MD Nellie Della Schiava
email: dellaschiava.nellie@neuf.fr

MD Iris Naudin

MD Marine Bordet
email: marine.bordet@chu-lyon.fr

MD Matthieu Arsicot
email: matthieu.arsicot@chu-lyon.fr

MD Philippe Tresson
email: philippe.tresson@chu-lyon.f

MD Joris Giai
email: joris.giai@chu-lyon.fr

MD Jérémy Charles
email: jeremy_charles@orange.fr

MD Philip Robinson
email: philip.robinson@chu-lyon.fr

MD Patrick Lermusiaux

MD-PhD Antoine Millon
email: antoine.millon@chu-lyon.fr

Analysis of Preoperative CT Scan Can Help Predict Technical Failure of Endovascular Treatment of TASC C-D Aortoiliac Chronic Total Occlusions

Keywords: TASC C-D, aortoiliac chronic total occlusions, predictors, iliac rupture, technical failure Conflicts TASC C-D, aortoiliac chronic total occlusions, predictors, iliac rupture, technical failure

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Despite TASC II recommendations, [START_REF] Adam | TASC II document on the management of peripheral arterial disease[END_REF] and because of good outcomes in several large studies, [START_REF] Kasemi | Seven-year approach evolution of the aortoiliac occlusive disease endovascular treatment[END_REF][START_REF] Aihara | Long-term outcomes of endovascular therapy for aortoiliac bifurcation lesions in the real-AI registry[END_REF][START_REF] Suzuki | Efficacy and Safety of Endovascular Therapy for Aortoiliac TASC D Lesions[END_REF][START_REF] Kashyap | The management of severe aortoiliac occlusive disease: endovascular therapy rivals open reconstruction[END_REF] endovascular treatment is now the first choice for complex aorto-iliac occlusions in high-volume centers with high technical success (> 90 %) and very low major peroperative complications including iliac rupture (< 5 %). [START_REF] Clair | Strategies for managing aortoiliac occlusions: access, treatment and outcomes[END_REF][START_REF] Kashyap | The management of severe aortoiliac occlusive disease: endovascular therapy rivals open reconstruction[END_REF][START_REF] Moise | Treatment of Aortoiliac Occlusive Disease: Medical versus Endovascular versus Surgical Therapy[END_REF] But the risk of technical failure and the fear of per-operative iliac rupture, especially in heavily calcified lesions limit the widespread use of this technique. Predictors of failure have been studied for patency and clinical outcomes for TASC C-D aorto-iliac occlusions. [START_REF] Yacyshyn | Predictors of failure of endovascular therapy for peripheral arterial disease[END_REF][START_REF] Kavaliauskienė | Factors affecting primary patency of stenting for TransAtlantic Inter-Society (TASC II) type B, C, and D iliac occlusive disease[END_REF][START_REF] García-Fernández | Chronic infrarenal aortic occlusion: predictors of surgical outcome in patients undergoing aortobifemoral bypass reconstruction[END_REF] To the best of our knowledge, anatomic risks factor for technical failure or per-operative rupture have been studied for superficial femoral and popliteal arteries and for coronary disease but not for aortoiliac arteries. [START_REF] Itoga | Lower extremity computed tomography angiography can help predict technical success of endovascular revascularization in the superficial femoral and popliteal artery[END_REF] Oddly, predictors of technical failure and per-operative complications have been studied recently for transbrachial or transradial accesses but not for femoral accesses. [START_REF] Roy | Comparison of Transradial vs Transfemoral Access for Aortoiliac and Femoropopliteal Interventions: A Single-Center Experience[END_REF][START_REF] Antov | Transradial approach as first choice for stenting of chronic total occlusion of iliac and femoral superficial artery. Pril Makedon Akad Na[END_REF] Yet, for the endovascular treatment of aorto-iliac TASC C-D chronic total occlusion (CTO), transbrachial access alone cannot be sufficient because of the diameter of the stent used, the necessity of kissing stent. Moreover, contrary to coronary occlusive disease, [START_REF] Sianos | The SYNTAX Score: an angiographic tool grading the complexity of coronary artery disease[END_REF][START_REF] Hamburger | Recanalization of total coronary occlusions using a laser guidewire (the European TOTAL Surveillance Study)[END_REF][START_REF] Leaman | Coronary artery atherosclerosis: severity of the disease, severity of angina pectoris and compromised left ventricular function[END_REF][START_REF] Ryan | Guidelines for percutaneous transluminal coronary angioplasty. A report of the American College of Cardiology/American Heart Association Task Force on Assessment of Diagnostic and Therapeutic Cardiovascular Procedures (Subcommittee on Percutaneous Transluminal Coronary Angioplasty)[END_REF] for peripheral arterial disease there is no precise score analyzing the complexity of lesions. Most technical failures are associated with failure to cross the occlusion or for re-entry in the arterial lumen. In the TASC II classification, [START_REF] Adam | TASC II document on the management of peripheral arterial disease[END_REF] diffuse multiple stenosis in the iliac artery is TASC D whereas short occlusion of external iliac artery (EIA) is TASC B. For endovascular treatment, the short occlusion of EIA is more technically difficult. Moreover, this classification does not take into account the degree of calcifications of aorto-iliac lesions. Thus, this classification seems relatively unsuitable to select between open surgical repair and endovascular treatment as highlighted by Ohana et al. in 2013 for superficial femoral artery occlusions. [START_REF] Ohana | Detailed cross-sectional study of 60 superficial femoral artery occlusions: morphological quantitative analysis can lead to a new classification[END_REF] Moreover, as was well demonstrated for coronary disease, [START_REF] Ryan | Guidelines for percutaneous transluminal coronary angioplasty. A report of the American College of Cardiology/American Heart Association Task Force on Assessment of Diagnostic and Therapeutic Cardiovascular Procedures (Subcommittee on Percutaneous Transluminal Coronary Angioplasty)[END_REF] comparison between open surgery and endovascular treatment of aorto-iliac occlusive disease is also difficult because patients included can be relatively different (TASC D lesions are very heterogeneous), [START_REF] Adam | TASC II document on the management of peripheral arterial disease[END_REF] and series are heterogeneous including stenosis and occlusions, including femoro-popliteal segments. [START_REF] Kasemi | Seven-year approach evolution of the aortoiliac occlusive disease endovascular treatment[END_REF][START_REF] Clair | Strategies for managing aortoiliac occlusions: access, treatment and outcomes[END_REF][START_REF] Moise | Treatment of Aortoiliac Occlusive Disease: Medical versus Endovascular versus Surgical Therapy[END_REF] Technical success is very high (> 90 %) but for chronic total occlusion (CTO), failure persists despite the use of re-entry devices and antegrade approach. [START_REF] Ryan | Guidelines for percutaneous transluminal coronary angioplasty. A report of the American College of Cardiology/American Heart Association Task Force on Assessment of Diagnostic and Therapeutic Cardiovascular Procedures (Subcommittee on Percutaneous Transluminal Coronary Angioplasty)[END_REF][START_REF] Ohana | Detailed cross-sectional study of 60 superficial femoral artery occlusions: morphological quantitative analysis can lead to a new classification[END_REF][START_REF] Kitrou | Targeted True Lumen Re-Entry With the Outback Catheter: Accuracy, Success, and Complications in 100 Peripheral Chronic Total Occlusions and Systematic Review of the Literature[END_REF][START_REF] Varcoe | Endovascular reconstruction of the occluded aortoiliac segment using « double-barrel » self-expanding stents and selective use of the Outback LTD catheter[END_REF][START_REF] Millon | The Antegrade Approach Using Transbrachial Access Improves Technical Success Rate of Endovascular Recanalization of TASC C-D Aortoiliac Occlusion in Case of Failed Femoral Access[END_REF] Even if it is thought that heavily calcified lesions are more at risk for this complication, this has never been clearly defined. [START_REF] Clair | Strategies for managing aortoiliac occlusions: access, treatment and outcomes[END_REF] The aim of this study was to evaluate anatomic predictors of technical failure and peroperative iliac rupture of endovascular treatment of TASC C-D aorto-iliac CTO with a detailed analysis of pre-operative CT-scan.

