多孔材料吸能行为对相对密度和冲击速度的依赖性

多孔材料是一种优异的吸能缓冲材料,但由于其变形模式的非单一性以及动态应力应变曲线的难获取性,其吸能行为对相对密度和冲击速度的依赖性关系还并不完全明朗。本文基于不需要提前作本构假定的波传播法,开展了多孔材料的吸能行为研究。采用多孔材料的细观有限元模型进行Taylor冲击虚拟实验,获取全场质点速度时程曲线,结合Lagrange分析法得到多孔材料的局部应力应变信息,进而探讨了动态吸能性能对材料相对密度和冲击速度的依赖性。研究结果表明多孔材料的吸能行为可依据变形模式分为三个阶段。在冲击模式下,多孔材料单位体积吸能与相对密度成线性增加关系,此时惯性起主导作用;在过渡模式下,惯性的主导作用减弱,单位体积吸能量的增加速率随相对密度的增加而减弱;在准静态模式下,多孔材料只能发生微小的变形,其吸能很少。本文进一步获得了区别于多孔材料准静态应力-应变曲线的动态应力-应变状态曲线,并考察了其与相对密度之间的关系。结果表明：随着相对密度的增加,多孔材料的动态压实应变将变小,而动态塑性平台应力将提高。     

软基体混合胞孔材料的力学性能及抗多次冲击性能

为了探索具有优异吸能性能的软基体混合胞孔材料的力学性能,研究该类材料在多次冲击下的冲击响应和材料的可恢复性,对一种软基体混合胞孔材料—人工软骨仿生超材料（artificial cartilage foam,ACF）进行了不同速度下的单轴拉伸和压缩实验,得到了ACF材料在不同应变率条件下的应力-应变曲线。并利用落锤冲击实验机对ACF材料和另一种软基体混合胞孔材料—发泡聚丙烯材料（expanded polypropylene,EPP）进行了多次冲击下的对比测试,得到了2种材料在单次和多次冲击下的动力学响应。实验结果表明:ACF材料是一种应变率敏感的材料,随着应变率的提升,材料的弹性模量、抗拉强度和抗压强度均逐渐提高;在50 J 冲击能量作用下,ACF材料能够吸收96%以上的冲击能量,远高于EPP材料的70%,ACF材料具有更加优异的吸能性能;5次冲击后ACF材料的最大峰值力、最大变形量和吸能能力几乎不变。相比于EPP材料,ACF材料有良好的可恢复性,且具有稳定的多次抗冲击能力。这些研究为软基体混合胞孔材料在多次冲击防护中的应用提供了实验依据。     

Evaluation of the stress–strain curve of metallic materials by spherical indentation

A method for deducing the stress–strain uniaxial properties of metallic materials from instrumented spherical indentation is presented along with an experimental verification.An extensive finite element parametric analysis of the spherical indentation was performed in order to generate a database of load vs. depth of penetration curves for classes of materials selected in order to represent the metals commonly employed in structural applications. The stress–strain curves of the materials were represented with three parameters: the Young modulus for the elastic regime, the stress of proportionality limit and the strain-hardening coefficient for the elastic–plastic regime.The indentation curves simulated by the finite element analyses were fitted in order to obtain a continuous function which can produce accurate load vs. depth curves for any combination of the constitutive elastic–plastic parameters. On the basis of this continuous function, an optimization algorithm was then employed to deduce the material elastic–plastic parameters and the related stress–strain curve when the measured load vs. depth curve is available by an instrumented spherical indentation test.The proposed method was verified by comparing the predicted stress–strain curves with those directly measured for several metallic alloys having different mechanical properties.This result confirms the possibility to deduce the complete stress–strain curve of a metal alloy with good accuracy by a properly conducted instrumented spherical indentation test and a suitable interpretation technique of the measured quantities.     

