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Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6
Accepted Manuscript Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6 Jingye Yang, Guozheng Kang, Kaijuan Chen, Qianhua Kan
PII:
S0142-9418(18)30728-1
DOI:
10.1016/j.polymertesting.2018.06.018
Reference:
POTE 5515
To appear in:
Polymer Testing
Received Date: 3 May 2018 Accepted Date: 13 June 2018
Please cite this article as: J. Yang, G. Kang, K. Chen, Q. Kan, Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6, Polymer Testing (2018), doi: 10.1016/ j.polymertesting.2018.06.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Material Behaviour
Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6
a
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Jingye Yanga,b, Guozheng Kanga,b,*, Kaijuan Chenb, Qianhua Kana,b State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, PR China b
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of
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Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, PR China *
Correspondent author: Dr. Prof. G.Z. Kang, Tel: 86-28-87634671; Fax: 86-28-87600797
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Email address: [email protected] or [email protected]
ABSTRACT
The whole-life ratchetting and fatigue failure, as well as the ratchetting-fatigue interaction,
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of polyamide-6 (PA6) were investigated by performing a set of uniaxial stress-controlled cyclic tests at room temperature and with different stress levels. The effects of mean stress, stress amplitude and stress ratio on the evolution of ratchetting strain and the fatigue life of
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PA6 are discussed. Simultaneously, the evolution of damage variable, which is defined as a function of equivalent modulus, is summarized to reflect the interaction of ratchetting and
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fatigue damage. The experimental results show that the uniaxial whole-life ratchetting and fatigue life of PA6 are sensitive to the mean stress, stress amplitude and stress ratio. The evolution of damage variable and its dependence on the stress level are similar to that of whole-life ratchetting, and present a tri-phased feature with respect to the damage rate. By comparing the fatigue lives obtained in the asymmetrical and symmetrical tests, a detrimental effect of ratchetting deformation on the fatigue life of PA6 is found.
Keywords：Polyamide-6; Uniaxial; Stress-controlled cyclic loading; Ratchetting; Fatigue.
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1. Introduction Polyamide-6 (PA6), one of the high-performance polymeric materials, has been widely used in the automotive industry, electronics and other engineering fields as a structural material due to its good resistance to environmental corrosion, excellent mechanical
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properties and low cost. In such applications, many components made from PA6 are usually subjected to a cyclic loading in service. Therefore, fatigue life is an important factor to be considered for these components.
It is well-known that ratchetting, a cyclic accumulation of inelastic deformation, will
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occur in materials and components subjected to asymmetrical stress-controlled cyclic loading. As a new phenomenon observed in asymmetrical stress-controlled cyclic tests, the ratchetting
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of structural materials, especially for metals, had been extensively investigated experimentally and theoretically in recent decades, as summarized in [1-3]. Recently, the low-cycle fatigue failure of some metals accompanied by the occurrence of ratchetting deformation was studied [4-11], and it was concluded from the existing results that the ratchetting is generally detrimental to the fatigue life of metallic materials. For polymeric materials, ratchetting has
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also been studied, as done by Pan et al. [12], Zhang and Chen [13], Lu et al. [14, 15], Zhang et al. [16], Chen et al. [17-19], Xia and Shen [20], Shen et al. [21], Chen and Hui [22], Kang et al. [23], Xi el al. [24], Yu el al. [25], Averett et al. [26] and so on. The existing results show
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that the ratchetting of polymers also varies with the different types of polymer and is sensitive to the stress level and test temperature. However, the existing works only focused on the
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ratchetting of polymers within a given small number of cycles and its constitutive model. The interaction between the whole-life ratchetting (which means that the ratchetting of the specimen in the whole process of a fatigue test is considered) and fatigue damage was not involved there for polymers. So far, only few researches were related to the ratchetting-fatigue interaction: for examples, Liu et al. [27] observed the ratchetting of polymethyl methacrylate (PMMA) at varied temperature and thought that the ratchetting strain could be a criterion to predict the failure of the material; Holopainen et al. [28] studied the damage-ratchetting interaction of polycarbonate (PC) and the obtained results showed that the fatigue damage increased with the ratchetting strain; Tao and Xia [29] investigated the effect of ratchetting on
ACCEPTED MANUSCRIPT the fatigue life of an epoxy and thought that there was no obvious detrimental effect of ratchetting strain on the fatigue life. Since the ratchetting-fatigue interaction is very important in the design and assessment of structural components made from polymers, more research considering different polymers is necessary for an in-depth understanding on the whole-life
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ratchetting and its effect on the fatigue life of different polymeric materials. Therefore, in this work, a series of uniaxial stress-controlled fatigue tests were performed to investigate the whole-life ratchetting of PA6 and its effect on the fatigue failure. Firstly, the dependence of whole-life ratchetting on the applied mean stress, stress amplitude and stress
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ratio was investigated, then, the fatigue lives of PA6 obtained in various load cases are discussed. Finally, the ratchetting-fatigue interaction of PA6 is addressed in detail by
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comparing the evolutions of ratchetting strain and damage variable. Some significant conclusions are obtained, which are useful to understand the ratchetting-fatigue interaction of polymers and to construct a failure model to predict the fatigue life of the polymers with ratchetting included
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2. Experimental procedure
The PA6 was TECAST L (made by Ensinger, Germany), with density, glass transition temperature and melt point of 1150 kg/m 3 , 45 °C (in a dry state) and 220 °C , respectively.
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Dumb-bell shaped specimens with a gauge length of 12 mm and section diameter of 6 mm were machined from the as-received PA6 bars with a diameter of 20 mm. The test machine
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was a MTS858 Bionix-5kN, and a MTS axial extensometer (634.31F-24) with a gauge length of 10 mm and measurable strain range from -20% to 40%was used to measure the axial strain, . Stress-strain data were collected by a Flex-Text 40 control system. All the tests were performed at room temperature (i.e., 21 °C ) controlled by an air conditioner (e.g., the fluctuation of test temperature was less than 1 °C ). Monotonic tensile and uniaxial stress-controlled fatigue tests were performed. The specimens were first loaded to an axial nominal strain of 25% under a strain-controlled loading condition at a strain rate of 5 × 10 −3 s −1 ; then unloaded to zero stress under a stress-controlled mode at a stress rate of 1.8 MPa·s-1; and finally were held at zero stress for
ACCEPTED MANUSCRIPT one hour to assess the recoverable part of the residual strain presented immediately after unloading. In the uniaxial symmetrical and asymmetrical stress-controlled fatigue tests, the applied stress rate was set as 30MPa·s-1. The effects of mean stress, stress amplitude and stress ratio on the whole-life ratchetting and fatigue failure of PA6 were investigated by
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performing a series of stress-controlled fatigue tests. To illustrate the experimental results more clearly, some parameters used in this work are defined by referring to [3] as follows: (1) Ratchetting strain
ε max + ε min
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εr =
2
(1)
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where, ε max and ε min are the maximum and minimum strains per cycle, respectively. (2) Ratchetting strain rate (i.e., the increment of ratchetting strain per cycle) ∆ε r = ε n ,r − ε n −1,r
(2)
where, ε n ,r and ε n−1,r are the ratchetting strains obtained in the n-th and (n-1)-th cycles,
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respectively.
