Katja Bartsch

Andreas Brandl

Patrick Weber

Jan Wilke

Sabine F Bensamoun

Wolfgang Bauermeister

Werner Klingler

Robert Schleip
email: robert.schleip@tum.de

Assessing reliability and validity of different stiffness measurement tools on a multi-layered phantom tissue model

Keywords: soft tissue, muscle stiffness, myotonometry, ultrasound, indentometry

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Low back pain is the leading cause of years lived with disability, burdening health care systems worldwide [START_REF] Wu | Global low back pain prevalence and years lived with disability from 1990 to 2017: estimates from the Global Burden of Disease Study 2017[END_REF] . Historically, soft tissues in general and the connective tissues of the thoracolumbar region in particular have received little attention when attempting to clarify the pathophysiological mechanisms of this condition. In recent years, however, research has shed light on the layered soft tissue structures of the low back and their biomechanical characteristics as they contribute to low back health [START_REF] Langevin | Pathophysiological model for chronic low back pain integrating connective tissue and nervous system mechanisms[END_REF][START_REF] Langevin | Reduced thoracolumbar fascia shear strain in human chronic low back pain[END_REF][START_REF] Langevin | Ultrasound evidence of altered lumbar connective tissue structure in human subjects with chronic low back pain[END_REF][START_REF] Willard | The thoracolumbar fascia: anatomy, function and clinical considerations[END_REF][START_REF] Brandl | Immediate Effects of Myofascial Release on the Thoracolumbar Fascia and Osteopathic Treatment for Acute Low Back Pain on Spine Shape Parameters: A Randomized, Placebo-Controlled Trial[END_REF] .

Soft tissue stiffness is a mechanical property, which is defined as a material's resistance to deformation [START_REF] Holzapfel | Biomechanics of Soft Tissue[END_REF] . Changes in the mechanical properties of soft tissues have been linked to musculoskeletal disorders, injuries, pain conditions, and cancer biology, leading to a rising demand in diagnostic methods for research and clinical practice [START_REF] Langevin | Pathophysiological model for chronic low back pain integrating connective tissue and nervous system mechanisms[END_REF][START_REF] Langevin | Connecting (T)issues: How Research in Fascia Biology Can Impact Integrative Oncology[END_REF][START_REF] Alvarez-Diaz | Effects of anterior cruciate ligament injury on neuromuscular tensiomyographic characteristics of the lower extremity in competitive male soccer players[END_REF][START_REF] Sakai | Pericranial muscle hardness in tensiontype headache. A non-invasive measurement method and its clinical application[END_REF][START_REF] Kuo | Neck muscle stiffness quantified by sonoelastography is correlated with body mass index and chronic neck pain symptoms[END_REF][START_REF] Tafazzoli | Mechanical behaviour of hamstring muscles in low-back pain patients and control subjects[END_REF][START_REF] Li | Quantifying the stiffness of lumbar erector spinae during different positions among participants with chronic low back pain[END_REF] . However, little data exists to provide evidence-based recommendations for current stiffness assessment tools, requiring further research investigating their measurement properties [START_REF] Zügel | Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics: consensus statement[END_REF][START_REF] Muckelt | Protocol and reference values for minimal detectable change of MyotonPRO and ultrasound imaging measurements of muscle and subcutaneous tissue[END_REF] . Prior research has suggested to use material phantoms with known viscoelastic properties to obtain valuable results regarding the reliability and concurrent validity of stiffness assessment tools [START_REF] Wilke | Reliability and validity of a semi-electronic tissue compliance meter to assess muscle stiffness[END_REF][START_REF] Oflaz | A new medical device to measure a stiffness of soft materials[END_REF][START_REF] Sohirad | Feasibility of using a handheld device to characterize tendon tissue biomechanics[END_REF] .

The use of tissue stiffness assessment tools provides a comparatively cost-effective and easyto-use option for research and clinical practice. Current technologies comprise methods of indentation, myotonometry, as well as ultrasound imaging [START_REF] Zügel | Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics: consensus statement[END_REF][START_REF] Avila Gonzalez | Frontiers in fascia research[END_REF] .

To our knowledge, none of these devices have been tested for reliability on a material phantom model representing the layered soft tissue structures of the human low back area. Analog to 'The Princess of the Pea' fairy tale (where the princess demonstrates her sensitivity to feel the slightest stiffness change created by a pea through layers of bedding and thereby proves herself to be a princess) it can be assumed that the sensitivity of a stiffness assessment may be altered when the tissue layer of interest is positioned underneath one or several other tissue layers. In our study, we aimed to create a multi-layered material phantom tissue model (MPTM) mimicking the different layers of the thoracolumbar region. The present study's objective was to evaluate the reliability of various tissue stiffness assessment devices on the MPTM.

2

Materials and methods

Multi-layered material phantom tissue model

A multi-layered phantom model was developed to mimic the soft tissue layers of the human thoracolumbar region (Figure 1). The model simulated four human tissue layers: cutis (CUT), subcutaneous connective tissue (SCT), fascia profunda (FPR), and erector spinae (ERS). A literature search yielded typical values for the thickness of those tissue layers located lateral to the spinous process of the L3 vertebra, as this measurement site has been used by prior research for stiffness evaluation [START_REF] Langevin | Ultrasound evidence of altered lumbar connective tissue structure in human subjects with chronic low back pain[END_REF][START_REF] Moreau | Non-invasive assessment of human multifidus muscle stiffness using ultrasound shear wave elastography: A feasibility study[END_REF][START_REF] Nair | Stiffness of resting lumbar myofascia in healthy young subjects quantified using a handheld myotonometer and concurrently with surface electromyography monitoring[END_REF][START_REF] Lohr | Reliability of tensiomyography and myotonometry in detecting mechanical and contractile characteristics of the lumbar erector spinae in healthy volunteers[END_REF] (Figure 2). Accordingly, a thickness of 3 mm, 6 mm, and 1 mm was chosen for CUT, SCT, and FPR respectively. For the ERS -as the most inferior of the four layers -a thickness of 10 mm was chosen, since preliminary explorations of our group had revealed that thickness as upper limit of a reliable assessment of the ultrasound assessment method. Typical stiffness values for the four layers were determined using literature searches as well. Gel pad layers with the identified typical thickness and stiffness values constituted the default measurement set. To mimic stiffness alterations, nine additional phantoms with varying stiffness parameters were produced for each tissue layer, resulting in 40 phantom layer variations overall. The parameters for the artificial stiffness changes for the four tissue layers were determined individually for each layer.

All gel pad phantoms measured 30x21 cm, were manufactured from polyurethane material and coated with a 25 µm thick polyurethane foil (Technogel Germany GmbH, Berlingrode). Stiffness values were specified in Shore OOO values, which describe very soft plastic and rubber materials. For further analysis, Shore OOO values were converted to Young's modulus in kPasc [START_REF] Mix | Standardized Polymer Durometry[END_REF] .

2.2 Tissue stiffness assessment tools

Shore Durometer

The Shore Durometer (Type 1600-OO, Rex Gauge, Brampton, ON, Canada) is a standard device for measuring the hardness of various non-metallic materials including rubber and plastic. The instrument contains a spring-loaded interior that senses hardness by applying an indentation load on the material through a probe tip (Ø 2.4 mm). For measurements, the durometer is held perpendicular to the medium and rested by gravity against the material. Hardness in degrees of Shore OO from 0 to 100 can be read from the analogue dial of the device, with lower Shore values indicating a softer material [START_REF] Falanga | Use of a durometer to assess skin hardness[END_REF] .

Semi-electronic Tissue Compliance Meter

The Semi-electronic Tissue Compliance Meter (STCM, Technical University of Chemnitz, Germany) consists of a force gauge (probe tip surface of 1 cm 2 ) and a platform ring (Ø 8 cm), which slides downward on the force gauge shaft. Through a scale with millimeter increments equipped with a fixable ring, a desired penetration depth can be set. The device furthermore contains a button cell which is used to generate a beep signal upon contact between the ring and the disk. To perform a measurement, the probe tip is placed on the underlying tissue and the examiner applies a downward force on the top of the device until the disk and the ring are brought into contact. This contact generates a beep sound, indicating the end of the measurement. The applied force (in N) can be read from the analogue display of the force gauge. The known penetration force and the applied force can be used to analyze the forcedeformation relationship of the material or tissue at hand [START_REF] Wilke | Reliability and validity of a semi-electronic tissue compliance meter to assess muscle stiffness[END_REF][START_REF] Fischer | Tissue compliance meter for objective, quantitative documentation of soft tissue consistency and pathology[END_REF] .

IndentoPRO

The IndentoPRO is a digital indentometer (Fascia Research Group, Ulm University; Department of Human Movement Sciences, University of Chemnitz, Germany). The device comprises a device body with a load cell (Compression Load Cell FX1901, TE Connectivity, Schaffhausen, Switzerland) and a membrane potentiometer (ThinPot 10kOhm, Spectra Symbol, Salt Lake City, USA) to measure the resistance force and displacement of a circular indentation probe (Ø 11.3 mm) [START_REF] Kett | Sedentary behaviour at work increases muscle stiffness of the Stiffness measurement tools' reliability and validity 13 back: Why roller massage has potential as an active break intervention[END_REF][START_REF] Koch | Reliability of a New Indentometer Device for Measuring Myofascial Tissue Stiffness[END_REF] . To perform a measurement, an indentation depth is selected, and the probe is positioned on the material. The examiner then applies force on top of the device until a beep signal indicates the end of the measurement. Tissue stiffness is defined by the slope of the relationship between indentation depth and force increase. Stiffness values can be read from a digital display and are specified in N/mm, with lower values indicating lower tissue stiffness [START_REF] Kett | Sedentary behaviour at work increases muscle stiffness of the Stiffness measurement tools' reliability and validity 13 back: Why roller massage has potential as an active break intervention[END_REF][START_REF] Kett | Sitting for Too Long, Moving Too Little: Regular Muscle Contractions Can Reduce Muscle Stiffness During Prolonged Periods of Chair-Sitting[END_REF] .

