Mathematical Problems in Engineering
Volume 2021 (2021), Article ID 7136846, 12 pages
https://doi.org/10.1155/2021/7136846

Research Article

Continuum Damage Mechanics Approach for Modeling Cumulative-Damage Model

Haoran Li,¹ Jiadong Wang,¹ Juncheng Wang,¹ Ming Hu,¹ and Yan Peng²

¹Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
²School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China

Correspondence should be addressed to Haoran Li; lihaoranysu@163.com

Received 10 April 2021; Revised 28 April 2021; Accepted 15 May 2021; Published 2 June 2021

Academic Editor: José António Fonseca de Oliveira Correia

Copyright © 2021 Haoran Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

In this study, we propose a novel cumulative-damage model based on continuum damage mechanics under situations where the mechanical components are subjected to variable loading. The equivalent completely reversed stress amplitude accounting for the effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths on high-cycle fatigue under variable loading is elaborated. The effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths is considered by averaging the superior limit of the intrinsic damage dissipation work in the critical domain. We developed a novel cumulative-damage model by introducing the equivalent completely reversed stress amplitude into the damage-evolution model. For better comparison, existing cumulative-damage models, including the Palmgren–Miner law, corrected Palmgren–Miner law, Morrow’s plastic work interaction rule, and Wang’s rule, were employed to predict the fatigue life under variable loading. The proposed model performed better, considering the error scatter band obtained by plotting the predicted and experimental fatigue life on the same coordinate system. The model precisely predicts fatigue life under variable loading and easily identifies its material constants.

1. Introduction

Fatigue failure should be considered in the engineering design to ensure safety and reliability during service life [1]. Fatigue failure assessment plays an important role in the design of engineering structures since it ensures the safety of engineering structures during their service lives. Since its initiation by Wohler in 1860, despite enormous efforts, reliable and consistent fatigue models applicable to complex loading history are still under development [2]. Substantial engineering structures in the industry fail by fatigue.

Engineering structures in the industry are usually subjected to variable loading. Variable loading, including variable amplitude and loading paths, is related to the fatigue life of engineering structures. Comparing the fatigue on constant loading, the fatigue on variable loading is always additionally investigated for the interactive effect associated with two adjacent load steps on fatigue life. For constant-amplitude and path loading, several researchers have proposed various fatigue criteria and described the effect of additional hardening behavior related to nonproportional loading paths [3], mean stress [4], and stress gradients [5, 6] on high-cycle fatigue. In general, those approaches can be roughly categorized into three, namely, strain energy method [7], critical plane approach [8, 9], stress-field intensity [10]. Stress gradients, well known as a factor affecting fatigue strength of metals, can be predicted by the theory of stress-field intensity since it was initially proposed aiming to the damage domain. Qylafku [11], Taylor [12], and Zeng [13] employed the stress-field intensity concept to model several fatigue criteria. Despite the significant efforts made on stress-field intensity methods, there is no general consensus as to the suitability of various loading situations, e.g., nonproportional loading. For high-cycle fatigue under variable loading, it has been reported that loading history significantly affects fatigue life, and several damage-accumulation models have been proposed. Despite the significant efforts made on damage-accumulation models, none has gained widespread acceptance. Among them, Miner’s damage-accumulation rule remains the most commonly adopted in practice [14]. Zhao [15] proposed a corrected Miner’s damage-accumulation rule to improve the accuracy of prediction, while life predictions’ accuracy has still been found unsatisfactory [16]. Drawbacks associated with the rules include their inability to express definite effects of the loading sequence on fatigue life [17]. Some other researchers, including Morrow et al. [18], Wang et al. [19], and Zhu et al. [20] established damage-accumulation models aiming at definite effects. Wang’s rule was validated by multiaxial variable loading tests. Notably, damage parameters and fatigue life under constant-amplitude loading were employed to model Morrow’s plastic work interaction rule and Wang’s rule. Zhu et al. focused on isodamage lines-based methods and proposed a new nonlinear fatigue damage-accumulation model. Nevertheless, Xia et al. [21] reported that either damage parameter or fatigue life under constant-amplitude loading cannot reveal the definite effect of the loading sequence on fatigue life.

