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Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6
Journal Pre-proofs Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6 Jingye Yang, Guozheng Kang, Kaijuan Chen, Qianhua Kan, Yujie Liu PII: DOI: Reference:
S0142-1123(19)30506-7 https://doi.org/10.1016/j.ijfatigue.2019.105402 JIJF 105402
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 October 2019 25 November 2019 28 November 2019
Please cite this article as: Yang, J., Kang, G., Chen, K., Kan, Q., Liu, Y., Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue.2019.105402
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Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6 Jingye Yanga,b, Guozheng Kanga,b*, Kaijuan Chenb, Qianhua Kana,b , Yujie Liub a
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of
Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, PR China b
Institute of Applied Mechanics, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, PR China
*
Correspondent author: Dr. Prof. G.Z. Kang, Tel: 86-28-87634671; Fax: 86-28-87600797
Email address: [email protected] or [email protected] Abstract Rate-dependent whole-life ratchetting and fatigue failure of polyamide 6 were explored by conducting a series of stress-controlled uniaxial fatigue tests at room temperature. Meanwhile, the temperature rises on the surface of specimens were recorded to reflect the self-heating occurred during the fatigue tests. The experimental results demonstrate that ratchetting strain rate is sensitive to the variation of prescribed stress rate, and the whole-life ratchetting of PA6 presents a tri-staged evolution feature at high stress rate but a four-staged one at low stress rate. Two failure modes (i.e., the necking controlled by unstable self-heating and resultant large ratchetting strain; and the fracture controlled by the low-cycle fatigue damage) are experimentally observed in the tests at different stress rates. By considering the relationship between ratchetting evolution and temperature rise, it is found that whether increasing the stress rate retards or promotes the ratchetting is dependent on the magnitude of self-heating produced at each fatigue stage, and whether it will be beneficial or detrimental to the total fatigue life is determined by the competition of resultant strain hardening and self-heating softening. Keywords：Polyamide-6; Rate-dependent; Ratchetting; Fatigue; Self-heating
1. Introduction
As a high-performance structural material with good mechanical properties, excellent corrosion resistance and low cost, polyamide-6 (PA6) has been extensively applied in the automobile industry and electronic engineering fields. In these applications, PA6 components generally experience a cyclic loading and encounter a fatigue failure in service. Therefore, to optimize the design of these components, fatigue behavior of PA6 is an important factor to be considered. Ratchetting is a cyclic accumulation of inelastic deformation occurred in the components and materials subjected to a kind of asymmetrical stress-controlled cyclic loading. For metals, experimental and theoretical studies on ratchetting had been extensively conducted in the last three decades, as reviewed by Refs. [1-3]. Besides, some studies had been conducted on the interaction of ratchetting and fatigue, and it was found that appearance of ratchetting was harmful to the fatigue life of metals in general [4-11]. In recent years, for the ratchetting of polymers, many researches had also been conducted [12-27]. These studies demonstrated that the ratchetting of polymers depended on the stress level, stress rate, ambient temperature and loading path, and varied among different polymers. However, most of them just paid attention to the ratchetting within a limited number of cycles; whole-life ratchetting (i.e., over the whole fatigue test) and its interaction with fatigue failure were not considered yet. So far, only few investigations about the ratchetting-fatigue interaction of polymeric materials were reported, e.g.: Tao and Xia [28] studied uniaxial ratchetting for an thermosetting epoxy resin and found that the ratchetting strain was not detrimental to fatigue life; Liu et al. [29] investigated the ratchetting and fatigue behaviors of polymethyl methacrylate (PMMA) at different temperatures and considered that fatigue life might be judged by ratchetting strain; Shariatic el al. [30] investigated the uniaxial whole-life ratchetting of polyacetal and it was observed that the ratchetting strain relied on the variation of stress amplitude and mean stress; Liu and Yang [31] conducted uniaxial fatigue tests of PMMA with various peak stresses at room temperature and found that the growth rate of cyclic creep (i.e., ratchetting) strain and relaxed modulus degradation rate were two important indicators for characterizing the damage
evolution; Chen el al. [32] investigated the multiaxial ratchetting of Acrylonitrile-ButadieneStyrene (ABS) and found that the tensile mean stress promoted the ratchetting and was detrimental to fatigue life, while the compressive mean stress retarded the ratchetting and was beneficial to fatigue life; Holopainen el al. [33] investigated the interaction of ratchetting and damage for polycarbonate (PC) and it was found that fatigue damage accumulated with the evolution of ratchetting which indicated that the ratchetting strain could be used to predict the fatigue life; Yang el al. [34] found that uniaxial ratchetting was detrimental to the fatigue life of PA6 and the evolutions of damage variable and ratchetting strain were similar. However, the stress-rate dependence of whole-life ratchetting and fatigue life has not been considered in these existing studies. Experimental studies on the rate-dependent whole-life ratchetting and fatigue life of polymers are necessary extremely. Therefore, series of uniaxial fatigue tests were carried out at various stress rates to figure out the stress-rate dependence of the whole-life ratchetting and fatigue failure of PA6 in this work. Firstly, the whole-life ratchetting of PA6 is investigated at various stress rates. Then, the fatigue life at various stress rates is addressed. Finally, referring to the temperature rise of specimen during the whole fatigue test, how the change in stress rate influences the whole-life ratchetting and fatigue life is addressed. Some significant conclusions are obtained, which are useful to understand the rate-dependent whole-life ratchetting and fatigue life of polymers, and to establish a fatigue life prediction model considering the influences of stress rate and ratchetting.
2. Experimental procedure
PA6 used in this study was TECAST L with a glass transition temperature of 45 °C and a melting point of 220 °C. As-received PA6 rods were machined to dumbbell specimens, whose section diameter and gauge length are 6mm and 12mm respectively. Both monotonic tensile and fatigue tests were carried out by using a MTS858-Bionix, and experimental data were recorded by a Flex-Test 40 control system. An axial extensometer with a gauge length of 10mm was used in strain measurement and its measurable range of strain is from -20% to
40%. The ambient temperature was set as 21°C by using an air-conditioner and the temperature variation on the surface of specimen was measured by an infrared thermal imager, i.e., FLIRA655sc, during the fatigue test. In the monotonic tensile tests, specimens were loaded to a displacement of 24mm (nearly an engineering strain of 200%) at the displacement rates of 0.02, 0.1 and 0.5mm/s, respectively. In the fatigue tests, the applied stress rates were set as 90, 30, 10 and 5.3MPa/s and various stress levels (i.e., different stress amplitudes, mean stresses and stress ratios) were prescribed at each stress rate.
3.
Results and discussion
3.1 Monotonic tensile test The rate-dependent tensile properties of PA6 were investigated by conducting monotonic tensile tests at various displacement rates and the results are shown in Fig. 1. Due to a good repeatability of test data, only one stress-strain curve for each loading case is provided in Fig. 1. As illustrated in Fig. 1, the stress-displacement curves of PA6 at all displacement rates are basically linear and coincident at the beginning stage of monotonic tensile tests. With increasing the tensile displacement, the stress-displacement curves behave non-linear and the responding stress is higher at higher displacement rate. The yield strength of PA6 (defined as the value of corresponding stress when strain softening occurs) increases with the increase of displacement rate and is marked in Fig. 1. After the yielding point, apparent strain softening occurs and stress-strain curves at all displacement rates gradually approach to each other and intersect at the displacement of roughly 5mm (about at the engineering strain of 41.6%). Then, with increasing the loading displacement further, the responding stresses at all rates become stable after a significant drop; but unlike the previous stage where the loading displacement is less than 5mm, the responding stress is lower at higher displacement rate here. Furthermore, obvious necking is observed when the responding stress becomes close to the stable value (i.e., at the points marked by blue cycles in Fig. 1) and expands from the center of the gauge length to both ends of tested specimens as the applied displacement increases. Such a kind of
rate-dependent monotonic tensile deformation of PA6 is nearly the same as that of the high-density polyethylene observed in Ref. [35].
Fig. 1 Monotonic tensile responses of PA6 at various displacement rates.
3.2 Whole-life ratchetting at different stress rates By referring to [3], some parameters are used to show the whole-life ratchetting more clearly. The ratchetting strain is defined as the mean value of maximum strain and minimum strain per cycle, i.e., Eq. (1); and the ratchetting strain rate is defined as the increment of ratchetting strain from (n-1)-th to n-th cycle, i.e., Eq. (2).
max min 2
(1)
r n ,r n 1,r
(2)
r =
In the asymmetrical stress-controlled fatigue tests at different stress rates, PA6 presents remarkable ratchetting and a typical evolution of whole-life ratchetting obtained in a test with 14±50MPa (i.e., applied stress amplitude is 50MPa and mean stress is 14MPa) and at a stress rate of 90MPa/s is shown in Fig. 2a. From Fig. 2a, it can be seen that the peak strain obviously accumulates with increasing the number of cycles, while the accumulation of valley strain is not obvious in the tensile direction. At the final stage of fatigue process, the valley strain even accumulates obviously in the compression direction. In this case, the area of hysteresis loop, which represents the dissipated energy density per cycle, becomes larger and larger at an increasing rate before fatigue failure. Besides, the curve of ratchetting strain vs. number of cycle is provided in Fig. 2b directly. It can be observed from Fig. 2b that typical whole-life
ratchetting of PA6 presents a tri-staged evolution feature: Stage I with a decreasing ratchetting strain rate; Stage II with a nearly constant ratchetting strain rate; and Stage III with a rapidly increasing ratchetting strain rate. Such a kind of whole-life ratchetting is also reported in some researches for metals [5, 6] and other polymers [29, 30].