MATERIALS AND METHODS

STUDY DESIGN AND PATIENT SAMPLE

This is a single-center retrospective analysis of a prospective cohort. All patients treated in our department by endovascular techniques for an aorto-iliac CTO TASC C-D between December 2009 and June 2016 were analyzed. Patients with no pre-operative CT-scan, with stenosis and no CTO and with an acute or subacute ischemia were excluded. We included 148 iliac arteries from 107 patients. All CT-scan were analyzed by 2 surgeons independently (NDS and AM); in case of discordance, the CT-scan was reviewed jointly. Mean age was 62 years (SD 51-73). The indication for treatment was claudication in 104 limbs (70,3 %), rest pain in 28 limbs (18,9 %) and tissue loss in 16 limbs (10,8 %). Patients were TASC C in 32 cases and TASC D in 75 cases. Baseline patient characteristics are given in Table I. Detailed lesions are described in Table II.

The study has been performed according to the principles of the Declaration of Helsinki and approval has been obtained from ethic committee of the hospital.

CTO EVALUATION

We analyzed 2 characteristics of CTO: the location and the extension of the CTO on the aorta or iliac artery and the degree of calcifications of the aorta and iliac arteries (Figure 1). For this characteristics, we divided CTO into 3 groups: the black occlusion group (BO) was defined by the presence of mild non-protrusive calcifications or the complete absence of calcifications in the total lesion length; the white occlusion group (WO) was defined by moderate calcifications of more of 50 % of the arterial circumference but little or no protrusive into the arterial lumen; the white protrusive occlusion group (WPO) was defined by the presence of heavy endoluminal arterial calcifications of more of 50 % of the arterial lumen.

Each iliac artery was analyzed separately.

ENDOVASCULAR PROCEDURE

The procedures were performed by a team of experienced vascular surgeons in a surgical theater using a recent generation mobile C-arm. A detailed description of our technique has been previously published. [START_REF] Millon | The Antegrade Approach Using Transbrachial Access Improves Technical Success Rate of Endovascular Recanalization of TASC C-D Aortoiliac Occlusion in Case of Failed Femoral Access[END_REF] For external iliac artery (EIA) occlusions that involve the common femoral artery (CFA), a superficial femoral puncture was performed if possible; if not, an antegrade approach using the contralateral femoral access was used. [START_REF] Thiney | Angioplasty of the common femoral artery and its bifurcation[END_REF] CFA lesions were treated as described in the TECCO study. [START_REF] Gouëffic | Stenting or surgery for de novo common femoral artery stenosis[END_REF] In case of failure by a retrograde approach, all patients had an antegrade approach by contralateral femoral access or by the brachial access. No re-entry device was used.

ENDPOINTS

The primary endpoint was the technical failure rate defined by the impossibility to cross the lesion or to re-entry in the true lumen. Secondary endpoint was the per-operative iliac rupture rate defined by an extravasation of contrast agent in angiogram. For these two endpoints, each iliac artery was analyzed separately.

STATISTICAL ANALYSIS

Means with standard deviations were presented for continuous data and counts with percentages for categorical data. Groups were compared using Fisher's exact or Wilcoxon test as appropriate. Univariate and multivariate logistic regression models were performed to identify separately any independent predictors of technical failure and per-operative iliac rupture. Values of p < 0.05 were considered statistically significant. All analyses were performed using R Core Team Software (version 3.1.0, R Foundation for statistical computing, Vienne, Austria)

RESULTS

Occlusions were located in the external iliac artery (EIA) in 37 cases (25 %), in the common iliac artery (CIA) in 41 cases (27.7 %), in both the external and the common iliac artery (BIA) in 42 cases (28.4 %), and in the on aortic bifurcation (AB) in 14 cases (18.9 %). There were 66 iliac arteries (44.6 %) in the BO group, 45 (30.4 %) in the WO group and 37 (25 %) in the WPO group. In 70 patients and 83 iliac arteries (56.1 % of the total number of cases), an antegrade access was attempted because of failure of the retrograde access, including 58 brachial accesses (39.2 %). For 93 iliac arteries (62.8 %), recanalization were subintimal. The interpretation of CT-scan were concordant between the 2 surgeons in 90 % of cases.

TECHNICAL FAILURE

Technical failure occurred in 11 iliac arteries (7.4 % of cases). Technical failures were impossibility to reentry in all the cases despite the use of antegrade and retrograde approach.

Cases with technical failure were comparable to those without with regard to all baseline characteristics. Technical failure differed according to CTO location (p = 0.001), it was more frequent when CTO was located in the EIA (p= 0.001), and less frequent when CTO was located in CIA (p = 0.035;Table III)

In univariate analysis, the location of the CTO in the EIA was the only factor significantly associated with technical failure (OR = 9.93; p = 0.0012; Table III). In multivariate analysis, after adjustment on age and renal failure, the location of the occlusion on EIA was also significantly and strongly associated with technical failure (OR = 15.26; p= 0.0006). The presence of heavy endoluminal calcifications (WPO group) was a further risk factor of technical failure in comparison with the WO group (OR = 13.88; p = 0.0365; Table IV).

PER-OPERATIVE ILIAC RUPTURE

Per-operative iliac rupture occurred in 6 iliac arteries (4 %). Four ruptures were successfully treated with a cover stent; the 2 other ruptures led to the death of the patient.

There was no risk factor significantly associated with per-operative iliac rupture in univariate model (Table V). There were 3 per-operative iliac ruptures in the BO group, 2 in the WO group and 1 in the WOP group (p = 0.881). The occlusion of both the external and the common iliac artery was more frequently found in the per-operative iliac rupture group, although this difference was not significant (p = 0.282).