Initiated by Kachanov in 1958, continuum damage mechanics has been employed in modeling cumulative-damage models. Shang et al. [22], Hua et al. [23], and Yuan [24] proposed cumulative-damage models based on the damage-evolution model proposed by Lemaitre, which predicts the life expectancy of engineering structures subjected to variable loading. However, many material parameters in these models have to be identified, making them inconvenient for applications.

Here, we propose a new accumulative-damage model based on continuum damage mechanics, to improve the abovementioned shortcomings. First, the equivalent completely reversed stress amplitude, which accounts for the effect of additional hardening behavior related to nonproportional loading paths, mean stress, stress gradients, and loading history on high-cycle fatigue under variable loading, is elaborated using the stress-field intensity concept. The effect of loading history on fatigue life is established by combing damage parameters and fatigue life under constant-amplitude loading. Here, the equivalent completely reversed stress amplitude under single-stage loading is called the damage parameters. By introducing equivalent completely reversed stress amplitudes into the damage-evolution model, a new cumulative-damage model is established. The obtained rule compares very well with experimental data in the literature, and it is consistent with the previously proposed models, including the Palmgren–Miner law [17], corrected Palmgren–Miner law [15], Morrow’s plastic work interaction rule [18], and Wang’s rule [19]. Moreover, only one parameter is evaluated in our model, and it is very simple to obtain the model parameter.

2. Equivalent Completely Reversed Stress Amplitude

High-cycle fatigue failure is a local phenomenon, and the locality, also called the critical domain, is taken as a research object in stress-field intensity concepts. Nevertheless, the application of stress-field intensity concepts in investigating multiaxial high-cycle fatigue, especially under nonproportional loading, has not been extensively studied. Here, we propose damage parameters, based on continuum damage mechanics and stress-field intensity concepts, to model the cumulative-damage model.

Continuum damage mechanics has provided a method for analyzing damage development by introducing a damage variable into the constitutive stress-strain relationship. As one of the outstanding examples, Lemaitre et al. [25] proposed a differential equation for damage development. Distinguishingly, the damage development equation can be expressed as follows for the components subjected to fully reversed tension:

To develop the damage development equation available for multiaxial high-cycle fatigue, equation (1) is modified as follows:

where is the damage parameter describing the effect of additional hardening behavior related to nonproportional loading paths and mean stress on high-cycle fatigue under single-stage constant loading. The damage parameter is expressed as equation (3), as proposed by Freitas et al. [26]. The parameter c proposed by Yao et al. [27], which is employed when considering the effect of stress gradients, is also utilized here, and it is expressed as equation (4). Considering the variety of c under situations where the mechanical component is subjected to nonproportional loading, c is calculated when reaches the maximum value. Certainly,

the damage evolution equation can also be obtained from the explicit expression of damage variables as follows:

where is the fatigue life of a point located at the critical domain and is the predicted life equivalent to that of structural components subjected to fully reversed tensile loading. Both are, respectively, expressed as follows:

Introducing stress-field intensity concepts, the average superior limit of the intrinsic damage dissipation work [28] in the critical domain can be obtained as the left side of equation (8). The hypothetical condition that the same average superior limit of the intrinsic damage dissipation work in the critical domain implies the same fatigue life is captured to formulate the damage parameters in our model. To simplify, the average superior limit of the intrinsic damage dissipation work in the critical domain for smooth structural components subjected to fully reversed tensile loading can be obtained as the right side of the following equation:

Then, expanding equation (8), the following equation is obtained:

Substituting equations (5)–(7) into equation (9) and employing first-order approximation, the damage parameters are finally expressed as follows. Notably, several material constants are contracted to consider the self-consistency of the damage parameters:

Numerous fatigue experiments of variable amplitude have shown that loading history has a remarkable effect on fatigue life. For structural components subjected to uniaxial loading, different loading sequence makes Miner’s cumulative critical value fall in different regions. When structural components are subjected to a high-low loading sequence, Miner’s cumulative critical value falls below one, and conversely, for a low-high loading sequence, the value is greater than one. Here, by combing the damage parameters, the equivalent completely reversed stress amplitude considering the loading sequence is proposed as follows:

where is the contraction towards the partial variables in equation (11).