An indentation technique for estimating the energy density as fracture toughness with Berkovich indenter for ductile bulk materials

A technique is proposed to estimate the energy density as fracture toughness for ductile bulk materials with an indentation system equipped with a Berkovich indenter based on the theory of plastic deformation energy transforming into the indentation energy of fracture. With progressive increase of penetration loads, the material damage is exhibited on the effective elastic modulus. A quadratic polynomial relationship between the plastic penetration depth and penetration load, and an approximate linear relationship between logarithmic plastic penetration depth and logarithmic effective elastic modulus are exhibited by indentation investigation with Berkovich indenter. The parameter of damage variable is proposed to determine the critical effective elastic modulus at the fracture point. And the strain energy density factor is calculated according to the equations of penetration load, plastic penetration depth and effective elastic modulus. The fracture toughness of aluminum alloy and stainless steel are evaluated by both indentation tests and K_IC fracture toughness tests. The predicted S_cr values of indentation tests are in good agreement with experimental results of CT tests.     

基于能量密度等效的超弹性压入模型与双压试验方法

针对超弹性材料压入问题, 本文基于能量密度中值等效原理, 提出了描述球、平面、锥3类压头独立压入下载荷、深度、压头几何尺寸和Mooney-Rivlin本构关系参数之间关系的半解析超弹性压入模型(semi-theoretical hyperelastic-material indentation model, SHIM), 进而提出了球、平面、锥压入组合的双压试验方法(indentation method due to dual indenters, IMDI). 正向验证表明, 基于系列超弹性材料的本构关系参数, 由SHIM分别预测的球、平面、锥3类压入下的载荷-位移曲线与有限元分析(finite element analysis, FEA)结果之间密切吻合; 反向验证表明, 基于系列超弹性材料的FEA条件本构关系下3类压入的载荷-位移曲线, 由双压试验方法预测的Mooney-Rivlin本构关系与FEA条件本构关系密切吻合. 针对3种超弹性橡胶, 完成了球、平面、锥压入试验, 应用双压试验方法获得的3组Mooney-Rivlin本构关系均与单轴拉伸试验结果吻合良好.      

Representation of the glass-transition in mechanical and thermal properties of glass-forming materials: A three-dimensional theory based on thermodynamics with internal state variables

In the vicinity of the glass transition, glass-forming materials exhibit pronounced frequency-dependent changes in the mechanical material properties, the thermal expansion behaviour and the specific heat. The frequency dependence becomes apparent under harmonic stress, strain or temperature excitations. The Prigogine-Defay ratio is a characteristic number which connects the changes in magnitude of these quantities at the glass transition. In order to represent the thermoviscoelastic properties of glass-forming materials in continuum mechanics, a three-dimensional approach which is based on the Gibbs free energy as thermodynamic potential is developed in this article. The Gibbs free energy depends on the stress tensor, the temperature and a set of internal variables which is introduced to take history-dependent phenomena into account. In the vicinity of an equilibrium reference state, the specific Gibbs free energy is approximated up to second order terms. Evaluating the Clausius-Duhem inequality, the constitutive relations for the strain tensor, the entropy and the internal variables are derived. In comparison with other approaches, the entropy, the strain tensor and the internal variables are functionals not only of the stress tensor but also of the temperature. Applying harmonic temperature- or stress-controlled excitations, complex frequency-dependent relations for the specific heat under constant stress, for the thermal expansion coefficients as well as for the dynamic mechanical compliance are obtained. The frequency-dependence of these quantities depicts the experimentally observed behaviour of glass-forming materials as published in literature. Under the assumption of isotropic material behaviour, it is shown that the developed theory is compatible with the Prigogine-Defay inequality for arbitrary values of the material parameters.     

