can be explained by generation cluster of new dislocations that can be seen in photo images in the form of black dots. As the number of cycles and rmax grow up, reduction in Young’s modulus and in ultimate strength of the specimens takes place. This reduction is accompanied by local decrease in electrical conductivity due to formation of the microcracks. Changes in Young’s modulus and electrical conductivity at high values of rmax (higher than the yield limit) follow the theoretically predicted cross-property connection for microcracked materials. Correlation between strength reduction and maximum value of local resistivity across the specimen has been observed at qualitative level. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The paper aims at the development a new methodology to monitor degradation of mechanical properties of fatigued structural elements via electrical resistivity measurements. For this goal, we examine the connections between changes in mechanical and conductive properties of a material that occur in the process of cyclic loading. Experimental study is done on commercially available stainless steel 304 widely used as a structural material for various civil and aerospace engineering applications. The possibility of the cross-property connection is based on the fact that cyclic loading produces certain changes in materials microstructures-generation of new dislocations that is followed by nucleation and growth of microcracks, their coalescence and, finally formation and propagation of the macrocracks (Klesnil & Lucas, 1980; Wen & Keer, 2002). These microstructural changes lead to deterioration of both mechanical performance and conductive properties of the specimens (that are usually considered in literature separately). In the context of mechanical properties deterioration during fatigue loading, the problem that attracted most attention of the researchers is evaluation of strength reduction. The comprehensive reviews on this topic can be found in books of Klesnil
⇑ Corresponding author. Tel.: +1 575 646 3322; fax: +1 575 646 6111. E-mail address: [email protected] (I. Sevostianov). 0020-7225/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijengsci.2013.02.006
M.A. Omari, I. Sevostianov / International Journal of Engineering Science 65 (2013) 40–48
41
and Lucas (1980), Pook (2007), Stephens, Fatemi, Stephens, and Fuchs (2000) and Suresh (1998). Among more recent papers relevant to our study, we would mention work of Kwofie (2001) showed that relationship between fatigue strength and mean stress is non-linear and reflects the true characteristics of the conventional stress–strain curves. Using Mura’s dislocation theory model, Wen and Keer (2002) suggested a formula for critical number of cycles for microcracks initiation near an existing penny-shape crack under unidirectional shear. Kim, Chen, Han, and Lee (2002) studied different methods to determine fatigue properties of steels. They observed that fatigue life of a specimen is correlated with the equivalent strain amplitudes. Puchi-Cabrera, Staia, Tovar, and Ochoa-Perez (2008) evaluated the changes in the tensile mechanical properties due to fatigue loading for stainless steel 316L at high number of cycles. They fatigued specimens at maximum stress 476 MPa min (which is below the yield stress of 516 MPa) and the ratio rrmax ¼ 0:1. A significant increase in the yield stress was observed, while other mechanical properties remained almost constant. It can be explained by process of generation of new dislocations. An interesting observation was made by Heino and Karlsson (2001a, 2001b) who shown that hardening occurs during the first few cycles at large strain amplitudes followed by softening. This phenomenon is explained by accumulation of dislocations followed by microcracks formation. The changes in mechanical properties are initiated by changes in microstructures of fatigued specimens. Different methods are used to reveal metals microstructure defects: Optical Microscope, Scanning Electron Microscopy (SEM) and Transmission Electron Microscope (TEM). TEM has five times more magnifications capability over the SEM; the drawback of TEM is that specimens must usually fit into a 3 mm diameter cup and be less than 100 microns in thickness (Hull & Bacon, 2011). Iacoviello, Boniardi, and Vecchia (1999) used SEM to study the mechanisms of fatigue crack propagation in 22 Cr 5 Ni Duplex Stainless Steels (DSSs). They showed that effect of roughness of fracture surface on fatigue crack growth depends on loading conditions. Heino and Karlsson (2001a, 2001b) considered the development of dislocation structures and surface slip markings under fatigue loading for stainless steel using TEM and SEM, respectively. They concluded that single slip is dominant at low strain amplitudes, and slowly changes to multiple slip with increasing the amplitude. Surface cracks appear at the slip markings on the surface and then grow up to. Man, Petrenec, Obrtlik, and Polak (2004) studied the surface relief evolution at emerging persistent slip bands (PSBs) in individual grains of the X10CrAl24 stainless steel under cyclic loading using both atomic force microscopy (AFM) and SEM. They showed that the surface relief starts to develop early in the fatigue life due to the localization of the cyclic plastic strain into PSBs and the extrusions grow continuously during the fatigue life. Krupp et al. (2010) studied crack initiation and microstructural features for austenitic 304L under fatigue damage processes using SEM supported by electron backscatter diffraction (EBSD). They showed that fatigue-induced strain localization causes the formation of a martensite. Increasing martensite transformation has strong impact on crack propagation rate as proven qualitatively. Shintani and Murata (2011) used Xray diffraction, TEM and Vickers hardness tests to quantitatively evaluate the change in dislocations density and dislocations character in 304 steel. They showed that two factors have strongest effect on changes in mechanical properties: formation of strain-induced second phase and work-hardening induced by increase in dislocation densities. Alvarez-Armas et al. (2012) evaluated the damage in stainless steel due to high and low cyclic loading. Their analysis of