Results and discussions
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3.1. Stress-strain responses in monotonic tensile and fatigue tests To realize the basic mechanical properties of PA6, two monotonic tensile tests with the
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same loading conditions were first carried out. The results obtained are shown in Fig. 1. It should be noted that only the stress-strain curve of one specimen and its correspondent recovery curve of remained strain are provided in Fig. 1, since the repeatability of experimental data is confirmed to be very good for the tested specimens of PA6 with the same loading conditions. It can be observed from Fig. 1a that the stress-strain curve of PA6 is linear at the initial loading stage with low stress level, but is obviously non-linear at the sequent loading stage near yielding. Beyond the yield point, apparent strain softening occurs, which is followed by a stable stress-strain plateau until the applied maximum strain (i.e., 25%) is reached. The yield strength of PA6 (defined as the value of corresponding stress when strain
ACCEPTED MANUSCRIPT softening occurs according to the standard [30]) is obtained as 82.7MPa and the correspondent strain is 3.4%. After unloading, a large strain of 18.5 % remains temporarily. As shown in Fig. 1b, the temporarily remaining strain will be recovered partially during the zero-stress holding, and reaches 13.4% after holding for 3600s. It is also seen from Fig. 1b
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that after holding for 3600s, the recovering rate of remained strain becomes very slow so that the remaining strain at this moment (i.e., 13.4%) can be approximately taken as irreversible, e.g., visco-plastic strain.
Fig. 2 shows the stress-strain hysteresis loops of PA6 obtained in the fatigue tests with
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zero mean stress and two stress amplitudes (i.e., 0±48 and 0±56MPa), and it is seen from Fig. 2 that the peak and valley strains increase and decrease with increasing number of cycles,
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respectively, and the hysteresis loops become wider and wider. However, the changing rates of peak and valley strains are different and the increasing rate of peak strain is apparently higher than that of valley strain, especially for that presented at the final stage of fatigue tests. This implies that the effect of fatigue damage on the tensile stress-strain response of PA6 is more significant than that on the compression. Fig. 3 shows the stress-strain results of PA6 obtained
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in the asymmetrical stress-controlled fatigue tests with various stress levels (i.e., 8±48, 12±48, 14±44 and 20±44MPa). It is observed that the responding peak strain remarkably accumulates in the tensile direction with increasing number of cycles, but the valley strain accumulates in the compressive direction at a much lower rate, when the applied mean stress is relatively
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small (such as 8, 12 and 14MPa in the cases of 8±48, 12±48 and 14±44MPa), as shown in Figs. 3a, 3b and 3c. However, when the applied mean stress is relatively high (such as 20MPa in the
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case of 20±44MPa) the valley strain accumulates in the tensile direction in the same manner as the peak strain, even if its accumulation rate is much smaller than that of peak strain, as shown in Fig. 3d. The detailed evolution process of peak and valley strains during the asymmetrical stress-controlled fatigue tests of PA6 can be illustrated more clearly by Fig. 4. Such phenomena are different from that observed in references [27-29] for other polymers, and might be caused by the applied stress levels with the large stress amplitudes and small mean stresses. 3.2. Whole-life ratchetting
ACCEPTED MANUSCRIPT The curves of ratchetting strain vs. number of cycles obtained in the uniaxial stress-controlled fatigue tests of PA6 with various stress levels (i.e., with a constant stress amplitude and various mean stresses, with a constant mean stress and various stress amplitudes and with a constant peak stress and various stress ratios, respectively) are shown
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in Figs. 5 to 10 (to demonstrate the ratchetting in the initial stage of cyclic loading more clearly, the ratchetting evolution curves of PA6 within the first 100 cycles are shown in Figs. 5, 7 and 9). It can be seen from Figs. 5 to 10 that:
(1) The PA6 presents remarkable ratchetting under the asymmetrical stress-controlled
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cyclic loading conditions and the evolution of whole-life ratchetting strain can be roughly divided into three stages. In the first stage, the ratchetting strain increases but the ratchetting
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strain rate (i.e., the increment of ratchetting strain per cycle) goes down quickly. In the second stage, the ratchetting strain increases continuously at an almost constant ratchetting strain rate. In the final stage, the ratchetting strain increases rapidly at a progressively increasing rate until failure of the specimen occurs, which is similar to that summarized by [9, 10] for some metallic materials. However, it should be noted that no shakedown of ratchetting occurs until
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the PA6 specimens fail in the prescribed loading cases, as shown in Figs. 6, 8 and 10. Although the ratchetting evolution of PMMA in the previous two stages [27] are like that shown in Figs. 5 to 10, the final stage with a progressively increasing ratchetting strain rate does not occur in the cyclic tests of PMMA at lower temperatures or with lower stress levels.
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Also, the observed ratchetting evolution of PA6 in Figs. 5 to 10 is different from that of an epoxy resin [29], where the ratchetting strain rate decreased continuously with increase of
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number of cycles until failure of the specimens occurred. (2) The whole-life ratchetting of PA6 greatly depends on the applied stress level, and the ratchetting strain rate increases with the increase of applied mean stress or stress amplitude, as shown in Figs. 6 and 8. It should be noted that the final ratchetting strain obtained before the PA6 specimen fails monotonically decreases with increase of stress amplitude, but does not monotonically increase with increase of mean stress, which is similar to that observed by [9, 10] for some metals. Furthermore, when the stress level (i.e., applied mean stress or stress amplitude) increases, the first and second stages in the ratchetting evolution of PA6 are ended but the final stage appears more quickly and can occupy the majority of total fatigue life, as
ACCEPTED MANUSCRIPT shown in Fig. 6 and 8. However, unlike that of PA6, the final stage of the whole-life ratchetting of PMMA [27] always occupies a tiny part of total fatigue life, even when the stress level is high enough. (3) The whole-life ratchetting of PA6 is also dependent on the prescribed stress ratio.
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Generally speaking, in the fatigue tests of PA6 with a constant peak stress, the ratchetting strain produced within the first 100 cycles increases with increase of stress ratio from -0.71 to -0.53 or from -0.60 to -0.42, as shown in Figs. 9a and 9b; but the final ratchetting strain does not exhibit a monotonic dependence on the increase of stress ratio, as shown in Figs. 10a and
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10b. It also can be observed from Figs. 9 and 10 that the effect of stress ratio on the ratchetting strain rate is not as monotonic as that of stress amplitude/mean stress. In the early
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(i.e., from 0% to 5% of fatigue life) and late (i.e., from 90% to 100% fatigue life) stages of fatigue tests, the ratchetting strain rate decreases with increase of stress ratio. However, in the medium stage (i.e., from 40% to 60% of fatigue life), the ratchetting strain rate does not exhibit an obvious monotonic dependence on the increase of stress ratio. Except for the results discussed above, the fatigue failure of PA6 with a very long fatigue
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life is observed in some fatigue tests with relatively high stress ratios (such as -0.25 and -0.258 for the loading cases of 24±40MPa and 23.75±40.25MPa), where the evolution of whole-life ratchetting strain is quite different from that discussed earlier, as shown in Figs. 11 and 12.
