Aravind Rajan Ayagara

André Langlet
email: andre.langlet@univ-orleans.fr

Ridha Hambli

On dynamic behavior of bone: experimental and numerical study of porcine ribs subjected to impact loads in dynamic three-point bending tests $

Keywords: Blunt Impact, Porcine Ribs, HR-pQCT, Finite Element Simulations, Fracture, Split Hopkinson Pressure

This study covers the characterization of the dynamic behavior of isolated porcine ribs based on experimental and numerical approaches. A Split Hopkinson Pressure Bar (SHPB) setup for three-point bending tests was used. Data of 20 tests were considered to be comprehensible for experimental characterization, thereby, showing an influence of strain rate on both time for fracture and amplitudes of force response. A three-dimensional porcine rib model was generated from the DICOM (Digital Imaging and Communication in Medicine) images of High-Resolution peripheral Quantitative Computed Tomography (HR-pQCT) scans. Material properties having been fitted by power law regression equations based on apparent density were assigned to the numerical rib.

A modified elastic-plastic constitutive law, capable of considering the effects of strain rate was adopted. An incremental and stress-state dependent damage law, capable of considering effects of strain rate on fracture propagation, non-linear damage accumulation and instabilities was coupled to the constitutive law. The Finite Element (FE) model shows high efficiency in predicting both force-displacement curve and the fracture patterns of tested ribs. Predictions prove the ability of the proposed model to investigate the fracture behavior of human ribs under dynamic loads.

Introduction

Rib fractures are frequent thoracic injuries, which are the principal causative factors in 30% of Road Traffic Accidents (RTA's) - [START_REF] Cavanaugh | Injury and Response of the Thorax in Side Impact Cadaveric Tests[END_REF] -or High-Speed Ballistic Impacts (HSBI's), [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript Shen | Modified Bilston nonlinear viscoelastic model for finite element head injury studies[END_REF]. The human thorax contains vital and primary elements of respiratory and circulatory systems. The bone fragments originating form rib fracture may injure the heart, lung pleura, and lung parenchyma causing medical conditions like pneumothorax or hemothorax. This is why thoracic trauma is considered the second lethal trauma next to head trauma. In general, a chest trauma can be encountered either by Blunt thoracic trauma (BTT) or by Penetrating thoracic trauma (PTT), [START_REF] Arunan | Chest trauma[END_REF]. The recent study on chest trauma by [START_REF] Fallouh | Blunt thoracic trauma[END_REF] had reported that 98% of thoracic trauma is due to BTT. [START_REF] Burnside | Blunt thoracic trauma[END_REF] had presented a detailed summary on injury mechanisms and the severity of injury for BTT. Moreover, it is proved that RTA's are the principal cause for BTT and can be seen in [START_REF] Liman | Chest injury due to blunt trauma[END_REF], [START_REF] Shirley | Trauma and critical care III: chest trauma[END_REF] and Horst et al. (2017). In fact, these mechanisms play an important role in the prediction of injury severity prior to radiological examination. Despite the existence of a concrete medical database, the mechanical behavior of ribs under impact loads is still vague. The knowledge of dynamic mechanical behavior and fracture patterns will aid us to understand the relationship between injury mechanism and the severity of the injury from Biomedical point of view.

The advances in computational ability and their advantages over expensive experimental procedures have led to the development of FE human body models such as Isolated thorax model [START_REF] Schoell | Age-and sex-specific thorax finite element model development and simulation[END_REF], the H-Model (Haug et al., 2004), the RADIOSS model [START_REF] Arnoux | Radioss finite element model of the Thor dummy[END_REF], the THUMS model [START_REF] Maeno | Development of a Finite Element Model of the Total Human Model for Safety (thums) and Application to Car-Pedestrian Impacts[END_REF]) and the HUMOS model [START_REF] Robin | HUMOS: Human model for safety˜A joint effort towards the development of refined human-like car occupant models[END_REF]. These FE human models have been used as a promising tool to overcome the limitations of experimental methods in the study of thoracic injuries. Even though these human FE models have advantages, they still have their respective constraints such as the representation of the structure, type of elements used and accuracy in prediction of fracture occurrence and mechanical behavior.

For a better comprehension of the dynamic behavior of ribs, the mechanical properties, numerical constitutive and damage laws should be addressed with equal priority. Regarding the mechanical properties, several authors have presented power law regression models. For example, [START_REF] Carter | The compressive behavior of bone as a two-phase porous structure[END_REF], [START_REF] Gibson | The mechanical behaviour of cancellous bone[END_REF] and Keyak et al. (1994) have put forth power law regression equations with apparent density (ρ app ) as an independent variable as opposed to Rice et al.

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ACCEPTED MANUSCRIPT (1988), who considered porosity (P o) or volume fraction (V f ) as independent variable. Apart from ρ app based models, there are also models based on mineralization or ash fraction. For example, [START_REF] Vose | Bone strength-its relationship to X-ray-determined ash content[END_REF] had considered ash fraction, whilst, Currey (1969), [START_REF] Burstein | Contribution of collagen and mineral to the elastic-plastic properties of bone[END_REF] and [START_REF] Schaffler | Stiffness of compact bone: effects of porosity and density[END_REF] had considered mineralization as independent variable. Similar to elastic properties, significant amount of researches can be found on mechanical behavior. For example, cortical bone shows evidence of elastic-plastic behavior [START_REF] Garcia | Elastic plastic damage laws for cortical bone[END_REF] whilst, trabecular bone shows evidence of behavior similar to polymeric foams [START_REF] Gibson | The mechanical behaviour of cancellous bone[END_REF], Kelly and McGarry (2012) and Karkar (2017). In fact, this difference in mechanical behavior is due to the architectural arrangement. Moreover, the bone material is strain rate ( ε) sensitive as underlined by [START_REF] Mcelhaney | Dynamic response of bone and muscle tissue[END_REF] and [START_REF] Carter | The compressive behavior of bone as a two-phase porous structure[END_REF]. Thereby leading us to apply constitutive laws such as viscoelastic-viscoplastic (Johnson et al., 2010) andelastic-viscoplastic (Li et al., 2010). Zioupos et al. (2008) had shown that "the strain rate has more effects on post-yield" when the sample is subjected to high strain rates, thereby justifying the use of elasto-viscoplastic constitutive law in this study. Moreover, Zioupos et al. (2008) have also stated that "microcracking is inversely proportional to strain rates", which justifies the use of a homogeneous model of the porcine rib in this study.

Numerous studies put forth concerning fracture criteria of bones have pointed out the limitations of basic fracture criteria models (e.g. von-Mises criteria, Hill's criteria) to model the damage of bone. For example [START_REF] Malik | Equine cortical bone exhibits rising R-curve fracture mechanics[END_REF], [START_REF] Taylor | Microdamage and mechanical behaviour: predicting failure and remodelling in compact bone[END_REF], [START_REF] Vashishth | Experimental validation of a microcracking-based toughening mechanism for cortical bone[END_REF], [START_REF] Ural | Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study[END_REF] and Abdel-Wahab and Silberschmidt (2011) had used fracture mechanics approach but failed to predict the complete fracture pattern, since these models are restricted to single dominant idealized planar crack. On the other hand, Hambli (2011a), Hambli (2011b) and [START_REF] Dall'ara | A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro[END_REF] have proposed damage models based on continuum damage mechanics (CDM). Most of these models are constrained to simulate bone fracture under monotonic load.

