L Boutrih

L Ben Ayed

M Nouari

Modeling of the interface delamination process when machining hybrid multi-material assemblies

Keywords: CFRP/Ti assembly, Finite element method, cohesive elements, delamination

Modeling of the interface delamination process when machining hybrid multi-material assemblies

Lhoucine Boutrih, Lanouar Ben-Ayed, Mohammed Nouari

Nomenclature

Metallic model

Equivalent plastic stress (MPa) Equivalent plastic strain Equivalent plastic strain rate Reference strain rate (s - Fiber orientation (°)

Introduction

During the last decade, the demand for composite materials increased significantly. They have been widely used in building equipment for aircraft industry since they provide high strengthto-weight ratio, good damage tolerance, and excellent resistance to fatigue and corrosion.

However, the expanding development in the aerospace field urges engineers to come up with other materials in order to improve their mechanical properties. Stacked materials (metal/composite) have been proposed for this purpose because they provide an effective method for improving bending rigidity and enhancing global mechanical properties. Carbon fiber reinforced polymer (CFRP) combined to titanium alloys (Ti) is a typical stack composite configuration of a new hybrid material. Other combinations could also be found as GFRP/Al or GLARE. Some examples of application concern doorframes, formers and reinforcement profiles within the construction of the new generation of aircrafts such as Boeing 787

Dreamliner and Airbus A350 XWB, [1].

Despite their widespread applications, machining such stack configurations still represents a most challenging task due to the disparate properties of each constituent and their poor machinability. For instance, the CFRP layer shows anisotropic behavior, and abrasive nature, which may cause poor machined surface quality and severe induced damage in machining processes, [START_REF] Shetty | A review on finite element method for machining of composite materials[END_REF][START_REF] Teti | Machining of Composite Materials[END_REF]. For the metal phase, the titanium alloy exhibits low thermal conductivity and strong chemical affinity, which result in high heat generation and premature tool wear during machining, [START_REF] Calamaz | Approche expérimentale et numérique de l'usinage à sec de l'alliage aéronautique TA6V[END_REF][START_REF] Ezugwu | Materials Titanium alloys and their machinability[END_REF]. Several authors showed that the machinability is strongly influenced by the tool geometry, cutting conditions and induced cutting damage. Omanath et al. [START_REF] Pawar | Analysis of hole quality in drilling GLARE fiber metal laminates[END_REF] found that for the four drill bits studied only two fluted and four faceted drills are suitable for drilling GLARE laminate since they give zero delamination. Piotr et al. [START_REF] Tyczynski | Drilling of CFRP, GFRP, glare type composites[END_REF] highlighted the requirement to modify the standard drill geometry to match the properties of each phase under drilling process. Galal et al. [START_REF] Mohamed | Blast resistance and damage modelling of fibre metal laminates to blast loads[END_REF] showed that GLARE is a possible blast reduction structure since aluminum plate dissipate all the energy as a plastic deformation while glass fiber contributes to enhance the blast attenuation due to its positive strain rate sensitivity. Concerning the effect of cutting conditions on machinability, knowledge of the cutting tool behavior has proven to be the key to optimizing the cutting process. Mozammel et al. [START_REF] Mia | Intelligent optimization of hard-turning parameters using evolutionary algorithms for smart manufacturing[END_REF] proposed an intelligent optimization of hard-turning machining by modifying the cutting parameters, the cutting process can be optimized to achieve the intended results.

Zitoune et al. [START_REF] Zitoune | Experimental and numerical analysis on drilling of carbon fibre reinforced plastic and aluminium stacks[END_REF] analyzed the drilling operation of FRP and aluminum stacks and observed that the machining quality is mainly influenced by the feed rate parameter f. When f equals approximately 0.15mm/rev, the maximum size of CFRP/Al interface delamination is found to be around 0.38µm. Montoya [START_REF] Montoya | Optimisation du perçage de multi-matériaux CFRP / Titane et / ou Aluminium[END_REF] addressed the WC tool operating parameters when drilling Ti/CFRP/Al stacks, thrust force was found by the author to be lowest in the CFRP (44-190 N)

followed by Al (135-342) and Ti (285-600N) resulting in a principal damage of titanium plate rather than aluminum or CFRP.

The most used machining operations for the composite metal assemblies is drilling. Drilling operation is considered as oblique configuration for which the tool has at least three cutting angles. In this case, machining quality and more especially the induced defects in the manufactured part are the critical points that have to be considered. During machining holes, the composite-metal stacks are drilled together to join the requirement of assembly precision and improved productivity, [START_REF] Luo | Investigation on the interface damage in drilling low-stiffness CFRP/Ti stacks[END_REF][START_REF] Alonso | Influence of flute number and stepped bit geometry when drilling CFRP/Ti6Al4V stacks[END_REF], although each material requires different cutting parameters, [START_REF] Vijayan | Comprehensive Review on Drilling of Multimaterials Stacks[END_REF]. To ensure the structural integrity of the part, it is important to reduce damage at the CFRP/Ti interface and interactions influenced by stacking sequence between CFRP and Ti materials, [START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF].

It is believed that the fundamental analysis of cutting mechanisms and chip formation process of metallic and composite materials can help increasing the machining efficiency. Compared to drilling process (with complex tool geometry and cutting kinematic), orthogonal cutting can be a simple and helpful machining operation to understand the cutting process of composite metal assemblies. In this configuration, the cutting edge of the tool is perpendicular to the direction of the tool motion.

Some remarkable research work on orthogonal cutting has been found through the literature study but many physical phenomena, responsible for the poor quality of machining, have remained unanswered. Understanding chip formation mechanisms of composite and metallic parts continues to be a vital part in research. There are some remarkable differences of these mechanics between metallic and composite materials whereas the case of composite materials remained left behind. The chip formation process of composite materials is affected by many parameters. Koplev et al. [START_REF] Koplev | The cutting process, chips, and cutting forces in machining CFRP[END_REF] mentioned that the chip formation in machining fiber reinforced polymer (FRP) materials is critically controlled by the fiber orientation and the cutting edge rake angle. Other authors explained that during the chip formation, there are four modes of failure that occur in a composite structure which are matrix cracking, fiber-matrix shearing, fiber failure, and delamination, [START_REF] Ilyas | Damage modeling of carbon epoxy laminated composites submitted to impact loading[END_REF]. The damage of different components like fiber, matrix, and fiber matrix interface, simultaneously progress until the complete chip formation process, [START_REF] Florent | Etude de la coupe en perçage par le biais d'essais élémentaires en coupe orthogonale[END_REF].

In metal cutting, the chip formation depends on the local conditions of stress at the tool-chip interface (contact pressure and frictional stress), sliding velocity, cutting temperature and local properties of the tool-work material. Consequently, a fundamental understanding of the thermomechanical behavior of the machined material is needed to prove the quality of the machined surface. Several authors summarized that during the chip formation, the energy dissipation comes from three main deformation zones: (i) the primary shear zone where the flow direction change of the removed work material occurs. (ii) the secondary shear zone which is in contact with the tool rake face and (iii) the tertiary shear zone which is in contact with the tool clearance face, [START_REF] Atlati | Thermomechanical modelling of the tool-workmaterial interface in machining and its implementation using the ABAQUS VUINTER subroutine[END_REF].

To address some physical aspects observed during the machining of CFRP/Ti stack composite, experimental investigations have been performed. Isbilir et al. [START_REF] Isbilir | Comparative study of tool life and hole quality in drilling of CFRP/titanium stack using coated carbide drill[END_REF] studied the influence of drilling parameters on the thrust force, torque, burr formation and delamination phenomenon when drilling the CFRP/Ti6Al4V stacks. The results were compared to those of drilling thses materials separetly. They found that the feed rate was a predominant factor on the thrust force magnitude. Drilling stacked materiel causes a growth in the torque force by 44.5% in Ti and 83.5% in CFRP compared to single CFRP or Ti. The extent of delamination in CFRP is however much smaller in the CFRP/Ti stack compared to drilling the CFRP alone.

This was explained by the presence of the titanium backup plate.

A recent experimental study on drilling CFRP/Ti stacks was conducted by Xu et al. [START_REF] Xu | Experimental study on mechanical drilling of carbon/epoxy composite-Ti6Al4V stacks[END_REF] for four drilling trails including individual CFRP and Ti drilling and CFRP/Ti stacks with and without cooling. The results show that elevated cutting temperature causes an increase in the tool wear level, and significantly affects the hole quality by increasing the cutting force. Thus, the cooling process reduces temperature and contributes to a better chip ejection, which has a significant impact on the delamination inside the CFRP material.

In orthogonal cutting, detailed damage comprehension in composite phase nor the appropriate chip formation in the Ti-phase were found in previous study, [START_REF] Xu | Cutting modeling of hybrid CFRP/Ti composite with induced damage analysis[END_REF]. In composite material, the lack of physical meaning of damage criteria of Hashin or Tsai Hill makes it difficult to properly predict the fiber/matrix damage progression. A strong influence of fiber orientation on the direction of crack generation and propagation in composite laminates has been found by Blanchet et al. [START_REF] Florent | Etude de la coupe en perçage par le biais d'essais élémentaires en coupe orthogonale[END_REF]. Pramanik et al. [START_REF] Pramanik | An FEM investigation into the behavior of metal matrix composites: Tool-particle interaction during orthogonal cutting[END_REF] reported that rupture is generated due to debonding of particles (case of glass-fiber and matrix debonding) in front of the tool. Whereas Shchurov et al. [START_REF] Shchurov | SPH-Simulation of the Fiberreinforced Composite Workpiece Cutting for the Surface Quality Improvement[END_REF] argued that the main reason for this fact is the high strength of fibers in comparison with the matrix one. To understand this physics in detail, it is more reasonable to focus on the damage mechanism of a composite part in the assembly. According to Lasri et al.