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It can be seen from Figs. 11 and 12 that: (1) Different from that shown in Figs. 5 to 10, a plateau apparently occurs in the evolution curves of ratchetting strain vs. the number of cycles
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after certain cycles, as shown in Figs. 11a and 12a. In the plateau, the ratchetting rate becomes a nearly constant value near to zero. (2) Correspondently, the responding strain amplitude gradually decreases with the number of cycles in the plateau, rather than progressively increasing before the plateau occurs. (3) The plateau of ratchetting strain will last for a long time and occupy the majority of total fatigue life. (4) Two kinds of failure will occur: one is ductile failure like that with low stress ratio (i.e., more negative) discussed earlier, as shown in Fig.11; and the other is brittle failure occurring at the end of the plateau, as shown in Fig. 12.
ACCEPTED MANUSCRIPT The results shown in Figs. 11 and 12 illustrate that, in these cases, there should be a certain hardening mechanism causing the decreases of responding strain amplitude and ratchetting strain rate, and then a long fatigue life of PA6. The micro-mechanism of such a hardening phenomenon as well as its effect on the fatigue life of PA6 should be investigated
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in future work.
3.3. Fatigue life
The effects of mean stress, stress amplitude and stress ratio on the fatigue life of PA6 are
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now considered and the results are shown in Fig. 13. From Fig. 13(a), it is seen that the fatigue life of PA6 decreases with increase of mean stress, which is more obvious when the
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applied stress amplitude is lower. From Fig. 13(b), it can be concluded that increasing stress amplitude apparently shortens the fatigue life of PA6. Comparing Fig. 13(a) with Fig. 13(b), it is found that the effect of stress amplitude on the fatigue life is stronger than that of mean stress. This phenomenon implies that the fatigue life of PA6 presented under the asymmetrical stress-controlled cyclic loading conditions is still mainly controlled by the applied stress
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amplitude.
When the applied peak stress is constant, the influence of stress ratio can be seen from Fig. 13(c). It is demonstrated that the fatigue life of PA6 increases with increase of stress ratio (i.e., becoming closer to zero) generally; but when the peak stress is 64MPa, the fatigue life with a
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stress ratio of -0.406 is higher than that with a stress ratio of -0.375. Additionally, as the stress ratio increases, the increase rate of fatigue life with the stress ratio becomes higher and higher.
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It also can be observed from Fig. 13(c) that, when the stress ratio is constant, a higher peak stress results in a shorter fatigue life. 3.4. Discussion
3.4.1 Damage and its evolution in the process of fatigue From the evolution of stress-strain hysteresis loops during the stress-controlled fatigue tests of PA6 shown in Figs. 2 and 3, it is seen that the slope of the line connecting the peak and valley points of each stress-strain hysteresis loop (which is denoted as the equivalent modulus per cycle) decreases with increase of the number of cycles, and the decrease rate is more remarkable in the last stage of fatigue tests. It is known that the decrease of equivalent
ACCEPTED MANUSCRIPT modulus per cycle is caused by the different effects of the fatigue damage on the tensile and compressive stress-strain responses of PA6. Hence, this implies that the variation of such an equivalent modulus during the fatigue tests of PA6 can indirectly represent the evolution of fatigue damage, and then the damage variable D can be defined as
En E1
(3)
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D =1-
where, En is the equivalent modulus of current cycle and E1 is the initial equivalent modulus, as shown in Fig. 14.
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To characterize the growth rate of damage variable D, the increment of damage variable per cycle ∆D (also can be called the damage rate) and its variation with the number of cycles
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are used in the following sections, that is ∆D = Dn − Dn −1
(4)
where, Dn is the damage variable in the current cycle and Dn −1 is that of last cycle. By using the above-mentioned definition of damage variable and the experimental data
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discussed in Sections 3.1 and 3.2, the evolution of fatigue damage during each fatigue test of PA6 can be investigated and the corresponding results are shown in Figs. 15 to 20. From Figs. 15 to 20, it is concluded that: (1) the evolutions of damage variable and its rate are very similar to that of ratchetting strain and its rate, and the evolution of damage variable also
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presents a tri-phased feature as regards to the variation of damage rate, that is, Stage I with a decreased damage rate, Stage II with an almost constant damage rate and Stage III with a
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rapidly increased damage rate. (2) The damage and its rate are also greatly dependent on the applied mean stress, stress amplitude and stress ratio. With the increase of applied mean stress or stress amplitude and the decrease of stress ratio (i.e., becoming more negative), the damage variable and damage rate generally increase. However, the final values of damage variable do not present a remarkable variation with the changes of stress levels, and they are almost the same in the fatigue tests with a constant peak stress and various stress ratios, as shown in Fig. 20. This implies that a single critical value of damage variable can be assumed and obtained from the experimental data when the failure model is established in future work. 3.4.2 Effect of ratchetting on fatigue life
ACCEPTED MANUSCRIPT To illustrate the effect of ratchetting strain on the fatigue life more directly, the fatigue lives of symmetrical stress-controlled cyclic tests (almost no ratchetting, as shown in Fig. 2 and regardless of that presented in the final instable stage) and asymmetrical stress-controlled cyclic tests (with obvious ratchetting) are compared. The experimental results show that the
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fatigue lives of PA6 obtained in the fatigue tests with zero mean stress and stress amplitudes of 48 and 46MPa are 1396 and 2308 cycles, respectively; but the lives in the tests with the mean stresses of 8 and 12MPa and stress amplitudes of 48 and 46MPa are 684 and 670 cycles, respectively. Furthermore, the responding strain amplitude and its variation during the
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corresponding fatigue tests are given in Fig. 21.
As shown in Fig. 21, the evolution of responding strain amplitude with the number of
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cycles in the fatigue tests with zero mean stress are almost the same as that with the mean stresses of 8 and 12MPa, but the values of responding strain amplitudes in the tests with the mean stresses of 8 and 12MPa are smaller than that with zero mean stress. If the fatigue life of PA in the stress-controlled fatigue test is controlled only by the corresponding strain amplitude, the fatigue lives obtained in the tests with mean stresses of 8 and 12MPa should be
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longer than that with zero mean stress. However, it has been demonstrated that the fatigue lives with the mean stresses of 8 and 12MPa are much shorter than that with zero mean stress. Considering the apparent ratchetting in the tests with mean stresses of 8 and 12MPa and almost no ratchetting with zero mean stress, it can be concluded that the ratchetting occurring
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in the asymmetry stress-controlled cyclic test is detrimental to the fatigue life of PA6, which is different from that observed for a thermosetting polymer epoxy resin by [29], where a
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conclusion was reached that the ratchetting has no obvious effect on the fatigue life of epoxy resin. It should be noted that the whole-life ratchetting of epoxy resin is much weaker than that of PA6.