3. Proposed Cumulative-Damage Model

For smooth structural components subjected to single-stage fully reversed tensile loading, the damage-evolution equation can be obtained from the explicit expression of the damage variable:

Substituting equation (11) into (12), the expression of the damage-evolution associated with ith loading step can be obtained as follows:

Then, the expression of damage-evolution associated with the first loading step (equation (13)) should be rewritten as follows:

For structural components subjected to two-step loading, the expression of damage-evolution associated with the second loading step can be expressed as follows:

Based on the damage-equivalent concepts [19], if the fatigue life and applied cycles under th constant-amplitude loading are and , then the damage caused by cycle loading can be equivalent to that caused by cycle loading at the ith level, i.e., . Then, the equivalent damage of the first loading step can be obtained through the second loading step by combining equations (14) and (15). The equivalent relation can be expressed as follows:

Applying the superposable fatigue-life condition to a single-loading step, , and the cumulative-damage model for two steps loading can be established as follows:

Distinguishingly, the cumulative-damage rule for structural components is subjected to two-step uniaxial loading (fully reversed tensile loading), and we conclude that different loading sequence makes Miner’s accumulative critical value fall in different regions. The principle associated with the conclusion is expressed in equation (18). For structural components subjected to high-low two-step uniaxial loading (fully reversed tensile loading), Miner’s cumulative critical value falls below one, and conversely, the sum is greater than one:

Furthermore, for structural components subjected to three-step loading, the expression of damage-evolution associated with the third loading step can be expressed as equation (19), and it is obtained from equation (13). The damage-evolution associated with the second loading step can be obtained from equation (15), and it is explicitly expressed in equation (20):

Then, one can obtain the cumulative-damage model for three-step loading based on the damage-equivalent concepts. The resulting cumulative-damage model for three-step loading is expressed as follows:

Similarly, the recurrence formula of the ith level loading can be expressed as follows:

The application of the new cumulative-damage model for predicting the fatigue life of structural components under variable loading involves identifying the material parameter p. Material parameter p can be obtained by analyzing the experimental data associated with a specimen subjected to fully reversed tensile loading employing the least square method. Certainly, the resulting identification model (equation (23)) is derived by combing equation (12) and the least-square method:

4. Evaluation by the Experimental Data

4.1. Uniaxial Loading Condition

The uniaxial two-level step-loading test data for C35, SAE4130, and 7050-T7451 (Table 1) were used to evaluate the proposed damage-cumulative model. For better comparison, existing popular cumulative-damage models, including Palmgren–Miner law, corrected Palmgren–Miner law, and Wang’s rule, were employed to predict the fatigue life under the loading conditions. All experimental data and material parameters required in these models are listed in Table 2.

Table 1: Uniaxial two-level step-loading test data and predicted life using the tested rules [29, 30].

Materials

Min.
C. Miner
Wan.
Pro.
Exp.

