Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

Effect of reflected stress waves on the stress intensity factor of an anti-plane strain edge crack during crack propagation and after crack arrest

Analytic solutions have been obtained for the stress intensity factor for a propagating and arresting anti-plane strain edge crack in a semi-infinite plate. Kostrov's analysis for this system has been used, and solutions have been obtained up to the time it takes for a stress wave emitted from the crack tip at the start of crack propagation to be reflected first from the edge of the plate, then from the crack tip, from the edge of the plate again and to arrive again at the crack tip. To simplify the analysis a constant velocity of crack propagation has been assumed. If the crack arrests before the arrival at the crack tip of a stress wave emitted from the crack tip at the start of propagation and reflected from the edge of the plate, the stress intensity factor remains constant after arrest until this stress wave arrives. The stress intensity factor then increases until the time of arrival of a reflected stress wave emitted at the instant of arrest. After this the stress intensity factor decreases again. If the crack arrests after the arrival of the first reflected stress wave, the stress intensity factor increases after arrest under the influence of reflected stress waves emitted earlier during the propagation of the crack. The changes in the stress intensity factor are more pronounced at higher crack velocities.

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Résumé Des solutions analytiques ont été obtenues pour le calcul du facteur d'intensité de contrainte relatif à une fissure de bord dans une plaque semi-infinie en cours de propagation ou en cours d'arrêt dans des conditions d'état anti-plan de contrainte. Une analyse de Kostrov appliquée à ce système a été utilisée et les solutions ont été obtenues jusqu'au moment où une onde de contrainte émise de l'extrémité de la fissure sur le point du démarrage de la propagation de la fissure se trouvent réfléchie en premier lieu par les bords de la plaque et ensuite par l'extrémité de la fissure, à nouveau par le bord de la plaque et revenant à nouveau à l'extrémité de la fissure. Pour simplifier l'analyse, une vitesse constante de propagation de fissure a été supposée. Si la fissure est arrêtée avant que l'onde de contrainte émise par l'extrémité de la fissure au démarrage de la propagation et après réflexion contre le bord de la plaque n'arrive à l'extrémité de la fissure, le facteur d'intensité de contrainte demeure constant après l'arrêt, jusqu'à ce que l'onde de contrainte arrive. Ensuite, le facteur d'intensité de contrainte augmente jusqu'au moment où arrive l'onde de réflexion émise au moment de l'arrêt de la fissuration. Ensuite le facteur d'intensité de contrainte se réduit à nouveau. Si la fissure s'arrête après l'arrivée du premier train d'ondes réfléchies, le facteur d'intensité de contraintes s'accroît jusqu'à l'arrêt, sous l'influence des ondes réfléchies émises précédemment au cours de la propagation de la fissure. Les changements de facteur d'intensité de contrainte sont plus prononcés lorsqu'augmente la vitesse de fissuration.

     

Crack extension and arrest in contact stress fields

Sudden crack extension and arrest is observed when indenters are pressed into the surface of brittle materials. The energetics of this system are examined. Crack extension is defined by a condition of decreased free energy (after A. A. Griffith) and crack arrest is defined by a condition of increased free energy with a further increase in crack size. The analysis shows that the critical stress required for crack extension depends on the dimension of the stress field and other factors, viz., crack size and material properties, usually associated with Griffith's fracture equation. The dependence on the dimension of the stress field explains Auerbach's empirical law which shows that the apparent strength of a brittle material increases with the decreasing size of the contact stress field. Experimental observations for hot-pressed Si₃N₄ and SiC are presented to examine this size effect and its predicted relation to material properties.     

Initiation, propagation and arrest of an interface crack subjected to controlled stress wave loading

An experimental study has been conducted to investigate the initiation, propagation, and arrest of bimaterial interface cracks subjected to controlled stress wave loading in the form of a tensile dilatational stress wave pulse. The tensile pulse is generated by detonating lead azide explosive in a specially designed specimen. Dynamic loading of the bimaterial interface results in crack initiation, propagation, and arrest, all in the same experiment. This failure event is observed using photoelasticity in conjunction with high speed photography. Full field data from the experimentally obtained isochromatic fringe patterns is analyzed to determine time histories of various fracture parameters such as the crack tip speed, the dynamic complex stress intensity factor, the energy release rate, and the mixity. The experimental data is also used to quantify the values of the dynamic initiation and arrest toughness and to evaluate a recently proposed dynamic interface fracture criterion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Energy loss in Homalite 100 during crack propagation and arrest

Dynamic photoelastic experiments were conducted with a modified compact tension specimen to study energy loss in Homalite 100 during the fracture process. The method of analysis utilizes an energy balance in the system. The results showed that approximately 40% of the initial strain energy was lost due to damping during propagation and after arrest.

Total energy loss was then partitioned into energy loss during propagation and energy loss after arrest by studying oscillations in the stress intensity factor in the post arrest period. Results indicated almost equal energy loss during propagation and after arrest.     

