Analysis of the Polypropylene Mechanical Behaviour Response

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Analysis of the polypropylene mechanical behaviour response:Experiments and numerical modelingH.M. Meddaha,*, N. Selinib, M. Benguediabb, M. Bouziane Mohamedb, M. BelhamianibaDepartment of Mechanical Engineering, University Mustapha Stambouli of Masacra, Masacra, AlgeriabDepartment of Mechanical Engineering, University of Sidi Bel Abbes, Bp 89, Cit Ben Mhidi, Sidi Bel Abbes 22000, Algeriaa r t i c l e i n f oArticle history:Received 26 February 2009Accepted 26 April 2009Available online 8 May 2009Keywords:PolypropyleneSemi-crystallineMechanical behaviourFEMa b s t r a c tThe security requirements in the industrial world incite an ever deeper understanding of the behaviourand the fracture of polymeric materials used as structural parts of the passenger compartment. We arelooking at a polypropylene commonly used in this eld in order to identify the physical processes respon-sible for their mechanical properties. The mechanical characterization of the response of the polymerunder simple and complex strain relies on a unique method of combining performing numerical analysistechniques. The behaviour of polypropylene with large deformations dissipative involves several pro-cesses. Its consequences on the mechanical properties of materials are signicant. The analysis of theseresults to emphasis that the plasticity of the polymer involves addition mechanical properties. Takentogether, these observations can lay the groundwork for a thermodynamic modeling of the behaviourlaw to this class of polymer. The contribution of this approach was demonstrated by experimental andnumerical modeling of the polypropylene mechanical behaviour. 2009 Elsevier Ltd. All rights reserved.1. IntroductionThe semi-crystalline polymers are materials with a complexmicrostructure consisting of a disordered amorphous phase vis-cous nature of a phase and crystalline structure. The coexistenceand the interaction of these two phases of very different naturesare at the root of the complexity of their macroscopic behaviourthat could come within the purview of such behaviour elastovisco-plastic [17]. It must be seen in the point of microscopic view;polymer material is as complex as each of the three levels of micro-structure plays a role in the deformation. A wide spherolites, crazesmay be formed at interspherolitics. Meanwhile, spherolites may bedeformed, leading to the destruction of tapes. In terms of crystal-line lamellae and the amorphous phase, we can see a stretch ofthe whole or shear, which will be translated obviously on a smallerscale by slipping chains amorphous phase.Several avenues of study of the rupture have come to our atten-tion in the literature. The rst takes place at the scale of themechanics of continuous media. Position of initial defect (crackor discontinuity), this approach can predict the evolution of the lat-ter depending on the condition of loading and led a mechanicalcharacterization of quantities at time of the rupture. Other ap-proaches include phenomenological look simple mathematicalmodels to bring sufcient conditions for the beginning of failure.The expression of the criteria as well as the descriptors set gamecan be different depending on the size of plastic processes develop-ing in the material.Polypropylene is a polyolen catalyst obtained by linear stereo-specique of propene. This type of catalyst allows the synthesis ofisotactic polypropylene (most recently syndiotactique), which onlyshows the properties required a structural use.Our work takes place in this context, and is being conducted inpartnership with major players in the industry.The objective is to portray the different ways of possible studyand choose the most appropriate approach of description of ourpolypropylene, the establishment of the constitutive laws and offracture criteria relevant in a nite element simulation of polypro-pylenes structure behaviour usually used in industry. We will rstpresent some information that will glimpse the signicance of theeffects combines the formulation and implementation of the poly-propylene behaviour law.After a presentation of the background and the general princi-ples, we show the performance of a numerical approach.2. Theoretical principle of polymers deformationThe modeling of polymers is based on the rst step the Voigtand Maxwell reological model types. These models allow tocombine with the viscoelasticity and viscoplasticity, the twobehaviours which is identied in polymers. In the case of semi-crystalline polymers, there are different behaviours of crystalline0261-3069/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2009.04.043* Corresponding