求解双材料界面裂纹应力强度因子的扩展有限元法

基于双材料界面裂纹尖端的基本解,构造扩展有限元法(eXtended Finite Element Methods, XFEM)裂尖单元结点的改进函数。有限元网格剖分不遵从材料界面,考虑3种类型的结点改进函数:弱不连续改进函数、Heaviside改进函数和裂尖改进函数,建立XFEM的位移模式,给出计算双材料界面裂纹应力强度因子(Stress Intensity Factors, SIFs)的相互作用积分方法。数值结果表明:XFEM无需遵从材料界面剖分网格,该文的方法能够准确评价双材料界面裂纹尖端的SIFs。     

基于内聚力模型的热障涂层失效行为研究

热障涂层以其优异的隔热、耐磨和耐蚀性而被广泛应用于航空涡轮发动机中,其能够提高发动机的热效率和延长涡轮叶片的使用寿命。热障涂层的失效往往是裂纹扩展导致,其主要失效形式为表面开裂和界面分层失效。针对热障涂层的裂纹扩展行为,最重要也最直接的研究方法就是对热障涂层的整个损伤失效过程进行数值模拟,以便深入了解涂层失效过程及失效机理。内聚力模型能够比较精确地描述界面开裂问题,在一定程度上可减轻甚至消除裂纹尖端的应力奇异性,可以模拟任意裂纹扩展,故而在裂纹扩展研究中得到了广泛应用。采用内聚力模型模拟热障涂层表面开裂和界面分层失效的过程中,通常把内聚力单元预埋在可能出现裂纹的实体单元之间,当材料发生破坏时,裂纹就会沿着内聚力单元排布的方向形成和扩展。然而造成热障涂层损伤失效的因素较多,失效机理复杂,以及内聚力模型本身的缺陷性,使得利用内聚力模型模拟热障涂层失效过程的研究还不够全面。目前已经通过内聚力模型实现了热障涂层的损伤失效过程模拟,包括表面开裂过程和界面分层失效过程。当前研究大多忽略了涂层内部的微细观缺陷而将热障涂层视为均质材料进行研究,并且内聚力模型本身还存在一些问题,如参数的确定等。随着热障涂层的发展以及对内聚力模型认识的不断加深,内聚力模型模拟热障涂层损伤失效过程也在不断发展与完善。在表面开裂模拟方面,通过在陶瓷涂层内垂直嵌入内聚力单元来模拟陶瓷层内表面裂纹的扩展行为。陶瓷涂层内裂纹扩展行为的模拟大多采用扩展有限元法,内聚力模型的应用相对较少,而内聚力模型可有效解决界面开裂问题,特别是粘结层/陶瓷界面开裂问题,故而被广泛应用于热障涂层界面失效问题的研究中。本文对内聚力模型进行了简要介绍,总结了内聚力模型在模拟热障涂层损伤失效过程方面的研究进展,指出了当前研究中存在的问题并对其下一步的发展进行了展望。     

Nylon-230T/TPU织物蒙皮撕裂性能的数值模拟和试验研究

针对每平方厘米由230根尼龙纱平纹编织并复合热塑性聚氨酯（Nylon-230T/TPU）的织物蒙皮,通过数值模拟和撕裂试验研究了预制裂纹对其撕裂性能的影响,主要包括裂纹长度、裂纹倾斜角度和裂纹位置对蒙皮撕裂强度的影响,通过数字图像相关技术（DIC）获取蒙皮撕裂过程中的应变场,研究了撕裂过程中蒙皮应变场变化规律;分别利用扩展有限元法（XFEM）、内聚力单元法（CZM）及虚拟裂纹闭合技术（VCCT）对预制裂纹Nylon-230T/TPU织物蒙皮的裂纹扩展过程和路径进行了数值模拟,模拟结果与试验结果吻合较好。研究结果表明：Nylon-230T/TPU织物蒙皮的撕裂强度与预制裂纹长度、裂纹倾斜角度及裂纹位置都密切相关;裂纹极大地影响了蒙皮的应变场分布;本文数值模拟方法能够准确预测织物蒙皮裂纹的扩展过程和路径。     

用裂纹单元分析双压电材料界面力电耦合奇异场

为了求解双压电材料在机械荷载和(或)外加电场的作用下,界面裂纹尖端的力电耦合奇异场,提出了一种全数值方法。该全数值方法的实施可以分为两个部分:首先,用一维有限元方法求解不同压电材料界面裂纹尖端力电耦合奇异场特征解;然后,采用杂交有限元列式构造一种所谓的裂纹单元,在该杂交有限元的列式中,假设应力场和电位移场是利用上述一维有限元方法计算得到的特征解推导出来的;利用该单元可以得到全部的力电耦合奇异场的解。通过对单一压电材料中心裂纹尖端力电耦合奇异场的计算,该方法的准确性和高效性得到了验证;进而用该方法研究了双压电材料界面力电耦合场奇异场。     

