Evolution of plastic anisotropy in amorphous polymers during finite straining

The large strain deformation response of amorphous polymers results primarily from orientation of the molecular chains within the polymeric material during plastic straining. Molecular network orientation is a highly anisotropic process, thus the observed mechanical response is strongly a function of the anisotropic state of these materials. Through mechanical testing and material characterization, the nature of the evolution of molecular orientation under different conditions of state of strain is developed. The role of developing anisotropy on the mechanical response of these materials is discussed in the context of assessing the capabilities of several models to predict the state of deformation-dependent response. A three-dimensional rubber elasticity spring system that is capable of capturing the state of deformation dependence of strain hardening is used to develop a tensorial internal state variable model of the evolving anisotropic polymer response. This fully three-dimensional constitutive model is shown to be successfully predictive of the true stress vs. true strain data obtained in our isothermal uniaxial compression and plane strain compression experiments on amorphous polycarbonate (PC) and polymethylmethacrylate (PMMA) at moderate strain rates. A basis is established for providing the polymer designer with the ability to predict the flow strengths and deformation patterns of highly anisotropic materials. A companion paper by Arruda, Boyce, and Quintus-Bosz [in press] shows how the model developed herein is used to predict various anisotropic aspects of the large strain mechanical response of preoriented materials. Additional work has been done to extend the model to include the effects of strain rate and temperature in Arruda, Jayachandran, and Boyce [in press].     

Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: Experiments and constitutive modelling

The mechanical stress-strain behaviour of polyethylene (PE) materials under finite strains is studied both experimentally and theoretically. In order to gain insight into the structure and physical properties of investigated PE materials, a series of thermal (DSC and DMTA) and microstructural (small-angle X-ray scattering and AFM) characterizations have been undertaken. The influence of crystallinity on the various features of the tensile stress-strain response is considered over a large strain range, implying thermoplastic-like to elastomer-like mechanical behaviour. A physically-based hyperelastic-viscoplastic approach was adopted to develop a pertinent model for describing the mechanical behaviour of PE materials under finite strains. The semicrystalline polymer is being treated as a heterogeneous medium, and the model is based on a two-phase representation of the microstructure. The effective contribution of the crystalline and amorphous phases to the overall intermolecular resistance to deformation is treated in a composite framework, and coupled to a molecular network resistance to stretching and chain orientation capturing the overall strain hardening response. In order to extract the individual constitutive response of crystalline and amorphous phases, a proper identification scheme based on a deterministic approach was elaborated using the tensile test data of PE materials under different strain rates. Comparisons between the constitutive model and experiments show fair agreement over a wide range of crystallinities (from 15% to 72%) and strain rates. The constitutive model is found to successfully capture the important features of the observed monotonic stress-strain response: the thermoplastic-like behaviour for high crystallinity includes a stiff initial response, a yield-like event followed by a gradual increase of strain hardening at very large strains; for the elastomer-like behaviour observed in the low crystallinity material, the strain hardening response is largely predominant. Strain recovery upon unloading increases with decreasing crystallinity: this is quantitatively well reproduced for high crystallinity materials, whereas predictions significantly deviate from experiments at low crystallinity. Model refinements are finally proposed in order to improve the ability of the constitutive equations to predict the nonlinear unloading response whatever the crystal content.     

ZrCuNiAlAg块体非晶合金JH-2模型研究

为了更好的进行ZrCuNiAlAg块体非晶合金药型罩的爆炸成形及侵彻仿真研究,首要就是建立其材料模型。本文结合ZrCuNiAlAg块体非晶合金力学性能试验结果计算得到了材料的JH-2模型参数,研究确定了ZrCuNiAlAg块体非晶合金JH-2模型。为了验证ZrCuNiAlAg块体非晶合金JH-2模型的准确性,采用Autodyn建立了平板撞击试验有限元模型,模拟了ZrCuNiAlAg块体非晶合金材料在高压、高应变率等环境条件下的变形过程,仿真计算得到的靶板背面自由面粒子速度与试验结果相比,速度平均偏差均在3%以内,表明ZrCuNiAlAg块体非晶合金JH-2模型能很好的描述该材料在大变形、高应变率、高压等环境条件下的力学行为,验证了ZrCuNiAlAg块体非晶合金JH-2模型准确性。     

Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates

A robust physically consistent three-dimensional constitutive model is developed to describe the finite mechanical response of amorphous polymers over a wide range of temperatures and strain rates, including the rubbery region and for impact loading rates. This thermomechanical model is based on an elastic–viscoplastic rheological approach, wherein the effects of temperature, strain rate, and hydrostatic pressure are accounted for. Intramolecular, as well as intermolecular, interactions under large elastic–inelastic behavior are considered for the mechanisms of deformation and hardening. For a wide range of temperatures and strain rates, our simulated results for poly(methyl methacrylate) (PMMA) and polycarbonate (PC) are in good agreement with experimental observations.     

半晶态聚合物拉伸变形的微观机理

应用大规模分子动力学方法,采用粗粒化聚乙烯醇模型,模拟了晶区与非晶区随机交杂的半晶态聚合物模型系统,研究了半晶态聚合物在单轴拉伸变形过程中的应力-应变行为和微观结构演变.应力-应变曲线表现出4个典型变形阶段:弹性变形、屈服、应变软化和应变强化.在拉伸变形过程中,主要存在晶区折叠链之间的滑移、晶区破坏、非晶区的解缠结,以及分子链沿拉伸方向重新取向等4种主要的微结构演变形式.在屈服点附近,晶区分子链之间排列紧密程度减小而发生滑移,之后晶区变化需要的应力变小,从而形成应变软化现象.随着应变的增大,经各分子链段协同作用使非晶区分子链的解缠结和重新取向行为扩展到相对宏观尺度,导致拉伸应力增大而形成应变强化现象.      

ORIGIN OF HEAT EFFECTS AND SHEAR MODULUS CHANGES OF A Cu-BASED AMORPHOUS ALLOY 1)

剪切模量在非晶合金黏性流动、扩散及结构弛豫等行为中起着重要作用. 宏观剪切弹性决定非晶合金热流变化.探索非晶合金在结构弛豫和玻璃转变过程中宏观力学性能与热流的关联有助于理解其力学行为起源. 本研究基于自间隙理论对Cu$_{49}$Hf$_{42}$Al$_{9}$非晶合金热流、剪切模量及黏度进行研究,建立剪切模量与热流之间的关联. 通过测量剪切模量精确测定自间隙缺陷浓度演化规律.从能量角度出发,通过激活能图谱探索自间隙缺陷浓度对非晶合金热力学性能的影响. 借助于动态力学分析仪研究非晶合金从室温到过冷液相区的动态弛豫行为,探索物理时效引起的结构弛豫以及内耗演化规律. 研究结果表明,自间隙理论可准确描述非晶合金的弛豫动力学、剪切软化及结构弛豫诱导的力学行为. 结合热流数据可以很好描述铸态和弛豫态非晶合金剪切模量随温度演化过程,激活能图谱直观表述了单位激活能可激活的自间隙缺陷浓度. 自间隙缺陷在结构弛豫中湮灭,表现为玻璃体系结构向更稳定状态迁移.在玻璃化转变过程中,缺陷浓度显著升高伴随热吸收,表现为原子大规模协同运动和剪切软化. 物理时效诱导非晶合金内耗和原子移动性降低. 过冷液相区内原子移动性高至消除了结构弛豫影响.     