裂纹止裂技术及裂纹动态扩展规律研究

为了对动态荷载作用下水泥粉煤灰砂浆的裂缝动态扩展行为进行研究,提出了一种大尺寸带V型底边的半圆边裂纹(SECVB)试件,其V形底部具有止裂功能。SECVB试件的V形底部设计为180°,150°和120°三个角度。采用落锤冲击装置进行了冲击试验,并使用裂纹扩展计(CPG)用于测量裂纹扩展的相关参数。利用有限差分程序AUTODYN对裂纹扩展行为进行了数值模拟,并用有限元程序ABAQUS计算了裂纹的动态应力强度因子(DSIF);根据CPG测量的裂纹萌生时间和扩展时间来确定临界应力强度因子。试验和数值模拟结果表明,SECVB试件适合于研究动态荷载作用下水泥粉煤灰砂浆的裂纹扩展行为和止裂行为。在裂纹扩展过程中,裂纹可能在一段时间内止裂,并且裂纹在起始时刻的断裂韧度高于裂纹扩展时的断裂韧度。     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

Crack layer analysis of fatigue crack propagation in rubber compounds

A methodology to characterize the resistance of rubber compounds to crack propagation (fracture toughness) is presented. A constitutive model based on the crack layer theory is utilized to extract the specific energy of damage ^*, a material parameter characteristic of the material's resistance to crack propagation and the dissipative characteristic, . The model expresses the rate of crack propagation as% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqaaaOqaamaalaaabaGaam% izaGqaciaa-fgaaeaacaWGKbGaa8Ntaaaaaaa!3AFA!\[\frac{{da}}{{dN}}\]= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaalaaabaGaeq% OSdiMaamOsamaaDaaaleaacaaIXaaabaGaaGOmaaaaaOqaaiaadMha% caGGQaGaamOuamaaBaaaleaacaaIXaaabeaakiabgkHiTiaadQeada% WgaaWcbaGaaGymaaqabaaaaaaa!41A5!\[\frac{{\beta J_1^2 }}{{y*R_1 - J_1 }}\]where da/dN is the cyclic rate of fatigue crack propagation (FCP), J ₁ is the energy release rate (tearing energy) and R ₁ is the resistance moment which accounts for the amount of damage associated with the crack advance. Microscopic examination revealed that crack tip microcracking is the dominant damage mechanism. Hence, R ₁ was evaluated as the area (m²) of microcracking surfaces per unit crack advance.Fatigue crack propagation data for a particular rubber compound have been analyzed using the present model. The proposed equation describes the entire FCP history in the compound. According to this model, ^* and for the compound investigated, are found to be 9.3 kJ m^-2 and 9.7×10^-9 m⁴/J-cycle, respectively.

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Résumé On présente une méthodologie pour caractériser la résistance de composés de caoutchouc à la propagation des fissures du point de vue de la ténacité à la rupture. Un modèle constitutif basé sur la théorie de la couche de fissuration est utilisé pour obtenir l'énergie spécifique d'endommagement ^*, un paramètre du matériau représentatif de sa résistance à la propagation d'une fissure, et une caractéristique de dissipation . Le modèle exprime la vitesse de propagation d'une fissure de fatigue par cycle da/dN en fonction de ces deux paramètres, de la vitesse de relaxation de l'énergie de cisaillement J ₁, et du moment résistif R ₁ qui tient compte de état de l'endommagement associé à la progression de la fissure. Un examen microscopique révèle que la microfissuration à l'extrémité de la fissure est le mécanisme déterminant de l'endommagement. Dès lors, on évalue R ₁ en fonction de l'aire de microfissuration (en m²) par unité de progression de la fissure.Des données de propagation de fissure de fatigue sont analysées à l'aide du présent modèle pour un composé de caoutchouc particulier. L'équation proposée décrit l'entièreté de la propagation de la fissure dans le composé. Des valeurs numériques pour ^* et pour de respectivement 9,3 kJ m^-2 et 9,7×10^-9 m^-4/J-cycle sont trouvées.

     

Crack layer analysis of fatigue crack propagation in ABS polymer

Differences in damage formation during fatigue crack propagation in acrylonitrile-butadiene-styrene polymer, between tests both fulfilling and not fulfilling linear elastic fracture mechanics requirements, were related to differences in crack propagation behaviour through the crack layer (CL theory. At both test conditions, damage consisted of crazing and shear yielding of the matrix, as well as elongation of rubbery domains. For a given crack length, the lower load level showed a higher intensity of craze damage. CL analysis showed that the process-dependent dissipation coefficient, , is inversely proportional to the lifetime. Further, despite drastic differences in the amounts of each damage species, both tests were estimated to have the same specific enthalpy of damage (^*=105 cal g^–1), a material constant that is a measure of the intrinsic resistance to damage formation at the crack tip.     

