三维计算断裂力学

断裂力学理论从1921年Griffith研究玻璃的脆性断裂问题开始,经历了从线弹性体系到弹塑性以及蠕变理论体系、从单参数到多参数体系和从理想的二维平面理论到实际三维含裂纹结构的三维断裂理论的发展历程。针对应力强度因子K和J积分以及C(t)积分的计算方法从理想化模型的理论计算发展到实际复杂工程结构裂纹体计算的各种商业软件平台以及专业的断裂理论分析平台。尤其是随着计算机技术的发展,对三维含裂结构的静态和扩展裂纹的计算模拟已经能够融入计算机辅助设计。结合本研究组近30年来在三维疲劳断裂理论和应用研究方面的体会,简述了三维计算断裂力学从裂纹体应力应变分析和断裂参数计算到三维蠕变断裂和疲劳裂纹扩展模拟的国内外进展,并对涉及的计算方法,包括原子尺度和跨尺度的计算模拟,以及目前面临的挑战性问题作了简要介绍和分析。     

Creep crack growth on spent fuel zircaloy cladding in interim storage

The effect of creep failure mechanisms on the creep crack growth is examined on spent fuel Zircaloy cladding in interim storage. Based on the creep fracture mechanics parameter C^* and the strain energy density criteria, the relationship between the creep crack growth rate and the fracture mechanics parameter C^* is established theoretically. The effects of initial crack lengths and storage temperature profiles on cladding failure are discussed in detail. The results show that the initial crack length and the storage temperature profile play an important role in the interim dry storage. When the storage temperature remains at a constant temperature of 400 °C, it will be safe for the cladding which stores in the interim dry storage. The results presented in this study provide a reliable cladding integrity evaluation for spent fuel in the interim dry storage.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

Creep behavior of crack near bi-material interface characterized by integral parameters

Creep behavior of crack in dissimilar materials is studied using steady-state C^* path independent integral and ABAQUS finite element code. The specific geometry involves an edge crack parallel to the interface of a bi-material tensile specimen at high temperature. Under extensive creep, the C^* value for the bi-material specimen can be significantly higher than that for the homogeneous specimen. For small-scale creep material mismatch has little influence on the transient integral designated by C_t. The integral parameters C^* or C_t are shown to depend on the inhomogeneity of the system and cannot characterize the creep behavior of cracks.The approach is extended to creep crack growth in a welded compact tension specimen. Modification factors are introduced for different crack and weld interface geometries.     

岩石蠕变断裂特性的试验研究

以一类红砂岩为例对蠕变条件下岩石裂纹的起裂和扩展的机理、准则进行了试验研究和理论分析．试验结果表明，岩石裂纹常常在初始应力强度因子KI小于断裂韧度KIC的情况下，经过一段时间的持续蠕变变形产生裂纹起裂和扩展．当然，初始应力强度因子KI小于断裂韧度KIC是有限度的，KI不得小于另一固定值KIC2，KIC2表征了岩石在蠕变条件下抵抗裂纹起裂和扩展的能力，而且其值小于KIC，可称之为蠕变断裂韧度．在岩石工程的设计和计算中，KIC2是一个重要参数．     

Dislocation pile-up model of fatigue thresholds for 2024- and 7075-alike aluminium alloys

Two parameters, K_max^* and δK_th^*, are presented to describe fatigue threshold behaviour and damage under any load ratio without invoking crack closure. Modelled are two fatigue thresholds that are coherently related to fatigue limit δσ_FL; they predict the fundamental threshold curves for aluminium alloys. By using a continuous configuration of dislocations in pile-up, fatigue limit behaviour is simulated as pile-up of dislocations against grain boundaries. A fatigue limit is determined in terms of a critical condition at which a fictitious microcrack associated with the pile-up corresponds to the onset of propagation. These two fatigue thresholds are attainable as the local stresses at the crack front approaching the fatigue limit. Microstructure is incorporated in the model to account for the effect on threshold behaviour. As a result, two fatigue threshold criteria are required. Quantitative assessment of the two criteria requires only knowledge of the conventional material properties in conjunction with microstructure. The micromechanical modelling exhibits a strong dependence of fatigue thresholds upon local microstructure.     

