THE GROWTH OF THE VOID IN A HYPERELASTIC RECTANOULAR PLATE UNDERA UNIAXIAL EXTENSION

1.IntroductionInrecenttenyears,thevoidformationandgrowthinhyperelasticmaterialhaveattractedmoreandmoreattentionandinterest.Theearliertestsfoundthatthenucleationofthemicro-voidwouldbepossibleduringthestretchingdeformationinmaterandrubbermaterials.However,t…     

应用非线性有限元法对某止水橡皮进行仿真计算

应用有限元分析软件对某具有超弹性、不可压缩性和大变形性质的伸缩式止水橡皮进行应力应变仿真分析计算。考虑到材料非线性、几何非线性和边界非线性等问题。通过对超弹性橡皮材料的大变形性质作定性的分析。和对止水橡皮在安装过程中的变形分析。计算支臂翼头在受到刚性夹板央紧作用下的应力分布、橡皮与钢夹之间的接触应力分布。从而分析止水橡皮的止水性能。     

COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.     

CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS

I. INTRODUCTION The cavitation bifurcation problem, sudden formation and growth of voids in solid materials, haslong attracted much attention because of the fundamental role it plays in the local failure and fractureof materials. For hyperelastic materi…     

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…     

Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void

The effects of void size and hardening in a hexagonal close-packed single crystal containing a cylindrical void loaded by a far-field equibiaxial tensile stress under plane strain conditions are studied. The crystal has three in-plane slip systems oriented at the angle 60° with respect to one another. Finite element simulations are performed using a strain gradient crystal plasticity formulation with an intrinsic length scale parameter in a non-local strain gradient constitutive framework. For a vanishing length scale parameter the non-local formulation reduces to a local crystal plasticity formulation. The stress and deformation fields obtained with a local non-hardening constitutive formulation are compared to those obtained from a local hardening formulation and to those from a non-local formulation. Compared to the case of the non-hardening local constitutive formulation, it is shown that a local theory with hardening has only minor effects on the deformation field around the void, whereas a significant difference is obtained with the non-local constitutive relation. Finally, it is shown that the applied stress state required to activate plastic deformation at the void is up to three times higher for smaller void sizes than for larger void sizes in the non-local material.     

板中正交静应力与任意方向兰姆波波速的关系

运用部分波分析法(或子波分析)理论推导了在正交静应力下,板中任意方向的Lamb波的频散方程,给出了任意方向Lamb波波速、正交静应力和频率之间的关系. 进行了数值计算并讨论了对称方向的Lamb波波速对单向静应力的依赖关系,为将Lamb波用于应力测量提供了理论依据.      

Finite strains at the tip of a crack in a sheet of hyperelastic material: III. General bimaterial case

In this last in a series of three papers, we summarize an asymptotic analysis of the near-tip stress and deformation fields for an interface crack between two sheets of Generalized Neo-Hookean materials. This investigation, which is consistent with the nonlinear elastostatic theory of plane stress, allows for an arbitrary choice, on both sides of the three parameters characterizing this class of hyperelastic materials. The first three terms of the approximation series are obtained, showing the existence of a non-oscillatory and contact-free solution to the interface crack problem. The analytical results are compared with a full-field solution obtained numerically using the finite element method.     

Thin Hyperelastic sheets of compressible material: Field equations, airy stress function and an application in fracture mechanics

The equations of the equilibrium theory of thin hyperelastic sheets under plane stress condition and the associated Airy stress function are deduced for a compressible Mooney-Rivlin material. Such an analysis is then employed to formulate a nonlinear fracture mechanics problem. By means of an asymptotic procedure, the deformation and stress singular fields in proximity of the crack-tip are computed.     

Optimization of the stored energy and coaxiality of strain and stress in finite elasticity

The strain energy density of a hyperelastic anisotropic body which is rotated before being subjected to a given but arbitrary deformation is viewed as a smooth function defined on the group of rotations, parametrized by the deformation gradient. It is shown that the critical points of this function correspond to rotations which, when composed with the prescribed deformation, yield a total strain tensor which is coaxial with the corresponding stress. For any type of material symmetry, there are at least two such rotations. Coaxiality of stress and strain for all deformations is shown to be a sufficient condition for the isotropicity of hyperelastic materials.Research supported by GNFM of CNR (Italy).     

Cylindrical void in a rigid-ideally plastic single crystal III: Hexagonal close-packed crystal

The analytical solution is derived for the plane strain stress field around a cylindrical void in a hexagonal close-packed single crystal with three in-plane slip systems oriented at the angle π/3 with respect to one another. The critical resolved shear stress on each slip system is assumed to be equal. The crystal is loaded by both internal pressure and a far-field equibiaxial compressive stress. The deformation field takes the form of angular sectors, called slip sectors, within which only one slip system is active; the boundaries between different sectors are radial lines. The stress fields are derived by enforcing equilibrium and a rigid, ideally plastic constitutive relationship, in the spirit of anisotropic slip line theory. The results show that each slip sector is divided into smaller regions denoted as stress sectors and the stress state valid within each stress sector is derived. It is shown that stresses are unique and are continuous within stress sectors and across stress sector boundaries, but the gradient of stresses is not continuous across the boundaries between stress sectors. The solution shows self-similarity in that the stresses over the entire domain can be determined from the stresses within a small region adjacent to the void by invoking certain scaling and symmetry properties. In addition, the stress state exhibits periodicity along logarithmic spirals which emanate from the void. The results predict that the mean value of in-plane pressure required to activate plastic deformation around a void in a single crystal can be higher than that necessary for a void in an isotropic material and is sensitive to the orientation of the slip systems relative to the void.     

Effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials

Up to now, the indentation of hyperelastic soft materials has not been completely understood. In this paper, the spherical indentation on hyperelastic soft solids was systematically investigated through theoretical analysis and finite element method (FEM). The validation and application of the Hertzian load-displacement relation for indentation of hyperelastic soft materials were clarified, the effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials were analyzed and discussed. It was found that the complicated indentation behaviors of hyperelastic soft solids mainly depended on the coupling interactions of large deformation and material nonlinearity. Besides, we proposed two new nonlinear elastic contact models to separate the effects of large deformation and material nonlinearity on spherical indentation responses of hyperelastic soft solids. Our efforts might help to enhance the understanding of hyperelastic indentation problems and provided necessary instructions for the mechanical characterization of hyperelastic soft materials.     

A parametric-experimental study of void growth in superplastic deformation

Substantial void growth in metals constitutes a problem in many industrial operations that utilize superplastic deformation. This is because of the likelihood of material failure due to such growth. Hence, there is a need to study void growth mechanisms in an effort to understand the parameters governing it. In this work, numerical and experimental studies of void growth, and the parameters that affect it, in a superplastically deforming (SPD) metal have been performed. In the numerical studies, using the finite-element method, a 1×2 sized thin plate (i.e. plane stress conditions) of a viscoplastic material with pre-existing holes has been subjected to a constant extension rate. The experimental studies were performed under similar conditions to the numerical ones and provided for qualitative comparison. The parameters affecting void growth in SPD are: m (the strain-rate sensitivity), void size (i.e. diameter) and the number (density) of existing voids. The results showed that increased m values produced strengthening and decreased the rate of void growth. In addition, larger initial void size (or, equivalently, a larger initial void fraction) had the effect of weakening the specimen through causing accelerated void growth. Finally, multiple holes had the effect of increasing the metal ductility by reducing the extent of necking and its onset. This was realized through diffusing the plastic deformation at the different hole sites and reducing the stress concentration. The numerical results were in good qualitative agreement with the experiment and suggested the need to refine existing phenomenological void growth models to include the dependence on the void fraction.     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.     

A thermodynamically consistent large deformation elastic–viscoplastic model with directional tensile failure

The main objective of this paper is to develop a continuum model for directional tensile failure that can simulate weakening and void formation due to tensile failure. Directionality in the model allows simulation of weakening to tension applied in one direction, without weakening to subsequent tension applied in perpendicular directions. The model is developed within the context of a properly invariant non-linear thermomechanical theory. Specifically, it is shown how the model can be combined with general constitutive equations for porous compaction and dilation, as well as viscoplasticity. The thermoelastic response is hyperelastic, with the stress being determined by derivatives of the Helmholtz free energy, and the material is considered to be elastically isotropic. In particular, it is assumed that the rate of inelasticity due to tensile failure is coaxial with the tensor measure of elastic deformation (and hence stress). This causes the rate of dissipation to take a particularly simple form which can be shown to satisfy the second law of thermodynamics. A numerical procedure for integrating these evolution equations is proposed and a number of examples are considered to explore the response of the model to different loading histories.     

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields (K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals

The fracture toughness of ductile materials depends upon the ability of the material to resist the growth of microscale voids near a crack tip. Mechanics analyses of the elastic–plastic deformation state around such voids typically assume the surrounding material to be isotropic. However, the voids exist predominantly within a single grain of a polycrystalline material, so it is necessary to account for the anisotropic nature of the surrounding material. In the present work, anisotropic slip line theory is employed to derive the stress and deformation state around a cylindrical void in a single crystal oriented so that plane strain conditions are admitted from three effective in-plane slip systems. The deformation state takes the form of angular sectors around the circumference of the void. Only one of the three effective slip systems is active within each sector. Each slip sector is further subdivided into smaller sectors inside of which it is possible to derive the stress state. Thus the theory predicts a highly heterogeneous stress and deformation state. In addition, it is shown that the in-plane pressure necessary to activate plastic deformation around a cylindrical void in an anisotropic material is significantly higher than that necessary for an isotropic material. Experiments and single crystal plasticity finite element simulations of cylindrical voids in single crystals, both of which exhibit a close correspondence to the analytical theory, are discussed in a companion paper.     

Deformation, stress state and thermodynamic force for a growing void in an elastic–plastic material

The growth of a spherical void in an elastic–plastic body, subjected to external pressure or tension and a gas pressure as well as a surface stress at the void surface, is investigated. The deformation, strain and stress state in the full body is presented. In addition, the local and global energy terms are calculated. Finally the total thermodynamic force on the void surface as well as the total dissipation are evaluated and compared allowing the calculation of the mechanical contribution to void growth due to diffusion of vacancies generated by plastification or irradiation.