On the relationship between impact energy and delamination area

Thin glass/epoxy plates fabricated from 3M prepreg tape were subjected to low-velocity impact. Delamination in the impacted composite plates was measured by edge replication and was identified as the major damage mode. The effects of fiber orientation, thickness, and lamination on the delamination resistance were investigated. Experimental results verified three previous findings: (1) a linear relationship holds between delamination area and impact energy, (2) the mismatch of bending stiffness between adjacent laminae can be correlated with the delamination area on the interface, and (3) the behavior of a thin composite plate under low-velocity impact is very similar to that caused by global bending. In addition, based on the calculation of impact energy per unit delamination area, the dynamic fracture energy and the energy of dissipation in the thin glass/epoxy plates can be examined.     

2-D problem of a Mode-I crack for a generalized thermoelasticity under Green-Naghdi theory

A general model of the equations of the generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solved. The crack is subjected to prescribed temperature and stress distribution in the context of Green-Naghdi theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature and the couple stresses. Comparisons are made with the results predicted in the both type II, III of Green-Naghdi theory. It is found that a Mode-I crack has great effects on the distribution of field quantities with energy dissipation.     

加载角度对层理页岩裂纹扩展影响的实验研究

采用分离式霍普金森压杆（SHPB）系统对页岩进行冲击实验,研究层理角度对页岩动态断裂过程的影响,在裂尖设置裂纹扩展计,借助高速摄影和数字图像相关（DIC）技术对页岩中心切槽半圆盘弯曲（NSCB）试件断裂的全过程进行研究,得到了不同加载角度下页岩的动态起裂韧度、裂纹扩展速度、断裂过程中应变场和水平位移场的变化规律。实验发现:不同加载角度下,页岩的动态起裂韧度具有显著的各向异性,加载角度与动态起裂韧度呈正相关;加载角度对试样的裂纹扩展速度具有显著影响,与裂纹扩展速度呈负相关;当冲击速度较低时,切槽方向是裂纹扩展的优势方向,而当冲击速度较高时,试样会产生沿层理弱面的次生裂纹,次生裂纹对试样的断裂具有显著影响。     

冲击速度和轴向静载对红砂岩破碎及能耗的影响

地下岩体工程爆破开挖中，距爆源不同距离处岩体承受的地应力和动载荷大小不同，从动载荷的角度表征岩石动态破坏结果与工程实际更吻合。为研究动载荷和地应力大小对岩体破碎和能量耗散特性的影响，利用动静组合加载试验装置，分别设置7个冲击速度和轴向静应力等级，对红砂岩试件进行冲击试验。根据试件的破碎状况，分析不同静应力工况下冲击速度对岩石破坏模式和机理的影响。计算不同工况下的应力波能量值，研究冲击速度和轴向静应力对岩石能耗特性的影响。对破坏试件进行筛分试验，研究岩石破碎分形维数随冲击速度和轴向静应力的变化关系。结果表明，随着冲击速度的增大，试件的破坏程度逐渐加大。无轴压时岩石试件破坏后整体仍是一个圆柱体，属于张拉破坏；有轴压时岩石试件宏观破坏后呈沙漏状，属于拉剪破坏。岩石耗散能随冲击速度的升高呈二次函数关系递增；轴向静应力越高，递增幅度越小。随着冲击速度的升高，岩石分形维数由零逐渐增加；随着轴向静应力的升高，分形维数由零转为大于零的临界冲击速度先升高后降低。     

应变率及节理倾角对岩石模拟材料动力特性的影响

采用相似材料模拟实验方法并借助SHPB(split Hopkinson pressure bar)实验系统,探究应变率及节理倾角对节理岩石动态力学性状的影响,包括应力应变曲线特征、破坏模式、能量传递及耗散规律。该实验结果表明:应变率升高,动态弹性模量增大,试件破碎块度变小,完整试件裂纹缺陷沿着平行于压应力方向扩展;节理角度越大,峰值强度越低,但当应变率升高到一定程度,节理角度对岩石破坏形态的影响不再明显;不同试件的入射能、反射能、透射能和耗散能均随应变率升高呈非线性增加,含倾斜角度节理试件的能量耗散率随应变率的变化幅度明显大于完整试件。     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

