混凝土断裂及亚临界扩展的细观机制

通过模型和三点弯曲断裂SEM试验,详细研究了混凝土断裂全过程及亚临界扩展的细观机理。结果表明:混凝土断裂是一个复杂的不规则过程,存在明显的亚临界扩展现象。混凝土亚临界扩展路径是曲折的,并非经典断裂力学假定的平直路径,混凝土亚临界扩展和临界失稳扩展呈现分形特征。用起裂断裂韧性iICK和分形等效断裂韧性feICK,来描述混凝土抵抗初裂和临界失稳扩展的能力。给出了考虑亚临界扩展弯折效应的混凝土亚临界扩展长度、混凝土起裂断裂韧性iICK和分形等效断裂韧性feICK,的计算表达式。计算表明:混凝土失稳断裂时的分形等效断裂韧性feICK ,与混凝土亚临界扩展的分维数D成正比。     

Ein einfaches Hilfsmittel zum Konstruieren mit Keramik

A Simple Tool for Designing with Ceramics Today ceramics are successfully used for applications demanding high reliability. When evaluating ceramic designs the models used are based on linear‐elastic fracture mechanics and Weibull‐statistics. Nevertheless there is need for simple methods for evaluating designs. A safety factor based on the Weibull‐modulus, failure probability, and approved tensile stress may be used for evaluating designs of ceramic components. The prerequisite for using this concept is that the stress intensity K_I is always below the fatigue limit K_Io. If so, subcritical crack growth does not occur. An analysis of retrieved ceramic hip implants proves that this concept works.     

Critical stress intensity factors in steel cracked wires

In the conceptual framework of fracture mechanics analyses, the study of cracked wires axially loaded has the highest interest since numerous structural elements (e.g. wires, cables, cordons or tendons) work under such a type of loading during their service lives. So, a method that allows the determination of stress states at the crack front should be welcome as a useful way for ensuring the structural integrity of those components for different environmental conditions (air, stress corrosion cracking, hydrogen embrittlement,…). To fill this gap, an engineering estimation of the critical stress intensity factor (SIF) is proposed in this paper for eutectoid steel cracked wires under axial loading. The critical SIF is calculated by considering, apart from the fatigue precrack, the subcritical crack propagation before final fracture. Such a subcritical crack propagation is the process zone (by micro-void coalescence MVC) in the case of fracture in air, the subcritical cracking by localized anodic dissolution (LAD) in stress corrosion cracking (SCC) and the tearing topography surface (TTS) in hydrogen assisted cracking (HAC). In addition, different SIF solutions are used in the analysis so as to have a more complete picture of the different phenomena leading to failure and to provide the designer with sound scientific tools. This method allows the engineer to design in the framework of structural integrity and damage tolerance.     

Fracture toughness of concrete determined on large specimens

It has often been questioned whether linear elastic fracture mechanics can be applied to describe crack propagation and failure of concrete. An important argument is that most test results are obtained on specimens too small to be representative of a material with a composite structure such as concrete. Large specimens with four different geometries have been prepared and tested. Crack length was increased under controlled conditions to at least 250 mm. It was found that fracture toughness increases initially as a crack propagates, but that a length-independent value is reached asymptotically. Within the range of accuracy, asymptotic values obtained with the four different geometries were the same. It is concluded that failure of large size concrete elements can be predicted realistically on the basis of linear elastic fracture mechanics. For comparatively small specimens, however, an approach which takes total fracture energy into consideration (for instance the fictitious crack model) is more appropriate. It is pointed out that the role of subcritical crack growth on fracture toughness needs further investigation.     

Analysis of fatigue delamination growth in flip-chip package

An incremental crack extension procedure is implemented for simulating the growth of an interface defect in an electronic flip-chip device subjected to fatigue temperature cycling. The distributions of fracture mechanics parameters including the strain energy release rate, the stress intensity factors and phase angles along the curvilinear front of an embedded corner defect on the interface of silicon die and underfill are estimated and substituted into a subcritical crack growth model to predict the evolution of the defect under cyclic loading condition. It is observed from the analysis that the corner defect is under crack faces contact condition during temperature cycling, and consequently, the delamination growth is under mode-II and mode-III driving forces. In addition, the crack growth rate is highest in the middle of the crack front, and the corner crack evolves from an initially concave front to a quarter-circular front under temperature cycling.     