梯度蜂窝面外动态压缩力学行为与吸能特性研究

蜂窝材料具有优异的抗冲击吸能特性。为进一步提高蜂窝材料的比吸能与压缩力效率,提出了一种几何参数或材料参数沿厚度方向梯度渐变的蜂窝材料模型,并针对六边形蜂窝构型研究了胞元壁厚和屈服强度梯度变化的蜂窝材料在面外动态压缩载荷下的力学行为与吸能特性。研究结果表明,通过调控梯度变化的指数,胞元壁厚或母体材料屈服强度的梯度设计均可有效降低初始峰值应力,并使蜂窝材料的比吸能和压缩力效率同时增大。研究结果可为蜂窝材料的防撞性优化设计提供新的思路。     

高硬度聚脲涂层抗侵性能与断裂机制研究

鉴于高硬度聚脲与常规聚脲弹性体的区别,研究了高硬度聚脲涂覆钢板结构的抗侵性能及涂层断裂机制。通过弹道实验加载3.3 g立方体破片撞击无涂层、迎弹面涂层、背弹面涂层与双面涂层4种涂覆类型靶板,获得靶板的弹道极限,分析了不同涂覆方式下结构的抗侵性能、涂层断裂规律与微观断口形貌。结果表明:破片冲击作用下,迎弹面涂层断裂程度高且吸能性好,能够有效提高结构抗侵性能,而背弹面涂层破坏先于钢板层且吸能性差,对结构抗侵性能无提升作用;涂层断裂呈现一定的速度效应、厚度效应与微观特征,其规律反映了不同位置涂层的吸能差异。     

大锥角药型罩聚能装药侵彻混凝土实验研究

采用脉冲X光照相及威力效应实验,对两种大锥角药型罩装药结构侵彻体的形成及它们对混凝土的侵彻能力进行了研究,获得了两种大锥角药型罩装药结构形成侵彻体的形状、头尾速度及它们对混凝土靶的侵彻参量,对比了半无限厚混凝土靶板及多层有限厚薄靶板对侵彻威力的影响。结果表明,在小炸高条件下,两种大锥角药型罩装药结构能够形成较理想的爆炸成型杆式侵彻体,在混凝土靶中形成孔深与孔径兼顾的孔道。     

聚能装药对混凝土靶板的侵彻研究

系统开展了不同药型罩材料、不同锥角、不同壁厚的聚能装药在不同炸高下侵彻混凝土试验, 研究了罩材料、锥角、壁厚、炸高等结构参数对漏斗坑直径、侵彻孔洞直径、漏斗坑深度以及侵彻深度等参数的影响规律;应用空腔膨胀理论计算了混凝土靶体阻力, 采用改进的伯努利方程和两阶段空腔膨胀理论获得了混凝土靶板在侵彻体作用下的侵彻深度和孔洞直径, 理论结果与试验结果基本吻合;基于AUTODYN 软件平台, 采用与试验一致的聚能装药结构, 开展了57 种工况下侵彻体成形过程的数值模拟研究, 并对其中典型工况的侵彻混凝土过程进行了数值模拟, 计算所得孔洞直径和侵彻深度与试验结果吻合较好, 在此基础上深入探讨了聚能装药作用下混凝土漏斗坑的形成机理, 分析表明, 铝药型罩的开坑机理不同于钢和铜药型罩.      

On the time-dependence of the erosion rate—a probabilistic approach to erosion

A highly simplified model is presented of the erosion process under liquid impact. The theory outlined allows the mathematical expectation of the erosion rate as a function of time (erosion curve) to be predicted.This simplified theory of erosion is based on the statistical nature of the repetitive loading due to liquid impact. It employs a classification of individual impacts according to their quality of or effectiveness in removing material. The specific loss of material (per impact) is considered to be a random variable, which assumes different, discrete values depending on the order of repetitions of effective impacts at the same location on the target (surface). The probabilities of producing any of these repetitions are calculated. For particular applications, the theory requires characteristic data for the specific loss of material as well as typical data concerning the hydrodynamic loading conditions.For the case of a ductile erosion process, a very approximate solution is presented. Nevertheless, it exhibits the typical features of erosion curves as presented in the literature.     

