S Liu

A Kouadri-Henni
email: afia.kouadri-henni@insa-rennes.fr

A Gavrus

Numerical simulation and experimental investigation on the residual stresses in a laser beam welded dual phase DP600 steel plate: thermo-mechanical material plasticity model

Keywords: Constitutive Equations, Anisotropy, Laser Welding, DP600 Dual Phase Steel Behavior, Residual Stress, Neutron Diffraction

A thermo-mechanical plasticity material model, which consists of a hardening and a temperature sensitivity term, is built to describe the dual phase DP600 steel behavior. For the hardening term, a synthesis Ludwik -Voce hardening law is proposed, identified and compared with the classical Ludwik and the Voce hardening laws. For the temperature sensitivity function, a new proposed expression together with a classical Johnson-Cook term and an improved Chen term are analyzed and identified. Moreover, the plate anisotropy of DP600 is also taken into account using Hill-48 theory. Based on the plasticity material model, a numerical sequential coupled thermo-mechanical model is applied to investigate the residual stresses of laser welding process. It is shown that the material anisotropy and the thermo-mechanical elastic-plastic model have an important influence on numerical residual stresses results. An experiment is also carried out to verify the numerical model. Simulation results of residual stresses are in good accordance with neutrons diffraction measurements.

Introduction

In the aim of reducing energy consumption and CO 2 release, high strength alloy is widely used to reduce the car weight in automotive industries [START_REF] Davies | Materials for automobile bodies[END_REF]). Among the high strength low weight alloys, the dual-phase (DP) steel possesses adequate ductility and high strength. DP600 contains about 15% hard martensite in a soft ferrite matrix [START_REF] Calcagnotto | Deformation and fracture mechanisms in fine-and ultrafine-grained ferrite/martensite dualphase steels and the effect of aging[END_REF]; [START_REF] Marya | Development of requirements for resistance spot welding dual-phase (dp600) steels part 1-the causes of interfacial fracture[END_REF]). The body-centered-tetragonal martensite helps to improve the high strength while the body-centered-cubic ferrite contributes to ductility [START_REF] Chen | The dependence of near-threshold fatigue crack growth on microstructure and environment in dual-phase steels[END_REF]; [START_REF] Kuang | Effect of continuous annealing parameters on the mechanical properties and microstructures of a cold rolled dual phase steel[END_REF]). DP600 has no-yieldpoint elongation and a higher strain-hardening rate than traditional highstrength low-alloy (HSLA) steels [START_REF] Fekete | A comparison of the response of hsla and dual phase sheet in dynamic crush[END_REF]). The high strain-hardening rate can increase absorption energy in car collision, thus helps to decrease damage [START_REF] Bouaziz | Driving force and logic of development of advanced high strength steels for automotive applications[END_REF]).

Nd:YAG laser welding is an efficient way in car manufacture. With appropriate welding parameters, the process can produce a firm joint. But welding may also change material property and introduce potential safety and reliability issues. When laser welding is used on dual-phase (DP) materials, the influence of material property should be investigated, such as the microstructure, tensile strength, hardness and fatigue properties by N. Farabi et al [START_REF] Farabi | Microstructure and mechanical properties of laser welded dissimilar dp600/dp980 dual-phase steel joints[END_REF]), mechanical and metallurgical properties by M. Hazratine et al [START_REF] Hazratinezhad | Mechanical and metallurgical properties of pulsed neodymium-doped yttrium aluminum garnet laser welding of dual phase steels[END_REF]) and the formability by M. Xia et al (Xia et al. (2008)). To better evaluate the performance of DP600 welding joint, the residual stresses are investigated in this paper both numerically and experimentally.

In simulation domain, the strain hardening phenomenon can be modeled by defining the material plasticity. Among various mathematical expressions, Ludwik equation [START_REF] Ludwik | Element der technologischen[END_REF]) and Voce equation [START_REF] Voce | A practical strain-hardening function[END_REF]) are two widely used constitutive models for material plasticity. As plastic strain increases, the flow stress increases in Ludwik model, while reaches a constant value in Voce model. Ludwik constitutive model is suitable for martensite hardening phenomenon, while Voce model for ferrite. Since DP600 is a combination of martensite and ferrite, a synthesis constitutive equation is used to describe the material plasticity. Besides the hardening, a temperature sensitivity term is proposed and compared with Johnson-Cook model [START_REF] John | A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[END_REF]) and Chen model [START_REF] Chen | Mechanical properties and constitutive relationships of 30crmnsia steel heated at high rate[END_REF]) for plasticity model.

Along different directions, DP600 sheet presents different plastic behavior. The anisotropy of DP600 sheets is usually a result of large deformation during rolling operations in manufacturing. To describe anisotropy of material, a number of theory can be applied to material, such as Hill-48 (Hill (1948)), Srp93 [START_REF] Barlat | Anisotropic potentials for plastically deforming metals[END_REF]) and Yld-2004-18p (Barlat et al. (2005)). Among these theories, Hill-48 theory is one of the most famous theories which describes the material's anisotropy with six parameters F, G, H, L, M, N. The values for DP600 have been reported by works [START_REF] Padmanabhan | Effect of anisotropy on the deep-drawing of mild steel and dual-phase steel tailorwelded blanks[END_REF]; [START_REF] Rabahallah | Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction[END_REF]; [START_REF] Ozturk | Effects of anisotropic yield functions on prediction of forming limit diagrams of dp600 advanced high strength steel[END_REF]), which reveal that the anisotropy in rolled sheet influences subsequent material behavior and affects the strain distributions.

To ensure weld performance, residual stresses of DP600 lap welding joint is investigated. A thermo-mechanical finite element model (FEM) is built through commercial code ABAQUS. The hardening behavior and temperature sensitivity of DP600 are considered in the model through UHARD subroutine. The anisotropy of DP600 are considered in the simulation model and the result suggest that different material rolling orientations influence numerical simulation of residual stresses obviously. Simulation results of residual stresses are compared with the experimental measurements of neutron diffraction technique, and good accordances are found.

Numerical model

A laser beam of 4kW power and 3.4m/min welding speed was used to weld two plates of dual phase DP600 steel. Concerning the elastic properties of the DP600 dual phase steel the numerical simulations uses the following generic values: Young's modulus E = 210GPa, Poison's ratio ν = 0.28 and thermal expansion coefficient α = 1.2 × 10 -5 K -1 . The detail description about thermal analysis, elastic and expansion behaviors of laser welding DP600 steel can be referred to a previous work [START_REF] Seang | Nd: Yag laser welding of sheet metal assembly: Transformation induced volume strain affect on elastoplastic model[END_REF]). This paper focus on the thermo-plasticity material model. The residual stresses analysis uses a sequential coupled thermo-mechanical analysis. The simulation model consists of two parts:

1. Thermal analysis part Heat source, heat transfer and boundary condition of radiation and convection are considered to analysis the thermal data using an ABAQUS model

Mechanical analysis part

A predefined field is used to introduce thermal analysis results so that the previous calculated thermal data is used as an input data file for a mechanical analysis of residual stress distribution.

With the consideration of material property, such as the expansion behavior of the material due to temperature increase, the elastic and plastic behavior of the material, and the relaxation of the stresses at the cooling step, laser welding residual stresses are simulated.

In figure 1, the geometry, mesh and boundary condition of the mechanical model are presented. The path transversal to weld line, the rolling direction and the directions of residual stresses are illustrated. The angle between transversal path and rolling direction is θ. There are 44160 elements in total for the model and element type C3D8R is selected for analysis. According to the material rheological behavior, the hardening influence, the softening phenomena, the strain rate sensitivity and the anisotropy influence of a dual phase DP600 steel are discussed. As proposed by Gavrus [START_REF] Gavrus | Constitutive equation for description of metallic materials behavior during static and dynamic loadings taking into account important gradients of plastic deformation[END_REF]), based on theory of dislocations glides and mixture microstructures formulations proposed by Avrami, the plastic flow stress corre-sponding to numerical simulation of dynamic forming process can be expressed in a general form as:

σ(ε p ) = [σ h (ε p ) • (1 -ψ) + σ s • ψ] • F(T ) • G( ε) (1)
where ε p is the cumulated plastic strain, T is the temperature and ε is the plastic strain rate. In this equation, σ h (ε p ) represents the hardening component, σ s the saturation term and ψ the material fraction undergoing dynamic softening phenomena (dynamic recrystallization, phase transformation, twinning . . . ) or a dynamic recovery. F(T) is the temperature sensitivity, and G( ε) is the strain rate sensitivity function. In a first approximation, during the laser welding simulation, the strain rate sensitivity can be chosen to be equal to unity i.e. G( ε) = 1.