Fracture and safety analysis of nuclear pressure vessels

An evaluation of the safety factors of nuclear reactor pressure vessels for pressurized water reactors to resist fracture is an important feature in ensuring nuclear reactor safety. The safety analysis has to demonstrate that there is no danger of failure at all. By means of brittle and ductile fracture mechanics the safety factors against critical stress, critical crack size and critical stress intensity factor will be shown. The linear, elastic and plastic stress distributions for plane stress and plane strain conditions are derived for the different modes of fracture. A critical analysis of crack growth and of stress corrosion cracking extends the use of fracture mechanics. A comparison between stress intensity factors obtained by analytical computation and by the Finite Element Method for the case of emergency core cooling is shown.Some technical applications as the estimation of critical crack sizes, the evaluation of operating performance and undercladding cracks are briefly discussed.     

Subcritical crack-growth and lifetime behavior of glass and SiG under static load

Crack initiation and subcritical crack growth in glass sheet and SiC bar specimen under static loading were investigated to study the failure process. It has been demonstrated that the lifetime process of brittle materials involves three possible forms of crack growth: subcritical crack growth, partly subcritical crack growth and instantaneous fracture without subcritical crack growth. Curves of upsilon -K obtained in step-by-step static fatigue tests and in constant loading rate tests showed different trends for borosilicate glass sheet. alpha -SiC that is generally considered immune to mechanical fatigue effect and environmental attack was also tested under static loading and the lifetime was measured. The results showed that the threshold load to damage effect was over 80% of the initial strength for the SiC.     

Subcritical Crack-Growth and Lifetime Behavior of Glass and SiC under Static Load

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A phenomenological theory of subcritical creep crack growth under constant loading in an inert environment

The subcritical creep crack growth under constant loading is considered as due to the repeated rupture of the plastic zone in the vicinity of the crack tip. Fracture mechanics concepts are used to derive the rupture life of a centre-cracked thin sheet loaded in plane stress. The formulation is such that numerical results can readily be obtained for crack growth. Approximate analytical formulae are also given for crack growth against time.     

Subcritical crack growth of glass

The small radial cracks that occur around the microhardness indentation were used to measure the subcritical crack growth response of glass under constant-bend loading in water. The crack velocity versus stress intensity factor curves indicate that the crack velocity depends on the magnitude of the stress and that the velocity which is high decreases at the initial stage of crack growth, thereafter reaches a minimum and increases with the stress intensity factor until unstable fracture occurs.     

Subcritical crack growth of trip steels in air under static loads

Pre-fatigued compact tension fracture toughness specimens of TRIP steel were held at constant loads at 25°C in 40 per cent r.h. air. Testing was done using an MTS closed loop universal test machine in the load control mode and the displacement was monitored as a function of time using a clip-on gauge and a strip chart recorder. Subcritical crack growth was observed and the experimental data was used to obtain a correlation between stress intensity and the rate of crack growth. The curves usually exhibited three distinct regions, including a plateau of stress intensity insensitive constant crack growth rates which have been observed by other investigators for titanium alloys and high strength steels. Based on comparisons with other investigators, the mechanism of subcritical flaw growth was tentatively identified as being due to hydrogen embrittlement. Fracture was observed to follow austenite grain boundaries and it was hypothesized that the austenite → martensite transformation sensitizes them to hydrogen by causing a large strain accumulation to be accommodated at the boundaries resulting in a large dilatation. Metallography revealed that the crack growth rate decreased as the strain-induced martensite increased and this was attributed to crack tip blunting by plastic deformation due to the invariant shear of the transformation. There are thus two apparently competing processes in the subcritical flaw growth of TRIP steels. Fractography showed that numerous fracture micromechanisms were operative. The subcritical crack growth characteristics compared favorably with other high strength steels tested under almost equivalent conditions and an apparent threshold for subcritical growth in air was determined to occur at about 56 per cent of K_IC.     

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.     

The development of rational design criteria for brittle materials

Very brittle materials are finding increasing usage in critical engineering components. Howver, their fundamental property of brittle behaviour requires very accurate design methods if reliable applications are to result. In this paper the development of rational design criteria for these materials are described. Three major topics are discussed. The statistical techniques which enable the correlation of experimental data, and the effects of size and stress gradient to be taken into account are described, and the development of these methods to cases of non-uniform stresses through a unit volume concept are assessed. The phenomenon of static fatigue, in which failure occurs, often after a considerable time, under an applied load which is less than that required to produce instantaneous failure is considered. Recent applications of fracture mechanics techniques to the determination of the crack growth rate are described which leads to the development of methods for the estimation of component lifetimes under conditions of subcritical crack growth. Finally, the experimental results obtained from investigations into the fracture strength of various brittle materials when subjected to multiaxial stress states are compared. It is concluded that a great deal of further experimental evidence is required before fully reliable design criteria are available on which engineering decisions may be based.     

