Anne Ganteaume
email: anne.ganteaume@irstea.fr

Marielle Jappiot

Corinne Lampin

Mercedes Guijarro

Carmen Hernando

Flammability of some ornamental species in wildland-urban interfaces in Southeastern France: laboratory assessment at particle level

Keywords: ORNAMENTAL VEGETATION, FLAMMABILITY PARAMETERS, PLANT PARTICLES, FIRE HAZARD

Assessment of the flammability of ornamental vegetation (particularly hedges) planted around houses is necessary in light of the increasing urbanization of the wildland-urban interfaces (WUIs) and the high fire occurrence in such areas. The structure and flammability of seven of the species most frequently planted as hedges in Provence (Southeastern France) were studied at particle level. Spatial repartition of the different types of fuel particles within plants was assessed by means of the Cube Method. The leaf flammability was assessed using an epiradiator as a burning device and measurements of foliar physical characteristics and gross heat of combustion (GHC) helped to explain the results of burning experiments. Co-inertia analysis revealed that species with thin leaves were quick to ignite (Pyracantha coccinea, Phyllostachys sp.) and species with high leaf GHC burned the longest (Pittosporum tobira, Nerium oleander). Species presenting high ignitability (Photinia fraseri, Phyllostachys sp. and Pyracantha coccinea) were characterised by high foliar surface area-to-volume ratio, and species presenting lower ignitabilitywere characterised by high GHC (Pittosporum tobira, Nerium oleander, Cupressus sempervirens). Hierarchical cluster analysis of the flammability variables (ignition frequency, time-to-ignition and flaming duration) categorized the relative flammability of the seven species (including dead Cupressus sempervirens) in five clusters of species from poorly flammable (Pittosporum tobira) to extremely flammable (dead Cupressus sempervirens).This study provides useful information for reducing fire risk in WUIs in the study area.

Introduction

Around the world, concerns about the impact of wildland fires are increasingly focusing on the wildland-urban interface (WUI), where their occurrence is high and where they can affect people and structures [START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF]. Fires in wildland-urban interfaces regularly destroy dwellings when fuel and weather are conducive to fire [START_REF] Covington | Helping western forests heal[END_REF] and human-caused fire ignitions are most common in these areas [START_REF] Cardille | Environmental and social factors influencing wildfires in the Upper Midwest, United states[END_REF][START_REF] Jappiot | Traité IGAT "Information géographique et aménagement du territoire", Rubrique "Aménagement et gestion des territoires[END_REF]Lampin et al. 2006aLampin et al. , 2006b)). As a result, WUIs are now considered as priority areas for controlling wildfire [START_REF] Stephens | Forest fire causes and extent on United States Forest Service lands[END_REF]). In the Mediterranean region, the incidence of fire is often higher in wildland-urban interfaces and in wildland/network interfaces because of high urban pressure and accumulation of wildland biomass [START_REF] Davis | The wildland-urban interface: paradise or battleground?[END_REF][START_REF] Vélez | Recent history of forest fires in Mediterranean area[END_REF][START_REF] Cohen | Preventing disaster: home ignitability in the wildland-urban interface[END_REF][START_REF] Leone | The human factor in fire danger assessment[END_REF][START_REF] De La Riva | El factor humano en el riesgo de incendios forestales a escala municipal. Aplicación de técnicas SIG para su modelización[END_REF][START_REF] De La Riva | Wildland fire ignition danger spatial modelling using GIS and satellite data[END_REF][START_REF] Jappiot | Modélisation et cartographie de l'aléa d'éclosion d'incendie de forêt. Programme AIOLI[END_REF][START_REF] Jappiot | Caractérisation de la relation entre organisation spatiale d'un territoire et risqué d'incendie: le cas des interfaces habitat-forêt du sud de la France. Thèse en géographie[END_REF]. Furthermore, the higher incidence of extreme climate events (very high summer temperatures, strong winds and drought periods) expected under climate change, together with the high flammability of Mediterranean fuels, implies higher probability of ignition [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF][START_REF] Dimitrakopoulos | Flammability Assessment of Mediterranean Forest Fuels[END_REF].

The presence of ornamental vegetation around houses is one of the major concerns regarding the vulnerability of structures as this vegetation can act as "ladder fuel" and ignite houses and other structures [START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF]. Therefore, less flammable species are recommended as ornamental plants [START_REF] Monroe | Wildland fire in the Southeast: Negotiating guidelines for defensible space[END_REF]. According to [START_REF] Dimitrakopoulos | A statistical classification of Mediterranean species based on their flammability components[END_REF] and Dimitrakopoulos and Papaiannou (2001), classification of fuel in relation to its expected flammability is an essential component of fire hazard assessment. Homeowners in WUIs are often advised to minimize or eliminate the use of highly flammable vegetation when landscaping their homes, and lists containing species that are appropriate for use in fire-wise landscaping are often requested. Reducing the fire hazard associated with vegetation can be accomplished by appropriate arrangement, maintenance and selection of species. However, Lubin and Shelly (1997) highlighted many discrepancies in the recommendations for plant selection by species, which often relied on anecdotal information with little scientific basis, largely because of the scarcity of scientific data on the flammability of ornamental vegetation. Nonetheless, there is an increasing demand from forest managers, fire managers and fire-fighters for scientifically based information about ornamental species for use in WUIs.

Although losses of WUI vegetation and structures are substantial and are increasingly common, studies on fire performance of ornamental plants, performed mainly in USA [START_REF] White | Preliminary evaluation of the flammability of native and ornamental plants with the cone calorimeter[END_REF][START_REF] Irby | Wildland fire hazard assessment[END_REF][START_REF] Beall | Fire-safe vegetation[END_REF][START_REF] White | Cone calorimeter testing of vegetation: an update[END_REF][START_REF] Monroe | Wildland fire in the Southeast: Negotiating guidelines for defensible space[END_REF][START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF][START_REF] Weise | Use of the cone calorimeter to detect seasonal differences in selected combustion characteristics of ornamental vegetation[END_REF], have not been carried out in Europe. Some of the early studies sought to identify slow-burning plants that could survive in southern California, e.g. plants with high mineral content that could act as fire-retardant plants [START_REF] Ching | Research with slow burning plants[END_REF] and plant species with low fuel volume [START_REF] Nord | Low-volume and slow burning vegetation for planting on clearings in California chaparral[END_REF]. More recent studies [START_REF] Etlinger | Fire performance of landscape plants[END_REF][START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF]) have focused on the relationship between plant characteristics and flammability components as defined by [START_REF] Anderson | Forest fuel ignitability[END_REF] and [START_REF] Martin | Assessing the flammability of domestic and wildland vegetation[END_REF].

Plant flammability has been widely studied and experimentally assessed in the laboratory for various purposes, following several methods which took into account many different definitions and flammability parameters. Moreover, methods which allowed the assessment of vegetation flammability and the results obtained differed depending on the scale considered [START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF][START_REF] Madrigal | Evaluation of the flammability of gorse (Ulex europaeus L.) managed by prescribed burning[END_REF]. However, the combination of different methods for assessing the flammability parameters of ornamental vegetation as well as the description of its structure, have not been studied yet.

In WUIs, two types of fire ignition can occur regarding ornamental vegetation: (i) ignition of the vegetation directly subjected to the intensity of the flame front, as assessed in the present study (flammability at particle level), and (ii) in case of spot-fire, ignition of the litter (ignition of dead surface fuel) by a glowing firebrand that lands at the foot of the plant. The flammability of dead surface fuels, i.e. litter, that could be ignited during a spot fire, has been assessed in a previous study [START_REF] Ganteaume | Assessing the flammability of surface fuels beneath ornamental vegetation in wildland-urban interfaces[END_REF].

The objective of this work was to compare the potential flammability of some ornamental plants that could be used as hedges for instance in Provence (SE France), taking into account the plant structure, some variables of flammability and the gross heat of combustion of fine particles. According to the classical definition [START_REF] Anderson | Forest fuel ignitability[END_REF], flammability was considered as the result of ignitability (time until ignition), combustibility (rapidity of the combustion after ignition) and sustainability (ability to sustain combustion once ignited). Therefore, live leaf flammability was assessed by determining time-to-ignition, flaming duration and ignition frequency.

Material and methods

Study area and selection of species

Bouches du Rhône is one of the French "départements" which is located in eastern Provence (Fig. 1) and is one of the areas most seriously affected by wildfires in SE France (forest fire database Prométhée, www.promethee.com). The climatic conditions differ in the coastal fringe and in the inland part of the département (Météo France database, www.meteofrance.com); thus, the species planted as hedges will also differ depending on the location. Therefore, the study area was divided into two sub-areas (coastal and inland) for the purposes of sampling. To identify the main species used as ornamental vegetation, a survey of hedges was made in nine locations in both areas, taking into account a total of 117 hedges in four coastal locations and 110 hedges in five inland locations (Fig. 1). A total of 20 species were recorded during the survey and were considered representative of the species planted in the whole study area. Seven of these species were chosen for the present study, either because they were the most frequent species planted as hedges (Prunus laurocerasus, Pyracantha coccinea, Cupressus sempervirens, Nerium oleander, Photinia fraseri and Pittosporum tobira) or because of their singularity, like Phyllostachys sp., a type of bamboo, which may have particular flammability characteristics.

Field samplings

The species were sampled in summer (between July and August 2011) during the fire season, when the fuel moisture content is lowest and the fire risk is highest.