混凝土黏聚开裂模型若干进展

黏聚模型是用来描述混凝土断裂行为的基本模型, 首先介绍了混凝土的黏聚开裂模型的基本概念,总结了确定黏聚区的本构方程的各种方法,即直接单轴拉伸测试、J积分方法、R曲线法、柔度法和逆推法.然后介绍了黏聚模型在I型和复合型裂纹问题、疲劳断裂问题中的应用以及黏聚模型与混凝土尺寸效应的关系.最后对黏聚开裂模型与桥联模型、带状裂缝模型进行了比较和总结, 指出了该模型存在的问题, 并对其以后的发展方向提出了建议.      

Microstructure-performance relations of ultra-high-performance concrete accounting for effect of alpha-quartz-to-coesite silica phase transformation

The effect of the α-quartz-to-coesite silica phase transformation on the load-carrying and energy-dissipation capacities of ultra-high-performance concrete (UHPC) under dynamic loading with hydrostatic pressures of up to 10 GPa is evaluated. The model resolves essential deformation and failure mechanisms and provides a phenomenological account of the transformation. Four modes of energy dissipated are tracked, including inelastic deformation, distributed cracking, interfacial friction, and the energy dissipated through transformation of the quartz aggregate. Simulations are carried out over a range of volume fractions of the constituent phases. Results show that the phase transformation has a significant effect on the energy-dissipation capacity of UHPC for the conditions studied. Although transformation accounts for less than 2% of the total energy dissipation, the transformation leads to a twofold increase in the crack density and yields almost an 18% increase in the overall energy dissipation. Structure-response relations that can be used for materials design are established.     

Subgrid-modelling in LES of compressible flow

Subgrid-models for Large Eddy Simulation (LES) of compressible turbulent flow are tested for the three-dimensional mixing layer. For the turbulent stress tensor the recently developed dynamic mixed model yields reasonable results.A priori estimates of the subgrid-terms in the filtered energy equation show that the usually neglected pressure-dilatation and turbulent dissipation rate are as large as the commonly retained pressure-velocity subgrid-term. Models for all these terms are proposed: a similarity model for the pressure-dilatation, similarity andk-dependent models for the turbulent dissipation rate and a dynamic mixed model for the pressure-velocity subgrid-term. Actual LES demonstrates that for a low Mach number all subgrid-terms in the energy equation can be neglected, while for a moderate Mach number the effect of the modelled turbulent dissipation rate is larger than the combined effect of the other modelled subgrid-terms in the filtered energy equation.     

A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites

An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating interface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the frictionless contact condition.The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum approach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction.     

复合材料Ⅰ、Ⅱ混合型分层试验研究

通过对T300／5405、1300／913、1300／HD03三种航空材料Ⅰ、Ⅱ混合型分层研究，进一步研究了新的Ⅰ、Ⅱ混合型分层断裂测试的JJ法，并和MMB法进行了比较，发现两者较为吻合。但JJ法耗费试件少，简单易行，操作方便，有利于建立混合型分层的失效判据，它可以适用于不同环境下的混合型分层实验的测试。     

The role of plastic deformation on the impact behaviour of high aspect ratio aluminium foam-filled sections

