Materials and Design

Transcription

1 Materials and Design 34 (211) Contents lists available at SciVerse ScienceDirect Materials and Design journal hoepage: Technical Report An experiental study on the ratcheting and atigue behavior o polyacetal under uniaxial cyclic loading Mahoud Shariati, Hossein Hatai, Hossein Yarahadi, Haid Reza Eipakchi Departent o Mechanical Engineering, Shahrood University o Technology, Shahrood, Iran article ino abstract Article history: Received 26 May 211 Accepted 1 August 211 Available online xxxx Keywords: Polyers Fatigue Plastic behavior This paper presents an experiental study on the behavior o polyacetal or Polyoxyethylene (POM) under uniaxial cyclic loading. All experients were perored in the stress-controlled ode. The tests were divided into nine groups, where dierent cobinations o the ean stress or stress aplitude were used. Uniaxial atigue or cyclic testing o polyeric aterials is perored on speciens with geoetry according to ASTM D638-3 or its equivalent, ISO In this study, the diaeter o the polyacetal test speciens was 2. The speciens were prepared using a CNC lathe. The gage length o the speciens was 3, and the diaeter o the speciens was 1.1. The stress strain data were recorded during each cycle o the experiental tests. Based on the obtained stress strain data, quantitative analysis o the echanical paraeters were done in which the strain ratcheting, strain range, strain energy density and the slope o the stress strain hysteresis loops were calculated. The experiental data showed that the ratcheting strain and strain rate ratcheting are sensitive to the applied stress aplitude and the ean stress. Mean stress unctions were used in the equivalent daage paraetend included the ean stress eect on the atigue lie o the polyacetal. The aterial constants were calibrated using the stress, strain and energy approaches. Finally, it was ound that the stress and energy approaches were ore successul in predicting the atigue lie o polyacetal. Ó 211 Elsevier Ltd. All rights reserved. 1. Introduction Ratcheting is a kind o special cyclic deoration behavior that occurs in aterials and structures subjected to cyclic stressing with a non-zero ean stress, where the stresses are greater than the aterial s yield stress. Thus, the aterials or structures will yield under the applied loading. Ratcheting is particularly iportant in saety and atigue lie prediction o engineering structures because any types o structures are subjected to cyclic loading, where the applied stress exceeds the yield stress o the used aterial. For the design and analysis o these types o structures, accurately predicting the ratcheting response is critical because ratcheting can lead to catastrophic ailure o the structures. Even or structures that are designed to behave in the elastic liit, plastic zones ay exist at the discontinuities ot the tip o cracks, and atigue cracks can initiate at the plastic zones. Thereore, an accurate siulation that odels the cyclic plasticity response is iportant in predicting the high-cycle atigue lie as well [1]. In the last two decades, the ratcheting phenoena has been extensively studied by experients and siulations. Corresponding author. Tel.: ; ax: E-ail addresses: shariati@shahroodut.ac.ir, shariati44@gail.co (M. Shariati). Several studies have investigated the ratcheting behavior o etallic aterials. For exaple, Ki et al. studied the atigue and the ratcheting o a type o coppelloy [2]. Yang investigated the atigue and ratcheting o carbon steel C45 [3]. Kang et al. studied the ratcheting and atigue behavior o stainless steel SS34 [4]. Additionally, siilar studies have been done in this ield [5 8]. Such experiental tests and obtained data can help to better siulate and advance cyclic plasticity odels and, thus, progress the analytical odels on the ratcheting behavior o etals [9 12]. However, there are ore studies on etallic aterials than on polyeric aterials in recent years; there have been only a ew experiental tests perored that study the ratcheting behavior o polyeric aterials. Aong the studies that have ocused on polyeric aterials, Gang Tao and Zihui Xia studied a type o polyer [13,14]. Xu Chen and Shucai Hui studied the polyer, PTFE, and its ratcheting behavior unde copressive cyclic loading [15]. Other studies o polyeric aterials have also been perored [16 22]. However, to iprove the plasticity odels or polyeric aterials, ore experiental data are required. Due to the widespread applications o polyacetal, which is used to create bearings and gear types, and the lack o experiental data on the ratcheting behavior o polyeric aterials, a study on the atigue and ratcheting behavior o polyacetal is needed. Polyacetal, or POM, is an engineering polyer with a wide range o applications that exhibits echanical properties siilar to soe etals. This /$ - see ront atter Ó 211 Elsevier Ltd. All rights reserved. doi:1.116/j.atdes

