CRACK CLOSURE EFFECT ON CRACK GROWTH RATE AT 650°C IN DOUBLE NOTCHED SPECIMENS OF A NICKEL BASE SUPERALLOY

Abstract— Creep-fatigue tests were performed at 650°C in air on a N18 nickel base superalloy, using double notched and smooth specimens. The deformation mechanisms observed by TEM at the notch root are shown to be compatible with the constitutive set of equations used in the finite element analysis which is presented. For a given K _max at the notch root, the crack growth rate is much higher in a notched specimen than in a smooth one. This effect can be explained by a variation of the crack closure stress level with the local R ratio and the local stress. A strong accelerating effect of the R ratio, especially for negative values, is found in smooth specimens. Introducing a K _op correction in the experimental results leads to a good agreement between the measured crack growth rate plotted versus K _eff in notched and smooth samples.     

Modified Kitagawa–Takahashi diagram accounting for finite notch depths

The Kitagawa–Takahashi diagram in its commonly used form allows to predict, for cracks of given length and stress range, the allowable stress range for infinite life. However, caution is advised if a crack emanates not directly from the plane surface but from a sharp, crack-like notch instead. In this contribution, it is shown that taking the crack length equal to the total flaw depth (sum of notch depth and crack length) gives non-conservative results. Based on a simple mechanical model, a 3-dimensional Kitagawa–Takahashi diagram considering the build-up of crack growth resistance as well as the influence of the notch depth is developed. Comparison of model predictions and experimental results shows good agreement.     

2Cr13钢在弯曲受载下工程裂纹启裂的实际估计

本文介绍了2Cr13钢三点变曲缺口试样缺口顶端张开位移的估计方法,通过缺口顶端局部应力—应变计算,给出了三点弯曲加载状态下缺口顶端工程裂纹启裂条件,并说明了裂纹启裂长度,这对叶片的安全运行具有一定的指导意义。文中的理论预测值与试验值均能较好吻合。     

Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

On crack closure and the notch size effect in fatigue

A method for determining the fatigue notch-size-effect is presented based upon the development of closure in the wake of a newly formed crack growing from a notch. A comparison with experimental results is in accord with predictions. The effect of crack closure on the formation of non-propagating cracks at notches and on notch sensitivity is also discussed.     

Prediction of non propagating cracks

An explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop. Predicted lengths of these cracks based on solutions for the intensity factor are in good agreement with the experimental data. Intensity factor trends for cracks in notches are shown to vary from an initial decrease to a minimum value followed by an increase and eventual convergence with the trend for the equivalent long crack for sharp notches to the blunt notch curves that continuously increased during their approach to the long crack trend. The type of trend exhibited by a given notch depends both on notch geometry and notch size. In blunt notches the maximum value of the threshold stress for crack propagation is at initiation. However, for sharp notches the peak value of the threshold stress vs crack length curves shifts to a finite length. Stresses above the initiation level but below this peak stress level result in fatigue cracks which start but do not propagate to failure. Predicted values of the fatigue limit stresses for a variety of sizes in a circular and an elliptical notch are in good agreement with experimental results.     

Modelling the residual strength of fatigue damage at a single semicircular edge notch: Semielliptical crack and through‐the‐thickness crack

In the present paper, computational framework for fatigue performance analysis of a semicircular edge notch with a through‐the‐thickness crack or a semielliptical crack is discussed. The failure behaviour of such configurations is theoretically examined through the stress‐intensity analysis and residual life estimation. The stress field of a damaged notch configuration is herein investigated by employing analytical and numerical approaches. Further, a fracture mechanics–based methodology, developed for fatigue life assessment, is taking into account the crack growth model proposed by Huang and Moan in which the stress ratio is involved. The efficiency of the obtained fatigue damage assessments, related to the edge notch configurations, is verified through appropriate experimental observations.     

Growth of cracks under far-field cyclic compressive loads: Numerical and experimental results

Crack growth from a notch tip, under the influence of fully compressive far-field cyclic loads, is investigated both numerically and experimentally in notched specimens of a lower strength steel and an aluminum alloy. Such cracks, emanating from the root of the notch, progressively decelerate until complete crack arrest occurs. Analyses of the stress state along the crack plane indicate that while the extent of the residual tensile stress field diminishes with an increase in crack length, there is a progressive increase in crack closure during crack advance. Approximate numerical calculations of the crack closure loads are in reasonable agreement with experimental results.     