Hardening behavior

Table 1 presents all the rheological parameters of DP600 identified for different hardening models. The mathematical form of the hardening models are discussed in the following parts.

Ludwik model

The initial yield stress marked as "σ y " is the elastic limit after which the material starts its hardening. For a material phase such as the martensite one, the material flow stress σ(ε p ) can be expressed by the Ludwik hardening model using a classical power form:

σ(ε p ) = σ y + n 1 ε n 2 p (2)
Ludwik model can be interpreted as a particular term of the general constitutive equation (1) defined by [σ h (ε p ) • (1 -ψ) + σ s • ψ] using the hardening stress expressed by σ h (ε p ) = σ y + n 1 ε n 2 p and a softening material fraction equal to 0 i.e. ψ = 0.

For the DP600 steel, the Ludwik model cannot fully fit the original experimental curve, so a mathematically modified form of Ludwik model is proposed to represent the observed material behavior:

σ(ε p ) = σ y + n 1 ε n 2 p + n 3 ε p + n 4 (3)
As can be seen in figure 2, "Classical Ludwik model 01" correspond to the classical form (equation 2) and "Modified Ludwik model" becomes a mathematical improvement of the Ludwik one. It is important to note that the addition of the linear term "n 3 ε p + n 4 " in Equation 3 permits to fit more accurately the experimental data but has not any physical meaning. The straight line is used to obtain more accuracy of the obtained non-linear regression curve.

Voce model

The Voce law is a good rheological formulation used to describe the material recovery (hardening with saturation plateaus) such as the plastic flow of the ferrite. The Voce model can be expressed in the following form [START_REF] Voce | A practical strain-hardening function[END_REF]):

σ(ε p ) = σ y + n 1 • [1 -exp(-n 2 ε p )] (4)
In Equation 4, n 1 + σ y is the saturation stress and σ y is the initial yield stress. Voce model can be interpreted in term of the general constitutive equation ( 1) where the term

[σ h (ε p ) • (1 -ψ) + σ s • ψ] is written by the sum of (n 1 + σ y ) • [1 -exp(-n 2 ε p )
] and σ y • exp(-n 2 ε p ) defining the hardening term by σ h = n 1 + σ y , the saturation of plateaus term by σ s = σ y and the recovery fraction by ψ = exp(-n 2 ε p ).

For the DP600 material, the plastic flow stress can not be perfectly fitted by the Voce equation, so a mathematically modified form is written below in order to fit the experimental curve.

σ(ε p ) = σ y + n 1 • [1 -exp(-n 2 ε p )] + n 3 ε p (5)
As is seen in figure 3, "Classical Voce model 01" is the original form of Voce law and "Modified Voce model" is the mathematical improvement form of the classical Voce equation. The addition of the linear term "n 3 ε p " in Eqn. 5 only let the Voce equation to obtain a best fit of the original experimental data. This mathematical improvement is not based on the physical mechanisms characterizing the material plasticity and of the real mechanical behavior of hardness martensite / softening ferrite mixture, but can be regarded as a first approximation if an equal repartition of two phases is considered.

Proposed synthesis model

According to the above considerations, mathematical improvements only for classical hardening laws to fit more accurately the experimental data are generally not physically based on material microstructure or plastic phenomena. Since DP600 is a dual phase material containing both martensitic and ferritic phases, a proper and physical rheological hardening model should be defined. So based on equation (1), neglecting any phase transformation or dynamic softening phenomena (i.e. ψ = 0), using a hardening term σ h defined by a mixture Avrami formulation available for static recovery phenomenon with a classical Ludwik model describing the ferritic recovery, and introducing the material fraction w to define the content of martensitic phase, a synthesis model is proposed by authors to define the hardening function σ(ε p ) in the following form:

σ(ε p ) = w • (σ y + n 1 ε n 2 p ) + (1 -w) • {σ y + n 3 • [1 -exp(-n 4 ε p )]} (6)
The martensitic material fraction w can vary from 0 to 1. In this paper, w takes a value of 0.4 for the studied DP600 steel.

The figure 4 plot the difference between the experimental data, the classical Ludwik model and the classical Voce one (identified in the plastic strain range [0, 0.05]) and the proposed synthesis model (identified in the plastic strain range of all experimental results i.e. [0, 0.2]). It can be seen the advantage of the proposed synthesis model to obtain a very good agreement with all experimental measurements describing the real elasto-plastic behavior of dual phase DP600 steel, both for plastic strain range [0, 0.05] and [0.05, 0.2] corresponding to more localized deformations which can occur during the forming process.

Residual stresses obtained from different hardening models

In figure 5, all the three models of figure 4 and the two modified models of figure 2 and figure 3 are input into FEM of ABAQUS by user subroutines as material models. For all five models, a Johnson-Cook temperature sensitivity term F(T ) [START_REF] John | A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[END_REF]) is used and the conditions "F(298K)=1 and F(1803K)=0.05" is fulfilled with a mathematical value m = 0.104.

The simulation results of residual stresses along welding transversal path are shown. During this laser welding simulation, the maximum strain is no larger than 0.05, thus the five material hardening models are nearly the same within the range of 0 < ε p < 0.05, except for the "modified Ludwik" model where a straight line is added as is seen in figure 2. From the numerical simulation results analysis, one may conclude that as long as the stress-strain curves expressed by the material behavior models are similar within used small strain range, the forms of hardening equations have little influence on the numerical residual stresses estimation. However, the proposed synthesis rheological model describe precisely the experimental hardening material behavior of DP600 dual phase steel simultaneously for small and more important plastic strain values, it is already validated concerning numerical simulation of residual stresses corresponding to a laser welding process and can be used to analysis the process taking into account other initial operating conditions.

The contours of residual stresses σ 11 and σ 22 computed with the five hardening models are nearly the same and only results of the synthesis model is shown in the figure 6. The residual stresses at the plate surface are plotted with contour curves. There are tensile stresses at the center zone of weld line and compressive stresses adjacent to weld line. The magnitude of residual stresses are not precise because the use of basic parameters for a classical Johnson-Cook temperature sensitivity formulation. To improve simulation results, several temperature sensitivity models are discussed in the following part.

Temperature sensitivity

When a material is subjected to a high temperature, its strength tends to drop. In laser welding process, this phenomenon has a great effect on evaluation of elasto-plastic material behavior. In order to built a fine welding model and obtain good results of residual stresses, a proper material model taking into account the temperature sensitivity is investigated. Several temperature sensitivity models are taken into account and used to analysis the welding process. A lot of scientific works define the temperature sensitivity term F(T ) in function of the homologous temperature T * . Generally the homologous temperature T * can be defined as:

T * = T -T r T melt -T r (7)
T melt , T , T r are melting, current, and room temperature, respectively. For DP600 steel, T melt is supposed to be 1803.15 K and the room temperature is 298.15 K.

Arrhenius model

The temperature sensitivity of Arrhenius term [START_REF] Samantaray | Constitutive analysis to predict high-temperature flow stress in modified 9cr-1mo (p91) steel[END_REF]) is expressed by:

F(T ) = exp m Q RT ( 8
)
Where R is the universal gas constant, m is an adjustable parameter and Q the activation energy. Majority of thermo-mechanical plasticity applications consider a simplified expression using the thermal parameter β = m Q/R.