[25], damage mechanisms in CFRP composites include four types of failure modes: transverse matrix cracking, fiber-matrix interface debonding, fiber rupture and inter-ply delamination.

The authors carried out simulations with different stress criteria and found that in cases of Hashin and Maximum stress criteria, fiber-matrix interface debonding is the first damage developed in the composite structure during the chip formation process. Matrix failure starts and progresses in the same way as fiber-matrix interface failure before complete debonding, then continues to propagate in depth until completion of the chip formation. But in case of maximum stress criteria, matrix failure initiates late and then gradually progresses in the vicinity of the cutting tool edge. The fiber breaking is the last failure that occurs during the chip formation process in both Hashin and Maximum stress criteria.

Machining process of hybrid stacks made of CFRP and Ti alloy is a complex task that requires long and expensive trials. At the same time, experimental investigations only, cannot completely reveal the cutting process of the different phases and interface region, and it is impossible to observe the formation process of the subsurface damage at the interface zone.

Therefore, numerical simulations and theoretical modeling can be very helpful tools to overcome these limitations arising from the experimentation.

In the literature of this field of research, only little scholar research has been conducted on the cutting process and damage formation of hybrid CFRP/Ti stacks machining. Xu et al. [START_REF] Xu | Cutting modeling of hybrid CFRP/Ti composite with induced damage analysis[END_REF][START_REF] Xu | Numerical Modeling and FE Analysis of CFRP/Ti Stack Orthogonal Cutting[END_REF] developed under orthogonal cutting configuration a two-dimensional finite element model to simulate machining the CFRP/Ti stack. The results showed that the cutting sequence can have a significant influence on the machined quality and induced damage in the interface region. Zitoune et al. [START_REF] Zitoune | Experimental and numerical analysis on drilling of carbon fibre reinforced plastic and aluminium stacks[END_REF] established a numerical model to simulate the drilling process of CFRP/Al alloy stack composite. Their study indicated that the stacking sequence has a significant impact on the push-out delamination. However, in the case of machining CFRP/Ti stack, three typical cutting stages can be involved, the Ti alloy cutting, CFRP cutting, and the interface (the contact boundary of Ti and CFRP) cutting. Giasin et al. [START_REF] Giasin | 3D Finite Element Modelling of Cutting Forces in Drilling Fibre Metal Laminates and Experimental Hole Quality Analysis[END_REF] developed a threedimensional finite element-drilling model to simulate glass fiber aluminum reinforced epoxy GLARE stack composites. The aim of their study was to understand the mechanism of the process and to predict cutting forces. The results show, first , that the thrust force and torque were overestimated at low feed rates and high spindle speeds. On the other hand, no delamination was identified on the internal surfaces for the used cutting parameters.

The above literature has provided a better comprehension of the physical phenomena in cutting CFRP/Ti-CFRP/Al stacks composites. Whereas, the key activated factors, i.e., the interactions between two stacked materials on affecting the subsurface damage of the interface region are still not investigated. Nevertheless, a detailed damage comprehension in neither the composite phase nor the appropriate chip formation in the Ti phase were found in the previous studies. In composite material, the damage criteria such as Hashin, Tsai Hill or puck criteria make it very difficult to properly predict fiber/matrix damage progression.

Therefore, in this work an elastoplastic behavior coupled with damage is considered to realistically simulate all physical aspects that govern the machining process of composite.

Johnson-Cook model is used in the metallic phase as the model has proven its ability to simulate the chip separation and thus, is being widely used in machining problems. Finally, to study interface behavior cohesive elements approach is adopted. The model based on a traction-separation cohesive law, allowing for representation of both initiation and evolution of the failure process. Each model is presented in the following section.

Finite Element Model

In the chosen configuration of orthogonal cutting of the hybrid composite, we have two main parts: tool and workpiece. The tool is considered as a rigid part and the workpiece is composed of CFRP phase, interface and Ti phase. To consider the different aspects previously cited, a FE model is proposed for modeling the machining process of a hybrid CFRP/Ti stack.

It is based principally on three sub-models: The metallic model, which allows to predict the titanium behavior, the composite model to predict the CFRP behavior and the joint model, to predict the interface behavior between CFRP and Ti.

The constitutive damage law and the physical set up of the 2D FE model is explained in details in the following sections.

Metallic model

In the titanium phase, the built-in Abaqus/Explicit Johnson-Cook constitutive model [START_REF] Johnson | A-constitutive-model-and-data-for-metals-subjectedto-large-strains-high-strain-rates-and-high-temperatures[END_REF] was used because it can reflect the metal constitutive behavior under high strain, high strain rate and high temperature. The model dissociates plastic, viscous and thermal aspects in three independent terms as follows:

(

where is the equivalent plastic stress, is the equivalent plastic strain, is the equivalent plastic strain rate, is the reference strain rate, A is the initial yield stress, B is the hardening modulus, C is the strain rate dependence coefficient, is the dynamic temperature of materials, is the room temperature and is the material melting temperature. n and m are work hardening exponent and thermal softening coefficient, respectively. The first term describes an isotropic strain hardening behavior, the second describes strain rate sensitivity and the third term describes a thermal softening behavior.

To take into account the stiffness drops after a certain value of plastic deformation, Nasr et al.

[29] compared two damage modeling approaches in metal cutting using finite element simulations; (i) the Johnson-Cook shear failure model and (ii) the progressive damage model. They found that the use of JC damage model evolution is suitable to accurately predict the different process parameters such as cutting forces, shear angle, chip thickness and contact length. That is why, the JC damage law given by Equation ( 2) is adopted in this study. To allow the simulation of chip formation, a damage parameter is defined in Equation (3).

The failure is reached in the material once the parameter is equal to 1.

(

) ( 2
) 3
where and are the equivalent plastic strain increment and the equivalent plastic strain corresponding to the failure respectively, is the triaxiality rate, with (i= 1, 2, 3, 4, 5) are the JC damage parameter, , and are dynamic temperature of materials, room temperature and material melting temperature respectively.

To estimate the damage evolution, Abaqus software provides two laws (linear and exponential form) based on the energy dissipation during the process. These laws take into account the characteristic length of the element to overcome the mesh dependency of the results. Once the damage initiation criterion is reached, the linear form assumes that the damage variable increases with plastic displacement (or equivalent plastic strain) according to:

where , and represent the equivalent plastic displacement at failure, the equivalent plastic displacement and the characteristic length of the element, respectively. The exponential form of the damage variable is given as:

(

where is the fracture energy, and it's a key factor in the chip formation morphology [START_REF] Yaich | Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting process : application to the Ti6Al4V[END_REF][START_REF] Atlati | Développement d ' une nouvelle approche hybride pour la modélisation des échanges thermiques à l ' interface outil-copeau : application à l ' usinage de l ' alliage d ' aluminium aéronautique AA[END_REF]. The fracture energy needs to be inputted into the FE model and according to the study of Mabrouki et al. [START_REF] Mabrouki | Numerical and experimental study of dry cutting for an aeronautic aluminium alloy (A2024-T351)[END_REF] this energy depends on Young's modulus E, Poisson's ratio ν, Mode-I (II) stress intensity factor ( ) :

(6)

Composite model

In the CFRP phase, the proposed model is based on a combined elastoplastic damage constitutive law [START_REF] Zenia | Numerical analysis of the interaction between the cutting forces , induced cutting damage , and machining parameters of CFRP composites[END_REF]. Considering the case of a ply under plane stress and in 2D, the strain energy density can be written as: [START_REF] Tyczynski | Drilling of CFRP, GFRP, glare type composites[END_REF] where are the elastic modulus in the longitudinal (fiber direction) and transverse directions, respectively, and are the shear modulus and the Poisson's ratio, respectively. , and are the damage variables in the longitudinal, transverse and shear directions, respectively. The symbol <■> + is the Macaulay brackets it refers to the positive part of "■". To describe the initiation and progression of degradation mechanisms, the thermodynamics forces are computed using the following expression:

The damage variable , associated with the brittle fracture of the fibers decomposes into two failure modes: tensile and compression. In case of a tensile stress, the brittle fracture of the fiber is met when the value of reaches the critical value . In case of a compression stress, the fiber break, when the value of the force reaches the critical value . The damage variable, , is given as: [START_REF] Mia | Intelligent optimization of hard-turning parameters using evolutionary algorithms for smart manufacturing[END_REF] To compute the damage variables, transverse and shear , an equivalent force that governs their initiation and evolution, is defined: [START_REF] Zitoune | Experimental and numerical analysis on drilling of carbon fibre reinforced plastic and aluminium stacks[END_REF] where is a coupling term between the transverse and shear damage.

The transverse and shear damage variables are defined as: [START_REF] Montoya | Optimisation du perçage de multi-matériaux CFRP / Titane et / ou Aluminium[END_REF] where , and are the limit strength for damage, the threshold strength for initiation of damage and a coupling term between the transverse and shear damages, respectively.