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

A three‐dimensional (3D) weight function method is employed to calculate stress intensity factors of quarter‐elliptical corner cracks at a semi‐circular notch in the newly developed single‐edge notch bend specimen. Corner cracks covering a wide range of geometrical parameters under pin‐loading and remote tension conditions are analysed. Stress intensity factors from the 3D weight function analysis agree well with ABAQUS‐Franc3D finite element results. An engineering similitude approach previously developed for the half‐elliptical surface crack in single‐edge notch bend specimen is also applied to the present corner crack configuration. The results compare well with those from the present weight function analysis.     

EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic-plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through-thickness crack emanating from a notch root under elastic—plastic loading conditions.     

Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.     

陶瓷材料断裂韧性与缺口半径 Ⅱ 断裂韧性估算方法

在陶瓷材料裂纹尖端存在一个断裂过程区，当断裂过程区内平均应力达到断裂强度时，裂纹扩展。本文由理论推导结合实验数据，得到了新断裂过程区的大小是平均晶粒直径的四倍。并由平均应力断裂模型，给出了陶瓷材料断裂韧性和缺口半径及平均晶粒直径之间的关系式，由此关系式可以用宽缺口试件测出的断裂韧性去估算陶瓷材料的本质断裂韧性。     

Fatigue crack propagation into the residual stress field along and perpendicular to laser beam butt‐weld in aluminium alloy AA6056

Laser beam butt welds in Al‐alloys are very narrow and are accompanied by steep residual stress gradients. In such a case, how the initial crack orientation and the distance of the notch tip relative to the weld affect fatigue crack propagation has not been investigated. Therefore, this investigation was undertaken with two different crack orientations: along the mid‐weld and perpendicular to the weld. Fatigue crack propagation ‘along the mid‐weld’ was found to be faster in middle crack tension specimens than in compact tension specimens. For the crack orientation ‘perpendicular to the weld’, the relative distance between the notch tip and the weld was varied using compact tension specimens to generate either tensile or compressive residual stresses near the notch tip. When tensile residual stresses were generated near the notch tip, fatigue crack propagation was found to be faster than that in the base material, irrespective of the difference in the initial residual stress level and whether the crack propagated along the mid‐weld or perpendicular to the weld. In contrast, when compressive weld residual stresses were generated near the notch tip, fatigue crack arrest, slow crack propagation, multiple crack branching and out of plane deviation occurred. The results are discussed by considering the superposition principle and possible practical implications are mentioned.     

Interfacial debonds of layered anisotropic materials using a quasi-static interface damage model with Coulomb friction

The resistance to mode I failure of rubbers is studied by submitting single edge notch samples to uniaxial tension. Reproducing the seminal work of Rivlin and Thomas (J Polym Sci 10:291–318, 1953), single edge notch tension specimens, presenting notches of various lengths, are stretched until break. A styrene butadiene rubber, unfilled and filled with carbon-black, and an unfilled rubber from the latter mentioned work, were considered. When the notch is smaller than one fifth of the sample width, mode I crack opening is observed, leading to catastrophic failure that creates smooth mirror-like crack surfaces. Nonetheless, the experimental force-elongation responses show that the mode I critical energy release rate cannot be calculated by a classical Griffith elastic failure analysis. When notches are longer, the SENT samples are not submitted to pure uniaxial tension only. Structural bending leads to uncontrolled mixed mode crack propagation. The surfaces created when the long notches propagate are rough and bifurcations are witnessed for the filled rubbers.     