There is a lack of practical FE models capable of simulating bone fracture under dynamic impact environment. The primary hurdle for simulating fracture in dynamic loads is to consider the effects of ε.

This study discusses the dynamic response of porcine ribs when subjected to three-point bending (3PB) upon split Hopkinson pressure bars (SHPB) apparatus. The SHPB method has proven to be particularly appropriate to characterize the behavior of quasi-brittle materials (e.g. [START_REF] Ruiz | The hopkinson pressure bar: an alternative to the instrumented pendulum for charpy tests[END_REF] by applying a dynamic load to a specimen and to calculate both the impact force

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and the velocity at the point of impact (input bar interface) and the reaction forces at the support (output bar interfaces).

The 3PB test is used to determine the tensile strength of quasi-brittle beam-like structures.

In addition, the 3PB tests enable to analyze experimental measurements during the successive phases of the response, including the fracture phase. The dynamic response of the sample in the 3PB test depends on the relative order of magnitudes of the test duration (defined as time up to complete fracture) and the characteristic time of the structure. The response may be dynamic when its duration is comparable to the time taken by a wave for one to and fro motion from the point of impact to the sample extremities. This obliges to consider the transient motion of the sample. A spall response will be observed if the transit time through the specimen's transverse length and the test is of the same order as the the test duration. This has been pointed out by [START_REF] Delvare | A non-equilibrium approach to processing hopkinson bar bending test data: Application to quasi-brittle materials[END_REF]. In the present experiments, the rib responses were identified either in the dynamic response or in the spall response.

An elastoviscoplastic constitutive model coupled with an external damage law, which considers the effects of ε on behavior and fracture of rib, has been implemented on a FE model of the porcine rib.

The FE model shows high efficiency in predicting both the force-displacement curve and the fracture patterns of tested ribs. impacting the input bar. The duration of this wave is the time taken for one to and fro motion along the striker. As the wave arrives at the rib-bar interface, a part of it is reflected and the other part is transmitted to the output bars. Processing of the data required the strain histories measured on the three bars by three strain gages. The absolute time origin, t = 0, is defined by the optical velocity measurement device when the sriker passes a LASER beam, thereby triggering the measurement chain. On the input bar, the first gage measures the incident and reflected longitudinal normal strains vs. time t : ε inc (t ) and ε ref (t ), respectively. On each output bar, the second and third gages measure the transmitted strains ε tr1 (t ) and ε tr2 (t ).

Experimental Methods

Dynamic three-point bending tests

A time and space shifting procedure is applied in data processing. It consists of defining an origin t 0 which coincides with the arrival time of the incident wave at the input bar-sample interface:

t = t -t 0 (1)
All of the strains are then related to the relative time, as if they were measured at the bar-sample interfaces (this procedure is known as the "time and space" shifting of the strain waves).

In case of stress below yield limit of the bar material, application of formula describing the plane wave propagation would lead to the dynamic variables at the input and output bar-sample interfaces (subscripts "inp" and "out1", "out2" respectively): the reaction forces F , the interface velocity and displacement v, u:

F inp = A B E B [ε inc (t) + ε ref (t)] (2a)
F out1 = A B E B ε tr1 (t) (2b)
F out2 = A B E B ε tr2 (t) (2c) v inp = -c B [ε inc (t) -ε ref (t)] u inp = t 0 v inp dt (2d) v out1 = -c B ε tr1 (t) u out1 = t 0 v out1 dt (2e) v out2 = -c B ε tr2 (t) u out2 = t 0 v out2 dt (2f)
where E B , ρ B , and A B , are the bar Young modulus, mass density, and cross-sectional area respectively and the celerity of longitudinal waves is

c B = E B /ρ B . M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
The relative velocity V and displacement U of the input bar-sample interface are defined by:

V = v inp - (v out1 + v out2 ) 2 (3) U = t 0 V dt (4)
Since the mechanical impedance of rib (the mass density times the acoustic wave velocity in the material) is considerably lower than that of usual metallic bars, such classical bars cannot be used for this study as the impedance ratio would lead to a nearly zero transmission coefficient and a reflection coefficient close to 1. Thereby leading to a weak reaction force at the input barsample interface, as if the interface was a free interface. Hence, bars made of nylon were used in the present study.

The strains measured at the remote gage locations must be corrected to yield the signals at the interfaces. Several authors, among which Zhao and Gary (1995), Zhao et al. (1997),

proposed a visco-elastic correction based on the Pochammer-Chree model in infinite cylinders.

The dispersion equation was solved and provided a correction that takes both dispersion and damping into account. In the present work, the shifting procedure is carried out by the DAVID software [START_REF] Gary | David -instruction manual[END_REF] built under the LABVIEW R environment. The DAVID interface is used to calculate the dynamic forces F inp , F out1 , F out2 from the strain signals.

The second question to be addressed is non-plane wave effect, due to the possibility of nonuniform strain distribution over the normal cross-section of the bar. On the external bar surface, the strain can even be zero while being non-zero within the cross-section. This issue of great importance has been discussed by [START_REF] Zhao | On the errors associated with the use of large diameter shpb, correction for radially non-uniform distribution of stress and particle velocity in shpb testing[END_REF] considering the bar radius and the spectrum of the pulse wave and the material (steel, aluminum, nylon). For the experimental conditions of the present study, the assumption of uniform strain distributions (plane waves) leads to a maximum errors less than 5% (Merle and [START_REF] Zhao | On the errors associated with the use of large diameter shpb, correction for radially non-uniform distribution of stress and particle velocity in shpb testing[END_REF]. Therefore, the correction applied to measured strains was only for the dispersion, but not for three dimensional effects.

The application of the use of nylon bars for dynamic three-point bending tests on ribs can be seen in [START_REF] Aubert | On the use of Hopkinson bar-bending apparatus to study soft impact on porcine ribs[END_REF].

A mirror and a high-speed camera was placed on either side of the rib to record the test at an acquisition frequency ranging from 11000 images/s to 25000 images/s until rupture of the specimen.

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Rib geometrical model and elastic properties

A batch of porcine ribs was bought from a local meat processing plant in order to ensure homogeneity of samples. These ribs were stored in a cloth soaked in saline (9% NaCl) to avoid Simpleware R code, we obtained the linear calibration coefficients µ to convert the raw data into normalized data (GS), expressed in Hounsfield Units (HU) using the following linear expression [START_REF] Taylor | Determination of orthotropic bone elastic constants using FEA and modal analysis[END_REF][START_REF] Teo | Relationship between ct intensity, micro-architecture and mechanical properties of porcine vertebral cancellous bone[END_REF]:

GS = 1000 (µ b -µ w ) (µ w -µ a ) ; µ w = 0; µ a = -1000. (5)
where: µ b , µ w , and µ a are the values for bone, water and air respectively. This was done by calculating the average GS within each of the five calibration samples along the length of the scan and calculating the slope and intercept vs. the known equivalent K 2 HPO 4 and H 2 O densities.

