Research on high-cycle fatigue behavior of FV520B stainless steel based on intrinsic dissipation

Materials and Design 90 (2016) 248–255

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Research on high-cycle fatigue behavior of FV520B stainless steel based on intrinsic dissipation Qiang Guo, Xinglin Guo ⁎ Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China

a r t i c l e

i n f o

Article history: Received 14 February 2015 Received in revised form 23 September 2015 Accepted 18 October 2015 Available online 21 October 2015 Keywords: FV520B stainless steel High-cycle fatigue Intrinsic dissipation Microstructure motion

a b s t r a c t Systemic fatigue tests were carried out to research the high-cycle fatigue behavior of FV520B stainless steel based on the theory and the calculation model of intrinsic dissipation. Experimental results demonstrate that the method, utilizing intrinsic dissipation as the fatigue damage indicator, can rapidly evaluate the high-cycle fatigue behavior of FV520B stainless steel with a limited number of test specimens. It is shown that the intrinsic dissipation increases with the applied stress amplitude and there is a change point of the increases rate on the curve of intrinsic dissipation versus stress amplitude. The change point reveals a change of the generation mechanism of intrinsic dissipation, and the corresponding stress amplitude is precisely the fatigue limit. For the same stress amplitude, the rate of intrinsic dissipation remains substantially constant during the whole fatigue life. Fatigue failure occurs once the part of intrinsic dissipation associated with fatigue damage accumulates to a threshold value, which is a material constant independent of loading history. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction FV520B stainless steel is a kind of low-carbon martensitic precipitated hardening stainless steel developed by Firth-Vickers Materials Lab in Britain [1]. It is widely used in machine manufacturing due to its good corrosion resistance, high strength, high hardness, and well weldability [2]. Especially for centrifugal compressors, the core equipment of gas deliveries in energy, petroleum, chemical, and other important industries, FV520B stainless steel has already become the dominant material of impeller blade, where resistance towards fluctuating stresses induced by wake flow is of utmost importance [3,4]. Thus, the high-cycle fatigue behavior of FV520B stainless steel is urgently needed to be studied. High-cycle fatigue is an energy dissipation process accompanied by material degradation. Most of the dissipated energy is converted into heat, which manifests itself in the form of temperature change. It is appropriate to study high-cycle fatigue behavior through analysis of the temperature variation of material under fatigue loading. Many scholars have performed related research and obtained some achievements. For instance, Risitano et al. [5–7] proposed a thermographic method (called One Curve Method) to rapidly estimate the fatigue limit of material by utilizing the stabilization temperature. Luong [8,9] took into account the temperature increment below the fatigue limit, and accordingly developed Two Curve Method. Fargione et al. [10] described the fatigue life of material using the integral of the temperature over time up to fracture, and proposed a rapid method for defining the Wöhler curve. Khonsari et al. [11–13] successfully utilized the initial rate of ⁎ Corresponding author. E-mail address: [email protected] (X. Guo).

http://dx.doi.org/10.1016/j.matdes.2015.10.103 0264-1275/© 2015 Elsevier Ltd. All rights reserved.

temperature rise as a function of time during fatigue testing to rapidly predict the fatigue life. Moreover, those thermography-based research methods have been further developed [14–16] and widely applied to many kinds of industrial materials and mechanical components, such as magnesium alloy [17,18], composite materials [19,20], welded joints [21–24], riveted components [25], and components with holes [26,27]. Nevertheless, the temperature variation in high-cycle fatigue process is not an intrinsic manifestation of the microstructure evolution of material, since it is easily affected by the conditions of thermal exchanges, such as conduction, convection and radiation. It is therefore necessary to resort to the calculation of energy dissipation for obtaining the intrinsic data related to the material behavior. For this purpose, Chrysochooset et al. [28–31] developed an approach to determine the heat source development from a temperature field provided by an infrared camera. And then the thermoelastic source and the dissipative source in fatigue process were separately estimated. Maquin et al. [32–34] proposed a more accurate experimental method to measure the very small quantities of dissipated energy during the very first cycles of mechanical loading on metallic specimens, and identified two different kinds of energy dissipation mechanisms. Subsequently, Mareau et al. [35–37] proposed a micromechanical model to describe the two dissipation mechanisms in steels under cyclic loading. Two different mechanisms were assumed to be responsible for energy dissipation: the oscillation of pinned dislocations defined as an anelastic mechanism and the viscoplastic slip of dislocations considered as an inelastic mechanism. Meneghetti et al. [38–40] calculated the specific heat dissipation by measuring the cooling rate after stopping the fatigue loading process, and utilized it as a fatigue damage indicator to analyze the fatigue behavior of plain and notched specimens. Khonsari et al. [41–43]