The main objective of this work is to investigate the role of the plastic deformation of metal foams on the dynamic behaviour of aluminium foam-filled columns with respect to their energy absorbing capabilities. The influence of the cross-section shape as well as other parameters is thoroughly studied. A comparison with correspondent hollow-sections is performed concerning the dissipation of kinetic energy and the obtained deformed profiles. For this particular purpose, three-dimensional finite element modelling dynamic analyses are carried out using ABAQUS/Explicit in order to achieve an in-depth study of the structural crash behaviour, during which energy needs to be absorbed in a controlled manner. A comprehensive numerical study of the crush behaviour of aluminium foam-filled sections undergoing axial compressive loading is performed. The results obtained are also analysed with respect to the reduction in the length of the structural element and impact time, the effect of friction between the foam and the outer skin, the energy decomposition, the role of plastic deformation, the influence of the skin material and impact velocity, and the influence of the shape of the cross-section on the impact behaviour. A comparison with existing analytical expressions is made in order to corroborate the numerical results.     

TiNi柱壳在不同约束下的横向冲击实验

为了解TiNi柱壳横向压缩力学性能以制造可重复使用抗冲吸能装置, 对有、无侧向约束的TiNi柱壳进行了横向冲击实验。利用改进的霍普金森压杆装置(SHPB), 配套波形分离方法, 实现了较长时间(~3 ms)的波形测量, 获得了TiNi柱壳在动态加载下的载荷压缩量曲线。通过高速摄影, 捕捉了柱壳的动态变形过程。结果表明, 无约束试件具有优良的可恢复变形能力, 承载力平台段特征明显。侧向约束的引入, 可以有效提高柱壳的承载力和耗能能力, 可以承受更高速度的冲击。选择合适的约束组合, 可望同时实现较大压缩行程和高耗能, 制造实用的抗冲吸能装置。     

An analytical delamination model for laminated plates including bridging effects

A penalised interface model, whose strain energy is the penalty functional related to interface adhesion constraint, is introduced in conjunction with a damageable interface whose local constitutive law, in turn, represents bridging stress effects, in order to analyse delamination and bridging phenomena in laminated plates. The laminate is modelled by means of first-order shear deformable layer-wise kinematics and the governing equations are formulated in the form of a non-linear differential system with moving intermediate boundary conditions related to opportune delamination and bridging growth conditions. The problem is solved through an analytical approach. The model leads to an accurate and self-consistent evaluation of the energy release rate and its mode components due to the inclusion of significant contributions arising from coupling between in-plane and transverse shear stresses, and to an asymptotic estimate of interlaminar stresses. The salient features of the proposed model are investigated in the context of an energy balance approach and of a J-integral formulation, thus providing simple results useful to model delamination growth and bridging behaviour when mixed mode loading is involved. The accuracy of the proposed model is substantiated through comparisons with results from continuum analysis obtained by a finite element (FE) procedure. The effectiveness of the proposed model is highlighted by showing the solution of a two-layered plate scheme subjected to pure and mixed mode loading conditions and to fibre bridging stresses. The results point out that the present model, despite its low computational cost in comparison with more complex FE analyses, is an efficient tool to predict delamination and bridging evolution.     

Crack propagation in an orthotropic medium with coupled elastodynamic properties

In this paper the Mode-I elastodynamic problem of a crack propagating in an orthotropic medium is studied under the condition that the matrix of elastodynamic coefficients has repeated eigenvalues. It is shown that the crack is constrained in an elastodynamic state which is defined through a compulsory condition coupling its velocity with the elastic parameters of the orthotropic medium. The dynamic stress and displacement components ahead of the crack tip as well as the energy release rate are explicitly obtained.     

Electromechanical impact of a crack in a functionally graded piezoelectric medium

The Mode-I transient response of a functionally graded piezoelectric medium is solved for a through crack under the in-plane mechanical and electric impact. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. Numerical results display the effects of the loading combination parameter λ and the material parameter βa on the dynamic stress intensity factor and electric displacement intensity factor. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor and the direction of crack initiation.     