Fuel sampling at particle level

The sampling of particles (mainly leaves and twigs) was performed according to the "cube method" [START_REF] Cohen | Modeling fuel distribution with cellular-automata for fuel-break assessment[END_REF]. This method allowed us to determine the structure of the plant (proportion and spatial distribution of live and dead fuel particles of different sizes within the plant canopy) by use of a 0.008 m 3 cube (20 x 20 x 20 cm). The cube was placed on the plant, at breast height, at the base, the centre and the top of the plant and the biomass filling the cube was sampled (Fig. 2). For each species, the sampling was replicated in three different plants in the hedge. To characterise the flammability of the live fuel according to the protocol proposed by [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF], the leaves of each species were sampled homogeneously, and only leaves of the same age and size were collected. Because of the high proportion of dead fuel sampled within the canopy of Cupressus sempervirens, dead leaves were also sampled for this species. To ensure that the fuel moisture content (FMC) was minimal, in order to be in the worst case scenario in term of fire risk, each species was sampled in summer at the hottest time of the day (between 12

Photo : Cemagref

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z55 am and 2 pm) and the sampling was not carried out on days following rainfall events [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF]). The leaves sampled were placed in plastic bags and stored in a cool box for transportation to the laboratory, minimizing changes in water content.

Before burning, the physical characteristics of the live leaves of the different species (mass, surface, volume and surface-to-volume ratio) were measured because the importance of particle geometry in determining the combustion of fuel particles. To characterize the leaf surface exposed to hot gases and fire during combustion, leaf thickness was measured avoiding thick veins. Leaf surface area was measured using a 2400 dpi scanner and image analysis software. Particle thickness was measured using a 10 -4 m accuracy micrometer.

Description of laboratory protocols

Sorting of particles sampled by the "cube method"

In the laboratory, the samples were oven-dried (48h at 60°C) until the dry weight did not change (FMC <5%), then the particles were sorted into four classes and weighed: (i) leaves, (ii) particles < 2 mm in diameter, (iii) particles 2-6 mm, and (iv) particles > 6 mm. Particles were mainly composed of twigs and fractions of fruits. Very fine fuel was composed of leaves and particles < 2 mm and fine fuel was composed of leaves and particles up to 6 mm in diameter. Dead particles, that may affect the flammability, were separated from live particles in order to have available both proportions within a species. Bulk density was calculated as the dry weight of particles divided by the volume of the cube and expressed in kg m -3 . Bulk density was used to refer to the amount of fuel in a volume of airspace, for each class of particle, each cube location and each species.

Flammability experiments with the epiradiator

The epiradiator device consisted of a 500 W electric radiator with a 10 cm diameter radiant disk. The surface temperature achieved with the device at steady-state regime was 420 °C (Fig. 3). Fifty samples (each weighing 1g) of live leaves of each species studied (and dead leaves of Cupressus sempervirens) were exposed to the heat source [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF]). Use of larger fuel masses may increase the possibility that other fuel properties, such as fuel height on the epiradiator, would cause differences in flammability [START_REF] Hernando | Combustibles forestales: inflamabilidad[END_REF][START_REF] Petriccione | Preliminary studies on litter flammability in Mediterranean region[END_REF][START_REF] Pellizzaro | Seasonal variations of live moisture content and ignitability in shrubs of the Mediterranean Basin[END_REF]). The samples were in direct contact with the electric radiator, and the surface area of contact depended on the species. The surface in contact with the epiradiator was assumed to be close enough to the heat source to undergo homogeneous heat transfer effects. A pilot flame, which did not take part in decay of the sample, was located 4 cm above the centre of the disk and allowed more regular ignition of the gases emitted during combustion of the leaf. The device was placed under a hood to prevent air currents perturbing the convection column and gas plumes. Once the leaf samples were placed on the electric radiator, time to ignition (TTI) and flame extinction were recorded to enable calculation of the flaming duration (FD) of the sample. The ignition frequency (IF) was calculated as the percentage of tests in which the samples ignited. Each species was classified according to its ignition frequency and its mean time to ignition following the classification outlined by [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF] which combined ignition frequency ranging from <50% to >95% and time-to-ignition ranging from <12.5s to >32.5s and then rated the species from 0 to 5 ( 0 = slightly flammable; 1 = weakly flammable; 2 = moderately flammable; 3 = flammable; 4 = highly flammable; 5 = extremely flammable).

Before the experiments, a 5 g sample (fresh weight) of each species was oven-dried for 24h at 60°C to enable calculation of the FMC according to the following equation: FMC (%) = (Fresh weight (g) -Dry weight (g) )/ Dry weight (g) * 100

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z66

Fig. 3 Epiradiator used in the flammability experiments

Gross heat of combustion of very fine fuel

Gross heat of combustion (GHC) of the very fine live fuel1 (composite samples of leaves and particles <2 mm in diameter formed from all cubes collected within a species) was determined following Spanish Standard UNE 164001 EX (Asociación Española de Normalización y Certificación 2005). All fuel samples were ground individually to 5.10 -4 m in a mill. A hand press was used to make the ground material into 1 g-pellets, which were then oven-dried at 100±5°C for 24 h and weighed. Measurements were made with an IKA®C5000 adiabatic bomb calorimeter with a platinum resistance sensor (PT-100). Both mill and hand press were also manufactured by IKA®. For each type of particle, the same measurements were made on two samples. A third sample was included whenever the difference between the first two values was more than 2% of the mean value.

Data analyses

The effects of the species and of the cube location (sampled at the base, centre or top of the plant) on the proportions of the different classes of particle and on the flammability variables (TTI, FD, IF) were analyzed by two-way and one-way (when non-parametric tests were used) analyses of variance (ANOVA). In addition to the tests of overall significance with ANOVA, the LSD test was used to check for significant differences between the different means. A significant difference between the variables was assumed when the p-value was ≤ 0.05. Some of the variables were previously log-transformed to meet ANOVA assumptions of normality and homoscedasticity. In all cases, when the data distribution did not follow the expected parametric pattern or when a test condition provided insufficient data, a non-parametric Kruskal-Wallis test was used instead of a parametric Fisher test. All species and cube locations were tested at random as well as their interaction. During the experiments, the mean relative temperature was 23.6°C and mean relative humidity was 52% but these variables did not affect flammability (Fisher's LSD test, p>0.05). All analyses were performed using Statgraphics Centurion XV.

Co-inertia analysis [START_REF] Dolédec | Co-inertia analysis ; an alternative method for studying species-environment relationships[END_REF], suited to large number of variables compared with small number of samples, was performed on the dependent variables (flammability variables) and on the explanatory variables (leaf traits and leaf GHC) to examine associations between leaf characteristics and leaf flammability. The complete matrix of data was transferred to the statistical package under R 2.5.1 (R Development Core Team, 2005) then analyzed using the ADE-4 package [START_REF] Thioulouse | ADE-4: a multivariate analysis and graphical display software[END_REF]. Co-inertia is a statistical method commonly used to analyze the relationship between species and environmental variables (e.g. [START_REF] Moretti | Combining plant and animal traits to assess community functional responses to disturbance[END_REF]. The first step of the co-inertia analysis (Ter Braak and Schaffers 2004) was to conduct a correspondence analysis (CA) on the leaf characteristics, then a principal component analysis (PCA) on the flammability variables. A factorial plane was thus created and enabled a new ordination of each data set. The statistical significance of each effect or combination of effects has been tested using a Monte-Carlo permutation test with 1000 permutations using the 'coin' package on R. High sums of eigen values on the main axes indicate high correlation among datasets. Hierarchical cluster analysis of the flammability variables was performed to rank the seven species (including dead Cupressus sempervirens) according to their flammability. These multivariate analyses were performed with R software (R 2.11-1, ADE-4 1.5-1 package).

Results

Cube Method

The bulk densities of the most flammable classes of particles (leaves and particles < 2 mm) sampled in each cube location for the seven species studied are shown in Table 1. Regarding live particles, the highest bulk densities were located in the top and centre cubes. Cupressus sempervirens and Prunus laurocerasus presented the highest values (respectively 7.87 and 6.31 kgm -3 in total) contrary to Pyracantha coccinea and Phyllostachys sp. (respectively 0.96 and 0.93 kgm -3 in total). Regarding dead particles, Cupressus sempervirens presented huge amount of dead leaves, especially located in base cubes (10.36 kgm -3 for a total of 11.12 kgm -3 ). There was no dead fuel in the cubes sampled in Nerium oleander, Photinia fraseri and Phyllostachys sp. ; bulk densities of dead particles were very low in the other species (< 0.15 kgm -3 in total) .

The species and the cube location significantly affected the proportions of live leaves, particles <2mm and >6mm; the proportion of 2-6 mm particles was only affected by the species. When it was significant, the cube location was the most important factor (Two-way ANOVA, Tab. 2). Regarding live fuel, the proportion of leaves in Pyracantha coccinea was significantly lower than that in the other species but the proportion of 2-6 mm particles was the highest in this species. The proportion of particles < 2 mm in Phyllostachys sp. was significantly higher than that in the other species. The proportion of particles >6mm was significantly higher in Prunus laurocerasus and Nerium oleander than in Phyllostachys sp., Cupressus sempervirens and Pyracantha coccinea (Fig. 4). The proportions of leaves, particles <2mm and >6mm significantly differed between the cube locations (Fig. 5); top cubes presenting the highest proportions of leaves and particles <2mm and base cubes the Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z88 other highest proportion of particles >6mm. Centre cubes presented higher proportion of 2-6mm particles than the location (Fig. 5). The proportions of live and dead particles that differed significantly between species are presented in Figure 4 and the proportions of live and dead particles that differed significantly between cube locations are shown in Figure 5. Regarding live fuel, the proportion of leaves was significantly higher in the top cubes and regarding dead fuel, the proportion of very fine particles was significantly higher in the base cubes.

