Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris’ law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena.     

XFEM fracture analysis of shells: The effect of crack tip enrichments

In this study the effect of crack tip enrichment functions in the extended finite element analysis of shells is investigated. Utilization of crack tip enrichments leads to reduction of the required number of elements, mesh independency and increased accuracy in computation of fracture mechanics parameters such as the stress intensity factor, the crack tip opening displacement and the crack tip opening angle. The procedure is verified by modeling various shell and plate problems and available benchmark tests. Also, effects of enrichments of in-plane, out-of-plane and rotational degrees of freedom and high order out-of-plane enrichments on different fracture modes are studied. Moreover, reduction of the dependency of crack tip opening angle on the element size in crack propagation problems is discussed.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method

The newly-developed scaled boundary finite element method (SBFEM) is able to calculate stress intensity factors directly because the singularity in stress solutions at crack tips is analytically represented. By taking this advantage, a mixed-mode crack propagation model based on linear elastic fracture mechanics (LEFM) was developed in this study. A domain is first divided into a few subdomains. Because the dimensions and shapes of subdomains can be flexibly varied and only the domain boundaries or common edges between subdomains are discretised in the SBFEM, a remeshing procedure as simple as in boundary element methods was developed with minimum mesh changes whereas the generality and flexibility of the FEM is well maintained. Fully-automatic modelling of mixed-mode crack propagation is then achieved by combining the remeshing procedure with a propagation criterion. Three mixed-mode examples were modelled. Comparisons of the numerical results with those from available publications show that the developed model is capable of predicting crack trajectories and load-displacement relations accurately and efficiently.     

Analysis of stress intensity factors for three-dimensional interface crack problems in electronic packages using the virtual crack closure technique

In this study the fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles, along the curvilinear front of a three-dimensional bimaterial interface crack in electronic packages are considered by using finite element method with the virtual crack closure technique (VCCT). In the numerical procedure normalized complex stress intensity factors and the corresponding phase angles (Rice, J Appl Mech 55:98–103, 1988) are calculated from the crack closure integrals for an opening interface crack tip. Alternative procedures are also described for the cases of crack under inner pressure and crack faces under large-scale contact. Validation for the procedure is performed by comparing numerical results to analytical solutions for the problems of interface crack subjected to either remote tension or mixed loading. The numerical approach is then applied to study interface crack problems in electronic packages. Solutions for semi-circular surface crack and quarter-circular corner crack on the interface of epoxy molding compound and silicon die under uniform temperature excursion are presented. In addition, embedded corner delaminations on the interface of silicon die and underfill in flip-chip package under thermomechanical load are investigated. Based on the distribution of the fracture mechanics parameters along the interface crack front, qualitative predictions on the propensity of interface crack propagation under thermomechanical loads are given.     

基于应力强度因子评估WCP形状对WCP/Fe复合材料热疲劳裂纹扩展行为的影响

应力强度因子在断裂力学中广泛应用于预测由远程载荷或残余应力引起的裂缝尖端附近应力状态。本文基于平面应力条件下应力强度因子建立WC_P形状与其尖端应力之间的规律,利用有限元分析软件对含不同形状WC_P的WC_P/Fe复合材料的热应力进行模拟仿真,研究WC_P形状对WC_P/Fe复合材料热疲劳裂纹扩展行为的影响。研究结果表明,WC_P的形状显著影响应力强度因子,进一步影响WC_P/Fe复合材料的热疲劳裂纹扩展行为。含球状和不规则状WC_P的WC_P/Fe复合材料的极限抗压强度分别约为460 MPa和370 MPa。含不规则状WC_P的WC_P/Fe复合材料因应力集中而容易产生脆性开裂现象。通过热震实验进行验证,发现实验结果与模拟仿真结果相近,说明有限元法的准确性,同时为WC_P/Fe复合材料的热疲劳裂纹扩展行为研究提供科学依据和理论基础。      

基于磁记忆方法的抽油杆裂纹扩展监测

基于拉-拉疲劳实验,利用磁记忆检测仪监测了抽油杆试件疲劳裂纹扩展的整个过程,提取了表征应力集中程度的磁信号合成梯度极限状态系数指标;并结合有限元方法计算了裂纹尖端的断裂力学参量,得到不同裂纹长度所对应的应力强度因子。结果表明:基于实验数据和仿真结果所建立的磁记忆信号特征指标与应力强度因子之间具有很好的一致性,可以有效反映疲劳裂纹的扩展过程以及累积损伤,为再制造前的毛坯筛选提供理论依据。     

Post-buckling and debond propagation in sandwich panels subject to in-plane compression

Nonlinear finite element analysis is conducted to predict initiation of debond propagation in compression loaded foam cored sandwich panels containing a circular face/core debond embedded at the panel center. A three-dimensional geometrically nonlinear finite element model of the debonded sandwich panel combined with linear elastic fracture mechanics is used to determine the stress intensity factors K_I and K_II and energy release rate at the debond (crack) front parallel and perpendicular to the applied load. A range of core densities and debond sizes are analyzed. The opening mode (mode I) was found to dominate the fracture process. The critical load for crack propagation predicted using fracture mechanics concepts was found to agree with measured collapse loads for smaller debonds, but fell below measured debond propagation loads for larger debonds. In all cases the predicted direction of crack propagation was perpendicular to the loading direction, in agreement with experimental observations.     