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successfully applied the thermodynamic entropy production during the fatigue process to the estimation of the fatigue life of components undergoing cyclic bending, torsion and tension-compression, and they presented the concept of FFE, namely the fatigue fracture entropy. In addition, Guo et al. [44] proposed an energy method for rapid evaluation of high-cycle fatigue parameters. The energy method takes intrinsic dissipation as the fatigue damage indicator, and eliminates the interference of internal friction causing no damage on fatigue life evaluation. The outline of the paper is as follows. In Section 2, the theory and the calculation model of intrinsic dissipation are introduced followed by the description of the experiment in Section 3. Section 4 presents the experimental results and makes some discussion before drawing some conclusions in Section 5.

sensitivity to microstructure evolution. Those continuous irreversible changes of microstructure cause the fatigue damage of material and further result in the final fracture failure. Consequently, it is of great significance to utilize intrinsic dissipation as a fatigue damage indicator to evaluate high-cycle fatigue behavior of material. Nevertheless, it should be noted that intrinsic dissipation is not completely induced by the irreversible microstructure changes. Some recoverable motions of microstructure, such as stress-induced reorientation of solute atoms, viscous friction between grain boundaries and slight oscillation of dislocation lines, can also induce intrinsic dissipation, in spite that those effects do not induce fatigue damage of material [32–37].

2. Theoretical framework

As an irreversible energy dissipation process, high-cycle fatigue of material must be accompanied by its own temperature variation. A lot of fatigue experiments have proved that when the applied alternating stress is above the fatigue limit and below the yield limit, the temperature evolution of the material during the whole experimental process is well defined by three phases: initial temperature increase phase (phase I), temperature stabilization phase (phase II), and abrupt temperature increase phase before final failure (phase III) [5–7,10]. Among these three phases, phases I and III only account for less than 10% of the fatigue life, while phase II accounts for more than 90%. The material in phase II has achieved a dynamic thermal equilibrium between heat generation and dissipation (i.e., thermal conduction, convection and radiation). Consequently, the temperature signal of this phase, only fluctuating periodically with the applied alternating stress, contains a lot of valuable information related to fatigue damage, and is usually applied to assess the fatigue behavior of material [15,23]. In order to calculate the intrinsic dissipation from the variation of temperature filed by utilizing the local state equation of high-cycle fatigue (i.e., Eq. (1)), the following hypotheses are formulated:

2.1. The intrinsic dissipation theory According to the basic viewpoint of the continuum thermodynamics, high-cycle fatigue of material can be studied as an irreversible thermodynamic process under quasi-static conditions [28,29]. In order to accurately describe this process, the selected state variables include not only the absolute temperature T and the strain tensor ε, but also a set of internal variables αn (n = 1, 2, …, n) being in accordance with the physical mechanisms within the studied material. Combining the first and second principles of thermodynamics and introducing the specific Helmholtz free energy ψ, the local state equation of material in highcycle fatigue process is deduced [28–31]: 2

2

sthe

sic

∂ψ ∂ψ ∂ ψ ∂ ψ _ _ _ : ε−ρ  α_ þ ρT : ε_ þ ρT  α_ þr e ρCT−div ðk gradT Þ ¼ σ : ε−ρ ∂εffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ∂α ffl} |fflfflfflfflfflfflffl ∂T∂ε ∂T∂α |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} d1