Hirt model

Similar to Arrhenius model, the Hirt model is defined as:

F(T ) = exp (-β T ) (9)

Linear model

The linear model can be viewed as an one order Taylor development of the exponential Hirt model:

F(T ) = exp (-β T ) = 1 -β T + • • • (10)
Using "m" for "β " and "T -T r " to instead of "T" and avoid the rest, a simple linear model can be obtained.

The linear term of temperature sensitivity has been proposed by Hutchison [START_REF] Hutchison | The temperature dependence of the yield stress of polycrystalline iron[END_REF]) in 1960s. The material drops linearly with temperature increment.

F(T) = 1 -m • (T -T r ) ( 11
)
Where m is a material coefficient and T r is reference temperature. The linear model is simple in form but not suitable for rapid material strength drop.

Johnson-Cook model

About twenty years later, based on many experimental tests and phenomenological analysis, Johnson-Cook [START_REF] John | A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[END_REF]) proposed a well-founded material model which is still widely used nowadays to describe dynamic forming process. The temperature sensitivity term of Johnson-Cook model can well predict the material temperature sensitivity below about 1 2 T m but not well above. For Johnson-Cook model, T r is room temperature to define T * in Equation 7.

F(T ) = 1 -T * m (12)

Khan model

A power function with respect to temperature T is proposed by Khan [START_REF] Khan | Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys[END_REF]) as a temperature sensitivity model. For Khan model, T r is reference temperature, so Khan temperature sensitivity model can use different parameters "m" with different temperature range. The use of different parameters enable the model to predict material temperature sensitivity at high temperature range.

F(T ) = T m -T T m -T r m (13)

Chen model

The Chen model (Chen et al. ( 2008)) contains the temperature sensitivity term as the following form. The Taylor development of the Chen model is "1 + n • T * m + • • • ", so when "n" is set to "-1" and the Chen model can be viewed as a first order approximation of Johnson-Cook model.

F(T ) = exp(n • T * m ) (14)

Proposed model

The proposed model can be viewed as a more general form equation as Johnson-Cook temperature model (k = n = 1).

F(T ) = (1 -k • T * m ) n (15)
All the parameters of temperature sensitivity terms analyzed above are shown in Table 2. The parameters of the Chen model and the proposed model are identified by a non-linear least squares regression method. The temperature sensitivity of the DP600 steel is supposed to be the same of the high strength steel in the work of Chen [START_REF] Chen | Behavior of high strength structural steel at elevated temperatures[END_REF]). The thermal softening fraction is the ratio of the stress at elevated temperature to that at room temperature. As is seen in figure 7, the thermal soften fraction is presented with different temperature sensitivity models by setting F(T room ) = 1. The Johnson-Cook model and the Khan model can be suitable from room temperature to about 800 K, but not appropriate above 800 K. The Chen model and the proposed model are near to experiment data except for the data around 1000 K. A polynomial expression is used to precisely describe the experimental data.

Planar anisotropy

For nearly all plate materials, the rolling process would leave an anisotropy property. The anisotropy of DP600 steel is considered as planar anisotropy with Hill-48 theory. The Hill's potential function is an extension of the Mises function, which can be expressed in terms of rectangular Cartesian stress components as (Hibbitt et al. (1997)):

f (σ) = F(σ 22 -σ 33 ) 2 + G(σ 33 -σ 11 ) 2 + H(σ 11 -σ 22 ) 2 + 2Lσ 2 23 +2Mσ 2 31 + 2Nσ 2 12 1/2 (16)
where F, G, H, L, M, and N are the Hill coefficients obtained by tests of the material in different orientations. The effective stress f (σ) is a scalar that dependent on material stress state and is a key value defining the plastic flow. Generally it is assumed to estimate this effective stress from the equivalent stress corresponding to the plastic flow curve obtained by tensile tests along the rolling direction. The specimen geometry used for tensile tests is shown in figure 10. The planar anisotropy is estimated using Hill-48 theory and the parameters are estimated according to the computation method presented in the work of Ohashi [START_REF] Ohashi | Evaluation of r-value of steels using vickers hardness test[END_REF]). Specimen are prepared so that the angle between the stretch direction and the rolling direction of DP600 are θ = 0 • , θ = 45 • and θ = 90 • , respectively. At the beginning, the length and width of test area are noted as l 0 and w 0 , respectively. The tensile test are conducted with a strain rate of 10 -2 s -1 . When the total strain ε total = 0.15, specimen are unloaded and the length l 1 and width w 1 are measured. Along the three specimen directions, the corresponding measurements are presented in Table 3. The Lankford coefficient r (also known as width/thickness strain ratio) can be computed by

r = ln(w 1 /w 0 ) ln(w 1 • l 1 /w 0 • l 0 ) (17)
Specimens with different angles θ = 0 • , θ = 45 • and θ = 90 • are analyzed by tensile tests. The corresponding anisotropic coefficients are noted as r 0 , r 45 and r 90 respectively. Based on the r-values, the Hill parameters can be estimated from following formula:

F = r 0 (1 + r 0 )r 90 (18)
G = 1 1 + r 0 (19)
H = r 0 1 + r 0 (20) N = (1 + 2r 45 )(r 0 + r 90 ) 2(1 + r 0 )r 90 (21)
For planar anisotropy, if set R 11 = 1, the other anisotropic yield stress ratios R 22 , R 33 and R 12 are defined using the following relationships

R 22 = r 90 (r 0 + 1) r 0 (r 90 + 1) (22)
R 33 = r 90 (r 0 + 1) r 0 + r 90 (23)
R 12 = 3(r 0 + 1)r 90 (2r 45 + 1)(r 0 + r 90 )

Based on the test results presented in Table 3 and using the above equations, Lankford coefficients and Hill's coefficients of DP600 steel are presented in Table 4.

Model validation

To validate the obtained numerical results, specimen experiments have been realized using neutrons diffraction technique. A gauge volume of 1×1×5 mm 3 was defined with the 5 mm aperture along the axis of the laser weld to improve intensity while has been possible (i.e. for transverse and longitudinal measurements only). For axial measurements, a sampling volume of 1 × 1 × 1 mm 3 was used. The crystallographic texture of the base material was determined by neutron diffraction technique on the dedicated 4-circles diffractometer 6T1 at LLB [START_REF] Hutchings | Introduction to the characterization of residual stress by neutron diffraction[END_REF]). From the {110}, {200} and {211} pole figures, using a 5 • × 5 • grid, the Orientation Distribution Function (ODF) was calculated using LaboTex software [START_REF] Pawlik | Labotex: the texture analysis software[END_REF]). The texture exhibits slight {hkl}<110> reinforcements, typical of a cold rolled ferritic steel, but the calculated texture index is rather low (1.6). An elastic self-consistent calculation was performed considering the experimental texture to deduce the {110} dependent values for Young's modulus (E 110 ) and Poisson's ratio (ν 110 ): as a result, it appears that the elastic anisotropy should remain very low, with E 110 ranging between 220 and 226 GPa, and ν 110 between 0.31 and 0.35, depending on the considered direction. In a first approach, triaxial residual stresses were thus calculated from the measured strains applying the Hooke's law (equation 25) in the isotropic elasticity approximation:

σ i = E 110 1 + ν 110 ε i + ν 110 1 -2ν 100 j ε j ( 25
)
where i, j = axial, transverse and normal, and with the following values for Young's modulus E 110 = 220 GPa and Poisson's ratio ν 110 = 0.33.

Since the characterized zones close to (Heat Affected Zone, HAZ) and within the weld (Fusion Zone, FZ) may have their microstructures more or less strongly affected by the welding process, chemical composition is likely to be heterogeneous depending on the distance from the center of the weld. One would thus commit an error if considering the base material as the reference material for unstrained lattice spacing. So, due to the low thickness of the studied plates, a zero normal stress state was assumed (i.e. a plane stress state), and theoretical reference lattice spacing and diffraction angles 2θ 0 could thus be calculated for each measurement point, applying the following formula (26), [START_REF] Staron | Residual stress in friction stir-welded al sheets[END_REF]):

2θ 0 = 2 • sin -1 (1 + ν) • sinθ normal • sinθ axial • sinθ transverse (1 -ν) • sinθ axial • sinθ transverse + ν • sinθ normal • (sinθ axial + sinθ transverse ) (26)
Considering the difficulty to obtain a reliable unstressed reference sample, the reference (unstressed) d 0,{110} lattice spacing required for strain calculations was determined assuming a zero normal stress at 5 mm in the base metal from the center of the weld.