According to [START_REF] Taylor | Determination of orthotropic bone elastic constants using FEA and modal analysis[END_REF], GS is related to the effective density ρ eff (which includes the masses of: bone, bone marrow and fluids), whereas ρ app excludes the bone marrow.

Effective density ρ eff (Fig. 4) is defined as:

ρ eff = 0.523 GS + 1000 (6) M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
Apparent density ρ app is calculated using a linear relationship with zero intercept (see Fig. 4):

ρ app = 1.2097 GS (7)
To distinguish the different constituents of porcine rib, we had used the porosity (P o) calculated from volume fraction V f .

P o = 1 -V f = 1 - ρ app ρ tissue (8)
where, ρ tissue = 1850 kg/m 3 is the density of the solid bone tissue. As we assume that both cortical bone and trabecular bone are of similar composition, the tissue density was considered same for porosity calculation. The grey scales, the porosity values and standard deviation of the eight parts are given in Tab.1. The standard deviation was estimated through the resolution of the imaging system.

Based on the porosity, respective power law regression equations were used to obtain the mechanical properties (see Tab. 2). The equations for cortical bone and trabecular bone were adapted from [START_REF] Doblaré | Modelling bone tissue fracture and healing: a review[END_REF] and Kopperdahl and Keaveny (1998) respectively.

The mechanical properties of the constituents in terms of ρ app are plotted in Fig. 5 (the standard deviations are given in Tab. 1). Among the properties listed in Tab. 2 the following will intervene in material model of the rib: apparent density ρ app , Young Modulus E, and tensile yield stress σ yT .

Material models

Striker and Bars

As the nylon bars and striker are weakly viscoelastic, damping and dispersion of the waves during the first to and fro motion along the bars are moderate. Therefore, an elastic constitutive law is assumed for the bars and striker in numerical model. In the present case, this hypothesis does not fundamentally affect the simulation results as it will be justified later.

The material properties of bars and striker were determined through longitudinal wave celerity obtained after an impact of the striker on the free input bar. Knowing the mass density ρ B = 1200 kg.m -3 , the Young modulus E B was found to be 3.3 GPa. The Poisson's ratio 0.4 was determined from transverse and longitudinal strain measurements

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3.2. Rib

Constitutive law

The classic elastic-plastic law was modified to consider the effects of strain rate ε. Zioupos et al. The cortical and the trabecular bones were modeled using elastoviscoplastic behavior.

Cortical and trabecular bones were supposed to obey isotropic and kinematic hardening respectively, as it was demonstrated by previous studies: [START_REF] Garcia | Elastic plastic damage laws for cortical bone[END_REF] and Wolfram and Jakob

Damage law

Even though the material models offer element deletion based on fracture strain ε f , it is not sufficient to capture the evolution of crack and damage initiation whilst the bone is subjected to impact.

Thus, the constitutive law was coupled to an incremental and stress-state dependent damage law which also considers damage accumulation, (∆D), [START_REF] Frieder | Considering damage history in Crashwortihness simulations[END_REF], [START_REF] Fillipe | On the prediction of Damage and Failure in LS-DYNA: A comparison of GISSMO and DIEM[END_REF].

The triaxiality is defined as:

η = - -1 3 tr σ σ eq (10)
where: 1 3 tr σ is the hydrostatic pressure (average of the σ stress tensor trace) and σ eq is the equivalent stress.

The relation between the fracture strain ε fd and triaxiality η -Eq. ( 10) -is given in the form of an input curve plotted in Fig. 6a.

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In this study, the static fracture strain ε fs value is 2 × 10 -2 m/m for cortical and 3 × 10 -2 m/m for trabecular bone. To approach the realistic fracture and propagation behavior using our damage model, the influence of strain rate ε on the fracture strain ε fd was implemented by an equation from [START_REF] Wood | Dynamic response of human cranial bone[END_REF] as follows:

ε fd ε fs = A -B Ln ε ( 11
)
where A = 0.63. Five different values of B were tested. The corresponding expressions of Eq. ( 11) are listed in Tab. 3 and the input curves for ε fd /ε fs vs. ε are plotted in plotted in Fig. 6b.

Note that the static fracture strain provided by [START_REF] Wood | Dynamic response of human cranial bone[END_REF] is 0.86 × 10 -2 m/m, which corresponds to a quasi-static strain-rate of 3.18 × 10 -3 s -1 . Similarly, in the present study Eq. ( 11) is not applicable for ε lower than 3.00 × 10 -3 s -1 , which are quasi static. For all values 0 s -1 ≤ ε ≤ 3.00 × 10 -3 s -1 , a linear approximation is applied so that ε fd /ε fs = 1 at ε = 0 s -1 .

The increments in damage ∆D is expressed in terms of plastic strain ∆ε p , triaxility η and ε as follows:

∆D = n ε fd (η, ε) D (1-1/n) ∆ε p (12)
The damage exponent n is to differentiate between linear and non-linear damage accumulation.

The reduction in load carrying capacity due to increase of damage is taken into account through a modified equation of Lemaitre's effective stress principle:

σ = σ (1 -D m ) ( 13
)
where σ is the effective stress tensor.

When the damage D reaches 1.0, fracture occurs and the gaussian integral point of the corresponding element no longer exists in the calculation.

The parameters used for damage law are given in Tab 4. The damage exponent n values were adapted from [START_REF] Wolfram | Damage accumulation in vertebral trabecular bone depends on loading mode and direction[END_REF]. Unfortunately, the lack of database on the fading exponent m for bone had led us to use m = 1.0.

When the yield stress is reached damage D starts to accumulate according to Eq. ( 12). The fracture strain ε fd influences this accumulation. The more ε fd decreases with increasing strain-rate, more drastic will be the increase in damage accumulation ∆D and in ∆ε p .

The ultimate damage value D = 1 is reached through the non-linear coupling between damage

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D, fracture strain ε fd (η, ε), plastic strain ε p and softening. When D = 1, the corresponding element is removed from the structure, thereby initiating the crack propagation until fracture.

The strain rate influence on the post-yield behavior is also clear on the energy W absorbed by the structure. The more rapid is ε fd decreases with respect to ε, the less is the energy absorbed.

Average properties of rib

The constitutive law of cortical and trabecular bone of porcine rib could be recapitulated through mean values of the elastic properties. These values are summarized in Tab. 4 and the damage law parameters as well.

It is remarkable that the values presented here are the same order of magnitude to that of human ribs published by [START_REF] Charpail | Analyse du comportement mécanique des côtes humaines en dynamique[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Rib fractures under anterior-posterior dynamic loads: experimental and finite-element study[END_REF] and Yates and Untaroiu (2018).