ð1Þ where re denotes the external heat supply, σ the Cauchy stress tensor, ρ the mass density, C the specific heat capacity and k the heat conduction coefficient. The first left-hand term of the local state equation ρCT_ is the heat storage rate characterized by temperature change, and the second left-hand term −div(k gradT) is the heat loss rate induced by conduc_ −ρ ∂ψ : ε_ and −ρ ∂ψ  α_ unite tion. The first three right-hand terms σ : ε, ∂ε

∂α

together to denote the intrinsic dissipation source d1, the fourth right2

∂ ψ hand term ρT ∂T∂ε : ε_ denotes the thermoelastic source sthe, and the 2

∂ ψ  α_ denotes the heat source induced by fifth right-hand term ρT ∂T∂α the coupling effect between internal variables and temperature, sic. Among those terms, the intrinsic dissipation source d1 is the focus of particular concern in the present research. In fact, the essence of intrinsic dissipation is the energy form of the entropy generation contributed by non-heat-conduction factors in a unit time and a unit volume of material [45,46]:       k gradT k gradT d1 ¼ T ρs_ −div  gradT ¼ T η‐η2 ¼ Tη−d2 ð2Þ − 2 T T where T is the absolute temperature, s the entropy density. η ¼ ρs_ −

divðk

gradT Þ T

denotes the total entropy generation rate, η2 ¼ k

gradT T2

2.2. The calculation model of intrinsic dissipation

• the heat conduction coefficient k, the mass density ρ and the specific heat capacity C are material constants, independent of the internal states; • the thermoelastic source sthe and the intrinsic dissipation source d1 are uniform throughout the gauge volume at a mesoscopic scale; • the coupling heat source between internal variables and temperature, sic, is neglected; • the convection term included in the material time derivation is ); neglected (i.e., T_ ¼ ∂T ∂t • the external heat supply re is time-independent. Based on those hypotheses and considering the regularizing effect of heat diffusion, a local one-dimensional heat conduction equation is deduced for the flat and thin specimens with a constant cross-section [28–31]:

ρC

! 2 ∂θðx; t Þ θðx; t Þ ∂ θðx; t Þ ¼ sthe ðt Þ þ d1 ðt Þ þ 1D −k ∂t ∂x2 τ th

ð3Þ



gradT denotes the part contributed by heat-conduction factors, and the energy form of this part, d2 = Tη2, is referred to as the thermal dissipation. According to the Clausius inequality, the entropy generation rate, as the quantitative characterization of the irreversible process, is always positive, and hence the intrinsic dissipation source d1 is as well. Generally speaking, material inevitably contains some defects, such as vacancies, dislocations and grain boundaries. This permits irreversible microstructure evolution to occur even under relatively low alternating stress, including dislocation intersection, multiplication, and pile-up. Those irreversible changes of microstructure inevitably lead to entropy generation and are manifested as intrinsic dissipation on a macroscopic scale [41–43]. Just for this reason, intrinsic dissipation has relatively high

where θ = T − T0 is the temperature variation neglecting the thermal gradient along the thickness direction (T0 initial temperature), τ1D th a time constant characterizing the lateral heat exchanges between the specimen surface and the surroundings (i.e., thermal convection and radiation). Only cyclic loading with sinusoidal waveform is considered in the present research. For a certain number of successive complete cycles, averaging Eq. (3) in the time domain leads to: ! 2 θðxÞ ∂ θðxÞ _ ¼ sthe þ d1 ρC θðxÞ þ 1D −k ∂x2 τ th

ð4Þ

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where the overline symbols ‘−’ correspond to the mean values through this period of time, and θ_ is the mean value of the temperature change . For the specimen in the temperature stabilization phase, the acrate ∂θ ∂t cumulations of the thermoelastic source sthe and the temperature become zero at the end of per cycle. Therefore, Eq. (4) change rate ∂θ ∂t can be further simplified into the following form: 2

ρC

θðxÞ ∂ θðxÞ −k ¼ d1 : ∂x2 τ 1D th

ð5Þ Fig. 1. Dimensions of the specimens (unit: mm).

