梯度复合材料应力强度因子计算的梯度扩展单元法

推导了一种适用于梯度复合材料断裂特性分析的梯度扩展单元,采用细观力学方法描述材料变化的物理属性,通过线性插值位移场给出了4节点梯度扩展元随空间位置变化的刚度矩阵,并建立了结构的连续梯度有限元模型.通过将梯度单元的计算结果与均匀单元以及已有文献结果进行对比,证明了梯度扩展有限元(XFEM)的优越性,并进一步讨论了材料参数对裂纹尖端应力强度因子(SIF)的影响规律.研究结果表明:随着网格密度的增加,梯度单元的计算结果能够迅速收敛于准确解,均匀单元的计算误差不会随着网格细化而消失,且随着裂纹长度和属性梯度的增大而增大;属性梯度和涂层基体厚度比的增大导致涂覆型梯度材料的SIF增大;裂纹长度的增加和连接层基体厚度比的减小均导致连接型梯度材料的SIF增大.     

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。     

梯度复合材料热传导分析的梯度单元法

给出了一种适用于梯度复合材料热传导分析的梯度单元, 采用细观力学方法描述材料变化的热物理属性, 通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下, 矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果, 验证了梯度单元的有效性, 并讨论了相关参数对梯度单元的影响。结果表明, 梯度单元和均匀单元得到的温度场基本一致; 当热载荷垂直于材料梯度方向时, 梯度单元能够给出更加精确的局部热通量场; 当热载荷平行于材料梯度方向时, 4节点梯度单元性能恶化, 8节点梯度单元和均匀单元的计算结果与精确解吻合很好。     

梯度涂层材料中裂纹问题的非均匀元分析

本文采用非均匀等参有限元的方法研究了薄膜梯度涂层/均匀基材中的界面裂纹问题,并与双材料界面裂纹情况进行了对比计算。研究表明:在均匀基材上采用梯度涂层,与双材料相比可以有效地降低裂尖场应力强度因子;同时还分析了涂层厚度与梯度参数对界面应力强度因子的影响。结果表明:当薄膜厚度大于或等于裂纹长度时,应力强度因子(KI、KII)对其尺度的变化显得不敏感;对梯度参数的影响而言,当材料性能曲线的幂指数m大于1时,裂尖场的应力强度因子KII相对KI很小且基本不随m变化,因此裂尖场与均匀材料情况类似;当m小于1时,应力强度因子KII随m减小而急剧增大,裂尖场由KI及KII控制,断裂趋于混合型。     

梯度钛合金裂纹扩展速率测试及梯度对扩展寿命影响

为明确梯度材料中裂纹扩展速率分布情况,对含裂纹TC11-TC4以及TA15-TA2两种组合梯度钛合金进行标准三点弯疲劳试验。试验结果表明:梯度结构中不同部位的相同组分扩展性能相同,给出了4种3D打印组分钛合金的Paris公式;梯度材料组分弹性模量的变化会改变裂纹尖端应力强度因子,对位于模量较低一侧的裂纹扩展有抑制作用;过渡层影响厚度范围内裂纹扩展速率介于两种组分之间且连续过渡,表明梯度材料可以消除异种材料连接的界面效应,提出基于组分材料体积分量的混合率描述梯度层中扩展性能的分布规律;恒定载荷试验中仅扩展方向不同情况下寿命有显著差别,验证了合理安排梯度参数可提高结构出现裂纹后的生存能力,其中扩展性能以及模量的变化分布对扩展寿命均有影响。     

Cu/WCp叠层功能梯度材料疲劳裂纹扩展速率的数值模拟

本研究基于FRANC2D(Fracture Analysis Code in 2 Dimensions)二维断裂分析有限元软件,并结合大型有限元软件ABAQUS,对Cu/WC_p双层及多层功能梯度材料的疲劳裂纹扩展进行数值模拟研究,控制疲劳裂纹沿不同梯度方向扩展,计算出裂纹扩展中的应力强度因子幅(ΔK),绘制出疲劳裂纹扩展速率曲线,以及裂纹扩展速率和裂尖距界面距离l的关系曲线(da/dN-l),将模拟计算结果与试验结果进行对比分析。研究表明:结合FRANC2D和ABAQUS的数值模拟方法,在比较复杂的叠层功能梯度材料有限元模型建立中具有很大的优势,可以快速地计算功能梯度材料的应力强度因子值;发现材料梯度层间界面的存在以及材料梯度含量的变化,对功能梯度材料裂纹扩展的整个阶段都存在很大影响;梯度层的数量对功能梯度材料的疲劳裂纹扩展速率也有一定影响。     