2 M. Shariati et al. / Materials and Design 34 (211) polyer, which was introduced to the polyer industry in 196, has excellent echanical properties that ill the space between ordinary polyers and etals. Applications o this polyer include use in the autootive industries, electrical equipent, construction, hardware and electronics. Polyacetal is alost a crystalline polyer that can be produced ro polyerase oraldehyde ( CH 2 O ). Polyacetal is a copetitor with the nylons (polyaides), which have several serious deiciencies, such as their poor diensional stability in the presence o huidity. Because o their excellent olding ability, polyacetal resins are particularly useul when producing coplex, industrial experiental coponents. Fig. 2. Fixture geoetry. 2. Speciens and test setup Uniaxial atigue or cyclic testing o polyeric aterials is oten perored on lat, dog bone-shaped speciens with a geoetry according to ASTM D638-3 [23] or its equivalent, ISO [24 27]. Because the diaeters o the speciens in this study were quite sall copared with their length, copressive loads could not be applied due to the risk o the speciens buckling, even at very low load levels. Fully reversed loading cycles can be applied i cylindrical speciens are used, where the specien cannot be too slender to ensure that copressive loads can be applied without buckling. However, cyclic testing o polyers under ully reversed, uniaxial loading conditions is currently not a speciied standard, and in the literature, a variety o cylindrical specien sizes have been used, with dierent geoetries and diensions o gage length. In this study, the diaeter o the polyacetal test speciens was 2. The speciens were prepared using a CNC lathe. As seen in Fig. 1, the gage length o the speciens was 3, and the diaeter o the speciens was 1.1. The geoetry o the used ixture is shown in Fig. 2. The experiental device used in this study was a servo hydraulics INSTRON 882 achine, as shown in Fig Experiental procedure and results 7 6 Fig. 3. Servo hydraulic INTSRON 882 achine. To deterine the echanical properties o polyacetal, siple tension and standard copression tests were perored according to ASTM D638-3 standard test [23]. The obtained results are shown in Figs. 4 and 5, respectively. Table 1 shows the echanical properties o polyacetal obtained ro the experiental tests. All tests were perored in the stress-controlled condition at roo teperature. The loading rate was aintained at 1 MPa/s or each test. So all atigue tests were run at requency less than x = 1 Hz (in the range o Hz). It have been reported that interior teperature o polyeterial would not rise arkedly when the alternation requency was less than or equal to 1 Hz, so the theral eect during the atigue was ignored in the paper [17]. The ean stress and stress aplitude applied in each test is given in Table 2. Also, Table 2, shows the average values o the echanical properties, (ean strain (e avg ), strain aplitude (e avg a ), the dissipation strain energy density (DW d avg aplitude (DW e avg Fig. 1. Specien geoetry. σ (MPa) v =.4 /s v =.4 /s v =.4 /s ε (%) Fig. 4. Stress strain curve o polyacetal under siple tension. ) and the elastic strain energy density )). To investigate the eect o varying the ean stresses (r ) and aplitude stresses ( ), nine tests were perored (GT1 GT9). In groups GT1 GT5, the ean stress was constant, and the stress aplitude was variable. In groups GT6 GT9, the ean stress was variable, and the stress aplitude was constant. Thus, the eects o the loading in each experient could be clearly distinguished. This grouping is given in Table 3. The ollowing sections will explain the quantitative analysis o the echanical paraeters, (stress range, the ean stress and the strain energy density) using the stress strain data.