The interaction between the species and the cube location was significant in all the classes of particles except in the >6mm class (Two-way ANOVA, Tab. 2). Regarding live leaves, the effect of the cube location was not significant for Pyracantha coccinea and Cupressus sempervirens and it was significant only for Photinia fraseri regarding the particles<2mm. Regarding the 2-6mm particles, the species significantly interacted with the top cubes only (Fig. 6).

The species had always a significant effect on the proportions of the different classes of dead particles while the cube location significantly affected the proportion of 2-6 mm particles (One-way ANOVA, Tab. 2). Regarding dead fuel, cubes sampled in Cupressus sempervirens presented significantly higher proportions of very fine fuel (leaves and particles < 2 mm) than the other species.

Flammability experiments with the epiradiator

The flammability experiments performed on the live leaves of the different species showed that Phyllostachys sp. and Photinia fraseri were the most flammable species (short time-to-ignition, high ignition frequency and flaming duration), while Pittosporum tobira was the least flammable species (long time-to-ignition and low ignition frequency) according to Valette's classification (1990). Results also showed that, regarding live leaves, Cupressus sempervirens was among the least flammable species despite its high ignition frequency (Table 3) but the dead leaves of this species were the most flammable particles (IF = 100%, TTI < 3s and FD > 15s), regardless of the flammability variables and of the species. Because of this, data on dead leaves have not been taken into account in the ANOVAs.

ANOVAs performed on the data recorded during these experiments showed that the species had a highly significant effect on flammability variables obtained with this experimental device, especially on time-toignition (Table 3). The ignition frequency of Pittosporum tobira leaves was significantly lower than that of leaves of the other species, while the ignition frequency of Photinia fraseri leaves was significantly higher than that of Nerium oleander and Pyracantha coccinea leaves. Furthermore, Prunus laurocerasus leaves ignited more

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1111 Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1212 frequently than those of Nerium oleander. The time-to-ignition was shorter for Phyllostachys sp. leaves than for the the others, while Cupressus sempervirens leaves took the longest time to ignite. The time-to-ignition did not vary significantly between Photinia fraseri and Pyracantha coccinea, or between Prunus laurocerasus and Pyracantha coccinea. Prunus laurocerasus and Cupressus sempervirens leaves burned significantly faster than that of the other species, but the flaming duration of Cupressus sempervirens leaves was not significantly lower than that of Pyracantha coccinea leaves.

Gross heat of combustion

The gross heat of combustion (GHC) of very fine fuels (measured by calorimetry) was the highest in Nerium oleander and Photinia fraseri leaves and the lowest in Phyllostachys sp. leaves (Table 5). The GHC of twigs < 2 mm in diameter in this latter species was the highest and it was the lowest in Prunus laurocerasus. The species had a significant effect on GHC of twigs <2 mm in diameter, but not on GHC of leaves (Table 4). GHC of twigs <2 mm in diameter did not differ between Nerium oleander and both Pittosporum tobira and Prunus laurocerasus, nor between Pittosporum tobira and Prunus laurocerasus as well as between Photinia fraseri and Pyracantha coccinea.

Classification of species

The cloud plot extracted from the co-inertia analysis (Fig. 7) showed the position of the dependent variables (flammability variables) and of the explanatory variables (leaf traits and GHC). Axis 1 explained 58% of variance and differentiated species presenting high ignitability (Photinia fraseri, Phyllostachys sp. and Pyracantha coccinea), characterised by high foliar surface area-to-volume ratio, from species presenting lower ignitability characterised by high GHC (Pittosporum tobira, Nerium oleander, Cupressus sempervirens). Axis 2 explained 42% of variance and opposed species with short flaming duration (Cupressus sempervirens and Prunus laurocerasus), characterised by thick leaves and low foliar surface area-to-volume ratio with species presenting higher sustainability and ignitability (Photinia fraseri, Phyllostachys sp.).

Hierarchical cluster analysis of the flammability variables (ignition frequency, time-to-ignition and flaming duration) categorized the relative flammability of the seven species (including dead Cupressus sempervirens) in five clusters of species (Fig. 8): (i) poorly flammable (Pittosporum tobira), (ii) not very flammable (live Cupressus sempervirens), (iii) moderately flammable (Pyracantha coccinea, Nerium oleander and Prunus laurocerasus), (iv) highly flammable (Photinia fraseri and Phyllostachys sp.) and (v) extremely flammable (dead Cupressus sempervirens).

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1313 Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1414

Discussion

In this work, plant flammability was assessed through the measurement of physical characteristics such as the bulk density or the proportion of each class of particle composing the plant canopy and through the measurement of the gross heat content of these particles as well as through the measurements of the flammability variables (ignition frequency, time-to-ignition and flaming duration) when leaves of each species were burned.

Effects of species on the proportion of particles and on their size

A two-way ANOVA was used to assess the effects of the cube location and of the species on the proportions of the different classes of particles. These proportions were significantly influenced by the species and, except for the 2-6mm class, by the cube location. However, there is evidence of a significant interaction between the two Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1515 factors, except for the class of particles >6mm. Thus, it is worth noting that, when it was significant, the cube location had an effect that varied between the different species.

The sorting of the cubes sampled in the three locations of the plant canopy showed that the amount of live particles, which were mainly located at the periphery of the canopy (top and centre cubes), was much greater than that of dead particles, which were located more in depth in the canopy (base cube). Live fuel was mainly composed of leaves and particles < 2 mm in diameter contrary to dead fuel which was mainly composed of particles > 6 mm in diameter except for Cupressus sempervirens samples in which dead leaves dominated. Retention of fine dead fuel within the plant structure has been observed in several Australian fire-prone species [START_REF] Specht | Dark Island heath (Ninety-mile Plain, South Australia) -VI -Pyric succession: changes in composition, coverage, dry weight and mineral nutrient status[END_REF][START_REF] Moore | Effect of nitrogen source on growth of Eucalyptus in sand culture[END_REF][START_REF] Dickinson | The flammability and energy content of some important plant species and fuel components in the forests of southeastern Tasmania[END_REF], in the european gorse, Ulex europeus [START_REF] Baeza | Fire risk and vegetation structural dynamics in Mediterranean shrubland[END_REF] or in the American chamise Adenostoma fasciculatum [START_REF] Schwilk | Flammability is a niche construction trait: canopy architecture affects fire intensity[END_REF]) and fire performance is affected by the fraction of dead fuel because of its low water content [START_REF] Elvira | Inflamabilidad y energía de las especies de sotobosque, Monografía INIA nº. 68[END_REF][START_REF] Babrauskas | Ignition handbook[END_REF], which in ornamental vegetation is related to the age, health and maintenance of the plants. Thus, the great amount of dead leaves within the canopy of Cupressus sempervirens would confer high flammability to this species. Moreover, several studies have shown that fuel size affects the potential amount of fuel that would combust in a wildfire, with fine fuel being more flammable than coarse fuel (e.g. [START_REF] Bond | Fire and plants[END_REF][START_REF] Baeza | Factors influencing fire behaviour in shrublands of different stand ages and the implications for using prescribed burning to reduce wildfire risk[END_REF] because fine particles ignite more readily and release their heat more quickly than do thicker particles of an equivalent total weight [START_REF] Wilson | Assessing fire hazard on public lands in Victoria: fire management needs and practical research objectives[END_REF]. As the bulk density of branches and leaves, determines the rate of oxygen flow through the fuels as well as the heat transfer between fuel elements [START_REF] Scarff | Leaf litter flammability in some semi-arid Australian woodlands[END_REF], flammability mainly depends on the physical arrangement of the plant biomass [START_REF] Doran | Fire in the wildland-urban interface: selecting and maintaining fire-wise plants for landscaping[END_REF]). Thus, flammability would be high for hedges composed of species such as Pyracantha coccinea or Phyllostachys sp which are the species with the lowest bulk densities of particles. It is worth noting that, except for C. sempervirens and P. coccinea, the species with high proportion of a given class of particle were not the species with high bulk density of this class.