MyotonPRO

The MyotonPRO is a digital palpation device (MyotonAS; Tallinn, Estonia), consisting of a device body and an indentation probe (Ø 3 mm). Through the probe, a pre-pressure (0.18 N) is applied to the surface that causes the material underneath to be compressed. A mechanical impulse (0.4 N, 15 ms) is then released by the device, deforming the medium for a short interval. The tissues respond back with a damped oscillation that is recorded by the accelerometer in the MyotonPRO device. Stiffness is recorded in N/mm and can be read from a digital display. Lower values indicate lower tissue stiffness. [START_REF] Sohirad | Feasibility of using a handheld device to characterize tendon tissue biomechanics[END_REF][START_REF] Chuang | Quantitative mechanical properties of the relaxed biceps and triceps brachii muscles in patients with subacute stroke: a reliability study of the myoton-3 myometer[END_REF] .

Ultrasound with attached transducer

As described by Jafari and colleagues [START_REF] Jafari | Novel method to measure active myofascial trigger point stiffness using ultrasound imaging[END_REF] ultrasound images can be recorded in two states: with stress and without stress. For the stress state scenario, compressive stress is imposed by the ultrasound transducer (Philips Lumify with L12-4 linear transducer; contact area 19 x 43,5 mm). A force gauge attached through a ring holder measures the applied force (Digital Force Gauge FL-S-100, Kern & Sohn GmbH, Balingen, Germany). The ultrasound images with and without stress states are compared and the length of a vertical line perpendicular to the multilayered phantom tissue model surface is measured. To determine strain, the measured length of the vertical lines with and without stress are used. Stress is calculated by dividing the applied force (in N) by the transducer contact area. Tissue stiffness is determined as elastic modulus, using the relation between stress and strain under the assumption that stiffness follows linear behavior.

Measurements

Material phantoms were placed on top of each other according to their natural sequence. The default measurement set served as starting point. To mimic stiffness changes in the MPTM, 10 different layer variants representing 10 different stiffness parameters were exchanged one by one, with the other three layers remaining in default measurement set configuration (example: the 10 gel pads variants for CUT were exchanged and measured one by one with all measurement devices, while SCT, FPR and ERS remained in default measurement set configuration; analogous procedure was followed for the other layers). Measurements were performed by two investigators in a blinded manner, meaning that examiners were not aware of the stiffness parameters of each gel pad.

For the Shore Durometer, the average of five consecutive measurements was used for data analysis [START_REF] Periyasamy | Investigation of Shore meter in assessing foot sole hardness in patients with diabetes mellitus -a pilot study[END_REF] . Taken measurements were converted to Young's modulus in kPasc [START_REF] Mix | Standardized Polymer Durometry[END_REF] . For the semielectronic STCM, three consecutive measurements at 15 mm penetration depth were taken and averaged for data analysis [START_REF] Wilke | Reliability and validity of a semi-electronic tissue compliance meter to assess muscle stiffness[END_REF] . For the IndentoPRO, three consecutive measurements were taken [START_REF] Jafari | Novel method to measure active myofascial trigger point stiffness using ultrasound imaging[END_REF] at four different indentation depths (2 mm, 5 mm, 8 mm, 10 mm) and averaged for analysis. Measurements were only accepted when the coefficient of variation (CV) had maximum value of 5 %. Investigators trained beforehand to conduce indentations with a consistent force rate of 10 N/s to achieve said level of CV. For the MyotonPRO, the average value of five consecutive measurements was determined [START_REF] Muckelt | Protocol and reference values for minimal detectable change of MyotonPRO and ultrasound imaging measurements of muscle and subcutaneous tissue[END_REF][START_REF] Sohirad | Feasibility of using a handheld device to characterize tendon tissue biomechanics[END_REF] . For the ultrasound, measurements with 0 kPa, 5 kPa, 10 kPa, and 15 kPa pressure were taken 32 .

Data analysis and statistics

All descriptive data are means ± standard deviation (SD). To investigate the relationship between relative changes of stiffness determined with the SMTs and artificial relative Young's modulus changes of the MPTM, Pearson's product-moment correlation coefficients were calculated for normal distributed data and Spearman's rank correlation for data that violated normal distribution assumptions. Linear regression analysis (with log 10 transformation for non-normally distributed data) was performed with MPTM measurement as dependent variable and respective SMTs measurement as independent variable. According to Cohen [START_REF] Cohen | Statistical power analysis for the behavioral sciences[END_REF] , the resulting values were interpreted as 'small' (0.1 to 0.3), 'medium' (0.3 to 0.5) or 'large' (0.5 to 1.0) correlations. Intraclass correlation coefficient (ICC) estimates between MPTM and IndentoPRO measurement and their 95 % CI were calculated using the R package "irr" version 0.84.1 based on a 2-way mixed-effects model with absolute agreement. Non-normally distributed data were log-10-transformed. Resulting ICC values were interpreted according to Fleiss [START_REF] Fleiss | Reliability of Measurement[END_REF] as 'poor' (< 0.4), 'fair to good' (0.4 to 0.75) and 'excellent' (> 0.75). For relative reliability [START_REF] Furlan | The Applicability of Standard Error of Measurement and Minimal Detectable Change to Motor Learning Research-A Behavioral Study[END_REF] , the corresponding standard errors of measurement (SEM) were estimated using the formula: [1].

The MDC was estimated by reference to the SEM using the formula [2] 38 :

[2].

To complement the ICC reliability data, the Bland and Altman test with limits of agreement was conducted between the two raters and graphed.

An alpha level of 0.05 was used to determine statistical significance. LibreOffice Calc version 6.4.7.2 (Mozilla Public License v2.0) was used for descriptive statistics. Inferential statistics were carried out with the software R, version 3.4.1 (R Foundation for Statistical Computing, Vienna, Austria).

3 Results

Significant correlations with artificial Young's modulus changes of the MPTM were found for stiffness changes in all layers of the MPTM except for the FPR layer, with effect sizes ranging from 0.70 to 0.98 (all p < 0.01). The interrater reliability for all layers except FPR was good to excellent (ICC (2,2) = 0.75~0.98). Figure 3 gives an overview of the results. Figure 4 graphs results for the Bland and Altman test for MyotonPRO, Figure 5 depicts Bland and Altman test results for IndentoPRO.

The following values relate to CUT, SCT, and ERS layers:

Correlations for the Shore Durometer ranged from 0.53 to 0.92 (0.92 for detecting artificial stiffness changes in CUT, 0.77 for detecting changes in SCT, 0.53 for detecting changes in ERS).

Interrater reliability (ICC) was good and ranged from 0.51 (ERS) to 0.69 (CUT).

For SCTM, correlations ranged from 0.05 to 0.93. Measurements taken with 10 mm penetration depth showed higher correlations (0.70 for changes in CUT, 0.93 for SCT layer, 0.92 for ERS) than measurements with 5 mm penetration depth (0.55, 0.65, and 0.05 respectively). Excellent interrater-variability values were obtained for ERS (0.93), and SCT (0.8) (both related to10 mm penetration depth).

MyotonPRO stiffness (N/m) showed the highest correlations throughout all devices, amounting to 0.94 for changes in CUT, 0.98 for SCT and 0.91 for ERS. Interrater reliability for MyotonPRO was excellent throughout all MPTM layers (0.98 for CUT, 0.99 for SCT, 0.94 for ERS).

Correlations for IndentoPRO were also large. Highest correlations were found for measurements with a penetration depth of 10 mm (0.90 for stiffness changes in CUT, 0.98 for SCT, 0.97 for ERS). Values for 2 mm penetration depth amounted to 0.88 (cutis), 0.97 (SCT), 0.96 (ERS). Values for 5 mm penetration depth were 0.71 (CUT), 0.97 (SCT), 0.96 (ERS).

Correlations for 8 mm penetration depth were calculated at 0.87 (CUT), 0.98 (SCT), and 0.92 (ERS). Interrater reliability was excellent for all penetration depths except CUT at 5 mm penetration depth (ICC = 0.51) and SCT at 10 mm penetration depth (ICC = 0.71).

Ultrasound with attached force gauge showed large correlations for SCT (0.80 -0.95, for varying pressure levels), and ERS (0.87-0.96). Interrater reliability was excellent for ERS (all applied pressure parameters) and SCT (at 15 kPasc). Interrater reliability for SCT was good for 5 kPasc and 10 kPasc pressures.

The detailed results are presented in Table 1.

Discussion

To our knowledge, this is the first study examining the reliability of the Shore Durometer, SCTM, IndentoPRO, MyotonPRO, and ultrasound with force transducer on a MPTM mimicking different tissue layers of the human low-back region. The Shore Durometer, SCTM, IndentoPRO and MyotonPRO reliably detected stiffness changes in three of the four MPTM layers. With the ultrasound method, only stiffness changes in layers thicker than 3 mm (i.e., SCT and ERS) could be measured reliably. No method could detect stiffness changes in the thin (1 mm) layer simulating the FPR.