It should be noted that only the uniaxial whole-life ratchetting and fatigue failure of PA6 are observed in this work at room temperature, the multiaxial ratchetting-fatigue interaction of PA6 and its temperature dependence have not been discussed here. Much effort should be paid to such issues in future work.
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4. Conclusions (1) Apparent ratchetting occurs during the asymmetrical stress-controlled cyclic tests of PA6 like it does for other polymers, and the evolution of the whole-life ratchetting of PA6 can generally be divided into three stages: Stage I with a decreased ratchetting strain rate;
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Stage II with an almost constant ratchetting strain rate; and Stage III with a rapidly increased rate like that summarized by [9, 10] for some metallic materials. However, for PA6, when the applied stress levels are set as 24±40MPa and 23.75±40.25MPa, a plateau occurs at Stage III and then makes the ratchetting strain rate become very small again,
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which has not been observed by the existing literature, and its physical nature should be further investigated in future work.
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(2) The whole-life ratchetting of PA6 depends greatly on the applied stress level: when the applied stress level is relatively high, the ratchetting enters Stage III more quickly; when the applied stress level is lower, the ratchetting enters Stage III more slowly, and more cycles are needed before the specimen fails.
(3) Evolutions of damage variable (defined as the relative variation of equivalent modulus
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during the fatigue tests) with different stress levels are very similar to that of ratchetting strain and also present a tri-phased feature as regards the damage rate. Although the damage and its rate depend greatly on the applied stress level, the final values of damage
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variable obtained in the experiments do not apparently change with the prescribed stress levels. A single critical value of damage variable can be assumed and obtained from the
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experimental data when the failure model of PA6 is established in future work. (4) Fatigue life of PA6 decreases with the increase of mean stress/stress amplitude and the decrease of stress ratio (i.e., more negative). Ratchetting presented in the asymmetrical stress-controlled cyclic test has a detrimental effect on the fatigue life of PA6, which is different from that for epoxy resin by [29] where no apparent effect is observed.
Acknowledgements Financial supports of National Natural Science Foundation of China (11272269) are gratefully acknowledged.
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Fig. 1 Results obtained in the monotonic tensile test of PA6: (a) stress-strain curve; (b)
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curve of remained strain vs. hold time during the zero-stress holding.
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Fig. 2 Results of stress-strain hysteresis loops in the tests of PA6 with: (a) 0±48MPa; (b)
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0±56MPa.
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Fig. 3 Results of stress-strain hysteresis loops in the tests of PA6 with: (a) 8±48MPa; (b)
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12±48MPa; (c) 14±44MPa; (d) 20±44MPa.
Fig. 4 Results of peak and valley strains in the tests with: (a) 8±48MPa; (b) 12±48MPa; (c) 14±44MPa; (d) 20±44MPa.
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Fig. 5 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa;
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(d) 48MPa.
Fig. 6 Results of whole-ratchetting strain in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa; (d) 48MPa.
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Fig. 7 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with
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various stress amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 8 Results of whole-ratchetting strain in the tests of PA6 with various stress
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amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 9 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
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Fig. 10 Results of whole-ratchetting strain in the tests of PA6 with various stress ratios
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and a constant peak stress of: (a) 56MPa; (b) 60MPa.
Fig. 11 Evolutions of ratchetting strain (a) and responding strain amplitude (b) in the fatigue
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test of PA6 with a stress level of 24±40MPa.
Fig. 12 Evolutions of ratchetting strain (a) and responding strain amplitude (b) in the fatigue test of PA6 with a stress level of 23.75±40.25MPa
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10
(a)
10
Stress amplitude 48MPa 47MPa 45MPa 44MPa 43MPa
3
2
5
10
15
20
25
4
(b)
10
3
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Mean stress 12MPa 13MPa 0MPa
42
45
48
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(c) Peak stress 64MPa 60MPa 58MPa 56MPa
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10 -0.8
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Stress ratio R
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Fatigue life (N)
10
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Stress amplitude (MPa)
Mean stress (MPa)
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10
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Fatigue life (N)
Fatigue life (N)
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-0.1
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Fig. 13 Results of fatigue life in the tests of PA6 with: (a) various mean stresses and constant stress amplitude; (b) various stress amplitudes and constant mean stress; (c) various stress ratios and constant peak stress (the point with an arrow means that the specimen does
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not fail within the given numbers of cycles).
E1
N=n
En
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Stress
N=1
Strain
Fig. 14 Illustration for the definition of equivalent modulus.
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Fig. 15 Results of the damage variable within the first 100 cycles in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa;
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(d) 48MPa.
Fig. 16 Results of the damage variable in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa; (d) 48MPa.
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Fig. 17 Results of the damage variable within the first 100 cycles in the tests of PA6 with
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various stress amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 18 Results of the damage variable in the tests of PA6 with various stress amplitudes
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and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 19 Results of the damage variable within the first 100 cycles in the tests of PA6 with
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various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
Fig. 20 Results of the damage variable in the tests of PA6 with various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
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Fig. 21 Results of responding strain amplitudes in the tests of PA6 with the stress
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amplitudes of: (a) 48MPa; (b) 46MPa.
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Research Highlights for the paper
(1) Uniaxial Ratchetting-fatigue interaction of PA6 is observed. (2) Whole-life ratchetting of PA6 depends greatly on the applied stress levels.
(4) Occurrence of ratchetting reduces the fatigue life of PA6.
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(3) Fatigue life of PA4 also is dependent on the stress levels.
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(5) Damage evolution during the whole-life ratchetting is obtained from the test data.
PII:
S0142-9418(18)30728-1
DOI:
10.1016/j.polymertesting.2018.06.018
Reference:
POTE 5515
To appear in:
Polymer Testing
Received Date: 3 May 2018 Accepted Date: 13 June 2018
Please cite this article as: J. Yang, G. Kang, K. Chen, Q. Kan, Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6, Polymer Testing (2018), doi: 10.1016/ j.polymertesting.2018.06.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Material Behaviour
Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6
a
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Jingye Yanga,b, Guozheng Kanga,b,*, Kaijuan Chenb, Qianhua Kana,b State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, PR China b
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of
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Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, PR China *
Correspondent author: Dr. Prof. G.Z. Kang, Tel: 86-28-87634671; Fax: 86-28-87600797
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Email address: [email protected] or [email protected]
ABSTRACT
The whole-life ratchetting and fatigue failure, as well as the ratchetting-fatigue interaction,
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of polyamide-6 (PA6) were investigated by performing a set of uniaxial stress-controlled cyclic tests at room temperature and with different stress levels. The effects of mean stress, stress amplitude and stress ratio on the evolution of ratchetting strain and the fatigue life of
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PA6 are discussed. Simultaneously, the evolution of damage variable, which is defined as a function of equivalent modulus, is summarized to reflect the interaction of ratchetting and
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fatigue damage. The experimental results show that the uniaxial whole-life ratchetting and fatigue life of PA6 are sensitive to the mean stress, stress amplitude and stress ratio. The evolution of damage variable and its dependence on the stress level are similar to that of whole-life ratchetting, and present a tri-phased feature with respect to the damage rate. By comparing the fatigue lives obtained in the asymmetrical and symmetrical tests, a detrimental effect of ratchetting deformation on the fatigue life of PA6 is found.