Effect of species on flammability of leaves

Flammability of live leaves (and of dead leaves of Cupressus sempervirens) was assessed by epiradiator tests. Live leaves of species presenting the higher moisture content had longer time-to-ignition (Nerium oleander, Pittosporum tobira and Prunus laurocerasus) and those presenting the lowest moisture content were the most flammable (higher ignitability and sustainability), especially live leaves of Photinia fraseri and Phyllostachys sp. and dead leaves of Cupressus sempervirens. Currently, there is no work on the assessment of the flammability of ornamental species using such a burning device. Data analyses showed that the species significantly affected the different flammability variables, partly through their leaf moisture content. In addition to the burning experiments, it would have been interesting to perform analyses of the volatile organic compounds of the leaves. Indeed, [START_REF] Brown | Handbook for inventory surface fuels and biomass in the interior west[END_REF] showed that the flammability of fine fuel from different species may differ because of differences in physical and chemical attributes. Contrary to [START_REF] Alessio | Influence of water and terpenes on flammability in some dominant Mediterranean species[END_REF], [START_REF] Ormeño | The relationship between terpenes and flammability of leaf litter[END_REF], who used the same burning protocol as ours, showed that the species significantly affected flaming duration but not time-to-ignition and that ignitability was favoured by high terpene content in contrast to flaming duration. Theses authors worked on litter beds which had lower FMC than live fuels entailing shorter time-to-ignition values (between 2 and 4s) which were in the same range as those of dead leaves of Cupressus sempervirens recorded in the present work. This was also the case with the work of [START_REF] Pellizzaro | Seasonal variations of live moisture content and ignitability in shrubs of the Mediterranean Basin[END_REF] who compared the flammability of twigs of different species whose moisture contents were lower than that of leaves. Nevertheless, regarding time-to-ignition of live leaves, our results were in the same range as those of [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF] who also worked on live leaves using the same burning protocol.

According to Valette's classification, which takes into account ignition frequency and time-to-ignition, the different species were ranked from slightly flammable (Pittosporum tobira) to extremely flammable (Phyllostachys sp.); Nerium oleander and, surprisingly, live leaves of Cupressus sempervirens were not ranked as very flammable (Table 4), even if they are known to contain great amount of volatile oils. These results agreed with those of [START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF] who also found that Nerium oleander was not a very flammable species, and it could therefore be recommended for planting in WUIs. In the present study, Cupressus sempervirens displayed the longest time-to-ignition (among the species tested), contrary to the results reported by [START_REF] Liodakis | TG and autoignition studies on forest fuels[END_REF], who found that this latter species was one of the most flammable (of the species tested)

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1616 according to its short ignition delay. This different result could be explained, as the ignition device used in these authors' work differed from that used in the present study. Our results also showed that flaming duration was shortest for Prunus laurocerasus leaves and highest for Pittosporum tobira leaves what was difficult to explain through the leaf moisture content as both species presented high foliar moisture content. In this case, analyses of the foliar chemical content could have given more information for explaining this latter result as, according to [START_REF] Behm | Flammability of native understory species in pine flatwood and hardwood hammock ecosystems and implications for the wildland-urban interface[END_REF], chemical components may play a role in the fire sustainability of a plant.

Effect of species on gross heat of combustion of very fine particles

Data analysis showed that the species had a significant effect on GHC of particles < 2 mm in diameter, but not on the GHC of leaves. According to the classification proposed by [START_REF] Elvira | Inflamabilidad y energía de las especies de sotobosque, Monografía INIA nº. 68[END_REF], the GHC values obtained for leaves of the species studied were generally "intermediate" (18810 -20900 kJ kg -1 ), whereas the GHC values of the particles < 2 mm in diameter were either "low" (16720 -18809 kJ kg-1) (Prunus laurocesarus, Nerium oleander and Pittosporum tobira) or "intermediate" (Cupressus sempervirens, Pyracantha coccinea, Photinia fraseri and Phyllostachys sp.). For each species, except for Phyllostachys sp., the GHC was higher for leaves than for particles < 2 mm in diameter. A similar trend was observed by [START_REF] Dimitrakopoulos | A statistical classification of Mediterranean species based on their flammability components[END_REF] and [START_REF] Nuñez-Regueira | Calorific values and flammability of forest species in Galicia. Coastal and hillside zones[END_REF] in Mediterranean species and it was attributed by to the fact that leaves constituted sites for accumulation of essential oils in plants. However, the gross heat of combustion of the ornamental species tested in our work was generally lower than that of common Mediterranean forest fuels [START_REF] Madrigal | Effective heat of combustion for flaming combustion of Mediterranean forest fuels[END_REF]. The heat of combustion of leaves of Cupressus sempervirens (19548 kJ kg -1 ) given by [START_REF] Liodakis | TG and autoignition studies on forest fuels[END_REF], who worked on this species as a wildland species, was lower than that of other Mediterranean species but of the same order as those obtained in the present study kJ kg -1 ).

Classification of species

Co-inertia analysis revealed that species with thin leaves were quick to ignite (Pyracantha coccinea, Phyllostachys sp.) and species with high leaf GHC burned the longest (Pittosporum tobira, Nerium oleander). This result is consistent with the findings of [START_REF] Behm | Flammability of native understory species in pine flatwood and hardwood hammock ecosystems and implications for the wildland-urban interface[END_REF], who reported species as highly consumable when they have high energy content. Usually, flammability characteristics are mainly affected either physical structure and physiological or cellular elements. From a physical perspective, foliage characteristics, especially the foliage mass, foliar moisture content and surface area-to-volume ratio of fuel particles are often considered significant factors in flammability [START_REF] Fernandes | A new method to estimate fuel surface area-to-volume ratio using water immersion[END_REF][START_REF] Etlinger | Development of a laboratory protocol for fire performance of landscape plants[END_REF]. However, because we used a radiant disk (epiradiator) as burning device, foliar mass and volume should not be considered key variables for fire performance contrary to leaf surface area and thickness. Hierarchical classification revealed that Pittosporum tobira was the least flammable species according to the flammability variables, (ignition frequency, time-to-ignition and flaming duration). Dimitrakopoulos and Papaiannou (2001) ranked Nerium oleander as a low flammability species according to its time-to-ignition. In our experiment, this species also presented a long time-to-ignition but it was ranked as moderately flammable in the hierarchical analysis which combined its long time-to-ignition, intermediate ignition frequency and long flaming duration.

In their fuel classification, Dimitrakopoulos and Papaiannou (2001) highlighted four clusters of species according to their ignitability as a function of their foliage adaptations to prevent water loss. Contrary to our results, these authors ranked Cupressus sempervirens in the cluster of flammable species because of its short time-to-ignition due to high foliar surface area-to-volume ratio which facilitates heat absorption. Moreover, for these authors, high flammability was linked to richness in flammable volatile essential oils, what was not the case in the present work as none of the highly flammable species (Photinia fraseri or Phyllostachys sp.) are known to be aromatic plant species. According to the classification system described by [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF], which takes into account only ignition frequency and time-to-ignition of leaves, and according to the results of the hierarchical classification, live leaves of Pittosporum tobira and Cupressus sempervirens were the least flammable (respectively rated 0 and 1, Tab. 4 and Fig. 7), particularly because of their longer time-to-ignition. However, dead C. sempervirens was the most flammable, regarding both classifications. Thus, according to this last result, flammability within a species can strongly vary according to the type of fuel tested (dead or live).

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1717 This is confirmed by the work of [START_REF] Ganteaume | Assessing the flammability of surface fuels beneath ornamental vegetation in wildland-urban interfaces[END_REF] who assessed the flammability of the litters (dead surface fuels mainly composed of leaves) of the same ornamental species. These authors ranked litters of Cupressus sempervirens as moderately flammable (probably because of their high compaction), of Prunus laurocerasus as very flammable and of Phyllostachys sp as not very flammable whereas they were ranked respectively as not very flammable, moderately flammable and very flammable in the current work.

Conclusion

In the present work, the flammability of seven ornamental species was assessed by their description at particle level and by the measurements of flammability variables during burning experiments on leaves. Gross heat of combustion and foliar physical characteristics helped to explain the flammability and these species were ranked in five clusters according to the ignitability and sustainability of their leaves. Pittosporum tobira, ranked as poorly flammable species, can be considered a fire-wise species while Phyllostachys sp. and Photinia fraseri ranked as highly flammable, should not be planted in WUI. Regarding the flammability of its live leaves, Cupressus sempervirens was not very flammable, however, because this species had the greatest amount of dead material which was ranked extremely flammable, this ornamental species that should be avoided in WUI, especially close to the houses. Further experiments, especially burning experiments of whole plants, are needed to confirm the present results and to make them more widely applicable. Moreover, protocols for determining flammability must be standardized, and a common classification must be established for the test results as stated by several works [START_REF] Weise | Use of the cone calorimeter to detect seasonal differences in selected combustion characteristics of ornamental vegetation[END_REF][START_REF] White | Testing and classification of individual plants for fire behaviour: plant selection for the wildland-urban interface[END_REF].