The indentation and myotonometry devices included in this study are easy-to-use, with analog or digital displays allowing for an immediate reading of the stiffness-related measurement results. In addition, they are comparatively low in price [START_REF] Zügel | Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics: consensus statement[END_REF][START_REF] Wilke | Reliability and validity of a semi-electronic tissue compliance meter to assess muscle stiffness[END_REF][START_REF] Wilke | Die nicht invasive Untersuchung faszialer Strukturen -Eine narrative Übersichtsarbeit TT -Non-invasive Screening of Fascial Tissues -A Narrative Review[END_REF] . As none of the tools was able to detect stiffness alterations in the very thin fascia profunda layer, we assume that a certain thickness greater than 1 mm of a layer must be present for the devices, particularly for indentation and myotonometry technologies, to detect changes. While the STCM and IndentoPRO can specifically be set to different indentation depths, those tools alone cannot provide a final information about which tissue layers may present with stiffness alterations. To draw this conclusion, the specific thickness of each layer must be known. Compared to indentation and myotonometry technologies, ultrasound imaging allows for the distinction of different tissue layers, particularly regarding tissue thickness [START_REF] Wilke | Die nicht invasive Untersuchung faszialer Strukturen -Eine narrative Übersichtsarbeit TT -Non-invasive Screening of Fascial Tissues -A Narrative Review[END_REF] . Stiffness, however, can only be determined by ultrasound imaging by means of a force-deformation relationship. To quantify this ratio, the forces applied with the ultrasound transducer must be measured. The ultrasound set-up used in this study included a force gauge that was attached to a transducer by a firm, tight Velcro fastener. As this method could be sensitive to the alignment of the transducer and the force gauge, the used mounting might have impacted measurements as well as the resulting limits in measurement range observed in this study. Future studies should therefore use a firmer fixture when applying the same measurement set-up. Alternative, more cost-intensive technologies allowing for the evaluation of thickness as well as stiffness parameters comprise ultrasound elastography [START_REF] Taljanovic | Shear-wave elastography: Basic physics and musculoskeletal applications[END_REF][START_REF] Sigrist | Ultrasound elastography: Review of techniques and clinical applications[END_REF] and magnetic resonance elastography [START_REF] Chakouch | Viscoelastic shear properties of in vivo thigh muscles measured by MR elastography[END_REF][START_REF] Chakouch | New magnetic resonance elastography protocols to characterise deep back and thigh muscles[END_REF] .

Previous studies have indicated that the biomechanical properties of layered tissue structures make it difficult to reliably determine tissue hardness. As one exemplary assessment technology, earlier work has used Shore Durometers to measure tissue stiffness in distinct tissue layers of the body, particularly so regarding the skin layer [START_REF] Falanga | Use of a durometer to assess skin hardness[END_REF][START_REF] Periyasamy | Investigation of Shore meter in assessing foot sole hardness in patients with diabetes mellitus -a pilot study[END_REF][START_REF] Strzalkowski | Thresholds of skin sensitivity are partially influenced by mechanical properties of the skin on the foot sole[END_REF][START_REF] Beaudette | Spine postural change elicits localized skin structural deformation of the trunk dorsum in vivo[END_REF][START_REF] Holowka | Foot callus thickness does not trade off protection for tactile sensitivity during walking[END_REF][START_REF] Helili | An Investigation of Regional Plantar Soft Tissue Hardness and Its Potential Correlation with Plantar Pressure Distribution in Healthy Adults[END_REF][START_REF] Duan | Relationship Between Plantar Tissue Hardness and Plantar Pressure Distributions in People With Diabetic Peripheral Neuropathy[END_REF] . Recent research suggests that shore hardness, as measured by the Shore Durometer in the present study, is more representative of bulk tissue (i.e., skin plus underlying subcutaneous tissue) mechanics than it is of skin biomechanics alone. Stiffness may be influenced by the thickness of the individual tissue layers as well as by the size of the material probe. As a consequence, the thickness and size of individual tissue probes need to be known to draw conclusions about the stiffness values of the individual tissue layers [START_REF] Chatzistergos | Shore hardness is a more representative measurement of bulk tissue biomechanics than of skin biomechanics[END_REF][START_REF] Spears | The effect of heel-pad thickness and loading protocol on measured heel-pad stiffness and a standardized protocol for inter-subject comparability[END_REF] . While this prerequisite was met by the structure of the MPTM (individual tissue layers of homogenous materials with known thickness and stiffness properties), this might prove difficult in clinical practice. Ideally, thickness measurements with technologies such as ultrasound should be performed to secure these tissue properties. Alternatively, recent technologies such as ultrasound elastography or magnetic resonance elastography [START_REF] Chakouch | Viscoelastic shear properties of in vivo thigh muscles measured by MR elastography[END_REF] may serve as suitable methods to meet those requirements and to simultaneously determine soft tissue stiffness for all soft tissue layers including the fascia profunda [START_REF] Zügel | Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics: consensus statement[END_REF][START_REF] Avila Gonzalez | Frontiers in fascia research[END_REF][START_REF] Feng | Assessing the elastic properties of skeletal muscle and tendon using shearwave ultrasound elastography and MyotonPRO[END_REF][START_REF] Wilke | Effects of Maximal Eccentric Exercise on Deep Fascia Stiffness of the Knee Flexors: A Pilot Study using Shear-Wave Elastography[END_REF] . While our reasoning relates to the thoracolumbar region, the findings presented here are transferable to other anatomical areas that have similar layered structures as the MPTM as well.

When relating our findings to the clinical practice, several considerations must be made. To select therapeutic interventions for low back patients, knowledge of the morphometry (e.g. thickness) and biomechanical characteristics (e.g. stiffness) of the thoracolumbar soft tissues in a healthy state as well as in the presence of low back pathology can serve as valuable decision criterion. In clinical practice, thickness of different soft tissue layers is primarily determined with ultrasound imaging [START_REF] Cheung | Role of Ultrasound in Low Back Pain: A Review[END_REF] . With regards to stiffness assessment, manual examination has long been part of the clinical decision making. However, the validity and reliability of palpatory assessment have been described as poor [START_REF] Chatzistergos | Shore hardness is a more representative measurement of bulk tissue biomechanics than of skin biomechanics[END_REF][START_REF] Spears | The effect of heel-pad thickness and loading protocol on measured heel-pad stiffness and a standardized protocol for inter-subject comparability[END_REF][START_REF] Feng | Assessing the elastic properties of skeletal muscle and tendon using shearwave ultrasound elastography and MyotonPRO[END_REF][START_REF] Wilke | Effects of Maximal Eccentric Exercise on Deep Fascia Stiffness of the Knee Flexors: A Pilot Study using Shear-Wave Elastography[END_REF] . Stiffness assessment tools can be used by the clinical practitioner to document baseline measures and to track improvements over time and with interventions. The practitioner is posed with the challenge of finding evaluation methods able to discern stiffness changes across the different soft tissue layers as well as across the spectrum of different clinical presentations and populations. Our results support practitioners to choose appropriate measurement tools for different measurements depths.

In clinical practice, these findings should be linked with knowledge about morphological and biomechanical changes of the respective tissue layers in vivo in low back pain conditions. Various studies have examined these parameters: The cutis layer consists of the epidermis and dermis, with the latter providing most of the mechanical strength of this layer [START_REF] Wong | The dynamic anatomy and patterning of skin[END_REF] . Changes in cutis thickness (measured by ultrasound) and hardness (assessed with Shore durometer) have been reported in relation to different static spinal postures [START_REF] Beaudette | Spine postural change elicits localized skin structural deformation of the trunk dorsum in vivo[END_REF] . Skin in the trunk dorsum was reported to become thicker (~17%) and softer (~ 39 %) during spinal extension and to become thinner (~ 19 %) and harder (~ 106%) during spinal flexion compared to a neutral prone position. Such changes are of note when it comes to the postural positioning of the patient during clinical evaluation. Furthermore these findings are of clinical significance as mechanoreceptors may respond differently due to their altered positioning and spacing, which could contribute to the decreased tactile acuity reported in chronic low back patients [START_REF] Moseley | I can't find it! Distorted body image and tactile dysfunction in patients with chronic back pain[END_REF][START_REF] Catley | Is tactile acuity altered in people with chronic pain? a systematic review and meta-analysis[END_REF] .

The subcutaneous connective tissue (also termed hypodermis) consists of loose connective tissue and has been described to have mucous-like properties [START_REF] Guimberteau | The microvacuolar system: how connective tissue sliding works[END_REF] . For the subcutaneous connective tissue thickness, an ultrasound study by Langevin and colleagues [START_REF] Langevin | Ultrasound evidence of altered lumbar connective tissue structure in human subjects with chronic low back pain[END_REF] showed no significant differences between low back pain patients and asymptomatic controls. However, a recent retrospective study reviewing magnetic resonance images of low back patients revealed that the subcutaneous fat tissue thickness at the L1-L2 level proved to be superior to body mass index in predicting low back pain. The authors determined cutoff values to predict low back pain and spine degeneration for females (subcutaneous fat thickness > 8.45 mm) and males (> 9.4 mm) [START_REF] Berikol | Subcutaneous fat index: a reliable tool for lumbar spine studies[END_REF] . Furthermore, diet -particularly dietary salt intake -may influence lumbar subcutaneous edema, which could in turn influence non-specific low back pain [START_REF] Brown | Non-Specific Low Back Pain, Dietary Salt Intake, and Posterior Lumbar Subcutaneous Edema[END_REF] . Clinical practitioners should factor in such changes in subcutaneous tissue thickness and composition when examining thoracolumbar soft tissue structures.

For the fascia profunda layer, an ultrasound study found that the thoracolumbar fascia in people with chronic low back pain presented with 25% greater thickness compared to matched controls after adjusting for Body Mass Index 4 . Another biomechanical property of note for the clinical practice relates to the mobility between fascial tissue layers. Ultrasound investigations using cross-correlation analysis showed that the thoracolumbar shear strain was about 20% lower [START_REF] Langevin | Reduced thoracolumbar fascia shear strain in human chronic low back pain[END_REF] and deformability 28% smaller in patients with chronic low back pain during passive trunk flexion compared to controls [START_REF] Langevin | Reduced thoracolumbar fascia shear strain in human chronic low back pain[END_REF] . While these findings may support the clinical practitioner in their evaluation, the contribution of the thoracolumbar fascia to low back pain remains less studied than their muscular counterparts [START_REF] Cheung | Role of Ultrasound in Low Back Pain: A Review[END_REF] and should be further examined in future investigations.

