纤维金属层板低速冲击试验和数值仿真

为开展纤维金属层板（FML）低速冲击有限元数值仿真研究,改进了传统的连续损伤力学（CDM）模型,然后对FML落锤低速冲击试验进行数值仿真,并与实验结果进行对比验证。分别采用5.11 J 和10.33 J冲击能量对FML进行落锤低速冲击试验,得到冲击载荷、位移和能量时程曲线,分析FML的动态响应和失效模式。建立了考虑塑性应变、压缩刚度衰减特征和纤维拉伸断裂损伤的新CDM模型,描述S2-玻璃纤维/环氧树脂（S2-galss/epoxy）复合材料的损伤本构,并编写VUMAT子程序,通过ABAQUS/Explicit求解器对FML落锤冲击试验进行数值仿真。研究结果表明：低能量冲击条件下,FML背面主要为鼓包和裂纹等失效模式,位移峰值随冲击能量的提高而增加,冲击载荷峰值在穿透前也随冲击能量的提高而增加;采用改进的CDM模型描述FML中S2-galss/epoxy复合材料铺层后,有限元数值计算可以较好地预测FML低速冲击载荷下的动态响应;有限元数值仿真结果表明,FML中第2层复合材料铺层发生的纤维断裂损伤比第1层的更严重。     

Prediction for debonding damage process and effective elastic properties of glass-bead-filled modified polyphenylene oxide

A three-dimensional three-phase finite element unit cell model has been applied to predict the debonding damage process of particulate polymer composites (PPC) during tensile deformation. The model consists of a particle, an interface and a polymer matrix. The particle-matrix debonding process has been simulated by using a particle-matrix debonding criterion and a vanishing finite element technique. For verification of the predicted results, the results obtained in the in situ SEM experiments of our previous study on glass beads reinforced modified polyphenylene oxide (GB/PPO) were used The predicted results are in good agreement with the experimental micro-scale tensile debonding-damage process. Anisotropic damage in materials like PPC is very difficult to measure by conventional experimental methods. In order to provide anisotropic damage information of the damaged composites, this was amongst the first time to predict the effective elastic properties of PPC in different principal directions by performing a virtual load–unload test on the partially debonded cell model. Some predicted results would be compared with those of experimental load–unload test.     

Modeling and characterization of dynamic failure of borosilicate glass under compression/shear loading

In this paper, we study the impact-induced dynamic failure of a borosilicate glass block using an integrated experimental/analytical approach. Previous experimental studies on dynamic failure of borosilicate glass have been reported by Nie et al. [Nie X, Chen WW, Sun X, Templeton DW. Dynamic failure of borosilicate glass under compression/shear loading – experiments. J Am Ceram Soc, in press.] using the split Hopkinson pressure bar (SHPB) technique. The damage growth patterns and stress histories have been reported for various glass specimen designs. In this study, we propose to use a continuum damage mechanics (CDM)-based constitutive model to describe the initial failure and subsequent stiffness reduction of glass. Explicit finite element analyses are used to simulate the glass specimen impact event. A maximum shear stress-based damage evolution law is used in describing the glass damage process under combined compression/shear loading. The impact test results are used in quantifying the critical shear stress for the borosilicate glass under examination. It is shown that with only two modeling parameters, reasonably good comparisons between the predicted and the experimentally measured failure maps can be obtained for various glass sample geometries. Comparisons between the predicted stress histories for different sample designs are also used as model validations.     

三维四向编织复合材料宏观有限元模型冲击损伤仿真及试验验证

三维编织复合材料作为整体编织材料,能够克服层合复合材料层间强度低、易分层的缺陷,相对于金属材料,还具有质量轻、高比刚、高比强度以及良好的抗冲击性能、较高的损伤容限,在汽车、高铁、航海、航空及航天领域中具有广泛应用前景。使用空气炮发射系统开展了钢珠以约210 m/s速度冲击三维四向编织复合材料平板的不同位置试验,基于宏观观察和细观观测,分析了三维编织复合材料在受到钢珠高速冲击下的破坏模式和破坏机制。此外,本文建立了三维四向编织复合材料宏观连续介质损伤（CDM）有限元模型,其中模型计算剩余速度和试验测得剩余速度误差在5%以内,试验和数值模拟的破坏形貌也高度一致,验证了所建立的宏观CDM有限元模型的有效性。     

High temperature strength and multiaxial fatigue life assessment of a tubesheet structure

A continuum damage mechanics (CDM) model was adopted to calculate the multiaxial fatigue damage of perforated structure (also called ‘tubesheet’) of a heat exchanger. In achieving this goal, the structure strength was numerically investigated in terms of steady and transient state prior to perform fatigue life prediction. Due to the complexity of geometry and loading pattern, the three dimensional (3D) finite element (FE) model was established for the tubesheet, and the changes of the multiaxial factor were explored in the spatial and temporal perspective respectively. Furthermore, the fatigue damage evolution was analyzed by taking multiaxial factor into account. Finally, the results showed that the fatigue damage evolution was significantly accelerated by multiaxial factor, and the life prediction by multiaxial CDM was in good agreement with observed data for the tubesheet.     

