A hybrid finite element analysis of interface cracks

A versatile hybrid finite element scheme consisting of special crack-tip elements and crack face contact elements is developed to analyse a partially closed interface crack between two dissimilar anisotropic elastic materials. The crack-tip element incorporates higher-order asymptotic solutions for an interfacial crack tip. These solutions are obtained from complex variable methods in Stroh formalism. For a closed interfacial crack tip, a generalized contact model in which the crack-tip oscillation is eliminated is adopted in the calculation. The hybrid finite element modelling allows the stress singularity at an open and closed crack tip to be accurately treated. The accuracy and convergence of the developed scheme are tested with respect to the known interface crack solutions. Utilizing this numerical scheme, the stress intensity factors and contact zone are calculated for a finite interface crack between a laminated composite material.     

Numerical analysis of interaction and coalescence of numerous microcracks

The deformation and failure behaviors of brittle or quasi-brittle solids are closely related to interaction and propagation of stochastically distributed microcracks. The influence of microcrack interaction and evolution on the mechanical properties of materials presents a problem of considerable interest, which has been extensively argued but has not been resolved as yet. In the present paper, a novel numerical method is used to calculate the effective elastic moduli and the tensile strength, and to simulate the failure process of brittle specimens containing numerous microcracks. The influences of some crack distribution parameters reflecting the non-uniform spatial concentration, size and orientation distributions are examined. The effective elastic moduli and the tensile strength of brittle materials exhibit different dependences on microcrack interaction. For example, two microcrack distributions that lead to the identical effective elastic moduli may cause a pronounced difference in the tensile strengths and failure behaviors of materials. By introducing two criteria for microcrack growth and coalescence in terms of Griffith’s energy release rate, the above numerical method is extended to simulate the coalescence process of microcracks that results in a fatal crack and the final rupture of a specimen.     

单向受拉状态下的钢纤维混凝土本构模型

在混凝土中添加随机分布的钢纤维能有效提高混凝土力学性能。为了更好地考虑纤维对单向受拉状态下钢纤维混凝土（SFRC）的增强作用，提出一个钢纤维混凝土的弥散开裂本构模型。在弹性阶段，纤维混凝土被视为简单复合材料，基于两相复合材料理论，对SFRC的弹性刚度矩阵进行修正；在受拉开裂后，混凝土的塑性变形量被视为纤维与混凝土界面脱粘过程中滑移量，利用粘结滑移模型计算纤维在混凝土开裂面上的桥接作用。该文通过有限元软件ABAQUS中子程序二次开发接口Umat，进行Fortran编程，在ABAQUS中实现该本构模型。通过数值模拟结果与受拉实验数据进行对比，验证了该本构模型的准确性。通过数值模拟分析，进一步探究钢纤维混凝土相关参数对抗拉性能的影响，为钢纤维混凝土在实际的工程中的应用提供建议。     

The effect of porosity on the fatigue life of cast aluminium‐silicon alloys*

Fatigue strength optimization of cast aluminium alloys requires an understanding of the role of micropores resulting from the casting process. High cycle fatigue tests conducted on cast A356‐T6 show that the pore size and proximity to the specimen surface significantly influence fatigue crack initiation. This is supported by finite element analyses (both elastic and elastic–plastic) which demonstrate that high stress/strain concentration is induced by pores which are both large and near to the specimen surface. A new pore‐sensitive model based on a modified stress‐life approach has been developed which correlates fatigue life with the size of the failure‐dominant pore. The model prediction is in good agreement with experimental data.     

A FATIGUE CRACK GROWTH MODEL FOR FIBER-REINFORCED METAL–MATRIX COMPOSITES

A fracture-mechanics based model is proposed for fatigue crack growth in fiber-reinforced metal-matrix composites (MMCs). The model incorporates most of the fracture micromechanisms commonly observed in fiber-reinforced MMCs, including (1) formation of microcracks ahead of the crack tip by either fiber fracture or interface decohesion, (2) interactions of the main crack tip with fibers and microcracks, (3) linkage of the main crack with microcracks, and (4) crack deflection by fibers. Statistical variations of fiber or interface strength are also considered. The essential feature of the model is to compute the changes in the local stress intensity due to various fracture mechanisms; the local stress intensity is then utilized to predict crack growth rate in MMCs via an elastic modulus normalization procedure. Application of the model to predicting crack growth in an alumina fiber Mg-alloy composite is presented.     

Evolution of anodic stress corrosion cracking in a coated material

In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic dissolution, inherently leading to a blunt crack tip. The evolution of the crack surface is modelled as a moving boundary problem using an adaptive finite element method. The rate of dissolution along the crack surface in the substrate is assumed to be proportional to the chemical potential, which is function of the local surface energy density and elastic strain energy density. The surface energy tends to flatten the surface, whereas the strain energy due to stress concentration promotes material dissolution. The influence of the interface energy density parameter for the solid–fluid combination, interface corrosion resistance and stiffness ratios between coating and substrate is investigated. Three characteristic crack shapes are obtained; deepening and narrowing single cracks, branched cracks and sharp interface cracks. The crack shapes obtained by our simulations are similar to real sub-coating cracks reported in the literature.     