the dislocation structure in the near-surface and in ferritic grains shows that dislocation microbands are associated with microcracks initiation. The growth in dislocation density also produces noticeable changes in electrical resistivity of metals. This effect has been discussed in literature for more than half a century without connection to the process of fatigue. Basinski, Dugdale, and Howie (1963) developed the first dislocation resistivity model which has reasonable agreement with experimental results. They assumed that the resistivity is proportional to the mean square displacement of the ions from their unperturbated positions. Tanaka and Watanabe (1972) experimentally evaluated specific resistivity of dislocations for as 1 ± 0.4 1018 X cm3. They noted that there is no significant difference in electrical resistivity in continuous and discontinuous tests. Brown (1976) suggested a simple expression for the specific resistivity of dislocation assuming resonance scattering of Fermi electrons from the core of dislocation, and neglecting the interband scattering. This expression was verified by experimental data for seventeen different metals and it shows a good overall agreement. Watts (1988a, 1988b) discussed the scatter of electrons near the dislocation line and their effect on the electrical resistivity in metals. He observed a good agreement between calculated and measured values of specific dislocation resistivity. Karolik and Luhvich (1994) used the partial-wave method to calculate the electrical resistivity caused by dislocations and grain boundaries in different metals when the resistivity of line defects is known. In the context of the cross-property connections, Sevostianov, Bogarapu, and Tabakov (2002) suggested to use experimentally observed changes in electrical conductivity of fatigued metals to estimate changes in elastic stiffness. These phenomenological results showed a good agreement with theoretically developed cross-property connection for microcracked metals (Sevostianov & Kachanov, 2008; Sevostianov et al., 2002). Combined effect of fatigue induced dislocations on hardening coefficient and electrical properties of steel was discussed by Dominguez and Sevostianov (2011). 2. Materials and method Stainless steel 304 sheets of thickness of 1.905 mm have been purchased from TA CHEN INTERNATIONAL. The chemical composition reported by the manufacturer of the material is as follows: C 0.08 max, Cr 18–20%, Fe 66.5–74%, Mn 2% max, Ni 8–10.5%, P 0.045% max, S 0.03% max, Si 1% max. Material properties of stainless steel 304 are given in Table 1.
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M.A. Omari, I. Sevostianov / International Journal of Engineering Science 65 (2013) 40–48 Table 1 Mechanical properties of stainless steel 304 reported by the manufacturer. Young modulus
Ultimate tensile strength
Yield strength
Electrical resistivity
193 GPa
505 MPa
215 MPa
720 109 O m
Fig. 1. Geometry of the specimens; dimensions are given in millimeters.
Table 2 Changes in mechanical properties of fatigued specimens.
rmin– rmax
14–140 MPa
# of cycles
E exp. GPa
rult.
0 10,000 20,000 30,000 40,000 50,000 60,000 70,000
206 210 201 211 202 198
600 608 600 616 610 612
MPa
21.5–215 MPa E exp. GPa
rult.
206 201 198 190 182 184 180 182
600 605 515 455 435 425 418 428
MPa
23.7–237 MPa
25.8–258 MPa
E exp. GPa
E cal. GPa
rult.
206
206
198 180 177
194 192 188
600 550 512 450 430
MPa
28–280 MPa
E exp. GPa
E cal. GPa
rult. MPa
E exp. GPa
E cal. GPa
rult. MPa
206 173 167 155
206 184 181 176
600 520 375 315
206 165 134 125
206 182 145 132
600 510 345 250
To cut the specimens we used water jet cutter that provides continuous cooling during the cutting process to avoid any changes in mechanical properties. Geometry of the specimens was selected in accordance with the ASTM 557 M standard (Fig. 1). A rectangular damage initiation notch has been cut in the center of each specimen. Fatigue tests were performed using MTS Landmark Servo Hydraulic Test System at frequency f = 20 Hz. Specimens have min been tested under cyclic loading with five different loading rates and maintain loading ratio as R ¼ rrmax ¼ 0:1. The values of rmax used in the experiments were 140 MPa, 215 MPa, 237 MPa, 258 MPa and 280 MPa. The number of cycles varied from 10,000 to 70,000 cycles (or till specimens fracture) as shown in Table 2. Initial resistances readings were scanned at eleven different locations on each specimen as shown in Fig. 1 using HP 4338B milliohmmeter by four-probe method with high accuracy up to 0.4%; after loading the resistance has been scanned again. Before and after loading, microstructures of specimens have been tested with Scanning Electron Microscope model Hitachi S-3400 N that has accelerating voltages 0.3 kV to 30 kV and magnification range 5 to 300,000. In this experiment 10 kV and 6000 were used as accelerating voltages and maximum magnification respectively. At the final stage of the experiment, the fatigued specimens were subjected to the quasi-static loading using INSTRON 5882 universal testing machine to find the ultimate tensile stress and Young’s modulus. 3. Results and discussion 3.1. Changes in mechanical properties Fig. 2 illustrates stress–strain curves obtained in quasi-static tests of specimens previously subjected to cyclic loading. It is seen that Young’s modulus decreases already after 20,000 cycles if rmax > 237 MPa. Yield limit and ultimate strength also decrease with increasing rmax and the number of cycles. It can be explained by nucleation of microcracks in the process of low-cycle fatigue with rmax higher than the material yield limit (Bogarapu & Sevostianov, 2002; Sevostianov et al., 2002). In Fig. 2c with rmax > 280 MPa the specimens have more cracks and some cracks can be seen visually so the tensile test was not very accurate. Moreover, the specimens go to be brittle with low elongation as seen in Fig. 2. Fig. 3a shows experimental S–N min curves for rrmax ¼ 0:1. For comparison, Fig. 3b illustrates reduction in ultimate strength with the number of cycles for different
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Fig. 2. Stress–strain curves for the specimens subjected to loading with (a) rmax = 237 MPa; (b) rmax = 258 MPa; and (c) rmax = 280 MPa after various number cycles.
