Development of X-FEM methodology and study on mixed-mode crack propagation

The extended finite element method（X-FEM） is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effiect on fracture made by interface and loading condition.

MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path.For each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked structure.The J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method.The meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method.

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

(Ⅰ+Ⅱ)MIXED MODE HYDROGEN INDUCED CRACKING

Hydrogen induced cracking(HIC)of 0.3% C,1% Cr,1% Mn,1% Si high strength steel has been studied under simple mode Ⅰ,mode Ⅱ and(Ⅰ+Ⅱ)mixed mode loading conditions.Af- ter being hydrogen-charged in IN H_2SO_4 solution,the material behaved hydrogen embrittlement in all the cases studied.The threshold K_(ⅡH)/K_(ⅡX) of HIC under mode Ⅱ load- ing was 0.27,which was nearly the same as that K(ⅠH)/K_(ⅠX)=0.29 under mode Ⅰ loading. While the thresholds of-HIC under(Ⅰ+Ⅱ)mixed mode loading were 0.36,0.41 and 0.37 cor- responding to the K_Ⅱ/K_Ⅰ ratio of 0.27,0.4 and O.81.The results show that simple mode Ⅰ or mode Ⅱ loading is more susceptible to hydrogen embrittlement than(Ⅰ+Ⅱ)mixed mode. For explaining the experimental results,the effects of triaxial stress as well as plastic deformation ahead of crack tip has been discussed.

A MIXED MODE FRACTURE CRITERION BASED ON THE MAXIMUM TANGENTIAL STRESS IN BRITTLE INCLUSION

A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.

Computational Fracture Analysis of an AFM-Specimen under Mixed Mode Loading Conditions

Fracture processes in ship-building structures are in many cases of a 3-D character. A finite element （FE） model of an all fracture mode （AFM） specimen was built for the study of 3-D mixed mode crack fracture behavior including modes Ⅰ,Ⅱ, and Ⅲ. The stress intensity factors （SIFs） were calculated by the modified virtual crack closure integral （MVCCI） method, and the crack initiation angle assessment was based on a recently developed 3-D fracture criterion--the Richard criterion. It was shown that the FE model of the AFM-specimen is applicable for investigations under general mixed mode loading conditions, and the computational results of crack initiation angles are in agreement with some available experimental findings. Thus, the applicability of the FE model of the AFM-specimen for mixed mode loading conditions and the validity of the Richard criterion can be demonstrated.

A THEORETICAL MODEL OF MATRIX CRACKING IN COMPOSITE LAMINATES UNDER THERMOMECHANICAL LOADING

A theoretical approach is presented for analyzing the ply crackingin general symmetric lami- nates subjected to any combination ofin-plane mechanical loading and uniform temperature changes. Theequivalent constraint model proposed by the authors in a previouswork is used to account for the cracking in- teraction betweenlaminae in the laminates. By using a superposition schemce and thestress field solutions the energy release rate for a ply cracking isexplicitly as a function of stiffness reduction parameters of thelaminates. The ratio of mode Ⅰ to mode Ⅱ is introduced formconstruction of the fracture criterion. The effects of the laminateparameters and the crack spacing on the energy release rate and themode mixity are illustrated. Finally, the model is used to predictthe thermomechanical load for the first-ply-cracking.

ROUGHNESS-INDUCED SHEAR RESISTANCE OF MODE Ⅱ CRACK GROWTH

It is obtained in this paper that the fatigue threshold value of mode H was 1.9 times of that of mode Ⅰ in dual-phase steel(DPS),and the normal stress intensity factor range oJ mode Ⅱ branch crack tip was 2.2 times of that of mode Ⅰ.Above results illustrate that the resistance of mode Ⅱ crack growth was higher than that of mode Ⅰ,the former resulting from roughness-induced shear resistance,the latter,crack closure. The mode Ⅱ component can play two important roles in near-threshold fatigue crack growth:(1)increasing crack tip plasticity which accelerates the crack growth and(2)intro- ducing crack surface contact and rubbing to reduce the crack propagation rate.By means of crack closure,the quantity of shear resistance was easily solved in this paper.The friction shear stress strength factor range of mode Ⅱ,K_,is still much higher than the closure stress strength factor range of mode Ⅰ,K_(Ⅰ,cl).This illustrated that the roughness enlarged the second role and played a role of shielding crack tip from mode Ⅱ crack.

