Cavitation and morphological changes in polypropylene deformed at elevated temperatures

Polypropylene (PP) thick films were subjected to tensile drawing at various temperatures from the room temperature to 100 °C. Morphological alterations during drawing were followed by wide‐angle X‐ray scattering, small‐angle X‐ray scattering, and scanning electron microscopy (SEM) of sectioned and etched samples, volume strain measurement, and light transparency measurement at various level of strain. The morphological observations were paralleled with stress–strain determination. Samples drawn at 25 and 40 °C undergo severe cavitation contributing to their volume increase up to 90–95%. The volume increase contributes greatly to the engineering strain. PP drawn at 70 and 100 °C does not cavitate. At the strain up to 1.2, a high lamellae orientation is observed in SEM, whereas the 2D WAXS patterns show in contrary circular diffraction rings indicating low orientation of crystals. The rotation of lamellae toward drawing direction is associated with reverse rotation of chains in crystals due to fine chain slips. These two rotations in opposite directions counterbalance resulting in a much weaker crystal orientation than expected from the SEM images. Noncavitating samples retain their translucency up to a high strain. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1271–1280, 2010     

Nanofoam porosity by infrared spectroscopy

Infrared spectroscopy has been used to determine the porosity of polymer nanofoams produced from block copolymers of an aromatic polyimide with either poly(propylene oxide) or poly(α-methyl styrene). It is shown that, with an independent measurement of the film thickness, both the absorption bands and the interference fringes can yield an accurate measure of the void content. The results obtained are in quantitative agreement with density gradient methods. © 1995 John Wiley & Sons, Inc.     

Cavitation criterion for rubber materials: A review of void‐growth models

The principal criteria used to predict cavitation in rubber materials are reviewed, and experimental evidence is recalled for three different configurations: in the bulk, in the vicinity of a rigid particle, and in small rubber particles embedded in a rigid polymer matrix. Two major classes of cavitation criteria are defined, those based on an elastic instability (i.e., related to a stress state and finite strains) and those based on the energy balance (i.e., involving surface energies). The different criteria, in which various hyperelastic behavior laws are considered, are compared in numerical applications, and the tendencies are derived. The particular case of accounting for the surface tension of the rubber, a parameter common to the stress state and the energy balance, is treated in detail. It appears that the understanding of the genesis of a microcavity in a rubber material, when no pre‐existing flaw is assumed, still constitutes a difficulty for the analysis of mechanical damage in polymers containing a rubber phase. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2081–2096, 2001     

The Study of Cavitation in HDPE Using Time Resolved Synchrotron X-ray Scattering During Tensile Deformation

Real time synchrotron Small-Angle and Wide-Angle X-ray Scattering was performed during the tensile deformation of a high-density polyethylene copolymer. The changes of the structure in the crystalline and in the amorphous domains were followed during the three characteristic stages of the load-displacement curves: The elastic stage and the plastic range composed of the stage of the lowering load in the force-displacement-curve (yielding) and the strain hardening. Competitive phenomena like crystallite fragmentation and cavitation were found to occur simultaneously in the phase of lowering the load but at different length scale. We prove that the void formation occurs mainly during yielding. During strain hardening there was no further increase of the void volume fraction, only changes in void size.     

Transversely isotropic hyper-elastic material rectangular plate with voids under a uniaxial extension

IntroductionHyper_elasticmaterials ,suchasrubberandpolyurethane ,havemanyexcellentpropertiesandhavebeenusedwidelyinalmostallregionsofevery_daylifeandindustrialmanufacturing .Thevoidformationandgrowthinhyper_elasticmaterialsduetotheinstabilityofmaterialsplayafundamentalroleinthemechanismsofmaterialfractureandfailure.SotheproblemhasgotacertaindevelopmentinthepasttwentyyearsandtherecentreviewisthatofHorgan[1] .Chou_WangandHorgan[2 ] ,RenandCheng[3 ,4] studiedthegrowthofacentervoidinthecylindero…     

Flux-driven cellular precipitation in open system to form porous Cu3Sn

Recently, a new morphology of porous Cu₃Sn with lamellar structure is observed. Several possible explanations of the formation are proposed and compared. The most reasonable one seems to be the one based on a theory of flux-driven cellular precipitation in open system. Outflux of Sn from Cu₆Sn₅ generates simultaneously supersaturation with vacancies and with copper leading to the eutectoid-like transformation β → α + γ (where γ is void). The transformation is complete due to a complete outflux of Sn from the Cu₆Sn₅ phase. Simple formulae for prediction of the lamellar structure parameters and the propagation velocity are obtained and compared reasonably with experimental data. The suggested model can be interpreted as one more case of the flux-driven phase transformations in open systems.     

Thermodynamic theory for porous piezoelectric materials

In the context of a temperature rate-dependent formulation of thermodynamics for porous piezoelectric materials, we derive the basic equations of the linear theory by discussing restrictions on constitutive equations with the help of an antropy production inequality proposed by Green and Laws. Some basic theorems concerning reciprocity and uniqueness are also established.

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Sommario Nell'ambito di una teoria della termoelasticità generalizzata si stabiliscono le equazioni di base per mezzi piezoelecttrici porosi. Si studiano, inoitre, alcuni teoremi di reciprocità e unicità.

     

Approximate yield criteria for anisotropic metals with prolate or oblate voidsCritères macroscopiques pour des métaux plastiques anisotropes contenant des cavités non sphériques

Following the study of Gologanu et al. (1997) which has extended the well-known approach of Gurson (1975), we propose approximate yield criteria for anisotropic plastic voided metals containing non spherical cavities. The plastic anisotropy of the matrix is described by means of Hill's quadratic criterion. The procedure to establish the closed form expression of approximate macroscopic criteria, in which void shape and plastic anisotropic effects are included, is detailed. The new criteria allow us to recover existing results in the cases of spherical and cylindrical voids in an Hill type plastic matrix. Moreover, they agree with previous criteria for non spherical voids in an isotropic plastic matrix. Finally, for validation purposes, we provide, in the general case of non spherical cavities in the anisotropic matrix, a comparison with the numerical exact two field criteria. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006).     

Mode I fracture of sheet metal

The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5-). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of , both fracture and necking contributions have the same order of magnitude in most of the metals investigated.A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.     

Energy principles in theory of elastic materials with voids

According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author^[1], various energy principles in theory of elastic materials with voids can be established systematically. In this paper, an important integral relation is given, which can be considered essentially as the generalized pr. inciple of virtual work. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work in theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field generalized variational principles, and the principle of minimum potential and complementary energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly. The project supported by the National Natural Science Foundation of China