Characterising fibre compression fracture toughness of composites using bearing tests

In this paper we propose the use of a bearing test with a coupled experimental–numerical approach to characterise the critical strain energy release rate, or “fracture toughness”, for fibre compression failure in bearing. This property is used in continuum damage mechanics (CDM) approaches for progressive failure analysis of composite laminates. In the proposed approach, experimental results for a standard bearing test are used to calibrate the fracture toughness with a progressive failure analysis using a CDM damage model. The approach is demonstrated for a plain weave carbon/epoxy material using the CDM damage model available in a commercial finite element package (Abaqus). The results indicate that the bearing test method provides a simple and convenient means of quantifying fibre compression fracture toughness. Analysis results applying the characterised value show good comparison with experimental results, and confirm the value of the bearing test as part of a novel material characterisation technique.     

基于连续介质损伤力学的复合材料层合板低速冲击损伤模型

基于连续介质损伤力学（CDM）方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤（纤维和基体损伤）、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度（in-situ strength）。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元（cohesive element）预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。     

复合材料层合板缺口强度的CDM三维数值模型

针对复合材料层合结构缺口强度问题,基于连续损伤力学（CDM）提出了一种三维损伤数值模型。模型区分了层内损伤（纤维失效、纤维间失效）和层间分层损伤的不同失效模式。采用三维Puck准则与Aymerich准则对上述2类损伤进行判定,材料失效后基于CDM中线性软化模型对材料损伤进行演化。模型考虑了复合材料层合板子层的就位效应和剪切非线性行为。对Carlsson的AS4/3501-6缺口拉伸强度试验进行数值模拟。结果表明:分析结果与试验结果吻合良好,证明了该模型能够准确地预测含缺口复合材料层合板面内拉伸强度。      

Progressive damage analyses of angle‐ply laminates exhibiting free edge effects using continuum damage mechanics with layer‐wise finite element method

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi‐static, monotonic increasing loading are investigated using three‐dimensional (3D) CDM implementation in a finite element method that is based on the layer‐wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle‐ply composite laminates under quasi‐static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted.     

Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture

A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading-unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading-unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.     

Effect of Thermo-Mechanical Gradient on the Damage Mechanisms of Composite Laminates

The main purpose of this work is to characterize and discriminate the respective roles of the thermo-mechanical gradient in the damage mechanisms of composite laminates used in aeronautics in order to understand the initiation and evolution of damage modes. For this purpose, a finite element model of compact tension specimen with a series of virtual crack closure techniques is achieved in order to evaluate the energy release rate of transverse matrix cracking in composites. The continuum mechanics approach in combination with Hashin’s damage criterion is adopted to describe initiation and evolution for each damage mode proposed for carbon/epoxy laminates. The good agreement between the numerical results and experiments in other available literature shows the validation of the analysis and developed model in this paper.     

Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.     

Buffeting-induced fatigue damage assessment of a long suspension bridge

As modern suspension bridges become longer and longer, buffeting-induced fatigue damage problem for the bridges located in strong wind regions may have to be taken into consideration. Furthermore, there is a trend to install wind and structural health monitoring systems (WASHMS) to long suspension bridges for performance assessment. A systematic framework for assessing long-term buffeting-induced fatigue damage to a long suspension bridge is thus presented in this paper by integrating a few important wind/structural components with continuum damage mechanics (CDM)-based fatigue damage assessment method. By taking the Tsing Ma Bridge in Hong Kong as an example, a joint probability density function of wind speed and direction is first established based on wind data recorded by the WASHMS installed in the bridge. A structural health monitoring-oriented finite element model of the bridge and a numerical procedure for buffeting-induced stress analysis of the bridge are then used to identify stress characteristics at hot spots of critical steel members under different wind speeds and directions. The accumulative fatigue damage to the critical steel members at hot spots during the bridge design life is finally evaluated using a CDM-based fatigue damage evolution model. The proposed framework is found to be feasible and practical.     