3 34 M. Shariati et al. / Materials and Design 34 (211) Table 3 Categorize o tests. σ (MPa) v=.4 /s Nuber o group Mean stress Stress aplitude Nuber o tests GT1 Constant Variable T1, T2, T3, T4 GT2 Constant Variable T5, T6, T7, T8 GT3 Constant Variable T9, T1, T11, T12, T13 GT4 Constant Variable T14, T15, T16, T17 GT5 Constant Variable T23, T24, T25 GT6 Variable Constant T5, T1, T14, T18 GT7 Variable Constant T6, T11, T15, T19 GT8 Variable Constant T7, T12, T2, T17 GT9 Variable Constant T22, T21, T8, T ε (%) Fig. 5. Stress strain curve o polyacetal under siple copression. Table 1 Mechanical properties o polyacetal. Mechanical properties Tension Copression Modulus o elasticity (E) 31 MPa 34 MPa Yield stress (r y ) 39.9 MPa MPa Yield strain (e y ) 1.49% 1.37% 3.1. Stress strain hysteresis loops Basic inoration ro the cyclic behavior o a aterial can be obtained ro the hysteresis loops o the stress strain data. Cyclic deoration incurs a hysteresis loop or each cycle o the loading. For exaple, the hysteresis loops ro the stress strain tests, T2, T17 and T23, are shown in Fig. 6, and as can be seen, as the nuber o loading cycles (N) increased, the loop becoes atter. According to the deinition o ratcheting, ratcheting strain occurs when the ean stress is non-zero. However, because the echanical properties o polyacetal vary depending on the tension and the pressure, soe ratcheting strain was seen when the ean stress was zero (Fig. 6-T2), though the strain was uch less than that in the case o the non-zero ean stress Changes in the ratcheting strain The ratcheting strain (e r ) can be obtained ro the increental peak strain o the hysteresis loop ater each cycle (Eq. (1)). de ¼ e peak nþ1 þ epeak n However, the ratcheting strain can deined as the ean strain o each cycle. Eq. (2) is the atheatical expression o this deinition, and in this study, this relationship or the ratcheting strain was used. The ratcheting strain or the GT1 GT9 groups are shown in Fig. 7. e r ¼ 1 2 ðe ax þ e in Þ 3.3. Changes in the strain range Fig. 8 shows the changes in the strain range during the stresscontrolled tests or the constant ean stress and the variable stress aplitude. As seen ro the results, as the nuber o cycles increased, the changes in the strain range increased. Additionally, note that ð1þ ð2þ Table 2 Experiental result. r (MPa) (MPa) e avg (%) e avg a (%) DW d avg (KJ/3 ) DW e avg (KJ/3 ) N T T T T T T T T ,678 T T T T T ,93 T T T T ,96 T T ,488 T ,458 T T T T T ,784

4 M. Shariati et al. / Materials and Design 34 (211) σ (MPa) T 2 N = 1-2 N = 1 N = 7-4 N = 1 N = N σ (MPa) T 17 N = 1 2 N = 1 N = 1 1 N = 7 N = N σ (MPa) N = 1 N = 1 N = 1 N = 4 N = N T ε (%) ε (%) ε (%) Fig. 6. Hysteresis loops o T2, T17, T23. Fig. 7. The ratcheting strain or the GT1 GT9 groups.

5 36 M. Shariati et al. / Materials and Design 34 (211) in the low cycle atigue, the rate o the changes o the strain range was greater than the strain range changes in the high cycle atigue. However, in the experients with the variable stress aplitude and the constant ean stress, the aplitude o the applied stress on a specien was larger, and the rate o the strain range changes was larges well. Siilarly, or the experients with the constant stress aplitude and the variable ean stress, the applied ean stress on the specien was larger, and the rate o the strain range was larger (Fig. 8) Changes in the strain energy In the atigue ield, two types o strain energy density are discussed. One type is called the dissipation strain energy density, DSED or DW d, and the other is called the elastic strain energy density aplitude, ESEDA or DW e [13]. Based on the obtained stress strain and hysteresis loops data, DW d and DW e can be calculated by integrating the corresponding areas, as shown in Fig. 9. Both types o strain energy were calculated. According to Fig. 1, it is clear that oll the experiental groups (GT2 GT9), the DSED value decreased initially and then increased. As seen in the GT1 group test, where the ean stress was zero, the dissipation strain energy density either reained constant or increased. Any applied stress aplitude in the case o the zero ean stress was less steep, where the dissipation strain energy density increased less; so that in test T4, the rate o the change in the strain energy density reached zero. An interesting point is that in the case o the non-zero ean stress and or each stress range value, the rate o change in the Fig. 8. The changes in the strain range or the GT1 GT9 groups.