HA/HDPE 多尺度生物复合材料微观强韧化机制

通过电镜分析及理论推导对羟基磷灰石( Hydroxyapatite, HA) /高密度聚乙烯( High density polyethylene, HDPE) 复合材料界面粘结状态、HA 颗粒对裂纹扩展的钝化、钉扎作用、复合纤维对体系分子热激活能的影响及复合纤维的能量吸收机制与增强增韧等进行了深入研究。结果表明: HA/HDPE 复合材料通过纳米HA 颗粒与 HA/HDPE 复合纤维在不同尺度上协同作用达到增强增韧的效果。即在纳米尺度, 纳米HA 颗粒的均匀分散和高的HA/HDPE 界面结合强度显著提高了HDPE 的结晶度, 细化了HDPE 晶粒尺寸, 并在HA 颗粒表面形成取向结晶层, 从而使材料在断裂过程中通过HDPE 取向结晶层的基体形变和HA 脱粘过程对微裂纹起钝化和钉扎作用, 并扩大能量耗散的区域, 以阻滞微孔隙和银纹的长大和破断, 抑制大裂纹的早期形成。在微米尺度, 由于HA/HDPE 复合纤维的定向排列, 使体系的活化体积显著降低, 大大增加了材料的断裂热激活能, 从而显著提高材料的强度。另一方面, 复合纤维在应力作用过程中通过纤维断裂、纤维拔出、裂纹偏转机制使材料在形变与破坏过程中耗散更多的能量, 从而显著提高材料的强度和韧性。      

考虑材料组成特性的混凝土轴拉破坏过程细观数值模拟

为反映骨料、砂浆及其之间的界面过渡区的组合特点和材料性能,基于材料细观非均匀性和有限元方法的混凝土破坏过程细观数值模拟需进行复杂、细致的网格剖分,导致了繁重的前处理工作和可观的计算量。该文对混凝土材料细观单元材质组成的单一化假定进行改进,将内嵌界面过渡区材料的规则化单元视为一种广义复合材料单元,建立了复合型界面损伤模型。采用等效方法确定单元的复合弹性关系,通过有限元法计算单元的局部应力;用细观层次上弹性力学性能的弱化描述单元组成材料的损伤,混凝土材料的破坏过程通过单元各组分的损伤模拟。应用该复合型界面损伤模型研究了混凝土试件的单轴拉伸破坏过程,细观数值模拟结果符合混凝土试件的宏观破坏特征,表明该模型可作为分析混凝土材料破坏过程的一种有效途径。     

币形裂纹纤维桥联效应力学分析

本文基于Ｃａｓｔｉｇｌｉａｎｏ＇ｓ定理和界面剪滞模型，得到了含界面相效应的复合材料币形裂纹纤维桥联增韧和裂纹张开位移控制方程。并按照第二类Ｆｒｅｄｈｏｌｍ积分方程的迭代解法给出其数值结果。为便于分析界面相参数对增韧效果等影响，寻求了该控制方程的近似解，对近似解进行了误差估计。在此基础上得到了界面剪切模量、裂纹长度、界面厚度、纤维半径，纤维体积分数以及材料性质等参数对币形裂纹桥联效应的影响。     

Characterization of wake-zone tractions in an oxidation-inhibited carbon/carbon composite

A novel post-fracture tensile (PFT) experiment has been employed to study the bulk pull-out behavior of a two-dimensional, eight-harness satin-weave carbon/carbon composite. In the PFT test, a pre-cracked specimen is loaded in tension in order to characterize the microstructural features responsible for the bridging tractions that so strongly influence the R-curves of these continuous-fiber-reinforced composites. The initial crack extension was found to reduce the maximum tensile stress monotonically. This behavior was attributed to the increasing damage zone size developed with flexure. The arrest stress level, immediately following the maximum tensile stress, apparently arises from largely frictional mechanisms, as governed by the development of matrix damage. With increasing crack extension, the maximum tensile stress tends to decay toward the arrest stress, in keeping with a model for increasing interfacial damage. The development of damage with crack extension appears to be influenced by both specimen geometry and microstructure, which is emphasized by the characteristic interfacial properties of this composite with very high-strength fibers with respect to that of the matrix.     

The effects of size and stacking sequence of composite laminated patch on bonded repair for cracked hole

The performance of a bonded repair for cracked holes has been studied using the three dimensional finite element method, linear elastic fracture mechanics and strain energy density theory. Increasing the composite patch size reduces the strain energy level at the crack tip; increasing the patch length normal to the crack is a better choice. The stacking sequences of the laminated patch have little influence on the strain energy distribution in the vicinity of the crack. To repair the cracked holes of aircraft components subjected to variable direction loading during flight, the orientations of the patch ply, 90° and ±45° with respect to the crack direction, are the optimum selection in bonded repairs.     