This is a second order linear differential equation with constant coefficients about spatial coordinate x, and the general solution can be written: sffiffiffiffiffiffiffiffiffiffi! sffiffiffiffiffiffiffiffiffiffi! τ 1D d1 ρC ρC þ P þ th θðxÞ ¼ P 1 exp x exp −x 2 1D 1D ρC kτth kτ th

ð6Þ

where P1 and P2 are arbitrary constants. Eq. (6) indicates that the distribution of the mean temperature variation θðxÞ has the following double exponential function form within the specimen gauge part: θðxÞ ¼ C 1 erx þ C 2 e−rx þ C 3

ð7Þ

where C1 and C2 are the coefficients determined by the temperature qffiffiffiffiffiffiffi ρC the parameter determined by the lateral kτ1D

boundary conditions, r ¼

th

heat exchanges with the surroundings, and C 3 ¼

τ1D d th 1 ρC

the coefficient

jointly determined by the lateral heat exchanges and the intrinsic dissipation. As a consequence, the mean value of the intrinsic dissipation through this time period can be calculated: 2 d1 ¼ kr̂ Ĉ 3

ð8Þ

where k is the heat conduction coefficient, r̂ and Ĉ 3 the parameters obtained by fitting the mean temperature variation θðxÞ with Eq. (7). Moreover, it is necessary to point out that the following experimental research takes the 15 s before the end of each cyclic loading stage as the time period to calculate the mean value of the intrinsic dissipation, and takes this mean value as the intensity of intrinsic dissipation in the corresponding stress case. 3. Description of experiment 3.1. Material and specimen The investigated FV520B stainless steel was produced by electricfurnace smelting first and then electro-slag refining. The main chemical compositions of the steel are listed in Table 1. In order to optimize its mechanical properties, a series of specific heat treatments was performed before mechanical processing. The detailed technological process was as follows: solid solution treatment at 1050 °C for 1 h and air-cooling + thermal refining treatment at 850 °C for 2 h and oilcooling + aging treatment at 480 °C for 3 h and air-cooling. Then the uniaxial tensile test identified the ultimate tensile strength σb = 1343 MPa and the 0.2% offset yield strength σ0.2 = 1095 MPa. Moreover, the heat conduction coefficient was also experimentally measured with k = 15 m−1 k−1.

The specimens used for fatigue tests were manufactured from a 5 mm thick plate of FV520B stainless steel with the length direction parallel to the rolling direction, and the dimensions are shown in Fig. 1. All the specimens were polished with a sequence of emery papers to reduce the surface roughness and the stress concentration induced by mechanical processing, especially in the arris edges. Since infrared thermography technology was going to be adopted, thin mat black coatings were painted on the specimens before fatigue testing to avoid reflections from the environment and to increase their emissivity, ensuring an accurate temperature measurement. 3.2. Fatigue test procedures Fatigue tests were carried out at normal room temperature using a fully computerized MTS810 servo-hydraulic system with a 100 kN load capacity. A load-controlled mode was chosen to provide cyclic stress with sinusoidal waveform for test specimens. During the experiment, the full field surface temperature of the specimen was monitored by means of an infrared camera Cedip Jade III with the spectrum response range between 3 μm and 5 μm, resolution of 320 × 240 pixel, sensitivity/NETD of 0.02 at 25 °C, and image update rate of 15 Hz. The whole test procedures included five separate uniaxial tensioncompression fatigue tests. Each test was performed by imposing a series of loading blocks on a fresh specimen. Each loading block consisted of 10,000 cycles with constant loading frequency fL, constant stress amplitude σa, and constant load ratio Rσ (always being −1 in this study). Between two blocks, a twenty-minute pause of loading was made to ensure the test could restart at thermal equilibrium. Details of the loading block series for each fatigue test are as follows. Test 1 The series included 23 loading blocks, with the same loading frequency of 10 Hz and the stress amplitude starting from 220 to 440 MPa with a fixed step of 10 MPa, as shown in Fig. 2(a). Test 2 The series included enough loading blocks for the final fatigue failure, with the same loading frequency of 10 Hz and the same stress amplitude of 380 MPa. Test 3 The series was identical with that of Test 2, except for the stress amplitude of 400 MPa. Test 4 The series consisted of 7 identical sub-series. Each of them included 4 loading blocks, with the same loading frequencies of 10 Hz and the different stress amplitudes being 300, 320, 380 and 400 MPa respectively, as shown in Fig. 2(b). Test 5 The series consisted of 5 sub-series, with the different stress amplitudes being 300, 320, 340, 360 and 380 MPa respectively. Each of them included 7 loading blocks, with the same stress