In figure 14, along the transversal path of weld, experimental and numerical results of residual stresses variations with the different material orientations are shown. The residual stresses of σ 11 and σ 22 are measured by Neutron Diffraction method along transversal path. The material is assigned a material rolling orientation that have 30 • with transversal path. The simulation result shows a good accordance with experiment measurement.

Conclusion

In this study, a sequential coupled thermo-mechanical FE model is built for a lap laser welding simulation to analyze the elasto-plastic behavior and the residual stress distributions of dual phase steel DP600 joints. Different mechanical constitutive material models describing the hardening behavior, the temperature sensitivity and the anisotropy of the plasticity of the DP600 steel are identified, analyzed and employed in the numerical simulation. By comparisons with neutrons diffraction measurements of residual stresses, the elastic-plastic thermo-mechanical FE model is proved to be useful in predicting the welding residual stresses. According to the simulation and experimental results, we can draw the following conclusions:

1. The flow stress of DP600 at room temperature is obtained from tensile test. Both the classical Ludwik hardening model and the Voce model can represent the obtained true stress-strain hardening behavior of DP600 only with a little mismatch. Improvements of these two classical laws can be obtained only if parameters identification is made in the plastic strain range [0, 0.05]. Thus, a synthesis model formulation based on Voce and Ludwik models has been proposed in order to precisely describe the observed behavior of DP600 steel. Comparative simulations are done for the identified Ludwik, Voce and synthesis hardening models. Similar residual stresses results are acquired by the three hardening models. The obtained results reveal that, as long as flow stresses obtained from formulations of different hardening models are similar for a laser welding plastic strain range defined by 0< ε p <0.05, these ones have small influences on the corresponding numerical residual stresses . 2. Based on the experimental data corresponding to thermal mechanical properties of a high strength steel, the Johnson-Cook, Chen and Khan temperature sensitivity models together with a proposed model and a polynomial model are identified for DP600 material. Thermomechanical analyses show that the classical Johnson-Cook and the Khan temperature sensitivity terms are suitable to describe DP600 thermal softening behavior from room temperature to about 800K. For welding simulation that concerns high temperature up to about 1200K, the proposed and the Chen temperature sensitivity formulation show a better accordance with the obtained experimental data. The temperature sensitivity has a big influence on residual stresses simulation. Even the proposed temperature sensitivity formulation and the Chen model are nearly the same in description of temperature sensitivity, comparative simulations show some differences between the Chen model and the proposed one. Compared with the polynomial model (a best mathematical but not physical description of experimental temperature sensitivity), the proposed physical formulation results show better residual stresses of transversal direction while the Chen model results show better residual stresses of longitudinal direction. 3. Concerning the observed plane anisotropy of the DP600 steel, parameters of Hill-48 criterion are identified through several experiment tests. Simulations with different material rolling orientations of DP600 are assigned to material model. The material orientation of DP600 is found to have a big influence on simulation results of residual stresses σ 11 and σ 22 . The material orientation influence the magnitude of residual stresses σ 11 and σ 22 , increasing one while decreasing the other. 4. Experiment of laser welding with the same welding parameters of numerical model are conducted and residual stresses of the experiment sample are examined by a Neutron Diffraction technique. Based on the experiment measurements, increased residual tensile stresses are found at the weld area. Residual stresses of longitudinal direction σ 22 are found to be higher than residual stresses of transversal direction σ 11 . By comparison, the experimental results of residual stresses show good accordance with the numerical simulation results.

Acknowledge

The work was financially supported by China Scholarship Council, the Mecaprocess Team of INSA de Rennes and by CEA of Saclay for the experimental measurements. Xia, M., Biro, E., Tian, Z., Zhou, Y. N., 2008. Effects of heat input and martensite on haz softening in laser welding of dual phase steels. ISIJ International 48 (6), 809-814.

Figure 1 :

 1 Figure 1: Mesh and geometry of numerical model

Figure 2 :

 2 Figure 2: Comparison of Ludwik model and experimental DP600 data

Figure 3 :

 3 Figure 3: Comparison of Voce model and experimental DP600 data

Figure 4 :

 4 Figure 4: Comparisons of rheological models and experimental DP600 data

  Figure 5: Residual stresses of different hardening models along transversal path

  Figure 6: Simulation results of synthesis hardening model with a Johnson-Cook temperature sensitivity model

Figure 7 :

 7 Figure 7: Temperature dependence of experiment data and simulation models

  Figure 9: Contour of residual stresses with different temperature sensitivity

  Two yield surfaces predicted by Hill48 model and Von Mises criterion of the dual phase steel DP600 sheet are shown in figure11.The contour of residual stresses of two material rolling orientations θ = 0 • and θ = 90 • are presented in figure12. With the material rolling orientation

Figure 11 :

 11 Figure 11: Yield surface predicted by Hill48 anisotropic model and Von Mises criterion

  Figure 12: Contour of residual stresses with different material rolling orientations

Figure 14 :

 14 Figure 14: Comparison between the experimental and the numerical residual stresses

Table 1 :

 1 Rheological coefficients corresponding to different DP600 hardening models

		σ y	n 1	n 2	n 3	n 4	w	Equation Nonlinear regression ε p range
	Classical Ludwik model 01 400 980 0.48	-	-	-	(2)	[0, 0.2]
	Classical Ludwik model 02 400 1660 0.63	-	-	-	(2)	[0, 0.05]
	Modified Ludwik model	400 1690 0.5 -1240 -65	-	(3)	[0, 0.2]
	Classical Voce model 01	400 555 15.5	-	-	-	(4)	[0, 0.2]
	Classical Voce model 02	400 340 27.5	-	-	-	(4)	[0, 0.05]
	Modified Voce model	400 270	30	900	-	-	(5)	[0, 0.2]
	Proposed synthesis model 400 1660 0.63 340 27.5 0.40	(6)	[0, 0.2]

Table 2 :

 2 Parameters describing of temperature sensitivity

		m	n	k
	Johnson-Cook	1.5	-	-
	Khan model	0.5	-	-
	Chen model	-28.418 4.254	-
	Proposed model 4.207 38.629 0.699

Table 3 :

 3 Measurement of dimension change of tensile test θ = 0 • θ = 45 • θ = 90 •

	Initial length l 0 /mm	19.70	19.62	19.58
	Unload length l 1 /mm 21.18	21.30	21.04
	Initial width w 0 /mm 10.06	10.06	10.06
	Unload width w 1 /mm 9.70	9.74	9.72

Table 4 :

 4 The Lankford coefficients and Hill's parameters of DP600 steel

	r 0	r 45	r 90	R 11	R 22	R 33	R 12
	1.0123 0.6487 0.9160	1	0.9748 0.9777 1.1172
	F	G	H	N
	0.5492 0.4969 0.5031 1.2017


Konstantinos V Katsaros

Nikos Fotiou
email: fotiou@aueb.gr

Xenofon Vasilakos

Christopher N Ververidis

Christos Tsilopoulos

George Xylomenos

George C Polyzos
email: polyzos@aueb.gr

On Inter-domain Name Resolution for Information-Centric Networks

Keywords: content-centric, future internet, named data, rendezvous

is a paradigm that aims to better reflect current Internet usage patterns by focusing on information, rather than on hosts. One of the most critical ICN functionalities is the efficient resolution/location of information objects i.e., name resolution. The vast size of the information object namespace calls for a highly scalable and efficient name resolution approach. Currently proposed solutions either rely on a DHT structure, thus ensuring load balancing and scalability at the cost of inefficient routing, or on hierarchical structures, thus preserving routing efficiency at the cost of limited scalability. In this paper, we study in detail the tradeoff between state/signaling overhead versus routing efficiency for a generic name-resolution system based on a novel DHT scheme with enhanced routing properties, and compare it to DONA, an ICN architecture based on hierarchical resolution and routing.

