The Mori–Tanaka method for composite materials with nonlinear interface debonding

We have used the Mori–Tanaka method to study the effect of nonlinear interface debonding on the constitutive behavior of composite material with high particle volume fraction. The interface debonding is characterized by a nonlinear cohesive law determined from the fracture test of the high explosive PBX 9501. Using the example of the composite material with spherical particles subject to hydrostatic tension, we show that the particle size has an important effect on the behavior of the composite material, namely hardening for small particles and softening for large particles. The critical particle size that separates the hardening and softening behavior of the composite material is determined. For the composite material with large particles, the particle/matrix interface may undergo catastrophic debonding, i.e., sudden, dynamic debonding even under static load. The energy release during catastrophic debonding can be very large, thus may trigger the reaction or detonation of high explosives. For the high explosive PBX 9501, the energy release due to catastrophic debonding of coarse (large) particles is equivalent to the free drop of the high explosive from a height of 110 m. This value become much higher, 455 m, once the debonding of fine (small) particle is accounted for.     

The uniaxial tension of particulate composite materials with nonlinear interface debonding

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite material. We have used a nonlinear cohesive law for particle/matrix interfaces to study interface debonding and its effect on particulate composite materials subject to uniaxial tension. The dilute solution shows that, at a fixed particle volume fraction, small particles lead to hardening behavior of the composite while large particles yield softening behavior. Interface debonding of large particles is unstable since the interface opening (and sliding) displacement(s) may have a sudden jump as the applied strain increases, which is called the catastrophic debonding. A simple estimate is given for the critical particle radius that separates the hardening and softening behavior of the composite.     

压电复合材料粘接界面断裂有限元模拟

根据数字化FRMM(Fix-Ratio Mix-Mode)断裂试验,得到了压电复合材料试件的断裂韧性和位移及应变场。本文在试验的基础上,通过非线性有限元软件ABAQUS及用户子程序UMAT进行了模拟分析,采用基于损伤力学的粘聚区模型(CZM)对压电复合材料界面的起裂和脱胶扩展进行了分析,并与VCCT方法进行了比较。计算得到的荷载位移曲线更接近于试验结果,但在裂纹扩展路径上的吻合需要对粘聚区法则进一步修正。通过进一步对CZM参数进行分析,表明界面粘结强度和界面刚度对计算结果的影响很大。研究结果表明,粘聚区模型可以很好地表征压电复合材料弱粘接界面脱胶断裂问题。     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

JBO-9021炸药的冲击起爆Pop关系

采用激光干涉测速技术和高速扫描相机,对新型钝感高能炸药JBO-9021（TATB、HMX和黏结剂的质量分数分别为80%、15%和5%）的冲击起爆Pop关系进行了研究。通过激光干涉测速技术获得了JBO-9021炸药冲击起爆过程中不同光纤探针处（即不同冲击波位置）的粒子起跳瞬时速度,结合未反应炸药的雨贡纽曲线,获得了粒子起跳点的冲击波压力;通过高速扫描相机获得冲击到爆轰距离,结合光纤探针所处位置,得到不同压力下JBO-9021炸药的冲击到爆轰距离,进而拟合出反映JBO-9021炸药冲击起爆性能的Pop关系曲线。结果显示,相对于TATB基PBX9502炸药和HMX基PBX9501炸药,JBO-9021炸药的冲击起爆性能更加优异。     

Multi-scale Mechanical Characterization of Palmetto Wood using Digital Image Correlation to Develop a Template for Biologically-Inspired Polymer Composites

Palmetto wood is garnering growing interest as a template for creating biologically-inspired polymer composites due to its historical use as an energy absorbing material in protective structures. In this study, quasi-static three-point bend tests have been performed to characterize the mechanical behavior of Palmetto wood. Full-field deformation measurements are obtained using Digital Image Correlation (DIC) to elucidate on the strain fields associated with the mechanical response. By analyzing strain fields at multiple length scales, it is possible to study the more homogeneous mechanical behavior at the macro-scale associated with the global load-deformation response; while at the microscale the mechanical behavior is more inhomogeneous due to microstructural failure mechanisms. Thus, it was possible to determine that, despite the presence of discontinuous macro-fiber reinforcement, at the macro-scale the response is associated with classical bending and progressive failure processes that are adequately described by Weibull statistics proceeding from the tensile side of the specimen. At the microscale, however, the failure mechanisms giving rise to the macroscopic response consist of both shear-dominated debonding between the fiber and matrix, and inter-fiber matrix failure due to pore collapse. These microscale mechanisms are present in both the compressive and tensile regions of the specimen, most likely due to local macro-fiber bending, which is independent of the global bending state. The pore collapse mechanism observed during mechanical loading appears to improve the energy absorption of the matrix material, thereby, transferring less energy and shear strain to the macro-fiber-matrix interface for initiation of debonding. However, the pore collapse mechanism can also accumulate substantial shear strain, which results in matrix shear cracking. Through these complex failure mechanisms, Palmetto wood exhibits a high resistance to catastrophic failure after damage initiation, an observation that can be used as inspiration for creating new polymer composite materials.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