含裂纹压电材料的Cell-Based光滑扩展有限元法

为精确而有效地求解机电耦合作用下含裂纹压电材料的断裂参数,首先,通过将复势函数法、扩展有限元法和光滑梯度技术引入到含裂纹压电材料的断裂机理问题中,提出了含裂纹压电材料的Cell-Based光滑扩展有限元法;然后,对含中心裂纹的压电材料强度因子进行了模拟,并将模拟结果与扩展有限元法和有限元法的计算结果进行了对比。数值算例结果表明:Cell-Based光滑扩展有限元法兼具扩展有限元法和光滑有限元法的特点,不仅单元网格与裂纹面相互独立,且裂尖处单元不需精密划分,与此同时,Cell-Based光滑扩展有限元法还具有形函数简单且不需求导、对网格质量要求低且求解精度高等优点。所得结论表明Cell-Based光滑扩展有限元法是压电材料断裂分析的有效数值方法。      

薄板弯曲和振动分析的区间B样条小波有限法

基于二维张量积区间B样条小波及小波有限元理论,研究了用于薄板静动力学分析的区间B样条小波有限元法。在小波有限元用于薄板分析的列式过程中,采用区间B样条小波尺度函数对横向位移场逼近,从矩形和斜形薄板静动力学势能泛函出发,由变分原理得到小波有限元求解方程。该方法具有B样条函数数值逼近精度高和多种用于结构分析的小波基函数的特点。数值算例表明:区间B样条小波有限元法能以很少的计算自由度获得与其它方法同样的计算精度。     

热喷涂零件界面裂纹扩展行为影响因素研究

热喷涂技术在提高构件寿命等方面得到了广泛应用,但界面裂纹的存在对零件寿命的影响尤其明显。本工作利用有限元法研究了残余应力、涂层厚度以及初始裂纹长度等因素对界面裂纹扩展的影响。研究结果表明:残余压应力的增加会导致临界载荷的降低,促使裂纹尖端应力相角增大,更易萌生界面裂纹;而残余拉应力的增加会导致临界载荷的升高,促使裂纹尖端应力相角降低,更易萌生垂直于界面的裂纹。此外,厚涂层易产生平行于界面的裂纹,以剪切失效为主导;薄涂层易产生垂直于界面的裂纹,以拉伸失效为主导。初始裂纹长度越长越易出现涂层与基体的剥离,导致涂层的失效。通过三点弯曲实验对不同初始长度的裂纹进行验证,实验结果与有限元模拟结果相近,验证了有限元模拟的正确性,为精确控制热喷涂零件界面的裂纹扩展提供了科学依据和理论基础。     

混凝土裂纹扩展过程模拟的扩展有限元法研究

扩展有限元法(theextendedFiniteElementMethod,XFEM)为数值模拟结构裂纹扩展过程提供了一条有效途径。该文介绍了用扩展有限元法对混凝土结构裂纹扩展过程进行数值模拟的实现方法。采用虚拟裂缝模型模拟混凝土非线性断裂行为,针对二维四边形单元推导了详细的有限元列式。采用3种方案对非线性方程系统进行求解,分析了其求解思路并概括了其求解步骤。通过对带初始边缘裂纹的单向拉伸混凝土板的数值模拟,对3种求解方案的计算结果进行了分析和讨论。     

双相介质界面附近裂纹的断裂力学特征

复合材料界面附近的力学性态对于材料的性能和强韧化影响是非常重要的。首先研究和讨论了含裂纹的双相介质的J 积分守恒定律的适用性问题, 采用有限元法证明了当裂纹平行靠近界面时, 其J 积分数值与裂纹位置无关的假设。文中建立了一种双相介质界面附近存在斜裂纹的分析模型, 用有限元和数值拟合相结合的方法, 得到了在远场单轴拉应力作用下, 斜裂纹处在不同介质中, 近界面一端裂尖的é 型能量释放率近似计算公式, 和相应的应力强度因子的计算方法。     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

基于区间B样条小波有限元的移动荷载识别

小波有限元以区间B样条小波尺度函数为插值函数构造小波有限元单元,并通过单元转换矩阵建立小波空间与物理空间各参数之间的关系.采用动态规划法与Tikhonov正则化法识别移动荷载,避免了直接处理反问题时的振荡与数值计算病态解等问题.算例采用所测得的部分离散点的动态响应数据为已知信息,验证了小波有限元的优越性及小波的多尺度特...     

Strain energy release rates for an interface crack in orthotropic media--a finite element investigation

Strain energy release rate (SERR) components for an interface crack in two-dimensional orthotropic media were obtained using finite element (FE) analysis. The elastic analysis of interface cracks results in oscillatory singularity. This is prevalent over a very small zone near the crack-tip, where the traction free crack faces undergo unacceptable deformations resulting in the interpenetration of crack faces. The individual and total strain energy release rates are calculated using modified crack closure integral (MCCI) method. Although the total SERR converges, it is observed that the individual SERR components are dependent on the values of the smallest element size (Δa) at the crack-tip. It is observed that both the crack opening and sliding displacements are oscillatory when the interpenetration is allowed in the contact zone. The contact zone length (r_c) calculated using Suo's analytical expression [Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Royal Soc. London, Ser A427 (1990) 331] is in good agreement with the results from FE analysis and MCCI calculations. However, for the chosen material properties, the estimated contact zone length based on the analytical expression proposed by Ni and Nemat-Nasser [J. Mech. Phys. Solids 39 (1991) 113] exhibits a large deviation from the present FE results. It is seen that the mode-II behavior dominates the crack growth, even under mode-I loading.     