(a)
(b)
Fig. 3. (a) Experimental S–N curves for rmin/rmax = 0.1; (b) reduction in ultimate strength with the number of cycles for different values of rmax.
values of rmax. More than 2 times reduction of the ultimate strength have been observed after 30,000 cycles with rmax = 280 MPa. These results are also summarized in Table 2 for convenience of a reader. 3.2. Changes in electrical conductivity Fig. 4 illustrates effect of fatigue loading on electrical resistivity of the specimens. For cyclic loading with rmax = 140 MPa (Fig. 4a) one can see approximately uniform growth of the local resistivity over entire specimens with the number of cycles. It is related to approximately uniform growth of the dislocation density before the microcracks nucleation starts. When rmax reaches the value of the yield limit (215 MPa, Fig 4b) one can observe growth of the resistivity in the area close to the notch after 50,000 cycles. Before this point, the growth was approximately uniform. It is related to nucleation of microcracks near the notch. However, these microcracks do not yet form any cluster or macroscopic defect. The situation changes when rmax exceeds the yield limit. Fig. 4c–e illustrates the steep growth of resistivity near the notch after lower number of cycles. It corresponds to coalescence of microcracks and formation and propagation of the macrocrack.
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M.A. Omari, I. Sevostianov / International Journal of Engineering Science 65 (2013) 40–48
Fig. 4. Effect of fatigue loading on electrical resistivity of the specimens at different values of rmax: (a) 140 MPa; (b) 215 MPa; (c) 237 MPa; (d) 258 MPa; and (e) 280 MPa.
3.3. Changes in microstructure The changes in microstructure have been studied using Scan Electron Microscopy with 10 kV accelerating voltage. We compared the changes obtained at different levels of rmax before the loading and after each 10,000 cycles. Fig. 5 illustrates
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Fig. 4. (continued)
Fig. 5. Development of microstructural changes in a specimen subjected to fatigue loading at rmax = 237 MPa: (a) before loading; (b) after 20,000 cycles; (c) after 30,000 cycles; and (d) after 40,000 cycles.
development of microstructural changes in a specimen subjected to fatigue loading at rmax = 237 MPa. One can observe the dots corresponding to dislocations lines normal to the picture. Two types of dots can be seen: black dots called ‘‘pits’’ and a few white dots called ‘‘hillocks’’. Hull and Bacon (2011) shown that dislocations are responsible for both black dots and white dots. Vogel, Pfann, Corey, and Thomas (1953) proved the one-to-one relation between these pits and dislocations experimentally. Fig. 5a shows the microstructure before loading. After 20,000 cycles the dislocation cluster ‘‘dots’’ mildly increases (Fig. 5b). It further increases after 30,000 cycles (Fig. 5c) and, after 40,000 cycles, dislocations cluster starts forming microcracks nuclei that will transform later to microcracks. Fig. 6 illustrates formation and propagation of macroscopic cracks at the final step of the loading process. Fig. 6a at 45 times low magnification, then Fig. 6b at 700 times where the grains can be seen and Fig. 6c shows microcracks at 6000 times magnification, here microcracks branches are revealed. 3.4. Cross-property connections Cross-property connections between changes in elastic and conductive properties of metals induced by microcracks have been first discussed by Bristow (1960). Observing that changes in the said properties are expressed in terms of the same
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Fig. 6. Stages of the formation and propagation of macroscopic cracks at the final step of the loading process: (a) 45 magnification; (b) 700 magnification; (c) 6000 magnification.
crack density parameter and eliminating it. Bristow (1960) derived explicit elasticity-conductivity connections between them as,
E0 E 2 1 m20 ð10 3m0 Þ k0 k ¼ E k 5ð2 m0 Þ K 0 K 2 1 m20 k0 k ¼ 1 2m0 K k G0 G 4ð1 m0 Þð5 m0 Þ k0 k ¼ G 5ð2 m0 Þ k
ð1Þ
where E, K and G denote the Young’s, bulk, and shear moduli; m is Poisson’s ratio, and superscript ‘‘0’’ indicates properties of the bulk material (misprint in the last expression is corrected in Sevostianov & Kachanov, 2008). Results of Bristow were generalized for any kind of spheroidal inhomogeneities with arbitrary orientation distribution by Sevostianov and Kachanov (2002). For parallel cracks their result takes the form of a simple relation between the effective Young’s modulus Ei in certain direction xi and the conductivity ki ( ei k ei , no sum over i) in the same direction that is valid for any orientation distribution of the cracks
E0 Ei 4 1 m20 k0 ki ¼ Ei ki 2 m0
ð2Þ
Bogarapu and Sevostianov (2002) and Sevostianov et al. (2002) used this cross-property connection to estimate decrease in Young’s modulus of aluminum alloy subjected to cyclic loading from electrical conductivity measurements. Comparing our results for changes in Young’s modulus and electrical conductivity of fatigued specimens, we observed, that for high values of load, cross-property connection (2) is satisfied with good accuracy (Fig. 7). It indicates that nucleation of microcracks starts already at low number of fatigue cycles. For lower values of load the difference between experimentally observed and analytically predicted values is rather high. Actually, we observed certain changes on electrical conductivity and negligible changes in Young’s modulus. The reasonable explanation of this phenomenon is that the fatigue process is accompanied
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Fig. 7. Changes in Young modulus with the number of cycles for different values of rmax. Comparison of experimental measurements with prediction according to cross-property connections.