Regarding the role of the lumbar muscle layer in low back pain, the multifidus muscle has been extensively investigated [START_REF] Cheung | Role of Ultrasound in Low Back Pain: A Review[END_REF] . Differences in cross-sectional area (males present with larger crosssectional area than females), and asymmetry between sides (muscle atrophy has been described ipsilateral to the reported side of unilateral pain) have been reported [START_REF] Hides | Multifidus size and symmetry among chronic LBP and healthy asymptomatic subjects[END_REF] . Furthermore, fat infiltration of the multifidus muscle is common in adult low back patients, and especially among females. Interestingly, this finding seemed to be independent of overall body fat estimated through body mass index [START_REF] Catley | Is tactile acuity altered in people with chronic pain? a systematic review and meta-analysis[END_REF] . This local change in tissue composition could alter biomechanical properties and consequently stiffness measurements and may therefore inform the practitioner's assessment of the low back area. While these findings may inform the practitioner's evaluation of the thoracolumbar region, standardized protocols and a broad range of reference values for thickness and stiffness of the different tissue layers, particularly as they relate to low back pain, are lacking. Reference databases for each of the soft tissue layer properties with regards to factors such as age, gender, body composition, ethnicity, and lifestyle differences are needed. In addition, it remains unclear how the relationship between different tissue layers changes in response to therapeutic intervention.

Even though our findings support the reliability and easy usability of the examined devices, several limitations of the present study need to be addressed. Previous research has recommended to use material phantoms to assess reliability of stiffness measurement devices [START_REF] Wilke | Reliability and validity of a semi-electronic tissue compliance meter to assess muscle stiffness[END_REF] . Our gel pad model proved to be appropriate for compression stiffness measurements, characterized by a force applied perpendicular to the material. However, the buildup of the model did not allow for the consideration of shear strain, which would include force exerted sideways on the medium. In diagnostic measurements as well as in therapeutic applications, shear mobility between tissue layers may play an essential role when it comes to low-back health [START_REF] Cohen | Statistical power analysis for the behavioral sciences[END_REF][START_REF] Krause | Acute effects of foam rolling on passive stiffness, stretch sensation and fascial sliding: A randomized controlled trial[END_REF] . Accordingly, further development of the MPTM, allowing for shear mobility to be considered, would be desirable to produce valuable reliability and validity data for researchers and practitioners [START_REF] Wang | A Non-invasive Method to Estimate the Stress-Strain Curve of Soft Tissue Using Ultrasound Elastography[END_REF] .

For each MPTM layer, ten gel pads with varying stiffness parameters were manufactured. The stiffness alterations for those ten gel pads were determined individually for each layer. Accordingly, the absolute as well as relative stiffness changes for each layer set were not identical. While the ecological validity of the MPTM benefited from this approach, creating a MPTM with the same gradations for each layer would have increased the comparability of all measurements across the different tissue layers.

Furthermore, the thickness and stiffness values for the MPTM were determined from a literature search. To our knowledge, no current data map the various soft tissue layers of the thoracolumbar region by different ethnicities, age groups, or sexes. Therefore, none of these subgroups could be taken into account when we designed the MPTM. In reality, the layered structure of the low back may differ significantly for these subgroups. For instance, body composition has been reported to vary between different ethnicities [START_REF] Deurenberg | Body mass index and percent body fat: a meta analysis among different ethnic groups[END_REF] , and race-related errors in models of body composition assessment have been noted [START_REF] Fedewa | Examining Race-Related Error in Two-Compartment Models of Body Composition Assessment: A Systematic Review and Meta-Analysis[END_REF] . Such differences and assumption errors may result in varying biomechanical properties of the different tissue layers, as can easily be imagined for the subcutaneous connective tissue. Neighboring fields such as nutrition and cardiology are already considering differences in body compositions for their respective scopes [START_REF] Oguntade | Body composition and risk of heart failure: protocol for a systematic review and meta-analysis[END_REF][START_REF] Barone | Assessment of body composition: Intrinsic methodological limitations and statistical pitfalls[END_REF] . Future research should be dedicated to establishing tissue layer properties for different subgroups, as such data may positively increase the validity of measurement devices and phantom models alike. Future work should furthermore refine existing measurement protocols [START_REF] Muckelt | Protocol and reference values for minimal detectable change of MyotonPRO and ultrasound imaging measurements of muscle and subcutaneous tissue[END_REF] for the examined stiffness assessment tools with defined measurement locations 1 and reference values for different body regions in vivo. 2 Figure 3. CUT cutis. SCT subcutaneous connective tissue. FPR fascia profunda. ERS erector spinae. Blank denotes "no reliable measurement possible".  denotes moderate correlation (> 0.4).  denotes strong. correlation (> 0.7).  denotes very strong correlation (> 0.9). Photos (1 st to 5 th row): rows 1-3: fasciaresearch.org with permission; myotonpro.com with permission, fasciareasearch.org with permission.

Figure 1 .

 1 Figure 1. Multi-layered phantom tissue model.

Figure 2 .

 2 Figure 2. Cross-section of L3 region. Photo: Modified from Visible Human Project of U.S. National Library of Medicine 23 , accessed through NPAC/OLDA Visible Human Viewer 24 with permission.

Figure 4 .

 4 Figure 4. A: Scatter plot of the agreement between the two raters for the MyotonPRO. B: Bland-Altmann plot of the mean differences between the raters. The dashed line in the middle represents the mean difference; the lines above and below show the 95 % limits of agreement. The values indicate the relative stiffness changes.

Figure 5 :

 5 Figure5: A: Scatter plot of the agreement between the two raters for the IndentoPRO. B: Bland-Altmann plot of the mean differences between the raters. Legend: see Figure4.

Figure 1 .

 1 Figure 1.

Figure 2 . 22 Figure 3 .

 2223 Figure 2.

Figure 4 .

 4 Figure 4.

Figure 5 .

 5 Figure 5.

Acknowledgments

Not applicable.

Stiffness measurement tools' reliability and validity

Data Availability Statement

The datasets that will be used and/or analyzed during the current study will be available from the corresponding author on reasonable request.

Author Contributions

Conceptualization: R.S., W.B., K.B., W.K.; formal analysis: A.B., R.S.; investigation: K.B., R.S., P.W., W.B., S.B.; methodology: K.B., R.S., A.B., W.B., W.K., J.W., S.B.; project administration: K.B., R.S.; resources: K.B., R.S., visualization: A.B., S.B., R.S., K.B., writing -original draft: K.B.; writingreview and editing: K.B., R.S., A.B., J.W., W.B., W.K., S.B., P.W.. All authors have read and agreed to the published version of the manuscript.

Competing Interests

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.


C Keller

M Mokhtari

B Vieille

H Briatta

P Bernard

Influence of a rescanning strategy with different laser powers on the microstructure and mechanical properties of Hastelloy X elaborated by powder bed fusion

Keywords: Additive manufacturing, powder bed fusion, Superalloys, lasing strategy, mechanical properties, texture

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

Influence of a rescanning strategy with different laser powers on the microstructure and mechanical properties of Hastelloy X elaborated by powder bed fusion

Clément Keller, M. Mokhtari, Benoît Vieille, H. Briatta, P. Bernard

To cite this version:

Clément Keller, M. Mokhtari, Benoît Vieille, H. Briatta, P. Bernard. Influence of a rescanning strategy with different laser powers on the microstructure and mechanical properties of Hastelloy X elaborated by powder bed fusion. Materials Science and Engineering: A, 2021, 803, pp.140474. 10.1016/j.msea.2020.140474. hal-03133794

Introduction

Due to its layer by layer manufacturing strategy, Additive Manufacturing (A.M.) is a major breakthrough over the last decades on the elaboration technique of metal parts with complex shapes. Among the different existing technologies, Laser Powder Bed Fusion (P.B.F.) is one of the most employed industrially.

Nevertheless, this technique is still very challenging for the metallurgical and mechanical communities. Indeed, the overall quality of parts obtained from P.B.F. depends on the process parameters such as the laser power and speed, the hatch distance, the powder layer thickness, the laser focus . . . [START_REF] Debroy | Additive manufacturing of metallic components process, structure and properties[END_REF]. The building strategy based on the laser path in a given layer but also with respect to the previous layer also plays an important role on the microstructure and mechanical characteristics of the manufactured part [START_REF] Kruth | Part and material properties in selective laser melting of metals[END_REF][START_REF] Cheng | Stress and deformation evaluations of scanning strategy effect in selective laser melting[END_REF][START_REF] Guan | Effects of processing parameters on tensile properties of selective laser melted 304 stainless steel[END_REF][START_REF] Hanzl | The influence of processing parameters on the mechanical properties of slm parts[END_REF][START_REF] Robinson | Determination of the effect of scan strategy on residual stress in laser powder bed fusion additive manufacturing[END_REF]. Depending on these parameters and building strategy, mechanical properties may be considerably affected due to a significant porosity rate, lack of powder fusion, overheating, crystallographic texture, morphological texture . . . [1; 7]. It is hence of prime importance to correctly understand the role played by the manufacturing parameters on the microstructure and properties to improve the process reliability but also the mechanical performance of metal parts obtained by additive manufacturing.