基于界面断裂的粘聚区长度计算方法研究

基于各向异性双材料界面断裂力学理论,再根据D-B模型假设的有限裂纹尖端奇异性将消失,推导出复合材料分层裂纹尖端粘聚区长度的计算模型。结果显示复合材料分层裂纹尖端粘聚区具有振荡性(当振荡因子0时),并且粘聚区长度与裂纹长度、应力值及振荡因子有关。将新模型应用于界面单元法中,模拟了双悬臂梁(DCB)和混合型弯曲梁(MBB)分层扩展过程中的载荷-位移关系,并比较了不同的粘聚区长度对收敛性和计算精度的影响,结果表明该模型可较精确地计算复合材料的粘聚区长度,以此为基础划分网格能同时保证收敛性和计算精度要求,并可有效地节省运算时间。     

Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials

This work investigates elastic-plastic crack growth in ceramic/metal functionally graded materials (FGMs). The study employs a phenomenological, cohesive zone model proposed by the authors and simulates crack growth by the gradual degradation of cohesive surfaces ahead of the crack front. The cohesive zone model uses six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) to describe the constitutive response of the material in the cohesive zone. A volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model) describes the elastic-plastic response of the bulk background material. The numerical analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive zone model and the computational scheme to analyze crack growth in a single-edge notch bend, SE(B), specimen made of a TiB/Ti FGM. Cohesive parameters are calibrated using the experimentally measured load versus average crack extension (across the thickness) responses of both Ti metal and TiB/Ti FGM SE(B) specimens. The numerical results show that with the calibrated cohesive gradation parameters for the TiB/Ti system, the load to cause crack extension in the FGM is much smaller than that for the metal. However, the crack initiation load for the TiB/Ti FGM with reduced cohesive gradation parameters (which may be achieved under different manufacturing conditions) could compare to that for the metal. Crack growth responses vary strongly with values of the exponent describing the volume fraction profile for the metal. The investigation also shows significant crack tunneling in the Ti metal SE(B) specimen. For the TiB/Ti FGM system, however, crack tunneling is pronounced only for a metal-rich specimen with relatively smaller cohesive gradation parameter for the metal.     

Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method

This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for fully-automatic modelling of cohesive crack growth in quasi-brittle materials. The simple linear elastic fracture mechanics (LEFM)-based remeshing procedure developed previously is augmented by inserting nonlinear interface finite elements automatically. The constitutive law of these elements is modelled by the cohesive/fictitious crack model to simulate the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. The crack is assumed to grow when the mode-I stress intensity factor K_I vanishes in the direction determined by LEFM criteria. Other salient algorithms associated with the SBFEM, such as mapping state variables after remeshing and calculating K_I using a “shadow subdomain”, are also described. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the new method. The results show that this SBFEM-FEM coupled method is capable of fully-automatically predicting both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for problems with strong snap-back. Parametric studies were carried out on the crack incremental length, the concrete tensile strength, and the mode-I and mode-II fracture energies. It is found that the K_I ? 0 criterion is objective with respect to the crack incremental length.     

Comparison of cohesive zone model and linear elastic fracture mechanics for a mode I crack near a compliant/stiff interface

Cohesive zone model has been widely applied to simulate crack growth along interfaces, but its application to crack growth perpendicularly across the interface is rare. In this paper, the cohesive zone model is applied to a crack perpendicularly approaching a compliant/stiff interface in a layered material model. One aim is to understand the differences between the cohesive zone model and linear elastic fracture mechanics in simulating mode I crack growth near a compliant/stiff interface. Another aim is to understand the effects of elastic modulus mismatch and cohesive strength of the stiff layer on the crack behavior near the interface. To simulate crack growth approaching an interface, the cohesive zone model which incorporates both the energy criterion and the strength criterion is an effective method.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.     

复合材料DCB试件裂纹扩展理论分析

在弹性地基梁模型基础上,通过挠度与相对位移关系引入了双线性cohesive本构关系,并通过界面损伤因子统一描述界面损伤状态,在裂纹尖端考虑了损伤黏聚区存在,分别获得了各段通解。采用连续性边界条件求解积分常数,并以裂纹长度以及黏聚区范围为变量求解获得了载荷-位移曲线,从而获得了双悬臂梁（DCB）试件裂纹扩展过程。通过与已有理论模型结果对比,验证了本文理论分析的正确性,而文中理论考虑了弹性段后非线性的存在,且可同时考察3个cohesive参数的影响。通过研究界面参数变化对载荷-位移曲线的影响,从而对准确模拟界面时cohesive参数的选取提供一定的依据,并分析了界面参数与黏聚区长度的关系。