Finite element model

The simulations were executed with LS-DYNA R explicit solver (Livermore, LSTC R ,CA).

Mesh and Boundary Conditions

Mesh

The SHPB bars were meshed with solid hexahedral elements. For an accurate simulation of 1D longitudinal wave propagation in bars, the element length in the direction of propagation was considered to be 1 mm.

In the case of ribs, the 3D geometry generated through DICOM images was meshed with hexahedral elements using Simpleware R ScanIP (Synopsys R , CA) Fig. 7. Previous studies that investigated the model convergence recommended using an element of size less than 3 mm to accurately capture the heterogeneous variations in the mechanical properties (Keyak et al. 1994[START_REF] Bessho | Prediction of strength and strain of the proximal femur by a CT-based finite element method[END_REF]) and to ensure an accurate prediction of the fracture path growth (Hambli, 2013). Therefore, an element size of about 0.15 mm was retained to mesh the ribs leading to a total of 226520 eight nodes hexahedral (solid brick) elements. For the sake of optimization of calculation time, bar and rib elements were assigned one Gaussian integral point only. To avoid volumetric locking or Hourglass modes, a Flanagan-Belytschko stiffness form [START_REF] Flanagan | A uniform strain hexahedron and quadrilateral with orthogonal hourglass control[END_REF] with an exact volume integration Hourglass formulation was selected. In fact, to avoid instabilites in solid elements, the Hourglass coefficient for bars was set to 0.03 whilst, the Hourglass coefficient for bone elements was set as default (0.1).

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The trabecular and cortical properties presented in the subsection 2.2 were assigned through their spatial localization provided by the CT scan images. The resulting density (ρ app ) distribution is presented in Fig. 8, showing the imbrication of parts of differing properties.

Boundary Conditions

The nodes belonging to rib were left free i.e. no constraints in motion. However, they may be subjected to reaction forces at the contact interfaces. This is also applicable at the input bar and striker contact interface.

The nodes belonging to striker were assigned an user defined initial velocity, in this case, v striker = 17.39 m.s -1 , which corresponds to the selected experimental test to be modeled. For this case, fracture occurs before the dynamic equilibrium is established.

Contact

A penalty based "Surface-to-Surface Contact" algorithm was defined between the sample and bars. The friction coefficient is 0.1. A segment-based approach was invoked, which searches for penetration of master and slave segments and then applies the penalty force on segment nodes instead of searching the penetrating nodes and then applying the forces to segments. In addition to this, the segment based approach stores the initial penetration value of segments and removes them from the current penetration value before calculating the contact force, thereby avoiding nodeshoot-out if a large penalty force if detected. Thanks to the contact formulation, the interface forces can be extracted from the contact data thereby providing us a criterion to compare the numerical and experimental structural response.

Another contact algorithm ("Contact-Interior") is defined between each constituent (visible in Fig. 8) in order to represent the internal cohesion of the structure. By doing so, the solver is capable to apprehend that these constituents form a single structure.

Experimental Results

Analysis of force response

A total of 20 tests were considered to be worthy for analyzing the experimental response. The results can be distinguished into two categories: (1) tests with no fracture, (2) tests with fracture.

(1) Tests with no fracture. We observe three different phases in the force response. Phase A: during this short phase (till 300 × 10 -6 s), there is a brutal increase in input force whilst,

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the output force is still zero. The sample is in an out-of-equilibrium state. Phase A will be observed in any experimental test. Phase B: the rib is subjected to forces applied by the two output bars (between 300 × 10 -6 s and 700 × 10 -6 s). The input force F inp and the resultant ΣF out = F out1 + F out2 are almost equal meanwhile showing evidence of small oscillations. Phase C: a dynamic equilibrium is established between F inp and ΣF out which occurs beyond 700 × 10 -6 s, and the oscillations disappear. As no fracture occurred, the brutal decrease (similar to a discontinuity) in the contact force signals in not observed (Fig. 9a).

(2) Tests with fracture.

(a) During dynamic equilibrium phase: Similar to tests with no fracture, a brutal increase in F inp is observed, followed by a plateau phase. A dynamic equilibrium is established around 600 × 10 -6 s (see Fig. 9c) in this case. The important characteristic in this kind of response is that the crack propagation and fracture occur during the equilibrium phase. The fracture of the rib corresponds to the rapid fall in force signals.

(b) During the non-equilibrium phase: Fig. 9e shows respective characteristics of fracture during the non-equilibrium phase. The sample has no time to establish an equilibrium between F inp and ΣF out . The fracture of rib occurs around 500 × 10 -6 s, way before the equilibrium is established.

Structural response of rib and corridors

The structural response was studied through the force-displacement curve F inp vs. U . The interface relative velocity V and relative displacement U between the surface of bars and the rib are calculated through Eqs. (3), (4), respectively.

Three categories of structural responses are distinguished according to the interface velocity V . Maxima and minima of the ensemble of each category define the experimental corridors 1, 2 and 3.

(1) 5 ≤ V ≤ 7 m/s, Fig. 9b.

(2) 8 ≤ V ≤ 10 m/s, Fig. 9d.

(3) 11 ≤ V ≤ 13 m/s, Fig. 9f.

Through these experimental corridors, we notice that as the velocity V increases, the fracture of rib tends to occur at dynamic non-equilibrium phase.

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6. Numerical results and validation of the model

About the constitutive and damage laws

The FE model is capable of deleting element thereby resulting in "erosion" of the structure.

For tensile stresses or strains, elements can be deleted either when D = 1, and/or the strain reaches the dynamic fracture strain ε fd . For compressive stresses, element deletion is not allowed by the triaxiality criterion (Fig. 6a) but may occur only when damage D reachs the unit value in an element.

Therefore, the fracture propagation being simulated is essentially governed by the tensile behavior of the FE model, but, also slightly influenced by the damage caused by compressive stresses.

Note that the response mode of the rib is similar to a bending mode. Then, the compression and tension zones are in general symetrically localized about the cross-section centroid. In such case, erosion of a few elements by compression may accelerate the onset of fracture in tension.

For this reason, the tensile yield stress σ yT has been assigned to the yield stress σ y0 in the material model definition (section 3).

The fracture pattern can be observed in Fig. 10. It is evident that the crack starts to propagate from the surface subjected to tension towards the point of impact and is a purely local phenomenon.

It appears that the crack origins at the same point. Other common characteristics shared between experimental and numerical fracture pattern are the Mode-I crack and the time interval in both cases is 0.13 × 10 -3 s.

Consistency of the numerical strain, velocity and displacements time histories

To verify the pertinence of the FE model, the first stage is to validate the numerical time histories of strain at the interfaces. In effect, every physical quantity inferred from the SHPB tests are based on the interface strains. Therefore, it is mandatory to verify the relevancy of the numerical interface strains with the experimental results. Moreover, the relevancy of the velocity and displacement histories must also be verified.