3D FINITE ELEMENTANALYSIS OF THE DAMAGE EFFECTS ON THE DENTAL COMPOSITE SUBJECT TO WATER SORPTION

The damage effects of water sorption on the mechanical properties of the hydroxya-patite particle reinforced Bis-GMA/TEGDMA copolymer (HA/Bis-GMA/TEGDMA) have been predicted using 3D finite cell models. The plasticizer effect on the polymer matrix was considered as a variation of its Young's modulus. Three different cell models were used to determine the influence of varying particle contents, interphase strength and moisture concentration on the debonding damage. The stress distribution pattern has been examined and the stress transfer mode clarified. The Young's modulus and fracture strength of the Bis-GMA/TEGDMA composite were also predicted using the model with and without consideration of the damage. The former results with consideration of the debonding damage are in good agreement with existing literature experimental data. The shielding effect of our proposed model and an alternative approach were discussed. The FCC cell model has also been extended to predict the critical load for the damaged and the undamaged composite subject to the 3-point flexural test.     

PBX炸药的拉伸断裂损伤分析

采用巴西实验作为间接拉伸加载手段,研究了某PBX(polymer-bonded explosive)炸药试样拉伸作用下的断裂损伤特性.发展了PBX炸药的光学制备技术,获得了试样在光学显微镜下的细观表面形貌和断裂损伤形貌,结合高速摄影和数字相关分析技术获得了试样的形变和破坏过程.实验结果表明该PBX炸药的静态拉伸强度低于...     

固化温度对碳纤维/环氧基体界面行为影响的分析

对界面粘结性能及热残余应力影响下的单纤维复合材料的界面行为进行了分析。采用界面的弹性-软化内聚力模型,用解析法对单纤维复合材料由固化引起的热残余应力、以及单纤维碎断过程纤维的轴向应力分布进行了模拟,得到了碳纤维/环氧树脂在常温和高温固化两种情况的界面粘结性能。结果表明：与常温固化相比,高温固化后,界面的剪切强度增幅不大,界面的断裂韧性显著增加;高温固化后形成的界面,使界面的软化提前、界面的脱粘延迟;高温固化产生的纤维轴向和界面径向热残余应力对界面的软化均有延迟作用;界面径向热残余应力还对界面的脱粘有延迟作用。     

Constitutive modeling of fiber composites with a soft hyperelastic matrix

This paper presents an experimental and numerical study of unidirectional carbon fiber composites with a silicone matrix, loaded transversally to the fibers. The experiments show nonlinear behavior with significant strain softening under cyclic loading. The numerical study uses a plane-strain finite element continuum model of the composite material in which the fiber distribution is based on experimental observations and cohesive elements allow debonding to take place at the fiber/matrix interfaces. It is found that accurate estimates of the initial tangent stiffness measured in the experiments can be obtained without allowing for debonding, but this feature has to be included to capture the non-linear and strain-softening behavior.     

Progress in shakedown analysis with applications to composites

This paper reports on recent developments in the field of direct methods, in particular shakedown analysis (SA) from theoretical and numerical points of view. Emphasis is placed on problems connected with the failure of fibre-reinforced periodic composites under variable loads where special attention is paid to the problem of interface debonding between fibre and matrix materials. The approach is based on a local SA in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite. For numerical applications, the interior-point difference-of-convex-functions algorithm (IPDCA) is proposed as an efficient method for solving large-scale problems.     

Stiffness properties of particulate composites containing debonded particles

This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement.     