Although laboratory experiments help improve our knowledge of the effects of live and dead fuel properties (species, moisture content and other physical and chemical characteristics) on flammability, the results obtained cannot be used directly to describe or predict the flammability of fuels under natural and real conditions; they represent basic information that is useful for assessing the fire risk of Mediterranean ornamental vegetation planted as hedges for instance. Moreover, [START_REF] White | Testing and classification of individual plants for fire behaviour: plant selection for the wildland-urban interface[END_REF] showed that flammability characteristics for a particular species were influenced not only by the species itself but also by their maintenance (watering, pruning, trimming, removing dead biomass, etc.) what could reduce the potential fire hazard. Indeed, routine irrigation, allowing the increase in FMC, has been shown to reduce plant flammability in wildland and WUIs [START_REF] Narog | Burning irrigated and unirrigated chamise[END_REF][START_REF] Doran | Fire in the wildland-urban interface: selecting and maintaining fire-wise plants for landscaping[END_REF], and pruning of dead wood decreases fire temperature and heat release [START_REF] Schwilk | Flammability is a niche construction trait: canopy architecture affects fire intensity[END_REF], indicating that plant flammability can be manipulated by horticultural practices. 2 Results of the statistical analysis performed on the proportions of each class of particle compared across species and cube location (For the two-way ANOVAs, the <2mm, 2-6mm and >6mm classes were transformed (log(x+1) for <2mm and >6mm classes and squareroot (x) for 2-6mm class, italic=not significant)

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z2222

Table 3 Leaf traits, flammability variables of live leaves (and dead leaves of Cupressus sempervirens 1 ) and rating according to the classification of [START_REF] Valette | Inflammabilités des espèces forestières méditerranéennes. Conséquences sur la combustibilité des formations forestières[END_REF]

Fig. 2

 2 Fig. 2 Shape of the plant designed by three locations of cube (top, centre and base) and biomass sampling in a Cypress "top" cube

Fig. 4 Fig. 5

 45 Fig. 4 Proportions of the different classes of particle in the seven species studied (Phyllos.: Phyllostachys sp.). Different letters on the same bar indicate significant differences according to two-way ANOVA Fisher test for live particles and one-way ANOVA Kruskal-Wallis test for dead particles

Fig. 6

 6 Fig. 6 Interactions (and 95% Fisher LSD interval) between cube location and species for the different classes of live particles (Phy: Phyllostachys sp., Cu: Cupressus sempervirens, Ne: Nerium oleander, Pho: Photinia fraseri, Pi: Pittosporum tobira, Pr: Prunus laurocerasus and Py: Pyracantha coccinea)

Fig. 7

 7 Fig. 7 Results of the co-inertia analysis performed on the leaf traits (M: mass, S: surface area, V: volume, S/V: surface area to volume ratio, T: thickness) and Gross Heat Content (GHC) values as explanatory variables and on the flammability variables (TTI: time-to-ignition, FD: flaming duration, IF: ignition frequency) as dependent variables giving the position of species (Phy: Phyllostachys sp., Cu: Cupressus sempervirens, Ne: Nerium oleander, Pho: Photinia fraseri, Pi: Pittosporum tobira, Pr: Prunus laurocerasus and Py: Pyracantha coccinea) on the co-inertia Factor 1 x Factor 2 plane

  for the species studied (Rating: 0 = slightly flammable; 1 = weakly flammable; 2 = moderately flammable; 3 = flammable; 4 = highly flammable; 5 = extremely flammable, FMC: fuel moisture content, N1: initial number of trials; N2: number of trials with ignition)

Table 1

 1 Bulk density (kg m -3 ) of the very fine particles (leaves and particles < 2 mm) in each cube location in the seven species studied (mean (standard deviation))

	LIVE

Table

  Author-produced version of the article published in EnvironmentalManagement, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z2424

										Time-to-	Flaming
										ignition (s)	duration (s) Rating
	Cupressus sempervirens	150	0.42 (0.08)	6.9 (1.10)	0.093 (0.10) 0.51 (0.12)	13.82 (1.23)	50	94 (24)	47 35.55 (6.61) 6.51 (2.72)	1
	C. sempervirens (dead )	6	0.23 (0.04)	6.0 (1.10)	0.075 (0.003) 0.35 (0.06)	16.94 (0.61)	50	100	50	2.58 (0.93) 15.52 (4.02)	5
	Nerium oleander	213	0.96 (0.19)	23.4 (2.5)	0.044 (0.006) 1.03 (0.22)	23.36 (3.61)	50	86 (35)	42 23.67 (6.81) 8.14 (4.20)	2
	Photinia fraseri	92	0.76 (0.20)	25.3 (2.4)	0.038 (0.002) 0.95 (0.13)	26.69 (1.71)	50	100	50 14.96 (2.09) 8.26 (3.13)	4
	Phyllostachys sp.	117	0.094 (0.02)	10.6 (1.8)	0.027 (0.031) 0.28 (0.31)	37.89 (1.06)	50	96 (20)	48 10.71 (4.15) 8.75 (3.18)	5
	Pittosporum tobira	178	0.43 (0.05)	13.2 (1.6)	0.032 (0.002) 0.43 (0.05)	31.09 (2.10)	50	46 (50)	23 29.56 (11.73) 8.96 (6.80)	0
	Prunus laurocerasus	178	1.68 (0.27)	46.6 (7.5)	0.042 (0.003) 1.98 (0.41)	23.86 (1.73)	50	98 (14)	49 17.43 (4.27) 4.92 (2.04)	4
	Pyracantha coccinea	108	0.069 (0.02)	4.3 (0.5)	0.016 (0.004) 0.07 (0.02)	64.81 (11.82)	50	88 (33)	44 15.86 (5.70) 7.11 (4.99)	3
	Results of statistical							KW=91.84,		KW=203.26,	KW=46.35,
	tests							p<0.0001		p<0.0001	p<0.0001

1 Not taken into account in the statistical tests

Table 4

 4 Gross heat of combustion (GHC, in kJkg -1 ) of very fine fuels in the seven species studied (Lv: leaves, NA: no data, italic: not significant)

	Species	GHC_Lv_live	GHC_2 mm_live	GHC_Lv_dead	GHC_2 mm_dead
	Cupressus sempervirens	19819	19108	19265	19223
	Nerium oleander	20067	18172	NA	NA
	Photinia fraseri	20031	18859	NA	NA
	Phyllostachys sp.	18704	19676	NA	NA
	Pittosporum tobira	19929	18134	NA	NA
	Prunus laurocerasus	18797	18084	NA	NA
	Pyracantha coccinea	19358	18905	NA	NA
	Results of statistical tests	KW=12.57, p=0.0503	KW = 13.93, p = 0.0303

The GHC of the very fine dead fuel was also measured for Cupressus sempervirens because of the high fraction of dead fuel recorded in this species.

Acknowledgments

The authors wish to thank the technical staff at Irstea (Roland Estève, Aminata N'Diaye, Fabien Guerra, Jean-Michel Lopez, Marie Cabaret-Lampin, Florent Dalverny and Alice Lebeaux) and at INIA (Carmen Díez Galilea).

This study was funded by the French Ministry of Ecology (Service des Risques Naturels et Hydroliques) and the Direction Générale de la Prévention des Risques (DGPR).

Author-produced version of the article published in Environmental Management, 2013, vol. 52, pp 467-480 Original publication available at http://www.springer.com doi : 10.1007/s00267-013-0067-z1818


I Zidane

C Zhang

D Guines

L Léotoing

E Ragneau

Insa De Rennes -Lgcgm

OPTIMISATION OF BIAXIAL TENSILE SPECIMEN SHAPE FROM NUMERICAL INVESTIGATIONS

Keywords: Forming processes, dynamic tests, biaxial tensile, cruciform specimen, FE simulations

In innovative industrial processes such as hydroforming or incremental forming, strain rates up to 500s -1 can be reached. As a result, experimental setups allowing to obtain large deformations from static to intermediate strain rate levels have to be developed to predict the formability limits of sheet metal materials. The proposed experimental device is a servo-hydraulic testing machine provided with four independent dynamic actuators allowing biaxial tensile tests on cruciform specimen. The main difficulty to define an appropriate cruciform specimen shape is to force the onset of necking in the central region. In this paper, different specimens used in previous studies are numerically investigated through FE simulations. A modified cruciform specimen shape is then proposed and the best set of geometrical dimensions is defined from a parametric study. Finally, the efficiency of the proposed specimen shape is validated by experiments. Numerical and experimental results, i.e., the strain level in the specimen and the onset of necking are compared and discussed to boundary conditions corresponding to an equi-biaxial tensile test.