C35
353
275
0.1
689200
461200
645282
181625
353280

C35
353
275
0.25
583000
355000
522964
124743
226560

C35
353
275
0.5
406000
178000
350078
84092
108840

C35
353
275
0.75
229000
1000
195578
63672
80040

C35
334
275
0.1
695000
467000
665427
282970
425960

C35
334
275
0.25
597500
369500
555925
205401
209140

C35
334
275
0.5
435000
207000
395480
149872
203200

C35
334
275
0.75
272500
44500
248607
123416
141780

C35
353
294
0.1
365200
245200
347626
159006
218400

C35
353
294
0.25
313000
193000
288484
114354
200600

C35
353
294
0.5
226000
106000
202826
80373
129200

C35
353
294
0.75
139000
19000
125034
62535
80600

C35
334
294
0.1
371000
251000
360633
233743
245800

C35
334
294
0.25
327500
207500
312617
182448
214300

C35
334
294
0.5
255000
135000
240633
141918
173000

C35
334
294
0.75
182500
62500
173737
121174
137700

C35
275
353
0.1
122800
107200
125055
128000
134240

C35
275
353
0.25
229000
213400
232769
242000
243560

C35
275
353
0.75
583000
567400
585675
617765
614200

C35
294
334
0.1
139000
106000
141485
149837
156600

C35
294
334
0.25
182500
149500
186429
207822
205600

C35
294
334
0.75
327500
294500
330098
361257
385800

SAE4130
648
552
0.25
224875
140275
210665
110429
92617

SAE4130
648
552
0.5
167750
83150
154192
80376
57488

SAE4130
648
552
0.75
110625
26025
102410
63762
55353

SAE4130
607
552
0.25
239000
154400
231274
168434
94898

SAE4130
607
552
0.5
196000
111400
188474
137549
109990

SAE4130
607
552
0.75
153000
68400
148386
120257
104496

SAE4130
648
565
0.25
181375
114175
171584
101796
118431

SAE4130
648
565
0.5
138750
71550
129353
76481
84542

SAE4130
648
565
0.75
96125
28925
90412
62289
63421

SAE4130
607
565
0.25
195500
128300
190834
153281
132108

SAE4130
607
565
0.5
167000
99800
162428
130673
121080

SAE4130
607
565
0.75
138500
71300
135687
117725
113412

7050
176
133
0.074
58856
40436
57885
55929
54852

7050
176
133
0.148
56312
37892
54924
52311
58708

7050
176
133
0.5
44213
25793
42588
39868
30449

7050
176
133
0.741
35929
17509
34903
33249
37627

7050
176
85
0.074
211090
143350
201638
176399
274446

7050
176
85
0.148
196381
128641
183362
153578
204383

7050
176
85
0.741
78509
10769
69646
55401
92428

7050
176
85
0.395
147284
79544
131814
103301
80475

7050
133
85
0.082
212319
144579
206720
191883
200205

7050
133
85
0.164
198838
131098
191046
172476
244318

7050
133
85
0.821
90827
23087
86925
79630
216409

7050
133
85
0.5
143600
75860
135023
117757
68700

Note: Min.: Palmgren–Miner damage cumulative law, C. Miner: corrected Palmgren–Miner damage cumulative law, Wan.: Wang YY’s damage cumulative law, Pro.: our proposal, Exp.: median fatigue experimental life, 7050-7050-T7451 aluminum alloy.

Table 2: Experimental data and material parameters required in predicted models [29, 30].

Materials

C35
353
52000
334
110000
294
400000
275
760000
216
4.30

SAE4130
648
53500
607
110000
565
224000
552
282000
391
4.17

7050-T7451
176
27027
133
61400
85
225800
－－
－－
23
0.46

For better comparison, the total fatigue life under uniaxial two-level step loading and that predicted using the Palmgren–Miner law, corrected Palmgren–Miner law, Wang’s rule, and the proposed model are plotted on the same coordinate plane (Figure 1). 97.8% of the predicted data fall within an error factor of 2, and the proportion for the data predicted by the other models is 78.2%, 80.4%, and 82.6% for Palmgren–Miner law, corrected Palmgren–Miner law, and Wang’s rule, respectively. To predict fatigue life for uniaxial two-level loading, the proposed model yielded better results than other tested models.

(a)

(b)

(c)

Figure 1: Assessment for the proposed model by means of three kinds of materials. (a) Fatigue life predictions using test models for C35 under two-level step loading. (b) Fatigue life predictions using test models for SAE4130 under two-level step loading. (c) Fatigue life predictions using test models for 7050-T7451 under two-level step loading.

4.2. Multiaxial Loading Condition

To evaluate the proposed model for predicting structural components under multiaxial variable loading, multiaxial two-level and two-stage block-loading test data for LY12CZ (Table 3) were used. The cylindrical specimens were subjected to combined torsion and tension. First, the equivalent completely reversed stress amplitude in the specimen under the stress condition was evaluated. Then, the proposed cumulative-damage model was employed to predict the fatigue life of the cylindrical specimen under multiaxial variable loading.

Table 3: Total predicted fatigue life of LY12CZ under multiaxial two-level and two-stage block loading [21, 31].

No.
Loading paths

Min.
Mor.
Wan.
Pro.
Exp.