by generation of new dislocations only (without formation of microcracks). Possibility of cross-property connection between strength reduction of a material with accumulated microcracks and decrease in its overall stiffness was discussed in Sevostianov and Kachanov (2010); Sevostianov, Zagrai, Kruse, and Hardee (2010). 4. Concluding remarks The paper focused at the problem on the connection between changes in mechanical and electrical properties observed in the process of fatigue loading of stainless steel 304. At low values of rmax (rmax < 215 MPa) as well as at low number of cycles (lower than 30,000) no significant changes in mechanical properties have been observed. Mild decrease in electrical conductivity (approximately uniform over the specimen) can be explained by generation of new cluster of pits and hillocks that observed at SEM images. As the number of cycles and/or rmax grow up, reduction in Young’s modulus and ultimate strength of the specimens took place. This reduction is accompanied by local decrease in electrical conductivity due to formation of the microcracks, also seen in SEM images. Acknowledgment The financial support of New Mexico Space Grant Consortium is gratefully acknowledged. References Alvarez-Armas, I., Krupp, U., Balbi, M., Herenu, S., Marinelli, M., & Knobbe, H. (2012). Growth of short cracks during low and high cycle fatigue in a duplex stainless steel. International Journal of Fatigue, 41, 95–100. Basinski, Z. S., Dugdale, J. S., & Howie, A. (1963). The electrical resistivity of dislocations. Philosophical Magazine, 8, 1989–1997. Bogarapu, M., & Sevostianov, I. (2002). Cross property correlations for metals subjected to fatigue damage accumulation. ASME Conference Proceedings, 447, 111–116. Bristow, J. R. (1960). Microcracks, and the static and dynamic elastic constants of annealed heavily cold worked metals. British Journal of Applied Physics, 11, 81–85. Brown, R. A. (1976). Electrical resistivity of dislocations in metals. Journal of Physics, 7, 1283–1295. Dominguez, D., & Sevostianov, I. (2011). Cross-property connection between work-hardening coefficient and electrical resistivity of stainless steel during plastic deformation. International Journal of Fracture, 167, 281–287. Heino, S., & Karlsson, B. (2001a). Cyclic deformation and fatigue behavior of 7Mo–0.5N superaustenitic stainless steel-stress-strain relation and fatigue life. Acta Materialia, 49, 339–351. Heino, S., & Karlsson, B. (2001b). Cyclic deformation and fatigue behavior of 7Mo–0.5N super austenitic stainless steel-slip characteristics and development of dislocation structures. Acta Materialia, 49, 353–363. Hull, D., & Bacon, D. J. (2011). Introduction to Dislocations. London: Butterworth-Heinemann. Iacoviello, F., Boniardi, M., & Vecchia, G. (1999). Fatigue crack propagation in austeno-ferritic duplex stainless steel 22 Cr 5 Ni. International Journal of Fatigue, 21, 957–963. Karolik, A. S., & Luhvich, A. A. (1994). Calculation of electrical resistivity produced by dislocations and grain boundaries in metals. Journal of Physics: Condensed Matter, 6, 873–886. Kim, K., Chen, X., Han, C., & Lee, H. W. (2002). Estimation methods for fatigue properties of steels under axial and torsional loading. International Journal of Fatigue, 24, 783–793. Klesnil, M., & Lucas, P. (1980). Fatigue of Metallic Materials. Amsterdam: Elsevier Science. Krupp, U., Roth, I., Christ, H., Kubbeler, M., Fritzen, C., & Skrotzki, W. (2010). Scanning electron microscopy and computer modeling of microstructural changes in the vicinity of propagating short fatigue cracks in austenitic stainless steels. Journal of Physics, 240, 1–4. Kwofie, S. (2001). An exponential stress function for predicting fatigue strength and life due to mean stresses. International Journal of Fatigue, 23, 829–836. Man, J., Petrenec, M., Obrtlik, K., & Polak, J. (2004). AFM and TEM study of cyclic slip localization in fatigued ferritic X10CrAl24 stainless steel. Acta Materialia, 52, 5551–5561. Pook, L. (2007). Metal Fatigue, What It Is, Why It Matters. London: Springer.
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Puchi-Cabrera, E. S., Staia, M. H., Tovar, C., & Ochoa-Perez, E. A. (2008). High cycle fatigue behavior of 316L stainless steel. International Journal of Fatigue, 30, 2140–2146. Sevostianov, I., Bogarapu, M., & Tabakov, P. (2002). Correlation between elastic and electric properties for cyclically loaded metals. International Journal of Fracture, 118, 77–82. Sevostianov, I., & Kachanov, M. (2002). Explicit cross-property correlations for anisotropic two-phase composite materials. Journal of the Mechanics and Physics of Solids, 50, 253–282. Sevostianov, I., & Kachanov, M. (2008). Connections between elastic and conductive properties of heterogeneous materials. Advances in Applied Mechanics, 42, 69–252. Sevostianov, I., & Kachanov, M. (2010). Local minima and gradients of stiffness and conductivity as indicators of strength reduction of brittle-elastic materials. International Journal of Fracture, 164, 147–154. Sevostianov, I., Zagrai, A., Kruse, W., & Hardee, H. (2010). Connection between strength reduction, electric resistance and electro-mechanical impedance in materials with fatigue damage. International Journal of Fracture, 164, 159–166. Shintani, T., & Murata, Y. (2011). Evaluation of the dislocation density and dislocation character in cold rolled Type 304 steel determined by profile analysis of X-ray diffraction. Acta Materialia, 59, 4314–4322. Stephens, R., Fatemi, A., Stephens, R., & Fuchs, H. (2000). Metal Fatigue in Engineering. New York: John Wiley. Suresh, S. (1998). Fatigue of Materials. London: Cambridge University Press. Tanaka, K., & Watanabe, T. (1972). An electrical resistivity study of lattice defects. Applied Physics, 11, 1429–1439. Vogel, F. L., Pfann, W. G., Corey, H. E., & Thomas, E. E. (1953). Observations of dislocations in lineage boundaries in germanium. The American Physics of Society, 90, 489–490. Watts, B. R. (1988a). The contribution of the long–range strain field of dislocations in metals to their electrical resistivity. Journal of Physics, 18, 1183–1195. Watts, B. R. (1988b). Calculation of electrical resistivity produced by dislocations in various metals. Journal of Physics, 18, 1197–1209. Wen, S., & Keer, L. M. (2002). A theory of fatigue: A physical approach with application to lead-rich solder. Journal of Applied Mechanics, 69, 1–10.