Fig. 2 Whole-life ratchetting with 14±50MPa and at 90MPa/s: (a) detailed stress-strain hysteresis loop; (b) ratchetting strain vs. the number of cycles.
As shown in Fig. 2a, the accumulation rates of peak and valley strains are not always the same in the fatigue process and thus, the ratchetting strain defined in Eq. (2) (i.e., mean strain) cannot characterize the ratchetting evolutions at various stress rates fully. The similar investigation on the relationship between the mean strain evolution and ratchetting effect can be found in Ref. [36]. Therefore, the evolutions of valley and peak strains within the whole fatigue life are directly used to represent the whole-life ratchetting of PA6 and the results obtained with various stress levels and at different stress rates are shown in Figs. 3 to 5. It
should be noted that only the results before 0.98 fatigue life are shown in Figs. 3 to 5, since the deformation of the material at the final stage of fatigue failure is unstable. The results obtained in the tests with a constant mean stress (i.e., 14MPa) but various stress amplitudes (i.e., 48, 50 and 52MPa) are shown in Fig. 3 and it can be concluded from Fig.3 that: with three prescribed stress amplitudes, the whole-life ratchetting of PA6 is remarkably sensitive to the variation of stress rate (from 10 to 90MPa/s), but it is reflected mainly by the evolution of peak strain, not obviously by that of valley strain; generally, with the increase of stress rate, final peak strain decreases apparently, but final valley strain changes slightly. Figs. 4 and 5 provide the results obtained in the tests with a constant stress amplitude of 52MPa but various mean stresses (i.e., 8, 10, 12 and 14MPa) and with a constant peak stress of 66MPa but different stress ratios (-0.576 and -0.515), respectively, at the stress rates ranged from 10 to 90MPa/s. It is seen from Figs. 4 and 5 that the rate-dependence of whole-life ratchetting observed in the cases with various mean stresses and stress ratios is similar to that concluded from Fig. 3.
Fig. 3 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 4 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 5 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with a peak stress of 66MPa and a stress ratio of: (a) -0.576; (b) -0.515.
When the prescribed stress rate decreases to a relatively lower value (e.g., 5.3MPa/s for all prescribed stress levels or 10MPa/s for a relatively lower stress amplitude of 48MPa), the whole-life ratchetting of PA6 presents a four-staged evolution feature as illustrated in Fig. 6. Detailed evolution of whole-life ratchetting strain in each stage is plotted in Fig. 6b, and it is found that: (1) similar to the tri-staged whole-life ratchetting at higher stress rate discussed above, ratchetting strain rate still decreases in Stage I and keeps nearly constant in Stage II; (2) differently, in Stage III, the ratchetting strain rate decreases to a certain value after initial increase, and then keeps stable in the subsequent Stage IV. Moreover, as shown in Fig. 6a, the valley strain basically accumulates in the tensile direction even if its accumulation rate is still lower than that of peak strain, which is different from that obtained at higher stress rate shown in Fig. 2a. Such a four-staged whole-life ratchetting of PA6 at a low stress rate is further shown in Figs. 7 to 9 in more details.
Fig. 6 Whole-life ratchetting with 14±50MPa at 5.3MPa/s: (a) detailed stress-strain hysteresis loop; (b) ratchetting strain vs. the number of cycles.
Fig. 7 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 8 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 9 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with a peak stress of 66MPa and a stress ratio of: (a) -0.576; (b) -0.515.
In summary, the whole-life ratchetting of PA6 is affected obviously by the variation of stress rate, that is, a tri-staged ratchetting occurs at higher stress rate but a four-staged one takes place at relatively lower stress rate.
3.3 Fatigue failure modes and Fatigue lives at different stress rates Based on the experimental results in this study, it is summarized that two kinds of fatigue failure modes occur, depending on the prescribed stress rates, stress amplitudes and mean stresses. That is: (1) if the stress rate is higher (i.e., from 10 to 90MPa/s), or is lower (i.e., 5.3MPa/s) but with higher stress amplitude/mean stress, the fatigue failure mode is generally the necking controlled by unstable self-heating and resultant large ratchetting strain; (2) but if the stress rate is lower (i.e., 5.3MPa/s) with lower stress amplitude/mean stress, the fatigue failure mode is generally the fracture controlled by low-cycle fatigue damage. For the former, obvious necking can be observed when the peak strain approaches to 40% and thus, this kind of fatigue failure sounds to be ductile failure mode; while, for the latter, the fatigue failure is a typical brittle fatigue fracture mode. With different stress levels, the fatigue lives of PA6 at various stress rates are addressed in Fig. 10 and the dotted lines labeled in Fig. 10 are used to separate the fatigue lives corresponding to the two kinds of whole-life ratchetting discussed above (i.e., the symbols above the dotted line correspond to the four-staged whole-life ratchetting and the others below the dotted lines correspond to the tri-staged one). From Fig. 10, some conclusions can be drawn as follows: (1) form Fig. 10a, prescribing the mean stress as 14MPa, fatigue life always increases with decreasing the stress rate if the applied stress amplitude is lower (from 46 to 50MPa), but if the applied stress amplitude becomes higher (e.g., 52MPa), fatigue life decreases firstly with decreasing the stress rate (from 90 to 10MPa/s) and then increases significantly at 5.3MPa/s; (2) from Fig. 10b, prescribing the stress amplitude as 52MPa and changing the mean stress from 8 to 14MPa, the fatigue life still decreases firstly with decreasing the stress rate (from 90 to 10MPa/s) but increases significantly at 5.3MPa/s; (3) from Fig. 10c, prescribing the peak stress as 66MPa and varying the stress ratio from -0.64 to -0.33, fatigue life always decreases with decreasing the stress rate (from 90 to 10MPa/s), but increases significantly at 5.3MPa/s if the stress ratio is -0.58 or -0.52; (4) Furthermore,
whatever the applied stress rate (from 5.3MPa/s to 90MPa/s) is, fatigue life always increases with the increase of stress ratio and the decrease of stress amplitude/mean stress, as shown in Fig. 10a to Fig. 10c.
Fig. 10 Fatigue lives of PA6 at various stress rates and with different: (a) stress amplitudes; (b) mean stresses; (c) stress ratios.
3.4 Discussion 3.4.1 Stress-rate dependence of the whole-life ratchetting and fatigue failure modes As summarized in Section 3.2 and Section 3.3, PA6 presents two kinds of whole-life ratchetting at high and low stress rates, respectively, and the fatigue failure modes of PA6 are also associated with the variation of stress rate. Owing to the low thermal conductivity of polymers, self-heating resulting from the viscous dissipation always occurs in the process of cyclic deformation of polymers, especially for the cases at relatively higher stress rates or after certain successive loading cycles. The self-heating effect is primarily controlled by the magnitude of applied stress rate and has an obvious influence on the whole-life ratchetting
and fatigue failure modes of PA6. Therefore, in order to figure out the role of stress rate in the transition between two kinds of whole-life ratchetting and fatigue failure modes, corresponding temperature rise (representing the magnitude of self-heating) measured on the surface of the specimens in the whole fatigue process is provided in Fig. 11. It should be pointed out that the temperature rise oscillates in each cycle and the average temperature rise (i.e., the average value of maximum and minimum temperature rises per cycle) is addressed specifically in Fig. 11.
Fig. 11 Temperature rise in the fatigue tests: (a) corresponding to the tri-staged whole-life ratchetting shown in Fig. 2; (b) corresponding to the four-staged one shown in Fig. 6; (c) corresponding to the four-staged one shown in Fig. 7a.