6 M. Shariati et al. / Materials and Design 34 (211) on the daage paraeter selected, which could be a unction o the stress, strain or strain energy, the atigue analysis can be analyzed with either the stress, strain or energy. Each o the aoreentioned approaches and their ethod o analyzing the atigue lie o polyacetal under stress-controlled tests will be explained Fatigue based on the stress approach Fro Re. [28], a siple power law unction or the ean stress can be expressed as ollows: n ¼ ð4þ r 1 þ g r where n and g are aterial constants. It will be assued that the ean stress is a unction o the equivalent stress, r eq. dissipation strain energy density was initially negative, then zero and, inally, positive. Fig. 11 illustrates the elastic strain energy density aplitude. As seen, the rate o change in the elastic strain energy density range was positive, but its behavior was very irregular Slope changes in the hysteresis loops In this section, the paraeter that was introduced in Re. [17] is considered. This paraeter, the hysteresis loop slope (E), is the gradient o the line that connects the extree points o the hysteresis loops together. Fig. 12 shows this paraeter sybolically. Fro Fig. 13, it can be seen that the rates o the change in the slope o the hysteresis loops or the GT1 GT5 groups were always negative; however, the range o the applied stress on the specien was greater, where the gradient lessened and decreased signiicantly. In the GT6 GT9 tests, where the stress aplitude and the ean stress were variable, increasing the applied stress on the specien resulted in the hysteresis loop gradient being low, and the rate o changes o the hysteresis loops gradient increased. 4. Fatigue Experiental atigue tests were grouped into two categories: stress-controlled and strain-controlled atigue experients. I the aterial behaved elastically, the results o these tests were equivalent to each other; however, i the aterial behaved in the elastic plastic range, the results were quite dierent ro each other. In the stress-controlled experients, the ean stress could lead to an accuulation o plastic strain in each cycle, which is called the ratcheting strain. Ratcheting strain can cause ore daage and shorten the atigue lie. In the strain-controlled experients, in the early stages, the ean stress relaxation occurred and thus, thereore reduced the ean stress eects on the atigue lie. In general, the theories or the atigue lie o structures, depending on their vision, can be divided in three categories: atigue based on stress, atigue based on strain and atigue based on energy [27]. In each o the three approaches, the relationship between the aount o daage and the general atigue lie is generally expressed using the ollowing orula: w ¼ j:ðn Þ c þ w Fig. 9. Coponents o strain energy density [13]. where w is the daage paraeter, N is the atigue lie, j, c are aterial constants and w is the atigue liit. However, depending ð3þ nra r eq ¼ ð5þ 1 þ g r It should be noted that in ully reversed experients, where r =, Eq. (5) converts r eq = r 1, where the 1 represents the ully reversed test. Thus, in the ully reversed tests, the equivalent stress is the aplitude stress. Replacing r 1 with r eq, Eq. (5) becoes the ollowing: 1 þ g ðr n =r 1 Þ ¼ 1 ð6þ ð =r 1 Þ r 1 The relations, /r 1 and r /r 1, were plotted using dierent aterial constants in Fig. 14. For the liiting case, when /r 1?, we can see that or n >1, r /r 1?, and or <n < 1, then r /r 1? 