Keywords：Polyamide-6; Uniaxial; Stress-controlled cyclic loading; Ratchetting; Fatigue.
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1. Introduction Polyamide-6 (PA6), one of the high-performance polymeric materials, has been widely used in the automotive industry, electronics and other engineering fields as a structural material due to its good resistance to environmental corrosion, excellent mechanical
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properties and low cost. In such applications, many components made from PA6 are usually subjected to a cyclic loading in service. Therefore, fatigue life is an important factor to be considered for these components.
It is well-known that ratchetting, a cyclic accumulation of inelastic deformation, will
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occur in materials and components subjected to asymmetrical stress-controlled cyclic loading. As a new phenomenon observed in asymmetrical stress-controlled cyclic tests, the ratchetting
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of structural materials, especially for metals, had been extensively investigated experimentally and theoretically in recent decades, as summarized in [1-3]. Recently, the low-cycle fatigue failure of some metals accompanied by the occurrence of ratchetting deformation was studied [4-11], and it was concluded from the existing results that the ratchetting is generally detrimental to the fatigue life of metallic materials. For polymeric materials, ratchetting has
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also been studied, as done by Pan et al. [12], Zhang and Chen [13], Lu et al. [14, 15], Zhang et al. [16], Chen et al. [17-19], Xia and Shen [20], Shen et al. [21], Chen and Hui [22], Kang et al. [23], Xi el al. [24], Yu el al. [25], Averett et al. [26] and so on. The existing results show
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that the ratchetting of polymers also varies with the different types of polymer and is sensitive to the stress level and test temperature. However, the existing works only focused on the
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ratchetting of polymers within a given small number of cycles and its constitutive model. The interaction between the whole-life ratchetting (which means that the ratchetting of the specimen in the whole process of a fatigue test is considered) and fatigue damage was not involved there for polymers. So far, only few researches were related to the ratchetting-fatigue interaction: for examples, Liu et al. [27] observed the ratchetting of polymethyl methacrylate (PMMA) at varied temperature and thought that the ratchetting strain could be a criterion to predict the failure of the material; Holopainen et al. [28] studied the damage-ratchetting interaction of polycarbonate (PC) and the obtained results showed that the fatigue damage increased with the ratchetting strain; Tao and Xia [29] investigated the effect of ratchetting on
ACCEPTED MANUSCRIPT the fatigue life of an epoxy and thought that there was no obvious detrimental effect of ratchetting strain on the fatigue life. Since the ratchetting-fatigue interaction is very important in the design and assessment of structural components made from polymers, more research considering different polymers is necessary for an in-depth understanding on the whole-life
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ratchetting and its effect on the fatigue life of different polymeric materials. Therefore, in this work, a series of uniaxial stress-controlled fatigue tests were performed to investigate the whole-life ratchetting of PA6 and its effect on the fatigue failure. Firstly, the dependence of whole-life ratchetting on the applied mean stress, stress amplitude and stress
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ratio was investigated, then, the fatigue lives of PA6 obtained in various load cases are discussed. Finally, the ratchetting-fatigue interaction of PA6 is addressed in detail by
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comparing the evolutions of ratchetting strain and damage variable. Some significant conclusions are obtained, which are useful to understand the ratchetting-fatigue interaction of polymers and to construct a failure model to predict the fatigue life of the polymers with ratchetting included
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2. Experimental procedure
The PA6 was TECAST L (made by Ensinger, Germany), with density, glass transition temperature and melt point of 1150 kg/m 3 , 45 °C (in a dry state) and 220 °C , respectively.
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Dumb-bell shaped specimens with a gauge length of 12 mm and section diameter of 6 mm were machined from the as-received PA6 bars with a diameter of 20 mm. The test machine
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was a MTS858 Bionix-5kN, and a MTS axial extensometer (634.31F-24) with a gauge length of 10 mm and measurable strain range from -20% to 40%was used to measure the axial strain, . Stress-strain data were collected by a Flex-Text 40 control system. All the tests were performed at room temperature (i.e., 21 °C ) controlled by an air conditioner (e.g., the fluctuation of test temperature was less than 1 °C ). Monotonic tensile and uniaxial stress-controlled fatigue tests were performed. The specimens were first loaded to an axial nominal strain of 25% under a strain-controlled loading condition at a strain rate of 5 × 10 −3 s −1 ; then unloaded to zero stress under a stress-controlled mode at a stress rate of 1.8 MPa·s-1; and finally were held at zero stress for
ACCEPTED MANUSCRIPT one hour to assess the recoverable part of the residual strain presented immediately after unloading. In the uniaxial symmetrical and asymmetrical stress-controlled fatigue tests, the applied stress rate was set as 30MPa·s-1. The effects of mean stress, stress amplitude and stress ratio on the whole-life ratchetting and fatigue failure of PA6 were investigated by
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performing a series of stress-controlled fatigue tests. To illustrate the experimental results more clearly, some parameters used in this work are defined by referring to [3] as follows: (1) Ratchetting strain
ε max + ε min
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εr =
2
(1)
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where, ε max and ε min are the maximum and minimum strains per cycle, respectively. (2) Ratchetting strain rate (i.e., the increment of ratchetting strain per cycle) ∆ε r = ε n ,r − ε n −1,r
(2)
where, ε n ,r and ε n−1,r are the ratchetting strains obtained in the n-th and (n-1)-th cycles,
3.
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respectively.
Results and discussions
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3.1. Stress-strain responses in monotonic tensile and fatigue tests To realize the basic mechanical properties of PA6, two monotonic tensile tests with the
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same loading conditions were first carried out. The results obtained are shown in Fig. 1. It should be noted that only the stress-strain curve of one specimen and its correspondent recovery curve of remained strain are provided in Fig. 1, since the repeatability of experimental data is confirmed to be very good for the tested specimens of PA6 with the same loading conditions. It can be observed from Fig. 1a that the stress-strain curve of PA6 is linear at the initial loading stage with low stress level, but is obviously non-linear at the sequent loading stage near yielding. Beyond the yield point, apparent strain softening occurs, which is followed by a stable stress-strain plateau until the applied maximum strain (i.e., 25%) is reached. The yield strength of PA6 (defined as the value of corresponding stress when strain
ACCEPTED MANUSCRIPT softening occurs according to the standard [30]) is obtained as 82.7MPa and the correspondent strain is 3.4%. After unloading, a large strain of 18.5 % remains temporarily. As shown in Fig. 1b, the temporarily remaining strain will be recovered partially during the zero-stress holding, and reaches 13.4% after holding for 3600s. It is also seen from Fig. 1b
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that after holding for 3600s, the recovering rate of remained strain becomes very slow so that the remaining strain at this moment (i.e., 13.4%) can be approximately taken as irreversible, e.g., visco-plastic strain.