Table 1 Chemical compositions of FV520B steel (mass fraction/%). C

Si

Mn

Cr

Ni

Cu

Nb

S

P

Mo

0.02–0.07

0.15–0.70

0.3–1.00

13.0–14.5

5.0–6.0

1.3–1.8

0.25–0.45

≤0.025

≤0.03

1.3–1.8

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amplitude and the different loading frequency being 5, 7.5, 10, 12.5, 15, 17.5 and 20 Hz respectively, as shown in Fig. 2(c).

For avoiding too-large data, the infrared camera only recorded the temperature associated with the 5 s before the start of each loading

251

block and the 15 s before the end. In those two time periods, the specimen had reached thermal equilibrium with the surroundings by means of thermal conduction, convection and radiation. In order to ensure the stability of the temperature conditions, the bottom grip connected to the actuator was continuously cooled down by circulating water, and a blower was employed to provide a stable air flow field on the specimen surface.

4. Results and discussion

Fig. 2. Loading procedures for (a) Test 1, (b) Test 4 and (c) Test 5.

Fig. 3 presents a typical infrared thermographic image acquired before the end of a loading block. The distribution of the specimen temperature is substantially symmetric about the mid-section, with high in middle and low at two ends. Indeed, only the rectangular area on the image is the area associated with the calculation of intrinsic dissipation, and it is often referred to as the gauge area. Here the crosswise mean temperature of the gauge area is taken as the one-dimensional temperature date. The mean temperature variation θðxÞ, corresponding to the 15 s before the end of each loading block, is calculated with the mean value of the 5 s before the start as the initial temperature. And then, the corresponding mean intrinsic dissipation is obtained by fitting the mean temperature variation with Eq. (7) and calculating with Eq. (8). Fig. 4 shows the intrinsic dissipations under different stress amplitudes obtained from test 1. It can be seen that the intrinsic dissipation increases with the applied stress amplitude, and the increase rate has a significant change near 360 MPa. In order to effectively identify this change point, two fitting straight lines are utilized to interpolate the experimental data, one for the stresses below a value determined by an iteration procedure and the other for the stresses above the value. The intersection of them is exactly the change point of the increase rate, and the corresponding stress amplitude is 357.48 MPa. It is worth noticing that the slopes of the two fitting straight lines are 635.21 and 2436.59 respectively, with a significant difference of factor 2.84. This phenomenon indicates that the generation mechanism of intrinsic dissipation has a fundamental change below and above the stress amplitude of 357.48 MPa. Here we combine G–L dislocation model [47,48] and F–R dislocation multiplication theory [49,50] to reveal the microstructure motion of the material, which is hidden behind this macroscopic phenomenon related to energy dissipation. It is a fact that large amounts of dislocations exist within the material and that the dislocations are fixed by pinning points in the crystal lattice. The pinning points fall into two categories, namely, the weak pinning points (acted by solute atoms, vacancy defects, etc.) and the strong pinning points (acted by grain boundaries, secondary phase particles, etc.). The motion of the dislocations under cyclic loading is analogous to the motion of a damped vibrating string. When the stress amplitude increases from 220 to 357.48 MPa, the dislocation lines gradually break away from the weak pinning points and oscillate with damping between the strong points. In this case, the intrinsic dissipation is totally caused by internal friction (e.g., lattice friction), and it is proportional to the sweeping-over area of the dislocation lines. In the linear elastic range of the material, the sweeping-over area is positively correlated with the applied stress amplitude. Therefore, the intrinsic dissipation has a good linear relationship with it, as shown in Fig. 4. Although being irreversible due to internal friction, the oscillation of the dislocations is recoverable because of the presence of line tension that is responsible for a backstress bringing dislocation lines back in their equilibrium position [35,36]. Accordingly, no fundamental change of the microstructure takes place under such stress conditions, that is, there is no fatigue damage within the material. When the stress amplitude increases above 357.48 MPa, the dislocation lines not only oscillate between the strong pinning points, but also break away from some of them. Meanwhile, some other strong pins that still unable to be unpinned become dislocation sources to generate new dislocations. As unrecoverable microstructure evolution, the unpinning