DISCUSSION

To the best of our knowledge, this is the first study to analyze specifically anatomic predictors of technical failure and per-operative iliac rupture of endovascular treatment of TASC C-D aorto-iliac CTO. The main risk factor for technical failure identified by this study was the location of the CTO in the EIA. This can be explained by occlusive disease that can extend into the common femoral artery (CFA). In such cases, the arterial access is difficult. Superficial femoral artery puncture could be necessary and the proximity of the CTO leads to a lack of "push". For these cases, the antegrad approach seems really indispensable for us. We make this antegrade approach for all cases, we don't try retrograde recanalization. But for the antegrade approach, the necessity of re-entry in CFA or more distal artery can be difficult and controversial. However, we have previously published good results for stenting of CFA and its bifurcation [START_REF] Thiney | Angioplasty of the common femoral artery and its bifurcation[END_REF] and these results were confirmed by a recent multicenter randomized study. [START_REF] Gouëffic | Stenting or surgery for de novo common femoral artery stenosis[END_REF] If there is an appropriate landing zone in the CFA, results are good but if there is lesions of the bifurcation, it will be more complicated and results are worse. For these cases, hybrid surgery seems to be very interesting. Moreover, it appears important to obtain good results to use large diameter of stents in iliac arteries. If the CFA is of good diameter and with no important lesion, there is no problem but in the contrary, there is a risk of incomplete opening of the distal stent or even a risk of rupture of the CFA. So for all these reasons, hybrid surgery can be used with acceptable midterm results. [START_REF] Maitrias | Iliofemoral endarterectomy associated with systematic iliac stent grafting for the treatment of severe iliofemoral occlusive disease[END_REF] The study shows that the degree of calcifications, especially endoluminal calcifications, is associated with technical failure. In many series, CTO and heavy calcified lesions are excluded. [START_REF] Cortese | Safety and feasibility of iliac endovascular interventions with a radial approach. Results from a multicenter study coordinated by the Italian Radial Force[END_REF][START_REF] Rocha-Singh | Peripheral arterial calcification: prevalence, mechanism, detection, and clinical implications[END_REF] However, because most technical failures result in the impossibility to cross the lesions or for re-entry in the true lumen, the degree of arterial calcifications is cited as a risk factor for technical failure in several studies but is not scientifically proven. [START_REF] Clair | Strategies for managing aortoiliac occlusions: access, treatment and outcomes[END_REF][START_REF] Roy | Comparison of Transradial vs Transfemoral Access for Aortoiliac and Femoropopliteal Interventions: A Single-Center Experience[END_REF][START_REF] Kitrou | Targeted True Lumen Re-Entry With the Outback Catheter: Accuracy, Success, and Complications in 100 Peripheral Chronic Total Occlusions and Systematic Review of the Literature[END_REF][START_REF] Cortese | Safety and feasibility of iliac endovascular interventions with a radial approach. Results from a multicenter study coordinated by the Italian Radial Force[END_REF] A similar situation is found for per-operative iliac rupture. [START_REF] Clair | Strategies for managing aortoiliac occlusions: access, treatment and outcomes[END_REF][START_REF] Moise | Treatment of Aortoiliac Occlusive Disease: Medical versus Endovascular versus Surgical Therapy[END_REF] Despite vascular calcifications having been extensively studied, [START_REF] Rocha-Singh | Peripheral arterial calcification: prevalence, mechanism, detection, and clinical implications[END_REF][START_REF] Giachelli | Vascular calcification mechanisms[END_REF] their clinical implications for aortoiliac CTO remain unknown. For coronary occlusive disease, several risk scores have been published. [START_REF] Sianos | The SYNTAX Score: an angiographic tool grading the complexity of coronary artery disease[END_REF][START_REF] Hamburger | Recanalization of total coronary occlusions using a laser guidewire (the European TOTAL Surveillance Study)[END_REF][START_REF] Leaman | Coronary artery atherosclerosis: severity of the disease, severity of angina pectoris and compromised left ventricular function[END_REF] However, for peripheral arterial disease, the characterization of lesions is less well defined. 2015, Peripheral Academic Research Consortium (PARC) published a semi-quantitative classification but endoluminal calcifications were not studied. [START_REF] Patel | Evaluation and treatment of patients with lower extremity peripheral artery disease: consensus definitions from Peripheral Academic Research Consortium (PARC)[END_REF] For our statistical analysis about the role of calcifications, we decide to adjust on age and renal failure because these criteria have been described as risk factor of calcifications. [START_REF] Mizobuchi | Vascular calcification: the killer of patients with chronic kidney disease[END_REF] We don't adjust on diabetes because for diabetes, calcifications concern more infra-inguinal disease. [START_REF] Marso | Peripheral arterial disease in patients with diabetes[END_REF] An interesting aside is that in the present study that included complex lesions, technical success was high despite re-entry devices not being used. We believe that such devices are interesting but relatively dangerous in case of re-entry in the abdominal aorta. The complication rate is about 4.3 % while lesions treated are less severe and mostly infrainguinal lesions. [START_REF] Kitrou | Targeted True Lumen Re-Entry With the Outback Catheter: Accuracy, Success, and Complications in 100 Peripheral Chronic Total Occlusions and Systematic Review of the Literature[END_REF][START_REF] Varcoe | Endovascular reconstruction of the occluded aortoiliac segment using « double-barrel » self-expanding stents and selective use of the Outback LTD catheter[END_REF] Moreover, in a recent large study, technical success with the use of reentry device was similar to that reported herein. [START_REF] Kitrou | Targeted True Lumen Re-Entry With the Outback Catheter: Accuracy, Success, and Complications in 100 Peripheral Chronic Total Occlusions and Systematic Review of the Literature[END_REF] Heavy calcifications remains risk factor for technical failure despite the use of these devices. [START_REF] Kitrou | Targeted True Lumen Re-Entry With the Outback Catheter: Accuracy, Success, and Complications in 100 Peripheral Chronic Total Occlusions and Systematic Review of the Literature[END_REF][START_REF] Varcoe | Endovascular reconstruction of the occluded aortoiliac segment using « double-barrel » self-expanding stents and selective use of the Outback LTD catheter[END_REF] In our experience, the main trick to obtain good technical success is to try to make intraluminal recanalization. Indeed, the main explanation for failure is the impossibility to reentry, particularly in the aorta. To make intraluminal recanalization, we use a straight and rigid catheter immediately to prevent the guidewire from leaving the wall. We direct the guide with the catheter to progress in the lumen. But in some cases, the occlusion is too hard and the intraluminal crossing impossible. In such cases, the other trick to obtain technical success, is to rapidly use antegrad approach. In the beginning of our experience, we try with a retrograde approach for a long time. Actually, we try few minutes and rapidly we make the antegrad approach. For all these procedures, we install the patient with an upper arm (generally the left) in the surgical field as well as the 2 femoral accesses. If cross over is possible, we try and if not we use the brachial access.

For per-operative iliac rupture, we did not identify risk factors. Per-operative iliac rupture occurred similarly in the 3 CTO groups, which may suggest that heavily calcified lesions should not be specifically excluded from endovascular treatment on the basis of this criterion alone, but requires further investigation in large multicenter international studies.

LIMITATIONS

A general limitation of the study is that it was based on a single center. However, the cohort was prospective, and this design ensured exhaustive recruitment leading to a homogeneous and well defined population, but which was relatively small. This did not adversely affect the evaluation of technical success, but precluded meaningful conclusions as to iliac rupture.

Another aspect to consider is the semi-quantitative evaluation of arterial calcifications used herein. With specific 3D-reconstruction imaging software, quantitative analysis of arterial calcifications is possible but such software is not widely available to the vast majority of surgical teams. Although semi-quantitative, this classification is more precise than that described in guidelines published by Diehm et al. in 2008. [START_REF] Diehm | Clinical endpoints in peripheral endovascular revascularization trials: a case for standardized definitions[END_REF] This is more similar of a further classification, published recently by the Peripheral Academic Research Consortium (PARC) with more the analysis of endoluminal calcifications. [START_REF] Patel | Evaluation and treatment of patients with lower extremity peripheral artery disease: consensus definitions from Peripheral Academic Research Consortium (PARC)[END_REF] Another point to note is that we did not analyze specifically the length of lesions as a risk factor for technical failure, however among the 11 such cases in the present study, there were 3 BIA occlusions but 8 EIA occlusions, which suggests that longer lesions were not more technically difficult. Furthermore, the diameter of the vessel was not considered, but it is reported that in case of CTO this can be underestimated with pseudostenosis and lead to biased interpretation. [START_REF] Park | Pseudostenosis of the External Iliac Artery after Common Iliac Artery Occlusion: 2 Case Reports[END_REF] Moreover, recanalization are often subintimal so arteriel diameter can't really affect technical failure.

Finally, as the event rate is too low, it is impossible to generate a robust model.

CONCLUSION

This study shows anatomic predictors of technical failure of endovascular treatment of aortoiliac TASC C-D CTO. Open surgery could be discussed in first choice in patients with these risk factors especially in low-volume centers in order to avoid endovascular failure and its medico-economic consequences.

Figure 1 :

 1 Figure 1 : Pre-operative CT-scan. (A) WO group (B) BO group, (C) WOP group

Table 1 :

 1 Baseline Patient and Lesion characteristics aCategorical data are presented as the counts (percentage).

	Total
	population, n =
	107

a Continuous data are presented as the means ± standard deviation;

Table 3 :

 3 Technical failure a a Continuous data are presented as the means ± standard deviation; Categorical data are given as the counts (percentage).

	b Fisher's exact test for categorical data and Wilcoxon test for continuous data
	Abbreviations: AB, aortic bifurcation; BIA, both iliac arteries; BMI, body mass
	index; BO, black occlusion; CIA, common iliac artery; EIA, external iliac artery;
	GFR, glomerular filtration rate; WO, white occlusion; WPO, white protrusive
	occlusion.

Table IV .

 IV Predictors of technical failure from the multivariate model

	Characteristics	Odds Ratio	95 % CI	p
	Age	0.99	0.91 to 1.07	0.82
	Renal failure	1.24	0.06 to 11.26	0.86
	EIA lesion	15.27	3.59 to 87.77	0.0006
	BO group	4.03	0.54 to 85.12	0.2361
	WPO group	13.88	1.63 to 328.52	0.036
	Abbreviations : BO, black occlusion; CI, confidence interval; EIA, external iliac lesion; WPO, white
	protrusive occlusion


Hang Guo

Renaud G Rinaldi

Sourour Tayakout

Morgane Broudin

Olivier Lame

The correlation between the mixed-mode oligo-cyclic loading induced mechanical and microstructure changes in HDPE

Keywords: HDPE, oligo-cyclic tensile loading conditions, macro-micro correlations, tensile toughness

Two grades of HDPE (one is for PE-100 pipeline application and one is for blow molding) were processed to vary their crystallinity and molecular topology in order to investigate and understand the microstructural origin of the seismic performance of HDPE materials. For a given grade, the quenched sample exhibits a lower crystallinity, thinner crystallites, and a higher density of entanglement/tie molecules compared to the isothermal one. The HDPE samples are submitted to mixed-mode, oligo (plastic)-cyclic tensile deformation (that simulates the seism) with the applied maximum strain below or at the onset of necking propagation. The changes of numerous macroscopic mechanical metrics with increasing cycles were monitored (e.g. stress at maximum strain, residual strain at zero stress, secant modulus, and hysteresis loop area). These mechanical changes not only depend on the maximum imposed cyclic strain, but also the microstructure of HDPE. A physical scenario is proposed to describe the microstructural changes during the cyclic deformation and explicate the macro-micro correlations. Moreover, the postcyclic tensile (reloading) curve can return to the original one rapidly for each sample, this phenomenon indicates the neglecting effect of the following cycles on the further loading path. It is also found that the material designed for the PE-100 pipeline shows limited variation between the initial and post-cyclic tensile toughness, indicating that the pre-loaded materials require nearly the same energy to rupture as the pristine ones. This is evidence that the material for PE-100 pipeline has a good resistance against the damage induced by seismic events.