The signals presented in Fig. 12 were obtained during a test where fracture occurred before equilibrium. The striker velocity was 17.39 m/s both in the experiment and in the simulation.

For this test, the experimental force histories are plotted in Fig. 9e.

The numerical strain signals were post processed through a MATLAB subroutine to calculate the forces at interfaces with the porcine rib using Eq. (2a), Eq. ( 2b) and Eq.( 2c). In order to

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be coherent with the experimental procedure, this MATLAB subroutine applies an appropriate time shifting procedure to the numerical strains. The obtained incident, reflected and transmitted waves are plotted in Fig. 12a and 12b respectively. The velocity v inp and the displacement u inp of the input bar-rib sample are plotted in Fig. 12c and12d.

A keen observation to the ε inc and ε ref , reveals that there is a slight difference between numerical and experimental signals. On the other hand, the difference in the transmitted strain signals can be explained by the difference in geometry. Yet, the numerical interface velocities and displacements are almost similar to that of experimental.

The numerical displacement of output interface 2 shows a peculiar response. It is clear that it superposes with experimental signal till t ≈ 500 × 10 -4 s. Beyond this point of time the magnitude of u out2 Num. is greater than u out2 Exp., that can be explained by the loss of contact between the sample and output bar interface 2 in the simulation (see Fig. 11). One has to recall that the experimental samples were sanded at the anterior posterior ends to establish a good contact at the sample-output bar interface. Rather, the numerical sample was kept as natural as possible in order to avoid unnecessary penetration and unwanted noise in the strain signals and contact force. In Fig. 10 a crack starts to propagate towards the input bar-sample interface until rupture at t = 2.30 × 10 -3 s. This time translates to t ≈ 4.50 × 10 -4 s in Fig. 12d, at which the numerical sample is no more in contact with output bar 2. The increase in displacement beyond this time represents the rigid displacement of output bar.

Consistency of predictions of force vs. time response

The contact force history is highly sensible on the contact algorithm. If the simulated contact correctly represents its physical counterpart, the reaction force between the sample and the input bar obtained either through the strain signals or directly by the contact algorithm must be similar.

The forces calculated using these two methods are presented in Fig. 13.

Two keen observations can be made from Fig. 13: (i) The arrow in Fig. 13 indicates fluctuation of the force which arises due to an accuracy issue of the time shifting procedure (in the determination of the origin time t 0 to be precise). It is a well known issue of the SHPB experiments.

(ii) there is a time lag of about 0.19 × 10 -3 s between the force form contact and force from strain signals. Recalling that the formula used to process the SHPB signals assume a total contact at each bar interface. In reality, the sample does not stay in contact with the total bar cross-

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
section as illustrated in Fig. 14. Therefore, the more planar the contact surface, the less is the discrepancy between these forces (see Fig. 15). The aforementioned difference in contact surface between the entire rib sample and a cylindrical rib bone sample are presented in Fig. 14.

If the surfaces at the sample-input bar interface are of similar geometrical definition this time difference should be zero.

In addition, if the contact algorithm is physically and numerically veracious, the forces amplitude should be the same. These two exigencies are satisfied if the bar-sample interface area is made equal to the bar cross-section in a pure compressive test (SHPB) simulation. It can be seen that the force response from strain strain signals (solid line) and that obtained directly from contact (dashed line) superimpose.

The highest discrepancy noted in the present simulation (rib) is represented in Fig. 13.

In fact, care must be taken to compare the numerical results with the experimental data of similar characteristics, in this case, the time taken for fracture was considered as the control variable. As the numerical t f rac ≈ 0.512 × 10 -3 s, all the simulation data were compared with test with fracture during non-equilibrium phase in Sec. 5.1.

It is evident that there would always be a difference between the numerical force response and experimental force response since it is not possible to use the same sample for numerical and experimental purposes due to the drying process.

Comparison of numerical and experimental force displacement response

The structure behaves initially as an elastic body. At small times, the response is determined only by the material properties and the local stiffness distribution near the impact area. Therefore, during this time interval (on the left of the vertical dotted line in Fig. 16), the form of the response histories at the very beginning are similar for every numerical cases.

The numerical simulation was carried out with a striker velocity of 17.39 m/s, leading to a numerical interface velocity V of 10.46 m/s. The numerical results are compared to an experimental case of similar conditions i.e. Corridor-3. The best numerical result corresponds to that obtained with input curve 2 (Fig. 6b) of the damage law and is shown in Fig. 17.

The differences between experimental and numerical response arise due to the difference in the geometry of samples tested.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

Conclusion

The present study provides both experimental and numerical evidence for fracture propagation in ribs under certain dynamics impact environments.

The dynamic three-point bending split Hopkinson bar had led to the measurements of dynamic physical quantities characterizing the rib fracture.

Three types of responses were observed in our experiments, (i) no fracture, (ii) fracture during equilibrium between external forces and (iii) fracture before equilibrium was established. Also the numerical values belong in the range found by previous authors.

Concerning the numerical simulations, the current study indicates successful FE implementation of complicated constitutive and damage law with the consideration of strain rate effects and non-linear damage accumulation.

Even though the correlation between the experimental and numerical fracture pattern is adequate, an accurate representation of a more realistic fracture behavior requires model improvements such as: bone heterogeneity, transmission of forces between the different constituents of the rib. Moreover, optimization of the damage law parameters through respective experimental data, will further improve the efficiency of the proposed FE model.

The porcine rib was used as a human surrogate rib in order to develop an adapted methodology for the human rib. The improved human rib model will be implemented in numerical human body model.

Acknowledgments

The authors acknowledge the french Region Centre-Val de Loire for having provided the funds for the study. The authors would also thank Dr. Eric Lespessaille (MD, PhD, PAST) of Orleans Regional Hospital, for his valuable assistance in HR-pQCT procedure. Zhao, H. and G. Gary (1995)

Fresh

  porcine ribs were subjected to dynamic 3PB tests. The muscles and tissues surrounding the ribs were removed prior to tests. The experimental set-up consists of three bars: the input bar (3 m long) and two output bars (1.75 m). The rib sample is simply supported between the three bars as shown in Fig. 1. The rib extremities were sanded to a plane surface so that a stable and homogeneous contact is established with each output bar at the two output interfaces, Fig. 2. The signal acquisition frequency in the set up is 1 MHz. Strain gages were placed at the midpoint of input bar and at 400 mm from the output bar-sample interface on output bars to obtain strain signals for post-processing.The principle of the test is to generate a compressive pulse wave which is created by the striker

  dehydration and stored in a refrigerator at 4 • C whilst not in use. They were defatted in an aqueous solution of sodium hypochlorite (NaClO) and salt (NaCl) prior to the computed tomography (CT) scan. Later, they were scanned using High-Resolution peripheral Quantitative Computed Tomography(XtremeCT, Scanco, Switzerland). The DICOM image slices were obtained using a multi slice device at 120 kVp, 160 mAs with a 512 × 512 image matrix and 150 × 150 mm field view. Each image slice was 7 mm thick with a spatial resolution of 0.25 mm × 25 mm as in Fig.3.A 3D geometry was then created from the contours of the DICOM images in order to generate a hexahedral mesh for numerical simulations. ScanIP module of Simpleware R code Trial version, (Simpleware R , 2014), was used to import the DICOM raw data, perform image processing, visualization and segmentation of the rib geometry. A distribution of 8 grey scale intensities (see Tab. 1) was chosen to determine the heterogeneous mechanical properties of eight parts within the rib. A grey intensity (or level) is associated with a particular value of the linear attenuation coefficient µ. Five-sample calibration phantom (Mindways R ) with known equivalent K 2 HPO 4 and H 2 O densities was placed below the rib during the scan. Using an algorithm implemented into