Contents lists available at SciVerse ScienceDirect
International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci
Estimation of changes in the mechanical properties of stainless steel subjected to fatigue loading via electrical resistance monitoring Mohammad A. Omari, Igor Sevostianov ⇑ Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA
a r t i c l e
i n f o
Article history: Received 12 September 2012 Received in revised form 12 February 2013 Accepted 13 February 2013 Available online 22 March 2013 Keywords: Fatigue Resistivity Microcracks Dislocation cluster Elastic properties Microstructure
a b s t r a c t The paper focuses on experimental study of mechanical and electrical properties of fatigued specimens combined with the analysis of microstructural changes produced by cyclic loading. The specimens have been cut from stainless steel 304 and subjected to cyclic loading (up to 80,000 cycles) at several values of maximal stress rmax. At low values of rmax as well as at the low number of cycles no significant changes in mechanical properties and mild decrease in electrical conductivity (approximately uniform over the specimen) have been observed. The latter can be explained by generation cluster of new dislocations that can be seen in photo images in the form of black dots. As the number of cycles and rmax grow up, reduction in Young’s modulus and in ultimate strength of the specimens takes place. This reduction is accompanied by local decrease in electrical conductivity due to formation of the microcracks. Changes in Young’s modulus and electrical conductivity at high values of rmax (higher than the yield limit) follow the theoretically predicted cross-property connection for microcracked materials. Correlation between strength reduction and maximum value of local resistivity across the specimen has been observed at qualitative level. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The paper aims at the development a new methodology to monitor degradation of mechanical properties of fatigued structural elements via electrical resistivity measurements. For this goal, we examine the connections between changes in mechanical and conductive properties of a material that occur in the process of cyclic loading. Experimental study is done on commercially available stainless steel 304 widely used as a structural material for various civil and aerospace engineering applications. The possibility of the cross-property connection is based on the fact that cyclic loading produces certain changes in materials microstructures-generation of new dislocations that is followed by nucleation and growth of microcracks, their coalescence and, finally formation and propagation of the macrocracks (Klesnil & Lucas, 1980; Wen & Keer, 2002). These microstructural changes lead to deterioration of both mechanical performance and conductive properties of the specimens (that are usually considered in literature separately). In the context of mechanical properties deterioration during fatigue loading, the problem that attracted most attention of the researchers is evaluation of strength reduction. The comprehensive reviews on this topic can be found in books of Klesnil
⇑ Corresponding author. Tel.: +1 575 646 3322; fax: +1 575 646 6111. E-mail address: [email protected] (I. Sevostianov). 0020-7225/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijengsci.2013.02.006
M.A. Omari, I. Sevostianov / International Journal of Engineering Science 65 (2013) 40–48
41
and Lucas (1980), Pook (2007), Stephens, Fatemi, Stephens, and Fuchs (2000) and Suresh (1998). Among more recent papers relevant to our study, we would mention work of Kwofie (2001) showed that relationship between fatigue strength and mean stress is non-linear and reflects the true characteristics of the conventional stress–strain curves. Using Mura’s dislocation theory model, Wen and Keer (2002) suggested a formula for critical number of cycles for microcracks initiation near an existing penny-shape crack under unidirectional shear. Kim, Chen, Han, and Lee (2002) studied different methods to determine fatigue properties of steels. They observed that fatigue life of a specimen is correlated with the equivalent strain amplitudes. Puchi-Cabrera, Staia, Tovar, and Ochoa-Perez (2008) evaluated the changes in the tensile mechanical properties due to fatigue loading for stainless steel 316L at high number of cycles. They fatigued specimens at maximum stress 476 MPa min (which is below the yield stress of 516 MPa) and the ratio rrmax ¼ 0:1. A significant increase in the yield stress was observed, while other mechanical properties remained almost constant. It can be explained by process of generation of new dislocations. An interesting observation was made by Heino and Karlsson (2001a, 2001b) who shown that hardening occurs during the first few cycles at large strain amplitudes followed by softening. This phenomenon is explained by accumulation of dislocations followed by microcracks formation. The changes in mechanical properties are initiated by changes in microstructures of fatigued specimens. Different methods are used to reveal metals microstructure defects: Optical Microscope, Scanning Electron Microscopy (SEM) and Transmission Electron Microscope (TEM). TEM has five times more magnifications capability over the SEM; the drawback of TEM is that specimens must usually fit into a 3 mm diameter cup and be