High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

Investigation of high cycle and Very-High-Cycle Fatigue behaviors for a structural steel with smooth and notched specimens

The high cycle and Very-High-Cycle Fatigue (VHCF) properties of a structural steel with smooth and notched specimens were studied by employing a rotary bending machine with frequency of 52.5 Hz. For smooth specimens, VHCF failure did occur at fatigue cycles of 7.1 x 10(8) with the related S-N curve of stepwise tendency. Scanning Electron Microscopy (SEM) was used for the observations of the fracture surfaces It shows that for smooth specimens the crack origination is surface mode in the failure regime of less than 10(7) cycles While at VHCF regime, the material failed from the nonmetallic inclusion lies in the interior of material, leading to the formation of fisheye pattern. The dimensions of crack initiation region were measured and discussed with respect to the number of cycles to failure. The mechanism analysis by means of low temperature fracture technique shows that the nonmetallic inclusion in the interior of specimen tends to debond from surrounding matrix and form a crack. The crack propagates and results to the final failure. The stress intensity factor and fatigue strength were calculated to investigate the crack initiation properties. VHCF study on the notched specimens shows that the obtained S-N curve decreases continuously. SEM analysis reveals that multiple crack origins are dominant on specimen surface and that fatigue crack tends to initiate from the surface of the specimen. Based on the fatigue tests and observations, a model of crack initiation was used to describe the transition of fatigue initiation site from subsurface to surface for smooth and notched specimens. The model reveals the influences of load, grain size, inclusion size and surface notch on the crack initiation transition. (C) 2010 Elsevier Ltd. All rights reserved

Instrumented impact testing of phenolphthalein polyether ketone

The Charpy impact fracture behaviour of unnotched specimens of phenolphthalein polyether ketone (PEK-C) was studied over a temperature range from room temperature to 220 degrees C by using an instrumented impact tester. The load-time and energy-time curves of PEK-C at different temperatures were recorded. From these curves, some important parameters, such as the maximum impact load, the maximum stress, the total impact energy, the crack initiation energy, the crack propagation energy etc., were obtained and their temperature dependences of PEK-C were investigated. The point of 100 percent maximum load on the load-time trace was shown to be the yield point. Two parameters, the ductile ratio (D.R.) and the ductility index (D.I.) were applied to characterize the ductility of PEK-C and their relationships to the relaxation processes were discussed.

Tension-tension fatigue failure behaviour of poly(phenylene ether ketone) (PEK-C)

Tension-tension fatigue tests were conducted on unnotched injection moulded poly(phenylene ether ketone) (PEK-C) specimens with two stress ratios, R. The fatigue behaviour of this material is described. The S-N curves (S = alternating stress, N = number of cycles to failure) for different R values have the same general shape, but the curve for bigger R is shifted to long cycles. A fatigue lifetime inversion is observed from constructed S-N curves. Examinations of failure surfaces and analyses of the fatigue data reveal that the fatigue failure mechanism of the material studied is crack growth dominated. But the manner of the fatigue crack initiation and propagation depends on the maximum cyclic stress applied. At higher stresses, the fatigue crack originates at the corner of the specimen and propagates inward; at lower stresses, the fatigue crack nucleates at an internal flaw of the specimen and propagates outward. The fatigue lifetime inversion corresponds to the transition of crack initiation and propagation from one mode to the other. Copyright (C) 1996 Elsevier Science Ltd.

Multiple Axial Cracks in A Coated Hollow Cylinder due to Thermal Shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing. (c) 2005 Elsevier Ltd. All rights reserved.

Deformation and Failure of Polymer Bonded Explosives under Diametric Compression Test

The tensile deformation and failure of polymer bonded explosives (PBXs), a particulate composite, is studied in this paper. Two HMX-based PBXs with different binder were selected for study. A diametric compression test, in which a disc-shaped specimen is loaded diametrically, was chosen to generate tensile failure in the materials. The quasi-static tensile properties and the tensile creep properties were studied by using conventional displacement transducers to measure the lateral strain along the horizontal diameter. The whole-field in-plane creep deformation was measured by using the technique of high resolution moire´ interferometry. Real time microscopic examination was conducted to monitor the process of deformation and failure of PBXs by using a scanning electron microscope equipped with a loading stage. A manifold method (MM) was used to simulate the deformation and failure of PBX samples under the diametric compression test, including the crack initiation, crack propagation and final cleavage fracture. The mechanisms of deformation and failure of PBXs under diametric compression were analyzed. The diametric compression test and the techniques developed in this research have proven to be applicable to the study of tensile properties of PBXs.