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Q. Guo, X. Guo / Materials and Design 90 (2016) 248–255

Fig. 3. A typical infrared thermographic image acquired before the end of a loading block.

of strong pins and the dislocation multiplication can lead to permanent strain, which are collectively referred to as microplastic deformation. Therefore, the intrinsic dissipation under such stress conditions results from two kinds of micro-mechanisms, namely, internal friction and microplastic deformation. It is worth noting that microplastic deformation, comparing with internal friction, has higher sensitivity to the increase of the applied stress amplitude [32–34]. This is mainly because that both the unpinning of strong pins and the dislocation multiplication can directly increase the disorder of the material microstructure, accompanied with violent energy dissipation. It is just the continuous accumulation of microplastic deformation that eventually leads to the fatigue failure of the material. Consequently, the stress amplitude of 357.48 MPa corresponds to a critical value. The critical value is associated with the change of the

generation mechanism of intrinsic dissipation, namely, from the individual effect of internal friction to the combined effect of internal friction and microplastic deformation. Since the appearance of microplastic deformation marks the onset of fatigue damage, the stress amplitude of 357.48 MPa is precisely the fatigue limit of the material. In order to accurately describe the fatigue damage with intrinsic dissipation as the indicator, it is necessary to eliminate the interference of internal friction since it causes no fatigue damage. As we have already observed and analyzed from Fig. 4, the intrinsic dissipation below the fatigue limit has a good linear relationship with the stress amplitude, and the intrinsic dissipation under such stress conditions is induced only by internal friction. Hence, we apply this linear relationship to the data pairs ðσ a j ; d1 j Þ above the fatigue limit. Subsequently, the part of in

trinsic dissipation, d 1 which is associated with microplastic deformation (i.e., fatigue damage), can be obtained by subtracting the other part caused by internal friction from the whole. The results are presented in Table 2. Fig. 5 shows the evolution of intrinsic dissipation during the whole fatigue lives for two stress amplitudes of 380 and 400 MPa, obtained from tests 2 and 3 respectively. It can be observed that the intrinsic dissipation always remains basically stable, which indicates that the material microstructure evolves at a relatively stable rate when the stress amplitude keeps constant. Thus, it is reasonable to take the mean value of the final 15 s before the end of each stage as the intensity of intrinsic dissipation under the corresponding stress amplitude. The continual microstructure evolution leads to the final fatigue failure. The accumulation of fatigue damage can be quantitatively characterized by the accumulation of the part of intrinsic dissipation associated with 

Fig. 4. Intrinsic dissipation dependent of stress amplitudes.

microplastic deformation, d 1 . Therefore, fatigue failure occurs once the part accumulates to a threshold value EC, and the threshold value EC is considered as a material constant independent of loading history. Combining the calculation results under the stress amplitudes of 380 and 400 MPa in Table 2, we can obtain the corresponding cumulative values during the whole fatigue lives, namely, 1.3149 × 1010 and

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Table 2 Intrinsic dissipation caused by the irreversible microstructure evolution. σa/MPa  d1 =ð105