Fig. 2 shows the stress-strain hysteresis loops of PA6 obtained in the fatigue tests with
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zero mean stress and two stress amplitudes (i.e., 0±48 and 0±56MPa), and it is seen from Fig. 2 that the peak and valley strains increase and decrease with increasing number of cycles,
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respectively, and the hysteresis loops become wider and wider. However, the changing rates of peak and valley strains are different and the increasing rate of peak strain is apparently higher than that of valley strain, especially for that presented at the final stage of fatigue tests. This implies that the effect of fatigue damage on the tensile stress-strain response of PA6 is more significant than that on the compression. Fig. 3 shows the stress-strain results of PA6 obtained
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in the asymmetrical stress-controlled fatigue tests with various stress levels (i.e., 8±48, 12±48, 14±44 and 20±44MPa). It is observed that the responding peak strain remarkably accumulates in the tensile direction with increasing number of cycles, but the valley strain accumulates in the compressive direction at a much lower rate, when the applied mean stress is relatively
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small (such as 8, 12 and 14MPa in the cases of 8±48, 12±48 and 14±44MPa), as shown in Figs. 3a, 3b and 3c. However, when the applied mean stress is relatively high (such as 20MPa in the
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case of 20±44MPa) the valley strain accumulates in the tensile direction in the same manner as the peak strain, even if its accumulation rate is much smaller than that of peak strain, as shown in Fig. 3d. The detailed evolution process of peak and valley strains during the asymmetrical stress-controlled fatigue tests of PA6 can be illustrated more clearly by Fig. 4. Such phenomena are different from that observed in references [27-29] for other polymers, and might be caused by the applied stress levels with the large stress amplitudes and small mean stresses. 3.2. Whole-life ratchetting
ACCEPTED MANUSCRIPT The curves of ratchetting strain vs. number of cycles obtained in the uniaxial stress-controlled fatigue tests of PA6 with various stress levels (i.e., with a constant stress amplitude and various mean stresses, with a constant mean stress and various stress amplitudes and with a constant peak stress and various stress ratios, respectively) are shown
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in Figs. 5 to 10 (to demonstrate the ratchetting in the initial stage of cyclic loading more clearly, the ratchetting evolution curves of PA6 within the first 100 cycles are shown in Figs. 5, 7 and 9). It can be seen from Figs. 5 to 10 that:
(1) The PA6 presents remarkable ratchetting under the asymmetrical stress-controlled
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cyclic loading conditions and the evolution of whole-life ratchetting strain can be roughly divided into three stages. In the first stage, the ratchetting strain increases but the ratchetting
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strain rate (i.e., the increment of ratchetting strain per cycle) goes down quickly. In the second stage, the ratchetting strain increases continuously at an almost constant ratchetting strain rate. In the final stage, the ratchetting strain increases rapidly at a progressively increasing rate until failure of the specimen occurs, which is similar to that summarized by [9, 10] for some metallic materials. However, it should be noted that no shakedown of ratchetting occurs until
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the PA6 specimens fail in the prescribed loading cases, as shown in Figs. 6, 8 and 10. Although the ratchetting evolution of PMMA in the previous two stages [27] are like that shown in Figs. 5 to 10, the final stage with a progressively increasing ratchetting strain rate does not occur in the cyclic tests of PMMA at lower temperatures or with lower stress levels.
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Also, the observed ratchetting evolution of PA6 in Figs. 5 to 10 is different from that of an epoxy resin [29], where the ratchetting strain rate decreased continuously with increase of
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number of cycles until failure of the specimens occurred. (2) The whole-life ratchetting of PA6 greatly depends on the applied stress level, and the ratchetting strain rate increases with the increase of applied mean stress or stress amplitude, as shown in Figs. 6 and 8. It should be noted that the final ratchetting strain obtained before the PA6 specimen fails monotonically decreases with increase of stress amplitude, but does not monotonically increase with increase of mean stress, which is similar to that observed by [9, 10] for some metals. Furthermore, when the stress level (i.e., applied mean stress or stress amplitude) increases, the first and second stages in the ratchetting evolution of PA6 are ended but the final stage appears more quickly and can occupy the majority of total fatigue life, as
ACCEPTED MANUSCRIPT shown in Fig. 6 and 8. However, unlike that of PA6, the final stage of the whole-life ratchetting of PMMA [27] always occupies a tiny part of total fatigue life, even when the stress level is high enough. (3) The whole-life ratchetting of PA6 is also dependent on the prescribed stress ratio.
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Generally speaking, in the fatigue tests of PA6 with a constant peak stress, the ratchetting strain produced within the first 100 cycles increases with increase of stress ratio from -0.71 to -0.53 or from -0.60 to -0.42, as shown in Figs. 9a and 9b; but the final ratchetting strain does not exhibit a monotonic dependence on the increase of stress ratio, as shown in Figs. 10a and
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10b. It also can be observed from Figs. 9 and 10 that the effect of stress ratio on the ratchetting strain rate is not as monotonic as that of stress amplitude/mean stress. In the early
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(i.e., from 0% to 5% of fatigue life) and late (i.e., from 90% to 100% fatigue life) stages of fatigue tests, the ratchetting strain rate decreases with increase of stress ratio. However, in the medium stage (i.e., from 40% to 60% of fatigue life), the ratchetting strain rate does not exhibit an obvious monotonic dependence on the increase of stress ratio. Except for the results discussed above, the fatigue failure of PA6 with a very long fatigue
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life is observed in some fatigue tests with relatively high stress ratios (such as -0.25 and -0.258 for the loading cases of 24±40MPa and 23.75±40.25MPa), where the evolution of whole-life ratchetting strain is quite different from that discussed earlier, as shown in Figs. 11 and 12.
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It can be seen from Figs. 11 and 12 that: (1) Different from that shown in Figs. 5 to 10, a plateau apparently occurs in the evolution curves of ratchetting strain vs. the number of cycles
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after certain cycles, as shown in Figs. 11a and 12a. In the plateau, the ratchetting rate becomes a nearly constant value near to zero. (2) Correspondently, the responding strain amplitude gradually decreases with the number of cycles in the plateau, rather than progressively increasing before the plateau occurs. (3) The plateau of ratchetting strain will last for a long time and occupy the majority of total fatigue life. (4) Two kinds of failure will occur: one is ductile failure like that with low stress ratio (i.e., more negative) discussed earlier, as shown in Fig.11; and the other is brittle failure occurring at the end of the plateau, as shown in Fig. 12.