For the tri-staged whole-life ratchetting of PA6 shown in Fig. 2, the corresponding temperature rise is given in Fig. 11a. At the beginning, the ratchetting strain of PA6 is small and the temperature rises slowly. With increasing the number of cycles, more and more polymeric chains of PA6 disentangle and become aligned to the loading direction; thus,
ratchetting strain continues to increase and hysteresis loop becomes wider and wider. When the area of hysteresis loop reaches a value large enough, the temperature of specimen begins to increase significantly because a lot of self-heat from the dissipated energy per cycle cannot adequately transfer to the ambient media at higher stress rate. In this case, there is a mutual promotion between the cyclic deformation (specifically referring to the area of hysteresis loop and the ratchetting strain) and temperature rise of the specimen, that is, the ratchetting strain and hysteresis loop gets larger and larger due to the self-heating softening of PA6 caused by the increase of temperature, which can produce more energy dissipation to make the temperature increase again. Such an interaction becomes much stronger with the increase of loading cycles, and then an unstable self-heating and resultant softening occur after 440 cycles as shown in Fig. 2b and Fig. 11a. It can be observed from Fig. 11a that in the final phase of Stage III with an unstable self-heating, the specimen temperature is higher than 45℃ (the glass transition temperature of PA6) and the mobility of the polymer chain of PA6 is increased significantly due to the glass transition; as a result, resultant ratchetting strain accumulates rapidly in Stage III (i.e., the results after 440 cycles shown in Fig. 2b), which leads to the necking failure of PA6. For the four-staged whole-life ratchetting of PA6 shown in Fig. 6, the corresponding temperature rise is given in Fig. 11b. Due to relatively low prescribed stress rate (i.e., 5.3MPa/s), polymeric chains of PA6 have more time to deform along the direction of external force, and then ratchetting strain increases faster than that at higher stress rate. In Stage III of ratchetting, most of polymeric chains have stretched fully; thus, ratchetting strain rate begins to decrease (i.e., after 260 cycles shown in Fig. 6b) and the area of hysteresis loop no longer increases as quickly as before (i.e., the green and red hysteresis loops shown in Fig. 6a). Although the current magnitude of energy dissipation is not small, unstable self-heating does not happen in Stage III due to low stress rate. In Stage IV, the anti-deformability of material is reduced gradually owing to the damage caused by the nucleation and propagation of internal defects (i.e., microcrack or micro-void) in this stage; and thus, as shown in Fig. 6b and Fig. 11b, as the number of cycles increases, the ratchetting strain and temperature rise of the specimen increase stably and slowly in Stage IV (i.e., after 570 cycles shown in Fig. 6b). If the damage reaches its critical value, the specimen fractures but no unstable self-heating
occurs at the final phase of Stage IV, as shown in Fig. 11b. However, in the cases with relatively higher stress amplitude/mean stress (i.e., the cases shown in Figs. 7a, 8a and 8b), although the applied stress rate is relatively lower, the unstable self-heating occurs at the final of Stage IV as shown in Fig. 11c; thus, the fatigue failure mode is also the necking one similar to that at higher stress rate discussed above.
3.4.2 Stress-rate dependence of fatigue life For polymeric materials, the fatigue life is governed by a combination of inelastic deformation, micro-void and microcrack damage mechanisms [37]. Besides, some researches [31, 33, 34] found that ratchetting strain can be used to characterize the fatigue damage of polymeric materials. It implies that the evolutions of ratchetting strain at different stress rates can reflect the influence of stress rate on the fatigue life of PA6. Therefore, based on the evolutions of whole-life ratchetting at different stress rates shown in Figs. 3 to 5, the way how stress rate influences the fatigue life of PA6 is discussed first in this section. Meanwhile, to figure out whether the influence of stress rate on fatigue life of PA6 is dependent on the magnitude of self-heating, the corresponding average temperature rises in the fatigue tests are provided in Figs. 12 to 14. Moreover, the reason why the fatigue life of PA6 with a four-staged whole-life ratchetting is much longer than that of PA6 with a tri-staged one will be also discussed in the end of this subsection. It can be seen from Figs. 12 to 14 that in Stage II of whole-life ratchetting with different applied stress levels, the self-heating is always similarly weak at different stress rates; but in Stage III, the self-heating becomes to be obvious and stronger and stronger with increasing the stress rate. Correspondingly, as shown in Figs. 3 to 5, the peak strain increases more slowly at higher stress rate in Stage II and thus, as the occurrence of unstable self-heating is delayed, the number of cycles belonging to Stage II increases with the increase of stress rate; while in Stage III, the large ratchetting strain, leading to the final ductile fatigue failure, accumulates faster at higher stress rate and thus, the number of cycles being classified within Stage III decreases with increasing the stress rate. Therefore, it can be concluded that: (1) in Stage II with a weak self-heating, increasing the stress rate can retard the development of ratchetting due to the resultant strain hardening which is from that the polymeric chains of
PA6 have less time to deform along the direction of external force during the cyclic tests at higher stress rate, and is beneficial to the fatigue life of PA6. It should be noted that such strain hardening of polymers is different from that of traditional metals where dislocation density evolution results in the strain hardening; (2) however, in Stage III with a remarkable self-heating, increasing the stress rate can promote the evolution of ratchetting due to the self-heating softening which is stronger at higher stress rate, and is detrimental to the fatigue life of PA6. For the case with a tri-staged whole-life ratchetting, the number of cycles experienced by Stage I is usually small and can be neglected compared with the total fatigue life of PA6; thus, its fatigue life is considered as the number of cycles mainly experienced by Stages II and III. As discussed before, increasing the stress rate can increase the number of cycles experienced by Stage II but decrease that by Stage III; thus, the effect of increasing the stress rate on the total fatigue life of PA6 with a tri-staged whole-life ratchetting is determined by the competition of the resultant strain hardening in Stage II and the self-heating softening in Stage III. It can been seen from Fig. 3a, when the applied stress amplitude is higher (e.g., 52MPa), the retarding effect (caused by the resultant strain hardening) of increasing the stress rate on the development of ratchetting in Stage II is more dominating, and then increasing the stress rate leads to an increased fatigue life. However, as illustrated in Fig. 3b and Fig. 3c, when the applied stress amplitudes is lower (e.g., 50MPa and 48MPa), the promoting effect (caused by the self-heating softening) of increasing the stress rate on the evolution of ratchetting in Stage III is more dominating; thus, increasing the stress rate leads to a decreased fatigue life. For the case with a four-staged whole-life ratchetting, in Stage IV, only when the damage caused by the nucleation and propagation of internal defects (i.e., microcrack or micro-void) accumulates to a critical value after many cycles, can the final fatigue failure (i.e., fracture or necking at low stress rate) be caused. Thus, the number of cycles experienced by Stage IV is generally much higher than the sum of the numbers of cycles experienced by the first three stages. That is, prescribing the stress level as constant, when the applied stress rate decreases to 5.3MPa/s, the whole-life ratchetting of PA6 generally transforms from a tri-staged one to a four-staged one and correspondingly, the fatigue life of PA6 is much longer than that at higher stress rate, as shown in Fig. 10.
Fig. 12 Average temperature rise in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 13 Average temperature rise in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 14 Average temperature rise in the fatigue tests at various stress rates and with a constant peak stress of 66MPa and a constant stress ratio of: (a) -0.576; (b) -0.515.
4. Conclusion
(1)
The whole-life ratchetting of PA6 presents a tri-staged evolution feature at higher stress rate (e.g., 10, 30 or 90MPa/s): (i) Stage I with a decreasing ratchetting strain rate; (ii) Stage II with a constant ratchetting strain rate; and (iii) Stage III with a rapidly increasing ratchetting strain rate. However, when the applied stress rate decreases to a relatively lower value (e.g., 5.3MPa/s for all prescribed stress levels or 10MPa/s for a relatively lower stress amplitude, e.g., 48MPa), the whole-life ratchetting presents a four-staged evolution feature, that is: the ratchetting evolution rules in the first two stages are similar to that of the tri-staged one, but in Stage III, the ratchetting strain rate decreases to an relatively low value after an initial increase; and in the subsequent Stage IV, the ratchetting strain accumulates slowly and stably. Such a transition can be explained as following: the unstable self-heating will occur in Stage III at higher stress rate, but it is delayed to Stage IV or even doesn’t occur during the fatigue test at lower stress rate.
(2)
The fatigue failure mode of PA6 is also sensitive to the variation in the applied stress rate and stress level: for the case with a tri-staged whole-life ratchetting at relatively higher stress rate (from 10 to 90MPa/s), the fatigue failure mode is always a ductile necking one controlled by unstable self-heating and resultant large ratchetting strain; for the case with a four-staged whole-life ratchetting at low stress rate (e.g., 5.3MPa/s), when the applied stress amplitude/mean stress is relatively higher, the fatigue failure mode is also the necking one, but when the applied stress amplitude/mean stress is relatively lower, the fatigue failure mode becomes as a brittle fracture one controlled by low-cycle fatigue damage.
(3)
The effect of increasing the stress rate on the ratchetting evolution is dependent on the magnitude of self-heating resulted from the cyclic deformation of PA6, that is: when the self-heating is weak, the ratchetting strain rate decreases with increasing the stress rate due to the resultant strain hardening; but when the self-heating is significant, the ratchetting strain rate increases with increasing the stress rate due to the self-heating softening.
(4)
For the case with a tri-staged whole-life ratchetting, whether increasing the stress rate is detrimental or beneficial to the fatigue life of PA6 is determined by the competition
of resultant strain hardening and self-heating softening. When the stress amplitude is relatively higher, the retarding effect (from the resultant strain hardening) of increasing the stress rate on the development of ratchetting in Stage II is more dominating, and thus the fatigue life of PA6 increases with the increase of stress rate; when the stress amplitude is relatively lower, the promoting effect (from the resultant self-heating softening) of increasing the stress rate on the development of ratchetting in Stage III is more dominating, and then the fatigue life of PA6 decreases with the increase of stress rate. (5)
For the case with a four-staged whole-life ratchetting presented at lower stress rate, when the applied stress level is constant, the fatigue life of PA6 is generally much longer than that with a tri-staged one at higher stress rate.
Acknowledgements Financial supports from National Natural Science Foundation of China (11972312) are gratefully acknowledged.