1

0.5
－
48376
42383
37075
19738
19149

2

0.5
－
48376
47476
50023
53128
51304

3

0.25
－
29721
29271
31124
32433
28888

4

0.5
－
197263
170789
162735
64582
74635

5

0.5
－
197263
195890
198935
204827
196934

6

0.5
－
179564
155162
141583
49528
63348

7

0.5
－
179564
178732
180794
184378
184835

8

0.5
－
13949
13908
17421
14084
11811

9

0.5
－
13949
13887
9718
13747
9357

10

0.18
－
11394
11381
11667
11815
5236

11

0.5
－
68212
67776
68833
72565
132923

12

0.5
－
68212
67602
67336
62414
75311

13

0.5
－
6872
6865
8379
7252
6104

14

0.5
－
7991
7969
4684
7166
4673

15

0.4
－
36056
32048
15406
15135
24138

16

0.5
－
77703
74935
77846
68579
111423

17

0.5
－
77703
71814
77550
88552
98732

18

0.4
－
27873
27674
28477
30466
39078

19

0.4
－
37354
35565
33592
21323
16875

20

0.4
－
25582
25039
27225
27240
29967

21

0.5
－
20318
19910
20729
20901
20619

22

0.5
－
20318
18721
18912
18356
22650

23

－

13042
13430
12112
12000
8746

24

－

13106
13130
13916
8000
11986

25

－

13025
12565
14052
9000
18052

Note: : single program sequence including loading paths; : each life score for single program sequence.

Considering the cylindrical specimen subjected to combined torsion and tension, at each point located in the critical domain of the specimen, we define the coordinate system (Figure 2). In this frame, the stress state under combined torsion and tension is described by the following components and aimed at each point located in the critical domain:

(a)

(b)

Figure 2: Distribution of the critical damage domain of a smooth specimen in multiaxial stress states for combined torsion and tension.

Then, von Mises equivalent stress is expressed as follows (equation (24)):

Considering , the following approximate equation for equation (25) is established:

Substituting equation (26) into (4), the coefficient c will be zero, which expresses the effect of the stress gradient on fatigue life. Based on the same approximate principle, the following approximate equations are established:

Ultimately, the equivalent completely reversed stress amplitude for the cylindrical specimen subjected to combined torsion and tension can be obtained by substituting equations (26)–(28) into equation (10):

Note that equation (29) cannot be applied in the case of pure torsion since a large error is obtained by making c = 0. However, one can immediately establish the equivalent relationship between the endurance limits under fully reversed tension and torsion from equation (10):

Analogously, the following equation for expressing the equivalent completely reversed stress amplitude under pure torsion can be obtained:

A concise form of equation (31) can be obtained by introducing equation (30) into equation (31):

Therefore, the proposed cumulative-damage model for predicting the fatigue life of structural components under multiaxial two-level variable loading and combined torsion and tension can be explicitly expressed as follows:

Engineering structures are usually subjected to block program sequence loading. It is important to study certain fatigue issues, such as cumulative-damage under program sequence loading. Hence, we investigated cumulative-damage under multiaxial two-stage block loading and combined torsion and tension using the proposed model. Based on damage-equivalent concepts, the damage caused by cycle loading is equivalent to that caused by cycle loading at the ith level. The variable expresses the ratio of the absorbed fatigue with the total fatigue life under single-stage loading, and its expression is derived from equations (22) and (33) as follows:

For the fatigue-life prediction under program sequence loading, we may be ignorant of the level loading causing component failure, and consequently, cannot be calculated. However, the sequence of , i.e., , can be calculated from equation (34). According to the sequence of , component failure will result at the th level due to fatigue once . There may be two cases of cumulative-damage at th level, even under at . The predicted fatigue life for two cases can be, respectively, expressed as follows:

The proposed model was assessed for predicting the fatigue life of structural components under multiaxial two-level and two-stage block loading and combined torsion and tension using relevant data for LY12CZ (Table 3). The proposed model for predicting fatigue life under two kinds of loading is expressed in equations (33) and (35). For better comparison with other cumulative-damage models, including the Palmgren–Miner law, Morrow’s plastic work interaction rule, and Wang’s rule, the models were synchronously used to predict the fatigue life of LY12CZ, and all text data under single-stage loadings and material parameter required in these models are listed in Tables 4 and 5. Notably, multiaxial equivalent stress parameters are employed in Morrow’s plastic work interaction rule. However, in the proposed model, the equivalent stress parameters are replaced by Matake’s critical plane stress parameters [32], and the interaction exponent is set to −0.45 [33].