Effect of crack density and connectivity on the permeability of microcracked solids

In composite theory microcracks in solid are usually treated as degenerated inclusions separately embedded in matrix. For heterogeneous engineering composites like concrete and rock, the real cracking patterns are more complicate and quite different from this assumption due to the natural clustering and inter-connection of microcracks. This paper investigates the permeability of solids containing a crack network with finite connectivity following both theoretical and numerical approaches. Firstly, no connectivity is assumed for cracks and the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability of solids. Then the amplification of permeability by crack connectivity is quantified for parallel crack cases and for general crack patterns. This amplification effect is modeled by a crack length augmentation factor. In this way the IDD method is extended to evaluate the permeability of cracked solids for a finite crack connectivity before total percolation of cracks. Afterwards, by a carefully designed Monte-Carlo algorithm, the representative volume element (RVE) is built numerically for cracked solids with cracks having random spatial locations and random lengths. The permeability of 2D cracked solids is solved by finite element method (FEM). Through this numerical tool, the effect of both crack density and connectivity on the permeability is solved, and especially the relation between crack connectivity and the geometrical coefficient of crack clustering is put into evidence. From this study it is showed that the extended IDD method can be adapted to a microcracked solid with finite connectivity and can provide good estimates for the permeability.     

The influence of the fibre properties on the Behaviour of an Interface Crack in the unit cell and its representativity for the real composite

The influence of the elastic properties of the fibre on the profile of crack characteristics has been studied for an interface crack between the fibre and the matrix in the unit cell of a composite. The representativity of the unit cell for the whole composite has been proofed by using the method of finite elements. Die Arbeit entstand im Fachbereich 10 der Gesamthochschule Paderborn.     

Bridge-toughening analysis of the penny crack in a fiber reinforced composite with interfacial effect

A fracture mechanics analysis of bridge effect on a fiber reinforced composite containing a penny crack is presented. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castingliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using iteration solution of the Fredholm integral equation of the second kind. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is presented and its error analysis is performed, which demonstrated the approximation solution to be appropriate. A parametric study of the influence of the length, interfacial shear modulus, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out.     

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.     

Mixed-mode analysis of superimposed thermo-elastic effects in fiber-reinforced composites with embedded interface delaminations

This paper deals with the 3D finite element analysis of superimposed thermo-elastic effect on embedded interfacial delamination crack growth characteristics in fiber-reinforced laminated composites. Interlaminar fracture at the delamination front is found to be a mixed-mode phenomenon due to the anisotropy and heterogeneity of thermo-physical properties of composite materials. This leads to the requirement of finite element evaluation of energy release rates, based on the principles of linear elastic fracture mechanics. The strain energy release rate components along the delamination front due to a uniform temperature drop, during the manufacturing stages of composite laminates, to room temperature and subsequent mechanical loading is obtained by superimposing their respective effects based on the assumptions of linear elasticity. Numerical calculations are carried out for multi-layered cross-ply and angle-ply composite laminates and energy release rate plots demonstrate large asymmetries along the delamination front due to the interaction of residual stresses and superimposed transverse loading.     

Fracturing behaviors of FRP-strengthened concrete structures

In this paper, we focus on the study of concrete cracking behavior and interfacial debonding fracture in fiber reinforced polymer (FRP)-strengthened concrete beams. An experimental program is systematically reviewed according to the observed failure modes, in which it is found that the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. A finite element analysis is performed to investigate the different types of debonding propagation along FRP-concrete interface and crack distribution in concrete. For the numerical fracture models, interfacial debonding that initiates and propagates in adhesive layer is modeled by fictitious interfacial crack model. And concrete cracking, including the debonding fracture through interfacial concrete, is modeled by smeared crack model. Properties of the interfacial adhesive layer and concrete are considered to significantly influence the debonding propagation types and crack distribution. The interactions between interfacial bond strength, interfacial fracture energy of bond adhesive layer and tensile strength, fracture energy of concrete are discussed in detail through a parametric study. According to the results, the effects of these properties on different types of interfacial debonding, concrete cracking behavior and structural load-carrying capacity are clearly understood.     

EFFECT OF ELASTIC MISMATCH ON THE GROWTH OF A CRACK INITIALLY TERMINATED AT AN INTERFACE IN ELASTIC PLASTIC BIMATERIALS

Abstract A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch.     

A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks

Summary The damage in a composite material due to a distribution of cracks manifests itself as a reduction of moduli and/or change in elastic constants. This paper presents the effective elastic moduli of a solid containing inclusions and a general distribution of tunnel cracks. Both in-plane and out-of-plane elastic constants are determined. In addition to crack density and inclusion volume fraction, the effective elastic constants are found to depend on a function (), which characterizes the crack orientation distribution, while the anisotropy of a cracked composite is solely induced by the crack orientation distribution. It is established that the effect of inclusions and microcracks on effective moduli is decoupled, i.e., one can obtain the moduli of a solid containing microcracks and inclusions by the corresponding moduli of the solids with microcracks only and with inclusions only. For a solid containing a crack distribution with mirror symmetry, the effective elastic constants can be greatly simplified and can be expressed in terms of two scalar quantities rather than a general function (). This conclusion is particularly useful in the analysis of the micromechanical model. The effect of the asymmetry of () on the effective elastic constants is also investigated.