References [1] OHNO N. Recent progress in constitutive modeling for ratchetting. J Soc Mater Sci Jpn 1997; 46: 1-9. https://doi.org/10.2472/jsms.46.3appendix_1. [2] Chaboche J-L. A review of some plasticity and viscoplasticity constitutive theories. Int J Plasticity 2008; 24(10): 1642-1693. https://doi.org/10.1016/j.ijplas.2008.03.009. [3] Kang G. Ratchetting: Recent progresses in phenomenon observation, constitutive modeling and application. Int J Fatigue 2008; 30(8): 1448-1472. https://doi.org/10.1016/j.ijfatigue.2007.10.002. [4] Rider R, Harvey S, Chandler H. Fatigue and ratcheting interactions. Int J Fatigue 1995; 17(7): 507-511. https://doi.org/10.1016/0142-1123(95)00046-V. [5] Kang G, Liu Y, 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. https://doi.org/10.1016/j.msea.2006. 07.006.
[6] Kang G, Liu Y. Uniaxial ratchetting and low-cycle fatigue failure of the steel with cyclic stabilizing or softening feature. Mater Sci Eng A 2008; 472(1-2): 258-268. https://doi.org/10.1016/j.msea.2007.03.029. [7] Kang G, Liu Y, Ding J, Gao Q. Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: damage evolution and damage-coupled visco-plastic constitutive model. Int J Plasticity 2009; 25(5): 838-860. https://doi.org/10.1016/j.ijplas.2008.06.004. [8] Lim C-B, Kim K, Seong J. Ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress. Int J Fatigue 2009; 31(3): 501-507. https://doi.org/10.1016/j.ijfatigue.2008. 04.008. [9] Liu Y, Kang G, Gao Q. A multiaxial stress-based fatigue failure model considering ratchetting–fatigue interaction. Int J Fatigue 2010; 32(4): 678-684. https://doi.org/10.1016/j.ijfatigue.2009.10.006. [10] Paul SK, Sivaprasad S, Dhar S, Tarafder S. Ratcheting and low cycle fatigue behavior of SA333 steel and their life prediction. J Nucl Mater 2010; 401(1-3): 17-24. https://doi.org/10.1016/j.jnucmat.2010. 03.014. [11] Zhu S, Lei Q, Wang Q. Mean stress and ratcheting corrections in fatigue life prediction of metals. Fatigue Fract Eng M 2017; 40(9): 1343-1354. https://doi.org/10.1111/ffe.12569. [12] Xia Z, Shen X, Ellyin F. An assessment of nonlinearly viscoelastic constitutive models for cyclic loading: the effect of a general loading/unloading rule. Mech Time-depend Mat 2005; 9(4): 79-98. https://doi.org/10.1007/s11043-006-9004-3. [13] Xia Z, Shen X, Ellyin F. Biaxial cyclic deformation of an epoxy resin: experiments and constitutive modeling. J Mater Sci 2005; 40(3): 643-654. https://doi.org/10.1007/s10853-005-6302-0. [14] Hasanpour K, Ziaei-Rad S, Mahzoon M. A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation. Int J Plasticity 2009; 25(6): 1154-1176. https://doi.org/10.1016/j.ijplas.2008.06.012. [15] Kang G, Liu Y, Wang Y, Chen Z, Xu W. Uniaxial ratchetting of polymer and polymer matrix composites: time-dependent experimental observations. Mater Sci Eng A 2009; 523(1-2): 13-20. https:// doi.org/10.1016/j.msea.2009.06.055. [16] Wang Y, Chen X, Yu W, Yan L. Experimental study on multiaxial ratcheting behavior of vulcanized natural rubber. Polym Eng Sci 2009; 49(3): 506-513. https://doi.org/10.1002/pen.21314. [17] Zhang Z, Chen X. Multiaxial ratcheting behavior of PTFE at room temperature. Polym Test 2009; 28(3): 288-295. https://doi.org/10.1016/j.polymertesting.2008.12.012.
[18] Zhang Z, Chen X, Wang Y. Uniaxial ratcheting behavior of polytetrafluoroethylene at elevated temperature. Polym Test 2010; 29(3): 352-357. https://doi.org/10.1016/j.polymertesting.2010.01.001. [19] Hassan T, Çolak OU, Clayton PM. Uniaxial strain and stress-controlled cyclic responses of ultrahigh molecular weight polyethylene: experiments and model simulations. ASME J Eng Mater-T 2011; 133(2): 021010. https://doi.org/10.1115/1.4003109. [20] Pan D, Kang G, Jiang H. Viscoelastic constitutive model for uniaxial time‐dependent ratcheting of polyetherimide polymer. Polym Eng Sci 2012; 52(9): 1874-1881. https://doi.org/10.1002/pen.23144. [21] 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. https://doi.org/10.1016/ j.polymertesting.2014.07.019. [22] Haouala S, Doghri I. Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles. Int J Plasticity 2015; 70: 98-125. https:// doi.org/10.1016/j.ijplas.2015.03.005. [23] Chen K, Kang G, Lu F, Chen J, Jiang H. Effect of relative humidity on uniaxial cyclic softening/hardening and intrinsic heat generation of polyamide-6 polymer. Polym Test 2016; 56: 19-28. https://doi.org/10.1016/j.polymertesting.2016.09.020. [24] Chen K, Kang G, Yu C, Lu F, Jiang H. Time-Dependent Uniaxial Ratchetting of Ultrahigh Molecular Weight Polyethylene Polymer: Viscoelastic–Viscoplastic Constitutive Model. ASME J Appl Mech 2016; 83(10): 101003. https://doi.org/10.1115/1.4034120. [25] Yu C, Kang G, Lu F, Zhu Y, Chen K. Viscoelastic–viscoplastic cyclic deformation of polycarbonate polymer: experiment and constitutive model. ASME J Appl Mech 2016; 83(4): 041002. https://doi.org/ 10.1115/1.4032374. [26] Yu C, Kang G, Chen K. A hygro-thermo-mechanical coupled cyclic constitutive model for polymers with considering glass transition. Int J Plasticity 2017; 89: 29-65. https://doi.org/10.1016/j.ijplas.2016. 11.001. [27] Zheng X, Wen X, Gao J, Yu J, Lin W, Xu J. Temperature-dependent ratcheting of PTFE gaskets under cyclic compressive loads with small stress amplitude. Polym Test 2017; 57: 296-301. https://doi.org/ 10.1016/j.polymertesting.2016.12.002. [28] Tao G, Xia Z. Ratcheting behavior of an epoxy polymer and its effect on fatigue life. Polym Test 2007; 26(4): 451-460. https://doi.org/10.1016/j.polymertesting.2006.12.010.
[29] Liu W, Gao Z, Yue Z. Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA. Mater Sci Eng A 2008; 492(1-2): 102-109. https://doi.org/10.1016/j.msea.2008.03.042. [30] Shariati M, Hatami H, Yarahmadi H, Eipakchi HR. An experimental study on the ratcheting and fatigue behavior of polyacetal under uniaxial cyclic loading. Mater Des 2012; 34: 302-312. https://doi.org/ 10.1016/j.matdes.2011.08.017. [31] Liu W, Yang XJ. Damage evolution with growing cyclic creep and life prediction of MDYB-3 PMMA. Fatigue Fract Eng Mater Struct 2013; 36(6): 483-491. https://doi.org/10.1111/ffe.12017. [32] Chen G, Liang H-q, Wang L, Mei Y-h, Chen X. Multiaxial ratcheting-fatigue interaction on acrylonitrile-butadiene-styrene terpolymer. Polym Eng Sci 2015; 55(3): 664-671. https://doi.org/10.1002/ pen.23932. [33] Holopainen S, Barriere T, Cheng G, Kouhia R. Continuum approach for modeling fatigue in amorphous glassy polymers. Applications to the investigation of damage-ratcheting interaction in polycarbonate. Int J Plasticity 2017; 91: 109-133. https://doi.org/10.1016/j.ijplas.2016.12.001. [34] Yang J, Kang G, Chen K, Kan Q. Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6. Polym Test 2018; 69: 545-555. https://doi.org/j.polymertesting.2018.06.018. [35] Elleuch R, Taktak W. Viscoelastic Behavior of HDPE Polymer using Tensile and Compressive Loading. J Mater Eng Perform 2006; 15(1): 111-116. https://doi.org/10.1361/105994906x83475. [36] Gryguc A, Behravesh SB, Shaha SK, Jahed H, Wells M, Williams B, Su X. Low-cycle fatigue characterization and texture induced ratcheting behaviour of forged AZ80 Mg alloys. Int J Fatigue 2018; 116: 429-438. https://doi.org/10.1016/j.ijfatigue.2018.06.028. [37] Shojaei AK, Wedgewood AR. An anisotropic cyclic plasticity, creep and fatigue predictive tool for unfilled polymers. Mech Mater 2017; 106: 20-34. https://doi.org/j.mechmat.2017.01.003.
Highlights
Fatigue tests of polyamide-6 (PA6) were performed at various stress rates.
Whole-life ratchetting of PA6 depends greatly on the applied stress rates.
Fatigue life and failure mode of PA6 are also dependent on the stress rates.
Influence of stress rate on ratchetting depends on the magnitude of self-heating.
Effect of increasing the stress rate on the fatigue is determined by the competition of resultant strain hardening and self-heating softening.
S0142-1123(19)30506-7 https://doi.org/10.1016/j.ijfatigue.2019.105402 JIJF 105402
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 October 2019 25 November 2019 28 November 2019
Please cite this article as: Yang, J., Kang, G., Chen, K., Kan, Q., Liu, Y., Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6, International Journal of Fatigue (2019), doi: https://doi.org/10.1016/j.ijfatigue.2019.105402
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© 2019 Published by Elsevier Ltd.