1. Neither o these two behaviors are physically eaningul because when the stress aplitude,,is zero, the loading is in the static condition, and the ean stress, r, should be related to the static echanical properties o the aterials, where r /r 1 should approach zero. Thereore, in this study, only the value n = 1 was considered [12]. Accordingly, Eq. (6) becoes Eq. (7). þ g r ¼ 1 ð7þ r 1 r 1 Eq. (7) can be written as Eq. (8), where r r = r 1 /g is a reerence stress. þ g r ¼ 1 ð8þ r 1 r 1 The ter, r r, in the Soderberg orula is the yield stress, r y,in the Goodan relation is the ultiate strength, r u and in the orrow s orula is the atigue strength coeicient. Based on the suggestion ro Zihui Xia and Gang Tao, or polyeric aterials, r r should be a unction o r 1 [12]. In our case, g was taken to be an iplicit constant, and we assued that r r was a linear unction o r 1. Generally, based on Eq. (3), we can conside relationship between the equivalent stress, r 1, and the atigue lie as ollowing a power law equation [12]: r eq ¼ j:n c þ r As entioned beore, i testing was perored copletely ully reversed, then r eq = r 1 =. Thus, Eq. (9) can be written as r eq ¼ ¼ j:n c þ r. By itting a curve, we can ind the values o j, c, r. Then Eq. (9) becoes Eq. (1). r eq ¼ 13:7N :461 þ 4:93 ð1þ Ater deterining the coeicients, j, c, r, or the tests, where there is non-zero ean stress, the atigue lie can be placed on the right side o Eq. (1), and the equivalent stress can be deterined. Now, ro Eq. (5), we have the ollowing: ð9þ

7 38 M. Shariati et al. / Materials and Design 34 (211) Fig. 1. The change in the dissipation strain energy density. ¼ 1 ð11þ r eq r ra According to the aoreentioned discussions, we have the ollowing: r r eq ¼ ¼ 1 þ g r Cobining Eqs. (11) and (12) results in, Eq. (13). 1 þ g r ð12þ ð13þ By itting a curve ro the data to r eq / vs. r /, as seen in Fig. 15, g was deterined to be.655. Thereore, predicting the atigue lie o the polyacetal using a stress-controlled approach can be deterined using Eq. (14). 1 þ :655 r r r a ¼ 13:7N :461 þ 4:93 ð14þ a This equation and the experiental test results are shown in Fig Fatigue based on the strain approach Anothepproach to analyze the atigue lie is the strain approach, which predicts the equivalent strain using the ollowing equation: e eq ¼ 1 þ g e e a ð15þ ea during the stress-controlled tests, the ean strain and the strain aplitude values are not constant. Here, the ean strain is the ratcheting strain and is variable. Thus, in this study, the average values o the ean strain and strain aplitude are used or the atigue

8 M. Shariati et al. / Materials and Design 34 (211) Fig. 11. The change in the elastic strain energy density aplitude. or the GT1 test group, e is not zero because. copared with the other test groups, e is negligible or the GTI test group. Thus, in this study, e was zero. The reason or the non-zero value o e or the ully reversed tests is due to the non-linear behavior between the stress and the strain o polyacetal and also because o the non-syetric tensile and copression loading behaviors. To study the atigue ro the perspective o the strain, we can consider the ollowing equation or the equivalent strain: e eq ¼ e 1 ¼ j:n c þ e ð16þ By itting a curve to the data points ro the GTI test group, Eq. (16) is converted to Eq. (17). Fig. 12. The hysteresis loop slope [17]. calculations. Also according to Eq. (15), or the ully reversed tests (GTI test group), the value, e, ust equal zero until e eq = e a, whereas e eq ¼ 9:921N :421 þ 1:7 ð17þ Thereore, the obtained values o the j, c, e paraeters were 9.921,.421, and 1.7, respectively. Now, using Eq. (17) and placing the atigue lie o each test instead on the right side o this equation, we can calculate e eq.

9 31 M. Shariati et al. / Materials and Design 34 (211) Fig. 13. The change in the slope o the hysteresis loops. 2.4 σ eq /σ Curve Fitting σ /σ a Fig. 14. Function o ean stress with dierent aterial constants [13]. Fig. 15. Function o ean stress based on the stress approach.