Introduction

The Internet has been transformed from an academic curiosity to a global infrastructure for the massive distribution of information, with over 1 billion of connected devices [START_REF]Cisco: Cisco Visual Vetworking Index 2010-2015[END_REF], 1 trillion of indexed web pages [START_REF]We knew the web was big[END_REF] and Exabytes of annually transferred data [START_REF]Cisco: Cisco Visual Vetworking Index 2010-2015[END_REF]. Unlike this evolution in usage, at its core the Internet continues to operate upon a host-centric communication model, even though obtaining and disseminating information is currently the primary interest of users. This tussle between the core Internet functionalities and its actual usage has led the networking community to investigate new architectures for the Future Internet, many of which revolve around information-centrism (e.g. [START_REF] Jacobson | Networking named content[END_REF], [START_REF] Koponen | A data-oriented (and beyond) network architecture[END_REF]).

Information-centric networking (ICN) places information dissemination at the heart of the architecture. Information Objects (IOs) constitute the fundamental entity in ICN. Users in ICN issue requests by naming the desired IOs in order to obtain information; it is the responsibility of the network to locate and deliver the desired IOs to the requester, thus decoupling the communicating parties: end-users need not be aware of each other's network location or, even, identity. Locating IOs is therefore a core function in the context of ICN. In effect, the network operates as a system in which producers of information announce the availability of IOs and requests for IOs are resolved through a name-based anycast scheme, resulting in a name-resolution system (NRS).

To face the scalability requirements imposed by the vast number of IOs, several research initiatives have considered the use of Distributed Hash Table (DHT) schemes (e.g., [START_REF] D'ambrosio | MDHT: a hierarchical name resolution service for information-centric networks[END_REF][START_REF] Jarno | On name-based inter-domain routing[END_REF]), which exhibit significant scalability due to their inherent load balancing. However, this advantage comes at the cost of inefficient routing, which may overlook physical network proximity, administrative domain boundaries, routing policies, or a combination thereof. Other approaches, such as DONA [START_REF] Koponen | A data-oriented (and beyond) network architecture[END_REF], adapt to the underlying routing mechanism, requiring however extensive replication of routing information across the inter-domain topology.

In this paper, we examine the emerging tradeoff between state/signaling overhead versus routing efficiency in the context of ICN. To this end, we first design a DHT-based name-resolution system (DHT-NRS) based on H-Pastry, a hierarchical version of the Pastry DHT [START_REF] Rowstron | Pastry: Scalable, decentralized object location and routing for large-scale Peer-to-Peer systems[END_REF]; H-Pastry adapts to the underlying network topology, administrative structure and routing policies. We then present a detailed performance evaluation and comparison against the DONA scheme. Our purpose is to shed light on the expected performance of each approach, paying particular attention to the effect of the underlying inter-domain topology and the traffic workload. Our evaluation is based on a full-fledged simulation environment and considers a wide range of performance aspects, including routing efficiency and signaling overhead, as well as memory and processing load.

In the following, we describe name-resolution in the context of ICN and present our requirements for the envisioned name-resolution system (Section 2). Next, we discuss alternative approaches and position our work in the solution space (Section 3). In Section 4 we first describe the H-Pastry DHT scheme and then proceed with the description of DHT-NRS. We present and discuss the results of our performance evaluation in Section 5 and conclude in Section 6.

Name-resolution in ICN

In ICN, the network focuses on information itself rather than on the endpoints participating in the communication. The network acts as a mediator that decouples content providers from content consumers, radically changing the model of interaction with the network. The network (a) accepts end-user requests for IOs with the purpose of locating the content and enabling its delivery and (b) interacts with content providers which supply information about the availability and location of content. The basic functionality of the NRS in ICN is to match end-user requests with the accumulated information on available content and trigger the delivery of the corresponding data. This matching is based on the IO name, which thus becomes a first class entity in ICN. In this context, we outline below a set of requirements for an NRS, as derived by its central role in an ICN architecture, also identifying the key challenges in this new paradigm.

Flat identifiers. A critical factor in the design of an NRS is the form of the IO identifiers (IDs) employed. Existing systems achieve scalability by applying extensive aggregation on hierarchically structured identifiers (e.g., DNS, IP routing). A critical constraint of hierarchical systems is that the nodes in the root(s) of the tree(s) must be aware of all available prefixes in the name space. The use of flat, semantic-free identifiers has been proposed to decouple location from identity and thus achieve persistence and increased security [START_REF] Ghodsi | Naming in content-oriented architectures[END_REF][START_REF] Koponen | A data-oriented (and beyond) network architecture[END_REF][START_REF] Walfish | Untangling the web from DNS[END_REF]. Recent developments in DNS [START_REF]ICANN: ICANN Approves Historic Change to Internet's Domain Name System[END_REF] suggest that the increasing demand for naming information cannot be easily handled within the constraints imposed by hierarchical naming. Therefore, our NRS must operate on top of a flat namespace.

Scalability. An NRS must scale as the number of items and corresponding requests grows. Considering that (a) the current amount of unique web pages indexed by Google is greater than 1 trillion [START_REF]We knew the web was big[END_REF] and that (b) billions [START_REF]Cisco: Cisco Visual Vetworking Index 2010-2015[END_REF] of devices ranging from mobile phones to sensors and home appliances will be joining the network to offer additional content, we should plan for unique IOs in the order of 10 13 ; other studies raise this estimate to 10 15 [START_REF] D'ambrosio | MDHT: a hierarchical name resolution service for information-centric networks[END_REF]. This vast amount of IOs and related requests must be handled through the NRS.

Fault tolerance and fault isolation. The criticality of the NRS calls for a non-central point of failure, which is the major vulnerability of centralized architectures. Furthermore, the architecture should provide fault isolation i.e., the failure of a part of this distributed system should only have a local impact.

Low signaling overhead. The expected amount of available information, coupled with the corresponding demand by end-users, is expected to yield an increased signalling load for the NRS, in terms of IO announcements and requests for IOs. Hence, the required information exchange between the nodes of the distributed NRS should be kept to a minimum.

Low latency. Resolution should complete with minimum delay, yielding low response times for end-users. This calls for efficient routing and load distribution among system nodes.

Routing policy compliance. Finally, due to the high volumes of expected resolution traffic, routing should respect the policies of the Autonomous Systems (ASes). These policies reflect business relationships established between ASes, with policy violations having an economic impact on their operation.

Related work

The current equivalent of an NRS for the Internet is DNS, therefore we must first explain why DNS is inadequate for our purposes. To begin with, DNS is susceptible to Denial of Service (DoS) attacks. This vulnerability stems not only from the limited redundancy in name-servers, but also by the fact that many servers have a single point of attachment to the Internet [START_REF] Ramasubramanian | The Design and Implementation of a Next Generation Name Service for the Internet[END_REF]. In addition, load is not equally balanced between root servers due to the fact that names are not equally distributed among top level domains (e.g. .com names are far more than .edu names). Finally, DNS supports a hierarchical namespace, which constrasts with our requirement for flat identifiers.

The limitations of DNS have led the research community to look into DHTbased approaches for name resolution e.g., [START_REF] Ramasubramanian | The Design and Implementation of a Next Generation Name Service for the Internet[END_REF][START_REF] Walfish | Untangling the web from DNS[END_REF][START_REF] Pappas | A Comparative Study of the DNS Design with DHT-Based Alternatives[END_REF]; typical DHTs used in these approaches are Chord [START_REF] Stoica | Chord: a scalable peer-to-peer lookup protocol for internet applications[END_REF] and Pastry [START_REF] Rowstron | Pastry: Scalable, decentralized object location and routing for large-scale Peer-to-Peer systems[END_REF]. The main problem with DHTs is the logarithmic number of hops required (on average) for lookup/resolution. The common workaround for this problem is caching and/or replication, as well as incrementing the average node degree in the DHT. Furthermore, overlay routing in DHT approaches suffers from non-compliance to inter-domain routing policies i.e., the overlay routes followed when resolving a name may violate the routing policies of the underlying physical network [START_REF] Seetharaman | Inter-domain policy violations in multi-hop overlay routes: Analysis and mitigation[END_REF]. To the best of our knowledge, no solution has been proposed for this problem in any of the available DHT overlays, except for [START_REF] Fotiou | H-Pastry: An adaptive multi-level overlay inter-network[END_REF], which was developed for the purposes of this work.