less than 100 microns in thickness (Hull & Bacon, 2011). Iacoviello, Boniardi, and Vecchia (1999) used SEM to study the mechanisms of fatigue crack propagation in 22 Cr 5 Ni Duplex Stainless Steels (DSSs). They showed that effect of roughness of fracture surface on fatigue crack growth depends on loading conditions. Heino and Karlsson (2001a, 2001b) considered the development of dislocation structures and surface slip markings under fatigue loading for stainless steel using TEM and SEM, respectively. They concluded that single slip is dominant at low strain amplitudes, and slowly changes to multiple slip with increasing the amplitude. Surface cracks appear at the slip markings on the surface and then grow up to. Man, Petrenec, Obrtlik, and Polak (2004) studied the surface relief evolution at emerging persistent slip bands (PSBs) in individual grains of the X10CrAl24 stainless steel under cyclic loading using both atomic force microscopy (AFM) and SEM. They showed that the surface relief starts to develop early in the fatigue life due to the localization of the cyclic plastic strain into PSBs and the extrusions grow continuously during the fatigue life. Krupp et al. (2010) studied crack initiation and microstructural features for austenitic 304L under fatigue damage processes using SEM supported by electron backscatter diffraction (EBSD). They showed that fatigue-induced strain localization causes the formation of a martensite. Increasing martensite transformation has strong impact on crack propagation rate as proven qualitatively. Shintani and Murata (2011) used Xray diffraction, TEM and Vickers hardness tests to quantitatively evaluate the change in dislocations density and dislocations character in 304 steel. They showed that two factors have strongest effect on changes in mechanical properties: formation of strain-induced second phase and work-hardening induced by increase in dislocation densities. Alvarez-Armas et al. (2012) evaluated the damage in stainless steel due to high and low cyclic loading. Their analysis of the dislocation structure in the near-surface and in ferritic grains shows that dislocation microbands are associated with microcracks initiation. The growth in dislocation density also produces noticeable changes in electrical resistivity of metals. This effect has been discussed in literature for more than half a century without connection to the process of fatigue. Basinski, Dugdale, and Howie (1963) developed the first dislocation resistivity model which has reasonable agreement with experimental results. They assumed that the resistivity is proportional to the mean square displacement of the ions from their unperturbated positions. Tanaka and Watanabe (1972) experimentally evaluated specific resistivity of dislocations for as 1 ± 0.4 1018 X cm3. They noted that there is no significant difference in electrical resistivity in continuous and discontinuous tests. Brown (1976) suggested a simple expression for the specific resistivity of dislocation assuming resonance scattering of Fermi electrons from the core of dislocation, and neglecting the interband scattering. This expression was verified by experimental data for seventeen different metals and it shows a good overall agreement. Watts (1988a, 1988b) discussed the scatter of electrons near the dislocation line and their effect on the electrical resistivity in metals. He observed a good agreement between calculated and measured values of specific dislocation resistivity. Karolik and Luhvich (1994) used the partial-wave method to calculate the electrical resistivity caused by dislocations and grain boundaries in different metals when the resistivity of line defects is known. In the context of the cross-property connections, Sevostianov, Bogarapu, and Tabakov (2002) suggested to use experimentally observed changes in electrical conductivity of fatigued metals to estimate changes in elastic stiffness. These phenomenological results showed a good agreement with theoretically developed cross-property connection for microcracked metals (Sevostianov & Kachanov, 2008; Sevostianov et al., 2002). Combined effect of fatigue induced dislocations on hardening coefficient and electrical properties of steel was discussed by Dominguez and Sevostianov (2011). 2. Materials and method Stainless steel 304 sheets of thickness of 1.905 mm have been purchased from TA CHEN INTERNATIONAL. The chemical composition reported by the manufacturer of the material is as follows: C 0.08 max, Cr 18–20%, Fe 66.5–74%, Mn 2% max, Ni 8–10.5%, P 0.045% max, S 0.03% max, Si 1% max. Material properties of stainless steel 304 are given in Table 1.
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M.A. Omari, I. Sevostianov / International Journal of Engineering Science 65 (2013) 40–48 Table 1 Mechanical properties of stainless steel 304 reported by the manufacturer. Young modulus
Ultimate tensile strength
Yield strength
Electrical resistivity
193 GPa
505 MPa
215 MPa
720 109 O m
Fig. 1. Geometry of the specimens; dimensions are given in millimeters.
Table 2 Changes in mechanical properties of fatigued specimens.
rmin– rmax
14–140 MPa
# of cycles
E exp. GPa
rult.
0 10,000 20,000 30,000 40,000 50,000 60,000 70,000
206 210 201 211 202 198
600 608 600 616 610 612
MPa
21.5–215 MPa E exp. GPa
rult.
206 201 198 190 182 184 180 182
600 605 515 455 435 425 418 428
MPa
23.7–237 MPa
25.8–258 MPa
E exp. GPa
E cal. GPa
rult.