脆性岩石蠕变裂纹成核宏细观力学机理研究

脆性岩石内部细观裂纹扩展、贯通及成核影响下的脆性蠕变行为,对深部地下工程围岩微震及岩爆事件评价有着重要意义.然而,目前能够解释裂纹成核损伤突变影响下,脆性岩石完整蠕变宏细观力学机理模型的研究很少.本文基于脆性岩石亚临界裂纹扩展模型、裂纹?应变?声发射事件相关的损伤模型及裂纹成核损伤时间演化路径函数,提出了一种脆性岩石裂...     

Localisation issues in local and nonlocal continuum approaches to fracture

Continuum approaches to fracture regard crack initiation and growth as the ultimate consequences of a gradual, local loss of material integrity. The material models which are traditionally used to describe the degradation process, however, may predict premature crack initiation and instantaneous, perfectly brittle crack growth. This nonphysical response is caused by localisation instabilities due to loss of ellipticity of the governing equations and—more importantly—singularity of the damage rate at the crack tip. It is argued that this singularity results in instantaneous failure in a vanishing volume, even if ellipticity is not first lost. Adding strong nonlocality to the modelling is shown to preclude localisation instabilities and remove damage rate singularities. As a result, premature crack initiation is avoided and crack growth rates remain finite. Weak nonlocality, as provided by explicit gradient models, does not suffice for this purpose. In implementing the enhanced modelling, the crack must be excluded from the equilibrium problem and the nonlocal interactions in order to avoid unrealistic damage growth.     

A STATISTICAL INVESTIGATION OF FATIGUE CRACK INITIATION AND GROWTH PROCESS BASED UPON A LARGE SAMPLE SIZE EXPERIMENT

After finishing 102 replicate constant amplitude crack initiation and growth tests onLyl2-CZ aluminum alloy plate,a statistical investigation of the fatigue crack initiation and growthprocess is conducted in this paper.According to the post-mortem fractographic examination by scan-ning electron microscopy (SEM),some qualitative observations of the spacial correlation among fa-tigue striations are developed to reveal the statistical nature of material intrinsic inhomogeneity duringthe crack growth process.From the test data,an engineering division between crack initiation andgrowth is defined as the upper limit of small crack.The distributions of crack initiation life N.,growthlife N,and the statistical characteristics of crack growth rate da/dN are also investigated.It is hopedthat the work will provide a solid test basis for the study of probabilistic fatigue,probabilistic fracturemechanics,fatigue reliability and its engineering applications.     

高温结构蠕变裂尖拘束效应

如何对蠕变裂纹扩展寿命进行准确预测和评价是高温结构完整性评定、寿命设计和运行维护中需要解决的核心问题.基于宏观单参数C?的蠕变断裂行为的评价方法,未有效纳入裂尖拘束效应的影响,因而其评价结果过于保守或非保守.目前国内外还未建立起有效纳入裂尖拘束效应的高温结构蠕变寿命评价的理论体系和技术方法,还没有纳入蠕变拘束效应的高温结构完整性评定规范.本文综述了作者近年来在高温蠕变断裂拘束效应方面的研究工作.主要包括:裂尖拘束对材料蠕变裂纹扩展行为的影响及机理;蠕变裂尖场和拘束参数R的定义和影响因素;载荷无关的蠕变拘束参数R? 的提出及其应用基础;承压管道表面裂纹的拘束参数R? 解及纳入裂尖拘束的蠕变寿命评价方法;试样与管道轴向裂纹蠕变裂尖拘束的关联;基于裂尖等效蠕变应变的面内与面外蠕变裂尖拘束的统一表征参数Ac的研究;材料拘束相关的蠕变裂纹扩展速率的建立;宽范围C? 区蠕变裂纹扩展速率及其拘束效应的数值预测;材料拘束对焊接接头蠕变裂纹扩展行为的影响及机理等.这些研究为建立纳入裂尖拘束效应的高温部件的蠕变裂纹扩展寿命评价方法奠定了理论和技术基础.论文对后续拟开展的工作也进行了展望.     