铜基非晶合金热效应和剪切模量变化起源

剪切模量在非晶合金黏性流动、扩散及结构弛豫等行为中起着重要作用. 宏观剪切弹性决定非晶合金热流变化.探索非晶合金在结构弛豫和玻璃转变过程中宏观力学性能与热流的关联有助于理解其力学行为起源. 本研究基于自间隙理论对Cu$_{49}$Hf$_{42}$Al$_{9}$非晶合金热流、剪切模量及黏度进行研究,建立剪切模量与热流之间的关联. 通过测量剪切模量精确测定自间隙缺陷浓度演化规律.从能量角度出发,通过激活能图谱探索自间隙缺陷浓度对非晶合金热力学性能的影响. 借助于动态力学分析仪研究非晶合金从室温到过冷液相区的动态弛豫行为,探索物理时效引起的结构弛豫以及内耗演化规律. 研究结果表明,自间隙理论可准确描述非晶合金的弛豫动力学、剪切软化及结构弛豫诱导的力学行为. 结合热流数据可以很好描述铸态和弛豫态非晶合金剪切模量随温度演化过程,激活能图谱直观表述了单位激活能可激活的自间隙缺陷浓度. 自间隙缺陷在结构弛豫中湮灭,表现为玻璃体系结构向更稳定状态迁移.在玻璃化转变过程中,缺陷浓度显著升高伴随热吸收,表现为原子大规模协同运动和剪切软化. 物理时效诱导非晶合金内耗和原子移动性降低. 过冷液相区内原子移动性高至消除了结构弛豫影响.      

纳秒脉冲激光烧蚀非晶合金的研究进展

非晶合金是一类原子排列处于长程无序状态的新型结构材料，具有一系列优异的力学和物理性能，从而有望应用于国防、空天等关键领域。在这些领域的应用中，非晶合金易受到强激光或空间等离子体的作用而失效。同时，非晶合金在高能激光辐照下的结构响应本身也极具科学意义。因此，近年来这方面的研究得到了越来越多的关注。本文将重点关注纳秒脉冲激光对非晶合金在大气和水环境下的烧蚀，针对熔化、流体动力学失稳、爆炸沸腾、气泡动力学等烧蚀过程中的几种典型现象，简要介绍相关的实验和理论研究进展。最后，对未来值得进一步研究的方向进行了概述。     

A theory of amorphous solids undergoing large deformations,with application to polymeric glasses

This paper develops a continuum theory for the elastic–viscoplastic deformation of amorphous solids such as polymeric and metallic glasses. Introducing an internal-state variable that represents the local free-volume associated with certain metastable states, we are able to capture the highly non-linear stress–strain behavior that precedes the yield-peak and gives rise to post-yield strain softening. Our theory explicitly accounts for the dependence of the Helmholtz free energy on the plastic deformation in a thermodynamically consistent manner. This dependence leads directly to a backstress in the underlying flow rule, and allows us to model the rapid strain-hardening response after the initial yield-drop in monotonic deformations, as well as the Bauschinger-type reverse-yielding phenomena typically observed in amorphous polymeric solids upon unloading after large plastic deformations. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program. Using this finite-element program, we apply the specialized equations to model the large-deformation response of the amorphous polymeric solid polycarbonate, at ambient temperature and pressure. We show numerical results to some representative problems, and compare them against corresponding results from physical experiments.     

Multi-scale modelling of strongly heterogeneous 3D composite structures using spatial Voronoi tessellation

3D composite materials are characterized by complex internal yarn architectures, leading to complex deformation and failure development mechanisms. Net-shaped preforms, which are originally periodic in nature, lose their periodicity when the fabric is draped, deformed on a tool, and consolidated to create geometrically complex composite components. As a result, the internal yarn architecture, which dominates the mechanical behaviour, becomes dependent on the structural geometry. Hence, predicting the mechanical behaviour of 3D composites requires an accurate representation of the yarn architecture within structural scale models. When applied to 3D composites, conventional finite element modelling techniques are limited to either homogenised properties at the structural scale, or the unit cell scale for a more detailed material property definition. Consequently, these models fail to capture the complex phenomena occurring across multiple length scales and their effects on a 3D composite’s mechanical response. Here a multi-scale modelling approach based on a 3D spatial Voronoi tessellation is proposed. The model creates an intermediate length scale suitable for homogenisation to deal with the non-periodic nature of the final material. Information is passed between the different length scales to allow for the effect of the structural geometry to be taken into account on the smaller scales. The stiffness and surface strain predictions from the proposed model have been found to be in good agreement with experimental results.The proposed modelling framework has been used to gain important insight into the behaviour of this category of materials. It has been observed that the strain and stress distributions are strongly dependent on the internal yarn architecture and consequently on the final component geometry. Even for simple coupon tests, the internal architecture and geometric effects dominate the mechanical response. Consequently, the behaviour of 3D woven composites should be considered to be a structure specific response rather than generic homogenised material properties.     