ACCEPTED MANUSCRIPT The results shown in Figs. 11 and 12 illustrate that, in these cases, there should be a certain hardening mechanism causing the decreases of responding strain amplitude and ratchetting strain rate, and then a long fatigue life of PA6. The micro-mechanism of such a hardening phenomenon as well as its effect on the fatigue life of PA6 should be investigated
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in future work.
3.3. Fatigue life
The effects of mean stress, stress amplitude and stress ratio on the fatigue life of PA6 are
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now considered and the results are shown in Fig. 13. From Fig. 13(a), it is seen that the fatigue life of PA6 decreases with increase of mean stress, which is more obvious when the
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applied stress amplitude is lower. From Fig. 13(b), it can be concluded that increasing stress amplitude apparently shortens the fatigue life of PA6. Comparing Fig. 13(a) with Fig. 13(b), it is found that the effect of stress amplitude on the fatigue life is stronger than that of mean stress. This phenomenon implies that the fatigue life of PA6 presented under the asymmetrical stress-controlled cyclic loading conditions is still mainly controlled by the applied stress
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amplitude.
When the applied peak stress is constant, the influence of stress ratio can be seen from Fig. 13(c). It is demonstrated that the fatigue life of PA6 increases with increase of stress ratio (i.e., becoming closer to zero) generally; but when the peak stress is 64MPa, the fatigue life with a
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stress ratio of -0.406 is higher than that with a stress ratio of -0.375. Additionally, as the stress ratio increases, the increase rate of fatigue life with the stress ratio becomes higher and higher.
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It also can be observed from Fig. 13(c) that, when the stress ratio is constant, a higher peak stress results in a shorter fatigue life. 3.4. Discussion
3.4.1 Damage and its evolution in the process of fatigue From the evolution of stress-strain hysteresis loops during the stress-controlled fatigue tests of PA6 shown in Figs. 2 and 3, it is seen that the slope of the line connecting the peak and valley points of each stress-strain hysteresis loop (which is denoted as the equivalent modulus per cycle) decreases with increase of the number of cycles, and the decrease rate is more remarkable in the last stage of fatigue tests. It is known that the decrease of equivalent
ACCEPTED MANUSCRIPT modulus per cycle is caused by the different effects of the fatigue damage on the tensile and compressive stress-strain responses of PA6. Hence, this implies that the variation of such an equivalent modulus during the fatigue tests of PA6 can indirectly represent the evolution of fatigue damage, and then the damage variable D can be defined as
En E1
(3)
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D =1-
where, En is the equivalent modulus of current cycle and E1 is the initial equivalent modulus, as shown in Fig. 14.
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To characterize the growth rate of damage variable D, the increment of damage variable per cycle ∆D (also can be called the damage rate) and its variation with the number of cycles
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are used in the following sections, that is ∆D = Dn − Dn −1
(4)
where, Dn is the damage variable in the current cycle and Dn −1 is that of last cycle. By using the above-mentioned definition of damage variable and the experimental data
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discussed in Sections 3.1 and 3.2, the evolution of fatigue damage during each fatigue test of PA6 can be investigated and the corresponding results are shown in Figs. 15 to 20. From Figs. 15 to 20, it is concluded that: (1) the evolutions of damage variable and its rate are very similar to that of ratchetting strain and its rate, and the evolution of damage variable also
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presents a tri-phased feature as regards to the variation of damage rate, that is, Stage I with a decreased damage rate, Stage II with an almost constant damage rate and Stage III with a
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rapidly increased damage rate. (2) The damage and its rate are also greatly dependent on the applied mean stress, stress amplitude and stress ratio. With the increase of applied mean stress or stress amplitude and the decrease of stress ratio (i.e., becoming more negative), the damage variable and damage rate generally increase. However, the final values of damage variable do not present a remarkable variation with the changes of stress levels, and they are almost the same in the fatigue tests with a constant peak stress and various stress ratios, as shown in Fig. 20. This implies that a single critical value of damage variable can be assumed and obtained from the experimental data when the failure model is established in future work. 3.4.2 Effect of ratchetting on fatigue life
ACCEPTED MANUSCRIPT To illustrate the effect of ratchetting strain on the fatigue life more directly, the fatigue lives of symmetrical stress-controlled cyclic tests (almost no ratchetting, as shown in Fig. 2 and regardless of that presented in the final instable stage) and asymmetrical stress-controlled cyclic tests (with obvious ratchetting) are compared. The experimental results show that the
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fatigue lives of PA6 obtained in the fatigue tests with zero mean stress and stress amplitudes of 48 and 46MPa are 1396 and 2308 cycles, respectively; but the lives in the tests with the mean stresses of 8 and 12MPa and stress amplitudes of 48 and 46MPa are 684 and 670 cycles, respectively. Furthermore, the responding strain amplitude and its variation during the
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corresponding fatigue tests are given in Fig. 21.
As shown in Fig. 21, the evolution of responding strain amplitude with the number of
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cycles in the fatigue tests with zero mean stress are almost the same as that with the mean stresses of 8 and 12MPa, but the values of responding strain amplitudes in the tests with the mean stresses of 8 and 12MPa are smaller than that with zero mean stress. If the fatigue life of PA in the stress-controlled fatigue test is controlled only by the corresponding strain amplitude, the fatigue lives obtained in the tests with mean stresses of 8 and 12MPa should be
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longer than that with zero mean stress. However, it has been demonstrated that the fatigue lives with the mean stresses of 8 and 12MPa are much shorter than that with zero mean stress. Considering the apparent ratchetting in the tests with mean stresses of 8 and 12MPa and almost no ratchetting with zero mean stress, it can be concluded that the ratchetting occurring
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in the asymmetry stress-controlled cyclic test is detrimental to the fatigue life of PA6, which is different from that observed for a thermosetting polymer epoxy resin by [29], where a
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conclusion was reached that the ratchetting has no obvious effect on the fatigue life of epoxy resin. It should be noted that the whole-life ratchetting of epoxy resin is much weaker than that of PA6.
It should be noted that only the uniaxial whole-life ratchetting and fatigue failure of PA6 are observed in this work at room temperature, the multiaxial ratchetting-fatigue interaction of PA6 and its temperature dependence have not been discussed here. Much effort should be paid to such issues in future work.
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4. Conclusions (1) Apparent ratchetting occurs during the asymmetrical stress-controlled cyclic tests of PA6 like it does for other polymers, and the evolution of the whole-life ratchetting of PA6 can generally be divided into three stages: Stage I with a decreased ratchetting strain rate;
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Stage II with an almost constant ratchetting strain rate; and Stage III with a rapidly increased rate like that summarized by [9, 10] for some metallic materials. However, for PA6, when the applied stress levels are set as 24±40MPa and 23.75±40.25MPa, a plateau occurs at Stage III and then makes the ratchetting strain rate become very small again,
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which has not been observed by the existing literature, and its physical nature should be further investigated in future work.
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(2) The whole-life ratchetting of PA6 depends greatly on the applied stress level: when the applied stress level is relatively high, the ratchetting enters Stage III more quickly; when the applied stress level is lower, the ratchetting enters Stage III more slowly, and more cycles are needed before the specimen fails.
