Analyses of the fatigue crack propagation process and stress ratio effects using the two parameter method

In situ SEM observations (Zhang JZ. A shear band decohesion model for small fatigue crack growth in an ultra-fine grain aluminium alloy. Eng Fract Mech 2000;65:665–81; Zhang JZ, Meng ZX. Direct high resolution in-site SEM observations of very small fatigue crack growth in the ultra fine grain aluminium alloy IN 9052. Script Mater 2004;50:825–28; Halliday MD, Poole P, Bowen P. New perspective on slip band decohesion as unifying fracture event during fatigue crack growth in both small and long cracks. Mater Sci Technol 1999;15:382–90) have revealed that fatigue crack propagation in aluminium alloys is caused by the shear band decohesion around the crack tip. The formation and cracking of the shear band is mainly caused by the plasticity generated in the loading part of a load cycle. This shear band decohesion process has been observed to occur in a continuous way over the time period during the loading part of a cycle. Based on this observation, in this study, a new parameter has been introduced to describe fatigue crack propagation rate. This new parameter, da/dS, defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship between this new parameter and the conventional da/dN parameter which describes fatigue crack propagation rate per stress cycle is given.Using this new parameter, it is proven that two loading parameters are necessary in order to accurately describe fatigue crack propagation rate per stress cycle, da/dN. An analysis is performed and a general fatigue crack propagation model is developed. This model has the ability to describe the four general type of fatigue crack propagation behaviours summarised by Vasudevan and Sadananda (Vasudevan AK, Sadananda K. Fatigue crack growth in advanced materials. In: Fatigue 96, Proceedings of the sixth international conference on fatigue and fatigue threshold, vol. 1. Oxford: Pergamon Press; 1996. p. 473–8).     

Thermomechanical aspects of dynamic crack initiation

Dynamic fracture is generally addressed as an isothermal phenomenon. When specific phenomena such as shear band formation and propagation are involved, the analyses include thermomechanical conversion of strain and/or fracture energy into heat (thermoplasticity). In this case, it has been shown that very significant temperature rises can develop which cause softening of the crack-tip material. In these works, thermoelastic temperature changes at the tip of the crack are implicitly neglected. In a recent work, we have questioned this issue and shown that for a stationary crack subjected to transient loading, adiabatic thermoelastic effects were noticeable, thus causing a large temperature drop in the elastic zone surrounding the crack-tip (Rittel, 1998). In the present work, we pursue this line of investigation by presenting additional experimental results about temperature changes ahead of a dynamically loaded crack in commercial polymethylmethacrylate. We investigate mode I and mode II loading configurations. We observe, as expected, that the temperature drops for mode I loading while it rises for the mode II case. In each case, the crack initiates during the phase where the temperature changes (drop or rise). While showing that thermoelastic aspects of fracture should certainly be taken into account, the present results indicate that thermomechanical aspects in general should not be overlooked when addressing dynamic crack initiation.     

Nonsteady crack and craze behavior in PMMA under cyclical loading: III. Effect of load history on cohesive force distribution on the craze

Measurements of crack opening and craze profiles are made under a range of loading histories including cyclical deformations that lead to nonsteady crack propagation histories. Of particular interest is the comparison of the distribution of traction transmission of a newly formed craze relative to a cyclically stressed one as it approaches the slow-down phase. Real time, interferometric measurements provide precise and multiple craze profiles during individual cycles. Cyclic deformations reduce the stiffness of a craze in its center resulting in a stress drop as part of the craze strength evolution; also, its thickness changes nonuniformly during the acceleration/retardation phases of the advancing craze/crack. The implications are, that for quasi-statically formed crazes the craze material can be reasonably well characterized by a stress-strain relation, while that is no longer readily true for a cyclically deforming crack, since rate dependent characteristics of the craze and bulk material intervene. Cracks unloaded as part of cyclical deformation histories exhibit crack closure (compression) near the trailing end of the craze. This revised version was published online in July 2006 with corrections to the Cover Date.     

Damage evolution in Ti6Al4V–Al3Ti metal-intermetallic laminate composites

The crack propagation and damage evolution in metal (Ti6Al4V)-intermetallic (Al₃Ti) laminate composites were investigated. The composites (volume fractions of Ti6Al4V: 14%, 20% and 35%) were tested under different loading directions (perpendicular and parallel directions to laminate plane), to different strains (1%, 2%, 3%) and at different strain rates (0.0001 and 800–2000 s⁻¹). Crack densities and distributions were measured. The crack density increases with increasing strain, but decreases (at a constant strain) with increasing volume fraction of Ti6Al4V. Differences in crack propagation and damage evolution in MIL composites under quasi-static (10⁻⁴ s⁻¹) and dynamic (800–2000 s⁻¹) deformation were observed. The fracture stress does not exhibit significant strain-rate sensitivity; this is indicative of the dominance of microcracking processes in determining strength. Generally, the crack density after dynamic deformation is higher than that after quasi-static deformation. This is attributed to the decreased time for crack interaction in high-strain rate deformation. The effect of crack density, as quantified by a damage parameter, on elastic modulus and stress–strain relation were calculated and compared with experimental results.     

Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces

We have theoretically analysed the perimeter-area relation and simulated its application to measuring the fractal dimension of fracture surfaces. It is proved that the fractal dimension Dobtained by slit island method (SIM) is related to the dependence of measured area A(δ) ofthe slit island on yardstick δ. So in some cases, the dimension D obtained by SIM is dependenton yardstick and in other cases independent on yardstick δ. But in all cases, when δ→0 thedimension D obtained by SIM approaches the real fractal dimension (similar dimension) of coastline' of the island. We analysed some experimental data and found some new and interestingcharacteristics of crack propagation in steels.     

Simulation of the shear-tensile mode transition on dynamic crack propagations

We propose an approach to the simulation of the shear-tensile transition in dynamic crack growth based on two points: a new crack propagation criterion which is suitable for shear, and an algorithm which is capable of handling the transition from shear mode to tensile mode and back in the same simulation. The new crack propagation criterion for brittle crack growth is based on the maximum shear stress rather than the maximum hoop stress. The shear stress direction becomes the new crack??s direction in which propagation is initiated for shear-type failure. The stress state at the crack??s tip is obtained through a local approach which can be used even in the case of extensive plasticity. Additionally, we propose to control the transition from shear mode to tensile mode during the simulation of crack propagation using an equivalent strain estimated at the crack??s tip. Depending on a threshold strain, the propagation direction is predicted using the maximum shear stress (in the shear case) or the maximum hoop stress (in the tensile case).     

Implementation aspects of the bridging scale method and application to intersonic crack propagation

The major purpose of this work is to investigate the performance of the bridging scale method (BSM), a multiscale simulation framework for the dynamic, concurrent coupling of atomistics to continua, in capturing shear-dominant failure. The shear-dominant failure process considered in this work is intersonic crack propagation along a weak plane in an elastic material, similar to the seminal molecular dynamics (MD) simulations by Abraham and Gao (Phys. Rev. Lett. 2000; 84 (14):3113–3116). We show that the BSM simulations accurately capture the essential physics of the intersonic crack propagation, including the formation of a daughter crack and the sudden acceleration of the crack to a velocity exceeding the material shear wave speed. It is also demonstrated that the non-reflecting boundary condition can adequately dissipate the strongly localized wave formed by the Mach cone after the crack accelerates beyond the material shear wave speed. Finally, we provide the algorithm for our implementation of the BSM, as well as the code used to determine the damping kernels via a newly adopted technique which is less expensive than previous methods. Copyright © 2007 John Wiley & Sons, Ltd.     

A method for testing interlaminar dynamic fracture toughness of polymeric composites

Static and dynamic Mode I delamination fracture in two polymeric fiber composites was studied using a WIF test method. The dynamic test was conducted on a Split Hopkinson Pressure Bar apparatus. Crack speeds up to 1000 m/s were achieved. Dynamic fracture and crack propagation were modeled by the finite element method. Dynamic initiation fracture toughness of S2/8552 and IM7/977-3 composites were obtained. The dynamic fracture toughness of IM7/977-3 associated with the high speed propagating crack was extracted from the finite element simulation based on the measured data. It was found that the dynamic fracture toughness of the delamination crack propagating at a speed up to 1000 m/s approximately equals the static fracture toughness.     

Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method

A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK, 1999]. The entire crack geometry, including one or more cracks, is represented by a single signed distance (level set) function. Merging of distinct cracks is handled naturally by the FMM with no collision detection or mesh reconstruction required. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity [Comput. Meth. Appl. Mech. Engng. 139 (1996) 289]. This enables the domain to be modeled by a single fixed finite element mesh with no explicit meshing of the crack surfaces. In an earlier study [Engng. Fract. Mech. 70 (1) (2003) 29], the methodology, algorithm, and implementation for three-dimensional crack propagation of single cracks was introduced. In this paper, simulations for multiple planar cracks are presented, with crack merging and fatigue growth carried out without any user-intervention or remeshing.     