疲劳裂纹形成、扩展统计特性的大子样试验研究

针对疲劳损伤过程的随机性，该文开展了等幅谱大子样疲劳裂纹形成、扩展至破坏全寿命过程的试验研究．在计算确立了裂纹形成、扩展分界工程小裂纹长度的基础上，整理得到了裂纹形成，扩展寿命的统计分布数据．根据断口金相ＳＥＭ观察，进一步定性分析了疲劳条纹分布的相关性特征．     

Analysis of cyclic crack growth in high strength roller bearings

The lives of ball and roller bearings and raceways depend on the number of rolling contacts consumed by 3 stages of the failure process: (i) the preinitiation; (ii) crack initiation, and (iii) crack growth stages. This paper employs fracture mechanics analyses to estimate the portion of the bearing life residing in the crack growth stage. Rough estimates of: (a) the Mode II, ΔK_II driving force for small cracks below the rim surface subjected to repeated 2-dimensional, pure rolling contacts, (b) the corresponding crack growth rates, and (c) the number of contacts to failure, are obtained as a function of the peak contact pressure, initial flaw size and other variables. Factors influential to the growth stage are identified. Finally, the comparisons with measured total lives provide insights into the validity of the analysis and the importance of growth relative to the preinitiation and crack initiation stages.     

Creep deformation at crack tips in elastic-viscoplastic solids

The evaluation of crack growth tests under creep conditions must be based on the stress analysis of a cracked body taking into account elastic, plastic and creep deformation. In addition to the well-known analysis of a cracked body creeping in secondary (steady-state) creep, the stress field at the tip of a stationary crack is calculated for primary (strain-hardening) or tertiary (strain-softening) creep of the whole specimen. For the special hardening creep-law considered, a path-independent integral C¹_h, can be defined which correlates the near-tip field to the applied load.It is also shown how, after sudden load application, creep strains develop in the initially elastic or, for a higher load level, plastic body. Characteristic times are derived to distinguish between short times when the creep-zones, in which creep strains are concentrated, are still small, and long times when the whole specimen creeps extensively in primary and finally in secondary and tertiary creep. Comparing the creep-zone sizes with the specimen dimensions or comparing the characteristic times with the test duration, one can decide which deformation mechanism prevails in the bulk of the specimen and which load parameter enters into the near-tip stress field and determines crack growth behavior. The governing load parameter is the stress intensity factor K₁ if the bulk of the specimen is predominantly elastic and it is the J-integral in a fully-plastic situation when large creep strains are still confined to a small zone. The C¹_h-integral applies if the bulk of the specimen deforms in primary or tertiary creep, and C¹ is the relevant load parameter for predominantly secondary creep of the whole specimen.     

Creep crack-tip constraint effect in high temperature structures

如何对蠕变裂纹扩展寿命进行准确预测和评价是高温结构完整性评定、寿命设计和运行维护中需要解决的核心问题.基于宏观单参数C^*的蠕变断裂行为的评价方法,未有效纳入裂尖拘束效应的影响,因而其评价结果过于保守或非保守.目前国内外还未建立起有效纳入裂尖拘束效应的高温结构蠕变寿命评价的理论体系和技术方法,还没有纳入蠕变拘束效应的高温结构完整性评定规范.本文综述了作者近年来在高温蠕变断裂拘束效应方面的研究工作.主要包括：裂尖拘束对材料蠕变裂纹扩展行为的影响及机理;蠕变裂尖场和拘束参数R的定义和影响因素;载荷无关的蠕变拘束参数R^*的提出及其应用基础;承压管道表面裂纹的拘束参数R^*解及纳入裂尖拘束的蠕变寿命评价方法;试样与管道轴向裂纹蠕变裂尖拘束的关联;基于裂尖等效蠕变应变的面内与面外蠕变裂尖拘束的统一表征参数A_c的研究;材料拘束相关的蠕变裂纹扩展速率的建立;宽范围C^*区蠕变裂纹扩展速率及其拘束效应的数值预测;材料拘束对焊接接头蠕变裂纹扩展行为的影响及机理等.这些研究为建立纳入裂尖拘束效应的高温部件的蠕变裂纹扩展寿命评价方法奠定了理论和技术基础.论文对后续拟开展的工作也进行了展望.     