Experimental study on rate-dependent uniaxial whole-life ratchetting and fatigue behavior of polyamide 6 Jingye Yanga,b, Guozheng Kanga,b*, Kaijuan Chenb, Qianhua Kana,b , Yujie Liub a
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of
Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, PR China b
Institute of Applied Mechanics, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, 610031, PR China
*
Correspondent author: Dr. Prof. G.Z. Kang, Tel: 86-28-87634671; Fax: 86-28-87600797
Email address: [email protected] or [email protected] Abstract Rate-dependent whole-life ratchetting and fatigue failure of polyamide 6 were explored by conducting a series of stress-controlled uniaxial fatigue tests at room temperature. Meanwhile, the temperature rises on the surface of specimens were recorded to reflect the self-heating occurred during the fatigue tests. The experimental results demonstrate that ratchetting strain rate is sensitive to the variation of prescribed stress rate, and the whole-life ratchetting of PA6 presents a tri-staged evolution feature at high stress rate but a four-staged one at low stress rate. Two failure modes (i.e., the necking controlled by unstable self-heating and resultant large ratchetting strain; and the fracture controlled by the low-cycle fatigue damage) are experimentally observed in the tests at different stress rates. By considering the relationship between ratchetting evolution and temperature rise, it is found that whether increasing the stress rate retards or promotes the ratchetting is dependent on the magnitude of self-heating produced at each fatigue stage, and whether it will be beneficial or detrimental to the total fatigue life is determined by the competition of resultant strain hardening and self-heating softening. Keywords：Polyamide-6; Rate-dependent; Ratchetting; Fatigue; Self-heating
1. Introduction
As a high-performance structural material with good mechanical properties, excellent corrosion resistance and low cost, polyamide-6 (PA6) has been extensively applied in the automobile industry and electronic engineering fields. In these applications, PA6 components generally experience a cyclic loading and encounter a fatigue failure in service. Therefore, to optimize the design of these components, fatigue behavior of PA6 is an important factor to be considered. Ratchetting is a cyclic accumulation of inelastic deformation occurred in the components and materials subjected to a kind of asymmetrical stress-controlled cyclic loading. For metals, experimental and theoretical studies on ratchetting had been extensively conducted in the last three decades, as reviewed by Refs. [1-3]. Besides, some studies had been conducted on the interaction of ratchetting and fatigue, and it was found that appearance of ratchetting was harmful to the fatigue life of metals in general [4-11]. In recent years, for the ratchetting of polymers, many researches had also been conducted [12-27]. These studies demonstrated that the ratchetting of polymers depended on the stress level, stress rate, ambient temperature and loading path, and varied among different polymers. However, most of them just paid attention to the ratchetting within a limited number of cycles; whole-life ratchetting (i.e., over the whole fatigue test) and its interaction with fatigue failure were not considered yet. So far, only few investigations about the ratchetting-fatigue interaction of polymeric materials were reported, e.g.: Tao and Xia [28] studied uniaxial ratchetting for an thermosetting epoxy resin and found that the ratchetting strain was not detrimental to fatigue life; Liu et al. [29] investigated the ratchetting and fatigue behaviors of polymethyl methacrylate (PMMA) at different temperatures and considered that fatigue life might be judged by ratchetting strain; Shariatic el al. [30] investigated the uniaxial whole-life ratchetting of polyacetal and it was observed that the ratchetting strain relied on the variation of stress amplitude and mean stress; Liu and Yang [31] conducted uniaxial fatigue tests of PMMA with various peak stresses at room temperature and found that the growth rate of cyclic creep (i.e., ratchetting) strain and relaxed modulus degradation rate were two important indicators for characterizing the damage
evolution; Chen el al. [32] investigated the multiaxial ratchetting of Acrylonitrile-ButadieneStyrene (ABS) and found that the tensile mean stress promoted the ratchetting and was detrimental to fatigue life, while the compressive mean stress retarded the ratchetting and was beneficial to fatigue life; Holopainen el al. [33] investigated the interaction of ratchetting and damage for polycarbonate (PC) and it was found that fatigue damage accumulated with the evolution of ratchetting which indicated that the ratchetting strain could be used to predict the fatigue life; Yang el al. [34] found that uniaxial ratchetting was detrimental to the fatigue life of PA6 and the evolutions of damage variable and ratchetting strain were similar. However, the stress-rate dependence of whole-life ratchetting and fatigue life has not been considered in these existing studies. Experimental studies on the rate-dependent whole-life ratchetting and fatigue life of polymers are necessary extremely. Therefore, series of uniaxial fatigue tests were carried out at various stress rates to figure out the stress-rate dependence of the whole-life ratchetting and fatigue failure of PA6 in this work. Firstly, the whole-life ratchetting of PA6 is investigated at various stress rates. Then, the fatigue life at various stress rates is addressed. Finally, referring to the temperature rise of specimen during the whole fatigue test, how the change in stress rate influences the whole-life ratchetting and fatigue life is addressed. Some significant conclusions are obtained, which are useful to understand the rate-dependent whole-life ratchetting and fatigue life of polymers, and to establish a fatigue life prediction model considering the influences of stress rate and ratchetting.
2. Experimental procedure
PA6 used in this study was TECAST L with a glass transition temperature of 45 °C and a melting point of 220 °C. As-received PA6 rods were machined to dumbbell specimens, whose section diameter and gauge length are 6mm and 12mm respectively. Both monotonic tensile and fatigue tests were carried out by using a MTS858-Bionix, and experimental data were recorded by a Flex-Test 40 control system. An axial extensometer with a gauge length of 10mm was used in strain measurement and its measurable range of strain is from -20% to
40%. The ambient temperature was set as 21°C by using an air-conditioner and the temperature variation on the surface of specimen was measured by an infrared thermal imager, i.e., FLIRA655sc, during the fatigue test. In the monotonic tensile tests, specimens were loaded to a displacement of 24mm (nearly an engineering strain of 200%) at the displacement rates of 0.02, 0.1 and 0.5mm/s, respectively. In the fatigue tests, the applied stress rates were set as 90, 30, 10 and 5.3MPa/s and various stress levels (i.e., different stress amplitudes, mean stresses and stress ratios) were prescribed at each stress rate.
3.
Results and discussion
3.1 Monotonic tensile test The rate-dependent tensile properties of PA6 were investigated by conducting monotonic tensile tests at various displacement rates and the results are shown in Fig. 1. Due to a good repeatability of test data, only one stress-strain curve for each loading case is provided in Fig. 1. As illustrated in Fig. 1, the stress-displacement curves of PA6 at all displacement rates are basically linear and coincident at the beginning stage of monotonic tensile tests. With increasing the tensile displacement, the stress-displacement curves behave non-linear and the responding stress is higher at higher displacement rate. The yield strength of PA6 (defined as the value of corresponding stress when strain softening occurs) increases with the increase of displacement rate and is marked in Fig. 1. After the yielding point, apparent strain softening occurs and stress-strain curves at all displacement rates gradually approach to each other and intersect at the displacement of roughly 5mm (about at the engineering strain of 41.6%). Then, with increasing the loading displacement further, the responding stresses at all rates become stable after a significant drop; but unlike the previous stage where the loading displacement is less than 5mm, the responding stress is lower at higher displacement rate here. Furthermore, obvious necking is observed when the responding stress becomes close to the stable value (i.e., at the points marked by blue cycles in Fig. 1) and expands from the center of the gauge length to both ends of tested specimens as the applied displacement increases. Such a kind of
rate-dependent monotonic tensile deformation of PA6 is nearly the same as that of the high-density polyethylene observed in Ref. [35].
Fig. 1 Monotonic tensile responses of PA6 at various displacement rates.
3.2 Whole-life ratchetting at different stress rates By referring to [3], some parameters are used to show the whole-life ratchetting more clearly. The ratchetting strain is defined as the mean value of maximum strain and minimum strain per cycle, i.e., Eq. (1); and the ratchetting strain rate is defined as the increment of ratchetting strain from (n-1)-th to n-th cycle, i.e., Eq. (2).
max min 2
(1)
r n ,r n 1,r
(2)
r =
In the asymmetrical stress-controlled fatigue tests at different stress rates, PA6 presents remarkable ratchetting and a typical evolution of whole-life ratchetting obtained in a test with 14±50MPa (i.e., applied stress amplitude is 50MPa and mean stress is 14MPa) and at a stress rate of 90MPa/s is shown in Fig. 2a. From Fig. 2a, it can be seen that the peak strain obviously accumulates with increasing the number of cycles, while the accumulation of valley strain is not obvious in the tensile direction. At the final stage of fatigue process, the valley strain even accumulates obviously in the compression direction. In this case, the area of hysteresis loop, which represents the dissipated energy density per cycle, becomes larger and larger at an increasing rate before fatigue failure. Besides, the curve of ratchetting strain vs. number of cycle is provided in Fig. 2b directly. It can be observed from Fig. 2b that typical whole-life
ratchetting of PA6 presents a tri-staged evolution feature: Stage I with a decreasing ratchetting strain rate; Stage II with a nearly constant ratchetting strain rate; and Stage III with a rapidly increasing ratchetting strain rate. Such a kind of whole-life ratchetting is also reported in some researches for metals [5, 6] and other polymers [29, 30].