author.E-mail address: (H.M. Meddah).Materials and Design 30 (2009) 41924199Contents lists available at ScienceDirectMaterials and Designj our nal homepage: www. el sevi er . com/ l ocat e/ mat desand amorphous phases. The models employed a unique equationfor different behaviours of two phases [8]. Other models, basedon the equation of Eyring [9] can response rubber elasticity ofthe amorphous phase as far as deformation of the crystalline phase[10]. Other models have been chosen to introduce solely on themodeling of crystalline texture [1113]. The polymer is then con-sidered as a cluster comprised of polycrystalline crystallites ran-domly assigned. The crystalline phase is supposed to haveviscoplastic behaviour; the crystalline lamellae are distorted byshearing, parallel or perpendicular to the chains [1416]. In orderto take into account the contribution of the amorphous phase tothe plastic deformation implies an undervaluation plastic hard-ness, particularly in shearing. This will be checked that quantityof amorphous phase will be signicant in polymer.3. ExperimentThe analysis of polymer behaviour shows that a relevant mod-eling behaviour must be based on a mechanical approach, or atleast their mechanical effect.3.1. MaterialsA commercial polypropylene PP homopolymer supplied byGoodfellow is used. The number-average molecular weight andthe weight-average molecular weight are about Mn = 25 Kg/moland Mw = 180 Kg/mol, respectively. The crystal content is about55%. The glass transition temperature is about 20 C and themelting temperature is almost 170 C. Since the glass transitiontemperature of the amorphous phase is lower than ambient tem-perature, it is in the rubbery state [17].3.2. Behaviour law parameters3.2.1. Experimental methodsThe polypropylene material has initially studied starting fromtensile tests. Experimental uniaxial tensile tests are conducted todetermine the polypropylene constitutive law. The specimen wastaken from a plate. The geometry is corresponded to ASTM D638M1A standard (Fig. 1) such as the overall length is of 100 mm,the width of the barrel is of 35 mm, and in melts of notch is of10 mm.True axial stressstrains were locally measured using a video-extensometer connected to the Instron operating system to workon a wide eld of speeds 0.1, 0.01, and 0.001 mm/s. The mechanicalproperties of polypropylene withdrawn of the tests are presentedin Table 1.Young modulus (E) is given graphically to leave elastic slopes oftensile curves. It can be then considered like apparent because ittakes account of the viscosity of material. In calculations by niteelements, the elastic module chosen will be the apparent module.The Poissons ratio (m) is given to leave slope of longitudinaldeformation curve in function of the side deformation on the samespecimens. In the zone where the deformation remain homoge-neous (before necking), the Poissons ratio average value is 0.4.Just like graphical determination of the Young modulus, deter-mination of (r0) employ serious problems precise details on thetrue axial stressstrain curve. The stress (r0) represents limit be-tween the eld perfectly elastic and the beginning of plasticity.Determination of this limit is difcult to obtain, because of the vis-cosity presence.The different material properties can be drawn from the curve(Fig. 2). Curves who illustrate, respectively, the behaviour frequentat ambient temperature under uniaxial request slow of a semicrystalline polymer reveal three principal steps:Step 1: the beginning of the curve presents a quasi linear highslope at the origin. This part is called viscoelastic response. Asoftening almost absent, for which the yield stress present atransition round progressive.Step 2: deformation becomes irreversible, necking develops. Thisstep is associated partly with unfolding macromolecules underapplied the deformation effect. The necking stabilizes and theminimal diameter of specimen does not decrease almost anymore. Shoulders necking are propagated towards ends of thespecimen. This propagation is translated by a weak variationof load.Fig. 1. Specimens geometry on tension test.Table 1Mechanical properties of the S1 E (MPa) ry (MPa) t Density0.1 2240 52 0.4 0.90.01 2140 420.001 2100 380.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70102030405060708090b3r3+b4r2+b5r1.r. exp(-b1r) 2 . (1-exp(-b2r))3Step 3 Step 2 Step 1True axial Stress (MPa)True axial Strain0,001 /S0,01 /S0,1 /SFig. 2. Tensile true stressstrain curves of polypropylene.H.M. Meddah et al. / Materials and Design 30 (2009) 41924199 4193Step 3: this step, qualied of beginning of structural hardeningand truth similarly dependent on the orientation chains accord-ing to the strain principal dire