To limit the maximum damage rate and avoid numerical localization of damage, regularization parameters, and , are introduced and the damage variables are corrected as below: [START_REF] Luo | Investigation on the interface damage in drilling low-stiffness CFRP/Ti stacks[END_REF] The same constants, and are taken for the three damage evolution laws. For this model with delay effects, the variations of the forces, do not lead to instantaneous variations of the damage variables, . There is a certain delay defined by the characteristic time .

Therefore, from the above model, a brittle behavior was suggested in the fiber direction under traction or compression and a plastic behavior in the transverse and shear direction. Hence, the plasticity is given by a quantity called load function (where flow threshold function), as which delimits a multiaxial domain between two elastic and plastic zones as follows: [START_REF] Alonso | Influence of flute number and stepped bit geometry when drilling CFRP/Ti6Al4V stacks[END_REF] where is the equivalent stress given by and represents the updated elastic limit as a function of the cumulative plastic strain p given by: [START_REF] Vijayan | Comprehensive Review on Drilling of Multimaterials Stacks[END_REF] where c is a coupling parameter, is the initial yield stress, and are hardening coefficients. The plastic deformation rate combined with the effective stress are calculated by: (15)

Joint model

The cohesive element provided by Abaqus is used to model delamination of the interface phase directly in terms of traction-separation law. The model assumes that the behavior is initially linear elastic followed by the initiation and evolution of damage. The elastic behavior is written in terms of an elastic constitutive thickness that equals to one if tractionseparation response is specified, this condition ensures that the nominal strain is equal to the separation (i.e., relative displacement of the Ti and the CFRP faces). The nominal strain can be defined as. [START_REF] Koplev | The cutting process, chips, and cutting forces in machining CFRP[END_REF] where and are the components of the relative displacement between the left and the right of the cohesive element, and is the original thickness. The elastic behavior can then be written as: [START_REF] Ilyas | Damage modeling of carbon epoxy laminated composites submitted to impact loading[END_REF] where is the nominal traction stress vector, consisting of three components (the normal, the first and the second shear ) and is the elasticity matric.

The initial response of the cohesive element is assumed to be linear as discussed above.

However, once a damage initiation criterion is met, material damage can occur according to a user-defined damage evolution law. Fig. 1 shows a typical Traction-Separation response with a failure mechanism.

Fig. 1. Traction-separation law for cohesive material

In Fig. 1 represents the peak value of the nominal stress when deformation is either purely normal to the interface or purely in the first or the second shear direction, respectively.

, and are the initial and failure displacement. The superscript, 0 or , represents damage initiation or failure moment. The triangle area is the corresponding fracture energy of mode I, II and III, .

To model the damage initiation of the interface, a quadratic nominal strain criterion is used.

Damage is assumed to initiate when a quadratic interaction function involving the nominal strain ration reaches a value of one as described as: [START_REF] Florent | Etude de la coupe en perçage par le biais d'essais élémentaires en coupe orthogonale[END_REF] The scalar damage indicator d monitors the progression of damage, it initially has a value of 0 and evolves from 0 to 1 which indicates the complete decohesion of the interface .The indicator d affects the stress components of the Traction-Separation law according to the following equation: [START_REF] Atlati | Thermomechanical modelling of the tool-workmaterial interface in machining and its implementation using the ABAQUS VUINTER subroutine[END_REF] where i=n, s and t represent the interface strength under mode I, II and III respectively. This equation also implies that the damage is not accrued when (i.e., under compressive stiffness).

A power law of the energy required to cause failure governs the evolution of damage in our model. The dependence of the fracture energy under mixed mode is defined by the following linear interaction criterion:

(20)

Orthogonal cutting configuration

Numerical Set up

The numerical modeling of the orthogonal cutting process, of CFRP/Ti hybrid composite, is essential to investigate generated cutting forces, induced damage, and chip formation. As reported previously, the FE model has three main phases: composite (CFRP), interface (composite/titanium) and titanium (Ti). Geometry and boundary conditions are presented in Fig. 2. The tool is considered as a rigid body and tool geometry was defined in the work of Xu et al. [START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF]. The ISO reference for this tool is TCMW16T304FLPCD10 as shown in Table 1. The model was developed using the Abaqus/Explicit code with Lagrangian formulation to simulate the cutting process and analyze the chip formation mechanisms in both phases Ti and CFRP. Regardless of distortion problems in finites elements that can be generated using the lagrangian approach, it can still be an effective way to simulate composite chip morphology.

Fig. 2. Mesh generation, boundary conditions and geometry of the tool-workpiece

Adaptive meshing method can overcome distortion problems and leads to accurate results as it has been pointed by Wan et al. [START_REF] Wan | On material separation and cutting force prediction in micro milling through involving the effect of dead metal zone[END_REF] who adopted this method for predicting cutting force in micro milling process. However, this method can only be applied for ALE (Arbitrary Lagrangian-Eulerian) approach.

A regular and structured two-dimensional solid element with 4-node were chosen for the workpiece to meet the "share nodes" contact conditions between cohesive elements and the surrounding phases [START_REF]Abaqus Documentation Version 6.14 Dassault Système Simulia[END_REF]. The workpiece is meshed with roughly 17085 elements and the tool of about 134 elements. The CFRP phase is introduced into Abaqus code as an equivalent material (EM), considering plane stress assumption and using continuum solid elements CPS4R including automatic hourglass control and with reduced integration. A coupled temperature-displacement in a plane strain assumption is considered for the titanium phase and the element type CPE4RT is used. No separation zone is used in the JC damage model and therefore only one fracture energy is defined for the whole titanium phase. In fact, a separation zone is used to simplify the numerical analysis [START_REF] Shchurov | SPH-Simulation of the Fiberreinforced Composite Workpiece Cutting for the Surface Quality Improvement[END_REF][START_REF] Xu | Numerical Modeling and FE Analysis of CFRP/Ti Stack Orthogonal Cutting[END_REF][START_REF] Park | Tool wear in drilling of composite/titanium stacks using carbide and polycrystalline diamond tools[END_REF]. As for the cohesive bonding surface, a small thickness of the cohesive element (5 µm) was used. The material properties of the three phases can be found in Table 2. Table 3 shows the values of damage parameters as those chosen by [START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF][START_REF] Atlati | Développement d ' une nouvelle approche hybride pour la modélisation des échanges thermiques à l ' interface outil-copeau : application à l ' usinage de l ' alliage d ' aluminium aéronautique AA[END_REF].

Mechanical and thermal contacts

One of the important aspects that control the chip formation process is the interaction between the workpiece and the cutting tool. This interaction mainly depends on the mechanical and thermal contact properties, such as the coefficient of friction and the coefficient of conduction [START_REF] Yaich | Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting process : application to the Ti6Al4V[END_REF]. In the machining process of a hybrid CFRP/Ti stack, the contact properties of body surfaces that could potentially be in contact are difficult to characterize. In this study, there are mainly three interactions to manage effectively and correctly: tool-CFRP, tool-interface and tool-Ti.

For all interactions, the contact is defined between the workpiece node set and the tool surface using surface-to-surface built in contact algorithms, coupled to kinematic prediction contact with finite sliding formulation. The standard Coulomb friction model is adopted to model these interactions with a friction coefficient µ assumed to be constant for each phase (0.4 in CFRP phase [START_REF] Zenia | An elastoplastic constitutive damage model to simulate the chip formation process and workpiece subsurface defects when machining CFRP composites[END_REF] and 0.2 in Ti phase [START_REF] Yaich | Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting process : application to the Ti6Al4V[END_REF]). Tie constraint was used to link both CFRP phase and Ti phase together. During the tool-Ti machining phase, all energy generated by friction is converted to heat and governed by the following expression: [START_REF] Xu | Experimental study on mechanical drilling of carbon/epoxy composite-Ti6Al4V stacks[END_REF] where is the fraction of energy converted to heat (chosen equal to 1), is the friction stress, and is the sliding velocity.

Another source of heat is considered in contact property, which is plastic deformation heat generation, that can be expressed by: [START_REF] Xu | Cutting modeling of hybrid CFRP/Ti composite with induced damage analysis[END_REF] where is the Taylor-Quinney coefficient (equal to 0.9), and are respectively strain and stress components.

Results and discussion

Mesh density

The effect of the mesh density (or element size) on the average value of the cutting force Fc in both phases, titanium and CFRP, is shown through Fig. 3 a. Firstly, it should be noted that the average values varies slightly with the proposed meshes. However, marked differences are noticed between the minimum and maximum values of the predicted forces, revealing the presence of significant fluctuations in the evolution of Fc. These fluctuations are associated with the large amount of energy required to remove a coarse element. In fact, once the mesh element is totally damaged, a significant disturbance in the levels of contact pressure applied to the tool is obtained, leading to a sudden and important decrease in cutting forces. However, for CFRP measured cutting force the mesh size has not a significant impact. Finally, the CPU time is growing exponentially as shown in Fig. 3 The importance of minimizing computation times while maintaining an acceptable level of precision was found for element size of 10 µm × 10 µm providing not only results that are globally stable, but also a more efficient CPU time.