Nonsteady crack and craze behavior in PMMA under cyclical loading: I. Experimental preliminaries

This is the first of three papers devoted to the study of nonsteady crack propagation under cyclic loading in polymers, specifically PMMA. Drawing on experimental tools and measurement methods offering high spatial and real-time resolution at the subcycle level, we find that the change in craze behavior with load history is more complex than believed to date. At room temperature the change in fatigue cycle frequency on the order of slightly more than a decade gives rise to considerably different fracture surface morphologies, which are load history dependent. These observations are categorized and deductions for the variable cohesive force transmission by the craze are considered. In this first paper we outline the design of a special loading device which allows ultra-precise load or displacement control commensurate with the high resolution measurements of the crack tip material response. This development illustrates the precision of control for the experiments described in the subsequent papers. In addition, we delineate the software control and data acquisition methods to highlight the spatial resolution which provides the micron accuracy for measuring sub-cyclical crack propagation necessary for the later accounts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads

An extension of the Neuber-Novozhilov structural fracture propagation criterion is presented for mode I (tensile) and mode II (shear) propagation under compressive loads. In addition to allowing numerical simulation of crack growth, the criterion can be used to model change of propagation mode, crack branching, and coalescence. The criterion can be applied effectively when the SIF is calculated accurately (at least three significant digits). A numerical method is suggested for this purpose that consists of complementing the complex variable hypersingular boundary element method (CVH-BEM) with special procedures for automatically tracing crack propagation and coalescence. The CVH-BEM code with the structural criterion has been used to investigate crack propagation in compression for both small and non-small fracture process zone (FPZ). The results of numerical experiments are in agreement with the analytical conclusions available for the case of small FPZ that indicates the possibility of three distinct patterns of crack propagation under external compressive loads. These are: (i) smooth curvilinear tensile (wing) cracks, (ii) stair-step propagation pattern with changing modes, and (iii) in plane shear propagation. The numerical study also indicates that when the critical size of the FPZ is large enough, the non-singular terms in the expansion of the stress functions strongly influence the crack trajectories. Specifically, this occurs when the size of the FPZ approaches a quarter of the half-length of the initial crack. Calculations for a closed initial crack in a half-space under compression illustrate the general features of crack propagation. Although the dominant direction of crack growth is that of the applied compressive stress, the pattern of propagation strongly depends on the particular geometry, critical size of the FPZ, and the ratio of shear-to-tensile microscopic strength.     

A model for short crack propagation in polycrystalline materials

A model for microstructurally short crack propagation in a grain structure of a polycrystalline material is developed. The crack propagation model is based on a crystal plasticity model and a microstructurally short crack propagation model in the spirit of the model by Navarro and de los Rios [A model for short fatigue crack propagation with an interpretation of the short-long crack transition. Fatigue Fract Eng Mater Struct 1987;10:169-86]. Numerical examples, where the combined crystal plasticity and crack propagation model is implemented in a model of a microstructure representing a duplex stainless steel, concludes the paper. Results showing how the misorientation of the crack- and slip-directions between two adjacent austenitic grains influences the crack propagation rate, as the crack propagates across their common grain boundary, are given.     

基于XFEM的RC梁静态破碎研究

建筑基坑内支撑的拆除是影响施工进度的重要因素之一。为提高施工效率,提出一种在钢筋混凝土支撑梁内部沿着梁轴线预埋大直径孔道进行静态破碎的拆除方案。在此基础上,通过扩展有限元方法(Extended Finite Element Method,XFEM)建立含预埋静态破碎孔(孔径为90 mm)的钢筋混凝土梁(截面尺寸为500 mm×500 mm)模型,并对其在静态膨胀压力作用下的破碎及裂缝扩展过程进行了模拟分析。模拟结果表明:内支撑梁的静态破碎过程可分为弹性变形、裂缝稳定扩展和裂缝失稳扩展3个阶段;基于虚拟闭合技术,进一步计算得到了复合开裂模式下的应变能释放率,计算结果显示:裂缝扩展以Ⅰ型裂缝为主,当膨胀压力达到19.4 MPa时,可实现破碎钢筋混凝土内支撑梁的目的。     

基于XFEM的RC梁静态破碎研究

建筑基坑内支撑的拆除是影响施工进度的重要因素之一。为提高施工效率,提出一种在钢筋混凝土支撑梁内部沿着梁轴线预埋大直径孔道进行静态破碎的拆除方案。在此基础上,通过扩展有限元方法(ExtendedFiniteElementMethod,XFEM)建立含预埋静态破碎孔(孔径为90mm)的钢筋混凝土梁(截面尺寸为500mm ×500mm)模型,并对其在静态膨胀压力作用下的破碎及裂缝扩展过程进行了模拟分析。模拟结果表明:内支撑梁的静态破碎过程可分为弹性变形、裂缝稳定扩展和裂缝失稳扩展3个阶段;基于虚拟闭合技术,进一步计算得到了复合开裂模式下的应变能释放率,计算结果显示:裂缝扩展以Ⅰ型裂缝为主,当膨胀压力达到19.4MPa时,可实现破碎钢筋混凝土内支撑梁的目的。     