In MDHT [START_REF] D'ambrosio | MDHT: a hierarchical name resolution service for information-centric networks[END_REF] a multilevel DHT architecture is proposed for name resolution in the ICN context. MDHT aggregates IO registration entries at higher levels of the inter-domain hierarchy, which raises scalability concerns. The proposed solution is an indirection level which allows the NRS to resolve content provider names, with the resolution of the content itself taking place at a lower level. The description of the proposed system lacks details on the operation of the employed DHT, as well as a performance evaluation of the proposed architecture. A similar approach is followed in [START_REF] Jarno | On name-based inter-domain routing[END_REF], where an inter-domain name-resolution architecture is presented. Again, the aggregation of routing information at the higher levels of the hierarchy poses significant scalability concerns. In a similar manner to [START_REF] D'ambrosio | MDHT: a hierarchical name resolution service for information-centric networks[END_REF], an indirection level is introduced to map scopes of information to lower level resolution nodes. The presented performance evaluation is based on significant abstractions e.g., intra-domain routing overhead and caching have been coarsely modeled based on observations made in different contexts which do not reflect the proposed architecture's intrinsic characteristics. In both approaches ( [START_REF] D'ambrosio | MDHT: a hierarchical name resolution service for information-centric networks[END_REF] and [START_REF] Jarno | On name-based inter-domain routing[END_REF]), the routing inefficiency of DHTs is circumvented by the aggregation of information at higher levels of the inter-domain structure.

The Data-Oriented (and beyond) Network Architecture (DONA) [START_REF] Koponen | A data-oriented (and beyond) network architecture[END_REF] follows a similar approach in that it also concentrates routing information at the higher levels of the inter-domain structure. DONA builds an information-centric layer over the Internet, based on a network of Resolution Handlers (RHs). The deployment of the RHs strictly follows the AS-level structure of the Internet, allowing DONA to directly adapt its structure and operation to the underlying network. Flat, self-certifying names are used to represent information. Content providers issue Register messages to advertise their content to the closest RH which then propagates this information upwards in the hierarchy, also forwarding it across inter-domain peering links. Name resolution is based on a similar propagation of requests (Find messages) upwards in the hierarchy, until a relevant entry is found. At that point, requests follow the (downhill) reverse path of the corresponding Register message. In this process, shortest path routing is followed and inter-AS routing policies are taken into account.

In the work most similar to ours [START_REF] Choi | Performance comparison of content-oriented networking alternatives: A tree versus a distributed hash table[END_REF], a performance comparison of content delivery between a DONA-like, hierarchical architecture and a DHT based alternative is presented. The authors study several aspects such as transfer latency and robustness, as well as the impact of in-network caching. However, this investigation does not focus on name resolution and is based on oversimplified network topologies: the DONA-like architecture uses a tree overlay consisting of randomly selected nodes of a two-level, hierarchical inter-domain topology. Our work is far more accurate in that (i) we consider a more realistic topology model that takes into account both multihoming and peering relationships (see Section 5), (ii) we fully implement DONA, allowing the structure of the RH network to mimic the underlying inter-domain topology and (iii) we consider a DHT-scheme that better adapts to the underlying topology (see Section 4.1).

An enhanced DHT-based NRS

As already discussed, the load balancing and robustness characteristics of DHTs can directly address the scalability concerns posed for an NRS in the context of ICN. However, these features also imply several important disadvantages i.e., name resolution follows longer paths than those offered by the underlying shortest path routing fabric, often unnecessarily crossing administrative domain boundaries and/or violating the established inter-domain routing policies.

In our work we have investigated the extent to which DHT routing can be improved, without sacrificing its scalability advantages. Our purpose is to assess the ability of a DHT-based approach to support an NRS in the context of ICN. To this end, we have designed DHT-NRS, an NRS based on an enhanced DHT design named H-Pastry [START_REF] Fotiou | H-Pastry: An adaptive multi-level overlay inter-network[END_REF]. In the following, we first provide an overview of the H-Pastry scheme and then we proceed with the description of DHT-NRS. We do not discuss security issues, as they are outside the scope of this paper. However, existing solutions for securing DHTs are also applicable to our work.

H-Pastry

Based on Pastry [START_REF] Rowstron | Pastry: Scalable, decentralized object location and routing for large-scale Peer-to-Peer systems[END_REF] and the Canon paradigm [START_REF] Ganesan | Canon in G Major: Designing DHTs with Hierarchical Structure[END_REF], H-Pastry is a multi-level DHT scheme that improves routing by taking physical network proximity, administrative domain boundaries and inter-domain routing policies into account. In order to adapt to the multi-level structure of an inter-network, H-Pastry employs a corresponding multi-level structure to partition the information identifier space, and the corresponding routing state. Distinct routing tables are maintained for each level of the inter-domain topology. At each level, H-Pastry nodes maintain routing information about nodes that are numerically closer to certain points in the identifier space (i.e., their own identifier and the identifiers required to fill their Routing table) than any other node at that particular level. In this manner, the participating H-Pastry nodes recursively create H-Pastry rings that adapt to the AS-level topology of the network. Multihoming and peering agreements are also taken into account by appropriately introducing virtual nodes in the inter-domain topology graph [START_REF] Fotiou | H-Pastry: An adaptive multi-level overlay inter-network[END_REF]. H-Pastry presents good fault resilience properties: as described in [START_REF] Fotiou | H-Pastry: An adaptive multi-level overlay inter-network[END_REF], H-Pastry routing will fail in the event of a maximum of H • |L/2| concurrent failures of nodes grouped in H sets of |L/2| adjacent IDs each (the corresponding number of failures for Pastry is |L/2|) where H is the height of the domain level hierarchy and L the size of the leaf set.

By taking into account the aforementioned routing aspects, H-Pastry considerably improves DHT-based routing. As shown in [START_REF] Fotiou | H-Pastry: An adaptive multi-level overlay inter-network[END_REF], H-Pastry results in shorter routes, lowering path stretch by 55% and 47% compared to Chord [START_REF] Stoica | Chord: a scalable peer-to-peer lookup protocol for internet applications[END_REF] and hierarchical Chord [START_REF] Ganesan | Canon in G Major: Designing DHTs with Hierarchical Structure[END_REF], respectively, being comparable to regular Pastry. At the same time, H-Pastry also manages to confine traffic within administrative boundaries resulting in 27% less inter-domain hops and 55% shorter intra-domain paths than regular Pastry. Moreover, by taking routing policies into account, H-Pastry reduces valley-free policy violations per routing path by 56%, 31% and 36% compared to Chord, Pastry and hierarchical Chord, respectively.