Cutting forces prediction

Fig. 4 and Fig. 5 represent the cutting force profiles during the machining process for the two sequences: CFRP/Ti and Ti/CFRP. The profiles show that the force required for cutting Ti phase is higher than the one required for cutting CFRP phase and distinct chip morphologies.

This is related to the material behavior and failure threshold. When the tool cuts into CFRP phase, a dusty form chips are obtained due to the anisotropic and heterogeneity of the composite. In addition, the fiber orientation of 45° does not oppose to the tool-cutting direction and smoothly removes the damaged elements. During cutting process, the transition from the composite phase to the titanium phase shows a sudden change in the level of cutting forces (increase or decrease) depending on the considered cutting sequence (CFRP-Ti or Ti-CFRP). This sudden transition is caused by the difference in the mechanical behavior between the two materials and it is accompanied by significant delamination at the interface in Ti-CFRP cutting sequence unlike CFRP-Ti sequence, no delamination was observed. This was highlighted by Xu et al. [START_REF] Xu | Cutting modeling of hybrid CFRP/Ti composite with induced damage analysis[END_REF]. In addition, this jump could lead to a premature tool wear as illustrated by Poutord et al. [START_REF] Poutord | Local approach of wear in drilling Ti6Al4V/CFRP for stack modelling[END_REF]. Finally, when the tool penetrates the Ti phase, the gap force increases, and a segmented chip is obtained due to the ductile nature of titanium alloy. Furthermore, the experimental tendency of the Ti cutting forces (Fig. 6 a) are slightly decreasing for a fixed cutting length, this was attributed to thermal softening that happens with the elevation of the cutting speed, [START_REF] Calamaz | Approche expérimentale et numérique de l'usinage à sec de l'alliage aéronautique TA6V[END_REF]. However, the numerical cutting force shows a constant evolution which suggests that the temperature rise is very localized and the effect of thermal softening due to the rise in temperature is quite small. In Fig. 7 we observe for the titanium phase and CFRP phase a linear increase in the cutting force Fc.This was expected since the increase in the cutting length or depth f is equivalent to an increase in the removed material.

Ti chip morphology dependency to fracture energy

Yaich et al. [START_REF] Yaich | Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting process : application to the Ti6Al4V[END_REF] studied the effect of damage parameters on chip morphology in titanium phase and predicted cutting forces in terms of damage initiation and propagation (Table 3).

The study highlighted the importance of a proper definition of the parameter describing the evolution of the damage (fracture energy G f ) because it has a dominant effect on the FE results in terms of chip segmentation and numerical forces. As for the damage initiation model, it has little effect on the accuracy of the simulated cutting process. Fig. 8 iIllustrates the morphologies obtained of chips and the average of cutting forces for five fracture energies: 20, 25, 30, 35, and 40. The analysis was carried out with a cutting speed of 50 m/min and a cutting depth of 0.2 mm. A direct relationship should be noted between the fracture energy, the chip morphology, and the cutting forces. It can be noticed that fragmented, segmented, or continuous chips can be obtained for three energy levels: low (<20), medium [START_REF] Isbilir | Comparative study of tool life and hole quality in drilling of CFRP/titanium stack using coated carbide drill[END_REF][START_REF] Xu | Experimental study on mechanical drilling of carbon/epoxy composite-Ti6Al4V stacks[END_REF][START_REF] Xu | Cutting modeling of hybrid CFRP/Ti composite with induced damage analysis[END_REF][START_REF] Pramanik | An FEM investigation into the behavior of metal matrix composites: Tool-particle interaction during orthogonal cutting[END_REF][START_REF] Shchurov | SPH-Simulation of the Fiberreinforced Composite Workpiece Cutting for the Surface Quality Improvement[END_REF][START_REF] Lasri | Modelling of chip separation in machining unidirectional FRP composites by stiffness degradation concept[END_REF][START_REF] Xu | Numerical Modeling and FE Analysis of CFRP/Ti Stack Orthogonal Cutting[END_REF][START_REF] Giasin | 3D Finite Element Modelling of Cutting Forces in Drilling Fibre Metal Laminates and Experimental Hole Quality Analysis[END_REF][START_REF] Johnson | A-constitutive-model-and-data-for-metals-subjectedto-large-strains-high-strain-rates-and-high-temperatures[END_REF][START_REF] Nasr | An Evaluation of Different Damage Models when Simulating the Cutting Process Using FEM[END_REF][START_REF] Yaich | Numerical analysis of constitutive coefficients effects on FE simulation of the 2D orthogonal cutting process : application to the Ti6Al4V[END_REF][START_REF] Atlati | Développement d ' une nouvelle approche hybride pour la modélisation des échanges thermiques à l ' interface outil-copeau : application à l ' usinage de l ' alliage d ' aluminium aéronautique AA[END_REF][START_REF] Mabrouki | Numerical and experimental study of dry cutting for an aeronautic aluminium alloy (A2024-T351)[END_REF][START_REF] Zenia | Numerical analysis of the interaction between the cutting forces , induced cutting damage , and machining parameters of CFRP composites[END_REF][START_REF] Wan | On material separation and cutting force prediction in micro milling through involving the effect of dead metal zone[END_REF][START_REF]Abaqus Documentation Version 6.14 Dassault Système Simulia[END_REF] or high (>40) respectively. The cutting forces increase with increased fracture energy. When cutting an assembled structure, one of the most recurrent defects is the interface delamination, [START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF][START_REF] Giasin | 3D Finite Element Modelling of Cutting Forces in Drilling Fibre Metal Laminates and Experimental Hole Quality Analysis[END_REF][START_REF] Poutord | Local approach of wear in drilling Ti6Al4V/CFRP for stack modelling[END_REF]. Furthermore, the arrangement of the stacking materials has a major impact on the cutting process. The main objective of the study is to predict the inter-material delamination induced by the cutting operation, and to analyze its interaction with the cutting speed, fiber orientation in the composite phase and cutting length in both CFRP-Ti and Ti-CFRP cutting sequences.

Delamination analysis

Fig. 9 and Fig. 10 show a comparative surface state after the cutting process in the CFRP-Ti and Ti-CFRP sequences respectively for a cutting speed of 50 m/min, a cutting length of 0.1 mm and a fiber orientation in CFRP phase of 45˚. It is obvious that the CFRP-Ti cutting sequence gives a much smoother surface than the Ti-CFRP cutting sequence. During cutting operation, the titanium plate serves as a support for the composite, reducing their bending and therefore significantly limiting the risk of delamination when leaving the titanium phase. In contrast, the opening between the two phases is much deeper in Ti-CFRP cutting sequence (Fig. 10) due to the ejection of the titanium chip and the pressure applied on the composite boundary which results in a crack propagation at the interface. These observations are confirmed by multiple experimental studies of composite metal stacks machining, in which researchers agree that delamination in a composite-metal sequence is minimized due to the presence of the metal layer [START_REF] Montoya | Optimisation du perçage de multi-matériaux CFRP / Titane et / ou Aluminium[END_REF][START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF][START_REF] Giasin | 3D Finite Element Modelling of Cutting Forces in Drilling Fibre Metal Laminates and Experimental Hole Quality Analysis[END_REF][START_REF] Poutord | Local approach of wear in drilling Ti6Al4V/CFRP for stack modelling[END_REF]. The evolution of the cutting force in the composite phase illustrated in Fig 12 shows how fiber orientation contributes to strengthening the CFRP. Furthermore, a small delamination depth was observed when carbon fibers are horizontal (0°) and vertical (90°). However, the largest opening was observed when the fiber orientation is equal to 45°. This might be explained by the strength of the second phase provided by the 0° and 90° orientations which prevents the interface from opening once the cutting tool passes through. Moreover, the absence of delamination in CFRP-Ti cutting sequence as explained above, shows that the behavior of the interface depends on the resistance of the second material.

Conclusion

In this work, the cutting of different stack sequences was investigated using a new finite element model. The chip morphology and cutting forces were examined for the two cutting sequences (i)-CFRP/Ti6Al4V and (ii)-Ti6Al4V/CFRP along with delamination at the contact boundary. The following conclusions can be drawn:

 Three cutting phases were observed during machining CFRP/Ti and Ti/CFRP combining several material removal mechanisms. A brittle fracture in the CFRP phase was reproduced leading to a dusty like chips. In the Ti-phase, segmented chips have been obtained reflecting the ductile nature of this phase.

 Interface cutting was found to be more brutal, resulting to an extreme change in the level of cutting force which can cause a premature tool wear.

 Numerical cutting forces were found to be in a good agreement with the experimental results allowing to confirm the reliability of the proposed model.

 Delamination inspection at the boundary contact between the composite phase and titanium phase shows a significant dependency to the cutting sequence.

 The resistance of the second phase when cutting an assembled material plays a key factor on the extent of interface delamination.

Finally, the present model will be rolled out to study the drilling process. In addition, the presence of thermal behavior in Ti phase demands that we readapt the current approach to include the temperature into CFRP and interface phases in order to inspect thermal influence on the global behavior. In forthcoming work, our model will be completed by experimental validations of delamination damage process and surface finish after machining.

  b. The time needed to model the same machining period goes from 13 min to 268 min in a computer with two processors (frequency = 2.20 GHz and RAM = 16 Go). This difference in CPU computing time is comprehensible, because CPU time is driven by the size of the smallest element. The excessive decrease in element size leads to an increase in mesh density leading naturally to a very high computation time.