INTRODUCTION

High-density polyethylene (HDPE) is widely used in industrial pipeline applications. PE 80 and PE 100 refer to common grades applied for gas and/or water pipelines. Among other benefits, pipelines made of HDPE exhibit a great resistance against seismic events [START_REF] Nishonov | Behaviour and Calculation of Polymer Pipelines Under Real Earthquake Records[END_REF][START_REF] Omuro | POLYETHYLENE PIPELINE PERFORMANCE[END_REF], which are normally modeled by repeated loading-unloading cycles beyond the elastic limit (also defined as low cycle fatigue tests or oligo-cyclic tests) [START_REF] Masi | Cyclic tests on external RC beamcolumn joints: role of seismic design level and axial load value on the ultimate capacity[END_REF][START_REF] Cassese | Experimental study on the seismic performance of existing reinforced concrete bridge piers with hollow rectangular section[END_REF]. Therefore, it is valuable to carry out the investigations on the overall mechanical performances along with the deformation mechanisms and the damage evaluation in HDPE under (oligo-) cyclic loading conditions. At the microscale, HDPE is a well-known semi-crystalline polymer consisting of crystalline and amorphous phases, connected by tie molecules/entanglement. The microstructural changes occurring throughout the small strain viscoelastic to the large strain plastic regimes during monotonic tensile tests in HDPE have been widely discussed for a long time [START_REF] Xiong | In-situ SAXS study and modeling of the cavitation/crystal-shear competition in semi-crystalline polymers: Influence of temperature and microstructure in polyethylene[END_REF][START_REF] Xiong | In-situ SAXS study of the mesoscale deformation of polyethylene in the pre-yield strain domain: Influence of microstructure and temperature[END_REF][START_REF] Xiong | On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature[END_REF][START_REF] Séguéla | On the Natural Draw Ratio of Semi-Crystalline Polymers: Review of the Mechanical, Physical and Molecular Aspects[END_REF][START_REF] Humbert | A re-examination of the elastic modulus dependence on crystallinity in semi-crystalline polymers[END_REF][START_REF] Xiong | Critical stress and thermal activation of crystal plasticity in polyethylene: Influence of crystal microstructure and chain topology[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF]. The correlations between several mechanical indicators obtained from the stress-strain tensile profiles and the microstructure of HDPE are well established. In the elastic regime, the storage/elastic modulus is governed by the fraction of crystalline phase, apparent amorphous modulus, and percolation of the crystalline structure [START_REF] Humbert | A re-examination of the elastic modulus dependence on crystallinity in semi-crystalline polymers[END_REF][START_REF] Deplancke | 1D strain rate-dependent constitutive model of UHMWPE: From crystalline network to fibrillar structure behavior[END_REF]. At the onset of plasticity, the quasi-linear relation between the threshold stress and crystallinity is associated with the dislocation model (thickness of crystalline lamellae) and the concept of stress transmitters (STs) [START_REF] Xiong | Critical stress and thermal activation of crystal plasticity in polyethylene: Influence of crystal microstructure and chain topology[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF]. It worth noting that insights regarding the amorphous chains topology or density of stress transmitters (ST density) were also obtained by mechanical measurements such as the neck width [START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF], natural draw ratio, and hardening [START_REF] Xiong | On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF][START_REF] Xiong | Amorphous phase modulus and micro-macro scale relationship in polyethylene via in situ SAXS and WAXS[END_REF]. The STs include the tie molecules and the entangled loops/chains, they are capable of transmitting the stress and they are also believed to play a crucial role in long-term properties such as creep, fatigue behaviors [START_REF] Zhou | The mechanism of fatigue failure in a polyethylene copolymer[END_REF][START_REF] Runt | Effect of crystalline morphology on fatigue crack propagation in polyethylene[END_REF][START_REF] Yeh | Fatigue crack propagation in high-density polyethylene[END_REF][START_REF] Niinomi | Fatigue characteristics of ultra high molecular weight polyethylene with different molecular weight for implant material[END_REF] as well as the crack propagation and cavitation [START_REF] Yeh | Fatigue crack propagation in high-density polyethylene[END_REF][START_REF] Brown | Slow crack growth in polyethylene-a review[END_REF][START_REF] Zhang | Quantification of strain-induced damage in semicrystalline polymers: a review[END_REF][START_REF] Sandrine Humbert | New insight on initiation of cavitation in semicrystalline polymers: in-situ SAXS measurements[END_REF].

In the literature, procedures can vary to perform (oligo-) cyclic tensile tests: for so-called stress-controlled [START_REF] Liu | Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA[END_REF][START_REF] Tao | Fatigue behavior of an epoxy polymer subjected to cyclic shear loading[END_REF][START_REF] Kang | Uniaxial ratchetting of polymer and polymer matrix composites: time-dependent experimental observations[END_REF][START_REF] Mourglia-Seignobos | Physical mechanisms of fatigue in neat polyamide 6, 6[END_REF][START_REF] Drozdov | Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites[END_REF][START_REF] Fouchier | Fatigue life assessment of a Short Fibre Reinforced Thermoplastic at high temperature using a Through Process Modelling in a viscoelastic framework[END_REF][START_REF] Klimkeit | Fatigue damage mechanisms in short fiber reinforced PBT+ PET GF30[END_REF] or strain-controlled modes [START_REF] Avanzini | Mechanical characterization and finite element modelling of cyclic stressstrain behaviour of ultra high molecular weight polyethylene[END_REF][START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF], the cyclic paths are conducted between two prescribed forces (stresses) or displacements (strains) respectively. Besides these two modes, mixed-mode conditions can also be used [START_REF] Drozdov | Cyclic viscoplasticity of high-density polyethylene: experiments and modeling[END_REF][START_REF] Drozdov | Mullins' effect in semicrystalline polymers[END_REF][START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF][START_REF] Meyer | The effect of cyclic true strain on the morphology, structure, and relaxation behavior of ultra high molecular weight polyethylene[END_REF], for which the sample is repeatedly stretched to a prescribed maximum strain and then retracted to zero force. During the cyclic tests, the mechanical indicators (e.g. stress, strain, modulus, hysteresis area) are seen to evolve with the increasing number of cycles suggesting microstructural modifications. The change of the elastic modulus has been attributed to two competing mechanisms. On the one hand, the modulus decrease is related to the cavitation (or micro-voids) and/or fragmentation of crystalline lamellae [START_REF] Mourglia-Seignobos | Physical mechanisms of fatigue in neat polyamide 6, 6[END_REF][START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF][START_REF] Xu | Constitutive modeling of solid propellant materials with evolving microstructural damage[END_REF][START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF]. Generally, this mechanical loss is recognized as a macroscopic symbol of material damage [START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF][START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF]. On the other hand, the chain orientation might lead to an increase of the modulus along with the tensile deformation, also defined as "cyclic strengthening" as suggested by Drozdov [START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF]. Additionally, the density of dissipated energy of each stress-strain cycle, calculated as the hysteresis area, is ascribed to the generated heat by the plastic deformation and viscous loss mechanisms [START_REF] Qi | Failure of high density polyethylene under cyclic loading: Mechanism analysis and mode prediction[END_REF]. This parameter is related to the failure mode and lifetime of polymers [START_REF] Fouchier | Fatigue life assessment of a Short Fibre Reinforced Thermoplastic at high temperature using a Through Process Modelling in a viscoelastic framework[END_REF][START_REF] Qi | Failure of high density polyethylene under cyclic loading: Mechanism analysis and mode prediction[END_REF][START_REF] Janssen | Fatigue life predictions for glassy polymers: a constitutive approach[END_REF].