DHT-NRS

Basic functionality. The name resolution function in DHT-NRS follows the Publish/Subscribe paradigm i.e., publishers (content providers) and subscribers (content consumers) interact with DHT-NRS through a set of brokers responsible for matching publications and subscriptions. DHT-NRS is realized by the deployment of these brokers, named Rendezvous Nodes (RNs), across the interdomain topology. Each RN is an H-Pastry node with a unique ID. We envision at least one RN per AS; more RNs will increase system scalability. For each IO a statistically unique ID is created (e.g., with a secure hash function). Publishers and subscribers interact with DHT-NRS via their local domain RNs, designated during network attachment. Name-resolution is then based on the exchange of the following control messages (an example is given in Figure 1):

-Adv: An advertisement message sent by the publisher(s) of an IO to register the IO with DHT-NRS (step I in Figure 1). This message contains information that maps the ID of the advertized IO to the network location of the issuing publisher. For each unique ID-publisher mapping, a corresponding IO entry (IOE) is maintained by an RN designated by H-Pastry as responsible for that ID (denoted as the Rendezvous Point (RVP) for the ID). Advertisement messages are routed towards the RVP through H-Pastry. -Sub: A subscription message is issued by a subscriber to request a specific IO (step II in Figure 1). Subscription messages contain the ID of the requested IO along with information on the subscriber's network location. Subscription messages reach the appropriate RVP through H-Pastry routing. Upon reception, an RVP searches its IOEs for the indicated IO ID. If the subscription message refers to an unknown IO, the RVP discards the subscription. -Ntf: A notification message is sent by an RVP to notify the publisher(s) of an IO to start the delivery of the corresponding data (step IV in Figure 1). -Pub: Upon notification from the RVP, a publisher sends the IO to the subscriber(s) (step V in Figure 1) via an underlying forwarding mechanism. Caching. Even though DHT-NRS is based on a novel DHT scheme that adapts to the underlying network topology, routing is still based on DHT primitives which are characterized by their logarithmic relation to the number of RNs in the inter-network. Adopting established practice (see Section 3), we employ caching to shorten the resolution paths. More specifically, we cache the route towards the publisher of an IO. During advertisement of an IO, a cache entry is created in all intermediate RNs encountered by the Adv message (step I in Figure 1). Moreover, when a Sub message reaches an RVP, the RVP actively pushes a copy of the respective IOE to all RNs in the path followed by the subscription (step III in Figure 1). Further subscriptions for an IO trigger Ntf messages directly towards the publisher upon a cache hit, reducing the part of the resolution path that follows H-Pastry's routing. Each cache entry contains a time to live (TTL) value that allows for its invalidation and is subject to application level criteria. Cache replacement follows a Least Recently Used (LRU) mechanism.

Node failures. Due to the vital role of the NRS in locating information in ICN, we expect the deployment process to follow a path similar to DNS i.e., rely on highly provisioned RN servers. However, the multitude of DoS attacks against DNS signifies the critical role of system resilience, while the vast size of the expected workload further urges for a design able to cope with node failures. The use of a highly distributed DHT-based solution is a design choice aligned with this desire. Based on the uniform distribution of IO and node IDs in the identifier space, a DHT based solution accomplishes an even distribution of IOEs to nodes, so that a node's failure has a a modest impact to the entire system, proportional to deployment density. The fault resilience properties of H-Pastry add to the DHT-NRS robustness (see Section 4.1). In contrast, hierarchical designs (e.g., DONA) allow even a single node failure to affect the routing of messages to/from the entire sub-tree rooted at the failed node. Obviously, the impact of a node failure is isolated to that part of the inter-domain topology, but the consequences become more severe for nodes at higher levels. Multiple physical incarnations of resolution nodes ameliorate this problem, but only at an additional cost.

Performance Evaluation

In order to investigate the extent to which the DHT-NRS proposed fulfills our requirements, we focus on two major aspects: (i) system load, including memory, signaling and processing overheads, and (ii) routing performance. Our investigation offers a detailed comparison with DONA, with the purpose of revealing, as well as quantifying, the inherent (dis)advantages of both architectures. Particular attention is paid to (i) the effect of the underlying inter-network structure on perceived performance and its relation to the structural characteristics of each architecture and (ii) the effect of the popularity characteristics of content on the effectiveness of DHT-NRS's caching scheme.

Topologies. Understanding the Internet topology is a crucial factor in designing new inter-domain protocols. Typically, the AS-level topology is described as a multi-tier hierarchy of interconnected ASes, mostly using transit customerprovider links. However, several measurements and studies argue that the Internet topology is evolving into a mesh dominated by multi-homing and peering relationships [3,[START_REF] Labovitz | Internet inter-domain traffic[END_REF][START_REF] Oliveira | The (in)completeness of the observed internet AS-level structure[END_REF]. These studies converge on the number of the ASes, which is estimated to be around 35.000. Evaluating a protocol using a realistic topology of 35.000 ASes (and approximately 200.000 annotated links) is obviously a technical challenge on its own. To overcome this constraint, while also preserving memory and processing resources for the evaluation of non trivial DHT sizes, we used inter-domain topologies generated by the algorithm presented in [START_REF] Dimitropoulos | Graph annotations in modeling complex network topologies[END_REF]. The size of these topologies is manageable for evaluation and they maintain the same characteristics (i.e., business relationships) as in the measured graphs.

Workload. Our evaluation considers a detailed model of inter-domain Internet traffic. Based on the measurements presented in [START_REF] Labovitz | Internet inter-domain traffic[END_REF], we generate a mixture of various traffic types (e.g., Web, Video, P2P)1 . The resulting traffic mix does not distinguish between user and control plane traffic i.e., the signaling required to locate and start content transmission, except for DNS which only constitutes 0.17% of all traffic. However, our evaluation focuses on the control plane requests made to the NRS to support user plane traffic. Therefore, we translated the user plane traffic mix into a control plane equivalent. To this end, we derived the actual number of IOs for each traffic type by dividing the corresponding data volume with the median IO size of that traffic type as measured in relevant studies [START_REF] Busari | ProWGen: a synthetic workload generation tool for simulation evaluation of web proxy caches[END_REF][START_REF] Bellissimo | Exploring the use of BitTorrent as the basis for a large trace repository[END_REF][START_REF] Cheng | Understanding the Characteristics of Internet Short Video Sharing: YouTube as a Case Study[END_REF]. We used the median instead of the mean object size, so as to avoid skewing the results due to the long-tail characteristics of some distributions (e.g., the Pareto tail of Web object size distribution). The set of subscription messages is then shaped based on studies for each traffic type which model its popularity characteristics, including its temporal evolution [START_REF] Busari | ProWGen: a synthetic workload generation tool for simulation evaluation of web proxy caches[END_REF][START_REF] Cheng | Understanding the Characteristics of Internet Short Video Sharing: YouTube as a Case Study[END_REF][START_REF] Guo | A performance study of BitTorrent-like peer-to-peer systems[END_REF].

Results

Our evaluation employs a 400 domain topology, which follows a hierarchical model with six levels, but also contains multi-homing and peering links between the domains. We deploy a population of 4400 RNs/RHs uniformly across the domains. The cache size in DHT-NRS is expressed as a proportion of the median number (m) of registration entries per RH in DONA. We choose the median value, since the distribution of state in DONA is considerably skewed, as we show below. Moreover, we examine scenarios with infinite cache size (ICS) i.e., no limitation on the available cache size; this reflects the upper limit for the performance of caching in DHT-NRS. In each scenario, we use a workload corresponding to 25 GBs of traffic, resulting in an average2 of 2430379 subscription messages for 1032030 IOs. This size limit was imposed by the limitations of the simulation environment. Since end hosts typically reside in access networks i.e., networking domains that have no customer domains and thus do not act as transit domains, all Adv/Sub messages in DHT-NRS (Register/Find in DONA) are injected into the network from a randomly chosen RN (or RH respectively) residing in an access network. Finally, we considered a single publisher per IO.

Routing. The routing performance of the name-resolution system affects both the latency perceived by the end-users, as well as the traffic load on the network. We express the routing performance of DHT-NRS with the stretch metric, defined as the ratio of the number of inter-domain hops required for a Sub message to reach the RVP and the corresponding Ntf message to reach the RN serving the publisher of the desired IO, over the hop count required by an identical Find message to reach the same target in DONA i.e., the RH that issued the corresponding Registration.