206
206
198 180 177
194 192 188
600 550 512 450 430
MPa
28–280 MPa
E exp. GPa
E cal. GPa
rult. MPa
E exp. GPa
E cal. GPa
rult. MPa
206 173 167 155
206 184 181 176
600 520 375 315
206 165 134 125
206 182 145 132
600 510 345 250
To cut the specimens we used water jet cutter that provides continuous cooling during the cutting process to avoid any changes in mechanical properties. Geometry of the specimens was selected in accordance with the ASTM 557 M standard (Fig. 1). A rectangular damage initiation notch has been cut in the center of each specimen. Fatigue tests were performed using MTS Landmark Servo Hydraulic Test System at frequency f = 20 Hz. Specimens have min been tested under cyclic loading with five different loading rates and maintain loading ratio as R ¼ rrmax ¼ 0:1. The values of rmax used in the experiments were 140 MPa, 215 MPa, 237 MPa, 258 MPa and 280 MPa. The number of cycles varied from 10,000 to 70,000 cycles (or till specimens fracture) as shown in Table 2. Initial resistances readings were scanned at eleven different locations on each specimen as shown in Fig. 1 using HP 4338B milliohmmeter by four-probe method with high accuracy up to 0.4%; after loading the resistance has been scanned again. Before and after loading, microstructures of specimens have been tested with Scanning Electron Microscope model Hitachi S-3400 N that has accelerating voltages 0.3 kV to 30 kV and magnification range 5 to 300,000. In this experiment 10 kV and 6000 were used as accelerating voltages and maximum magnification respectively. At the final stage of the experiment, the fatigued specimens were subjected to the quasi-static loading using INSTRON 5882 universal testing machine to find the ultimate tensile stress and Young’s modulus. 3. Results and discussion 3.1. Changes in mechanical properties Fig. 2 illustrates stress–strain curves obtained in quasi-static tests of specimens previously subjected to cyclic loading. It is seen that Young’s modulus decreases already after 20,000 cycles if rmax > 237 MPa. Yield limit and ultimate strength also decrease with increasing rmax and the number of cycles. It can be explained by nucleation of microcracks in the process of low-cycle fatigue with rmax higher than the material yield limit (Bogarapu & Sevostianov, 2002; Sevostianov et al., 2002). In Fig. 2c with rmax > 280 MPa the specimens have more cracks and some cracks can be seen visually so the tensile test was not very accurate. Moreover, the specimens go to be brittle with low elongation as seen in Fig. 2. Fig. 3a shows experimental S–N min curves for rrmax ¼ 0:1. For comparison, Fig. 3b illustrates reduction in ultimate strength with the number of cycles for different
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Fig. 2. Stress–strain curves for the specimens subjected to loading with (a) rmax = 237 MPa; (b) rmax = 258 MPa; and (c) rmax = 280 MPa after various number cycles.
(a)
(b)
Fig. 3. (a) Experimental S–N curves for rmin/rmax = 0.1; (b) reduction in ultimate strength with the number of cycles for different values of rmax.
values of rmax. More than 2 times reduction of the ultimate strength have been observed after 30,000 cycles with rmax = 280 MPa. These results are also summarized in Table 2 for convenience of a reader. 3.2. Changes in electrical conductivity Fig. 4 illustrates effect of fatigue loading on electrical resistivity of the specimens. For cyclic loading with rmax = 140 MPa (Fig. 4a) one can see approximately uniform growth of the local resistivity over entire specimens with the number of cycles. It is related to approximately uniform growth of the dislocation density before the microcracks nucleation starts. When rmax reaches the value of the yield limit (215 MPa, Fig 4b) one can observe growth of the resistivity in the area close to the notch after 50,000 cycles. Before this point, the growth was approximately uniform. It is related to nucleation of microcracks near the notch. However, these microcracks do not yet form any cluster or macroscopic defect. The situation changes when rmax exceeds the yield limit. Fig. 4c–e illustrates the steep growth of resistivity near the notch after lower number of cycles. It corresponds to coalescence of microcracks and formation and propagation of the macrocrack.
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Fig. 4. Effect of fatigue loading on electrical resistivity of the specimens at different values of rmax: (a) 140 MPa; (b) 215 MPa; (c) 237 MPa; (d) 258 MPa; and (e) 280 MPa.
3.3. Changes in microstructure The changes in microstructure have been studied using Scan Electron Microscopy with 10 kV accelerating voltage. We compared the changes obtained at different levels of rmax before the loading and after each 10,000 cycles. Fig. 5 illustrates
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Fig. 4. (continued)
Fig. 5. Development of microstructural changes in a specimen subjected to fatigue loading at rmax = 237 MPa: (a) before loading; (b) after 20,000 cycles; (c) after 30,000 cycles; and (d) after 40,000 cycles.
development of microstructural changes in a specimen subjected to fatigue loading at rmax = 237 MPa. One can observe the dots corresponding to dislocations lines normal to the picture. Two types of dots can be seen: black dots called ‘‘pits’’ and a few white dots called ‘‘hillocks’’. Hull and Bacon (2011) shown that dislocations are responsible for both black dots and white dots. Vogel, Pfann, Corey, and Thomas (1953) proved the one-to-one relation between these pits and dislocations experimentally. Fig. 5a shows the microstructure before loading. After 20,000 cycles the dislocation cluster ‘‘dots’’ mildly increases (Fig. 5b). It further increases after 30,000 cycles (Fig. 5c) and, after 40,000 cycles, dislocations cluster starts forming microcracks nuclei that will transform later to microcracks. Fig. 6 illustrates formation and propagation of macroscopic cracks at the final step of the loading process. Fig. 6a at 45 times low magnification, then Fig. 6b at 700 times where the grains can be seen and Fig. 6c shows microcracks at 6000 times magnification, here microcracks branches are revealed. 3.4. Cross-property connections Cross-property connections between changes in elastic and conductive properties of metals induced by microcracks have been first discussed by Bristow (1960). Observing that changes in the said properties are expressed in terms of the same
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Fig. 6. Stages of the formation and propagation of macroscopic cracks at the final step of the loading process: (a) 45 magnification; (b) 700 magnification; (c) 6000 magnification.