Moreover, the accumulation of residual strain (by stress-controlled or mixed modes) and the stress softening (by strain-controlled or mixed modes) are also relevant features to probe the microstructural changes [START_REF] Liu | Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA[END_REF][START_REF] Kang | Uniaxial ratchetting of polymer and polymer matrix composites: time-dependent experimental observations[END_REF][START_REF] Drozdov | Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites[END_REF][START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF][START_REF] Drozdov | Mullins' effect in semicrystalline polymers[END_REF][START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF][START_REF] Meyer | The effect of cyclic true strain on the morphology, structure, and relaxation behavior of ultra high molecular weight polyethylene[END_REF]. In particular, during mixed-mode cyclic tests, the semi-crystalline polymers display both stress softening at maximum strain and the accumulation of residual strain at zero stress with increasing cycles [START_REF] Drozdov | Mullins' effect in semicrystalline polymers[END_REF][START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF]. These two phenomena are largely considered as the macroscopic features of the Mullins-like effect, thus differing from the classically so-called Mullins effect enounced in the filled and crystallizing rubbers [START_REF] Mullins | Permanent set in vulcanized rubber[END_REF][START_REF] Mullins | Softening of rubber by deformation[END_REF][START_REF] Diani | A review on the Mullins effect[END_REF]. In detail, the first hysteresis loop is significantly different from the following ones, which is recognized as a primary property of the Mullins-like effect [START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF][START_REF] Gomes | Analysis of Mullins effect in polyethylene using ultrasonic guided waves[END_REF]. Although the mechanisms are complex and controversial, the network alteration theory has been successfully applied to explain this phenomenon. Makki et al. [START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF] described the microstructural changes of the Mullins-like effect in PE basing on a framework proposed for styrene-butadiene rubber [START_REF] Ayoub | Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: application to styrene-butadiene rubber[END_REF]. In their work, the authors assign the difference in mechanical behaviors between the first cycle and the following ones to the rearrangement of the network. During the following cycles (after the first one), the additional rupture of chains reaching their limit extensibility is associated with the stress softening behavior. Moreover, a new equilibrium state at zero stress leads to an increase in the residual strain. Another striking manifestation of the Mullins phenomenon is that the post-cyclic reloading response for strain greater than the one already endured by the material coincides with the pristine response [START_REF] Mullins | Permanent set in vulcanized rubber[END_REF][START_REF] Mullins | Softening of rubber by deformation[END_REF][START_REF] Diani | A review on the Mullins effect[END_REF]. This phenomenon has been observed in polypropylene [START_REF] Drozdov | Mullins' effect in semicrystalline polymers[END_REF], with the maximum applied strain in the vicinity of the yield point. However, few studies discuss the post-cyclic behavior in PE, especially the properties related to the final rupture such as tensile toughness.

In this work, investigations of the Mullins-like stress softening/accumulation of residual strain in HDPE samples with different pristine microstructures and molecular topologies are carried out. Noticeably, mixed-mode oligo-cyclic tests with maximum strains preventing pronounced necking (below or at the onset of necking propagation phase) are performed. This strain range ascertains that the lamellar or spherulitic structure globally remains and the fibrillary structure [START_REF] Xiong | On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature[END_REF][START_REF] Deplancke | 1D strain rate-dependent constitutive model of UHMWPE: From crystalline network to fibrillar structure behavior[END_REF][START_REF] Humbert | Memory effect of the molecular topology of lamellar polyethylene on the strain-induced fibrillar structure[END_REF][START_REF] Jiang | Two lamellar to fibrillar transitions in the tensile deformation of high-density polyethylene[END_REF] induced by large deformation is not completely formed. The relative changes of the secant modulus and hysteresis loop areas are also computed. A physical scenario is proposed to interpret the correlation between the mechanical changes and the pristine microstructure of the PE samples. Moreover, the post-cyclic mechanical behaviors are also discussed.

EXPERIMENTAL SECTION

Materials

Two types of HDPE denoted PE-A and PE-B, are studied. PE-A refers to a blow molding grade and PE-B is a grade for the commercial PE-100 widely used in piping application. The molar masses were characterized and provided by the supplier INEOS (Brussels, Belgium) (see Table 1). The PE pellets were pressed into about 0.5 mm plates at 180°C in an aluminum-alloy mold.

Once molded, quenching and isothermal thermal treatments were performed in order to vary the pristine microstructures of the two materials. The "quenched samples" were shaped in cold water whereas the "isothermal samples" were shaped in the oil bath for about 17h at a temperature Tiso around the crystallizing temperature, yet preventing the secondary crystallization [START_REF] Alizadeh | Influence of structural and topological constraints on the crystallization and melting behavior of polymers. 1. Ethylene/1-octene copolymers[END_REF][START_REF] Humbert | Influence de la topologie moléculaire et de la microstructure sur les propriétés mécaniques des Polyéthylènes[END_REF]. Mn, Mw and Mz are the number-average molar mass, the weight-average molar mass and zaverage molar mass.

Differential Scanning Calorimetry (DSC) tests

6 to 10 mg samples were taken from the HDPE plates and heated up to 150°C at 10°C/min with a DSC 7 PerkinElmer machine under nitrogen flow. The following equation ( 1) was used to estimate the material's crystallinity (Xc):

X = ∆ ∆ ( 1
)
Where ∆ is the melting enthalpy calculated as the area under the DSC melting peak and ∆ is the melting enthalpy of polyethylene of 100% crystallinity (290 J/g [START_REF] Hubert | Physical and mechanical properties of polyethylene for pipes in relation to molecular architecture. I. Microstructure and crystallisation kinetics[END_REF]). The overall density ρ could thus be estimated as follow:

= + ( 2
)
Where ρc is the crystalline phase density (1.003 g/cm 3 ), ρa is the amorphous phase density (0.850 g/cm 3 ) [START_REF] Crist | Mechanical properties of model polyethylenes: tensile elastic modulus and yield stress[END_REF]. Xc and ρ were also used for calculating the thickness of crystalline lamellae as shown in the next subsection.

SAXS (Small-angle X-ray scattering) characterizations

The small-angle X-ray scattering experiments were performed on the SWING beamline of the French SOLEIL synchrotron with the X-ray wavelength of 0.103 nm. The sample-detector distance was 2003 mm so that the scattering vector q ranged between 0.036 and 0.52 Å . The determination of the long period (Lp), the thicknesses of crystalline lamellae (Lc), and the amorphous layers (La) were obtained according to equations (3), ( 4) and [START_REF] Xiong | In-situ SAXS study and modeling of the cavitation/crystal-shear competition in semi-crystalline polymers: Influence of temperature and microstructure in polyethylene[END_REF].

L = (3)
L = L X (4)
L = L -L (5)
It worth noting that the scattering wave vector qmax corresponds to the maximum Lorentzcorrected scattering intensity. These nano-dimensions could be used for the estimation of the ST density by Brown's model [START_REF] Xiong | On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature[END_REF][START_REF] Xiong | Amorphous phase modulus and micro-macro scale relationship in polyethylene via in situ SAXS and WAXS[END_REF][START_REF] Huang | The effect of molecular weight on slow crack growth in linear polyethylene homopolymers[END_REF][START_REF] Huang | Dependence of slow crack growth in polyethylene on butyl branch density: morphology and theory[END_REF] and for building the macro-micro correlations.

Mechanical tests: Uniaxial tensile, mixed-mode oligo-cyclic tensile and multi-step tests

Mechanical tests (uniaxial tensile, mixed-mode oligo-cyclic tensile, and multi-step tests) were performed on dumbbell-shaped samples of 8 mm gauge length, 4 mm width, and about 0.5 mm thickness punched out of the polymer sheets at room temperature. The tests were conducted using an MTS 1/ME machine equipped with a 100N load cell at a nominal strain rate = 3 × 10 # $ .

Uniaxial tensile tests were conducted till failure to guide the selection of the oligo-cyclic strain εOC (the maximum imposed strain in each cycle). These tests also allow characterizing the mechanical properties such as the neck width [START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF] and initial tensile toughness defined as the area under the stress-strain profile until failure. 100 mixed-mode cycles with εOC = 0.08/0.16/0.24/0.5 were performed. In multi-steps tests, the samples were initially subjected to 10 mixed oligocycles with the same εOC = 0.08/0.16/0.24/0.5 and then immediately stretched up to failure, special attention is drawn to the post-cyclic behavior in each sample.