Figure 2(a) shows the stretch values derived for several scenarios with different cache sizes. Stretch ranges from 2.84 without caching to 1.95 in the ICS scenario. Under current traffic patterns, DONA significantly outperforms DHT-NRS in routing efficiency. This is only possible however because DONA extensively replicates IOEs throughout the hierarchy, thus guarantying the existence of the desired registration on the shortest, policy-compliant path towards the publisher. DONA is superior to DHT-NRS regardless of cache size, since caching is less aggressive than replication, reactively adapting to, and therefore highly depending on, the request patterns. Hence, non popular IOEs are evicted from DHT-NRS caches, or even never requested again, yielding low cache hit ratios. As shown in Figure 2(b), the cache hit ratio is 27.17, 31.75, 37.76 and 53% for the 50%m, 100%m, 150%m and ICS scenarios respectively. For each scenario, the corresponding savings in the resolution path lengths are 13, 15.39, 18.24 and 31%, respectively. These values are subject to the popularity characteristics of the workload, and show that with current workload patterns route caching in DHT-NRS cannot exceed a cache hit ratio value of 53%, even with unrealistically large cache sizes, resulting in low routing improvements.

In order to provide an insight of the potential benefits of caching in scenarios where item popularity does allow higher cache hit ratios, we also consider the stretch value of resolution paths in which the Sub messages have hit a cache. As shown in Figure 2(a), stretch ranges from 1.34 in the hypothetical, best case scenario (ICS) to 1.67 in the 50%m scenario. These results show that caching achieves a substantial reduction of resolution path lengths in the case of popular IOs, which are still however at least 34% longer compared to DONA. This is due to the indirection mechanism in DHT-NRS, as the RVP may not reside in the shortest path connecting a subscriber and a publisher. However, in cases of multiple publishers per IO (e.g., replication points), we expect the routing properties of H-Pastry and the caching mechanism to further shorten resolution paths by selecting the closest publisher.

State.

In our evaluation, we use the term "state" to refer to the IOEs maintained at each node of the name-resolution system. The state size is related to the total number of IOs and determines the amount of resources required to support the operation of the architecture wrt memory and lookup processing load. Figure 2(c) shows the cumulative distribution function of the state size for both DHT-NRS and DONA. Note that the x axis is in log scale. The difference between the two architectures is significant, with the size of the state maintained by RN nodes in DHT-NRS being considerably lower than the corresponding load imposed on DONA's RHs. More importantly, we see that DHT-NRS achieves a more uniform distribution of state across the participating nodes compared to DONA. For instance, 95% of the RNs in DHT-NRS maintain less than 550 IOEs (0%m scenario), while 95% of the RHs in DONA maintain up to almost 33000 IOEs. The highly skewed state distribution in DONA is due to the accumulation of registrations at higher levels of the inter-domain hierarchy, and poses a significant challenge for network operators, who would have to resort to dense deployments of RHs in order to cope with the associated resource requirements.

Moreover, it is important to point out the relation of the observed state distribution skewness to the structure of the inter-domain topology. In the considered topologies, slightly less than 50% of access networks reside at level 2, meaning that a major part of the registrations is stored only at the first two levels of the hierarchy. This is demonstrated in Figure 2(d) which shows the average state size per node at each level of the hierarchy. Note that the y axis is presented in log-scale. This figure suggests that the inter-domain topology structure causes the concentration of excessive state in DONA at the top-most levels of the hierarchy. On the one hand, these top-level domains face disproportionate overhead compared to lower level domains, incurring the corresponding CAPEX/OPEX overheads. On the other hand, however, it also suggests that the scalability challenge in DONA is mostly concentrated in a limited sub-area of the inter-domain topology, making cloud-based solutions a compelling option. (c) and 2(d) also show the amount and distribution of state required to avoid cache replacement (i.e., the ICS scenario). This hypothetical scenario requires a considerable amount of memory which is highly unlikely to be available in practice (see Section 2). However, even in this scenario, almost 8% of RHs in DONA have higher memory requirements than any RN in DHT-NRS. Moreover, we see that in DHT-NRS state is distributed more evenly across the hierarchy levels, with the exception of level 1 RNs in the ICS scenario where the routing scheme causes a concentration of cached IOEs (see also the next section).

Processing overhead. The state size per node determines the processing overhead per IOE lookup at the RVP and the overall processing overhead is determined by the actual number of lookups performed by a node. For each architecture, we define the lookup overhead (LO) metric as the sum of the total number of Sub/Find messages forwarded by each RN/RH respectively, and the total number of messages terminating at each node i.e., triggering communication with the publisher. Figure 2(e) shows the cumulative distribution function of LO for both architectures. A major fraction of DONA RHs is subject to less LO than RNs in DHT-NRS, due to the considerably worse routing performance of DHT-NRS that results in Sub messages traversing longer networking distances and thus consuming resources at more intermediate RNs. However, a closer look at the LO distribution across the inter-domain hierarchy reveals a disproportionate overhead for the top-level domains in DONA (Figure 2(f)). Evidently, the fact that a major part of the access domains resides at level 2 of the hierarchy results in a corresponding resolution overhead for the top-level domains, which again calls for the use of considerable processing (as well as memory) resources.

Interestingly, Figure 2(f) also shows that RNs at the top-most domains of the hierarchy in DHT-NRS are subject to considerably higher processing overhead compared to lower level RNs. The additional overhead is due to the forwarding of Sub and Ntf messages (ID ownership is evenly distributed across the RNs) and is attributed to the structure of the inter-domain topology and the design of H-Pastry: to adapt to the inter-domain hierarchy structure, H-Pastry causes the top level domains to be included in the first non-local ring of each of the access networks at level 2. Therefore, paths towards non-local RVPs are most likely to pass through these domains. As a substantial fraction of access networks resides at level 2, a proportional number of IOs are served from publishers at these domains, resulting in a significant part of the overall Ntf messages reaching RNs at these domains via the top-level domains. Similarly, H-Pastry causes the Sub messages originating from level 2 access domains to first traverse the top-level domains before taking a downhill direction towards the RVP.

Advertisement/registration overhead. In addition to subscriptions, signaling overhead is also generated by IO registrations. We characterize this overhead as the total number of single inter-domain hop transmissions required for the registration of a single IO to complete. Our measurements show that DHT-NRS requires on average 6.34 inter-domain transmissions per IO in the 0%m scenario, while DONA requires on average 35.56 transmissions. These numbers indicate an excessive inter-domain traffic load in the case of DONA, attributed to the (limited) flooding method used to disseminate registration messages to the upper levels of the inter-domain hierarchy (as well as to peering domains). Multihoming plays an important role in this as it results in registration messages being transmitted to multiple domains at higher levels. In the employed topologies 56.75% of all domains are multihomed, with 2.4 providers on average. Unlike DONA, by carefully partitioning the identifier space DHT-NRS forms a structured overlay that only requires the targeted routing of Adv messages.

Conclusions

In this paper we investigated name-resolution in the context of ICNs, focusing on the emerging tradeoff between routing state overhead and routing efficiency. Motivated by the significant scalability characteristics of DHTs, but also concerned about their routing inefficiency, we engaged in the design of a name resolution system based on an enhanced DHT scheme, aiming to improve routing performance. Then we engaged in a detailed performance evaluation and comparison against DONA, an alternative that yields efficient routing performance but raises significant scalability concerns. Our findings reveal the effect of the inter-domain topology structure and traffic patterns. With current traffic patterns, route caching in DHT-NRS cannot compete with the extensive replication of routing information in DONA, yielding stretch values ranging from 1.95 to 2.84. However, this comes at the cost of a heavily skewed distribution of memory and processing overhead, as well as significant signaling overhead for the registration of content in DONA. The replication mechanism of DONA along with the structural characteristics of the inter-domain topology result in disproportionate resource requirements for a limited area of the internetwork, at the top-most level domains in the hierarchy, indicating the need for large-scale centralized solutions (e.g. cloud computing).

Fig. 1 .

 1 Fig. 1. DHT-NRS Example; the (i, P ) records are stored at RNs 4, 5, 6 and 7 during step I, and at RNs 1, 2 and 3 during step III.

Fig. 2 .

 2 Fig. 2. Performance evaluation results: DHT-NRS vs. DONA

We did not use DNS trace data as they reflect the current Internet architecture. For example, they omit requests sent directly to content owners (e.g., HTTP requests).

We used a different workload instance in each experiment to increase randomness.

⋆ Work supported by the ICT PURSUIT project, under contract ICT-2010-257217.