A directional crack path criterion for crack growth in ductile materials subjected to shear and compressive loading under plane strain conditions

A directional crack growth criterion in a compressed elastic perfectly plastic material is considered. The conditions at the crack-tip are evaluated for a straight stationary crack with a small incipient kink. Remote load is a combined hydrostatic pressure and pure shear applied via a boundary layer. Crack surfaces in contact are assumed to develop homogenous Coulomb friction.The crack opening displacement of an extended kink is examined in a finite element analysis to judge the risk of opening mode failure. It has been found that the direction that maximizes the crack opening displacement of an extended kink tip coincides very well with a prediction of the crack growth direction obtained by using a criterion for continued crack growth direction discussed by the authors elsewhere [Int. J. Fract. 108 (2001) 351].Moreover, the by the model predicted incipient crack growth directions are qualitatively comparable with reported crack paths obtained in ductile materials in a limited number of experiments performed under a combined load of in-plane shear and compression.     

An energy-based crack growth criterion for modelling elastic–plastic ductile fracture

A crack growth criterion is derived based on the Griffith energy concept and the cohesive zone model for modelling fracture in elastic–plastic ductile materials. The criterion is implemented in the finite element context by a virtual crack extension technique. An automatic modelling of the ductile fracture process is realised by combining a local remeshing procedure and the criterion. The validity of the derived criterion is examined by modelling a compact tension specimen.     

A pseudo-elastic material damage model,part I: Strain energy density criterion

A failure criterion is presented which relates the strain energy density of the material to both yielding and fracture. Cumulative material damage throughout a structural component may be monitored and the relative influence of yielding and stable crack growth assessed. The criterion is demonstrated, using finite element analysis, for center cracked panel specimens differing by material toughness values. From crack growth increment predictions using the uniaxial stress-strain behavior of the material, the criterion predicts the critical value of the strain energy density factor S_c governing crack instability.     

A pseudo-elastic material damage model, part II: Application to the scaling of specimen size, material behavior and loading rate

A failure criterion is presented which relates the strain energy density of the material to both yielding and fracture. Cumulative material damage throughout a structural component may be monitored and the relative influence of yielding and stable crack growth assessed. The criterion is demonstrated, using finite element analysis, for center cracked panel specimens differing by material toughness values. From crack growth increment predictions using the uniaxial stress-strain behavior of the material, the criterion predicts the critical value of the strain energy density factor S_c governing crack instability.     

Crack kinking in sandwich structures under three-point bending

Sandwich beams under three-point bending containing cracks in the core material very close to the upper skin interface are investigated. The cracks considered parallel or with an imperceptible inclination to the longitudinal beam axis and at different distances from the upper skin interface, are analyzed with static non-linear elastic two and three dimensional finite element analyses. From the proposed analyses stress intensity factors are calculated using linear elastic fracture mechanics. It is demonstrated that the crack propagation on the compression side of the core is mainly subjected in shear. The strain energy density criterion is used in order to determine the angle of kinking of the crack into the core.     

晶体取向对单晶体断裂特征影响的模拟分析

结合Ni基单晶合金制三种不同晶体取向的紧凑拉伸试样试验,本文利用考虑有限变形和品格转动效应的晶体滑移有限元程序对单晶体三维断裂特征进行了模拟计算分析,详细考察了裂纹尖端三维应力场特征和断裂特征,结果表明:晶体取向对裂纹尖端应力场有较大影响,但应力沿试样厚度方向明显分成两个部分,在试样心部,应力沿厚度方向变化不大,在试样外表面则明显变化。裂纹尖端张开位移(CTDD)沿厚度方向类似分成两个部分。垂直于滑移面的应力分量致单晶体的准解理断裂,即裂纹的起裂和扩展途径均与该应力分量有关。     

PZT-4紧凑拉伸试样的断裂分析

基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法. 首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract, 1993, 62: 203$\sim$218)相比较,表明该方法具有很高的精度和很好的计算效率. 随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则. 进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析.      

基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔—库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力—应变曲线各阶段之间的对应关系. 结果表明: 连续—非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.      