RESULTS AND DISCUSSION

Pristine microstructural characteristics

The microstructural properties (crystallinity Xc, long period Lp, thickness of crystallites Lc, and thickness of amorphous layers La) of the PE materials are listed in Table 2. It worth noting that

Lc and La are precisely obtained according to the results of SAXS, the deviation is too small to present. As for crystallinity measurement, the deviation is ±1%. The density of STs has been approximated by both the statistic approach (Brown's model) [START_REF] Xiong | On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature[END_REF][START_REF] Xiong | Amorphous phase modulus and micro-macro scale relationship in polyethylene via in situ SAXS and WAXS[END_REF][START_REF] Huang | The effect of molecular weight on slow crack growth in linear polyethylene homopolymers[END_REF][START_REF] Huang | Dependence of slow crack growth in polyethylene on butyl branch density: morphology and theory[END_REF] and the neck width [START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF] (with deviation ±0.05) measured from the nominal uniaxial tensile stress-strain curves reported in Figure 1. The PE having enhanced ST density tends to exhibit a more diffuse neck indicating a more homogenous deformation [START_REF] Séguéla | On the Natural Draw Ratio of Semi-Crystalline Polymers: Review of the Mechanical, Physical and Molecular Aspects[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF]. The results obtained by these two methods are consistent with each other. For a given grade (PE-A or PE-B), the isothermal sample has a relatively higher crystallinity, thicker crystallites, and lower ST density [START_REF] Xiong | In-situ SAXS study and modeling of the cavitation/crystal-shear competition in semi-crystalline polymers: Influence of temperature and microstructure in polyethylene[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF][START_REF] Humbert | Small strain behavior of polyethylene: in situ SAXS measurements[END_REF] thanks to its slower crystallization process [START_REF] Alizadeh | Influence of structural and topological constraints on the crystallization and melting behavior of polymers. 1. Ethylene/1-octene copolymers[END_REF] compared to the quenched sample.

Mixed-mode oligo-cyclic tensile behaviors

Figure 1 superimposes the nominal uniaxial (up to a nominal strain ε = 1) and the oligo-cyclic tensile stress-strain profiles (maximum applied strain εOC = 0.08, 0.16, 0.24 and 0.5) of all four PE samples. The 2 nd and 100 th cycles are highlighted for better reading of the overall change of the mechanical loops. Throughout the mixed-mode oligo-cyclic tests, the stress at maximum strain, the residual strain at zero stress, the tangent modulus and the hysteresis response are seen to evolve and progressively saturate as the cycle number increases. (εOC = 0.08, 0.16, 0.24 and 0.5).

In order to quantify the mechanical alterations during the oligo-cyclic tests and tend to express their dependencies on the pristine sample microstructure and/or εOC values, several mechanical indicators are monitored. They are illustrated in Figure 2 and defined as follow:

σ ' ( : The nominal stress corresponding to the maximum-strain state at i th cycle (1 ) i )

100+.

-Δσ ( : The magnitude of stress softening between 1 st and i th cycle (2 ) i ) 100+.

ε ./0 ( : The residual strain at zero-stress state at i th cycle (1 ) i ) 100+.

ε ./0 : The residual strain at zero-stress state induced by the following cycles (from 2 nd to 100 th ).

ε 34 : The applied maximum strain in oligo-cyclic tests.

-W 6 ( : The hysteresis energy corresponding to the dissipated energy per unit volume at i th cycle

(1 ) i ) 100+.

9

-E ( : Secant modulus of i th cycle determined as E ( = -E ( : Comparative modulus measured in the first cycle within the same span of strain ε ( as

E ( >2 ) i ) 100+.
It is used for evaluating the relative change of modulus from the 1 st to the i th cycle. The detail of the calculation will be introduced in the following section Change of modulus.

Mechanical alterations and associated mechanisms

Stress softening

As shown in Figure 3, the stress-softening magnitude (Δσ) decreases as εOC increases for all the four samples whatever the cycle number. The negative correlation between the total stress softening magnitudes @A BB and εOC is further displayed, in Figure 4a. For a given grade, it worth noting that more pronounced stress softening is observed in the isothermal sample when εOC is identical. Moreover, an indicator @A * determined by equation ( 6)

is evoked for evaluating the improvement of the stress-softening resistance with increasing εOC in each sample (from εOC = 0.08 to εOC = 0.5). In particular, when εOC = 0.08, @A * is set as zero.

Δσ * >ε 34 + = D8 EE > . F+ D8 EE >; GH + D8 EE > . F+ (6)
As shown in Figure 4b, it has been found that @A * also depends on the PE initial microstructure.

A more significant increase of @A * is observed in the sample with lower crystallinity and higher ST density. disputable. Firstly, the rupture of short chains reaching their limit of extensibility, along with the disentanglement and breakdown of chains being stuck between two entanglement/crystallites are raised [START_REF] Makki | Mullins effect in polyethylene and its dependency on crystal content: a network alteration model[END_REF][START_REF] Ayoub | Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: application to styrene-butadiene rubber[END_REF]. These mechanisms occurring in the amorphous phase could also potentially induce cavitation [START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF]. Furthermore, when a semi-crystalline polymer is deformed beyond yielding, the fragmentation of crystallites can also be considered as an origin of the macroscopic material softening [START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF]. This phenomenon could also be related to the elimination of the crystalline percolation.

The aforementioned dependencies of stress softening on εOC and PE microstructure can be explicated as follow: i) the stress-softening-related microstructure changes are mainly induced by the first cycle. And the higher εOC, the more important these structural changes. As these phenomena could induce the softening, they are thus globally named as "structural deteriorations" in the following sections. As the εOC increases, the microstructure after the 1 st cycle tends to become an "extreme state" where the crystalline percolation is all eliminated and the remained STs are difficult to be disentangled/ruptured by the following cycles, the progressive stress-softening is thus more limited. ii) It has another compensating mechanism being stronger with increasing εOC. Also, its enhancement with increasing εOC should be more pronounced in the samples with lower crystallinity but higher ST density due to the lower value of stress softening. As mentioned in the introduction, under uniaxial tensile loading, the stress transmitters can be highly stretched, oriented along the loading direction, and induce recrystallization [START_REF] Gaucher-Miri | Reversible strain-induced order in the amorphous phase of a low-density ethylene/butene copolymer[END_REF]. This phenomenon is related to the strengthening effect and should compensate for the stress softening [START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF][START_REF] Adams | Direct visualization of microstructural deformation processes in polyethylene[END_REF]. Also, it is reasonable that this compensating phenomenon is more important in the samples with more STs [START_REF] Xiong | Critical stress and thermal activation of crystal plasticity in polyethylene: Influence of crystal microstructure and chain topology[END_REF][START_REF] Humbert | Polyethylene yielding behaviour: What is behind the correlation between yield stress and crystallinity?[END_REF] that promote their stretching and strain-induced recrystallization.

Residual strain accumulation

The residual strain (or inelastic strain) εres in semi-crystalline polymers can be divided into two parts, one being associated with the plastic deformation whereas the other one is due to the viscous effect of the amorphous phase that can be recovered after relaxation [START_REF] Drozdov | Mullins' effect in semicrystalline polymers[END_REF][START_REF] Diani | A review on the Mullins effect[END_REF][START_REF] Gomes | Analysis of Mullins effect in polyethylene using ultrasonic guided waves[END_REF]. The residual strain accumulation-saturation behavior in each sample is displayed in Figure 5. The first-cycle-induced residual strain is the most important one. all samples, with increasing εOC, the inelastic strains induced by the first and the remaining cycles are both seen to increase. For εOC = 0.08, 0.16, and 0.24, the difference in residual strains between the four materials is not clearly measurable. However, when εOC = 0.5, the IJK is larger in the samples with higher crystallinity, whereas the tendency is the opposite for IJK .

As a physical interpretation, when the imposed strain in the first cycle is high enough (i.e. εOC = 0.5), The percolation of the crystalline network is most likely ruptured in numerous locations during the first cycle, and the majority of the residual strain can be considered as the irreversible/plastic one. The plasticity is thus stronger in the sample with higher crystallinity.

However, the residual strain induced by the following cycles could be mainly attributed to the deformation in the amorphous phase. Therefore, the sample with lower crystallinity should have a macromolecular network more "inelastically" deformable due to the larger quantity of STs.

However, in the lower strain range (εOC = 0.08, 0.16 and 0.24), the crystalline network is not completely broken by the first loading, the following cycles may continually and slightly induce the residual strains in both the crystalline and amorphous phases, thus, the magnitudes of IJK and IJK are not clearly differed.