Stable growth of a crack interacting with a circular inclusion

The problem of failure of a plate containing a circular inclusion and a crack is studied. The crack is oriented along a diameter of the inclusion and the plate is subjected to a remote uniaxial stress perpendicular to the crack axis. The process of slow stable crack growth from initiation to termination is studied by the strain energy density theory. The crack growth is simulated by predicting finite increments of crack extension when material elements near the crack tip absorb a critical amount of strain energy density level, . Unstable crack growth occurs when the strain energy density factor S reaches a critical value where r_c is the critical size of the final crack increment prior to instability. The stress at crack initiation and the critical stress and crack length at failure are determined. The influence of the mechanical properties of the plate and the inclusion, the relative position of the inclusion and the crack and the crack length on the characteristic quantities of stable crack growth is analyzed. The dependence of the stable crack growth process on the loading rate is also investigated. Results are displayed in graphical form.     

A numerical method for crack growth analysis in linearly viscoelastic materials

This paper presents a numerical method for the analysis of crack initiation and extension in linearly viscoelastic materials undergoing Mode I plane stress deformation. Plastic deformation near the crack tip is considered by a strip-yielding model. The crack initiation and growth are taken to follow a critical energy release rate fracture criterion, and the plastic work per unit crack extension is included in the calculation of the total energy release rate. The resulting numerical method is presented in algorithmic form and two example problems are solved to demonstrate its application. The two example problems represent unstable and stable crack propagations respectively. The results obtained lend insight into the effect of creep deformation on the initiation and growth of a crack.     

Strain energy density prediction of crack initiation and direction in cracked T-beams and pipes

In this paper, the S-theory is applied to determine crack initiation and direction for cracked T-beams and circumferentially cracked pipes. It makes use of a parameter called strain energy density factor, S, which is a function of the stress intensity factors. The strain energy density theory provides a more general treatment of fracture mechanics problems by virtue of its ability in describing the multiscale feature of material damage and in dealing with mixed mode crack propagation problem. A simple method for obtaining approximate stress intensity factors is also applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Some basic loading conditions in beams and pipes are studied.     

Crack growth instability studied by the strain energy density theory

The strain energy density theory has successfully been used to address the problem of material damage and structural failure in problems of engineering interest. The theory makes use of the strain energy density function, dW/dV, and focuses attention in its stationary values. The directions of crack growth and yielding are determined from the minimum and maximum values of dW/dV, respectively, along the circumference of a circle centered at the point of failure initiation. Failure by crack growth or yielding takes place when these values of dW/dV become equal to their critical values which are material constants. In the present work the basic principles of the strain energy density theory were reviewed. Furthermore, this theory was used to study three problems of structural failure, namely the problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension, the problem of fracture instability of a plate with a central crack and two notches, and the problem of unstable crack growth in a circular disc subjected to two equal and opposite forces. The results of stress analysis were combined with the strain energy density theory to obtain the whole history of crack growth from initiation to instability. A length parameter was introduced to define the fracture instability of a mechanical system. Fracture trajectories were obtained for fast unstable crack propagation.     

A generalized force measure of conditions at crack tips

A tentative measure of the forces tending to cause crack growth—the apparent crack extension force—is defined within the framework of continuum mechanics. By an associated fracture criterion initiation of growth may be predicted as well as the direction of preferred growth. The theory is specialized to elastic, viscoelastic and elastic-plastic materials. Under specified conditions the apparent crack extension force may be expressed by surface integrals over the boundary of an arbitrary part of the body for quasi-static deformation and for steady-state propagation of the crack. For plane deformation and for infinitesimal deformation under plane stress conditions these surface integrals reduce to path independent line integrals which include the J integral by Rice[1] and the G integral by Sih[2] as special cases.