聚合物梯度材料黏弹性断裂的双控制参数

针对组分材料体积分数任意分布的聚合物功能梯度材料,研究其在蠕变加载条件下Ⅰ型裂纹应力强度因子（SIFs）和应变能释放率的时间相依特征。由Mori-Tanaka方法预测等效松弛模量,在Laplace变换域中采用梯度有限元法和虚拟裂纹闭合方法计算断裂参数,由数值逆变换得到物理空间的对应量。分析边裂纹平行于梯度方向的聚合物功能梯度板条,分别考虑均匀拉伸和三点弯曲蠕变加载。结果表明,聚合物梯度材料应变能释放率随时间增加,其增大的程度与黏弹性组分材料体积分数正相关;材料的非均匀黏弹性性质产生应力重新分布,导致裂纹尖端应力场强度随时间变化,当裂纹位于黏弹性材料含量较低的一边时,应力强度因子随时间增加,反之,随时间减小。而且,材料的应力强度因子与时间相依的变化范围和体积分数分布以及加载方式有关,当体积分数接近线性分布时,变化最明显,三点弯曲比均匀拉伸的变化大。SIFs随时间的延长增加或减小、加剧或减轻裂纹尖端部位的“衰坏”,表明黏弹性功能梯度裂纹体的延迟失稳需要联合采用应力强度因子与应变能释放率作为双控制参数。     

纤维增强复合材料界面脱层和基体裂纹的模拟分析

基于Ghosh提出的Voronoi单元有限元方法,构造能同时反映纤维增强复合材料界面脱层和基体裂纹扩展的单元(X-VCFEM单元);应用界面力学理论和断裂力学理论,建立界面脱层、界面裂纹扩展方向和基体裂纹扩展的判断准则;结合网格重划分技术,模拟分析了只含有一个夹杂时界面脱层和基体裂纹扩展的过程,并通过与传统有限元计算结果的比较,验证X-VCFEM单元的可靠性和有效性;同时,模拟分析含任意随机分布夹杂的纤维增强复合材料界面脱层和基体裂纹的产生和扩展过程。结果表明：应用该方法模拟复杂多相复合材料裂纹问题具有计算速度快和精度高的优越性。     

倾斜应力作用下垂直于功能梯度材料夹层的币型裂纹扩展问题

分析了功能梯度材料中币型裂纹扩展问题。该裂纹体受有与裂纹面成任意角度的张应力或压应力,裂纹垂直于无限域中功能梯度材料夹层。假定非均匀介质的功能梯度材料夹层与两个半无限域完全结合,其弹性模量沿厚度方向变化。利用已发表的裂纹应力强度因子数据和线弹性断裂力学的叠加原理,将应力强度因子耦合于最小应变能密度因子断裂判据,讨论了裂纹扩展的临界荷载;并讨论了荷载方向和材料性质对临界荷载的影响。     

岩石材料动载下泛形裂纹扩展数值模拟

岩石材料性能的非均匀性导致断裂面呈现不规则的泛形特性,基于此应用ABAQUS软件建立细观有限元模型,由Weibull分布表征岩石材料性能的非均匀性,对动态拉伸载荷下岩石材料泛形裂纹扩展进行研究。计盒维数计算得到的泛形断裂面的复杂度与实验结果吻合。不同应变率下的泛形裂纹扩展路径及复杂度的计算结果表明,断裂面的复杂度随应变率的增加而减小。进一步分析不同应变率下裂纹扩展的泛形断裂能,发现裂纹扩展的能量释放率随应变率增大而增大。低加载率下,裂纹向断裂韧性较小的单元扩展,但随着加载率的提高,裂纹瞬间穿过断裂韧性相对较高的单元,沿自相似方向扩展。上述结果揭示了应变率对泛形裂纹扩展路径的影响与材料性能的细观非均匀性有关,加深了对岩石材料泛形断裂机制的理解。     

Cracking in coating-substrate composites with multi-layered and FGM coatings

This investigation evaluates, by finite element method, the stress intensity factors (SIF) of cracked multi-layered and functionally graded material (FGM) coatings of a coating-substrate composite, due to the action of uniform normal stress on the crack surfaces. The substrate is assumed to be homogeneous material, while the coating consists of multi-layered media or sigmoid FGMs. The sigmoid FGM is a kind of FGM in which the material properties of the coating are governed by two power-law functions of volume fractions such that the functions of the material property represent sigmoid distributions in the thickness direction, simply called S-FGM in this paper. For the multi-layered coatings, one, two, and four-layered homogeneous coatings with stepwise changing volume fractions are considered. The primary problem addressed herein is the appearance of a crack in the coating surface and its expansion into the substrate along the direction perpendicular to the interface between the coating and the substrate. The results show that if the coating is stiffer than the substrate, a crack in a one-layered coating is much more susceptible to propagation into the substrate than a crack in the two- or four-layered coating. But crack growth can be effectively averted by using an S-FGM coating. However, if the coating is softer than the substrate, the S-FGM coating behaves like a bridge to connect the soft coating and the stiff substrate, and facilitates the expansion of the crack expanding into the substrate. Whereas the one-layered coating can more effectively prevent the crack from propagating into the substrate than can the two- or four-layered coating. The investigation also indicates that the material gradations of S-FGMs influence SIFs obviously only when the crack tip is inside the coating that is stiffer than the substrate. As the crack extends through the coating and into the substrate, the material gradation of the S-FGM coating and the material mismatch of the multi-layered coating slightly bear on the values of SIF.     

Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element

We present new numerical results in buckling failure analysis of cracked composite functionally graded plates subjected to uniaxial and biaxial compression loads. An accurate extended 3-node triangular plate element in the context of the extended finite element method (XFEM) is developed, integrating the discrete shear gap method (DSG) to eliminate shear-locking. The plate kinematics is based on the Reissner–Mindlin theory, and material properties are assumed to vary through thickness direction, obeying a power law distribution. The developed DSG-XFEM is found to be effective and accurate as it owns many desirable advantages: conveniently representing crack geometry which is independent of the mesh; shear-locking effect is no longer valid; mesh distortion is insensitive and controllable; thin plates is possible; triangular elements are easily generated for problems even with complex geometries; and high accuracy. All these arisen features are demonstrated through numerical examples and the effects of crack-length, material gradation, mesh distortion, inclined angles of cracks, boundary conditions, width-to-thickness ratio, length ratio, etc. on the critical buckling coefficient (CBC) are analyzed. Numerical results reveal that the material gradation, crack-length, thickness, length ratios, etc. have a strong effect on the behavior of CBC. This phenomenon is mainly attributed to the plate stiffness degradation due to the presence of local defects and material composition. Also, the boundary conditions greatly alter the CBC whereas the inclination of cracked angle is found to be insignificant.     

Modal analysis of an aluminum beam coated with damaged and porous functionally graded material

In this paper modal analysis is performed on a symmetric aluminum beam which is coated with functionally graded material containing porosities. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with classical lamination theory. To achieve a truthful modeling the gradually changing mechanical properties of the coating are modeled as 25 layers of material, while each individual layer is isotropic and homogeneous. MATLAB is used to write a finite element code and Timoshenko beam elements are used to include shear deformation effects. To show the influences of crack location, crack depth, porosity and the polynomial function index on the natural beam frequencies a parametric study is conducted. Multiple boundary conditions were also considered and it was found that the natural frequency values were significantly affected by the studied parameters.     

STRESS INTENSITY FACTORS FOR A FUNCTIONALLY GRADED MATERIAL CYLINDER WITH AN EXTERNAL CIRCUMFERENTIAL CRACK

This paper presents mode I stress intensity factors for external circumferentially cracked hollow cylinders, which are assumed to be made of functionally graded materials and subjected to remote uniform tension. The conventional finite element method is improved by introducing isoparametric transformation for simulating the gradient variations of material properties in the finite elements. This improved finite element method is verified to be effective and efficient. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors.     

Stress intensity factor evaluations for a curved crack in orthotropic particulate composites using an interaction integral method

This paper develops a domain-independent interaction integral (DII-integral) for extracting mixed-mode stress intensity factors (SIFs) for orthotropic materials with complex interfaces. The DII-integral does not require material property gradients, and moreover its validity is not affected by material interfaces. Combined with the extended finite element method (XFEM), the DII-integral is employed to investigate a straight crack in an orthotropic functionally graded plate and a curved crack in orthotropic particulate composites.     

涂层基体条件对梯度涂层残余应力影响研究

采用有限元法，对结构一定的Al/Ni-ZrO2梯度涂层在基体条件改变时涂层的残余应力进行了分析，结果表明，基体材料的热膨胀系数对涂层的残余应力有显著的影响，对于基体为圆柱形的涂层，其基体与涂层界面的残余应力梯度，最大轴向拉应力均随热膨胀系数的增大而线性增大，表面纯陶瓷层与次层界面残余应力梯度则随之减小，增大基体的直径和厚度，可缓和涂层残余应力，并在基体直径为36mm,厚度为20mm时各残余应力基本稳定。     

The interface crack problem under a concentrated load for a functionally graded coating–substrate composite system

The plane crack problem for a functionally graded coating–substrate system under a concentrated load is studied in this paper. The medium consists of a functionally graded coating bonded to a homogeneous substrate of finite thickness, containing an interface crack of finite length. With use of the integration transform and differential factor methods, the displacement form can be obtained. By introducing auxiliary functions, the present problem can be turned into solving a group of singular integral equations. The mixed-mode stress intensity factors (SIFs) and strain energy release rates (SERRs) are obtained. The influences of the parameters such as the load location, nonhomogeneity constants and the geometry parameters on the SIFs and SERRs are studied.