Due to aforementioned induced defects, metal parts obtained by AM are generally subjected to post-elaboration Heat Treatments (H.T.), sometimes coupled with mechanical loading (for instance Hot Isostatic Pressure -HIP), to reduce the residual stresses, the mechanical anisotropy and yield stress [START_REF] Debroy | Additive manufacturing of metallic components process, structure and properties[END_REF]. However these thermomechanical treatments increase both the overall elaboration time and costs limiting, hence, the interest of AM compared to conventional forming processes. Elaboration strategies which do not require further thermal or mechanical treatments deserve hence specific investigations. Moreover, depending on the industrial applications of the final part elaborated by AM, different mechanical properties may be desired at different locations. In the case of forged parts, these mechanical behavior modifications are obtained by local heat treatments using inductors for instance. For additive manufacturing parts, similar modifications of mechanical properties may be achieved from a local modification of the building strategy which ultimately influences the microstructure and the mechanical properties.

In literature, different strategies have been reported to increase the mechanical properties without H.T. . Besides the elaboration of optimized laser path for residual stresses reduction [3; 6], scanning strategies based on one or several laser rescans after the melting of a given powder layer has gained interest in the recent years. Indeed, despite a significant building time increase, that kind of elaboration strategy has been proved to improve the mechanical properties particularly in aluminum alloys, titanium alloys and stainless steels. Hence, it has been reported that the rescanning methods result in a decrease in residual stresses [START_REF] Shiomi | Residual stress within metallic model made by selective laser melting process[END_REF][START_REF] Kruth | Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method[END_REF][START_REF] Mercelis | Residual stresses in selective laser sintering and selective laser melting[END_REF][START_REF] Ali | Effect of scanning strategies on residual stress and mechanical properties of selective laser melted ti6al4v[END_REF][START_REF] Wei | Effect of laser remelting on deposition quality, residual stress, microstructure, and mechanical property of selective laser melting processed ti-5al-2.5sn alloy[END_REF], a decrease in porosity rate [13; 14], a decrease in surface roughness [START_REF] Yu | Influence of re-melting on surface roughness and porosity of alsi10mg parts fabricated by selective laser melting[END_REF][START_REF] Tian | Material interactions in laser polishing powder bed additive manufactured ti6al4v components[END_REF][START_REF] Liu | Selective laser remelting of an additive layer manufacturing process on alsi10mg[END_REF], an increase in hardness [START_REF] Liu | Selective laser remelting of an additive layer manufacturing process on alsi10mg[END_REF] or ultimate tensile strength [START_REF] Xiao | Effect of rescanning cycles on the characteristics of selective laser melting of ti6al4v[END_REF] and a modification of the microstructure [START_REF] Griffiths | Effect of laser rescanning on the grain microstructure of a selective laser melted al-mg-zr alloy[END_REF]. However, these improvements seem to depend on the number of laser rescanning [12; 17], laser speed [9; 11], laser power [10; 11] and laser path during the successive laser scan on a given layer [START_REF] Xiao | Effect of rescanning cycles on the characteristics of selective laser melting of ti6al4v[END_REF].

All these works point out the interest of rescanning strategies which may help to improve the microstructure and mechanical properties of metallic parts obtained by A.M. . However, for Ni superalloys, to the authors' best knowledge no investigation of such re-melting strategies has been published despite the huge industrial interest of these materials. Several questions still arise from these works, i) are rescanning strategies suitable for Ni superalloys ? ii) what is the effect of the power during the second laser scan ? iii) is remelting necessary for properties improvements ? iv) what is the influence of rescanning on microstructure? and v) what is the origin of these improvements ? Thus, the aim of this article is hence to try to answer to these questions by investigating the role played by laser rescanning with different powers during a P.B.F. manufacturing on the microstructure and mechanical properties of a Hastelloy X superalloy. Such rescanning strategy, depending on its application (i.e: locally or during the entire manufacturing), may help to improve the properties of the part without post-elaboration heat treatments.

Material and experimental procedure

Material and Elaboration

This investigation was performed on Hastelloy X superalloys. This material is used in aeronautics applications for its good mechanical properties and corrosion resistance at elevated temperature [START_REF]Application of Hastelloy X in Gas-Cooled Reactor Systems, Standard[END_REF][START_REF] Lee | A study on the microstructure and cyclic oxidation behavior of the pack aluminized hastelloy x at 1100 c[END_REF][START_REF] Zhao | Phase precipitation and timetemperature-transformation diagram of hastelloy x[END_REF]. Like other Ni-based superalloys, this material is suitable for additive manufacturing [START_REF] Tomus | Influence of post heat treatments on anisotropy of mechanical behaviour and microstructure of hastelloy-x parts produced by selective laser melting[END_REF][START_REF] Etter | Reduction in mechanical anisotropy through high temperature heat treatment of hastelloy x processed by selective laser melting (SLM)[END_REF][START_REF] Han | Laser powder bed fusion of hastelloy x: Effects of hot isostatic pressing and the hot cracking mechanism[END_REF][START_REF] Tomus | Effect of minor alloying elements on crack-formation characteristics of hastelloy-x manufactured by selective laser melting[END_REF].

The precursor powder of this material was provided by Auber and Duval with powder particle average diameter around 30 µm. The typical chemical composition of this alloy is reported in table 1. The elaboration was performed on an EOS M290 powder bed fusion machine at ArianeGroup company. The basic parameters set employed for the elaboration is summarized in table 2. For the double laser scan strategy, for a given sample, the second scan starts immediatly after the first one and follows the same path as the previous one. In order to investigate the role played by laser rescanning with different powers, six parameter sets were considered for the elaboration (see table 2): one reference Single-Laser Scan (LS) strategy (labelled -Ref. 1LS -in the following paragraphs) and 5 double-laser scan strategies with different laser powers during the second scan (referred to as -2LSxx -in the text, where xx represents the % of 1st laser scan power during the second scan). To investigate the microstructure and mechanical properties, 3 cylinders of 20 mm diameter and 90 mm height were manufactured for each parameter sets. Figure 1 illustrates the position of the cylinders on the elaboration plate. For the reference single-laser scan strategy, one sample was submitted to a solution Heat Treatment (H.T.) at 1175 • C during 2 hours at air and then air cooled (H.T. similar to the one reported by Heynes data sheet) [START_REF]Hastelloy x alloy[END_REF]. This sample is labelled Ref. 1LS H.T. in the following paragraphs. employed in this study. For each sample of the two laser scan strategies, the laser power on the second scan is expressed in % of the applied power during the first scan.

Mechanical characterization

In order to avoid typical A.M. surface roughness which may affect the mechanical properties, the cylinders were machined to obtain conventional tensile test specimens following the ISO 12126:2017 standards with a gauge length of 16 mm and a 8 mm diameter. One monotonic and two loading/unloading tensile tests were performed for each condition using an electromechanical MTS C45 tensile machine with a cross head displacement control. The axial strain was recorded by means of conventional "clip-on" extensometer. The applied strain rate was about 5.10 -3 s -1 .

Compared to monotonic tensile tests, loading/unloading tests enable us to investigate of the loading surface as a function of the axial strain. Using this loading surface, the flow stress can be divided into two components named backstress and effective stress [START_REF] Feaugas | Grain-size effects on tensile behaviour of nickel, AISI 316L stainless steel[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF][START_REF] Dickson | A comparaison of two simple methods for measuring cyclic internal, effective stresses[END_REF]. The backstress is then associated with the center of the loading surface whereas the effective stress is related to the radius of this surface as illustrated in figure 2. These two stress components are linked to different interactions of mobile dislocations with the microstructure. The effective stress corresponds to short range ones such as forest dislocation interactions or small coherent precipitates with dislocations. Backstress is related to long range interactions between mobile dislocations and strong defects like heterogeneous dislocation structures, incoherent precipitates or grain boundaries. The knowledge of the evolution of these stress components along with strain gives valuable information of the plasticity mechanisms. More details on the computation of these two stress components and their physical meaning can be found in other articles [27; 28].

Material and microstructural characterization

To understand the origin of this change in mechanical properties resulting from the different elaboration parameter sets, microstructural characterization was performed. First, density was measured for each elaboration conditions using an Archimedes type balance (precision measurement of 0.1 g) and a 5 mm heigh sample extracted at the top of the manufactured cylinders. 10 measurements were recorded for each sample and the average value along with the statistical error with a confidence index of 95% were computed.

Second Scanning Electron Microscope (SEM -JEOL 7900F) coupled Secondary Electrons (SE), BackScattered Electrons (BSE) and Electron BackScattered Diffraction (EBSD) were employed to investigate the melting pools and dendrites, the fracture surfaces, the grain sizes, the crystallographic texture, the precipitates and dislocation structures. These features were analysed in three planes: x-y, x-z and y-z, these three directions corresponding to the elaboration plate (see figure 1). For these analysis, samples were mechanically polished up to a 1200 SiC paper. A final step of electropolishing using A2 Struers electrolyte (20 V -30 s) was systematically applied prior to the observations. For melting pool analysis, this electropolishing step was followed by an electrochemical attack at 10 V during approximately 3 s. For EBSD, the sample observations were performed with a high voltage of 25 kV and with a electron current of 5 nA. Same scan area dimensions (800 x 600 µm) and step (0.7 µm) were employed for each sample. For dislocation imaging, Electron Channeling Contrast Imaging (ECCI) was performed using BSE detector with the following SEM conditions: 25kV of high voltage, 5 nA current and about 6 mm for the working distance.

Results

Initial material characterization

Figure 3 illustrates the Melting Pools (M.P.) in the plane y-z observed by scanning electron microscope (secondary electrons) for the reference parameters set (Ref. 1LS) in fig. 3(a), the 2LS100 conditions in fig. 3(b), the 2LS80 conditions in fig. 3(c) and the 2LS60 conditions in fig. 3(d). For the reference conditions (fig. 3(a)), conventional pools are observed. Their width dimensions correspond to the hatch distance. For the two conditions with laser rescanning at 100% and 80% powers, observed in fig. 3(b) and in fig. 3(c), changes in the melting pools are observed compared to the reference conditions.