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, "mesofracture mechanics" could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.

Mixed-mode fracture mechanisms near the fatigue threshold of aisi-316 stainless-steel

Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.

Experimental investigation of Very-High-Cycle Fatigue behavior for a structural steel

Very-High-Cycle Fatigue (VHCF) test for a medium carbon structural steel (40Cr) has been performed and a stepwise S-N curve was obtained by employing cantilever-type rotary bending fatigue machine with hourglass shape specimen. The S-N curve was well explained as a combination of curves for surface-induced fracture and interior inclusion-induced fracture with fish-eye patterns. The morphology of the fish-eye pattern was illustrated in order to clarify subsurface crack initiation and propagation behavior.

层片TiAl合金的微结构对力学行为的影响

本论文针对可能应用于叶片零部件的铸造全层片TiAl基合金进行了多方面的实验研究。目的着重于观测该材料的力学性能对微结构因素的敏感性及其失效行为，并以裂纹萌生为线索探讨其相关的物理和力学内禀机制的表征。研究工作涉及到多种跨越毫米尺度的宏－细－微观力学测试方法和技术，其中，新型试样的应力分析和可行性说明针对于脆怀板材试样并具有良好自对中能力的夹具设计是成功的。单调拉伸实验和拉一拉疲劳实验得到了所研究试样的基本力学性能和影响疲劳性能的微结构敏感因素，如晶粒取向、晶粒大小等。实验研究重点说明了层片取几因素对疲劳抗力的影响一与拉伸轴方向平行的晶粒具有最好的裂纹萌生抗力。扫描电镜和透射电镜下的原位拉伸实验得到了沿层片裂纹萌生的等征，这些等征包括：层片裂纹与拉伸轴夹角呈40°／60°／90°的方向倾向性、裂纹沿γ相真孪晶层片界面萌生的位置倾向性等。纳米压痕实验和原子力显微实验证了层片的弹性模量差异，为宏一细一微观分析提供了依据。分析和讨论工作针对于沿层片萌裂纹的方向的选择性和位置的倾向性等实验现象，以宏观界面力学方法和晶体学理论，侧重表征了与层间变形特性相关的力学和物理机制：（１）以模理量失配理论为基础提出了等效失配概念，得到瞪层片TiAl合金的等效失配度为0.16；（2）以界面能量释放率断裂准则为基础，提出了模式因子（TiAl,0.24）方法来评价拉、剪力的耦合作用；（3）根据以汤普森四面体所构筑的γ层间组合模型，并采用γ层片的惯习面间异类原子对数（NAT值）、穿层几何协调因子和穿层几何协调加和因子等方法分别表征其原子结构尺度下的界面结全强度和层间变形的位错协调性。分析和讨论重阐明了全层片TiAl有序合金的层间抗剪切能力较弱和γ层间真孪晶界面易于裂纹萌生等结果。

Effects of rubber content and temperature on dynamic fracture toughness of ABS materials

The effects of rubber content and temperature on dynamic fracture toughness of ABS materials have been investigated based on the J-integral and crack opening displacement (COD, delta) concepts by an instrumented Charpy impact test. A multiple specimens R-curve method and stop block technique are used. It is shown that the materials exhibit a different toughness behavior, depending on rubber content and temperature. The resistance against stable crack initiation (J(0.2) or delta(0.2)) increases with increasing rubber content. However, J(0.2) first increased with increasing temperature until reaching the maximum value; after that, it decreases with further increasing the temperature. (C) 2000 John Wiley & Sons, Inc.

TEMPERATURE EFFECT ON IMPACT FRACTURE-TOUGHNESS AND FRACTURE MECHANISM OF PHENOLPHTHALEIN POLY(ETHER KETONE)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K-c and critical strain energy release rate G(c). Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.