金属材料的率-温耦合响应与动态本构关系综述

金属材料在冲击、爆炸等高应变率加载下的塑性流动行为具有不同于静载下的率-温耦合性和微观机制。航空航天、航海、能源开采、核工业、公共安全、灾害防治等方面的金属结构设计与性能评估需要进行大量的动载实验和数值模拟,建立准确的材料动态本构模型是结构数值模拟可靠性的基础和关键。本文中,总结了金属材料的率-温耦合变形行为及内在机理,回顾了金属动态本构关系研究的起源与发展脉络,分别针对唯象模型、具有物理基础的模型和人工神经网络模型进行了详细介绍和横向比较。唯象模型和人工神经网络模型分别因易应用和高预测精度而受到青睐,基于物理概念的宏观连续介质模型可以描述体现内部演化的真实物理量,从而涵盖更大的应变范围,更好地反映应变率、温度和应变的影响机制。     

基于微观结构非均匀性的非晶合金力学行为

非晶合金弛豫/晶化、玻璃转变、塑性变形等热力学和动力学行为都与其固有的结构非均匀性密切相关. 但是, 由于淹没在亚稳的长程无序结构中, 探究非晶合金的结构非均匀性十分困难. 尤其, 非晶合金微观结构非均匀性与其力学性能之间的本征关联是一个亟待解决的重要科学问题. 本文基于多尺度时空下的力学激励阐述非晶合金微观结构非均匀性特征与演化规律. 从实验、理论和数值模拟方面出发, 梳理了非晶合金微观结构非均匀性与弛豫机制和力学行为之间的关联. 最后, 针对非晶合金微观结构非均匀性与其物理/力学性能研究的方向提出了建议和展望.      

An effective temperature theory for the nonequilibrium behavior of amorphous polymers

Amorphous polymers lack an organized microstructure, yet they exhibit structural evolution, where physical properties change with time, temperature, and inelastic deformation. To describe the influence of structural evolution on the mechanical behavior of amorphous polymers, we developed a thermomechanical theory that introduces the effective temperature as a thermodynamic state variable representing the nonequilibrium configurational structure. The theory couples the evolution of the effective temperature and internal state variables to describe the temperature-dependent and rate-dependent inelastic response through the glass transition. We applied the theory to model the effect of temperature, strain rate, aging time, and plastic pre-deformation on the uniaxial compression response and enthalpy change with temperature of an acrylate network. The results showed excellent agreement with experiments and demonstrate the ability of the effective temperature theory to explain the complex thermomechanical behavior of amorphous polymers.     

非晶态固体的结构可以决定性能吗?

晶态固体的力学性能与塑性变形主要由结构缺陷, 比如位错的运动决定. 而在非晶态固体中结构如何决定性能, 仍然是固体力学、材料学和凝聚态物理学共同关心但尚未解决的核心问题之一.传统材料学研究的经典范式为"结构决定性能". 遵循这一信条, 已经有大量的实验表征与理论、模拟研究, 尝试将非晶态固体的某种结构特征与性能建立一一对应关系. 但是, 科学界对于非晶固体结构-性能关系成立与否, 以及背后隐藏的规律知之甚少. 本文针对非晶态固体的变形机制以及其微结构特征, 基于分子动力学模拟, 定量评估短程简单结构与中长程复杂结构在决定非晶态固体动力学性能方面的效用. 通过海量抽样每种具体玻璃结构的激活能(标识激发难易程度), 尝试将结构参数与激活能建立定量关系, 从而揭示出非晶态固体结构-性能关系的隐藏主控因素为结构的空间关联, 受限比几何结构本身更关键. 只有某种结构在空间上呈现亚纳米级的空间关联长度, 这种完备结构才有可能有效地决定非晶态固体的力学性能, 而短程简单结构则无效. 进一步, 给出了评价非晶态固体结构预测性能有效性的普适定量方法, 为建立广义无序物质的结构-性能关系提供了筛选准则.      