低速冲击下纤维/金属层合板抗分层性能研究

本文采用内聚力模型,对纤维/金属层合板(FMLs)在低速冲击载荷作用下抗分层性能进行研究。内聚力模型对裂纹的模拟具有它独特的优势：一是该模型不需要预先假设初始缺陷;二是在计算过程中随着裂纹的扩展,该方法不需要重新对结构进行网格划分。借助该模型,本文对低速冲击载荷作用下,纤维层合板(FRP)分层进行了模拟,并验证了该模型计算的有效性。在此基础上,本文研究了低速冲击载荷作用下,不同金属含量的纤维/金属层合板抗分层性能,并与纤维层合板进行了比较。最后从能量的角度讨论了金属含量与铺层结构对FMLs低速冲击性能的影响。     

TEMPERATURE EFFECT ON LOW-CYCLE FATIGUE BEHAVIOR OF NICKEL-BASED SINGLE CRYSTALLINE SUPERALLOY

The low-cycle fatigue （LCF） behavior of a nickel-based single crystal superalloy with [001] orientation was studied at an intermediate temperature of T0℃ and a higher temperature of To ＋ 250℃ under a constant low strain rate of 10^-3 s^-1 in ambient atmosphere. The superalloy exhibited cyclic tension-compression asymmetry which is dependent on the temperature and applied strain amplitude. Analysis on the fracture surfaces showed that the surface and subsurface casting micropores were the major crack initiation sites. Interior Ta-rich carbides were frequently observed in all specimens. Two distinct types of fracture were suggested by fractogaphy. One type was characterized by Mode-I cracking with a microscopically rough surface at To ＋ 250℃. Whereas the other type at lower temperature T0℃ favored either one or several of the octahedral {111} planes, in contrast to the normal Mode-I growth mode typically observed at low loading frequencies （several Hz）. The failure mechanisms for two cracking modes are shearing of γ＇ precipitates together with the matrix at T0℃ and cracking confined in the matrix and the γ/γ＇interface at To - 250℃.     

Constitutive behaviour of mixed mode loaded adhesive layer

Mixed mode testing of adhesive layer is performed with the Mixed mode double Cantilever Beam specimen. During the experiments, the specimens are loaded by transversal and/or shear forces; seven different mode mixities are tested. The J-integral is used to evaluate the energy dissipation in the failure process zone. The constitutive behaviour of the adhesive layer is obtained by a so called inverse method and fitting an existing mixed mode cohesive model, which uses a coupled formulation to describe a mode dependent constitutive behaviour. The cohesive parameters are determined by optimizing the parameters of the cohesive model to the experimental data. A comparison is made with the results of two fitting procedures. It is concluded that the constitutive properties are coupled, i.e. the peel and shear stress depend on both the peel and shear deformations. Moreover, the experiments show that the critical deformation in the peel direction is virtually independent of the mode mixity.     

Compliance rate change of tapered double cantilever beam specimen with hybrid interface bonds

This paper presents a combined numerical and experimental study of compliance rate change of Tapered Double Cantilever Beam (TDCB) specimens for Mode-I fracture of hybrid interface bonds. The easily machinable TDCB specimen, which is designed to achieve a constant rate of compliance change with respect to crack length, is developed for Mode-I fracture tests of hybrid material bonded interfaces, such as wood bonded to fiber-reinforced plastic (FRP) composite. The linearity of compliance crack-length relationship of the specimen is verified by both Rayleigh–Ritz method and finite element analysis. An experimental compliance calibration program for specimens with wood–wood and FRP–FRP bonded interfaces is carried out, and a constant rate change of compliance with respect to crack length is obtained for a specific range of crack length. Fracture tests are further performed using TDCB specimens for wood–wood and wood–FRP bonded interfaces to determine the critical loads for crack initiation and crack arrest, and using the constant compliance rate change of the specimens determined by experiment or analysis, the respective critical strain energy release rates, or fracture energies, are obtained. This study indicates that the constant compliance rate change obtained from experiment or finite element analysis for linear-slope TDCB specimens can be used with confidence for fracture studies of hybrid material interface bonds.