(3) Evolutions of damage variable (defined as the relative variation of equivalent modulus
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during the fatigue tests) with different stress levels are very similar to that of ratchetting strain and also present a tri-phased feature as regards the damage rate. Although the damage and its rate depend greatly on the applied stress level, the final values of damage
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variable obtained in the experiments do not apparently change with the prescribed stress levels. A single critical value of damage variable can be assumed and obtained from the
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experimental data when the failure model of PA6 is established in future work. (4) Fatigue life of PA6 decreases with the increase of mean stress/stress amplitude and the decrease of stress ratio (i.e., more negative). Ratchetting presented in the asymmetrical stress-controlled cyclic test has a detrimental effect on the fatigue life of PA6, which is different from that for epoxy resin by [29] where no apparent effect is observed.
Acknowledgements Financial supports of National Natural Science Foundation of China (11272269) are gratefully acknowledged.
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[2] Chaboche JL. A review of some plasticity and viscoplasticity constitutive theories. Int J
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[4] Gao H, Chen X. Effect of axial ratcheting deformation on torsional low cycle fatigue life of lead-free solder Sn–3.5Ag. Int J Fatigue 2009;31:276-283.
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[5] Lim C, Kim K, Seong J. Ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress. Int J Fatigue 2009;31:501-507.
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[10] Kang GZ, Liu YJ, Li Z. Experimental study on ratchetting-fatigue interaction of SS304 stainless steel in uniaxial cyclic stressing. Mater Sci Eng A 2006;435-436:396-404. [11] Kang GZ, Li YG, Zhang J, Sun YF, Gao Q. Uniaxial ratcheting and failure behaviors of two steels. Theor Appl Fract Mec 2005;43:199-209. [12] Pan DX, Kang GZ, Zhu ZW, Liu YJ. Experimental study on uniaxial time-dependent ratcheting of a polyetherimide polymer. J Zhejiang Univ Sci A 2010;11:804-810. [13] Zhang Z, Chen X. Multiaxial ratcheting behavior of PTFE at room temperature. Polym Test 2009;28:288-295.
ACCEPTED MANUSCRIPT [14] Lu F, Kang G, Jiang H, Zhang J, Liu Y, Lu F, Kang G, Jiang H, Zhang J, Liu Y. Experimental studies on the uniaxial ratchetting of polycarbonate polymer at different temperatures. Polym Test 2014;39:92-100. [15] Lu F, Kang G, Zhu Y, Xi C, Jiang H. Experimental observation on multiaxial ratchetting
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of polycarbonate polymer at room temperature. Polym Test 2016;50:135-144. [16] Zhang J, Jiang H, Jiang C, Kang G, Lu F. Accelerated ratcheting testing of polycarbonate using the time-temperature-stress equivalence method. Polym Test 2015;44:8-14.
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ultra‐high molecular weight polyethylene. Fatigue Fract Eng M 2016;39:839-849.
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Model. ASME J Appl Mech 2016;83.
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Ultrahigh Molecular Weight Polyethylene Polymer: Viscoelastic-Viscoplastic Constitutive
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ACCEPTED MANUSCRIPT [27] Liu W, Gao Z, Yue Z. Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA. Mater Sci Eng A 2008;492:102-109. [28] Holopainen S, Barriere T, Cheng G, Kouhia R. Continuum approach for modeling fatigue in amorphous glassy polymers. Applications to the investigation of damage-ratcheting
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Beijing: China Standards Press, 2006.
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Fig. 1 Results obtained in the monotonic tensile test of PA6: (a) stress-strain curve; (b)
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curve of remained strain vs. hold time during the zero-stress holding.
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Fig. 2 Results of stress-strain hysteresis loops in the tests of PA6 with: (a) 0±48MPa; (b)
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0±56MPa.
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Fig. 3 Results of stress-strain hysteresis loops in the tests of PA6 with: (a) 8±48MPa; (b)
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12±48MPa; (c) 14±44MPa; (d) 20±44MPa.
Fig. 4 Results of peak and valley strains in the tests with: (a) 8±48MPa; (b) 12±48MPa; (c) 14±44MPa; (d) 20±44MPa.
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Fig. 5 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa;
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(d) 48MPa.
Fig. 6 Results of whole-ratchetting strain in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa; (d) 48MPa.
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Fig. 7 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with
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various stress amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 8 Results of whole-ratchetting strain in the tests of PA6 with various stress
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amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 9 Results of ratchetting strain within the first 100 cycles in the tests of PA6 with various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
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Fig. 10 Results of whole-ratchetting strain in the tests of PA6 with various stress ratios
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and a constant peak stress of: (a) 56MPa; (b) 60MPa.
Fig. 11 Evolutions of ratchetting strain (a) and responding strain amplitude (b) in the fatigue
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test of PA6 with a stress level of 24±40MPa.
Fig. 12 Evolutions of ratchetting strain (a) and responding strain amplitude (b) in the fatigue test of PA6 with a stress level of 23.75±40.25MPa
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Stress amplitude 48MPa 47MPa 45MPa 44MPa 43MPa
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Mean stress 12MPa 13MPa 0MPa
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(c) Peak stress 64MPa 60MPa 58MPa 56MPa
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Fig. 13 Results of fatigue life in the tests of PA6 with: (a) various mean stresses and constant stress amplitude; (b) various stress amplitudes and constant mean stress; (c) various stress ratios and constant peak stress (the point with an arrow means that the specimen does
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not fail within the given numbers of cycles).
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Fig. 14 Illustration for the definition of equivalent modulus.
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Fig. 15 Results of the damage variable within the first 100 cycles in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa;
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(d) 48MPa.
Fig. 16 Results of the damage variable in the tests of PA6 with various mean stresses and a constant stress amplitude of: (a) 43MPa; (b) 44MPa; (c) 47MPa; (d) 48MPa.
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Fig. 17 Results of the damage variable within the first 100 cycles in the tests of PA6 with
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various stress amplitudes and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 18 Results of the damage variable in the tests of PA6 with various stress amplitudes
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and a constant mean stress of: (a) 12MPa; (b) 13MPa.
Fig. 19 Results of the damage variable within the first 100 cycles in the tests of PA6 with
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various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
Fig. 20 Results of the damage variable in the tests of PA6 with various stress ratios and a constant peak stress of: (a) 56MPa; (b) 60MPa.
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Fig. 21 Results of responding strain amplitudes in the tests of PA6 with the stress
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amplitudes of: (a) 48MPa; (b) 46MPa.
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Research Highlights for the paper
(1) Uniaxial Ratchetting-fatigue interaction of PA6 is observed. (2) Whole-life ratchetting of PA6 depends greatly on the applied stress levels.
(4) Occurrence of ratchetting reduces the fatigue life of PA6.
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(3) Fatigue life of PA4 also is dependent on the stress levels.
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(5) Damage evolution during the whole-life ratchetting is obtained from the test data.