Fig. 2 Whole-life ratchetting with 14±50MPa and at 90MPa/s: (a) detailed stress-strain hysteresis loop; (b) ratchetting strain vs. the number of cycles.
As shown in Fig. 2a, the accumulation rates of peak and valley strains are not always the same in the fatigue process and thus, the ratchetting strain defined in Eq. (2) (i.e., mean strain) cannot characterize the ratchetting evolutions at various stress rates fully. The similar investigation on the relationship between the mean strain evolution and ratchetting effect can be found in Ref. [36]. Therefore, the evolutions of valley and peak strains within the whole fatigue life are directly used to represent the whole-life ratchetting of PA6 and the results obtained with various stress levels and at different stress rates are shown in Figs. 3 to 5. It
should be noted that only the results before 0.98 fatigue life are shown in Figs. 3 to 5, since the deformation of the material at the final stage of fatigue failure is unstable. The results obtained in the tests with a constant mean stress (i.e., 14MPa) but various stress amplitudes (i.e., 48, 50 and 52MPa) are shown in Fig. 3 and it can be concluded from Fig.3 that: with three prescribed stress amplitudes, the whole-life ratchetting of PA6 is remarkably sensitive to the variation of stress rate (from 10 to 90MPa/s), but it is reflected mainly by the evolution of peak strain, not obviously by that of valley strain; generally, with the increase of stress rate, final peak strain decreases apparently, but final valley strain changes slightly. Figs. 4 and 5 provide the results obtained in the tests with a constant stress amplitude of 52MPa but various mean stresses (i.e., 8, 10, 12 and 14MPa) and with a constant peak stress of 66MPa but different stress ratios (-0.576 and -0.515), respectively, at the stress rates ranged from 10 to 90MPa/s. It is seen from Figs. 4 and 5 that the rate-dependence of whole-life ratchetting observed in the cases with various mean stresses and stress ratios is similar to that concluded from Fig. 3.
Fig. 3 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 4 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 5 Valley (hollow points) and peak (solid points) strains in the fatigue tests at various stress rates and with a peak stress of 66MPa and a stress ratio of: (a) -0.576; (b) -0.515.
When the prescribed stress rate decreases to a relatively lower value (e.g., 5.3MPa/s for all prescribed stress levels or 10MPa/s for a relatively lower stress amplitude of 48MPa), the whole-life ratchetting of PA6 presents a four-staged evolution feature as illustrated in Fig. 6. Detailed evolution of whole-life ratchetting strain in each stage is plotted in Fig. 6b, and it is found that: (1) similar to the tri-staged whole-life ratchetting at higher stress rate discussed above, ratchetting strain rate still decreases in Stage I and keeps nearly constant in Stage II; (2) differently, in Stage III, the ratchetting strain rate decreases to a certain value after initial increase, and then keeps stable in the subsequent Stage IV. Moreover, as shown in Fig. 6a, the valley strain basically accumulates in the tensile direction even if its accumulation rate is still lower than that of peak strain, which is different from that obtained at higher stress rate shown in Fig. 2a. Such a four-staged whole-life ratchetting of PA6 at a low stress rate is further shown in Figs. 7 to 9 in more details.
Fig. 6 Whole-life ratchetting with 14±50MPa at 5.3MPa/s: (a) detailed stress-strain hysteresis loop; (b) ratchetting strain vs. the number of cycles.
Fig. 7 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 8 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 9 Valley (hollow points) and peak (solid points) strains in the fatigue tests at a low stress rate and with a peak stress of 66MPa and a stress ratio of: (a) -0.576; (b) -0.515.
In summary, the whole-life ratchetting of PA6 is affected obviously by the variation of stress rate, that is, a tri-staged ratchetting occurs at higher stress rate but a four-staged one takes place at relatively lower stress rate.
3.3 Fatigue failure modes and Fatigue lives at different stress rates Based on the experimental results in this study, it is summarized that two kinds of fatigue failure modes occur, depending on the prescribed stress rates, stress amplitudes and mean stresses. That is: (1) if the stress rate is higher (i.e., from 10 to 90MPa/s), or is lower (i.e., 5.3MPa/s) but with higher stress amplitude/mean stress, the fatigue failure mode is generally the necking controlled by unstable self-heating and resultant large ratchetting strain; (2) but if the stress rate is lower (i.e., 5.3MPa/s) with lower stress amplitude/mean stress, the fatigue failure mode is generally the fracture controlled by low-cycle fatigue damage. For the former, obvious necking can be observed when the peak strain approaches to 40% and thus, this kind of fatigue failure sounds to be ductile failure mode; while, for the latter, the fatigue failure is a typical brittle fatigue fracture mode. With different stress levels, the fatigue lives of PA6 at various stress rates are addressed in Fig. 10 and the dotted lines labeled in Fig. 10 are used to separate the fatigue lives corresponding to the two kinds of whole-life ratchetting discussed above (i.e., the symbols above the dotted line correspond to the four-staged whole-life ratchetting and the others below the dotted lines correspond to the tri-staged one). From Fig. 10, some conclusions can be drawn as follows: (1) form Fig. 10a, prescribing the mean stress as 14MPa, fatigue life always increases with decreasing the stress rate if the applied stress amplitude is lower (from 46 to 50MPa), but if the applied stress amplitude becomes higher (e.g., 52MPa), fatigue life decreases firstly with decreasing the stress rate (from 90 to 10MPa/s) and then increases significantly at 5.3MPa/s; (2) from Fig. 10b, prescribing the stress amplitude as 52MPa and changing the mean stress from 8 to 14MPa, the fatigue life still decreases firstly with decreasing the stress rate (from 90 to 10MPa/s) but increases significantly at 5.3MPa/s; (3) from Fig. 10c, prescribing the peak stress as 66MPa and varying the stress ratio from -0.64 to -0.33, fatigue life always decreases with decreasing the stress rate (from 90 to 10MPa/s), but increases significantly at 5.3MPa/s if the stress ratio is -0.58 or -0.52; (4) Furthermore,
whatever the applied stress rate (from 5.3MPa/s to 90MPa/s) is, fatigue life always increases with the increase of stress ratio and the decrease of stress amplitude/mean stress, as shown in Fig. 10a to Fig. 10c.
Fig. 10 Fatigue lives of PA6 at various stress rates and with different: (a) stress amplitudes; (b) mean stresses; (c) stress ratios.
3.4 Discussion 3.4.1 Stress-rate dependence of the whole-life ratchetting and fatigue failure modes As summarized in Section 3.2 and Section 3.3, PA6 presents two kinds of whole-life ratchetting at high and low stress rates, respectively, and the fatigue failure modes of PA6 are also associated with the variation of stress rate. Owing to the low thermal conductivity of polymers, self-heating resulting from the viscous dissipation always occurs in the process of cyclic deformation of polymers, especially for the cases at relatively higher stress rates or after certain successive loading cycles. The self-heating effect is primarily controlled by the magnitude of applied stress rate and has an obvious influence on the whole-life ratchetting
and fatigue failure modes of PA6. Therefore, in order to figure out the role of stress rate in the transition between two kinds of whole-life ratchetting and fatigue failure modes, corresponding temperature rise (representing the magnitude of self-heating) measured on the surface of the specimens in the whole fatigue process is provided in Fig. 11. It should be pointed out that the temperature rise oscillates in each cycle and the average temperature rise (i.e., the average value of maximum and minimum temperature rises per cycle) is addressed specifically in Fig. 11.
Fig. 11 Temperature rise in the fatigue tests: (a) corresponding to the tri-staged whole-life ratchetting shown in Fig. 2; (b) corresponding to the four-staged one shown in Fig. 6; (c) corresponding to the four-staged one shown in Fig. 7a.