微粒填充流变材料界面开裂的局部临界应力及尺寸效应的理论分析

研究了以等轴粒子填充流变材料的边界开裂机理，采用能量准则导出了以界面能表示的界面开裂局部临界应力的简洁表达式。由于临界应力正比于１√α，从而可以非常方便地研究粒子开裂的尺寸效应，以碳酸钙微粒填充的聚丙烯复合材料为例进行了理论分析，通过比较界面开裂的能量准则和张应力准则得出结论：即使按照保守的方法估算，即在界面强度等于基体强度的条件下，只要粒径不超过０．２微米，若能量准则得到满足，则张应力准则也会得     

基于力热耦合材料模型的Steven试验数值模拟方法

在力热耦合材料模型中,增加炸药自热放能模型,建立了Steven试验的力-热-化耦合的数值模拟方法。数值计算模型中,应力应变关系采用双线性硬化弹塑性模型,炸药受力后的热作用采用各向同性热材料模型,炸药的化学反应采用Arrhenius反应率函数,同时还考虑了升温和熔化对材料力学、热学性能的影响。针对标准Steven试验,通过数值分析得到了靶板的变形情况和炸药点火的速度阈值,将计算结果与实验数据进行了比较,两者符合较好。表明该方法可以较好地模拟Steven试验,而且与以往的分析模型和方法相比,本文的方法不需要增加经验性的点火准则和判据,具有更广泛的适用性,可以为研究低速撞击条件下炸药的力热响应和局域化点火问题提供参考。     

Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials

The mechanisms of interfacial debonding of particle reinforced rheological materials are studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived and expressed in terms of the interfacial energy. The particle size effect on interface debonding can then be analyzed easily owing to the fact that critical stress is inversely proportional to the square root of particle radius. By taking PP/CaCO₃ system as an example, the present energy criterion is compared with the mechanical debonding criterion, and it is found that under the condition that bond strength is equal to matrix strength and particle radius not over 0.2μm, the mechanical debonding criterion can be automatically satisfied if the energy criterion is satisfied. A relation between critical time and interface energy is calculated by using the energy criterion. The influences of the particle volume fraction and the parlicle size, the loading rate and the relaxation time of the matrix on the critical time of interfacial debonding are also discussed. Supported by the National Natural Science Foundation of China (19632030 and 19872007) and Natural Science Foundation of Jiangsu Province.     

Experimental simulation of matrix cracking and debonding in a model brittle matrix composite

A model composite material system was designed to simulate typical damage mechanisms in unidirectional fiber reinforced brittle matrix composites. Experiments were performed at low to high quasistatic, macroscopic loading rates . At all loading rates reversal of the transverse strain was observed and was correlated to matrix cracking and debonding. The optical method of coherent gradient sensing (CGS) was used to obtain qualitative information regarding the stress fields and to observe the progression of damage. It was found that the sequence of damage formation (damage path) depended on the macroscopic loading rate. At lower loading rates periodic matrix cracks developed; minimal debonding of the reinforcement-matrix interface occurred only much later in the experiment. At higher loading rates extensive debonding followed propagation of the initial matrix crack, and periodic cracking was not observed. Several features of the material response of the model material system were also observed in a previously studied unidirectional ceramic matrix composite.     

Cohesive zone model of intermediate crack-induced debonding of FRP-plated concrete beam

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FPR–concrete interface can lead to premature failure of the structures. In this study, debonding induced by a flexural crack in a FRP-plated concrete beam is analyzed through a nonlinear fracture mechanics method. The concrete beam and FRP plate are modeled as linearly elastic simple beams connected together through a thin layer of FRP–concrete interface. A bi-linear cohesive (bond-slip) law, which has been verified by experiments, is used to model the FRP–concrete interface as a cohesive zone. Thus a cohesive zone model for intermediate crack-induced debonding is established with a unique feature of unifying the debonding initiation and growth into one model. Closed-form solutions of interfacial stress, FRP stress and ultimate load of the plated beam are obtained and then verified with the numerical solutions based on finite element analysis. Parametric studies are carried out to demonstrate the significant effect of FRP thickness on the interface debonding. The bond-slip shape is examined specifically. In spite of its profound effect on softening zone size, the bond-slip shape has been found to have little effect on the ultimate load of the plated beam. By making use of such a unique feature, a simplified explicit expression is obtained to determine the ultimate load of the plated concrete beam with a flexural crack conveniently. The cohesive zone model in this study also provides an efficient and effective way to analyze more general FRP–concrete interface debonding.