Fatigue of V-notched members: Short crack behavior and endurance limit

A previous experimental investigation showed that the short crack behavior in severe V-notched geometries is essentially characterized by an initial transient variation of the crack opening level within the notch plastic zone. This result is exploited to derive a general formulation of the endurance limit of V-notched members. Analytical solutions for the stress intensity factor and the notch plastic zone extent are obtained to compute the effective crack driving force ΔK_eff as a function of notch geometry, crack length and nominal stress. Then, the endurance limit is determined as the nominal stress below which an initiated crack becomes non-propagating, i.e. by equating the minimum ΔK_eff value at the end of the plastic zone to a threshold value. By using Irwin's redistribution principle which allows us to make relations between the V-notch elastic and plastic fields, the following results are obtained. The endurance limit can be computed only from the V-notch “stress intensity factor” and the material threshold and cyclic yield stress. The endurance limit dependence on the threshold diminishes as the notch angle increases from zero and vanishes in the limit case of a smooth surface. When the notch contains a pre-existing crack, a Kitagawa-type endurance diagram is obtained. The uncracked notch endurance limit, the critical crack length and the slope of the decrease beyond this length, increase with increasing notch angle, and there is a total coincidence with the Kitagawa diagram in the limit case where the notch angle tends to 180°. This result shows that a global theory should govern at one and the same time the short crack behavior in smooth and severe geometries.     

Strain-based approach to fatigue crack initiation and propagation in welded steel joints with arbitrary notch shape

In this paper, a novel strain-based approach for the fatigue strength modelling of welded steel joints is introduced. The actual weld notch geometry and the variation in the microstructure characteristics of the material are considered, and thus, the approach enables the fatigue crack growth simulation from the crack initiation to the critical crack length before the final fracture. The predicted fatigue strength is in line with the experimental results. By considering the crack tip plasticity and stress triaxiality, the approach is able to describe the different crack growth periods of the fatigue life: the short crack, long crack, and tearing-related long crack growth periods. For a welded joint with a smooth notch shape, the short crack growth period is observed to be dominant and to have a significant influence on fatigue life.     

纯Ⅰ型加载条件下有机玻璃中心切口圆盘断裂的尺寸相关性

采用直槽式和尖槽式中心切口圆盘试件,对有机玻璃在纯Ⅰ型准静态加载条件下的断裂行为进行了实验研究.结果表明,中心切口圆盘试件的切口形状对断裂行为和断裂韧度的测试结果有显著的影响.直槽切口偏离理想裂纹,裂纹起裂始于切口端部的角点,实测的断裂韧度值偏高且具有尺寸相关性;尖槽切口接近理想裂纹,裂纹起裂始于尖角的顶点,实测的断裂韧度不存在尺寸相关性,即是材料常数.     

Response of cracks to impact by caustics

A study of the behaviour of notched plexiglas specimens under stress pulses created from an air-gun was undertaken. It was concluded that the initial notch is propagated by steps under the action only of tensile stress pulses, while the compressive stress pulses do not have any influence on crack propagation. It was also found that the maximum crack propagation velocity depends on the magnitude of the applied stress pulse, as well as on the initial notch length. Furthermore, the dependence of the crack-tip stress intensity factor on the crack propagation velocity was established and the critical strain energy release rate was determined. Finally, a comparison of the results of the present paper with the corresponding theoretical or experimental data of previous investigations was made.     

PREDICTION OF FATIGUE LIFETIME OF NOTCHED MEMBERS

Abstract— A simple model for the estimation of the total fatigue life of notched members is presented. The number of cycles to failure is estimated as the summation of the cyclic life spent in: (1) the initiation of a dominant fatigue crack at the notch root; (2) the very early growth of this crack within the notch plastic zone; (3) the subsequent fatigue crack growth in the elastic stress-strain field of the notch; and (4) the elastic stress field of the bulk material. Theoretical and experimental results are compared.     

Notch tensile behavior of extruded Mg–Y–Zn alloys containing long period stacking ordered phase

The notch tensile behavior of extruded Mg–6RY–4Zn and Mg–9RY–4Zn (RY: Y-rich misch metal) alloys containing long period stacking ordered (LPSO) phase tested from room temperature to 250 °C was investigated. LPSO long-strips crack more severely in notch samples compared with that in smooth samples. The UTS values are above 300 MPa and the notch sensitivity ratio (NSR) values are larger than 1 in both alloys because the severe crack of LPSO phase costs more energy in notch samples. Furthermore, the NSR value rises with increasing the RY content or elevating the test temperature. The strengthening effect of LPSO phase is more remarkable at high temperatures. The notch leads the fracture mode of the two alloys changing from ductile fracture to brittle fracture. Designing complex shape components should consider the NSR and plasticity of Mg–Y–Zn alloys together.