锦屏电站地下厂房卸荷岩体参数研究

It is a basic work to ascertain the parameters of rock mass for evaluation about stability of the engineering. Anisotropism、inhomogeneity and discontinuity characters of the rock mass arise from the existing of the structural plane. Subjected to water、weathering effect、off-loading, mechanical characters of the rock mass are greatly different from rock itself, Determining mechanical parameters of the rock mass becomes so difficult because of structure effect、dimension effect、rheological character, ‘Can’t give a proper parameter’ becomes one of big problems for theoretic analysis and numerical simulation. With the increment of project scale, appraising the project rock mass and ascertaining the parameters of rock mass becomes more and more important and strict. Consequently, researching the parameters of rock mass has important theoretical significance and actual meaning. The Jin-ping hydroelectric station is the first highest hyperbolic arch dam in the world under construction, the height of the dam is about 305m, it is the biggest hydroelectric station at lower reaches of Yalong river. The length of underground factory building is 204.52m, the total height of it is 68.83m, the maximum of span clearance is 28.90m. Large-scale excavation in the underground factory of Jin-ping hydroelectric station has brought many kinds of destructive phenomenon, such as relaxation、spilling, providing a precious chance for study of unloading parameter about rock mass. As we all know, Southwest is the most important hydroelectric power base in China, the construction of the hydroelectric station mostly concentrate at high mountain and gorge area, basically and importantly, we must be familiar with the physical and mechanical character of the rock mass to guarantee to exploit safely、efficiently、quickly, in other words, we must understand the strength and deformation character of the rock mass. Based on enough fieldwork of geological investigation, we study the parameter of unloading rock mass on condition that we obtain abundant information, which is not only important for the construction of Jin-ping hydroelectric station, but also for the construction of other big hydroelectric station similar with Jin-ping. This paper adopt geological analysis、test data analysis、experience analysis、theory research and Artificial Neural Networks （ANN） brainpower analysis to evaluate the mechanical parameter, the major production is as follows: (1)Through the excavation of upper 5-layer of the underground powerhouse and the statistical classification of the main joints fractures exposed, We believe that there are three sets of joints, the first group is lay fracture, the second group and the fourth group are steep fracture. These provide a strong foundation for the following calculation of and analysis; (2)According to the in-situ measurement about sound wave velocity、displacement and anchor stress, we analyses the effects of rock unloading effect，the results show a obvious time-related character and localization features of rock deformation. We determine the depth of excavation unloading of underground factory wall based on this. Determining the rock mass parameters according to the measurement about sound wave velocity with characters of low- disturbing、dynamic on the spot, the result can really reflect the original state, this chapter approximately the mechanical parameters about rock mass at each unloading area; (3)Based on Hoek-Brown experienced formula with geological strength index GSI and RMR method to evaluate the mechanical parameters of different degree weathering and unloading rock mass about underground factory, Both of evaluation result are more satisfied; (4)From the perspective of far-field stress, based on the stress field distribution ideas of two-crack at any load conditions proposed by Fazil Erdogan (1962)，using the strain energy density factor criterion (S criterion) proposed by Xue changming(1972)，we establish the corresponding relationship between far-field stress and crack tip stress field, derive the integrated intensity criterion formula under the conditions of pure tensile stress among two line coplanar intermittent jointed rock，and establish the corresponding intensity criterion for the exploratory attempt; (5)With artificial neural network, the paper focuses on the mechanical parameters of rock mass that we concerned about and the whole process of prediction of deformation parameters, discusses the prospect of applying in assessment about the parameters of rock mass，and rely on the catalog information of underground powerhouse of Jinping I Hydropower Station, identifying the rock mechanics parameters intellectually，discusses the sample selection, network design, values of basic parameters and error analysis comprehensively. There is a certain significance for us to set up a set of parameters evaluation system，which is in construction of large-scale hydropower among a group of marble mass.