For the tri-staged whole-life ratchetting of PA6 shown in Fig. 2, the corresponding temperature rise is given in Fig. 11a. At the beginning, the ratchetting strain of PA6 is small and the temperature rises slowly. With increasing the number of cycles, more and more polymeric chains of PA6 disentangle and become aligned to the loading direction; thus,
ratchetting strain continues to increase and hysteresis loop becomes wider and wider. When the area of hysteresis loop reaches a value large enough, the temperature of specimen begins to increase significantly because a lot of self-heat from the dissipated energy per cycle cannot adequately transfer to the ambient media at higher stress rate. In this case, there is a mutual promotion between the cyclic deformation (specifically referring to the area of hysteresis loop and the ratchetting strain) and temperature rise of the specimen, that is, the ratchetting strain and hysteresis loop gets larger and larger due to the self-heating softening of PA6 caused by the increase of temperature, which can produce more energy dissipation to make the temperature increase again. Such an interaction becomes much stronger with the increase of loading cycles, and then an unstable self-heating and resultant softening occur after 440 cycles as shown in Fig. 2b and Fig. 11a. It can be observed from Fig. 11a that in the final phase of Stage III with an unstable self-heating, the specimen temperature is higher than 45℃ (the glass transition temperature of PA6) and the mobility of the polymer chain of PA6 is increased significantly due to the glass transition; as a result, resultant ratchetting strain accumulates rapidly in Stage III (i.e., the results after 440 cycles shown in Fig. 2b), which leads to the necking failure of PA6. For the four-staged whole-life ratchetting of PA6 shown in Fig. 6, the corresponding temperature rise is given in Fig. 11b. Due to relatively low prescribed stress rate (i.e., 5.3MPa/s), polymeric chains of PA6 have more time to deform along the direction of external force, and then ratchetting strain increases faster than that at higher stress rate. In Stage III of ratchetting, most of polymeric chains have stretched fully; thus, ratchetting strain rate begins to decrease (i.e., after 260 cycles shown in Fig. 6b) and the area of hysteresis loop no longer increases as quickly as before (i.e., the green and red hysteresis loops shown in Fig. 6a). Although the current magnitude of energy dissipation is not small, unstable self-heating does not happen in Stage III due to low stress rate. In Stage IV, the anti-deformability of material is reduced gradually owing to the damage caused by the nucleation and propagation of internal defects (i.e., microcrack or micro-void) in this stage; and thus, as shown in Fig. 6b and Fig. 11b, as the number of cycles increases, the ratchetting strain and temperature rise of the specimen increase stably and slowly in Stage IV (i.e., after 570 cycles shown in Fig. 6b). If the damage reaches its critical value, the specimen fractures but no unstable self-heating
occurs at the final phase of Stage IV, as shown in Fig. 11b. However, in the cases with relatively higher stress amplitude/mean stress (i.e., the cases shown in Figs. 7a, 8a and 8b), although the applied stress rate is relatively lower, the unstable self-heating occurs at the final of Stage IV as shown in Fig. 11c; thus, the fatigue failure mode is also the necking one similar to that at higher stress rate discussed above.
3.4.2 Stress-rate dependence of fatigue life For polymeric materials, the fatigue life is governed by a combination of inelastic deformation, micro-void and microcrack damage mechanisms [37]. Besides, some researches [31, 33, 34] found that ratchetting strain can be used to characterize the fatigue damage of polymeric materials. It implies that the evolutions of ratchetting strain at different stress rates can reflect the influence of stress rate on the fatigue life of PA6. Therefore, based on the evolutions of whole-life ratchetting at different stress rates shown in Figs. 3 to 5, the way how stress rate influences the fatigue life of PA6 is discussed first in this section. Meanwhile, to figure out whether the influence of stress rate on fatigue life of PA6 is dependent on the magnitude of self-heating, the corresponding average temperature rises in the fatigue tests are provided in Figs. 12 to 14. Moreover, the reason why the fatigue life of PA6 with a four-staged whole-life ratchetting is much longer than that of PA6 with a tri-staged one will be also discussed in the end of this subsection. It can be seen from Figs. 12 to 14 that in Stage II of whole-life ratchetting with different applied stress levels, the self-heating is always similarly weak at different stress rates; but in Stage III, the self-heating becomes to be obvious and stronger and stronger with increasing the stress rate. Correspondingly, as shown in Figs. 3 to 5, the peak strain increases more slowly at higher stress rate in Stage II and thus, as the occurrence of unstable self-heating is delayed, the number of cycles belonging to Stage II increases with the increase of stress rate; while in Stage III, the large ratchetting strain, leading to the final ductile fatigue failure, accumulates faster at higher stress rate and thus, the number of cycles being classified within Stage III decreases with increasing the stress rate. Therefore, it can be concluded that: (1) in Stage II with a weak self-heating, increasing the stress rate can retard the development of ratchetting due to the resultant strain hardening which is from that the polymeric chains of
PA6 have less time to deform along the direction of external force during the cyclic tests at higher stress rate, and is beneficial to the fatigue life of PA6. It should be noted that such strain hardening of polymers is different from that of traditional metals where dislocation density evolution results in the strain hardening; (2) however, in Stage III with a remarkable self-heating, increasing the stress rate can promote the evolution of ratchetting due to the self-heating softening which is stronger at higher stress rate, and is detrimental to the fatigue life of PA6. For the case with a tri-staged whole-life ratchetting, the number of cycles experienced by Stage I is usually small and can be neglected compared with the total fatigue life of PA6; thus, its fatigue life is considered as the number of cycles mainly experienced by Stages II and III. As discussed before, increasing the stress rate can increase the number of cycles experienced by Stage II but decrease that by Stage III; thus, the effect of increasing the stress rate on the total fatigue life of PA6 with a tri-staged whole-life ratchetting is determined by the competition of the resultant strain hardening in Stage II and the self-heating softening in Stage III. It can been seen from Fig. 3a, when the applied stress amplitude is higher (e.g., 52MPa), the retarding effect (caused by the resultant strain hardening) of increasing the stress rate on the development of ratchetting in Stage II is more dominating, and then increasing the stress rate leads to an increased fatigue life. However, as illustrated in Fig. 3b and Fig. 3c, when the applied stress amplitudes is lower (e.g., 50MPa and 48MPa), the promoting effect (caused by the self-heating softening) of increasing the stress rate on the evolution of ratchetting in Stage III is more dominating; thus, increasing the stress rate leads to a decreased fatigue life. For the case with a four-staged whole-life ratchetting, in Stage IV, only when the damage caused by the nucleation and propagation of internal defects (i.e., microcrack or micro-void) accumulates to a critical value after many cycles, can the final fatigue failure (i.e., fracture or necking at low stress rate) be caused. Thus, the number of cycles experienced by Stage IV is generally much higher than the sum of the numbers of cycles experienced by the first three stages. That is, prescribing the stress level as constant, when the applied stress rate decreases to 5.3MPa/s, the whole-life ratchetting of PA6 generally transforms from a tri-staged one to a four-staged one and correspondingly, the fatigue life of PA6 is much longer than that at higher stress rate, as shown in Fig. 10.
Fig. 12 Average temperature rise in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 14±50MPa; (c) 14±48MPa.
Fig. 13 Average temperature rise in the fatigue tests at various stress rates and with: (a) 14±52MPa; (b) 12±52MPa; (c) 10±52MPa; (d) 8±52MPa.
Fig. 14 Average temperature rise in the fatigue tests at various stress rates and with a constant peak stress of 66MPa and a constant stress ratio of: (a) -0.576; (b) -0.515.
4. Conclusion
(1)
The whole-life ratchetting of PA6 presents a tri-staged evolution feature at higher stress rate (e.g., 10, 30 or 90MPa/s): (i) Stage I with a decreasing ratchetting strain rate; (ii) Stage II with a constant ratchetting strain rate; and (iii) Stage III with a rapidly increasing ratchetting strain rate. However, when the applied stress rate decreases to a relatively lower value (e.g., 5.3MPa/s for all prescribed stress levels or 10MPa/s for a relatively lower stress amplitude, e.g., 48MPa), the whole-life ratchetting presents a four-staged evolution feature, that is: the ratchetting evolution rules in the first two stages are similar to that of the tri-staged one, but in Stage III, the ratchetting strain rate decreases to an relatively low value after an initial increase; and in the subsequent Stage IV, the ratchetting strain accumulates slowly and stably. Such a transition can be explained as following: the unstable self-heating will occur in Stage III at higher stress rate, but it is delayed to Stage IV or even doesn’t occur during the fatigue test at lower stress rate.
(2)
The fatigue failure mode of PA6 is also sensitive to the variation in the applied stress rate and stress level: for the case with a tri-staged whole-life ratchetting at relatively higher stress rate (from 10 to 90MPa/s), the fatigue failure mode is always a ductile necking one controlled by unstable self-heating and resultant large ratchetting strain; for the case with a four-staged whole-life ratchetting at low stress rate (e.g., 5.3MPa/s), when the applied stress amplitude/mean stress is relatively higher, the fatigue failure mode is also the necking one, but when the applied stress amplitude/mean stress is relatively lower, the fatigue failure mode becomes as a brittle fracture one controlled by low-cycle fatigue damage.
(3)
The effect of increasing the stress rate on the ratchetting evolution is dependent on the magnitude of self-heating resulted from the cyclic deformation of PA6, that is: when the self-heating is weak, the ratchetting strain rate decreases with increasing the stress rate due to the resultant strain hardening; but when the self-heating is significant, the ratchetting strain rate increases with increasing the stress rate due to the self-heating softening.
(4)
For the case with a tri-staged whole-life ratchetting, whether increasing the stress rate is detrimental or beneficial to the fatigue life of PA6 is determined by the competition
of resultant strain hardening and self-heating softening. When the stress amplitude is relatively higher, the retarding effect (from the resultant strain hardening) of increasing the stress rate on the development of ratchetting in Stage II is more dominating, and thus the fatigue life of PA6 increases with the increase of stress rate; when the stress amplitude is relatively lower, the promoting effect (from the resultant self-heating softening) of increasing the stress rate on the development of ratchetting in Stage III is more dominating, and then the fatigue life of PA6 decreases with the increase of stress rate. (5)
For the case with a four-staged whole-life ratchetting presented at lower stress rate, when the applied stress level is constant, the fatigue life of PA6 is generally much longer than that with a tri-staged one at higher stress rate.
Acknowledgements Financial supports from National Natural Science Foundation of China (11972312) are gratefully acknowledged.