INTRODUCTION

Simulation of sheet metal forming requires accurate constitutive models and prediction of formability limits of the material. Those material behaviors have to be characterized at strain, strain rate and temperature ranges corresponding to the process ones. The constitutive model describes into a single equation, the hardening behavior of the material as a function of strain, strain rate and temperature. The constants of these constitutive relationships are usually identified from force versus displacement curves through monoaxial tension tests. The determination of the forming limit diagram (FLD) is usually obtained from static conventional tests (Marciniak test [START_REF] Marciniak | Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension[END_REF], Nakazima test [START_REF] Nakazima | Study on the formability of steel sheets[END_REF], bulge test [START_REF] Duddedar | Measurement of shapes of foil bulge test samples[END_REF], …) by observing the onset of necking. In such tests, only linear loading paths can be realized. The paths are defined from the specimen geometry and many different specimens are required to cover the whole forming limit curve. Moreover, depending on the considered test, the friction effect between the specimen and the tool can influence the prediction of the material formability and it is still a difficulty to evaluate the coefficient friction value. Using an other technique, Andrews and Ellison [START_REF] Andrews | A testing rig for cyclic at high biaxial strains[END_REF] used thin-walled tubes solicited by traction-torsion loadings associated with an internal-external pressure to create bi-axial stress/strain states. Although this technique appears to be efficient, it presents three major disadvantages [START_REF] Boehler | Optimal design of biaxial tensile cruciform specimens[END_REF]: -the stress-strain state is not exactly bi-axial because the radial stress caused by the pressure is not zero, -the level of temperature is often limited by the properties of fluid, -material anisotropy obtained by the tube extrusion is not compatible with the anisotropy of a sheet metal. In order to overcome the drawbacks of the above mentioned tests, Pascole and Villiers [START_REF] Pascole | Low cycle fatigue of steels under biaxial straining[END_REF], Hayhurst [START_REF] Hayhurst | A biaxial-tension creeprupture testing machine[END_REF] and Kelly [START_REF] Kelly | Problems in creep testing under biaxial stress systems[END_REF] use a plate cruciform specimen submitted to a static biaxial tensile in its plane. Depending on the device, two or four actuators are used and any ratio of biaxiality can be obtained by changing the proportion of the applied load or displacement [START_REF] Xiang-Dong | Biaxial tensile testing of cruciform specimen under complex loading[END_REF]. Although cruciform specimens have been studied extensively, a general review on biaxial tensile tests and their applications proposed by Hannon and Tiernan [START_REF] Hannon | A review of planar biaxial tensile test systems for sheet metal[END_REF] indicates that there is no standard geometry existing to this day. Moreover, in the whole of previous work published to date, the cruciform specimens were used within the framework of static characterizations of the behavior of the materials (anisotropy, work hardening, plasticity criteria) under biaxial solicitations. But in innovative industrial processes such as hydroforming or incremental forming, strain rates up to 500s -1 can be reached. As a result, a new experimental setup making it possible to obtain large deformations until intermediate strain rate levels, independently of any friction phenomena, has been developed. This device will be used at the same time to predict the formability of metallic material sheets and to study the constitutive laws necessary to feed the numerical simulations codes. The proposed experimental device is a servohydraulic testing machine provided with four independent dynamic actuators allowing biaxial tensile tests on cruciform specimen. For each actuator, the maximum velocity is 1m.s -1 and the maximum load capacity is 50kN. In order to study the forming limits at different strain rates and under complex loading paths, a specimen shape has to be defined. The main difficulties to define an appropriate cruciform specimen shape are to force the onset of necking in the central zone and not on the arms of the specimen. Moreover, for dynamic tests, the maximum stiffness of the specimen, (which is the initial one), has to be adjusted according to the experimental setup capacities in order to control tensile test velocities. For the considered experimental device, the stiffness of the specimens should not exceed 45kN/mm for dynamic tests. Others considerations like manufacturing constraints must also be taken into account. In this study, different specimen shapes used in previous works are numerically investigated through FE simulations. A modified cruciform specimen shape is then proposed and the best set of geometrical dimensions is defined from a parametric study. Finally, the efficiency of the proposed specimen shape is validated by experiments. The central area of the cruciform specimen is filmed by a camera and strain fields are determined by means of an image correlation technique. Numerical and experimental results, i.e., the strain level in the specimen and the onset of necking are compared and discussed to boundary conditions corresponding to an equi-biaxial tensile test.

VARIOUS SHAPES OF CRUCIFORM SPECIMENS

To characterize the mechanical behavior of materials subjected to biaxial loadings, various cruciform specimens were defined. Several researchers [START_REF] Hayhurst | A biaxial-tension creeprupture testing machine[END_REF][START_REF] Kelly | Problems in creep testing under biaxial stress systems[END_REF] have proposed a cruciform specimen shape with a reduced thickness square central zone and grooves in the arms. An example of such geometry is shown Figure 1. Makinde and Ferron [START_REF] Ferron | Design and development of a biaxial strength testing device[END_REF] and Demmerle and Boehler [START_REF] Boehler | Optimal design of biaxial tensile cruciform specimens[END_REF] to study the influence of bi-axial loadings on hardening anisotropic materials, optimized this specimen and obtain a homogeneous stress-strain field over a large part of the square zone.

Johnston and al [START_REF] Johnston | Biaxial Testing of 2195 Aluminum Alloy Using Cruciform Specimens[END_REF] modified the specimen 1 and added a circular central zone with a smaller thickness (Figure 2). Replacing arm grooves, Yong and al [START_REF] Min | Design of a cruciform biaxial tensile specimen for limit strain analysis by FEM[END_REF] proposed the shape shown Figure 3. This form has been developed in order to determine the FLD under complex loading paths by numerical finite element simulations. The initial specimen dimensions defined by the authors lead to a very stiff specimen: the arm width is 90mm and the central area diameter is 20mm. But to date, to our knowledge, no experimental results were published to validate this shape. An other cruciform specimen shape (Figure 4) with reduced thickness in the central area and variable width arms has been proposed by Zhang and Sakane [START_REF] Zhang | Multiaxial creepfatigue life prediction for cruciform specimen[END_REF]. This specimen has been used to realize fatigue tests, i.e. to low strain levels.

FINITE ELEMENT ANALYSIS OF THE VARIOUS SPECIMEN SHAPES

Through FE simulations, the efficiency of the four various specimen shapes mentioned above is numerically investigated. For that, equi-biaxial tensile test is simulated by means of the FE software package ABAQUS. The selected material is an aluminium alloy (AA 2017) with an isotropic elastoplastic behavior. Considering the symmetry of the specimen geometries and the use of isotropic material, only one quarter of the specimen is analyzed. Tetrahedron elements are used to mesh the geometry and a refined particularly mesh is adopted in the sensitive areas where strain localizations can occur (central zone, intermediate section, fillet, grooves). The various shapes suggested (figure 1 to 4) were dimensioned with the following rules: (i) the characteristic dimension of the central zone is fixed at a value ranging between 20 and 30mm. This dimension is mainly imposed by the acquisition capacities of the camera, (ii) other principal dimensions (width and thickness of the arms, thickness of the central area) are chosen according to either the maximum load capacities of the experimental setup or the maximum stiffness of the sample. The maximum value of this one is defined by the capacities of the experimental device. Consequently, the thickness of the central area and arms are respectively fixed to 1 and 4mm. For specimens 2 to 4, the thickness of the intermediate zone is 2mm.

RESULTS AND DISCUSSIONS

To ensure that necking always appears in the central zone, the design of the cruciform specimens must induce the greatest deformations in the central zone and no strain localizations in the other areas (grooves, fillet, ...). Both the equivalent plastic strain and the maximal principal strain in the specimen are observed. In the geometrical singularities (grooves for example), the observation of the equivalent plastic strain is not sufficient, since the major principal strain can reach high values leading to a localization of the deformation (then the rupture will appear in this point) although the equivalent strain is not very high. The figures 5 and 6 show the equivalent plastic strain (PEEQ) and the maximal principal strain fields for respectively the specimens 1 to 4. Only the interesting zone, i.e. the central zone is presented.

All the results presented correspond to the moment when the maximum value of the equivalent plastic strain reaches 30% in a point of the specimen. In order to evaluate the influence of the shape details such as the grooves, the fillet of the arms, the evolution of the strain (equivalent plastic and maximal principal) is also plotted along a path (represented by a mixed line). According to figures 5 and 6, one can see that the strain concentration is more homogeneous in the central test section of the specimens with grooves (specimens 1 and 2). But, for the specimen 1, the maximum strain value (30%) is reached in the grooves. This phenomenon is less pronounced for specimen 2 where an intermediate zone has been added. The equivalent plastic strain is then slightly Specimen 1 Specimen 2 higher in the central zone than in the grooves. But, the maximal principal strain is always much higher (27.5%) in those last ones than in the central area (15%).

For the specimen 3, the maximal principal strain is obtained in the fillet of the arms (25%) whereas in the central zone the level reached is approximately 15%.

For the specimen 4, the highest strain values (maximal principal strain or equivalent plastic strain) are located in the fillet of the arms whereas in the central area, the value of the maximum principal strain is the lowest one of those obtained on the 4 specimens (11%). The results of the FE simulations show that the specimen 2 and 3 seem to be the more efficient specimens since they lead to the maximum values of strain in the central zone among the 4 specimens tested. Specimen 3 is, for all the specimens tested, stiffest (Tab. 1). Moreover, to reduce the stress/strain concentrations in the fillets of the arms, it would be advisable to increase the width of the arms but that would result in increasing the stiffness of the specimen. Finally, the shape of specimen proposed figure 2 seems most effective and most promising. The positioning of the grooves on the arms make it possible to limit the stiffness of the specimen. An optimization can be performed, FE simulations show notably that the distance between the ends of the grooves and the edge of the square central zone, had a great influence on the level of deformation in the grooves or fillets of the arms. Thereafter, on the basis of the shape of the sample 2, a modified form is proposed and optimized in order to reduce the strain localization in the grooves.

OPTIMIZED CRUCIFORM SPECIMEN SHAPE

A modification of specimen 2 is proposed by replacing the fillet between the central circular zone and the intermediate square zone by a chamfer with an outer diameter of 25mm (Figure 7). The aim of the chamfer is to improve the strain homogeneity and localization in the central test section.

According to the preliminary study, four important geometric parameters (Figure 7) have been identified: -the length L between the ends of the grooves and the edge of the square central zone,the fillet of arms R c , -the thickness of the central test section T, -the diameter of the central test section D i . The figures 8 and 9 show respectively the strain fields and the evolution of strain in function of the tensile displacement for the optimized shape given above. As one can see it in figure 8, the strain fields are homogeneous in the central zone.

Moreover, the equivalent plastic strain and the maximal principal strain are always greater in the central zone than anywhere in the specimen (figure 9). Numerically, the necking well appears in the central area.