(

  2008) and Li et al. (2010) have shown that the effect of strain-rate is of much less importance in the elastic regime. Therefore, in the present work, the strain-rate effect is taken into consideration only in post-yield regime. This could be achieved by two ways: (i) by providing stress-strain curves defined at various ε; (ii) by scaling the dynamic yield stress with respect to ε. The second way is based on Cowper-Symmonds model, expressed as: where, σ y d is the dynamic yield stress, C and P are Cowper-Symmonds parameters. The initial yield stress σ y 0 is identified as σ yT given in Tab. 2. The values of C and P were taken from Li et al. (2010): C = 2.5 GPa, P = 7.

(

  2016) for cortical, Keaveny et al. (1999) and Li et al. (2010) for trabecular.

  . and C. Untaroiu (2018). Subject-Specific Modeling of Human Ribs: Finite Element Simulations of Rib Bending Tests, Mesh Sensitivity, Model Prediction with Data Derived From Coupon Tests. In 15th International LS Dyna User's Conference proceedings, Detroit, Michigan, USA, pp. 7.

Fig. 6b )Figure 2 :Figure 3 :Figure 4 :

 6b234 Fig. 6b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 17 Comparison with experimental response . . . . . . . . . . . . . . . . . . . . . . . 44 18 Graphical abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 5 :Figure 6 :Figure 7 :Figure 8 :FFigure 11 :

 567811 Figure 5: Mechanical properties for constituents of porcine rib for different porosities or mass densities. Co: Cortical bone, Tr: Trabecular bone

Figure 12 :Figure 17 :

 1217 Figure 12: Experimental and numerical quantities (strains, velocities, diplacements) at the bars-rib interfaces.

  Thanks to the High-Resolution peripheral Quantitative Computer Tomography technique and the current image resolution, it is possible to obtain an accurate geometrical and material representation of the rib. The geometrical description permits to construct a FE model including the distribution of different parts. The apparent density is correctly correlated with grey scale of bone. As in previous studies in the literature, mechanical properties (Young modulus, yield stress, ultimate stress, strain at fracture) were correlated with apparent density. The present study proves that this methodology provides an appropriate simulation of the fracture process.

Table 1 :

 1 . A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. application to experimental techniques. Journal of the Mechanics and Physics of Solids 43 (8), 1335 -1348. Grey scale values for porcine rib in Hounsfield Units HU and corresponding standard deviation (S. dev.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Power law regression equations used for mechanical properties (unit for stresses is here MPa) and standard deviation estimations based on the power laws and of the standard deviation of the grey scale intensity . . . . . . . . . . . . . . . . . . . . . 26 3 List of different ε fd /ε fs vs. ε relations tested (plotted Fig. 6b) . . . . . . . . . . . . 27 4 Average properties of rib and parameters used in numerical calculation . . . . . . 27 Grey scale values for porcine rib in Hounsfield Units HU and corresponding standard deviation (S. dev.)

	Zhao, H., G. Gary, and J. R. Klepaczko (1997, April). On the use of a viscoelastic split hopkinson
	pressure bar. International Journal of Impact Engineering 19 (4), 319-330.
	Zioupos, P., U. Hansen, and J. D. Currey (2008, October). Microcracking damage and the fracture
	process in relation to strain rate in human cortical bone tensile failure. Journal of Biomechan-
	ics 41 (14), 2932-2939.

Table 2 :

 2 Power law regression equations used for mechanical properties (unit for stresses is here MPa) and standard deviation estimations based on the power laws and of the standard deviation of the grey scale intensity

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Table 3 :

 3 List of different ε fd /ε fs vs. ε relations tested (plotted Fig.6b)

	Law	Parameter [units] cortical bone trabecular bone
		ρ app [kg.m -3 ]	1690.90	772.90
		E [GPa]	9.374	1.80
		ν	0.3	0.45
	Constitutive	σ y0 = σ yT [MPa]	70.876	20.48
		E T AN [GPa]	0.937	0.0450
		C [GPa]	2.5	2.5
		P	7.0	7.0
		n	1.2	2.0
	Damage	m	1.0	1.0
		ε fs [m/m]	2.0 × 10 -2	3.0 × 10 -2

Table 4 :

 4 Average properties of rib and parameters used in numerical calculation bending tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2 The rib sample placed in between the bars with a visible fracture . . . . . . . . . 30 3 Treated porcine rib and CT scan images . . . . . . . . . . . . . . . . . . . . . . . 30 4 Effective and apparent density with respect to GS value. . . . . . . . . . . . . . . 31 5 Mechanical properties for constituents of porcine rib for different porosities or mass densities. Co: Cortical bone, Tr: Trabecular bone . . . . . . . . . . . . . . . . . . 32 6 Input curves of damage law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7 Finite element mesh of porcine rib and bars (a) and zoom of the left rib extremity showing the hexahedral elements (b) -dimensions in mm . . . . . . . . . . . . . . 34 8 Cross-sectional views of the rib FE model showing the density distribution (color SHPB test). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 15 Comparison of Numerical Force data in the pure compression simulation. . . . . . 42 16 Numerical F inp vs. t response corresponding to different ε fd /ε fs curves tested (see

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code is the same as in Fig.

5

). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 9 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 10 Comparison of experimental (top) and numerical fracture pattern (bottom) at different t times values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 11 Loss of contact between rib and output bar 2 after fracture (simulation) . . . . . . 38 12 Experimental and numerical quantities (strains, velocities, diplacements) at the bars-rib interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 13 Comparison of numerical forces obtained from the strain histories (solid line) and directly from the contact algorithm (dashed line) . . . . . . . . . . . . . . . . . . 40 14 Influence of contact surface. Left: bending rib model. Right: pure compression model (


Xipeng Tan

Carine Perrin-Pellegrino

Khalid Hoummada

Dominique Mangelinck

Aurélie Rouaix

Vande Put

Marie-Christine Lafont

Djar Oquab

Daniel Mo Nceau

Atom probe tomographie study of L1 0 martensite in a Pt-modified NiCoCrAlYTa bond coating

The Llo martensite formed in a Pt modified NiCoCrAIYTa bond coating has b een investigated b y atom probe tomography. It was found that o b vious segregation of Co and Cr occurred in the micro twins zone inside the martensite lath. Based upon the compositional analysis , it is known that Pt destabilizes the 13 phase and Co and Cr a ct as 13 sta b il izers with respect to the 13 -+ L 1 0 martensitic transformation. ln addi lion, some CJ. Cr particles precipitated inside the martensite lath.