Fig. 3 .

 3 Fig. 3. Mesh density analysis for Vc =80 m/min, f=0.2mm, θ=45˚ (a) Effect of mesh density on the cutting force F c (b) evolution of CPU time in terms of the mesh density.

Fig. 4 .Fig. 6 .Fig. 7 .

 467 Fig. 4. Generated cutting force signal with FE simulation for f=0.2mm, θ=45˚ and Vc =50 m/min with

Fig. 8 .

 8 Fig. 8. Chip morphology dependency to fracture energy for f=0.2mm and Vc =50 m/min Delamination analysis

Fig. 9 .Fig. 10 .

 910 Fig. 9. Surface quality in CFRP-Ti cutting sequence for f=0.1mm, Vc =50 m/min and θ=45˚

Fig. 11 .

 11 Fig. 11. Delamination dependency on (a) cutting speed Vc ( θ=45˚ , f=0.2mm ), (b) cutting length f (θ=45˚ and Vc=50 m/min) for Ti-CFRP cutting sequence.

Fig. 11

 11 Fig. 11 shows the depth of the Ti-CFRP interface delamination under diff erent cutting speeds (a), cutting lengths (b). Delamination ranged from 0.02 mm to 0.1 mm, it is minimal when Vc = 50 m/min and f = 0.05 mm, and maximal when Vc = 80m/min and f = 0.2 mm. Cutting speed does not have much impact on delamination. However, delamination increases with the increase of the cutting length. The amount of the removed material increases the pressure applied to the composite face which results in a higher extent of delamination on the interface, Fig 11.

Fig. 12 .

 12 Fig. 12. Combined Cutting force in CFRP phase and delamination dependency on fiber orientation ( f=0.2mm and Vc=50 m/min ) for Ti-CFRP cutting sequence.

Table 1

 1 Cutting parameters,[START_REF] Xu | Numerical and experimental study of machining titanium-composite stacks[END_REF].

	Rake angle α	Clearance angle γ Tool edge radius R	Cutting length f Cutting speed V c
	0°	7°	0.3969 mm	2 mm	50 m/min

Table 2

 2

	Material parameters [15, 33]
	Ti6A14V	CFRP T300/914	Interface
	Young's	113.375 GPa Longitudinal	136.6 GPa	Normal	400 GPa
	modulus		modulus E 1		stiffness E nn
	Poisson's	0.342	Transverse	9.6 GPa	Tangential	300 GPa
	ratio		modulus E 2		stiffness E ss =E tt
	Thermal	2 x10 -9	In plane shear	5.2 GPa	Poisson's ratio	0.33
	expansion		modulus G 12
	coefficient
	Density	4430 kg/m 3	Poisson's	0.29
			ratio
	Table 3 Parameters for the constitutive and damage laws [15, 33]
	Ti6A14V		CFRP T300/914		Interface
	A	1098 MPa		8 MPa	60 MPa
	B	1092 MPa		0.03 MPa	80 MPa

It is obvious that the numerical results regarding Ft forces do not fit the experimental ones in both phases (titanium Fig. 6a and composite Fig. 6b) with a relative error up to 55%. This important difference was explained by several authors [START_REF] Arola | Orthogonal cutting of fiber-reinforced composites: A finite element analysis[END_REF][START_REF] Zenia | Numerical prediction of the chip formation process and induced damage during the machining of carbon / epoxy composites[END_REF][START_REF] Wojciechowski | Prediction of cutting forces during micro end milling considering chip thickness accumulation[END_REF] as a result of using a Lagrangian approach coupled with the Delete Element method and the absence of the Elastic recovery phenomena. However, it can be observed that the average value of the cutting force Fc (Fig. 6a) is relatively in good agreement with the experimental results in both phases.


R Quispe-Tarqui

J Yujra Pari

F Callizaya Condori

F Rebaudo

The effect of diet interacting with temperature on the development rate of a Noctuidae quinoa pest

Keywords: nutrition, temperature, development, proteins

The quinoa pest Copitarsia incommoda Walker is a cause of significant damage, and it is thus critical for Andean countries to have access to phenological models to maintain production and food safety. These models are key components in pest control strategies in the context of global warming and in the development of sustainable production integrating agroecological concepts. Phenological models are mainly based on outlining the relationship between temperature and development rate. In this study we investigated the combined effect of protein content within the diet (artificial diet; artificial diet with -20% protein; artificial diet with +20% protein; natural quinoa diet) and temperature (12, 16.9, 19.5, 22.7, 24.6°C) as drivers of the development rate. Our study supports the literature, since temperature was found to be the main driver of the development rate. It highlights the significant role played by protein content and its interaction with temperature (significant effects of temperature, diet, and diet:temperature on development time using GLMs for all foraging life stages). We discuss the implications of such drivers of the development rate for implementing and applying phenological models that may benefit from including factors other than temperature. While performance curves such as development rate curves obtained from laboratory experiments are still a useful basis for phenological development, we also discuss the need to take into account the heterogeneity of the insect response to environmental factors. This is critical if pest control practices are to be deployed at the optimal time.

Introduction

Insects are ectotherm organisms, so that most phenological models use temperature as their main input variable to represent performances and development rate in particular [START_REF] Pollard | phenModel: A temperature-dependent phenology/voltinism model for a herbivorous insect incorporating facultative diapause and budburst[END_REF], since performances can be modelled (and pre-dicted) from a knowledge of the temperature experienced by insects [START_REF] Golizadeh | Estimating temperature-dependent developmental rates of potato tuberworm, Phthorimaea operculella (Lepidoptera: Gelechiidae)[END_REF]. However, while temperature is the main factor allowing us to build developmentrate models [START_REF] Angilletta | The evolution of thermal physiology in ectotherms[END_REF], other factors can also be considered, such as photoperiod, as shown in the beet webworm Loxostege sticticalis L. (Lepidoptera: Crambidae) [START_REF] Kutcherov | Stable and variable life-history responses to temperature and photoperiod in the beet webworm, Loxostege sticticalis[END_REF], or diet, as shown in the red floor beetle Tribolium castaneum Herbst (Lepidoptera: Tenebrionidae) [START_REF] Scharf | The Effects of Temperature and Diet during Development, Adulthood, and Mating on Reproduction in the Red Flour Beetle[END_REF]. The importance of factors other than temperature and their interactions is nothing new (Uvarov 1931, Lee and[START_REF] Lee | Temperature-by-nutrient interactions affecting growth rate in an insect ectotherm: Nutrientdependence of thermal sensitivity[END_REF]), yet these interactions may be more complex than previously appreciated in the literature, notably because of plasticity in life traits [START_REF] Clissold | Temperature, food quality and life history traits of herbivorous insects[END_REF]. A study on the gypsy moth Lymantria dispar L. (Lepidoptera: Erebidae), demonstrated that development rate of gypsy moth populations were different depending on the host plant, and that each population had host preferences [START_REF] Keena | Comparison of Survival and Development of Gypsy Moth Lymantria dispar L. (Lepidoptera: Erebidae) Populations from Different Geographic Areas on North American Conifers[END_REF]. Even when a single population is considered, the effect of diet is of practical importance as resources can vary significantly in space (eg, crop rotation) and time (eg, plant growth, agricultural practices such as harvest). Another study on the gypsy moth L. dispar showed that the protein:carbohydrate ratio mattered for the species development and growth, with significant development time differences depending on the diet used [START_REF] Perkovich | Protein:Carbohydrate Ratios in the Diet of Gypsy Moth Lymantria dispar Affect its Ability to Tolerate Tannins[END_REF].

Here, we focus on the development and survival as a function of temperature and diet of an agricultural insect pest attacking the quinoa crop (Chenopodium quinoa Willd., Chenopodiaceae) in the Bolivian Andes, Copitarsia incommoda Walker (Lepidoptera: Noctuidae). Specifically, we focus on protein source content. Protein content was isolated as a single nutritive variable given its fundamental importance in insect development. Proteins are degraded by protease enzymes into amino acids, which are essential components for the production of new proteins, enzymes and tissues. If protein content can be controlled in artificial diets, it is known to vary within plant species and within plant parts (Le [START_REF] Gall | Effects of Protein and Carbohydrate on an Insect Herbivore: The Vista from a Fitness Landscape[END_REF]. Quinoa has gained global interest in recent years due to its nutritional qualities with a balanced composition of amino acids [START_REF] Repo-Carrasco | Nutritional Value and Use of the Andean Crops Quinoa (Chenopodium quinoa) and Kañiwa (Chenopodium pallidicaule)[END_REF][START_REF] Vega-Gálvez | Nutrition facts and functional potential of quinoa (Chenopodium quinoa willd.), an ancient Andean grain: a review[END_REF], hardiness, and adaptability in the context of cli-mate change [START_REF] Ruiz | Quinoa biodiversity and sustainability for food security under climate change. A review[END_REF]. It is currently cultivated in over 50 countries on all continents and in different ecosystems (Bazile and Baudron 2015). However, most production occurs in the Andes of Bolivia and Peru, covering 80% of international demand [START_REF] Mujica | La quinua (Chenopodium quinoa Willd.) y sus parientes silvestres. Bótanica económica de los Andes Centrales[END_REF]. For Bolivia, quinoa constitutes a major crop contributing to food security and exports. It has helped raise the living standards of thousands of families in the highlands in the past decade (Blajos et al. 2014). However, the low fertility of the highland soils and attacks from pests reduce the yield of quinoa and increase production costs. Because of quinoa's strategic importance for the Andean highlands, it is of critical importance to document and predict insect pest phenology if control practices are to be deployed at the right time and production costs for farmers minimized. Among the key insect pests in quinoa are Copitarsia incommoda (Walker, 1865) (Lepidoptera: Noctuidae), Helicoverpa quinoa Pogue and Harp, 2014 (Lepidoptera: Noctuidae) and Eurysacca melanocampta Meyrick, 1917 (Lepidoptera: Gelechiidae) [START_REF] Cruces | Guía de identificación y control de las principales plagas que afectan a la quinua en la zona andina[END_REF], Barrionuevo et al. 2019). This study is focused on C. incommoda.