With a full power laser rescan (2LS100), two different pools can be observed as schematically indicated in fig. 3(b). The first M.P. boundary, illustrated by a black solid line, represents the extend of the melting during the first scan. The second one, represented with a white solid line, illustrates the M.P. boundary of the second scan. For instance, the zoom inserted in the figure highlights an example of these two kinds of melting pools. Due to the larger thermal conductivity of solid material compared to powders [30; 31], remelting during the second laser scan is only partial. With a decrease in second scan laser power, the depth difference between the first and second scan M.P. increased as illustrated in fig. 3(c). For 2LS60 samples, no remelting is observed in fig. 3(d). The same observations can be made for 2LS40 and 2LS20 samples (not shown here).

To better characterize the microstructural modifications resulting from the 2LS conditions, the morphological and crystallographical texture were investigated by EBSD on all samples. The analysis were performed on the three observation planes, x-y, x-z and y-z. For the reference sample (Ref. 1LS), the laser direction is clearly visible in the x-y plane (fig. 4(a)). In this plane, grains are rectangular in shape with an elongation perpendicular to the laser direction with a dominance of the [011] orientation along the normal of the plane (z-building direction). Small equiaxed grains are also observed between each laser track. On the x-z and y-z planes, illustrated fig. 4 coordinates. However, the preferential grain orientations correspond to a single texture component if similar sample coordinates are employed for both pole figures. This Goss texture component has been already characterized for Ni-alloys obtained by additive manufacturing [32; 33] and steels [34; 35] and is related to the specific heat flux direction and associated solidification in A.M. [32; 34]. Compared to the reference 1LS sample, as illustrated in figure 7(a) and in figure 7(b), a grain orientation spread can be observed in the y-z plane of the 2LS100 and 2LS60 samples with a decrease in the maximal density pole. For the third double laser scanned sample at 20% laser power, no difference is observed compared to the reference 1LS sample with similar poles and corresponding densities. 8((a)), the double laser scanned sample at 100% of power, 2LS100 (fig. 8((b)) and the double laser scanned sample at 60% power, 2LS60 (fig. 8((c)). These observations were carried out on the y-z plane with a sample tilt of 0 • with respect to the electron axis. For each sample, several grains in various melting pools were observed in order to ensure that the differences in microstructure between the manufacturing conditions are statistically representative and may not result from a difference in grain orientation (not characterized for each observed area) which could change the dislocation contrast [START_REF] Kriaa | Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope[END_REF].

For the reference sample, firstly, heterogeneous dislocation structures are observed inside the grains. As illustrated in the blue inset of the figure 8(a), dislocations are mainly distributed in the interdentritic spaces with some isolated dislocations inside these dendrites. These dislocations appear as straight segments revealing the planar glide character of this material [37; 38]. In this figure, inside the grains, some misorientations also appear together with inclusions. Secondly, a fine interdentritic precipitation is characterized in the interdentritic spaces as highlighted in the red inset. The rough diameter of the precipitates is lower than 100 nm. These observations are similar to those reported by Pourbabak et. al. [START_REF] Pourbabak | Microscopic investigation of as built and hot isostatic pressed hastelloy x processed by selective laser melting[END_REF] for the sample material manufactured using a slighly lower volumic energy.

For the samples manufactured using the double laser scan conditions, the observations are similar to those of the reference sample. However, for the 2LS100 sample (fig. 8(b)), dislocation density seems to be higher than for the reference sample and several traces of activated slip systems are observed (see red inset), probably due to higher thermal stresses during the manufacturing process. The interdentric precipitation also seems to be coarser (blue inset) compared to the reference sample. This coarse dendritic precipation is also characterized for the 2LS60 sample as illustrated in figure 8(c) which does not exhibit various activited slip systems.

Mechanical properties assesment

Table 3 summarizes the volume mass computed using Archimedes method of all samples elaborated in this study. Taking into account the experimental errors on this measurement, all samples exhibit the same volume mass. The lasing strategy has, hence, no effect on this parameter. Figure 9 illustrates the tensile curves for the six elaboration conditions without heat treatment. The tensile curve related to the reference condition followed by the 1175 • C heat treatment during 2h is also indicated in this graph. Excepted for the heat treated sample, the flow stress level is similar for all samples obtained by additive manufacturing. Nevertheless, as observed in the inset of this figure, which represents a zoom on the plastic part of the tensile curves, several differences appear between the different elaboration conditions. First of all, as already observed in the pole figures, the mechanical response in tension of the Ref. 1LS sample and the 2LS20 sample are very similar. Second of all, for higher laser power during the second scan, a decrease in strain hardening rate is observed. Finally, the sample manufactured with 60% power during the second scan exhibits lower flow stress and larger plastic strain at necking compare to other samples. In order to better analyse the differences in mechanical properties resulting from the rescanning strategies, the evolution of the average value of the yield stress, maximal stress, necking and failure strains are plotted as a function of the elaboration conditions in fig. 10(a With regard to the yield stress (figure 10(a)), a higher value of this parameter is observed for the rescanning strategy with full power (2LS100 sample). With a decrease in the laser power during the second laser scan, the yield stress tends to the value obtained in the reference 1LS conditions. All samples manufactured by AM without heat treatment exhibit values larger than the heat treated samples.

For the ultimate tensile strength, the larger values are obtained in the reference conditions and the rescanning with a laser power of 20%. The lower value is obtained for a rescanning with a power reduction of 40% (2LS60) whereas 2LS100, 2LS80 and 2LS40 exhibit intermediate values. Taking into account the experimental scattering indicated by the error bars, the differ- ences are, nevertheless, not statistically significant. It should be mentionned that all the values of P.B.F. samples remain lower of about 100 MPa than the expected one for a heat-treated cast samples.

As far the necking strain is concerned, the maximal value 0.5 is obtained in the 2LS60 conditions whereas other samples have similar values close to 0.3. This significant necking strain for the 2LS60 sample is similar to the one of the ref. 1LS H.T. samples and higher than values reported for the same alloy elaborated by P.B.F. (without rescanning) and heat treated in the same conditions [START_REF] Tomus | Influence of post heat treatments on anisotropy of mechanical behaviour and microstructure of hastelloy-x parts produced by selective laser melting[END_REF] and also with HIP treatment [START_REF] Montero-Sistiaga | Microstructure and mechanical properties of hastelloy x produced by hp-slm (high power selective laser melting)[END_REF]. This 0.5 necking strain characterized for the 2LS60 sample is, moreover, similar to the value reported for a H.T. cast sample [START_REF]Hastelloy x alloy[END_REF]. For strain at failure, taking into account the experimental scatterring, the elaboration conditions do not seem to affect this property for Hastelloy X samples elaborated by P.B.F. and subjected to mechanical loading in the building direction.

These changes in the mechanical properties resulting from the elaboration conditions are also observed in the evolution of the backstress and the effective stress obtained from the loading/unloading tests. Figure 11(a) illustrates the evolution of the effective stress as a function of strain for the different samples. Regardless the elaboration conditions, this flow stress component is reduced with an increase in strain up to 0.1. For higher strain values, the effective stress is constant. The reference sample exhibits slightly larger values than those of the samples obtained with the rescanning strategy which do not seem to depend on the power of the second laser scan, except for the 2LS20 with similar values as Ref. 1LS sample. Compared to the heat treated sample, all the AM samples have higher effective stress values (difference lower than 50 MPa) for strain lower than 0.4. Due to its strain hardening capacity resulting from recrystalization, the effective stress of the H.T. sample strongly increases along with large strains to reach similar values as in other samples. The evolution of the backstress along with strain is also similar for all samples. Nevertheless, contrary to the effective stress, an increase in strain results in an increase in backstress. The backstress level weakly depends on the elaboration conditions as similar values are obtained for all samples. However, the 2LS60 sample exhibits the lowest value. Similarly to the effective stress, the backstress of the heat treated sample is about 200 MPa lower than the A.M. samples at the onset of plasticity. With an increase in plastic strain, backstress difference between all samples tends to be reduced. These results suggest that the higher flow stresses of A.M. samples compared to casted ones are clearly correlated to the backstress component.

After sample failure, fracture surfaces were observed by SEM. Figure 12 represents these fracture surfaces for four elaboration conditions: 1LS reference with heat treatment (Ref. 1LS H.T. -fig. 12(a)), 1LS reference without heat treatment (Ref. 1LS -fig. 12(b)), 2LS100 (fig. 12(c)) and 2LS60 (fig. 12(d)). For all conditions, ductile fracture is revealed by dimples in agreement with the large fracture strain observed in figure 10(b). For the heat treated conditions, the conventional cup and cone surface is observed with void nucleation, growth and coalescence in the center part of the sample and shear fracture near the surface. For the three other conditions these cups and cones fractures are not observed. Fracture seem, hence, to be dominated by shear. Moreover, for these latter conditions without H.T., voids are observed and the sample section is not longer circular. Elliptical shape is observed which is more pronounced for the double laser scanned samples (fig. 12(c) and fig. 12(d)). These non circular fracture surfaces suggest a important plastic anisotropy associated with the strong crystallographic texture. Secondary cracks aligned with the larger dimension of the cross section are also observed in these samples.

Discussion

All results presented in the previous sections show a significant effect of the rescanning strategy on both microstructures and mechanical properties. These changes are discussed in the following paragraphs in terms of remelting, crystallographical and morphological texture, backstress and laser power.