Modeling adiabatic shear failure from energy considerations

The numerical simulation of dynamic structural failure by localized shear is quite complex in terms of constitutive models and choice of adequate failure criteria, along with a pronounced mesh-sensitivity. As a result, the existing numerical procedures are usually quite sophisticated, so that their application for design purposes is still limited. This study is based on the implementation of a simple energy-based criterion, which was developed on experimental considerations (Rittel et al., 2006), and uses a minimal number of adjustable parameters. According to this criterion, a material point starts to fail when the total strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual structural behavior. The criterion was embedded into commercial finite element software and tested by simulating numerically four typical high-rate experiments. The first is the dynamic torsion test of a tubular specimen. The second concerns the failure mode transition in mode II fracture of an edge crack in plain strain. The last two involve dynamic shear localization under high rate compression of a cylindrical and a shear compression specimen. A very good adequation was found both qualitatively and quantitatively. Qualitatively, in terms of failure path selection, and quantitatively, in terms of local strains, temperatures and critical impact velocity. The proposed approach is enticing from an engineering perspective aimed at predicting the onset and propagation of dynamic shear localization in actual structures.     

Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature.     

Stress and energy density fields near a blunted crack front in power hardening material

Using Jaumann and Dienes rates of Euler stress in elastic-plastic constitutive equations of finite deformation, plane strain finite element analysis for a compact tension specimen with a blunted crack front is made. The Euler stress, Kirchhoff stress and volume strain energy density near a blunted crack tip are computed. Constitutive relations with different deformation rates affect the the near crack tip solution in a region within an order of magnitude of the crack opening displacement. The results differed from the corresponding solution of deformation plasticity (or nonlinear elasticity) with increasing deformation. They are smaller in a local region of about 2 to 10 times of the crack opening distance.The volume energy density near the crack tip is computed, the stationary values of which determine the locations of extensive yielding and possible sites of crack initiation. It remained nearly constant with increasing deformation. Such a character tends to support the volume energy density criterion as a means for quantifying the ductile fracture behavior of metals.     

CRACK INTERACTING WITH AN INDIVIDUAL INCLUSION BY THE FRACTURE CRITERION OF CONFIGURATIONAL FORCE

基于构型力概念提出一种可判断裂纹起裂以及裂纹扩展方向的新断裂准则.该准则假设当构型合力值达到一个临界值时裂纹开始扩展,而裂纹扩展的方向则为构型合力的矢量方向.基于此断裂准则,本文开发构型力的有限元计算方法,实现对裂纹扩展的数值模拟,并着重对工程中常见的含孔洞/夹杂结构的裂纹扩展问题展开研究.研究结果表明,基于构型力的裂纹扩展准则可以很好地预测裂纹与孔/夹杂的干涉作用,其数值模拟结果与实验结果相符,从而验证了该裂纹扩展模拟方法的有效性.通过对裂纹和夹杂（圆孔、软夹杂、硬夹杂）干涉问题的数值模拟表明,裂纹前端夹杂对裂纹的扩展具有重要影响.裂纹的扩展方向与裂纹和夹杂的相对位置、以及夹杂类型密切相关.软夹杂和圆孔会吸引裂纹向其扩展,而硬夹杂会排斥裂纹扩展,裂纹在扩展过程中会绕开硬夹杂.当裂纹与夹杂夹角较小时,夹杂对裂纹扩展的影响作用明显,当夹角较大时,夹杂对裂纹扩展的影响较小;特别当裂纹与夹杂夹角为45°时,软夹杂和圆孔可能会抑制裂纹的扩展,使裂纹扩展发生止裂.研究结果有助于认清含孔洞/夹杂结构中的裂纹扩展或止裂问题,对于工程中的断裂问题具有重要指导意义.     

Fatigue failure of polyethylene methacrylate in adhesive assembly under unsymmetrical bending

In this paper, a special bending fatigue experiment was firstly performed to investigate the fatigue behavior of polyethylene methacrylate in adhesive assembly. Fatigue lifetime property (S–N curve) was obtained. Finite element calculations on the whole structures also gave the same results with the testing. Based on the experimental data and finite element analysis, a local stress law of predicting bending fatigue lifetime was put forward. The predication lifetime for the polyethylene methacrylate agreed well with the experimental results. Following the strain energy density (SED) criterion was applied to predict the crack initiation and growth path of the adhesive assembly. The predicted results were in good agreement with the optical microscopy (OM) failure image of the failure specimen. SEM image of fracture further showed that there were lots of parallel fatigue lines with perpendicularity to the direction of crack, and an obvious boundary from the crack propagation failure to final brittle fracture.     