C. incommoda is a polyphagous species that feeds on over 30 crops. It is distributed from Mexico to southern Chile and Argentina, including the Andean mountains of Bolivia and Peru [START_REF] Angulo | Taxonomic update of the species of Copitarsia Hampson 1906[END_REF]Olivares 2003, Cruces et al. 2016). In Bolivia, it is one of the key pests for quinoa crops due to its larval stage that can cause yield losses of more than 30% [START_REF] Saravia | Lepidoptera associated to quinoa crop in the Bolivian Altiplano: Taxonomic updating[END_REF]. C. incommoda has six larval stages with coloration varying according to the habitat and organ of the consumed quinoa [START_REF] Pogue | Larval Description of Copitarsia incommoda (Lepidoptera: Noctuidae). ann. entom[END_REF][START_REF] Cruces | Guía de identificación y control de las principales plagas que afectan a la quinua en la zona andina[END_REF]. After hatching, small larvae feed on tender leaves, while medium and large larvae consume the quinoa panicle until they complete their development. They pupate on the ground and later emerge as moths, which oviposit between 800 to 1600 eggs in approximately two weeks of life (Choquehuanca [START_REF] Tapia | Ciclo biológico de Copitarsia incommoda Walker plaga del cultivo de la quinua en condiciones de laboratorio[END_REF][START_REF] Gandarillas | State of the Art Report on Quinoa around the World[END_REF].

Regarding temperature-and diet-dependent development rates and survival in C. incommoda, we expect that in an arid environment like the Bolivian highlands, where resources are limited and temperatures extreme, both factors could be of importance, as well as the interaction between them. We designed an experimental protocol to quantify the importance of each parameter, focusing on their interaction. Accordingly, we address how temperature (five different temperature), diet composition (artificial diet as a control treatment with varying protein content), and the interaction between them affect C. incommoda development and survival, and discuss the implication of diet-and temperature-dependences for the characterization of the relationship between temperature and development rate.

Materials and methods

Insect rearing. Rearing of C. incommoda and the experiments were carried out in 2018 in the Entomology laboratory of the Kiphakiphani Center (PROINPA Foundation: 16º40 30 LS and 68º17 58 LO; 3880 m.a.s.l.), La Paz, Bolivia, from a laboratory colony originally collected from quinoa-producing areas in La Paz and Oruro, Bolivia, in 2008 and supplemented with new individuals in 2016 from La Paz department quinoa-producing areas. The larvae from the colony were fed an artificial diet based on quinoa (diet 1 in Table 1), adapted from [START_REF] Murúa | Evaluación de cuatro dietas artificiales para la cría de" Spodopetera frugiperda"(Lep.: Noctuidae) destinada a mantener poblaciones experimentales de himenópteros parasitoide[END_REF], while adults were fed with a solution of honey and water (1:3). The colony was reared at 21±3°C, 60±5%RH and photoperiod 12:12 (L:D).

Temperatures and diets. To study the effect of diet in interaction with temperature on the development and survival of C. incommoda, three artificial diets and one natural diet were used, using an artificial diet as control treatment. The artificial diets were based on a standard diet from [START_REF] Murúa | Evaluación de cuatro dietas artificiales para la cría de" Spodopetera frugiperda"(Lep.: Noctuidae) destinada a mantener poblaciones experimentales de himenópteros parasitoide[END_REF], adapted by modifying the protein source content. The first diet used an average amount of soya flour and wheat germ (Diet 1, control treatment), with a decrease of 20% for the second diet (Diet 2), and an increase of 20% for the third (Diet 3). The diet compositions are described in Table 1. This artificial diet was originally designed to be able to study C. incommoda life cycle under laboratory conditions, and served to characterize the relationship between temperature and development rate [START_REF] Rebaudo | Relationship between temperature and development rate of Copitarsia incommoda (Lepidoptera: Noctuidae) in the Bolivian Andes[END_REF]. Quinoa leaves and panicles (the Kurmi variety characterized by a green plant, a pink panicle and white grain) were used for the natural diet, produced continuously in the Kiphakiphani Center greenhouse. The natural diet was solely comprised of the leaves and panicles. Larval stages 1 to 3 were fed with leaves only, while larval stages 4 to 6 were fed with panicles, based on feeding behavior observed in the field [START_REF] Saravia | Lepidoptera associated to quinoa crop in the Bolivian Altiplano: Taxonomic updating[END_REF]. The protein content of leaves and panicles (before grain maturation) is estimated to five and nine percent, respectively (Caballero et al. 2015). Breeding environments were established in rearing units at five constant temperatures (12, 16.92, 19.5, 22.68, 24.6°C). Five breeding rooms (3 * 2.5 * 2 m) conditioned at 12±1.2, 16.92±0.9, 19.5±1.6, 22.68±0.7, 24.6±1.3°C (temperature ± standard deviation) and 60±5% RH and 12:12h L:D photoperiod were used. Each room had air conditioning equipment (White-Westinghouse, WAS 09P5AHLW, 1600W), a fan heater (De'Longhi HTF3020, 2000 W) and humidifier (Megafesa 1903 VAPEA, 300W). Throughout the period the temperature and relative humidity of each breeding room were controlled manually every eight hours using a digital thermo-hygrometer (Halthen -TTH 002). The temperature accuracy in each breeding environment was tested in a previous study [START_REF] Rebaudo | Relationship between temperature and development rate of Copitarsia incommoda (Lepidoptera: Noctuidae) in the Bolivian Andes[END_REF] 1,5 ml 1,5 ml 1,5 ml tetracycline 0,5 ml 0,5 ml 0,5 ml Carrageenan 8,5 g 8,5 g 8,5 g Water 750 ml 740 ml 755 ml 16.92, 19.5, 22.68, 24.6°C, respectively, with each individual as a replicate from the same cohort. Eggs were not obtained at the same time so that they could not be systematically distributed across all treatments, but each treatment was based on several females to minimize the maternal effects. Once hatched, the newborn larvae (<12 hours) were individualized in 50 ml plastic rearing containers with 15 cc of artificial diet (based on quinoa) or 15 gr natural diet (quinoa leaves and panicles) and were monitored until they pupated. On the fifth day of pupation they were weighed and sexed based on previous studies in Lepidoptera [START_REF] Rueda | Dimorfismo sexual en pupas de Tecia solanivora (Povolny)(Lepidoptera: Gelechiidae)[END_REF]Ávila 2004, Rondon and[START_REF] Rondon | Practical techniques and accuracy for sexing the potato tuberworm, Phthorimaea operculella (Lepidoptera: Gelechiidae)[END_REF], and were then transferred to 10 pairs of pupae per plastic copula cage and oviposition of 3,800 cc (0.15 x 0.15 x 0.2 m) with strips of paper towel (15 x 5 cm) arranged on the inner walls of the cage for egg laying. Once emerged, the adults were fed with a solution of honey and water (1:3) and the eggs in the paper towel strips were removed and placed in Petri dishes (diameter 10 cm and height 2 cm) until hatching. Data analysis. All data analyses were performed using R version 4.0.3 (R Core Team 2020). From the date of each life stage change, we computed the inverse of the duration of each life stage in days (development rate) for eggs, the six larval stages, prepupa, and pupa, as well as the entire life cycle duration from egg to adult, and the survival rate for each life stage and each temperature. The relationship between temperature and development rate in insects is known to be non-linear, but can be considered as linear in a small range of temperatures [START_REF] Campbell | Temperature requirements of some aphids and their parasites[END_REF][START_REF] Roy | Relationship Between Temperature and Developmental Rate of Stethorus punctillum (Coleoptera: Coccinellidae) and Its Prey Tetranychus mcdanieli (Acarina: Tetranychidae)[END_REF][START_REF] Shi | Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects:(I) Empirical Models[END_REF][START_REF] Sinclair | Can we predict ectotherm responses to climate change using thermal performance curves and body temperatures?[END_REF][START_REF] Quinn | A critical review of the use and performance of different function types for modeling temperaturedependent development of arthropod larvae[END_REF][START_REF] Rebaudo | Modeling temperaturedependent development rate and phenology in insects: review of major developments, challenges, and future directions[END_REF]. The temperatures used in this study fall within the zone that can be considered as linear for all life stages of C. incommoda [START_REF] Rebaudo | Relationship between temperature and development rate of Copitarsia incommoda (Lepidoptera: Noctuidae) in the Bolivian Andes[END_REF]. We tested for the relationship between temperature and development rate using simple and polynomial linear models. Then, for each temperature and each life stage, we tested for the effect of diet on development time using general linear models (Poisson family) using the artificial diet as the control treatment, and Tukey tests. We then tested for the effect of diet and temperature on survival rates using a general linear model of the binomial type (link logit), and performed a pairwise comparison of proportions for each diet and each temperature.