Nanoindentation of hyperelastic polymer layers at finite deformation and parameter re-identification

Thin polymer layers on substrates have a wide range of application in important areas. However, it is impossible to measure the mechanical properties with the traditional testing methods. Recently, nanoindentation became a new but primary testing technique of thin layers. In the present work, based on a finite element model of contact mechanics and hyperelastic materials, nanoindentation of polymer layers is simulated with the finite element code ABAQUS^?. Three often used hyperelastic models, that is, the neo-Hookean, Mooney–Rivlin and Yeoh models are investigated. The behaviour of these three models is compared to each other in different boundary value problems of nanoindentation in order to get some feeling of the different behaviour of various hyperelastic models under nanoindentation. In contrast to the traditional analytical method, the penetration depth is not restrained to avoid the influence of the substrate. A parameter re-identification strategy is employed to extract the parameters of the material models at small and finite deformation based on the principle of biological evolution. Furthermore, it is investigated how large the penetration depth has to be chosen in order to distinguish different models in reference to the load–displacement curves. Finally, the possibility is discussed of describing the data obtained by a non-linear complex model using the relatively simple approach based on the neo-Hookean model.     

弹体高速侵彻效率的实验和量纲分析

为了研究高速侵彻时弹体撞击速度、材料强度等对质量侵蚀特性和侵彻效率的影响规律,开展了不同材料强度和长径比的弹体高速侵彻半无限厚素混凝土靶实验,弹体撞击速度为880~1 900 m/s,弹头形状为尖卵型(半径口径比为3),口径为30 mm。由实验发现:弹体撞击速度对侵彻效率的影响呈抛物线分布,最大侵彻效率时的弹体特征撞击速度约1 400 m/s;高速侵彻时弹体的质量侵蚀主要发生在卵形头部,弹身及尾部损伤极少;速度超过特征撞击速度时,弹体侵蚀严重,甚至弯曲变形或解体;弹体强度提高至约2倍时,质量侵蚀率降低约80%。基于实验,利用量纲分析原则建立了量纲一侵彻效率和量纲一弹体撞击速度的函数关系式,可估算出最大侵彻效率对应的弹体撞靶速度,为高速侵彻效应模拟实验提供理论指导。     

Asymmetric Equilibrium Configurations of Symmetrically Loaded Isotropic Square Membranes

The homogeneous deformations provided by the equilibrium problem of nonlinear isotropic hyperelastic symmetrically loaded membranes are analyzed. Besides the universal symmetric solutions, the problem considered, depending on the form of the stored energy function, may admit asymmetric solutions. For general incompressible materials, the mathematical conditions governing the global development of these asymmetric solutions are investigated. Explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a Valanis–Landel and an Ogden material. For this last case, which is frequently used to model rubberlike materials, a broad numerical analysis was performed. The more qualitatively interesting branches of asymmetric equilibria are shown and the influence of the material parameters is discussed. Finally, using the energy criterion a number of considerations are made on stability. This revised version was published online in July 2006 with corrections to the Cover Date.     

金属材料的强度与应力-应变关系的球压入测试方法

压入法获取材料单轴应力-应变关系和抗拉强度对服役结构完整性评价有重要的基础意义.假定材料均匀连续、各向同性、应力应变关系符合Hollomon律,基于能量等效假定,即代表性体积单元(representativevolume element, RVE)的vonMises等效和有效变形域内能量中值等效假定,本文提出了关联材料载荷、深度、球压头直径和Hollomon律的四参数半解析球压入(semi-analyticalspherical indentation,SSI)模型.通过球压入载荷-深度试验关系获得材料的应力-应变关系和抗拉强度.考虑压入过程中的损伤效应,针对金属材料提出了用于球压入测试的材料弹性模量修正模型.对11种延性金属材料完成了球压入试验,采用本文提出的球压入试验方法测到的弹性模量、应力-应变关系和抗拉强度与单轴拉伸试验结果吻合良好.      

Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors

Enhanced functional integration in modern electron devices requires an accurate modeling of energy transport in semiconductors in order to describe high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. The standard drift-diffusion models cannot cope with high-field phenomena because they do not comprise energy as a dynamical variable. Furthermore for many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function must be necessarily involved. Therefore these phenomena cannot be described within the framework of the drift-diffusion equations (which are valid only in the quasi-stationary limit). Therefore generalizations of the drift-diffusion equations have been sought which would incorporate energy as a dynamical variable and also would not be restricted to quasi-stationary situations. These models are loosely speaking called hydrodynamical models. One of the earliest hydrodynamical models currently used in applications was originally put forward by Blotekjaer [1] and subsequently investigated by Baccarani and Wordeman [2] and by other authors [3]. Eventually other models have also been investigated, some including also non-parabolic effects [4–6, 8–20]. Most of the implemented hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem (lacking a physically convincing motivation) and the modeling of the production terms (usually assumed to be of the relaxation type and this, as we shall see, leads to serious inconsistencies with the Onsager reciprocity relations). In these lectures we present a general overview of the theory underlying hydrodynamical models. In particular we investigate in depth both the closure problem and the modeling of the production terms and present a recently introduced approach based on the maximum entropy principle (physically set in the framework of extended thermodynamics [21, 22]). The considerations and the results reported in the paper are exclusively concerned with silicon.     

Propagation of compaction waves in metal foams exhibiting strain hardening

One-dimensional models for compaction of cellular materials exhibiting strain hardening are proposed for two different impact scenarios. The models reveal the characteristic features of deformation under the condition of decreasing velocity during the impact event. It was established that an unloading plastic wave of strong discontinuity propagates in the foam and it has a significant dynamic effect on the foam compaction and energy absorption. The proposed models are based on the actual experimentally derived stress strain curves. The compaction mechanism in three aluminium based foam materials, two of them with relatively low density – Alporas and Cymat with 9% and 9.3% relative density, respectively and a higher density Cymat foam with 21% relative density, is analysed. Numerical simulations were carried out to verify the proposed models.The predictions of the proposed models are compared with published analytical models of compaction of cellular materials which assume a predefined densification strain. It is shown that the approximation of a cellular material with significant strain hardening by the Rigid Perfectly-Plastic-Locking (RPPL) model can lead to an overestimation of the energy absorption capacity for the observed stroke due to the non-uniform strains along the compacted zone of the actual material in contrast to the predefined constant densification strain in the RPPL model. The assumption of a constant densification strain leads also to an overestimation of the maximum stress, which occurs under impact.     

具有填充材料的金属格栅夹层板在高速冲击下动态响应的数值分析

利用大型非线性有限元程序ABAQUS和LS-DYNA,对具有填充材料的金属格栅结构的冲击问题进行数值模拟.研究了不同的填充材料(金属泡沫和陶瓷)分别填充到不同的格栅构型(波纹型、蜂窝型和加强六边形)夹层板后,各类夹层板受到金属泡沫子弹和不锈钢子弹冲击时变形与能量吸收特性,探讨了夹层板上下面层板、支撑格栅及填充材料等各部分的吸能比率.研究结果表明,泡沫填充夹层板在缓冲吸能方面具有优势,陶瓷填充夹层板则在抵抗冲击穿透方面更具有优势,不同构型的夹层板,性能略有不同.     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

头部对称刻槽弹体侵彻半无限厚铝合金靶实验与理论模型

在综合考虑弹体结构稳定性及截面比动能的前提下, 提出一种介于尖卵形弹体及尖锥形弹体间的头部对称刻槽弹体, 以期达到提高侵彻深度的目的。以尖卵形弹体侵彻深度为基准, 开展头部对称刻槽弹体侵彻半无限厚铝合金靶实验。在此基础上, 推导得到可描述头部对称刻槽弹体侵彻2A12铝合金靶过程的局部相互作用模型。同时, 结合头部对称刻槽弹体侵彻后靶体破坏现象, 提出适用于头部对称刻槽弹体的靶体响应力, 进而确立头部对称刻槽弹体的侵彻深度模型。实验结果与理论计算表明, 头部对称刻槽弹体具有相对于尖卵形弹体更好的侵彻能力。头部对称刻槽弹体侵彻深度提高的原因是弹体头部结构截面比动能增加及其侵彻过程中的靶体弱化效应, 其中弱化效应是侵彻深度提高的主控因素。