crack density parameter and eliminating it. Bristow (1960) derived explicit elasticity-conductivity connections between them as,
E0 E 2 1 m20 ð10 3m0 Þ k0 k ¼ E k 5ð2 m0 Þ K 0 K 2 1 m20 k0 k ¼ 1 2m0 K k G0 G 4ð1 m0 Þð5 m0 Þ k0 k ¼ G 5ð2 m0 Þ k
ð1Þ
where E, K and G denote the Young’s, bulk, and shear moduli; m is Poisson’s ratio, and superscript ‘‘0’’ indicates properties of the bulk material (misprint in the last expression is corrected in Sevostianov & Kachanov, 2008). Results of Bristow were generalized for any kind of spheroidal inhomogeneities with arbitrary orientation distribution by Sevostianov and Kachanov (2002). For parallel cracks their result takes the form of a simple relation between the effective Young’s modulus Ei in certain direction xi and the conductivity ki ( ei k ei , no sum over i) in the same direction that is valid for any orientation distribution of the cracks
E0 Ei 4 1 m20 k0 ki ¼ Ei ki 2 m0
ð2Þ
Bogarapu and Sevostianov (2002) and Sevostianov et al. (2002) used this cross-property connection to estimate decrease in Young’s modulus of aluminum alloy subjected to cyclic loading from electrical conductivity measurements. Comparing our results for changes in Young’s modulus and electrical conductivity of fatigued specimens, we observed, that for high values of load, cross-property connection (2) is satisfied with good accuracy (Fig. 7). It indicates that nucleation of microcracks starts already at low number of fatigue cycles. For lower values of load the difference between experimentally observed and analytically predicted values is rather high. Actually, we observed certain changes on electrical conductivity and negligible changes in Young’s modulus. The reasonable explanation of this phenomenon is that the fatigue process is accompanied
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Fig. 7. Changes in Young modulus with the number of cycles for different values of rmax. Comparison of experimental measurements with prediction according to cross-property connections.
by generation of new dislocations only (without formation of microcracks). Possibility of cross-property connection between strength reduction of a material with accumulated microcracks and decrease in its overall stiffness was discussed in Sevostianov and Kachanov (2010); Sevostianov, Zagrai, Kruse, and Hardee (2010). 4. Concluding remarks The paper focused at the problem on the connection between changes in mechanical and electrical properties observed in the process of fatigue loading of stainless steel 304. At low values of rmax (rmax < 215 MPa) as well as at low number of cycles (lower than 30,000) no significant changes in mechanical properties have been observed. Mild decrease in electrical conductivity (approximately uniform over the specimen) can be explained by generation of new cluster of pits and hillocks that observed at SEM images. As the number of cycles and/or rmax grow up, reduction in Young’s modulus and ultimate strength of the specimens took place. This reduction is accompanied by local decrease in electrical conductivity due to formation of the microcracks, also seen in SEM images. Acknowledgment The financial support of New Mexico Space Grant Consortium is gratefully acknowledged. References Alvarez-Armas, I., Krupp, U., Balbi, M., Herenu, S., Marinelli, M., & Knobbe, H. (2012). Growth of short cracks during low and high cycle fatigue in a duplex stainless steel. International Journal of Fatigue, 41, 95–100. Basinski, Z. S., Dugdale, J. S., & Howie, A. (1963). The electrical resistivity of dislocations. Philosophical Magazine, 8, 1989–1997. Bogarapu, M., & Sevostianov, I. (2002). Cross property correlations for metals subjected to fatigue damage accumulation. ASME Conference Proceedings, 447, 111–116. Bristow, J. R. (1960). Microcracks, and the static and dynamic elastic constants of annealed heavily cold worked metals. British Journal of Applied Physics, 11, 81–85. Brown, R. A. (1976). Electrical resistivity of dislocations in metals. Journal of Physics, 7, 1283–1295. Dominguez, D., & Sevostianov, I. (2011). Cross-property connection between work-hardening coefficient and electrical resistivity of stainless steel during plastic deformation. International Journal of Fracture, 167, 281–287. Heino, S., & Karlsson, B. (2001a). Cyclic deformation and fatigue behavior of 7Mo–0.5N superaustenitic stainless steel-stress-strain relation and fatigue life. Acta Materialia, 49, 339–351. Heino, S., & Karlsson, B. (2001b). Cyclic deformation and fatigue behavior of 7Mo–0.5N super austenitic stainless steel-slip characteristics and development of dislocation structures. Acta Materialia, 49, 353–363. Hull, D., & Bacon, D. J. (2011). Introduction to Dislocations. London: Butterworth-Heinemann. Iacoviello, F., Boniardi, M., & Vecchia, G. (1999). Fatigue crack propagation in austeno-ferritic duplex stainless steel 22 Cr 5 Ni. International Journal of Fatigue, 21, 957–963. Karolik, A. S., & Luhvich, A. A. (1994). Calculation of electrical resistivity produced by dislocations and grain boundaries in metals. Journal of Physics: Condensed Matter, 6, 873–886. Kim, K., Chen, X., Han, C., & Lee, H. W. (2002). Estimation methods for fatigue properties of steels under axial and torsional loading. International Journal of Fatigue, 24, 783–793. Klesnil, M., & Lucas, P. (1980). Fatigue of Metallic Materials. Amsterdam: Elsevier Science. Krupp, U., Roth, I., Christ, H., Kubbeler, M., Fritzen, C., & Skrotzki, W. (2010). Scanning electron microscopy and computer modeling of microstructural changes in the vicinity of propagating short fatigue cracks in austenitic stainless steels. Journal of Physics, 240, 1–4. Kwofie, S. (2001). An exponential stress function for predicting fatigue strength and life due to mean stresses. International Journal of Fatigue, 23, 829–836. Man, J., Petrenec, M., Obrtlik, K., & Polak, J. (2004). AFM and TEM study of cyclic slip localization in fatigued ferritic X10CrAl24 stainless steel. Acta Materialia, 52, 5551–5561. Pook, L. (2007). Metal Fatigue, What It Is, Why It Matters. London: Springer.
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