Results

Within the range of experimented temperatures, we observed a diminution in the development time as temperature grew, as expected and previously documented for C. incommoda [START_REF] Rebaudo | Relationship between temperature and development rate of Copitarsia incommoda (Lepidoptera: Noctuidae) in the Bolivian Andes[END_REF]. The relationship between temperature and development rate seemed linear in this range of temperatures (Figure 1A), with the natural diet giving the higher development rate at all experimented temperatures. We also observed a higher variance for higher temperatures (heteroskedasticity), which is expected for insects development rate at extreme temperatures [START_REF] Couret | Temperature, Larval Diet, and Density Effects on Development Rate and Survival of Aedes aegypti (Diptera: Culicidae)[END_REF]. The linear models of development rate against temperature demonstrated heteroscedasticity and a pattern in the distribution of residuals, suggesting that we may be at the limit of the linear zone, so we used a polynomial linear model of degree two to adjust to the experimental results (Figure 1B), resulting in a better goodness-of-fit using the Akaike information criterion (eg, AIC of -1624 vs -1471, -1832 vs -1581, -1900 vs -1667, -1860 vs -1597 for the polynomial model vs simple linear model for the total development rate of C. incommoda for the four different diets).

Temperature had a significant effect on the development rate for all life stages, as expected and documented in previous studies on the relationship between temperature and development rate. Diet also had a significant effect on development rate except for the egg life stage (F=374.6, df=3, p-value<0.001 for the number of days from egg to adult). When focusing on the three artificial diets, we also observed no significant effect of the diet on life stage L5 and prepupa, the later corresponding to the shortest life stage with a mean development time of 4.5 days. Interestingly, the interaction between temperature and diet had a significant effect on the development rate (F=4.2, df=3, p-value=0.006 for the number of days from egg to adult). We observed that natural diet allowed a faster development at all temperatures. Also, the artificial diet with less protein negatively affected development, and the diet with additional protein did not confer any significant advantage over the reference artificial diet (Figure 1). When analyzing the development for each life stage, we observed that eggs were not affected by diet (no resource consumption; eggs can be used as a control), and differences were observed from the first larval stage (Table 2). Moreover, we observed that significant differences were detected for the prepupa and pupa life stages (i.e., for life stages without feeding activity), suggesting that the history of larval resource consumption had an effect on following life stages' development rate.

On the range of temperatures used in this experiment, we observed no significant effect of temperature or diet on the survival rate. The pairwise comparison of proportions for each diet and each temperature demonstrated some significant differences between experimental conditions (Figure 2A and Figure 2B), that may be imputed to experimental conditions (overall low survival at 19.5°C).

Discussion

The temperature dependence of development rate in insects has been frequently investigated in the literature [START_REF] Roy | Relationship Between Temperature and Developmental Rate of Stethorus punctillum (Coleoptera: Coccinellidae) and Its Prey Tetranychus mcdanieli (Acarina: Tetranychidae)[END_REF][START_REF] Quinn | A critical review of the use and performance of different function types for modeling temperaturedependent development of arthropod larvae[END_REF][START_REF] Rebaudo | Modeling temperaturedependent development rate and phenology in insects: review of major developments, challenges, and future directions[END_REF], notably in the context of climate change [START_REF] Fand | Predicting the impact of climate change on regional and seasonal abundance of the mealybug Phenacoccus solenopsis Tinsley (Hemiptera: Pseudococcidae) using temperature-driven phenology model linked to GIS[END_REF][START_REF] Mwalusepo | Predicting the Impact of Temperature Change on the Future Distribution of Maize Stem Borers and Their Natural Enemies along East African Mountain Gradients Using Phenology Models[END_REF]. Our results support the idea that temperature is the main driver of insect development (Bale et al. 2002), yet our study of C. incommoda suggests that nutrition may have a more important role than previously anticipated, especially for studies aiming to predict insect phenology in the face of climate change.

In the laboratory, quinoa crop pests are whenever possible reared using artificial diets [START_REF] Rebaudo | Relationship between temperature and development rate of Copitarsia incommoda (Lepidoptera: Noctuidae) in the Bolivian Andes[END_REF], mostly for convenience, since obtaining fresh material all year long involves access to greenhouses and technical staff to maintain both the insects and plants. However, it has been shown that animals with different developmental histories may respond differently to experimental treatments such as diet [START_REF] Wiggins | Laboratory-reared and field-collected predators respond differently to same experimental treatments[END_REF]. The use of an artificial diet where nutrients may not mirror those available in the field has practical consequences as laboratory-reared individuals may respond differently to field-collected individuals, as exemplified in spiders [START_REF] Wiggins | Laboratory-reared and field-collected predators respond differently to same experimental treatments[END_REF]. Acknowledging this limitation and even if the present study focused in the comparison of artificial diets with variation in the protein content, it revealed that insect development may be faster using natural diet at all experimented temperatures, as reported for Drosophila suzukii (Diptera: Drosophilidae) reared on fruits versus artificial diet [START_REF] Aly | Effects of Postharvest Cold Storage on the Development and Survival of Immature Drosophila suzukii (Diptera: Drosophilidae) in Artificial Diet and Fruit[END_REF]. Not only natural diet can affect development time, but also its quality, as reported for Plodia interpunctella (Lepidoptera: Pyralidae) using different natural diets and highlighting the importance of moisture content and the difficulty of representing the variety of food resources available in the insect ecosystem in a performance model [START_REF] Johnson | Effect of diet and temperature on development rates, sur-vival, and reproduction of the Indianmeal moth (Lepidoptera: Pyralidae)[END_REF]. Also, different diets can result in significant changes in the life cycle, as shown in Spodoptera exigua Hübner (Lepidoptera: Noctuidae) where different numbers of larval instars have been observed as a consequence of diet [START_REF] Ali | Effects of temperature and larval diet on development of the beet armyworm (Lepidoptera: Noctuidae)[END_REF]. In our case, the observed effect of natural diet may be caused by the presence of natural trace nutrients, or the pest shifts in diet across developmental stage between larval stages 1 to 3 and larval stages 4 to 6 (see [START_REF] Phalnikar | Dietary and developmental shifts in butterfly-associated bacterial communities[END_REF]). An evaluation of the benefit of using natural over artificial diet would have required to complement artificial diets with natural diets. Also, following results on diet quality in P. interpunctella study, by specifically selecting the optimal plant part for each life stage, we can hypothesize that an optimized development could have been obtained.

To add a layer of complexity, insect development rate response to diet may be strain-specific, as demonstrated for Plutella xylostella (Lepidoptera: Plutellidae) in a study under laboratory conditions [START_REF] Carpenter | Interaction between insect strain and artificial diet in diamondback moth development and reproduction[END_REF]. This is all in accordance with a necessary complexity in models making use of development rate performance curves, as acknowledged in the literature [START_REF] Clissold | Temperature, food quality and life history traits of herbivorous insects[END_REF]. In our study, we observed an interaction between temperature and diet in the development rate of C. incommoda. This may be the consequence of the effect of temperature on food intake, as food intake decrease with growing temperatures, as shown in Eupterote mollifera Walker (Lepidoptera: Eupterotidae) [START_REF] Palanichamy | Effect of temperature on food intake, growth and conversion[END_REF], or in S. exigua [START_REF] Lee | Temperature-by-nutrient interactions affecting growth rate in an insect ectotherm: Nutrientdependence of thermal sensitivity[END_REF], with direct consequences on development rate, as shown in Aedes aegypti Linnaeus (Diptera: Culicidae) [START_REF] Couret | Temperature, Larval Diet, and Density Effects on Development Rate and Survival of Aedes aegypti (Diptera: Culicidae)[END_REF]. This could explain the deleterious effect of the diet with a smaller protein content on development rate.

The implication is that models making use of such a performance curve based solely on a single diet might over-or under-estimate development rate, because of the mismatch between available resources in the field and diet in the laboratory. Such an incorrect estimation could however be exceeded by taking into account both i) genetic and environmental variations of individual responses to temperature and diet, for example, plasticity in feeding behavior and foraging activity, or dispersal linked to microclimate selection (Clissold and Simpson 2015), and ii) the spatial and temporal variation in food resources and temperatures [START_REF] Johnson | Effect of diet and temperature on development rates, sur-vival, and reproduction of the Indianmeal moth (Lepidoptera: Pyralidae)[END_REF][START_REF] Rebaudo | Microclimate Data Improve Predictions of Insect Abundance Models Based on Calibrated Spatiotemporal Temperatures[END_REF][START_REF] Faye | Does heterogeneity in crop canopy microclimates matter for pests? Evidence from aerial high-resolution thermography[END_REF]. For the later and as mentioned above, it could be difficult to reproduce in the laboratory the different resources encountered in the fields, as shown in P. interpunctella [START_REF] Johnson | Effect of diet and temperature on development rates, sur-vival, and reproduction of the Indianmeal moth (Lepidoptera: Pyralidae)[END_REF]. The study of C. incommoda using different temperatures and diets may suggest another approach, enabling us as to characterize insect temperature-dependent development rate variance and to propose individual-based models integrating such variance in their predictions [START_REF] Regniere | Effects of temperature on development, survival and reproduction of insects: experimental design, data analysis and modeling[END_REF]

Fig. 1 .