10 M. Shariati et al. / Materials and Design 34 (211) Equivalent Stress Aplitde (MPa) Lie (Cycle) Fitting Curve Equivalent Strain Aplitude (%) Lie (Cycle) Curve Fitting Fig. 16. Equivalent stress aplitude vs. atigue lie. Fig. 18. Equivalent strain aplitude vs. atigue lie. e ea ¼ 1 þ g e ea ð18þ By calculating e eq and plotting the e eq /e a vs. e /e a, Fig. 17 shows the itted line as described by Eq. (18), where g was deterined to be.143. Using the deterined g and Eq. (15), we once again calculate e eq, where the results vs. the atigue lie o each experient are shown in Fig. 18. Thus, the relationship between the atigue lie o the stress- controlled tests using the strain approach was achieved. 1 þ :143 e e a ¼ 9:921N :421 þ 1:7 ð19þ ea 4.3. Fatigue based on the energy approach (Δ W eq - Δ W d avg )/ Δ W e avg 5 4 Curve Fitting σ /σ a The strain energy approach is dierent ro the previous two approaches because beore, the stress or strain approach calculations were based on only one quantity. For exaple, in the stress approach, the calculations were based on only the stress value, and the strain values did not aect the results. This approach is appropriate when the aterials exhibit linear stress strain behavior (like etals); however, when the stress strain behavior is nonlinear, such as with polyeric aterials, ore than one quantity is needed, so the energy approach is superior than the other two approaches because both the stress and the strain quantities are used in the calculations. Using the energy approach, the ean stress unction can be written as Eq. (2). Siilar to the previous two stress and strain approaches, a relationship or the total energy associated with the atigue lie can be obtained (Eq. (21)). 2 Total Strain Energy Density (KJ/ 3 ) Fig. 19. Function o ean stress based on the energy approach Lie (Cycle) Curve Fitting Fig. 2. Total strain energy density vs. atigue lie. ε eq /ε a Curve Fitting DW eq DW d avg ¼ 1 þ g r DW e avg DW eq ¼ DW d 1avg þ DWe 1avg ¼ j:nc þ DW ð2þ ð21þ ε /ε a Fig. 17. Function o ean strain based on the strain approach. Using the results ro the ully reversed tests and Eq. (21), a curve can be itted to the data points ro the tests. Thus, the unknown coeicients o Eq. (21) can be obtained. Thereore, the equation is as ollows: DW eq ¼ 3135N :747 þ 438 ð22þ

11 312 M. Shariati et al. / Materials and Design 34 (211) Now, using the relations in Eq. (22), the values o DW eq can be calculated or each test, where Fig. 19 shows the plot, ðdw eq DW d avg Þ=DWd avg vs. r /. By itting a line ro the points, g, as deined in Eq. (21), was deterined to be Using g and Eq. (2), the values o DW eq were calculated, and Fig. 2 shows the draw vs. atigue lie. By coparing the predicted results with the obtained results ro the stress, strain and energy approaches, it is clear that the energy and stress approaches perored better than the strain approach. 5. Conclusions In this study, stress-controlled tests on polyacetal were perored at laboratory abient teperature, where dierent cobinations o the ean stress and stress aplitude were used. Mechanical paraeters, such as the strain range, the ratcheting strain, the slope o the hysteresis loops and the strain energy density, were investigated. The ollowing results were obtained ro this study. (1) By reducing the applied stress aplitude and the constant ean stress, the ratcheting strain rate decreased. (2) By reducing the applied ean stress and the constant stress aplitude, the ratcheting strain rate decreased. (3) Generally, reducing the stress aplitude and the ean stress constant resulted in the ratcheting strain decreasing. (4) Generally, reducing the ean stress with constant stress aplitude resulted in the ratcheting strain decreasing. (5) The stress and energy approaches were ore successul in predicting the atigue