Table 4: Test results under single-stage loadings for LY12CZ [21, 31].

Loading paths

A1
247.52
0
142.91
0
0
16831
333
242

A2
176.81
0
102.08
0
0
377694
238
173

A3
250
0
0
0
0
56316
250
179

A4
0
0
144.3
0
0
75299
204
146

A5
0
0
202.08
0
0
8911
285
202

A6
350
0
0
0
0
31725
350
250

B1
247.52
0
142.91
0
45
10229
326
246

B2
176.81
0
102.08
0
45
348899
234
176

B3
158
0
125
0
45
57004
246
188

C1
247.52
0
142.91
0
90
11067
308
246

C2
176.81
0
102.08
0
90
85684
220
176

C3
250
0
144.34
0
90
4634
312
248

Table 5: Material parameters required in the proposed model for LY12CZ [31].

Materials

LY12CZ
350
31725
300
140670
250
272123
169
2.15

The predicted fatigue life of LY12CZ under multiaxial two-level step and two-stage block loading based on the test cumulative-damage models is shown in Figure 3. The percentage of the predicted data falling within the factor of 2.05 scatter band is 80%, 80%, 88%, and 96% for the Palmgren–Miner law, Morrow’s plastic work interaction rule, Wang’s rule, and our model, respectively. For predicting the fatigue life of LY12CZ under multiaxial variable loading, including two-level step loading and two-stage block loading, our model yielded results comparable to those of the test cumulative-damage models.

Figure 3: Fatigue life predictions for LY12CZ under multiaxial variable loading based on test damage cumulative models.

5. Conclusions

Here, we propose a cumulative-damage model based on continuum damage mechanics to evaluate the fatigue life of smooth structural components under axial and multiaxial variable loading. The conclusions can be obtained as follows:

(1)The model is very competitive with the existing test cumulative-damage models. It adopts a kind of equivalent completely reversed stress amplitude that expresses the effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths on high-cycle fatigue under variable loading.(2)Only one parameter is evaluated for the application of our model, and it is very simple to obtain the model parameter which is a simple function on the slope of S-N curve of materials.(3)The concept of equivalent completely reversed stress amplitude provides a new conception to investigate the cumulative damage for structural components under variable loading. Cumulative damage during fatigue progress and fatigue life can be precisely predicted by combining the equivalent completely reversed stress amplitude and damage development equation.

Abbreviations

: | Volume of the critical domain
, , and : | Stress amplitude under fully reversed loading in tension, damage parameters, and equivalent completely reversed stress amplitude, respectively
: | Internal damage variable
: | Maximum von Mises equivalent stress in the critical domain
: | Polar diameter within polar coordinates and polar angle within polar coordinates, respectively
: | Material parameters dependent on the slope of S-N curve
and : | Damage parameters for the ith level loading and equivalent completely reversed stress amplitude for the ith level loading, respectively
: | Fatigue life and applied cycles, respectively, under the ith level constant-amplitude loading
: | Endurance limits in reversed tension
: | Applied cycles under fully reversed loading in tension
: | Internal damage variable of the ith step loading
: | Equivalent internal damage variable and applied cycles, respectively, based on damage-equivalent concepts, respectively
: | ith level stress amplitude under fully reversed loading in tension
: | Stress amplitude and fatigue life plotted in S-N curve
: | Damage parameters proposed by Matake et al.
: | Elastic modulus
: | von Mises equivalent stress
: | Three axis factor
: | Maximum hydrostatic stress in one cycle
: | Maximum value in symbol
: | Maximum generalized force of damage driving in one cycle
: | Poisson ratio
: | Hydrostatic stress
: | Stress distribution function in the critical domain
: | Predicted life of smooth specimen
: | The critical value of damage
: | Normal stress amplitude, normal mean stress, shear stress amplitude, and shear mean stress, respectively
: | Phase difference between normal loading path and shear-loading path
: | Radius of smooth specimen
: | Polar diameter of the critical domain.

Data Availability

The data are from previously reported studies, and these prior studies are cited at relevant places within the text as references [21, 29–31].

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors gratefully acknowledge the research support for this work provided by the Scientific Research Start-Up Project of Zhejiang Sci-Tech University (11133132612019) and National Natural Science Foundation of China (52075471).

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