Finite element analysis of magnetic disk with a horizontal subsurface crack

Sliding contact of a rigid rough surface with a semi‐infinite medium including a horizontal subsurface crack was investigated by using linear elastic fracture mechanics and finite element method (FEM). The fractal geometry was used to characterize the rigid rough surface. The propagation of crack was studied with the shear and tensile stress intensity factors. The effect of surface roughness, crack length to depth ratio and friction at the contact and crack interfaces was investigated by using the FEM. It was shown that increasing friction coefficient at the contact interface increases both K_II and K_I.     

裂纹止裂技术及裂纹动态扩展规律研究

为了对动态荷载作用下水泥粉煤灰砂浆的裂缝动态扩展行为进行研究,提出了一种大尺寸带V型底边的半圆边裂纹(SECVB)试件,其V形底部具有止裂功能。SECVB试件的V形底部设计为180°,150°和120°三个角度。采用落锤冲击装置进行了冲击试验,并使用裂纹扩展计(CPG)用于测量裂纹扩展的相关参数。利用有限差分程序AUTODYN对裂纹扩展行为进行了数值模拟,并用有限元程序ABAQUS计算了裂纹的动态应力强度因子(DSIF);根据CPG测量的裂纹萌生时间和扩展时间来确定临界应力强度因子。试验和数值模拟结果表明,SECVB试件适合于研究动态荷载作用下水泥粉煤灰砂浆的裂纹扩展行为和止裂行为。在裂纹扩展过程中,裂纹可能在一段时间内止裂,并且裂纹在起始时刻的断裂韧度高于裂纹扩展时的断裂韧度。     

Investigation of fatigue crack growth and crack turning on integral stiffened structures under mode I loading

Integral structures have benefits compared to riveted structures, but they offer lower damage tolerance. This investigation analysed possible decrease of crack growth in integral structures by means of design analysis on stringer cross-sections. For this purpose the finite element analysis (FEA) was applied. First the reliability of FEA was proven by comparing calculated crack growth rates (CGR) to test results. Since CGR in linear elastic fracture mechanics is controlled by the stress intensity factors (SIF), different cross-sections were analysed. These configurations were evaluated regarding their crack turning behaviour (T-stress). The SIF was reduced about 18%. Crack turning is more probable when the crack is far away from stringer.     

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。     

非均匀材料界面裂纹的Cell-Based光滑有限元法

为提高非均匀材料界面裂纹尖端断裂参数的求解精度,基于非均匀材料界面断裂力学、Cell-Based光滑有限元(Cell-SFEM)和非均匀材料的互交作用积分法,提出了求解非均匀材料界面裂纹尖端断裂参数的CellBased光滑有限元法,推导了基于Cell-Based光滑有限元法的非均匀材料的互交作用积分法,对非均匀材料间的界面裂纹尖端处正则应力强度因子进行了求解,并与参考解进行了比较,讨论了互交积分区域大小和光滑子元个数与正则应力强度因子的关系。数值算例结果表明:本方法具有很高的计算精度,对积分区域大小不敏感,可为设计、制造抗破坏非均匀材料提供依据。     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

Rim Thickness Effects on Gear Crack Propagation Life

Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. The retarded crack growth and increased the number of crack propagation cycles to failure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Plastic intensity factors for cracked plates

An elastic-plastic analysis is performed for two problems relevant to fracture mechanics: a semiinfinite body with an edge crack in a far out-of-plane shearing field and an infinite plate under plane stress conditions containing a finite line crack in a remote tensile field. Amplitudes of the dominant singularity in the plastic region at the crack tip, the plastic stress and strain intensity factors, are calculated for applied stress levels approaching the yield stress. A technique is developed for using the dominant singular solution in conjunction with the finite element method to make accurate calculations for the near-tip fields. Additionally, a comparative study of deformation theory with flow theory is performed for cracks in an anti-plane shear field. Elastic fracture mechanics is extended to high levels of applied stress for which the plastic zone is no longer small compared to the crack length by relating the critical stress for fracture initiation to the plastic intensity factors.     

Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral

This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.This work has been supported by ONR, with Dr. Y. Rajapakse as the program official.     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.