A Metal coating B.TEM C. Segregation

Introduction

MCrAIY type overlay coatings (M = Ni and/or Co) are used as bond coatings in the four layered thermal barrier coating (TBC) system (i.e. (i) the superalloy substrate, (ii) the bond coat, (iii) the thermally grown oxide (TGO), and (iv) the ceramic top coat) as they provide superior oxidation and corrosion resistance for hot section components in gas turbine engines [1 3]. They are capable of bonding the yttria stabilized zirconia (YSZ) top coat and superalloy substrate. Many studies have addressed the micro structural characterization of TBC multi layered systems [4 7]. Moreover, the oxidation [8] and hot corrosion [9,10] behaviour of MCrAIY type coating or TBC systems have been widely investi gated. It is well known that each element in the MCrAIY coatings would play different rotes, e.g., Ni acts as the matrix, Co stabilizes � and y phases, Al is responsible for aluminum oxide ( a. Al 2 0 3 ) for mation to protect the system against oxidation, Cr provides corro sion resistance and helps the formation of alumina ("third element effect"), Y is beneficial for TGO adherence, etc. [11,12]. In addition, Pt was intentionally deposited on the externat surface of MCrAIY coatings to obtain improved oxidation and corrosion resistance in practical use [13].

Recently, the benefi t of Pt on MCrAIY coatings has received increasing interest. Vande Put et al. [14,15] studied the effect of Pt on the microstructure and oxidation resistanoe of NiCoCrAIYTa coatings manufactured by different prooesses. Herein, L1 0 * Corresponding author. Tel.: +33 0667416065.

E-mail address: xptan1985@gmail.com (X. Tan).

http: //doi.org/10.101 6/j.corsci2013.07 .041 martensite appeared in the externat zone of Pt modifi ed NiCoCrA IYTa coatings after fabrication This martensite phase formed a continuous layer in the case of vacuum plasma sprayed NiCoCrA IYTa and a discontinuous but dense layer in the case of electrolytic NiCoCrAIYTa. This layer formation was explained by the uphill dif fusion of Al during the heat treatment after the electrolytic deposi tion of Pt [14]. As observed in Ni rich � NiAI phase (82 structure), this phase will undergo a martensitic transformation during cool ing [16]. It is referred to the Llo or 3R martensite with face cen tered tetragonal (fct) lattice. Moreover, the reverse transformation from martensite to � phase occurs upon heating. This martensitic transformation has been commonly observed in � NiAI [17,18] or Pt modified � NiAI bond coatings when Al was depleted by interdiffusion and alumina scale spallation and refor mation [ 19 22]. The volume change associated with this transfor mation in Pt modified � NiAI lies between 1% [19] and 1.9% [16] depending on composition. In Pt modifi ed aluminide coatings, this volume change can favor bond coating surface rumpling which is detrimental to the thermal barrier system durability [23].

Furthermore, several studies have shown the martensitic trans formation in MCrAIY coatings, which contain a volume fraction of � NiAI, during thermal cycling [24,25]. Multiply twinned contigu rations are widely recognized as the most important structural fea tures of L1 0 martensite [26]. Numerous papers have reported the occurrence of micro twins in the martensite laths in NiAI bond coatings or related NiAI alloys [19,27,28]. Liang et al. [29] observed the 82-. L1 0 martensitic transformation and the macro twinned martensite plates as well as large numbers of micro twins inside each plate in a model NiCrAIY alloy. It is believed that the micro twin planes could accommodate the constant shear of the martensitic transformation, i.e. the habit plane stress, which exists due to the small twin surface energy of NiAl parent phase [30]. Therefore, the high density of micro twins in martensitic micro structures is of great concern during the transformation process.

It is noted that the Llo martensite has been extensively studied both on crystallography and chemistry with the aid of transmission electron microscopy (TEMi However, it still lacks of quantitative chemical characterization on the Llo martensite, especially for the sub microstructures inside the martensite laths. Atom probe tomography (APT) is the unique and powerful technique, which is able to locate the alloying elements and quantify the composi tion at the atomic scale and in the three dimensions [31,32]. This should allow a more detailed understanding of the martensitic transformation and any alloying effects. This work presents the chemical analysis of micro twins in the martensite lath by utilizing APT, with the goal of studying the sol ute redistribution among these sub microstructures as well as the effect of alloying elements on the formation of L 1o martensite.

The NiCoCrAIYTa coating was deposited on the first generation Ni based superalloy AM3 (see its composition in Table 1) by vac uum plasma sprayed (VPS) at the LERMPS laboratory (Sévenans, France). The AMDRY powder with a composition of Ni 23Co 20Cr 8.SAl 4Ta 0.6Y (wt.%) or Ni 20.9Co 20.9Cr 16.9Al 12Ta 0.4Y (at.%) was employed for the NiCoCrAlYTa deposition. In order to reduce the roughness resulting from the VPS process, P1200 SiC paper was used to partially polish the NiCoCrAlYTa surface. Polish ing would be terminated once a "partially machined" surface (namely between 24 % and 34% of polished surface) was obtained, which was estimated by means of optical microscopy and image analysis. After the partial polishing, Pt was deposited by sputtering at Cranfield University (England). The NiCoCrAIYTa coating was 70 80 µm. The thickness of Pt layer was 7 µm with an uncertainty of ±1 µm. Moreover, heat treatment was carried out for 6 h at 1080 °C under vacuum after Pt deposition.