lie o polyacetal. Reerences [1] Kang G. Ratchetting: recent progresses in phenoenon observation, constitutive odeling and application. Int J Fatigue 28;3: [2] Li C-B, Ki KS, Seong JB. Ratcheting and atigue behavior o a coppelloy under uniaxial cyclic loading with ean stress. Int J Fatigue 29;31:51 7. [3] Yang X. Low cycle atigue and cyclic stress ratcheting ailure behavior o carbon steel 45 under uniaxial cyclic loading. Int J Fatigue 25;27: [4] Kang G, Liu Y, Li Zh. Experiental study on ratchetting-atigue interaction o SS34 stainless steel in uniaxial cyclic stressing. Mater Sci Eng A 26; : [5] Nip KH, Gardner L, Davies CM, Elghazouli AY. Extreely low cycle atigue tests on structural carbon steel and stainless steel. J Constr Steel Res 21;66: [6] Gao H, Chen X. Eect o axial ratcheting deoration on torsional low cycle atigue lie o lead-ree solder Sn 3.5Ag. Int J Fatigue 29;31: [7] Chen G, Shan S-C, Chen X, Yuan H. Ratcheting and atigue properties o the high-nitrogen steel X13CrMnMoN under cyclic loading. Coput Mater Sci 29;46: [8] Chen X, Yu D-H, Ki KS. Experiental study on ratcheting behavior o eutectic tin lead solder under ultiaxial loading. Mater Sci Eng A 25;46: [9] Kang G. A visco-plastic constitutive odel or ratcheting o cyclically stable aterials and its inite eleent ipleentation. Mech Mater 24;36: [1] Chen X, Jiao R, Ki KS. On the Ohno Wang kineatic hardening rules or ultiaxial ratcheting odeling o ediu carbon steel. Int J Plast 25;21: [11] Colak OU. Kineatic hardening rules or odeling uniaxial and ultiaxial ratcheting. Mater Des 28;29: [12] Abdel-Kari M. Modiied kineatic hardening rules or siulations o ratchetting. Int J Plast 29;25: [13] Tao G, Xia Z. Mean stress/strain eect on atigue behavior o an epoxy resin. Int J Fatigue 27;29: [14] Tao G, Xia Z. Ratcheting behavior o an epoxy polyend its eect on atigue lie. Poly 27;26: [15] Chen X, Hui S. Ratcheting behavior o PTFE under cyclic copression. Poly 25;24: [16] Zhang Z, Chen X. Multiaxial ratcheting behavior o PTFE at roo teperature. Poly 29;28: [17] Liu W, Gao Z, Yue Z. Steady ratcheting strains accuulation in varying teperature atigue tests o PMMA. Mater Sci Eng A 28;492:12 9. [18] Bles G, Gadaj SP, Nowacki WK, Tourabi A. Experiental study o a PA66 solid polyer in the case o cyclic shear loading. Arch Mech 22;54: [19] Avanzini A. Mechanical characterization and inite eleent odelling o cyclic stress strain behaviour o ultrahigh olecular weight polyethylene. Mater Des 28;29: [2] Rakuar A, Gnanaoorthy R. Axial atigue behaviour o polyaide-6 and polyaide-6 nanocoposites at roo teperature. Copos Sci Technol 28;68: [21] Mallick PK, Zhou Y. Eect o ean stress on the stress-controlled atigue o a short E-glass iber reinorced polyaide-6,6. Int J Fatigue 24;26: [22] Tao G, Xia Z. Biaxial atigue behavior o an epoxy polyer with ean stress eect. Int J Fatigue 29;31: [23] ASTM D Aerican society or testing aterials. Standard test ethod or tensile properties o plastics. Philadelphia, USA; 24. [24] NF EN ISO International organization or standardization, plastics. Deterination o tensile properties. Geneva, Switzerland; [25] Meyer RW, Pruitt LA. The eect o cyclic true strain on the orphology, structure, and relaxation behavior o ultrahigh olecular weight polyethylene. Polyer 21;42: [26] Niinoi M, Wang L, Enjitsu T, Fukunaga K. Fatigue characteristics o ultrahigh olecular weight polyethylene with dierent olecular weight or iplant aterial. J Mater Sci Mater Med 21;12: [27] Urries I, Medel FJ, Rıos R, Goez-Barrena E, Puertolas JA. Coparative cyclic stress strain and atigue resistance behavior o electron-bea- and gaairradiated ultrahigh olecular weight polyethylene. J Bioed Mater Res Part B Appl Bioater 24;7B: [28] Kujawski D, Ellyin F. A uniied approach to ean stress eect on atigue threshold conditions. Int J Fatigue 1995;17:11 6.