Density of energy dissipated

The hysteresis area L M N represents the density of energy dissipated during the i th loadingunloading cycle. The dissipated energy can be ascribed to several mechanisms: for example, the friction between the chains (viscosity), and potential plastic mechanisms such as lamellae fragmentation and/or cavitation [START_REF] Qi | Failure of high density polyethylene under cyclic loading: Mechanism analysis and mode prediction[END_REF][START_REF] Janssen | Fatigue life predictions for glassy polymers: a constitutive approach[END_REF]. The changes of Wd as a function of the cycle number are shown in Figure 7. Similar to the residual strain profiles, L M is much higher than L M N (with i >1), confirming major differences between the first and the remaining cycles.

Where σth and εth are the threshold stress and strain corresponding to the initiation of plasticity (where the stress σth is set to be 80% of yield stress σy obtained by uniaxial tensile curves). The approximated relations are also displayed in Figure 8a. Such approximation seems adapted so that the first-cycle induced energy dissipation can be mainly ascribed to the plasticity, it is consistent with the conclusion obtained by residual strain analysis.

The consumed energy per cycle tends to be saturated and approximately identical from the 90 th -

100

Change of modulus

As evidenced in Figure 1, the experimental stress-strain curves are highly non-linear, therefore, the secant method is widely used to evaluate the modulus at the beginning of each cycle (zerostress state) [START_REF] Mourglia-Seignobos | Physical mechanisms of fatigue in neat polyamide 6, 6[END_REF][START_REF] Fouchier | Fatigue life assessment of a Short Fibre Reinforced Thermoplastic at high temperature using a Through Process Modelling in a viscoelastic framework[END_REF][START_REF] Klimkeit | Fatigue damage mechanisms in short fiber reinforced PBT+ PET GF30[END_REF][START_REF] Drozdov | Cyclic strengthening of polypropylene under strain-controlled loading[END_REF]. However, to our knowledge, this method has been yet applied to characterize the mixed-mode oligo-cyclic responses of polymers. Indeed, the secant modulus should be measured in the "cycle" with constant stress or strain range, so that the non-linearity effect can be ignored. Yet, by mixed-mode, neither the stress nor the strain amplitude is constant in different cycles. Therefore, an indicator DE is proposed to evaluate the relative change of the secant modulus is defined as follow. The modulus of each following cycle (2 nd -100 th cycle) is compared with the modulus of the first cycle respectively. E ( and E ( are already defined in the last section "Description of oligo-cyclic tensile behaviors":

D R ( = 1-E ( / E ( >2 ) U ) 100+ (8)
Although this mechanical indicator DE is commonly used to evaluate the material damage at macroscale in semi-crystalline polymers [START_REF] Zhang | Quantification of strain-induced damage in semicrystalline polymers: a review[END_REF][START_REF] Mourglia-Seignobos | Physical mechanisms of fatigue in neat polyamide 6, 6[END_REF][START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF], which means that a positive indicator V W N reflecting the decrease of secant modulus is expected. In this work, the negative value is also observed under certain condition and suggest that the modulus of the i th cycle is superior to the initial modulus and indicating a strengthening effect. The changes of DE in all four PE samples are shown in Figure 9 as a function of the cycle number. In each sample, it is found that V W is negative (modulus increases) when εOC = 0.08 and 0.16. However, V W becomes positive (modulus decreases) when εOC = 0.24 and 0.5. From negative to positive, V W tends to be higher with increasing εOC. However, during the remaining cycles, DE values decrease monotonically, indicating the growth of modulus with increasing cycles prior to progressively stabilizing. elastic modulus and the microstructure of PE [START_REF] Humbert | A re-examination of the elastic modulus dependence on crystallinity in semi-crystalline polymers[END_REF][START_REF] Deplancke | 1D strain rate-dependent constitutive model of UHMWPE: From crystalline network to fibrillar structure behavior[END_REF], introducing the use of a mechanical coupling parameter k (the ratio between the stresses concentrated in hard phase and soft phase, σh/σs), which is physically related to the percolation level of the crystalline phase. The more percolated crystalline structure, the higher k value. The modulus is estimated using relation [START_REF] Humbert | A re-examination of the elastic modulus dependence on crystallinity in semi-crystalline polymers[END_REF] where X Y is the volume fraction of hard phase and Es is the modulus of the soft phase.

Z [ \E 0 × ] ^ ] ^ (9)
Neglecting the influence of the interphase, the hard and soft phases are simply considered as the crystalline and amorphous phases [START_REF] Deplancke | 1D strain rate-dependent constitutive model of UHMWPE: From crystalline network to fibrillar structure behavior[END_REF]. Within this theoretical framework, three microstructural parameters (k, Es, and X Y ) can directly determine the macroscopic modulus. Therefore, the modulus change can be related to different mechanisms that modify these parameters.

Firstly, the plastic deformation can provoke the decrease of Z K and k due to the disentanglement/rupture of weak chains (they may also induce cavitation) and fragmentation of the percolated crystalline structure respectively. However, to interpret the initial negative values of DE (the first-cycle induced increase of modulus) under certain loading conditions (εOC = 0.08 and 0.16) and the decrease of DE in the subsequent cycles (rest-cycles induced increase of modulus), the aforementioned competing mechanism should be mentioned again. As it compensates the stress softening, the orientation/alignment of chains and the stretching of stress transmitters can result in partial recrystallization, potentially increasing both the fraction of hard phase X Y , amorphous modulus Z K . Also, the recrystallization may bridge the fragmented crystalline network and increase the k value.

Regarding V W , with increasing εOC, the effect of "structural deteriorations" on the modulus becomes more and more dominant compared to the recrystallization at the zero-stress state.

However, differing from the first cycle, the chain orientation/recrystallization governs the modulus of the consecutive cycles.

Figure 10 shows that the values of V W in all four samples increase as a function of εOC. For the relatively lower εOC (0.08/0.16/0.24), the dependency of V W on the microstructural properties remains unclear. However, when εOC = 0.5, V W value becomes higher as the sample crystallinity increases or ST density decreases. Indeed, the sample with higher crystallinity should have a more percolated crystalline structure, when the imposed strain is high enough, the crystalline network is nearly all broken, so it shows a more important loss of percolation, k decreases from a very high value to almost 1 [START_REF] Deplancke | 1D strain rate-dependent constitutive model of UHMWPE: From crystalline network to fibrillar structure behavior[END_REF]. Additionally, the lower ST density promotes the disentanglement and chain rupture that could also induce a more important loss of amorphous modulus.

Physically, it seems reasonable that under a given loading condition, the recrystallization at zero-stress state should be more effective in the quenched samples during the following cycles due to their larger number of STs and higher residual strain in the amorphous phase (the chains are more stretched). However, the relation between the following-cycles-induced strengthening effect (decrease of DE as a function of cycle number) and pristine PE microstructure is not clear.

It may be interpreted as the complicated relations between the orientation of chains/recrystallization and the relative evolutions of the three parameters (k, Z K , and X Y ). It worth noting that the cavitation is not mentioned here, indeed, the origin of this phenomenon is related to the disentanglement/rupture of chains [START_REF] Detrez | Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification[END_REF][START_REF] Gomes | Analysis of Mullins effect in polyethylene using ultrasonic guided waves[END_REF].

The pristine HDPE microstructure is composed of spherulites with radially oriented crystalline lamellae within the amorphous matrix. Several lamellae are percolated. Considering the εOC range under investigation, STs have different resistance against the deformation. The "strong" tie molecules can continually act without rupture, whereas the "weak" entanglement or loops, can be unfolded due to the slip of chains.

During the first loading, the very weak active entanglement/loops slip and unfold even at low macroscopic strain, followed by the elimination of percolation and shearing of crystals when the imposed strain reaches the plastic regime. The higher imposed strain, the more complete breakage of the crystalline network and disentanglement. In particular, the elimination of crystalline percolation tends to activate the confined STs that do not transmit the stress during the first cycle due to the percolated crystalline structure. The tie molecules with high deformation capacity can be aligned and may lead to the recrystallization, which can partially disappear during the unloading. Comparing the pristine (undeformed) state and the 1 st zero-stress state, the orientation of chains/recrystallization competes with the structural deteriorations (disentanglement/rupture of STs and breakage of the crystalline network): in the low strain range (εOC = 0.08 and 0.16), the recrystallization dominates and results in a higher apparent modulus whereas in the high strain range (εOC = 0.24 and 0.5), the structural deteriorations prevail, the modulus after the first cycle is inferior to the initial one.