Microstructure and thermal history modifications

As observed in the previous paragraphs, the elaboration conditions influence the microstructure of the sample. The melting pools, the morphological texture or dominant grain orientations are dependent on these conditions. Table 4 summarizes the different microstructural characteristics, grain size, grain circularity, and the maximal density pole for the Goss texture component for five samples: Ref. 1LS H.T., Ref. 1LS, 2LS100, 2LS60 and 2LS20. These three double laser conditions correspond to: deep remelting, no remelting with best mechanical properties, no remelting with mechanical properties close to the reference sample, respectively. The grain size was computed using the average area converted then into diameter assuming, at first approximation, spherical grains. In addition, this value was obtained considering an average value based on each plane one (no huge difference was found between each plane). For the heat treated reference sample, full recrystallization occured leading to an isotropic texture with a low maximal density pole (6 MRD) ensuring no plastic anisotropy. Based on the analyses of these data, it appears that the rescanning strategy does not affect the grain size and grain circularity as very similar values are obtained for all samples. Grain size is, hence, not the revelant length scale to understand the dependence of mechanical properties with the lasing strategy. For the texture analysis, except for the heat treated sample, the strong Goss texture component reveals no strong modification of solidification during the process. Nevertheless, as already suggested by the comparison of the pole figures for the Ref. 1LS (fig. 5) and 2LS conditions (fig. 7), revealing a spread of the preferential grain orientations for the 2LS100 and 2LS60 sample, these two samples exhibit a slight reduction in the maximal density pole for the Goss texture component. In order to highlight this feature, a analysis of the grain orientation distribution with respect to the dominant {110} plane normal aligned with the Z sample direction was considered. Figure 13 illustrates the cumulative grain number fraction as a function of the crystal orientation. As illustrated in this figure, compared to the reference sample, the spread of preferential grain orientations for the 2LS100 and 2LS60 samples is clearly evidenced. For these two samples, the number fraction of grains oriented within 20 • with respect to the theoretical crystal direction is about 40% vs 60% for the reference sample. Considering the relationship between the process, i.e., directional solidification, it seems that the second lasing strategy affects the solidification. For the 2LS20 sample, with a second laser scan power about 20% of the first one, the grain orientation distribution is very close to the reference sample.

In f.c.c. and some b.c.c. materials, solidification occurs with the < 001 > direction aligned with the heat flux or thermal gradient [START_REF] Lee | Factors determining crystal orientation of dendritic growth during solidification[END_REF]. For additive manufacturing processes, this feature may lead to a strong Goss texture with the < 011 > aligned with the bulding direction if no laser scanning rotation is applied between each layer [START_REF] Ishimoto | Crystallographic texture control of beta-type ti15mo5zr3al alloy by selective laser melting for the development of novel implants with a biocompatible low young's modulus[END_REF]. In this case, dendrite growth will occur following the maximal thermal gradient which is oriented at 45 • with the building direction. When a scanning rotation is applied, the thermal gradient direction will change from a layer to another and a competition will take place between the nucleation and growth of new dendrites aligned with the thermal gradient, and the epitaxial dendrite growth from the former solidified ones (in the previous layer or in the same one). From this competition, significant misorientations are observed inside the grains giving rise to the so-called chevron patterns [START_REF] Andreau | Texture control of 316l parts by modulation of the melt pool morphology in selective laser melting[END_REF]. Moreover, different crystalographical and morphological texture may appear depending on the scanning strategy [START_REF] Bahl | Non-equilibrium microstructure, crystallographic texture and morphological texture synergistically result in unusual mechanical properties of 3d printed 316l stainless steel[END_REF].

Despite the 67 • laser scanning rotation between each layer, the strong Goss texture in the ref. 1LS and 2LS20 samples suggests that, for these two samples, epitaxial growth is the main solidification mechanism. However, as observed in figure 4 and in figure 6(c), for the Ref. 1LS and 2LS20 samples respectively, the chevron patterns indicate that dendrite nucleation also takes place during solidification.

For the 2LS100 and 2LS60 conditions, despite a similar laser scanning strategy, the reduction in the well oriented grain volume fraction with respect to the theoretical Goss texture, reveals that the the solidification process is affected. During the process, due to the double laser scan strategy, the temperature of these samples will be larger than the one for the reference conditions for which the sample can cool down between each laser scanning. Consequently, the thermal gradient or heat flux will be lower if the laser power during the second scan is high enough. Following the conclusions drawn by Andreau et. al. [START_REF] Andreau | Texture control of 316l parts by modulation of the melt pool morphology in selective laser melting[END_REF], this decrease in thermal gradient will enhance epitaxial grain growth as the driving force for nucleation is lower. This feature, first, will reduce the dominant < 011 > crystal direction parallel with the building direction as observed in figure 13. Second, it will also reduce the chevron pattern as observed qualitatively in figure 6(a) and figure 6(b) compare to the reference sample (see fig. 4). This increase in temperature for the high energy double laser scanned samples, involving the modification of the thermal gradient may also induce a modification in the cooling rate compared to the reference conditions. As already reported in literature, for IN718 Ni-superalloys, the cooling rate ( Ṫ ) is related to the dendrite size (λ) following equation 1 [START_REF] Dehoff | Crystallographic texture engineering through novel melt strategies via electron beam melting: Inconel 718[END_REF]:

λ = 97 Ṫ -0.36 (1)
An image analysis of the dendrite size was performed on the SEM observations carried out in the y-z plane for the Ref. 1LS, 2LS100 and 2LS60 conditions. Average values of λ, based on 8 images taken from different melting pools, are summarized in table 5. The comparison of the cooling rate values for the reference and 2LS60 conditions (which does not induce remelting) reveals that, due to the increase in temperature related to the second laser scan, the cooling rate is slighly increased for this double laser scan sample. When it comes to the 2LS100 samples, for which large remelting occurs, the cooling rate was increased by a factor 2.5 compared to the reference sample. For this sample, remelting occurs on a full solidified layer. Due to the increase in thermal conductivity for solids compared to powders [30; 31] this remelting leads to larger cooling rates which strongly influence the dendritic space. This increase in Ṫ can explain, hence, the activation various slip systems during the cooling down of the 2LS100 samples, as illustrated in figure 8(b).

Effect on the mechanical properties

The microstructural modifications due to the relationship between the manufacturing strategy and the thermal history are expected play a role on the mechanical properties.

As observed in figure 10(a), the yield stress is dependent on the scanning strategy. As the grain size is virtually the same for all samples (see table 4), the yield stress is not related to this parameter. The differences in dendrite size characterized in the previous section between Ref. 1LS, 2LS100 and 2LS60 samples may explain this modifications in yield stress. 2LS100 sample exhibits the larger yield stress (607 MPa) and lower dendrite size (0.33 µm) compared to the two other samples with similar values of yield stress (581 and 582 MPa for Ref. 1LS. and 2LS60 samples, respectively) and dendrite size ( 0.46 µm -Ref. 1LS vs 0.42 µm -2LS60). In plasticity, the dendrite walls will act as strong dislocation barriers which involve, in turn, an increase in yield stress following the well known Hall-Petch relationship [START_REF] Hall | The deformation and ageing of mild steel: III discussion of results[END_REF][START_REF] Petch | The cleavage strength of polycrystals[END_REF][START_REF] Thompson | Polycrystal hardening[END_REF].

However, despite a similar initial dendrite size value and yield stress, the Ref. 1LS and 2LS60 samples exhibit different strain hardening involving different flow stress level during plasticity (see figure 9). The evolution of the effective stress and backstress for the different samples considered in this study (figure 11) reveal that both stress components are affected by the elaboration strategy and can help to understand the effect of the second lasing.

For the effective stress, related to short range interactions between mobile dislocations and the microstructure, the higher values for the Ref. 1LS and 2LS20 suggest that the slight differences in dislocation density or precipitation, characterized in figure 8, play a role on the mechanical properties. These defects will participate to the dislocation anchorage which will increase the strain hardening [28; 48] as observed in figure 9. This increase in strain hardening will, in turn, lead to larger flow stress during plasticity for the Ref. 1LS and 2LS20 compared to the 2LS60 sample despite a similar initial dendrite size.

For the backstress, this stress component can be divided into two parts, a intragranular corresponding to the formation of heterogeneous dislocation structures and, a intergranular one, related to the strain incompatibilities between grains (grain size effect) [27; 28]. As the grain size is virtually the same for all samples, the backstress is expected to be related to the intragranular component only. Following a previous work on pure nickel, the intragranular backstress is inversely proportional to the dislocation cell size [START_REF] Keller | On the origin of the stress decrease for nickel polycrystals with few grains across the thickness[END_REF]. Taking into account this empirical relationship, according to the initial dendrite size of the Ref. 1LS, 2LS100 and 2LS60 samples, a larger value of backstress at the beginning of plasticity is expected for the 2LS100 samples compared to the two other specimens. However, this feature is not characterized experimentally as illustrated in figure 11(a) and consequently, other mechanisms must be responsible for the larger backstress for the reference 1LS sample.

The grain orientation scattering with respect to the Goss texture for the 2LS100 and 2LS60 samples may first have modified the average Schmid factor and may lead to the activation, locally, of different slip systems. Second, the qualitatively larger density of chevron patterns associated with Geometrically Necessary Dislocations (G.N.D.) [START_REF] Andreau | Texture control of 316l parts by modulation of the melt pool morphology in selective laser melting[END_REF] for the single laser scan strategy may also contribute to the larger backstress value for the Ref. 1LS sample compared to the 2LS100 and 2LS60 ones.