Williams单元分析I-II混合型裂纹应力强度因子

为了建立高效、精确的混合型裂纹应力强度因子分析的裂尖奇异区单元,文章在改进Williams级数的基础上建立了裂尖应力奇异域单元的整体位移场,基于普通有限元形函数建立了奇异域子单元的局部位移场,利用整体位移场控制局部子单元的节点位移,结合有限项等比级数求和公式建立了I-II混合型Williams单元刚度方程。根据该单元模型中与应力强度因子相关的参数,可以直接计算裂尖I型、II型应力强度因子,克服了普通单元和奇异单元需要通过中间物理量回归分析、外推计算裂尖处应力强度因子的缺陷,并能取得很高的计算精度和计算效率。结合算例,分析了裂纹长度和倾斜角等参数对应力强度因子的影响,确定了Williams单元的径向比例因子、子单元数、级数项等三个重要参数的取值。

I-II复合型裂缝断裂角的分层剪滞模型与分析

采用修正的剪滞理论建立了岩石、混凝土等准脆性材料的I-II复合型裂缝在单向拉伸荷载作用下的计算模型,得到了与实验相吻合且优于传统S判据的断裂角。通过对远场应力、斜裂缝区应力以及子层位移的合理简化,得到了求解剪滞分析模型的边界条件,进而得到了含斜裂缝的各子层位移分布函数。引入最大应力集中因子,对I-II复合型裂缝前缘应力场进行简化;基于斜裂缝沿最大应力集中因子方向扩展,得到裂缝的断裂角。根据斜裂缝的应力分布,设置不同的子层分区,得到了更为细化的位移分布模式。通过对计算数据的分析,针对单向拉伸荷载作用下的I-II复合型裂缝,建立了按应力场分区设置子层的分层剪滞模型,得到更为精确的斜裂缝断裂角。

Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).

Evaluation of mixed mode-Ⅰ/Ⅱ criteria for fatigue crack propagation using experiments and modeling

In this study, in-plane mixed mode-Ⅰ/Ⅱ fatigue crack growth simulations and experiments are performed for the Al 7075-T651 aluminum alloy which is widely used in the aerospace industry. Tests are carried out under different mode mixity ratios to evaluate the applicability of a fracture criterion developed in a previous study to mixed mode-Ⅰ/Ⅱ fatigue crack growth tests.Results obtained from the analyses and experiments are compared with existing and developed criteria in terms of crack growth lives. Compact Tension Shear（CTS） specimens, which enable mixed mode loading with loading devices under different loading angles, are used in the simulations and experiments. In an effort to model and simulate the actual conditions in the experiments, crack surfaces of fractured specimens are scanned, crack paths are modeled exactly, and contacts are defined between the contact surfaces of a specimen and the loading device for each crack propagation step in the analyses. Having computed the mixed mode stress intensity factors from the numerical analyses, propagation life cycles are predicted by existing and the developed mixed mode-Ⅰ/Ⅱ criteria and then compared with experimental results.

EFFECT OF NON-PROPORTIONAL OVERLOADING ON FATIGUE CRACK GROWTH

The effect of proportional and non-proportional overloading on mode l fatigue crack growth have been studied,and the influences of crack tip plastic zone,crack tip blunting as well as crack closure were discussed.Proportional(model I)overloading may cause more serious crack growth retardation than non-proportional(mixed mode)overloading.Therefore,for estimating the fatigue life of engineering structures to simplify a real overload which may of- ten be non-proportional as a proportional one is not always safe.

Analysis of composite material interface crack face contact and friction effects using a new node-pairs contact algorithm

A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem （e.g., resistant coating and thermal barrier coatings） subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors （SIFs） and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.