 Jm

−3 −1

s

Þ

360

370

380

390

400

410

420

430

440

0.1818

0.2713

0.3313

0.5838

0.6829

0.7848

1.0014

1.4134

1.6420

1.2901 × 1010 J m−3 respectively. Such small difference between the two values indicates that the threshold value EC associated with fatigue failure is indeed a material constant independent of loading history. To further reduce error, it is determined as the average value of the both, namely, EC = 1.3025 × 1010 J ⋅ m− 3. And then, the fatigue lives Nfj under different stress amplitudes σaj can be calculated according to the following formula:

amplitude, independently on the loading frequency. Furthermore, we can conclude that the fatigue life is not affected by the factor of loading frequency and is determined only by the applied stress amplitude, within the loading frequency range studied in the present work. 5. Conclusions

ð9Þ

The uniaxial tension-compression fatigue tests, performed at room temperature on 5 mm-thick dogbone specimens made of FV520B stainless steel, enable us to draw the following conclusions.

Fig. 6 shows the results in bi-logarithm scale. Meanwhile, the S–N curve under survival probability of 50% is also plotted by fitting the data pairs (Nfj,σaj) with the least-square method. Fig. 7 shows the experimental results of test 4. It can be recognized that for different sub-series, the intrinsic dissipations under the same stress amplitudes are practically consistent and approximately equal to the results of test 1. This consistency indicates that the rate of microstructure evolution is just determined by the stress amplitude, independently on the loading history. At the same time, it verifies the reasonability of utilizing only one specimen to measure the intrinsic dissipations under different stress amplitudes. In addition, according to the above analysis on the micro-mechanisms, the intrinsic dissipations are induced only by the damped oscillation of dislocation lines under the stress amplitudes of 300 and 320 MPa. However, for the stress amplitudes of 380 and 400 MPa, microplastic deformation takes place continuously, including unpinning of strong pins, and dislocation multiplication. Therefore, it can be concluded from the observation of Fig. 7 that, as for this material, damped oscillation of dislocation lines is not affected by unpinning of strong pins and dislocation multiplication. Fig. 8 shows the experimental results of test 5, namely, the intrinsic dissipation dependent of loading frequencies. It is obviously found that the intrinsic dissipation increases linearly with respect to the loading frequency for the same stress amplitude. The good linear correlation between them indicates that internal friction is a kind of rate-independent micro-mechanism, and that the magnitude of microplastic deformation caused by each loading cycle is basically constant for the same stress

(1) As the energy form of the entropy generation contributed by non-heat-conduction factors, intrinsic dissipation has definite physical meaning to characterize quantitatively the fatigue damage evolution of material. The experimental method, utilizing intrinsic dissipation as the fatigue damage indicator, can rapidly evaluate the high-cycle fatigue behavior of FV520B stainless steel with a limited number of test specimens. (2) The intrinsic dissipation of FV520B stainless steel increases with the applied stress amplitude. A change of the increase rate occurs at the point of 357.48 MPa, with a sudden increase of intrinsic dissipation. This change point is actually responsible for a change of the generation mechanism of intrinsic dissipation, namely, from the individual effect of internal friction to the combined effect of internal friction and microplastic deformation. The corresponding stress amplitude is precisely the fatigue limit of the material, σ0 =357.48 MPa. (3) Fatigue damage evolution of FV520B stainless steel has relatively stable rates for constant stress amplitudes. And the rates are determined by the applied stress amplitudes, independently on the loading history. For the same stress amplitude, the magnitude of fatigue damage caused by each loading cycle remains substantially constant and is not affected by the loading frequency. Fatigue failure occurs once the part of intrinsic dissipation associated with fa tigue damage, d 1 , accumulates to a threshold value EC, which is a material constant independent of loading history. (4) From the microscopic view, the damped oscillation of dislocation lines, within FV520B stainless steel, is not affected by the

Nfj ¼

EC



d

:

1 j

Fig. 5. Evolution of the intrinsic dissipation during whole fatigue lives.

Fig. 6. S–N curve of FV520B stainless steel.

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Fig. 7. Intrinsic dissipation dependent of loading sequences.

Fig. 8. Intrinsic dissipation dependent of loading frequencies.

unpinning of strong pins and the dislocation multiplication, and it is a kind of rate-independent micro-mechanism.

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