References [1] OHNO N. Recent progress in constitutive modeling for ratchetting. J Soc Mater Sci Jpn 1997; 46: 1-9. https://doi.org/10.2472/jsms.46.3appendix_1. [2] Chaboche J-L. A review of some plasticity and viscoplasticity constitutive theories. Int J Plasticity 2008; 24(10): 1642-1693. https://doi.org/10.1016/j.ijplas.2008.03.009. [3] Kang G. Ratchetting: Recent progresses in phenomenon observation, constitutive modeling and application. Int J Fatigue 2008; 30(8): 1448-1472. https://doi.org/10.1016/j.ijfatigue.2007.10.002. [4] Rider R, Harvey S, Chandler H. Fatigue and ratcheting interactions. Int J Fatigue 1995; 17(7): 507-511. https://doi.org/10.1016/0142-1123(95)00046-V. [5] Kang G, Liu Y, 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. https://doi.org/10.1016/j.msea.2006. 07.006.
[6] Kang G, Liu Y. Uniaxial ratchetting and low-cycle fatigue failure of the steel with cyclic stabilizing or softening feature. Mater Sci Eng A 2008; 472(1-2): 258-268. https://doi.org/10.1016/j.msea.2007.03.029. [7] Kang G, Liu Y, Ding J, Gao Q. Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: damage evolution and damage-coupled visco-plastic constitutive model. Int J Plasticity 2009; 25(5): 838-860. https://doi.org/10.1016/j.ijplas.2008.06.004. [8] Lim C-B, Kim K, Seong J. Ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress. Int J Fatigue 2009; 31(3): 501-507. https://doi.org/10.1016/j.ijfatigue.2008. 04.008. [9] Liu Y, Kang G, Gao Q. A multiaxial stress-based fatigue failure model considering ratchetting–fatigue interaction. Int J Fatigue 2010; 32(4): 678-684. https://doi.org/10.1016/j.ijfatigue.2009.10.006. [10] Paul SK, Sivaprasad S, Dhar S, Tarafder S. Ratcheting and low cycle fatigue behavior of SA333 steel and their life prediction. J Nucl Mater 2010; 401(1-3): 17-24. https://doi.org/10.1016/j.jnucmat.2010. 03.014. [11] Zhu S, Lei Q, Wang Q. Mean stress and ratcheting corrections in fatigue life prediction of metals. Fatigue Fract Eng M 2017; 40(9): 1343-1354. https://doi.org/10.1111/ffe.12569. [12] Xia Z, Shen X, Ellyin F. An assessment of nonlinearly viscoelastic constitutive models for cyclic loading: the effect of a general loading/unloading rule. Mech Time-depend Mat 2005; 9(4): 79-98. https://doi.org/10.1007/s11043-006-9004-3. [13] Xia Z, Shen X, Ellyin F. Biaxial cyclic deformation of an epoxy resin: experiments and constitutive modeling. J Mater Sci 2005; 40(3): 643-654. https://doi.org/10.1007/s10853-005-6302-0. [14] Hasanpour K, Ziaei-Rad S, Mahzoon M. A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation. Int J Plasticity 2009; 25(6): 1154-1176. https://doi.org/10.1016/j.ijplas.2008.06.012. [15] Kang G, Liu Y, Wang Y, Chen Z, Xu W. Uniaxial ratchetting of polymer and polymer matrix composites: time-dependent experimental observations. Mater Sci Eng A 2009; 523(1-2): 13-20. https:// doi.org/10.1016/j.msea.2009.06.055. [16] Wang Y, Chen X, Yu W, Yan L. Experimental study on multiaxial ratcheting behavior of vulcanized natural rubber. Polym Eng Sci 2009; 49(3): 506-513. https://doi.org/10.1002/pen.21314. [17] Zhang Z, Chen X. Multiaxial ratcheting behavior of PTFE at room temperature. Polym Test 2009; 28(3): 288-295. https://doi.org/10.1016/j.polymertesting.2008.12.012.
[18] Zhang Z, Chen X, Wang Y. Uniaxial ratcheting behavior of polytetrafluoroethylene at elevated temperature. Polym Test 2010; 29(3): 352-357. https://doi.org/10.1016/j.polymertesting.2010.01.001. [19] Hassan T, Çolak OU, Clayton PM. Uniaxial strain and stress-controlled cyclic responses of ultrahigh molecular weight polyethylene: experiments and model simulations. ASME J Eng Mater-T 2011; 133(2): 021010. https://doi.org/10.1115/1.4003109. [20] Pan D, Kang G, Jiang H. Viscoelastic constitutive model for uniaxial time‐dependent ratcheting of polyetherimide polymer. Polym Eng Sci 2012; 52(9): 1874-1881. https://doi.org/10.1002/pen.23144. [21] 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. https://doi.org/10.1016/ j.polymertesting.2014.07.019. [22] Haouala S, Doghri I. Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles. Int J Plasticity 2015; 70: 98-125. https:// doi.org/10.1016/j.ijplas.2015.03.005. [23] Chen K, Kang G, Lu F, Chen J, Jiang H. Effect of relative humidity on uniaxial cyclic softening/hardening and intrinsic heat generation of polyamide-6 polymer. Polym Test 2016; 56: 19-28. https://doi.org/10.1016/j.polymertesting.2016.09.020. [24] Chen K, Kang G, Yu C, Lu F, Jiang H. Time-Dependent Uniaxial Ratchetting of Ultrahigh Molecular Weight Polyethylene Polymer: Viscoelastic–Viscoplastic Constitutive Model. ASME J Appl Mech 2016; 83(10): 101003. https://doi.org/10.1115/1.4034120. [25] Yu C, Kang G, Lu F, Zhu Y, Chen K. Viscoelastic–viscoplastic cyclic deformation of polycarbonate polymer: experiment and constitutive model. ASME J Appl Mech 2016; 83(4): 041002. https://doi.org/ 10.1115/1.4032374. [26] Yu C, Kang G, Chen K. A hygro-thermo-mechanical coupled cyclic constitutive model for polymers with considering glass transition. Int J Plasticity 2017; 89: 29-65. https://doi.org/10.1016/j.ijplas.2016. 11.001. [27] Zheng X, Wen X, Gao J, Yu J, Lin W, Xu J. Temperature-dependent ratcheting of PTFE gaskets under cyclic compressive loads with small stress amplitude. Polym Test 2017; 57: 296-301. https://doi.org/ 10.1016/j.polymertesting.2016.12.002. [28] Tao G, Xia Z. Ratcheting behavior of an epoxy polymer and its effect on fatigue life. Polym Test 2007; 26(4): 451-460. https://doi.org/10.1016/j.polymertesting.2006.12.010.
[29] Liu W, Gao Z, Yue Z. Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA. Mater Sci Eng A 2008; 492(1-2): 102-109. https://doi.org/10.1016/j.msea.2008.03.042. [30] Shariati M, Hatami H, Yarahmadi H, Eipakchi HR. An experimental study on the ratcheting and fatigue behavior of polyacetal under uniaxial cyclic loading. Mater Des 2012; 34: 302-312. https://doi.org/ 10.1016/j.matdes.2011.08.017. [31] Liu W, Yang XJ. Damage evolution with growing cyclic creep and life prediction of MDYB-3 PMMA. Fatigue Fract Eng Mater Struct 2013; 36(6): 483-491. https://doi.org/10.1111/ffe.12017. [32] Chen G, Liang H-q, Wang L, Mei Y-h, Chen X. Multiaxial ratcheting-fatigue interaction on acrylonitrile-butadiene-styrene terpolymer. Polym Eng Sci 2015; 55(3): 664-671. https://doi.org/10.1002/ pen.23932. [33] Holopainen S, Barriere T, Cheng G, Kouhia R. Continuum approach for modeling fatigue in amorphous glassy polymers. Applications to the investigation of damage-ratcheting interaction in polycarbonate. Int J Plasticity 2017; 91: 109-133. https://doi.org/10.1016/j.ijplas.2016.12.001. [34] Yang J, Kang G, Chen K, Kan Q. Experimental study on uniaxial ratchetting-fatigue interaction of polyamide-6. Polym Test 2018; 69: 545-555. https://doi.org/j.polymertesting.2018.06.018. [35] Elleuch R, Taktak W. Viscoelastic Behavior of HDPE Polymer using Tensile and Compressive Loading. J Mater Eng Perform 2006; 15(1): 111-116. https://doi.org/10.1361/105994906x83475. [36] Gryguc A, Behravesh SB, Shaha SK, Jahed H, Wells M, Williams B, Su X. Low-cycle fatigue characterization and texture induced ratcheting behaviour of forged AZ80 Mg alloys. Int J Fatigue 2018; 116: 429-438. https://doi.org/10.1016/j.ijfatigue.2018.06.028. [37] Shojaei AK, Wedgewood AR. An anisotropic cyclic plasticity, creep and fatigue predictive tool for unfilled polymers. Mech Mater 2017; 106: 20-34. https://doi.org/j.mechmat.2017.01.003.
Highlights
Fatigue tests of polyamide-6 (PA6) were performed at various stress rates.
Whole-life ratchetting of PA6 depends greatly on the applied stress rates.
Fatigue life and failure mode of PA6 are also dependent on the stress rates.
Influence of stress rate on ratchetting depends on the magnitude of self-heating.
Effect of increasing the stress rate on the fatigue is determined by the competition of resultant strain hardening and self-heating softening.