Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

Model identification and FE simulations: Effect of different yield loci and hardening laws in sheet forming

The bi-axial experimental equipment [Flores, P., Rondia, E., Habraken, A.M., 2005a. Development of an experimental equipment for the identification of constitutive laws (Special Issue). International Journal of Forming Processes] developed by Flores enables to perform Bauschinger shear tests and successive or simultaneous simple shear tests and plane strain tests. Flores investigates the material behavior with the help of classical tensile tests and the ones performed in his bi-axial machine in order to identify the yield locus and the hardening model. With tests performed on one steel grade, the methods applied to identify classical yield surfaces such as [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic materials. Proceedings of the Royal Society of London A 193, 281–297; Hosford, W.F., 1979. On yield loci of anisotropic cubic metals. In: Proceedings of the 7th North American Metalworking Conf. (NMRC), SME, Dearborn, MI, pp. 191–197] ones as well as isotropic Swift type hardening, kinematic Armstrong–Frederick or Teodosiu and Hu hardening models are explained. Comparison with the Taylor–Bishop–Hill yield locus is also provided. The effect of both yield locus and hardening model choices is presented for two applications: plane strain tensile test and Single Point Incremental Forming (SPIF).     

含材料非线性的复合材料单钉接头累积损伤分析

发展了静拉伸复合材料接头层合板三维逐渐损伤模型,考虑了单层复合材料在材料1-2面及3-1面上具有明显非线性剪切应力-应变关系的叠层非线性效应,结合有限元技术即应力分析、失效判定准则及损伤过程中材料性能退化等,对接头层合板损伤扩展进行了模拟,结果表明考虑材料非线性的影响与实验结果吻合更好.     

混合状态Hamiltonian元的半解析解和叠层板的计算

本文给出混合状态方程的一种强有力的半离散半解析解法,并给出了矩形域和叠层板的算例,讨论了可能的发展和应用。     

Composite and filament models for the mechanical behaviour of elastomeric materials

In this work we present a composite model, which combines the approach of Poisson's function with the filament theory and requires three material parameters. We also suggest the form for a strain-energy function that approximates the constitutive equations of the composite model. Furthermore, a simple asymptotic analysis allows us to reduce the number of material constants to only two, thus, forming a new filament model. The predictive capability of the two models to reproduce the mechanical behaviour of elastomeric materials in deformation experiments is evaluated against the extensive data of Kawabata et al. (Macromolecules 14 (1981) 154). The models give excellent agreement in not only uniaxial and equibiaxial but also non-equibiaxial extension. Although being rather more simplistic in comparison with some successful network models involving non-Gaussian chain statistics, the two models conform much more closely to the classical experimental data of Treloar (Trans. Faraday Soc. 40 (1944) 59).     

A Binary Model of textile composites: III high failure strain and work of fracture in 3D weaves

Prior experiments have revealed exceptionally high values of the work of fracture (0.4-) in carbon/epoxy 3D interlock woven composites. Detailed destructive examination of specimens suggested that much of the work of fracture arose when the specimens were strained well beyond the failure of individual tows yet still carried loads . A mechanism of lockup amongst broken tows sliding across the final tensile fracture surface was suggested as the means by which high loads could still be transferred after tow failure. In this paper, the roles of weave architecture and the distribution of flaws in the mechanics of tow lockup are investigated by Monte Carlo simulations using the so-called Binary Model. The Binary Model was introduced previously as a finite element formulation specialised to the problem of simulating relatively large, three-dimensional segments of textile composites, without any assumption of periodicity or other symmetry, while preserving the architecture and topology of the tow arrangement. The simulations succeed in reproducing all qualitative aspects of measured stress-strain curves. They reveal that lockup can indeed account for high loads being sustained beyond tow failure, provided flaws in tows have certain spatial distributions. The importance of the interlock architecture in enhancing friction by holding asperities on sliding fibre tows into firm contact is highlighted.     

Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.     

幂硬化介质中平面应力动态裂纹的尖端弹塑性场

本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。     

零维物质体和微态物质体

在这篇文章里,R.G Muncaster的零维弹性体被推广到一般的高阶零维物质体。从非极连续介质力学理论出发,我们推出了零维物质体的所有平衡方程和热力学不等式。再从这些方程和不等式推出微态物质体的相应平衡方程和热力学不等式。这样,我们在零维物质体理论和微态物质体理论之间建立了一个类似于刚性质点力学和古典非极连续介质力学之间关系的关系。     

Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions

A two parameter asymptotic analysis is employed to investigate some unusual long wave dispersion phenomena in respect of symmetric motion in a nearly incompressible elastic plate. The plate is not subject to the usual classical traction free boundary conditions, but rather has its faces fixed, precluding any displacement on the boundary. The abnormal long wave behaviour results in the derivation of non-local approximations for symmetric motion, giving frequency as a function of wave number. Motivated by these approximations, the asymptotic forms of displacement components established and long wave asymptotic integration is carried out.