Finally the different microstructural modifications can also explain the larger necking strain for the 2LS60 samples. Necking phenomena is associated with the dislocation storage capactity (strain hardening rate). Materials characterized by a low strain hardening rate generally exhibit low necking strain as observed for instance for ultrafine grained or nanocrystalline materials [50; 51]. Due to its lowest dendrite size which reduces the probability of dislocation storage, the 2LS100 sample is characterized by the lowest strain hardening rate (fig. 9) and consequently to the lowest necking strain as observed experimentally (see fig. 10(b)). For the Ref. 1LS and 2LS60 samples, the larger value of the initial dendrite size compared to the 2LS100 enhances the strain hardening rate and, in turn, the necking strain. This improvement is, however, lower for the Ref. 1LS specimen. This feature could be due to the increase in strain hardening associated to due to the larger density of dislocations as explained in the previous paragraphs. Hence, compared to the 2LS60 samples, the dislocation storage capacity, for the reference 1LS specimen, is reached at lower strain such as necking. It is assumed that the improved mechanical properties of the 2LS60 are then due to a good compromise between yield stress and strain hardening capactity resulting from the microstructural modifications above associated with the second lasing condition with intermediate laser power.

Transmission electron microscopy should be conducted to quantitatively investigate the differences in microstructure between the different lasing strategies to be able to quantify the contribution of each microstructural modification (i.e. dislocation, G.N.D., precipitation, texture . . . ), associated with the second lasing strategy, on the mechanical properties.

Conclusions

In this study, the influence of a lasing strategy, with a systematic second lasing with different power, was investigated on the microstructure and mechanical properties of a Hastelloy X material elaborated by powder bed fusion processes. The main conclusions can be listed as follows:

1. the second lasing involves a partial remelting of the material resulting in two different melting pools if the power of the second scan is larger than 80% of the nominal power;

2. for high secondary lasing powers, the thermal gradient and cooling rates are modified leading to finer dendrites and lower Goss texture intensity;

3. the mechanical behavior is also affected by the double laser scan with a modification in strain hardening rate and an increase in ductility characterized by the necking strain;

4. the optimum mechanical properties (considering the processing conditions) are obtained for a second scan with a 60% power with a ductility similar to the one of a heat treated samples but with a yield stress increased by a factor 2.5;

5. a significant plastic anisotropy is observed for all samples characterized as-received due to the strong crystallographic texture.

Finally, this lasing strategy could be considered to manufacture high damage resistance material (high yield stress and necking plastic strain) taking advantage of the additive manufacturing processes without heat treatment. Further characterization of the microstructure and numerical simulations are nevertheless required to better understand the role played by the double laser scan strategy on the mechanical properties.

Acknowledgments

The Normandy Region and European Union (European Regional Development Fund) are greatly acknowledged for the financial support of the CLIP FAM project.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

  -0.15 1.0 max 0.04 max 0.03 max 1 max 20.5-23.0 8.0-10.0 0.5-2.5 17.0-20.0 0.2-1.0 bal.

Figure 1 :

 1 Figure 1: Illustration of sample distribution on the elaboration plate of the EOS M290 employed in this study. For each sample of the two laser scan strategies, the laser power on the second scan is expressed in % of the applied power during the first scan.

Figure 2 :

 2 Figure 2: Illustration of the stress decomposition during one unload/load sequence applied to an A.M. Hastelloy X sample.

Figure 3 :

 3 Figure 3: SEM analyses of the melting pools for: (a) the reference single-laser scanned sample (Ref. 1LS), (b) the double-laser scanned sample at 100% laser power (2LS100), (c) the double laser scanned sample at 80% laser power (2LS80) and (d) the double laser scanned sample at 60% laser power (2LS60). Building direction is vertical.

  (b) and fig. 4(c) respectively, elongated grains aligned with the building direction are observed with strong preferential crystal orientation. For these three observation planes, the corresponding pole figures are plotted fig. 5(a) (x-y plane), fig. 5(b) (x-z plane) and fig. 5(c) (y-z plane). As observed in the grain orientation maps, strong crystallographical textures with maximal density poles larger than 10 M.R.D. (for Multiple Random Distribution) are revealed for this reference sample. In the x-z plane (figure 5(b)), a Goss texture {110} 001 is observed. In the y-z plane (figure 5(c)), the same {110} 001 texture is also characterized. It is worth noticing that pole figures illustrated in figure 5(b) and figure 5(c) are given in different sample

Figure 4 :Figure 5 :

 45 Figure 4: Grain orientation maps for the reference single laser scan sample -1LS -for the three planes: (a) x-y, (b) x-z and (c) y-z. See figure 1 for the illustration of the axis with respect to the elaboration plate. Standard triangle is given with respect to the normal direction. For (b) and (c), building direction is vertical.

Figure 6

 6 Figure 6 illustrates the grain orientation maps on the three planes x-y, x-z and y-z for the 2LS100 (fig. 6(a) to fig. 6(c)), the 2LS60 (fig. 6(d) to fig. 6(f)) and 2LS20 (fig. 6(g) to fig. 6(i)). Compared to the reference 1LS sample, similar grain orientations are observed in the three planes for the three double laser scan conditions (2LS100, 2LS60 and 2LS20), revealing a similar Goss texture.

Figure 6 :

 6 Figure 6: Grain orientation maps for the double laser scanned samples with 100%, 60% and 20% of laser power. Observation planes are indicated in the subcaptions of the figure. See figure 1 for the illustration of the axis with respect to the elaboration plate. Standard triangle is given with respect to the normal direction of the observation plane.

Figure 7 :

 7 Figure 7: Pole figures of the crystallographic planes (001), (111) and (011) in the plane y-z for samples elaborated with the double laser scan conditions : (a) 100% laser power -2LS100, (b) 60% laser power -2LS60 and (c) 20% laser power -2LS20. See figure 1 for the illustration of the axis with respect to the elaboration plate.

Figure 8

 8 Figure 8 illustrates the microstructure observed by SEM using backscattered electrons of the reference 1LS sample (fig.8((a)), the double laser scanned sample at 100% of power, 2LS100 (fig.8((b)) and the double laser scanned sample at 60% power, 2LS60 (fig.8((c)). These observations were carried out on the y-z plane with a sample tilt of 0 • with respect to the electron axis. For each sample, several grains in various melting pools were observed in order to ensure that the differences in microstructure between the manufacturing conditions are statistically representative and may not result from a difference in grain orientation (not characterized for each observed area) which could change the dislocation contrast[START_REF] Kriaa | Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope[END_REF].

Figure 8 :

 8 Figure 8: SEM observations using backscattered electrons of the microstructure of: (a) reference one laser scanned sample (Ref. 1LS), (b) 100% double laser scanned sample (2LS100) and (c) 60% double laser scanned sample (2LS60).

Figure 9 :

 9 Figure 9: Engineering tensile curves of the different Hastelloy X samples elaborated by powder bed fusion using single laser scan (1LS) and double laser scan (2LS) strategies.

  ) for stresses and in fig.10(b) for strains. These average values and corresponding error bars (10%) are computed using the monotonic and loading/unloading tests. The typical values of a solution heat treated (1175 • 2 h air cooled) cast sample, provided by Heyne's data sheet[START_REF]Hastelloy x alloy[END_REF], are also indicated in these figures with horizontal lines.

Figure 10 :

 10 Figure 10: Influence of the elaboration conditions on (a) yield stress and ultimate tensile strength and (b) necking and fracture strains for Hastelloy X elaborated by powder bed fusion.

Figure 11 :

 11 Figure 11: Influence of elaboration conditions on the engineering backstress (a) and effective stress (b).

Figure 12 :

 12 Figure 12: Scanning electron microscope observations of the fracture surfaces for four Hastelloy X samples analysed in this study: (a) heat treated, (b) reference single laser scanned conditions, (c) double laser scanned with 100% power and (d) double laser scanned with 60% power.

Figure 13 :

 13 Figure 13: Cumulative grain number fraction as a function of the crystal misorientation with respect to the theoretical Goss texture.

Table 1 :

 1 Typical chemical composition of the Hastelloy X alloy employed in this study.

Table 2 :

 2 Summary of the elaboration parameters for the Hastelloy X samples using powder bed fusion investigated in this study. 1LS: single laser scan, 2LS: double laser scan.

		1st laser	2nd laser	Laser	Hatch	Powder	Scan	Total cumulated layer
	sample	power (W)	power (W)	speed (mm/s)	distance (mm)	height (µm)	angle ( • )	volumic energy (J/mm 3 )
	Ref. 1LS	285	-	960	0.11	40	67	67.5
	2LS100		285					135
	2LS80		228					121.5
	2LS60	285	171	960	0.11	N.A.	N.A.	108
	2LS40		114					94.5
	2LS20		57					81

Table 3 :

 3 Volume mass measured by Archimedes balance of the Hastelloy X samples elaborated in this study. Corresponding experimental errors are computed with a confidence index of 95%.

	Sample	Ref. 1LS	2LS100	2LS80	2LS60	2LS40	2LS20
	Volume	8.347	8.344	8.325	8.329	8.340	8.348
	mass (g.cm -3 )	± 0.008	± 0.013 ± 0.012 ± 0.016 ± 0.019 ± 0.009

Table 4 :

 4 Summary of some microstructural characteristics (grain size, grain circularity and maximal density pole -Imax) of the Hastelloy X samples investigated in this study. Grain size and circularity values are given with a relative error bar of 50%.

		grain	grain	Imax
	sample	size (µm) circularity (m.r.d.)
	Ref. 1LS H.T.	22	0.36	N/A
	Ref. 1LS	18	0.39	20
	2LS100	19	0.40	15
	2LS60	20	0.41	17
	2LS20	28	0.35	20

Table 5 :

 5 Dendrite space measurements and corresponding estimation of the cooling rate for the reference conditions and double lasing conditions with 100% and 60% nominal laser power. Error bars are given with a confidence index of 95%.

	sample	dendrite size (µm) cooling rate (K.s -1 )
	Ref. 1LS	0.46 ± 0.08	(2.86 ± 0.18) 10 6
	2LS60	0.42 ± 0.09	(3.68 ± 0.29) 10 6
	2LS100	0.33 ± 0.04	(7.2 ± 0.34) 10 6