The transition between stress corrosion crack growth and plastic fracture

The paper focuses on the behaviour of materials for which the onset of crack extension and unstable fracture coincide in a rising load fracture mechanics test. A theoretical analysis shows that use of the experimental test J_Ic value gives a non-conservative prediction of unstable fracture when a stress corrosion crack grows in a solid that is subject to a sustained high stress. Consequently, when an engineering component is to be used at high stress levels in an environment where stress corrosion cracking might be expected, there are clear advantages in having a material which exhibits stable crack growth in a fracture mechanics test.     

Versagen von Keramik im Hochtemperaturbereich

Failure of ceramics at high temperatures Failure of ceramic materials at high temperatures is very complicated. At low temperatures the failure of ceramics is governed by subcritical crack growth under quasistatic and cyclic loads. In the high temperature region the effects of creep crack growth and creep fracture have to be considered, too. The main part of the paper is addressed to the effects of subcritical crack growth and creep crack growth. The application of the fracture mechanical C*-concept is discussed in detail.     

Fracture of hot-pressed alumina and SiC-whisker-reinforced alumina composite

The flexural strength of hot-pressed alumina and SiC-whisker-reinforced alumina composite were evaluated as a function of temperature (20 to 1400° C in air environment), applied stress and time. Two mechanistic regimes were manifest in the temperature dependence of the fracture stress. A temperature-independent region of fast fracture (catastrophic crack extension) existed up to 800° C, in which the failure mode was a mixture of transgranular and intergranular crack propagation. In this region, the alumina composite showed significantly higher fracture strength and toughness compared to polycrystalline alumina. Above 800° C, both materials (alumina and alumina composite) displayed a decreasing fracture strength due to the presence of subcritical or slow crack growth which occurred intergranularly. Flexural stress rupture evaluation in the temperature range 600 to 1200° C has identified the stress levels for time-dependent and time-independent failures.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

基于断裂力学的裂隙岩体强度分析初探

基于断裂力学讨论裂隙岩体的强度一直是断裂力学与岩石力学等学科的重要课题。通过分析单个线性裂纹在压缩载荷作用下的剪切断裂条件,明确了压缩状态下张破裂剪切断裂韧性的物理意义及求解办法。使用复变函数和边界配置法求解了裂尖应力强度因子无量纲系数,进而对张破裂压剪准则进行了改进,使之更加便捷地进行有限裂纹体断裂的预测。基于修正的压剪判据推导了裂隙岩体试件的抗压强度求解公式,算例表明该文方法所建立的强度公式是准确、可靠的。最后,详细讨论了摩擦系数、裂隙倾角、裂隙长度、黏聚力以及围压对裂隙岩体试件抗压强度的影响机理。     

Effect of tempering treatment on hydrogen-induced cracking in high-strength steel

The fracture characteristics of high-strength steel ASTM A-490 under a hydrogen environment were investigated, with special emphasis placed on changes in fracture characteristics due to a tempering treatment at temperatures from 200 to 400 °C. A mechanical test was performed on cathodically charged specimens subjected to a constant load. Experimental analyses show that tempering treatment in the range from 200 to 400 °C does not alter the essential nature of delayed fracture due to crack growth. However, the role of intergranular (IG) cracking becomes prominent in the subcritical crack growth period with an increase in the tempering temperature to 400 °C. This development of IG cracks in the subcritical crack growth period is uniquely dependent on the tempering treatment performed in the tempering range from 250 to 400 °C. Furthermore, an increase in the fraction of the IG facet in the subcritical crack growth area is dependent on the increase in the stress intensity at the crack tip in those specimens tempered at 300 and 400 °C.     

Three-dimensional numerical investigation of brittle bond fracture

A fracture mechanics based analysis of interface bond failure is presented. The bond edge is regarded as an interface crack front loaded under combined mode 1, 2 and 3 loading, and results are obtained for the critical stress for initiation of bond failure and the location along the bond edge where failure is initiated. A numerical procedure is formulated to study the propagation of the interface crack following initiation. Assuming that the crack propagates at the interface, a criterion for propagation is formulated, and it is shown that the crack front shape predicted is consistent with the basic interface fracture mechanics assuming quasi-static crack propagation. Results for the bond strength are presented for different fracture criteria and different bond shapes.