On modeling the micro-indentation response of an amorphous polymer

Interest in instrumented indentation experiments as a means to estimate mechanical properties has grown rapidly in recent years. Although numerous nano/micro-indentation experimental studies on polymeric materials have been reported in the literature, a corresponding methodology for extracting material property information from the experimental data does not exist. This situation for polymeric materials exists primarily because baseline numerical analyses of sharp indentation using appropriate large deformation constitutive models for the nonlinear viscoelastic–plastic response of these materials appear not to have been previously reported in the literature. An existing, widely used theory for amorphous polymers (e.g. [Boyce, M., Parks, D., Argon, A.S., 1988. Large inelastic deformation of glassy polymers. Part 1: Rate dependent constitutive model. Mechanics of Materials 7, 15–33; Arruda, E.M., Boyce, M.C., 1993. Evolution of plastic anisotropy in amorphous polymers during finite straining. International Journal of Plasticity 9, 697–720]) has been recently found to lack sufficient richness to enable one to quantitatively reproduce the major features of the indentation load-versus-depth curves for some common amorphous polymers [Gearing, B.P., 2002. Constitutive equations and failure criteria for amorphous polymeric solids. Ph.D. thesis, Massachusetts Institute of Technology].This study develops a new continuum model for the viscoelastic–plastic deformation of amorphous polymeric solids. We have applied the constitutive model to capture salient features of the mechanical response of the amorphous polymeric solid poly(methyl methacrylate) (PMMA) at ambient temperature and stress states under which this material does not exhibit crazing. We have conducted compression-tension strain-controlled experiments, as well as stress-controlled compression-creep experiments, and these experiments are used to calibrate the material parameters in the constitutive model for PMMA.We have implemented our constitutive model in a finite-element computer program, and using this finite-element program we have simulated micro-indentation experiments on PMMA. We show that our constitutive model and finite element simulations reproduce the experimentally-measured indentation load-versus-depth response with reasonable accuracy.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

On the derivation of structural models with general thermomechanical prestress

The vibrating behaviour of thin structures is affected by prestress states. Hence, the effects of thermal prestress are important research subjects in view of ambient vibration monitoring of civil structures. The interaction between prestress, geometrically non-linear behaviour, as well as damping and its coupling with the aforementioned phenomena has to be taken into account for a comprehensive understanding of the structural behaviour. Since the literature on this subject lacks a clear procedure to derive models of thin prestressed and damped structures from 3D continuum mechanics, this paper presents a new derivation of models for thin structures accounting for generic prestress, moderate rotations and viscous damping. Although inspired by classical approaches, the proposed procedure is quite different, because of (i) the definition of a modified Hu–Washizu (H-W) functional, accounting for stress constraints associated with Lagrange multipliers, in order to derive lower-dimensional models in a convenient way; (ii) an original definition of a (mechanical and thermal) strain measure and a rotation measure enabling one to identify the main terms in the strain energy and to derive a cascade of lower-dimensional models (iii) a new definition of “strain–rotation domains” providing a clear interpretation of the classical assumptions of “small perturbations” and “small strains and moderate rotations”; (iv) the introduction of a pseudo-potential with stress constraints to account for viscous damping. The proposed procedure is applied to thin beams.     

Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers—polycarbonate and poly(methyl methacrylate)—at strain rates ranging from 10⁻⁴ to 10⁴ s⁻¹. This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on the servo-hydraulic machine (10⁻⁴ to 1 s⁻¹) and the split-Hopkinson pressure bar (10³ to 10⁴ s⁻¹) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the β-transition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.     

A Fully Symbolic Model of Multibody Systems Containing Flexible Plates

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multi-body dynamics and the area of structural mechanics and vibration theory. As regards the multibody approach, recursive formulations in relative coordinates are quite suitable and efficient for a large variety of applications. Such a formalism is developed here for a general multibody system containing flexible plates and in such a way that its full symbolic generation is possible within the ROBOTRAN program [1].