Scanning electron microscopy (SEM) observations of bond coat ing cross sections were perforrned by a LEO 43SVP microscope using the backscattered electron (BSE) mode. For the transmission electron microscopy (TEM) sample preparation, cross sections were taken from the "superalloy + bond coating" systems using a diamond wire saw. The two thin slices of sample were glued coat ing against coating with epoxy resin, and embedded in a 3 mm diameter brass tube. After curing, the tube was sectioned into approximately 300 µm thick dises. The dise was then polished on both sides and dimpled before ion milling to transparency with a Gatan precision ion polishing system. The dise was observed peri odically during the thinning processes to ensure that the hole was approximately located across the interface of interest. TEM obser vations of the thin foil were carried out using a JEOL JEM 2010 microscope operating at 200 kV. APT specimens were prepared by focused ion beam (FIB) on a FEI Helios dual beam via the lift out technique [33]. The micro tips were prepared by means of the annular milling method [34] to obtain an end radius of ~ 100 nm. APT analyses were performed with an Imago Sàentific Instruments LEAP 3000x HR at a speàmen temperature of SS K. a 100 kHz picosecond laser pulses with an energy of 0.2 nJ, an evaporation rate of 0.002 ions pulse 1 and a pressure of <2 x 10 11 Torr. Data reconstruction was perforrned using IVAS ™ 3.6.2 software. Fig. 1 a shows the cross section microstructure of this Pt modi fied NiCoCrAIYTa bond coating. Because Pt is a heavy metal, the outer "brighter" part should be considered as the Pt affected zone under the BSE mode. In particular, numerous martensite laths with the brightest contrast were cl early observed in the Pt affected zone. These laths have been identified as the L 1o martensite in Ref. [14]. One of the martensite laths is shown in Fig. lb. It reveals that a large number of micro twin bands exist inside the martens ite lath. In addition, many small precipitates were also present both inside and outside the martensite lath. The tip for APT analy sis was taken from the position as illustrated in Fig. 1 b. Fig. 2 re veals the atom maps in the 3 dimensional APT reconstruction volume, which consists of three different regions, i.e. the lamellar segregation region (at top), the irregular Cr rich particles region (in the middle) and the chemical homogeneous region (at bottom). Lamellar structures were apparently observed. The average thick ness of these segregation layers is deterrnined as 6.2 ± 0.7 nm in terms of the APT reconstruction, which is in good agreement with the width of micro twins inside the martensite lath (as shown in Fig. 1 b i Here, Cr and Co exhibit the most obvious segregation. In addition to these six elements in Fig. 2, a trace amount of Ti was also detected in the APT volume. Ti is expected to originate from the superalloy substrate via diffusion during the deposition of coating and the subsequent heat treatment. However, the only one isotope of element Y was not detected in the mass spectrum, either in the singly and doubly charged state or molecular ions. That may be due to the fact that most of the Y was bonded to oxygen and preferentially enriched at the splat boundaries inside the coating after deposition [35]. Moreover, several Cr rich parti des were seen in the reconstruction volume of Cr atom map.

Fig. 3a shows the reconstructed Cr rich precipitate. Due to the local magnification effect [36], it is difficult to resolve any atomic planes. Concentration profiles for each atom obtained from prox imity histogram (proxigram) analysis are shown in Fig. 3b. This proxigram was created using 0.1 nm bin size with respect to a 50 at.% iso concentration reference surface. It can be seen that the core region of the precipitate contains up to 80.0 ± 2.0 at.% Cr. Thus, it is a. Cr phase. This phase forms next or in � NiAl phase dur ing cooling because Cr solubility in � phase is low and decreases when temperature decreases. In addition, it is transparent that Co was segregated at the martensite/a. Cr heterophase interface.

The Gibbsian interfacial excess of an element i, r i , is defined by the excess number of solute atoms i (Nf xcess ) per unit area (A). r i can be de termined utilizing proxigram concentration profiles for an arbitrary interface by [37,38]:

p ri Ni/A pAJCI:(di cr) c1) j 1
where p is the atomic density (97.39 atoms nm 3 for the Llo mar tensite ), t!,.x is the distance between the p layers in the proxigram, C: is the concentration of the jth atom, and cf' is the average concen tration of element i in the matrix. In terms of the proxigram in extremely sensitive to the Al concentration, it was speculated that Cr and Co might be segregated at the micro twins of retained b parent phase. However, it still requires more work to verify this segregation phenomenon.

As the chemical analysis of martensite and b phase stated above, it was found that Pt destabilizes the b phase, i.e. promotes the martensitic transformation. By contrast, Co and Cr would stabi lize the b phase. Additionally, Pt and Co appear to have the higher solubility both in b phase and martensite compared to Cr. As the martensitic transformation proceeds, it is possible to imagine that Cr was continuously ejected from the forming martensite and then aggregated to form the a Cr precipitates.

Conclusion

In summary, APT has been employed to analyze the sub micro structures of L1 0 martensite lath formed in a Pt modified NiCoCrA lYTa bond coating. It was found that there exists obvious segregation of Co and Cr in the micro the mar tensite lath. According to the compositional analysis of martensite and b phase, it is known that Pt destabilizes the b phase. However, Co and Cr act as b stabilizers with respect to the b ? L1 0 martens itic transformation. In addition, some a Cr precipitated inside the martensite lath. Co was found to segregate at the L1 0 /a hetero phase interface with a Gibbsian interfacial excess of 8.41 ± 0.46 atoms nm 2 . The chemical information at the atomic scale obtained by APT is a good supplementary for understanding the L1 0 martensitic transformation only utilizing TEM techniques.

Fig. 1 .Fig. 2 .

 12 Fig. 1. (a) BSE image showing the cross-section of the outer part of the Pt-modified NiCoCrAIYTa bond coating. (b) TEM bright field image showing a martensite lath in (a).

15 ,

 15 ,...._ ........

10

 10

Fig. 3 .

 3 Fig. 3. (a)Selected portion of APT reconstruction showing the Cr-rich particle delineated with the 50 atX Cr is�oncentration surface. (b) Proximity histogram (proxigram) showing the concentration profiles across the above interface. (c) Enlarged concentration profile for Co in (b).

Fig. 3c ,

 3c Fig. 3c, Co segregated with a r i value of 8.41 ± 0.46 atoms nm 2 •In order to analyze the elemental segregation in the martensite lath, an 18 at.% Cr and Co iso concentration surface is shown in Fig.4a. According to the location of APT sample, it can be known

  region is the � NiAI phase. Therefore, Cr and Co are known to homogeneously disperse in the � phase. As shown in Fig. 4b, L1 0 martensite contains less Cr and Co in comparison with the � phase. On the contrary, more Pt appears in the martens ite, which results in the brightest contrast of martensites in the BSE image. It is noted that the concentrations of Ni and Al are almost identical ( ~35 at.%) in the martensite. Fig. 4c reveals the wave like concentration profiles for Ni, Al, Pt, Co and Cr. The concentration variations follow similar trends for each respective element. It is evident that these lamellar segregation zones correspond to the large number of micro twins inside the martensite lath. It has been known that the martensitic transformation only occurs in Ni rich NiAl alloys when some requirements are satisfied in Ni rich binary NiAl alloys, e.g., less than 37 at.% of Al content, higher than ~ 1000 °C of exposure temperature and sufficiently fast cooling rate [18]. Furthermore, the martensitic transformation is known to take place in the vicinity of the Ni 65 Al 35 composition based upon the Ni Al binary phase diagram and the excess Ni was randomly dis tributed on the Al sublattice [26]. In the present work, the concen tration of Al in martensite has been determined as 35.0 ± 0.5 at.% (see Fig.

  4b

Fig. 4 .

 4 Fig. 4. (a) APT reconstruction showing the 18 atX (Cr+ Co) isCK:oncentration surface. (b) 1-dimensional concentration profiles for each atomic species obtained from the region of interest (ROl)-1 in (a). (c) 1-dimensional concentration profiles for each atomic species obtained from ROl-2 in (a).

Table 1 Nominal composition of the alloy AM3. Ni Al Cr Co Ta li Mo w AM3 wtX Bal. 6.0 8.0 6.0 4.0 2.0 2.0 5.0 atX Bal. 12.85 8.89 5.88 128 2.41 120 1.57

 1