复杂裂隙岩体统计断裂本构关系与变形参数研究

Rock mass is widely recognized as a kind of geologic body which consists of rock blocks and discontinuities. The deformation and failure of rock mass is not only determined by rock block，but also by discontinuity which is virtually more important. Mutual cutting and combination of discontinuities controlled mechanical property of rock mass. The complex cutting of discontinuities determine the intense anisotropy on mechanical property of rock mass，especially under the effect of ground stress. Engineering practice has show that the brittle failure of hard rock always occurs when its working stress is far lower than the yield strength and compressive strength，the failure always directly related to the fracture propagation of discontinuities. Fracture propagation of discontinuities is the virtue of hard rock’s failure. We can research the rock mass discontinuous mechanical properties precisely by the methods of statistical analysis of discontinuities and Fracture Mechanics. According to Superposition Principle in Fracture Mechanics，A Problem or C Problem could be chosen to research. Problem A mainly calculates the crack-tip stress field and displacement field on internal discontinuities by numerical method. Problem C calculate the crack-tip stress field and displacement field under the assumption of that the mainly rock mass stress field has been known. So the Problem C avoid the complex mutual interference of stress fields of discontinuities，which is called crack system problem in Fracture Mechanics. To solve Problem C, field test on stress field in the rock mass is needed. The linear Superposition of discontinuities strain energies are Scientific and Rational. The difference of Fracture Mechanics between rock mass and other materials can mostly expression as：other materials Fracture Mechanics mostly face the problem A，and can’t avoid multi-crack puzzle, while the Rock mass Fracture Mechanics answer to the Problem C. Problem C can avoid multi-discontinuities mutual interference puzzle via the ground stress test. On the basis of Problem C, Fracture Mechanics could be used conveniently in rock mass. The rock mass statistics fracture constitutive relations, which introduced in this article, are based on the Problem C and the Discontinuity Strain Energy linear superposition. This constitutive relation has several merits: first, it is physical constitutive relation rather than empirical; second, it is very fit to describe the rock mass anisotropy properties; third, it elaborates the exogenous factors such as ground stress. The rock mass statistics fracture constitutive relation is the available approach to answer to the physical, anisotropic and ground stress impacted rock mass problems. This article stand on the foundation of predecessor’s statistics fractures constitutive relation, and improved the discontinuity distributive function. This article had derived the limitation of negative exponential distribution in the course of regression analysis, and advocated to using the two parameter negative exponential distribution for instead. In order to solve the problems of two-dimension stability on engineering key cross-sectional view in rock mass, this article derived the rock mass planar flexibility tensor, and established rock mass two-dimension penetrate statistics fracture constitutive relation on the basis of penetrate fracture mechanics. Based on the crack tip plasticity research production of penetrate fracture, for example the Irwin plasticity equifinality crack, this article established the way to deal with the discontinuity stress singularity and plastic yielding problem at discontinuity tip. The research on deformation parameters is always the high light region of rock mass mechanics field. After the dam foundation excavation of XiaoWan hydroelectric power station, dam foundation rock mass upgrowthed a great deal of unload cracks, rock mass mechanical property gotten intricacy and strong anisotropy. The dam foundation rock mass mostly upgrowthed three group discontinuities： the decantation discontinuity, the steep pitch discontinuity, and the schistosity plane. Most of the discontinuities have got partial unload looseness. In accordance with ground stress field data, the dam foundation stress field greatly non-uniform, which felled under the great impaction of tectonic stress field, self-weight stress field, excavation geometric boundary condition, and excavation, unload. The discontinuity complexity and stress field heterogeneity, created the rock mass mechanical property of dam foundation intricacy and levity. The research on the rock mass mechanics, if not take every respected influencing factor into consideration as best as we can, major errors likely to be created. This article calculated the rock mass elastic modulus that after Xiao Wan hydroelectric power station dam foundation gutter excavation finished. The calculation region covered possession monolith of Xiao Wan concrete double-curvature arch dam. Different monolith were adopted the penetrate fracture statistics constitutive relation or bury fracture statistics constitutive relation selectively. Statistics fracture constitutive relation is fit for the intensity anisotropy and heterogeneity rock mass of Xiao Wan hydroelectric power station dam foundation. This article had contrastive analysis the statistics fracture constitutive relation result with the inclined plane load test actual measurement elastic modulus and RMR method estimated elastic modulus, and find that the three methods elastic modulus have got greatly comparability. So, the statistics fracture constitutive relations are qualified for trust. Generally speaking，this article had finished following works based on predecessors job: “Argumentation the C Problems of superposition principle in Fracture Mechanics, establish two-dimension penetrate statistics fracture constitutive relation of rock mass, argue the negative exponential distribution limitation and improve it, improve of the three-dimension berry statistics fracture constitutive relation of rock mass, discontinuity-tip plastic zone isoeffect calculation, calculate the rock mass elastic modulus on two-dimension cross-sectional view”. The whole research clue of this article inherited from the “statistics rock mass mechanics” of Wu Faquan（1992）.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.