During the following cycles, the main deformation is ascribed to the amorphous phase. At the maximum-strain state, the level of chain orientation/recrystallization does not change with increasing cycles due to the constant imposed strain (εOC), therefore, the progressive stress softening is governed by the disentanglement occurring in the pre-confined regions and successive breakage of the crystalline network (if it is not completely broken by the first loading). With increasing εOC, the first cycle can induce more important structural deteriorations, which means that fewer STs that can be potentially disentangled, and less crystalline percolation remains after the first cycle. Regarding the zero-stress state, due to the accumulation of residual strain, the effect of recrystallization increases crucially as a function of cycle number. And the successive structural deteriorations cannot counteract this effect on modulus, the modulus thus tends to be a higher value with increasing cycles.

Post-cyclic tensile behavior

Uniaxial tension until failure was achieved after a series of 10 cycles as most of the microstructure changes were proven to occur within this period. All the PE samples show the Mullins-like behavior, as an example, the post-cyclic tensile behaviors of the PE-A isothermal sample are superimposed in Figure 12a: the post-cyclic curves tend to match the pristine one for strain larger than the ones endured during the oligo-cyclic test (ε>εOC), suggesting that all the changes occurring in the following cycles (2 nd -100 th ) have a limited influence on the overall short-term mechanical performance. However, regarding fracture performance, the remaining toughness, Wf was then estimated as indicated in Figure 12b, where the multi-step stress-strain profile of PE-A isothermal sample with εOC = 0.5 is displayed as an example. Within this method, the first-cycle-induced damage (related to the loss of tensile toughness) is also taken into account. Figure 12c gives the relation between Wf and εOC. Wf for εOC = 0 naturally corresponds to the tensile toughness of the pristine PE samples, and the error bar indicates the difference between the maximum/minimum values. For a given grade (PE-A or PE-B), the value Wf does not significantly differ by the heat treatments, the isothermal samples require just slightly more energy until fracture (10% for PE-B and 8% for PE-A). However, between PE-A and PE-B samples, the difference is important (about 30%), which means that pristine Wf shows a more crucial dependency on the molecular characteristics than thermal treatment. Also, it is found that the Wf values of all four samples remain almost constant indicating that the change of energy required to failure is not measurable when εOC does not exceed 0.24. However, when εOC = 0.5, in the PE-A isothermal sample, which has the lowest ST density and highest crystallinity, the Wf decreases about 25%. This result tends to confirm that the resistance to failure decreases so that the mechanical damage should be relatively more important in PE-A isothermal sample than others.

CONCLUSION

The performance of varying HDPE samples under oligo-cyclic loading conditions was evaluated and a physical scenario is proposed for the interpretation of the measured macro-micro correlations: the structural deteriorations, such as chain rupture/disentanglement and breakage of lamellae/percolation are mainly induced by the first cycle. These structural deteriorations can induce the loss of modulus and compete with the orientation of stress transmitters/recrystallization associated with the strengthening effect. When the imposed cyclic strain is high enough (εOC=0.5), during the following cycles, the structural deteriorations are mainly assigned to the pre-confined disentanglement in the amorphous phase, dominating the stress change (decrease) at maximum strain state. However, at the zero-stress state, the chain orientation/recrystallization plays a more crucial role as illustrated by the increase of apparent modulus. Noticeably, the mechanical losses during the cyclic deformation including the stress softening and the decrease of the apparent modulus are more crucial in the isothermal samples, especially the PE-A grade, having higher crystallinity and lower ST density. However, it seems that the microstructural/mechanical changes during the following cycles have a limited effect on the further tensile loading path. However, for the tensile toughness, considering the effect of the complete loading process including the first cycle, there is a loss in the PE-A isothermal sample with the "extreme" microstructural parameters.

Compared to the other HDPE, the one for PE-100 pipeline (PE-B in this study) has relatively lower yield stress, modulus and tensile toughness. However, this material shows a better resistance against the mechanical losses under oligo-cyclic loading conditions. Even when εOC = 0.5, neither the quenched nor the isothermal sample is significantly damaged after the tests.

Moreover, the more important energy dissipation at the end of oligo-cyclic tests is observed in PE-B samples especially the quenched one. It means that PE-B also has a more performant capacity to continually dissipate the seismic energy, due to the limited damage, it means that this material is more performable to consume the energy and protect the whole architecture.

Figure 1 :

 1 Figure 1: Nominal uniaxial and oligo-cyclic tensile stress-strain profiles.

Figure 2 :

 2 Figure 2: Oligo-cyclic curve with the description of the evaluated mechanical changes.

Figure 3 :

 3 Figure 3: Stress-softening magnitude in different samples as a function of cycle number: (a) PE-A Quenched; (b) PE-A Isothermal; (c) PE-B Quenched and (d) PE-B Isothermal

Figure 4 :

 4 Figure 4: a) Total stress-softening magnitudes between 1 st and 100 th loading; b) Relative decrease of stress softening as a function of εOC in different samples

Figure 5 :

 5 Figure 5: Residual strain in different samples as a function of cycle number: (a) PE-A Quenched; (b) PE-A Isothermal; (c) PE-B Quenched and (d) PE-B Isothermal

Figure 6 :

 6 Figure 6: Change of the residual strains as a function of the prescribed maximum strain a) after the 1 st cycle, b) from 2 nd to 100 th cycle

Figure 7 :

 7 Figure 7: Density of energy dissipation Wd as a function of cycle number in PE samples with different applied oligo-cyclic strains εOC: (a) PE-A Quenched; (b) PE-A Isothermal; (c) PE-B Quenched and (d) PE-B Isothermal

  th cycle. The energy dissipation during a whole saturated cycle (L M ) increases as the crystallinity decreases (or ST density increases). This relation is following the aforementioned assumption that the sample deformation remains primarily visco-elastic so that the energy dissipation is mainly caused by the additional viscous effect. L M as a function of εOC of each sample is displayed in Figure 8b. The PE-B quenched samples exhibit the highest L M value, indicating that this material has a superior energy dissipating capacity in the visco-elastic regime during cyclic deformation due to the more important friction (disentanglement) between the chains.

Figure 8 :

 8 Figure 8: Dissipated energy density of PE samples at different applied oligo-cyclic strains a) after the first loading cycle ( L M ) and b) after the 100nd loading cycle (L M )

Figure 9 :

 9 Figure 9: Relative change of the secant modulus evaluated by DE as a function of cycle number in PE samples with different applied oligo-cyclic strains: (a) PE-A Quenched; (b) PE-A Isothermal; (c) PE-B Quenched and (d) PE-B Isothermal

Figure 10 :

 10 Figure 10: V W of PE samples at different applied oligo-cyclic strains εOC

Figure 11 :

 11 Figure 11: The physical scenario of HDPE under mixed-mode oligo-cyclic loading conditions (spherulitic scale and lamellar scale)

Figure 12 :

 12 Figure 12: a) Mullins-like behavior of PE-A isothermal sample; b) Definition of remaining tensile toughness (ex. PE A isothermal sample, with εOC=0.5), c) Remaining tensile toughness in different samples as function εOC

Table 1 :

 1 Initial molecular characteristics and Tiso of the polyethylene pellets

	Materials	Mn (g/mol)	Mw (g/mol)	Mz (g/mol)	Tiso (°C)
	PE-A	7500	202200	1478900	121.5
	PE-B	6700	270800	1589400	118

Table 2 .

 2 Crystallinity Xc, long period Lp, thickness of crystallites Lc and amorphous layers La, ST density estimated by Brown's model and neck width of PE plates subjected to different

			thermal treatments.
	Methods	DSC		SAXS		Brown's model	Neck width
	Material characteristics	Xc (%) Lp (nm) Lc (nm) La (nm)	ST density
	Quenched	62	22	13	9	0.22	0.55
	PE-A
	Isothermal	73	35	24	11	0.07	0.27
	Quenched	57	20	11	9	0.27	0.65
	PE-B
	Isothermal	64	33	20	13	0.14	0.32

ACKNOWLEDGEMENTS

The authors are indebted to INEOS (Brussels, Belgium) for supplying the HDPE polymers and their molecular characteristics. The SWING beamline in French SOLEIL synchrotron is appreciated for time allocation. EDF-DIPNN Direction Technique and EDF lab R&D Les Renardières are acknowledged for the grant of a doctoral fellowship to H. GUO.