Stochastic fracture mechanics using polynomial chaos

Crack propagation in metals has long been recognized as a stochastic process. As a consequence, crack propagation rates have been modeled as random variables or as random processes of the continuous. On the other hand, polynomial chaos is a known powerful tool to represent general second order random variables or processes. Hence, it is natural to use polynomial chaos to represent random crack propagation data: nevertheless, no such application has been found in the published literature. In the present article, the large replicate experimental results of Virkler et al. and Ghonem and Dore are used to illustrate how polynomial chaos can be used to obtain accurate representations of random crack propagation data. Hermite polynomials indexed in stationary Gaussian stochastic processes are used to represent the logarithm of crack propagation rates as a function of the logarithm of stress intensity factor ranges. As a result, crack propagation rates become log-normally distributed, as observed from experimental data. The Karhunen–Loève expansion is used to represent the Gaussian process in the polynomial chaos basis. The analytical polynomial chaos representations derived herein are shown to be very accurate, and can be employed in predicting the reliability of structural components subject to fatigue.     

Rißausbreitung bei Leichtbauwerkstoffen

Fatigue Crack Propagation of High Strength Alloys Investigations of the crack propagation behaviour under variable amplitude loading conditions show a strong influence of sequence effects. The fatigue crack propagation as a consequence of changes in the loading conditions is not linear. New continuum mechanical analyses enable an interpretation of the influence of sequence effects on fatigue crack propagation by considering the plastic deformations and displacements around the crack tip and their correlation to the crack closure behaviour. In order to enable a direct investigation of the crack propagation and crack closure behaviour in the scanning electron microscope a special loading equipment was designed. The investigations led to the following results:

• there existed only a weak correlation between the crack propagation rates and mechanisms at the side surfaces and on the fracture surfaces of the specimens,
• the crack propagation behaviour was significantly influenced by the microstructural constitution of the alloy,
• the continuum mechanical analyses could be corroborated in the tests.

For the tests the high strength aluminum alloys 2024-T3 and X-7075 were applied.     

Influence of microscopically distributed inhomogeneity and anisotropy of grains on high-temperature crack propagation properties of directionally solidified superalloy

The fluctuation of J-integral, during high-temperature fatigue crack propagation, due to the microscopic inclination of crack and elastic anisotropy of each grain, is investigated by means of a series of finite-element-analyses on a cracked body. The simulated material is a nickel-based directionally solidified (DS) superalloy, where the DS axis, load direction, and crack propagation axis are set to be perpendicular to each other. The magnitude of J is estimated using two-dimensional models simulated after an experimental test: (i) with the actual crack shape and grain arrangement, (ii) with the actual crack shape in a homogeneous body, and (iii) with a straight crack in a homogeneous body (averaged deformation behavior of the material). The microscopic inclination of crack propagation direction causes the sporadic drop of J at the point where the crack direction is largely inclined from the direction normal to the load axis. The anisotropy of grains causes the stepwise change in the a (crack length) vs. J relationship. Such changes in J due to the microscopic inhomogeneity directly relates to the change of the crack propagation rate in the transgranular cracking. Then, J, which takes into accounts the anisotropy of grains, correlates well with the crack propagation rate in the transgranular cracking. The grain-boundary cracking possesses fluctuated J, and shows weaker resistance to the propagation than the transgranular one.     

On the Hertzian fatigue cone crack propagation in ceramics

The Hertzian cone crack initiation and propagation in ceramics under cyclic fatigue loading with a spherical indenter is studied. Unlike the so-called quasi-static Hertzian cone crack, the fatigue Hertzian cone crack propagation eliminates the dynamic effect on unstable crack propagation. As such, the crack is found to propagate following the path of pure mode I type. We use an elasticity approach, a finite element analysis, and an empirical analysis to investigate the Hertzian cone crack in three stages: crack initiation, crack propagation, and crack kinking. The mechanism of the multiple concentric cone cracks is also explained. The purpose is to understand and predict the behavior of the formation of the Hertzian fatigue cone crack using available modeling tools.Zheng Chen is currently with Space Power Institute, Auburn University.     

疲劳裂纹在奥氏体/铁素体异种钢焊接接头中的扩展行为

采用三点弯曲试样研究了疲劳裂纹在奥氏体/铁素体异种钢焊接接头中的扩展行为与显微组织的关系,测得疲劳裂纹在Cr25Ni13/13CrMo44异种钢焊接接头中的扩展速率da/dN,并且讨论了疲劳裂纹扩展与显微组织之间的关系。实验结果表明,疲劳裂纹在异种钢焊接接头熔合区中扩展的路径,是接头中韧性最低的热影响区过热区,裂纹在铁素体材料侧,跟随熔合线并平行于熔合线5～25μm扩展,而马氏体层对疲劳裂纹有较大的抗力,疲劳裂纹的扩展路径主要受组织韧性的控制。疲劳裂纹在Cr25Ni13/13CrMo44异种钢接头的扩展速率为：da/dN=7.07×10-13(△K)3.863。