COMPARISON BETWEEN EXPERIMENTS AND FE RESULTS

The experimental device is a servo-hydraulic testing machine provided with four independent dynamic actuators. The central area of the cruciform specimen is filmed with a camera. In order to validate the defined shape of the specimen, a static equi-biaxial test has been performed. A velocity of 1mm.s -1 is applied on each actuator. The sample is machined in a rolled aluminium alloy sheet (AA 2017). For the studied material, the results allow to identify the onset of necking in the zone A (figure 11) with a maximal principal strain of 16% and a minimal principal strain of 6%. The comparison of the experimental results and the numerical results reveals however differences in the strain versus displacement curves: the slopes of the experimental curves are different from those obtained numerically (either for the equivalent plastic deformation or for the maximal principal strain), the strain levels are also different. This can be explained by the material behavior considered in the FE simulations. Indeed, numerical simulations have shown a great influence of the hardening law on the strain evolutions. The simplistic isotropic hardening law introduced in the FE simulations has been established from an uniaxial tensile test in the roll direction.

CONCLUSIONS

Through numerical FE simulations, various cruciform specimen shapes have been investigated. A parametric study leads to the definition of an efficient shape for which the strain localization appears in the central zone. The numerical approach has been validated by experiment. The onset of necking has been well observed and measured in the zone of interest. From this cruciform specimen shape, different strain paths can be applied to determine the whole FLD independently of any friction phenomena. A great influence of the constitutive law on the strain level has been observed.

Figure 1 : 1 Figure 2 : 2 Figure 3 :

 11223 Figure 1: Dimensions of the specimen-1

Figure 4 :

 4 Figure 4: Dimensions of the specimen-4

Figure 5 :

 5 Figure 5: Equivalent plastic strain and maximal principal strain fields for specimens 1 and 2

Figure 6 :

 6 Figure 6: Equivalent plastic strain and maximal principal strain fields for specimens 3 and 4

Figure 7 :

 7 Figure 7: Geometry of the optimized specimen shape A parametric study was carried out and the best set of parameters obtained is the following: L = 4.5mm ; R c = 8mm ; D i = 10mm ; T = 0.75mm

Figure 8 :Figure 9 :

 89 Figure 8: Equivalent plastic strain and principal strain fields

Figure 10 :

 10 Figure 10: Central zone of the specimen testedIn the figure10, one can see an image of the specimen before the test. The strain fields are determined by means of a digital image correlation technique. The results of the image post-processing presented figure11show that a biaxial state of deformation is well obtained in the center of the specimen (zone B). For the studied material, the results allow to identify the onset of necking in the zone A (figure11) with a maximal principal strain of 16% and a minimal principal strain of 6%. The comparison of the experimental results and the numerical results reveals however differences in the strain versus displacement curves: the slopes of the experimental curves are different from those obtained numerically (either for the equivalent plastic deformation or for the maximal principal strain), the strain levels are also different. This can be explained by the material behavior considered in the FE simulations. Indeed, numerical simulations have shown a great influence of the hardening law on the strain evolutions. The simplistic isotropic hardening law introduced in the FE simulations has been established from an uniaxial tensile test in the roll direction.

Figure 11 :

 11 Figure 11: Experimental results

Table 1 :

 1 Stiffnesses of the tested specimens

	Specimens	1	2	3	4
	Stiffness (KN/mm)	42	45	62	38


Cunsheng Zhang

Lionel Leotoing

Dominique Guines

Eric Ragneau

THEORETICAL AND NUMERICAL STUDY OF STRAIN RATE SENSITIVITY ON FORMABILITY OF SHEET METAL

Keywords: Strain rate sensitivity, forming limit diagrams, M-K model

In the present work, the formability of an aluminium alloy (AA5083) sheet at elevated temperature (240 • C and 300 • C) is investigated by theoretical and numerical approaches, using the Swift hardening law. For the theoretical one, an algorithm based on Newton-Raphson method is developed to calculate the limit strains in the frame of the M-K (Marciniak-Kuczynski) model. Numerically, the M-K model is simulated with the commercially available finite-element code ABAQUS. The comparison between the theoretical and numerical evaluation of FLCs shows a good agreement between two approaches. Finally, the effect of strain rate sensitivity index (m) and forming speed on formability is analyzed. Results reveal that the formability is an increasing function of m while there is no significant influence of forming speed on the sheet formability.

INTRODUCTION

The formability evaluation is of considerable practical interest in the sheet metal forming operations, especially with the increasing use of new materials in the automotive and aerospace industry. Forming limit diagrams (FLDs), introduced by Keeler and Backofen [START_REF] Keeler | Plastic instability and fracture in sheets stretched over rigid punches[END_REF] in 1963, have been commonly used to evaluate the formability of sheet metals. The experimental methods for determining FLDs are well established. However, experimental procedures require tremendous amount of effort and special equipments [START_REF] Ozturk | Experimental and numerical analysis of out-of-plane formability test[END_REF]. Therefore, much effort has been made in theoretical prediction of FLDs. Among them, the most frequently used is M-K model, which was developed by Marciniak and Kuczynski in 1967 [START_REF] Marciniak | Limit strains in the processes stretch-forming sheet metal[END_REF]. Strain rate sensitivity has been experimentally identified as an important factor determining formability of sheet metal and can alter substantially the level and shape of FLDs [START_REF] Percy | The effect of strain rate on the fld for sheet metal[END_REF][START_REF] Broomhead | The effect of strain rate on the strain to fracture of a sheet steel under biaxial tensile stress conditions[END_REF]. However, up to now, relatively little attention has been drawn to the theoretical models taking into account the strain rate sensitivity. Hutchinson et al. [START_REF] Hutchinson | Mechanics of Sheet Metal Forming[END_REF] predicted the FLDs with Von Mises yield function considering the rate sensitivity. Their work has made important contributions to gaining insight into the roles of constitutive equations and plasticity theories on FLDs. Barata Da Rocha et al. [START_REF] Barata Da Rocha | Prediction of the forming limit diagrams of anisotropic sheets in linear and non-linear loading[END_REF] predicted the strain path-dependent FLD by taking into account the rate sensitivity using Hill's theory of plastic anisotropy. Graf and Hos-ford [START_REF] Graf | Calculations of forming limit diagrams[END_REF] analyzed the effect of rate sensitivity on the right-hand side of FLD with the Logan and Hosfords anisotropy yield criterion. However, relatively little attention has been paid to the prediction of left-hand side of FLDs because of the complex algorithms and lengthy calculations.

In addition, with the increasing application of computational techniques, numerical predictions of FLDs have become more attractive and the finite element method has been widely adopted in FLDs' determination. Narasimhan and Wagoner [START_REF] Narasimhan | Finite element modeling simulation of in-plane forming limit diagrams of sheets containing finite defects[END_REF] have used FEM to predict right-hand side of FLDs in the frame of the M-K model. The influence of material properties, failure criterion, and also defect geometry on the F LD 0 (the limit major strain under the plane strain condition) has been analysed. The shape of FLDs they calculated agreed fairly well with those obtained from the M-K theory. Later, Banabic et al. [START_REF] Banabic | Recent developments in the formability of aluminum alloys[END_REF] determined the whole range of FLDs using FE simulation of the M-K model with an inclined groove. For the left-hand side of FLDs, the imperfection orientation was taken according to Hill's zero extension assumption. A good correlation between predicted and experimental results has been obtained for right-side hand of FLDs, while in left area the predicted FLDs underestimate the experimental ones.

Until now, numerical prediction of FLDs taking into account rate sensitivity has never been considered. Hence, the aim of this paper is to evaluate the effect of strain rate sensitivity on formability of an aluminum sheet. Firstly, the constitutive equation parameters in work hardening law are identified for AA5083 at 240 • C and 300 • C. Then, sheet forma-bility is determined by the theoretical and numerical approaches based on the M-K model with a groove oriented perpendicular to the axis of the largest principal stress. Finally, the effect of strain rate sensitivity and forming speed on formability is analysed by the numerical approach.

MATERIAL CONSTITUTIVE LAW

Because of its good formability, AA5083 receives more and more application in automotive and aerospace industry. previous studies have shown a strain rate dependence of the alloy at elevated temperature [START_REF] Diot | Forming process of a 5083 aluminium alloy. constitutive model covering a large range of temperature[END_REF]. Hence, the following multiplicative Swift law has been chosen to describe the viscoplastic behaviour of this AA5083 alloy:

σ = K • (ε 0 + ε) n • εm (1)
where, ε and ε are equivalent plastic strain and equivalent plastic strain rate, respectively. K and ε 0 are material parameters, while n and m are the strain hardening and strain rate sensitivity indices. To characterize the material behaviour of AA5083, tensile tests have been performed on a high-speed servo-hydraulic testing machine (DARTEC, 20KN capacity) at temperatures of 240 • C and 300 • C at the constant crosshead speeds of 1.56, 15.6 and 156 mm/s, the true stress-true strain curves are shown in Figure 1 and Figure 2, respectively. With the least squares optimization, the parameters of above constitutive material model at 240

THEORETICAL APPROACH

The typical M-K model is shown in Fig. 3. The imperfection is mathematically represented by a long groove which is characterized by an initial imperfection factor

f 0 = e b 0 e a 0 ( 2
)
where e a 0 , e b 0 are the initial sheet thicknesses in zone a and zone b. The indexes a and b are respectively used to designate the outer and the inner regions of the groove. The plastic material behaviour is modelled by the Von Mises yield condition with the plane stress assumption (σ k 13 = σ k 23 = σ k 33 = 0): For the sake of convenience, the following notations are used:

σ k 2 = σ k 11 2 -σ k 11 σ k 22 + σ k 22 2 + 3 σ k 12 2 (3
ρ k = ∆ε k 22 ∆ε k 11 , Ω k = σ k 22 σ k 11 , ϕ k = σ k σ k 11 , Φ k = ∆ε k ∆ε k 11
where Ω k , ϕ k and Φ k are specific function of ρ k . For the Von Mises yield function,

Ω k = 2ρ k +1 2+ρ k ϕ k = 1 -Ω k + (Ω k ) 2 Φ k = 2ϕ k 2-Ω k (4)
Combining with the Swift hardening law (1) and the notations (4), the equilibrium equation (i.e. σ a 11 e a = σ b 11 e b ) becomes:

(ε 0 + ε a ) n ϕ a εa m = f (ε 0 + ε b ) n ϕ b εb m ( 5
)
where f is the current imperfection factor. The equivalent strain rate can be similarly expressed by the strain and time increments:

εk = ∆ε k ∆t (6)
where ∆ε k is the equivalent plastic strain increment. ∆ refers to a quantity corresponding to a small time increment ∆t. Considering the compatibility condition (i.e. ∆ε a 22 = ∆ε b 22 ) and Levy-Mises flow rule, the eq.( 5) can be expressed as follows:

(ε0+ε a ) n ϕ a 2ϕ a 2Ω a -1 m = f (ε0+ε b ) n ϕ b 2ϕ b 2Ω b -1 m (7)
Clearly observed in eq.( 7), with the disappearance of time increment, the level of the strain rate has no effect in the M-K model, therefore, only the ratesensitivity vis-à-vis the parameter m could be analyzed. Performing basic mathematical operations and taking into account a small strain increment, the eq.( 7) can be written in the form

(ε 0 + ε a + Φ a ∆ε a 11 ) n (ϕ a ) m-1 (2Ω a -1) m = f ε 0 + ε b + Φ b ∆ε b 11 n (ϕ b ) m-1 (2Ω b -1) m (8)
In zone a, the constant strain path and incremental strain are imposed. For every increment ∆ε a 11 , ∆ε a and ∆ε b are calculated. The system of the basic equations of the M-K model is solved by the Newton-Raphson method. The computation is stopped until the failure criterion (∆ε b /∆ε a ≥ 7) is satisfied and the corresponding strains ε a 11 and ε a 22 at this moment are retained as the limit strains. This point corresponds to a particular strain path defined by the coefficient ρ a . In order to obtain other points on the FLDs, the computations described above must be performed in a loop controlled by this parameter. The rheological parameter values at 240 • C and 300 • C in Table 1 and

NUMERICAL APPROACH

In this part, the M-K model is simulated with the commercially available finite-element program ABAQUS to numerically analyze the sheet formability. An initial defect in the sheet is characterized by two different zone thicknesses in Figure 4. The sheet is meshed by hexahedral elements. Due to symmetrical boundary conditions, only the half of the entire model is simulated. To compare with the theoretical results, the same constitutive law (1) and the same rheological parameter values in Table 1 as used in theoretical analysis of M-K model are implemented in ABAQUS by using the UHARD user subroutine. Various strain states can be covered by imposing various displacement ratios at 1 and 2 directions. To determine the limit strains, two different reference elements are required. One of the elements is placed in zone a (Element A), while the other is in zone b (Element B), as shown in Figure 4. When the equivalent plastic strain increment of the Element B exceeds 7 times that in the Element A, the final major and minor strains of Element A are noted as the limit strains in the FLDs. In Figure 5, the limit strains based on FEM are shown for 240 • C and 300 • C, respectively. For above numerical results, each point corresponds to a certain displacement ratio. As shown in Figure 5, the FLCs obtained by the two mentioned approaches at 300

EFFECT OF RATE SENSITIV-ITY AND FORMING SPEED ON FORMABILITY

As was previously stated, the goal of this paper is to evaluate the effect of strain rate sensitivity on formability. But with the theoretical approach, one can not investigate the effect of strain rate on formability. A better way to evaluate this effect is to simulate the necking process by the numerical approach.

INFLUENCE OF STRAIN RATE SENSI-TIVITY INDEX ON FLDS

In order to analyze the effect of strain rate sensitivity index m on formability, the rheological parameters under quasi-static condition (i.e. m=0) at 240 • C and 300 • C are implanted into ABAQUS in order to compare with the above results considering the strain rate sensitivity. As shown in Figure 6, the influence of strain rate sensitivity index (m) on FLDs can be clearly observed: a high m value produces a high level of the FLDs. For example, in comparison with m=0, there is approximately an increase of 86% for F LD 0 at 240 • C, while at 300 • C, this value reaches 458%.

As mentioned in Section 4, the FLC at 300 • C is slightly higher than that at 240 • C. However, the FLCs determined under quasi-static condition show a contrary tendency that the formability is greatly improved with decreasing temperature, i.e. with the increasing value of n. Compared to the formability at 300

INFLUENCE OF FORMING SPEED ON FLDS

To investigate the influence of forming velocity, the FEM condition includes varying forming times (This leads to variation of strain rate). Three scales of forming velocity (represented by the ratio of displacement in the direction-1 and forming times) are chosen: 0.1 mm/s, 2 mm/s and 1200 mm/s. The rheological parameters at 300 • C in Table 1 have been used in the simulation.

Figure 7 shows the effect of forming velocity on the FLDs. At forming speed from 0.1 mm/s to 1200 mm/s, the strain rates from 10 -2 s -1 to 10 2 s -1 are achieved, but the FLCs do hardly change, so it is concluded that forming velocity has little influence on material formability for the mentioned constitutive law. This conclusion coincides with the fact that the effect of strain rate on formability disappears in M-K model.

CONCLUSIONS

In this work, the formability of AA5083 sheet has been investigated by theoretical and numerical approach based on M-K model. Then by numerical approach, the effect of strain rate sensitivity coefficient m and forming speed on formability has been studied. After carrying out the FEM simulation, the following conclusions have been reached: 1 The FEM simulations based on M-K model can generate reliable results for the determination of the FLDs.

2 The formability is found to be significantly sensi- tive to the strain rate sensitivity index m.

3 The numerical result shows that the forming speed has little influence on the material formability. It is contrary to what strain rate influences the material formability in the literature [START_REF] Banabic | Formability of metallic material (plastic anisotropy, formability testing, Forming limits[END_REF]. One reason to explain this phenomenon may be that a simplistic hardening law has been used in the above analysis.

In the theoretical approach, it also leads to an independence of formability on strain rate. Therefore, a more complex constitutive laws, such as Johnson-Cook or Cowper-Symond law, should be considered.

In addition, to validate the numerical result, experimental investigations of strain rate effect on sheet formability are in progress.

Figure 1 :

 1 Figure 1: Experimental and fitting stress-strain curves at 240 • C

Figure 3 :

 3 Figure 3: Representation of the M-K model

  ) where σ k is the equivalent stress, σ k 11 , σ k 22 and σ k 12 are stress tensor components (k = a or b)

  the following ones have been used for the computation: e a 0 =1 mm, e b 0 =0.98 mm and ∆ε a 11 =0.0001. The FLCs based on the theoretical approach for AA5083 sheet are displayed in Figure 5.

Figure 4 :

 4 Figure 4: FEM model in ABAQUS

Figure 5 :

 5 Figure 5: Theoretical and numerical FLCs of the AA5083 sheet at 240 • C and 300 • C

Figure 6 :

 6 Figure 6: Effect of rate sensitivity index m on formability

Figure 7 :

 7 Figure 7: Effect of forming speed on formability

Table 1 :

 1 Constitutive model parameters

		200
	True stress(MPa)	50 100 150	1.56_EXP 15.6_EXP 156_EXP	1.56_Fitting 15.6_Fitting 156_Fitting
		0
		0	0.1	0.2	0.3	0.4
				True strain
	Figure 2: Experimental and fitting stress-strain
	curves at 300 • C
	T ( • C) K(M P a)	ε 0	n	m
	240	328.062	0.00126 0.1275 0.0280
	300	207.207	0.00035 0.0614 0.0657

• C and 300 • C have been identified to fit experimental data as shown in Table

1

. The corresponding fitting curves are displayed in Figure

1

and Figure

2

. As it can be seen in Table

1

, with the increasing temperature, the rate sensitivity index m for AA5083 increases, while the work hardening index n decreases.

  However, it is worth noticing that the predictions from the FEM simulations are in good agreement with the values calculated by M-K model. Therefore, it may be concluded that the FEM simulations developed in this work can generate reliable results for the determination of the FLDs.

		0.4
		0.3
	Major strain	0.2				240°C FEM 300°C FEM 240°C THE
		0.1				300°C THE
		0
	-0.2	-0.1	0	0.1	0.2	0.3	0.4
				Minor strain

• C are slightly higher than those at 240 • C.

  • C, there is a 164% increase of F LD 0 at 240 • C under quasi-static condition. Now, it is easy to conclude that both strain hardening and strain rate sensitivity indices could enhance the sheet formability by delaying the onset of localized necking. Therefore, to more accurately evaluate a sheet formability, one should take into account its both work hardening and strain rate sensitivity.

		0.4
		0.3
	Major strain	0.1 0.2				240°C 300°C 240°C m=0
						300°C m=0
		0
	-0.2	-0.1	0	0.1	0.2	0.3	0.4
				Minor strain