含雷击热-力耦合损伤复合材料层压板拉伸剩余强度预测

为了对含雷击热-力耦合损伤复合材料层压板的剩余强度进行预测,基于连续介质损伤力学法(CDM)和唯象分析法,建立了表征复合材料雷击热-力耦合损伤的刚度矩阵渐进损伤退化模型。基于该模型,通过ABAQUS有限元仿真软件,建立了含雷击热-力耦合损伤的复合材料层压板结构三维模型。结合UMAT子程序,完成了拉伸载荷下的剩余强度预测。结果表明:通过与试验对比,仿真结果与试验结果取得了良好的一致性。本文所建立模型,能够有效进行含雷击热-力耦合损伤复合材料层压板结构拉伸剩余强度预测。     

Indirect measuring of crack growth by means of a key-curve-method in pre-cracked Charpy specimens made of nodular cast iron

The determination of dynamic crack resistance curves from single specimen fracture tests requires information about the crack advance during the experiment. Here, attention is focused on crack resistance curves for nodular cast iron based on experimental data from instrumented Charpy tests. In order to estimate the actual crack length a key curve method (KCM) is employed. On the other hand, the Charpy impact tests were realized numerically using finite element calculations in conjunction with a continuum damage model (CDM) to simulate ductile crack growth. The parameters of the CDM model were determined from the experimental data of single specimen fracture tests. Equivalence between the experimental and the numerical realization of a fracture test was ensured by validating the predictions of the numerical simulations by means of low blow fracture tests. Comparison between the crack advance predicted by the numerical simulations and the results obtained using the proposed KCM shows a sufficiently well agreement with the actual crack length. Furthermore, crack resistance curves obtained from single specimen tests using either standard estimation schemes in conjunction with the KCM or numerical simulations are compared with the predictions based on low blow fracture tests.     

A numerical study on the impact resistance of composite shells using an energy based failure model

This paper presents a numerical study on the impact resistance of composite shells laminates using an energy based failure model. The damage model formulation is based on a methodology that combines stress based, continuum damage mechanics (CDM) and fracture mechanics approaches within a unified procedure by using a smeared cracking formulation. The damage model has been implemented as a user-defined material model in ABAQUS FE code within shell elements. Experimental results obtained from previous works were used to validate the damage model. Finite element models were developed in order to investigate the pressure and curvature effects on the impact response of laminated composite shells.     

A localization analysis of a non-uniform damage lattice in presence of strength gradient

The failure of a non-uniform axial damage chain under uniform tension is studied both with discrete damage mechanics (DDM) and continuum damage mechanics (CDM). It is shown that a micomechanics-based nonlocal CDM model may be built from a DDM formulation, that may include material heterogeneities. DDM is based on a microstructured model consisting in multiples elastic-damage springs, whose elastic yield threshold is variable and depends on the position along the chain. We aim to develop a nonlocal CDM model as a relevant continuous formulation of the lattice DDM system. To do this, we rely upon a continualisation procedure applied to the difference formulation of the lattice problem, which gives us a nonlocal propagating damage model. The boundary conditions of the nonlocal CDM problem are equivalent to a finite length damage cohesive law. Analytical and numerical results show a strong proximity of the discrete and enriched continuous approaches for this heterogeneous bar problem, as well as the effectiveness of the nonlocal damage model to capture the softening localization phenomenon in heterogeneous quasi-brittle fields.     

Anisotropic modelling and numerical simulation of brittle damage in concrete

A framework for damage mechanics of brittle solids is presented and exploited in the design and numerical implementation of an anisotropic model for the tensile failure of concrete. The key feature exploited in the analysis is the hypothesis of maximum dissipation, which specifies a unique damage rule for the elastic moduli of the solid once a failure surface is specified. A complete algorithmic treatment of the resulting model is given which renders a useful tool for large-scale inelastic finite element calculations. A rather simple three-surface failure model for concrete, containing essentially no adjustable parameters, is shown to produce results in remarkably good agreement with sample experimental data.     

Predicting low-velocity impact damage on a stiffened composite panel

An intralaminar damage model, based on a continuum damage mechanics approach, is presented to model the damage mechanisms occurring in carbon fibre composite structures incorporating fibre tensile and compressive breakage, matrix tensile and compressive fracture, and shear failure. The damage model, together with interface elements for capturing interlaminar failure, is implemented in a finite element package and used in a detailed finite element model to simulate the response of a stiffened composite panel to low-velocity impact. Contact algorithms and friction between delaminated plies were included, to better simulate the impact event. Analyses were executed on a high performance computer (HPC) cluster to reduce the actual time required for this detailed numerical analysis. Numerical results relating to the various observed interlaminar damage mechanisms, delamination initiation and propagation, as well as the model’s ability to capture post-impact permanent indentation in the panel are discussed. Very good agreement was achieved with experimentally obtained data of energy absorbed and impactor force versus time. The extent of damage predicted around the impact site also corresponded well with the damage detected by non destructive evaluation of the tested panel.     

An Improved Model for Fiber Kinking Analysis of Unidirectional Laminated Composites

This paper focuses on the fiber-kinking failure mode of unidirectional laminated composites under the compressive loading. An available stress based fiber-kinking model is explained and improved on the bases of strain concept. In the improved model, a new fracture surface is considered and the stresses are updated according to this new fracture surface. By taking the advantage of damage variables, the models are implemented into a finite element code and the results of numerical analysis such as prediction of kink band angles are discussed in details and compared with the available results in the literature. It is shown that the predicted kink band angles using the improved model are in good agreement with the experimental results.