 1 Fig.1. Development rate at different temperatures for different diets and for total development. Each jittered symbol represents a different diet (black circle: artificial with less protein, red triangle: artificial, green plus: artificial with more protein, blue cross: natural). The violin plots in A were performed using the violin R CRAN package[START_REF] Adler | vioplot: violin plot[END_REF]. In B, the lines correspond to a polynomial model of degree two.

Fig. 2 .

 2 Fig. 2. Survival rate at different temperatures and diets. Each bar represents the proportion of individuals reaching the adult stage. Significant differences are represented with stars in A between diets and in B between temperatures (pairwise comparison of proportions).

  Mean development time and standard deviation at different temperatures and diets. Each line corresponds to a different diet (artificial with less protein, artificial, artificial with more protein, natural), with the number of individuals in parenthesis, followed by the result of a Tukey test (distinct letters within a cell indicate a significant difference in development time). son, J. Farrar, J. E. G. Good, R. Harrington, S. Hartley, T. H. Jones, R. L. Lindroth, M. C. Press, I. Symrnioudis, A. D. Watt, and J. B. Whittaker. 2002. Herbivory in global climate change research: direct effects of rising temperature on insect herbivores. Global Change Biology. 8: 1-16. Barrionuevo, M. J., A. J. Barrionuevo, and M. I. Zamar. 2019. Lepidópteros asociados al cultivo de quinoa en zonas de altura de Jujuy, Argentina. AgriS. 36: 55. Bazile, D., and F. Baudron. 2015. The dynamics of the global expansion of quinoa growing in view of its high biodiversity, pp. 42-55. In State of the Art Report on Quinoa around the World. FAO, Santiago of Chili. Blajos, J., N. Ojeda, E. Gandarillas, and A. Gandarillas. 2014. Economía de la quinua: Perspectivas y desafíos. Revista de agricultura. Bolivia. Nro. 54: 3-8. Caballero, A., W. Maceda, R. Miranda, and H. Bosque. 2015. Rendimiento y contenido de proteina de la quinua (Chenopodium quinoa Willd), en cinco fases fenológicas, bajo cuatro niveles de incorporación de estiércol. Revista de Investigación e Innovación Agropecuaria y de Recursos Nat-

Table 1 .

 1 Composition of artificial diets for breeding larvae of C. incommoda.

	(Winkel et al. 2016) were measured every ten minutes at the
	Kiphakiphani Center. Average daily temperatures range from
	5 to 20°C (with local maximum up to 28°C during the day
	and a mean daily thermal amplitude of 17°C).
	1139 C. incommoda eggs of the same age (<12 hours) from
	30 pairs of adults were used, which were distributed to 256,
	225, 241, 205 and 212 eggs per breeding environment of 12,

  , Chuine and Régnière 2017, Rebaudo and Rabhi 2018).

		12°C	16.9°C	19.5°C	22.7°C	24.6°C
		0.05±0 (50) a	0.083±0 (50) a	0.143±0 (50) a	0.2±0 (50) a	0.25±0 (50) a
	Egg	0.05±0 (50) a 0.05±0 (50) a	0.083±0 (50) a 0.083±0 (50) a	0.143±0 (50) a 0.143±0 (50) a	0.2±0 (50) a 0.2±0 (50) a	0.25±0 (50) a 0.25±0 (50) a
		0.05±0 (50) a	0.083±0 (50) a	0.143±0 (50) a	0.2±0 (50) a	0.25±0 (50) a
		0.035±0.004 (49) c	0.077±0.011 (48) b	0.094±0.012 (49) a	0.143±0.034 (48) c	0.214±0.035 (49) a
	L1	0.053±0.011 (50) a 0.049±0.007 (50) a	0.082±0.012 (50) ab 0.084±0.013 (50) a	0.098±0.007 (48) a 0.097±0.01 (49) a	0.164±0.031 (49) a 0.169±0.029 (48) a	0.215±0.045 (50) a 0.216±0.046 (50) a
		0.063±0.013 (50) b	0.095±0.008 (50) c	0.14±0.038 (50) b	0.191±0.026 (50) b	0.248±0.012 (50) b
		0.087±0.053 (44) b	0.11±0.02 (47) c	0.155±0.04 (48) c	0.21±0.041 (48) b	0.29±0.08 (49) b
	L2	0.117±0.048 (48) ab 0.131±0.06 (49) a	0.139±0.03 (50) a 0.136±0.026 (49) a	0.255±0.087 (46) a 0.195±0.076 (47) b	0.242±0.057 (49) ab 0.251±0.051 (48) a	0.336±0.093 (47) ab 0.335±0.086 (50) a
		0.128±0.055 (50) a	0.172±0.047 (49) b	0.249±0.063 (49) a	0.423±0.112 (48) c	0.452±0.092 (50) c
		0.083±0.023 (40) a	0.105±0.035 (47) ab	0.161±0.044 (48) a	0.183±0.054 (47) c	0.353±0.154 (49) b
	L3	0.103±0.039 (44) a 0.091±0.026 (48) a	0.127±0.024 (50) a 0.102±0.021 (49) b	0.181±0.062 (46) a 0.178±0.069 (47) a	0.222±0.05 (49) a 0.238±0.041 (48) a	0.309±0.065 (47) ab 0.303±0.072 (49) a
		0.136±0.063 (49) b	0.16±0.077 (48) c	0.246±0.093 (45) b	0.305±0.06 (48) b	0.206±0.037 (48) c
		0.088±0.033 (38) a	0.127±0.067 (44) a	0.18±0.068 (46) a	0.178±0.088 (46) c	0.398±0.11 (48) bc
	L4	0.08±0.024 (44) a 0.086±0.028 (48) a	0.134±0.032 (49) a 0.156±0.07 (49) a	0.186±0.068 (45) a 0.164±0.045 (47) a	0.244±0.066 (49) a 0.228±0.059 (48) a	0.478±0.076 (47) a 0.455±0.184 (44) ab
		0.13±0.061 (49) b	0.136±0.076 (47) a	0.229±0.057 (43) b	0.286±0.056 (47) b	0.373±0.129 (41) c
		0.083±0.053 (35) a	0.115±0.032 (42) a	0.17±0.063 (43) a	0.198±0.081 (45) a	0.285±0.082 (48) a
	L5	0.075±0.022 (44) a 0.078±0.022 (47) a	0.104±0.049 (49) a 0.099±0.027 (49) a	0.152±0.048 (43) a 0.164±0.072 (44) a	0.197±0.052 (48) a 0.191±0.062 (48) a	0.257±0.06 (45) a 0.335±0.109 (44) b
		0.123±0.029 (26) b	0.181±0.071 (19) b	0.234±0.082 (33) b	0.301±0.054 (24) b	0.417±0.115 (23) c
		0.082±0.039 (33) b	0.095±0.046 (38) ab	0.077±0.028 (36) a	0.196±0.164 (43) a	0.179±0.073 (45) a
	L6	0.058±0.012 (44) a 0.062±0.024 (47) a	0.087±0.027 (47) a 0.12±0.064 (48) b	0.085±0.024 (39) a 0.082±0.026 (39) a	0.16±0.077 (46) a 0.149±0.051 (47) a	0.199±0.048 (42) a 0.279±0.107 (41) b
		0.086±0.04 (25) b	0.081±0.02 (19) a	0.129±0.027 (33) b	0.2±0.077 (23) a	0.327±0.131 (23) b
		0.18±0.092 (33) a	0.194±0.128 (38) b	0.302±0.113 (30) a	0.273±0.061 (42) b	0.443±0.207 (41) a
	Prepupa	0.153±0.079 (43) a 0.162±0.073 (47) a	0.247±0.083 (40) a 0.211±0.072 (42) ab	0.296±0.106 (31) a 0.352±0.112 (30) a	0.293±0.133 (41) ab 0.321±0.17 (42) ab	0.433±0.128 (40) a 0.374±0.107 (41) a
		0.157±0.05 (48) a	0.253±0.069 (43) a	0.34±0.065 (40) a	0.346±0.107 (42) a	0.367±0.099 (32) a
		0.015±0.002 (27) b	0.034±0.006 (32) b	0.034±0.003 (26) a	0.056±0.007 (37) a	0.075±0.007 (36) b
	Pupa	0.017±0.003 (40) ab 0.018±0.005 (43) a	0.031±0.002 (36) a 0.031±0.002 (33) a	0.034±0.004 (23) a 0.033±0.002 (23) a	0.055±0.007 (32) a 0.055±0.007 (38) a	0.071±0.007 (34) ab 0.069±0.008 (40) a
		0.021±0.006 (42) c	0.034±0.004 (42) b	0.046±0.005 (31) b	0.056±0.005 (32) a	0.088±0.016 (24) c

Quispe-Tarqui et al. | February 2, 2022 | 1-8

ACKNOWLEDGEMENTS

This work benefited from the support of the project PI2P ANR-19-CE32-0001 of the French National Research Agency (ANR). The implementation of the breeding of C. incommoda in the Laboratory was supported by the Collaborative Crop Research Program (CCRP) of the McKnight Foundation (USA).