Viscoplastic-dynamic crack propagation: Experimental and analysis research for crack arrest applications in engineering structures

The many practical situations in which the initiation of rapid crack propagation cannot be absolutely precluded and where the consequences of a large scale fracture would be catastrophic mandate the development and use of crack arrest fracture mechanics technology. Most currently applied procedures utilize linear elastic analyses and corresponding material fracture property characterizations. Even though the theoretical basis for the use of this level of approach is incomplete, selected practical applications are described in this paper that show that these can still be effectively made. In addition, to address the current deficiencies and to treat those conditions where small-scale yielding conditions are clearly not satisfied, more advanced viscoplastic-dynamic analyses are also being developed. An approach is described in this paper that performs well-instrumented fracture propagation experiments in concert with viscoplastic dynamic finite-element simulations. This approach, currently used to quantify critical values of the T ^* crack tip characterizing parameter developed by Atluri, is being pursued in order to provide transferable material crack arrest toughness values in the regime where viscoplastic-dynamic conditions dominate.

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Résumé Les nombreuses situations pratiques où l'amorçage d'une croissance rapide d'une fissure ne peut être formellement prévue, et où les conséquences d'une rupture à grande échelle seraient catastrophiques, requièrent le développement et l'usage de la technique de mécanique de la rupture du point de vue de l'arrêt de fissuration.La plupart des procédures actuelles recourent à des analyses linéaires et élastique et aux caractérisations correspondantes des propriétés de résistance à la rupture des matériaux. Même si la base théorique pour une approche de ce niveau est encore incomplète, des applications pratiques spécifiques peuvent en être faites, ainsi qu'on le décrit dans l'étude. En outre, pour répondre aux déficiences actuelles, et pour traiter les conditions qui ne peuvent s'accomoder des conditions de plastification à petite échelle, on développe une analyse dynamique viscoplastique plus évoluée. Dans l'étude, on décrit une approche qui associe des essais de propagation de fissure dûment instrumentés et des simulations dynamiques viscoplastiques par éléments finis. Cette approche, qui est déjà utilisée pour établir les valeurs critiques du paramètres T ^* développé par Atluri pour caractériser l'extrémité de la fissure, est approfondie en vue de fournir des valeurs transférables de la ténacité du matériau vis-à-vis de l'arrêt de propagation d'une fissure, là où prédominent des conditions de viscoplasticité dynamique.

     

Crack propagation in brittle heterogeneous solids: Material disorder and crack dynamics

Crack propagation in a linear elastic material with weakly inhomogeneous failure properties is analyzed. An equation of motion for the crack is derived in the limit of slow velocity. Predictions of this equation on both the average crack growth velocity and its fluctuations are compared with recent experimental results performed on brittle heterogeneous materials (Ponson in Phys Rev Lett, 103, 055501; Måløy et al. in Phys Rev Lett, 96, 045501). They are found to reproduce quantitatively the main features of crack propagation in disordered systems. This theoretical framework provides new tools to predict life time and fracture energy of materials from their properties at the micro-scale.     

Subcritical crack propagation under cyclic stress impulse

An equipment has been designed to observe subcritical crack propagation under cyclic impulse (impact) loads. The equipment design uses the concept of stress wave propagation in bars. A four point bend notched specimen is struck by an incident bar with a known stress wave. The test specimens were machined from PMMA sheet (Lucite^®). The crack, initiated from the notch, was detected by a step wise increase of a graphitic grid imprinted on one side of the specimen. The data was analyzed using fracture mechanics theory and compared with that of conventional fatigue.Although the applied strain rate was quite high (1s^–1), stable crack propagation was significant. It appears that the elastic energy stored in the specimen within the duration of each impulse is dissipated in craze formation at the tip of the advancing crack. Furthermore, the magnitude of stable crack propagation was larger under impulse loading than under sinusoidal fatigue. On the other hand, cracks were slower under impulse loading. Fractographic evidence attributes these phenomena to the nature of craze growth under each loading condition.     

Fatigue crack propagation under cyclic thermal stress

Structures used at elevated temperature subject to severe cyclic thermal stress. Therefore, accurate prediction procedures for thermal fatigue crack growth should be applied to rationalise component flaw assessment. Fatigue crack propagation tests under thermal stress were carried out using an modified type 316 stainless steel (316FR), which is a candidate material for the fast reactor in Japan. Thermal stress of the tests was generated by cyclically changed temperature distribution through thickness in a plate by induction heating and air-cooling. Numerical analysis was also carried out to examine the applicability of the J integral under cyclic thermal stress. The J integral under elasto-plastic condition under thermal stress is close to the elastically calculated J integral. Prediction by J integral tends to be conservative for deeper cracks, and modification of the J integral value using crack opening ratio gives good agreement with the experimental crack growth.