应力场常数项对Ⅰ型裂纹起裂扩展行为影响

对含裂纹材料与结构断裂力学评估中的最大环向应力准则(MTS)、最小应变能密度因子准则(SED)和平均应变能密度准则(ASED)以及在此基础上考虑应力场常数项影响修正的断裂准则进行介绍;基于考虑裂尖应力场奇异项和常数项的修正MTS准则、修正SED准则和修正ASED准则,对比分析了裂尖应力场常数项对Ⅰ型裂纹的起裂扩展行为,探究了裂纹尖端应力场常数项以及材料泊松比对Ⅰ型裂纹偏折、断裂极限的影响规律,掌握了应力场常数项对Ⅰ型裂纹偏折、起裂扩展影响阀值。研究结果表明,裂纹尖端应力场常数项T应力对Ⅰ型裂纹起裂扩展偏折角及断裂判据的影响不可忽略,研究结果可为含裂纹材料与结构断裂力学评估提供一定参考。

脆性材料统一断裂相场方法及其裂缝宽度的确定

岩石、混凝土等脆性材料的开裂问题一直是国内外关注的热点和难点,裂缝的演化使得脆性材料的力学性能难以预测。针对脆性材料的拉、剪和拉剪复合开裂问题,将统一拉伸断裂准则引入到相场理论,进而基于谱分解技术提出了统一断裂相场方法,并通过交错算法在商业有限元软件中实现了该方法。拉伸断裂试验和拉剪复合断裂试验数值模拟结果表明:统一断裂相场方法具有热力学一致性,该方法不仅能准确模拟裂缝演化过程中脆性材料的力学性能,还能精准预测拉剪复合裂缝的扩展路径。此外,运用水平集理论构建了一个相场函数,识别了相场裂缝的分界面,进而通过理论推导得出了相场裂缝宽度的计算公式,并对其进行了验证。该研究旨在提出精准预测脆性材料拉、剪和拉剪复合开裂的相场方法,以保障土木工程结构的安全。

含偏置裂纹三点弯曲梁的动态断裂行为研究

采用动态焦散线方法，对含偏置裂纹三点弯曲梁承受横向冲击的弯曲断裂行为进行了一系列动态断裂力学实验研究，分析了无量纲量ａ／ｌ的改变（ａ——初始裂纹偏离梁中心线的距离；ｌ——梁长度的一半）对于裂纹动态扩展行为（裂纹起始状态、裂纹尖端的复合应力强度因子、裂纹扩展速度、裂纹扩展轨迹）的影响，并借助动态光弹性应力分析，对应力波与扩展裂纹的相互作用以及应力波传播规律进行探讨．给出了裂纹尖端复合应力强度因子、裂纹扩展速度的变化。

类岩石材料表面裂纹复合型断裂准则探讨

开展含表面裂纹的类岩石材料试件的直接拉伸试验,分析表面裂纹倾角对试件峰值强度及破坏过程的影响。由于倾斜表面裂纹处于Ⅰ,Ⅱ,Ⅲ复合变形状态,为了进一步研究表面裂纹的断裂判据,利用断裂力学软件计算半圆形表面裂纹前缘的应力强度因子,分析表面裂纹前缘3种应力强度因子的变化规律。根据最小应变能密度准则、最大应力准则以及改进的最大应力准则分别预测半圆形表面裂纹的起裂角,并与前述试验结果进行对比,结果表明,考虑Ⅲ型应力强度因子影响的改进的最大应力准则预测的起裂角与试验结果更接近。

基于Abaqus二次开发的机身开口损伤容限分析

机身结构需要承受由飞行条件引起的机身剪力和弯曲力,以及由座舱压力引起的环向张力和纵向张力,开口损伤可能会逐渐形成裂纹并给飞机带来致命的影响。采用Python脚本语言对Abaqus进行二次开发,实现三维复合裂纹的参数化建模、自动扩展模拟和损伤容限评估,使整个裂纹扩展分析过程更加快速、方便和高效。然后对某运输机机身开口实际模型案例进行研究,预测裂纹扩展方向、输出裂纹扩展轨迹和应力强度因子,计算裂纹扩展寿命、剩余强度和检修周期。结果显示加强结构附近剩余强度可能发生不减反增的现象。为开口结构设计和检修提供参考及指导,具有一定工程意义。