Fracture behavior of a nickel-base single crystal superalloy as predicted by the strain energy density criterion

Results from compact tension specimens and scanning electronic microscopy are used to study the fracture characteristics of nickel-base single crystal superalloy DD3. Finite element analyses are also made to better understand the outcome. The experiments showed that the initiation and growth of cracks were dependent on the crystallographic orientation of specimens, and the fracture surfaces coincided with the slip planes. Three-dimensional stresses near the crack tip are obtained. The strain energy density criterion is applied to predict the fracture of the superalloy. Agreement with experiments is good.     

A criterion for the onset of void coalescence under combined tension and shear

Depending on the relative positions of voids and on the loading conditions, shear loading components can play an important role in the void coalescence process leading to ductile fracture. Yet, most void coalescence criteria including the original criterion of Thomason, and its various extensions/improvements, take only normal loads into account and neglect the contribution from shear loads to coalescence. Shear can affect both the stress/strain at the onset of coalescence and the direction of deformation localization. In this paper, first, the predictive capabilities of different coalescence criteria without shear effect are critically assessed and the expressions involved in the original Thomason criterion are fine-tuned by comparing with 3D finite element calculations performed on a unit cell containing a spheroidal void. Then, the improved Thomason criterion is theoretically extended—by using limit load analysis—to incorporate the effect of shear. The predictions of this new coalescence criterion are in good agreement with the results produced by 3D finite element calculations, for both loadings involving or not a shear component.     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

Constitutive equations for metal powders: application to powder forming processes

A new constitutive model for cold compaction of metal powders is developed. The plastic flow of metal powders at the macroscopic level is assumed to be representable as a combination of a distortion mechanism, and a consolidation mechanism. For the distortion mechanism the model employs a pressure-sensitive, Mohr–Coulomb type yield condition, and a new physically based non-associated flow rule. For the consolidation mechanism the model employs a smooth yield function which has a quarter-elliptical shape in the mean-normal pressure and the equivalent shear stress plane, together with an associated flow rule. The constitutive model has been implemented in a finite element program. The material parameters in the constitutive model have been calibrated for MH-100 iron powder by fitting the model to reproduce data from true triaxial compression experiments, torsion ring-shear experiments, and simple compression experiments. The predictive capability of the constitutive model and computational procedure is checked by simulating two simple powder forming processes: (i) a uniaxial strain compression of a cylindrical sample, and (ii) forming of a conical shaped-charge liner. In both cases the predicted load–displacement curves and density variations in the compacted specimens are shown to compare well with corresponding experimental measurements.     

单元类型和尺寸对裂尖疲劳塑性数值模拟的影响研究

本文采用Jiang-Sehitoglu循环塑性模型和多轴疲劳准则对紧凑拉伸式样裂尖的循环塑性变形、裂纹扩展速率和残余应力进行了有限元数值模拟,着重考察了单元的类型和最小单元尺寸对裂尖循环塑性和裂纹扩展速率的影响.紧凑拉伸试样的材料为1070钢,数值模拟采用了线性单元(四节点)和二次单元(八节点)两种单元,裂尖附近有限元单元的最小尺寸从0.007mm到0.24mm不等.文中将裂纹扩展速率的预测值与实验值进行了比较,通过对裂纹扩展速率的比较,确定在疲劳塑性分析时对单元类型和尺寸进行合理选取.     

平行于功能梯度材料夹层的币型裂纹起裂条件

分析了功能梯度材料中币型裂纹的扩展问题．裂纹平行于无限域中功能梯度材料夹层,受有与裂纹面成任意角度的拉应力．假定功能梯度材料夹层与两个半无限域均匀介质完全粘合,其弹性模量沿厚度方向变化．采用基于层状材料广义Kelvin基本解的边界元方法分析裂纹问题,给出了均布正应力和剪应力作用下裂纹的应力强度因子、将应力强度因子耦合于应变能密度断裂判据,讨论了裂纹体在拉伸应力作用下的起裂条件．     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.