High temperature strength and failure of the Ni-base superalloy PM 3030

The strength, fatigue life and fracture behavior of the oxide dispersion strengthened (ODS) nickel-base superalloy PM 3030 are investigated. The high Al content in PM 3030 leads to the formation of coherent γ′ particles and, thus, to additional precipitation strengthening. A coarse and elongated grain structure (R34) and two isotropic batches with mean grain sizes of 1 μm (R90) and 17 μm (R901315) are considered. Compressive constant strain rate tests and high cycle fatigue (HCF) tests are performed. Optical, scanning and transmission electron microscopy (OM, SEM and TEM) are carried out. The properties are compared with those of the solely oxide dispersion strengthened Ni-base alloy PM 1000 [Estrin, Y., Heilmaier, M., Drew, G., 1999. Creep properties of an oxide dispersion strengthened nickel-base alloy: the effect of grain orientation and grain aspect ratio. Mater. Sci. Eng. A 272(1), 163–173]. It is found that additional γ′ hardening provides an increase in quasi-static strength by about a factor 2 and in HCF life by about a factor 10²–10³ at temperatures up to 850 °C. When fatigue life is compared at a fixed ratio of stress amplitude-to-yield or ultimate compressive strength, R34 shows a fatigue life similar to that of PM 1000 at lower temperature (e.g. 600 °C) indicating that the quasi-static strength advantage is proportionally translated into improved fatigue performance; for higher temperatures (850 °C) however, R34 shows a shorter fatigue life as compared to PM 1000. Grain size reduction, as exemplified with the fine grain R90 batch, also provides an increase in strength up to the equicohesion temperature (T_E) [Dieter, G.E., 1986. Mechanical Metallurgy. SI Metric ed. McGraw-Hill Book Company, London]. Above T_E, faster diffusion and grain boundary sliding [Raj, R., Ashby, M.F., 1971. On the grain boundary sliding and diffusional creep. Metall. Trans. 2, 1113–1127; Spingarn, J.R., Nix, W.D., 1978. Diffusional creep and diffusionally accommodated grain rearrangement. Acta Metall. 26, 1389–1398] lead to a drastic drop in strength for the R90 material. In contrast, the batch with intermediate grain size (R901315) shows strength comparable to that of R34 up to 850 °C. Furthermore, R901315 shows improved crack tolerance compared to its coarse grain counterpart R34. Due to premature crack initiating coarse oxide particles however, R901315 does not show any improvement in elongation to failure during tensile tests. Eliminating those coarse particles is expected to improve the ductility and toughness of this isotropic batch.     

A statistical investigation of the behavior of short fatigue crack in medium carbon steels

Rotary bending fatigue tests were carried out by using smooth specimens of medium carbon steel with two ferrite grain sizes. In order to clarity the physical background of the scatter in fatigue behaviour, the statistical characteristics of the initiation and growth of short fatigue crack were investigated. Results show that the short crack initiation and growth life distribution can be express by two-or three-parameter Weibull distribution. The Weibull distribution of the mixed type is well fitted to the crack length distribution for both steels. The knee values of Weibull plots are related to the grain size. The crack length distribution before the knee point can be expressed by a two-parameter Weibull distribution, and that after the knee point can be represented by two-or three-parameter Weibull distribution. It was found that the initiation Life, growth life and crack length distribution were affected by the grain size.     

含缺口试件疲劳全寿命预测一种建议的方法

传统的研究含缺口构件的疲劳的方法是将疲劳启裂和疲劳裂纹扩展两个过程完全独立起来,用不同的方法来模拟,相互间并没有定量的关系。本文是基于最新发展的多轴疲劳损伤理论,建立了一种适用于各种载荷条件下的疲劳启裂和裂纹扩展的普适方法。根据从弹塑性分析中得到的应力应变,确定疲劳损伤模型,建立能够预测疲劳启裂、裂纹扩展速率和扩展方向的新方法。整个模拟可以分为两步:弹-塑性应力分析得到材料的应力应变分布;再运用一个通用的疲劳准则预测疲劳裂纹启裂和裂纹扩展。通过对1070号钢含缺口试件的疲劳全寿命预测,得到了与实验非常吻合的模拟结果。     

Very high cycle fatigue for GCr15 steel with smooth and hole-defect specimens

Very high cycle fatigue (VHCF) properties of a low temperature tempering bearing steel GCr15 with smooth and hole-defect specimens are studied by employing a rotary bending test machine with frequency of 52.5 Hz. Both smooth and hole-defect specimens break in VHCF regime with some difference in fatigue crack initiation. For smooth specimens, a fine granular area (FGA) is observed near the grain boundary in the fracture surface of the specimens broken after 10⁷ cycles. But no FGA is observed in the hole-defect specimens broken in VHCF regime, and the VHCF crack does not initiate from the small hole at the surface as it does at low or high cycle fatigue regime. Internal stress is employed to explain the VHCF behavior of these two types of specimens. At last, an advanced dislocation model based on Tanaka and Mura model is proposed to illustrate the internal stress process and to predict fatigue crack initiation life with FGA observed in the fracture region.     

Erratum to: Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.     

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.     

An energetic approach to predict fatigue crack initiation life of LY12CZ aluminum and 16 Mn steel

The local strain range is considered to be the main factor controlling the fatigue damage process. An energetic approach is applied to correlate the elastic-plastic stress and strain near a notch with the remotely applied stress. Fatigue crack initiation lives of LYI2CZ aluminum and 16 Mn steel are predicted from a knowledge of the uniaxial data involving parameters such as the elastic modulus, strain hardening strength and strain hardening exponent. These quantities are contained and identified with the fatigue strength coefficient C^* which together with the equivalent stress range provide an estimate for the fatigue life of metals. The results agree well with the test data available in the open literature.     

An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.     

Assurance of reliable time limits in fatigue depending on choice of failure simulation: Energy density versus stress intensity

The principle of least variance is applied to evaluate the reliability of the design conditions of the Runyang cable-stayed bridge. Monitored fatigue load in service data are analyzed in conjunction with the specimen fatigue crack growth data for bridge steel. Aside from size differences, the interactive effects of material behavior with load amplitude and frequency would vary with the depicted physical model for the reliability of life prediction. Based on the same crack growth history in time or cycle, the two choice selected for comparison are stress intensity factor (SIF) range, and the strain energy density (SED) range. Reliability is found to depend on the trade off between load amplitude and frequency. Considered are high-amplitude; low-frequency and low-amplitude; high-frequency. In each case, the chances are the reliable time span of fatigue crack growth will not coincide with the useful portion of bridge life, simply because the load frequency must be anticipated as an educated estimate. It is subject to change. Conversion of the crack length fatigue cycle history to the corresponding time history requires the specification of load frequency that can set the time span of the useful life. This is demonstrated for the Runyang bridge, where approximately 30 MPa and 8 MPa would correspond to the high and low fatigue load, respectively.Significant variances were found for the SIF and SED models. The difference can be attributed to the inclusion of the mean stress in the SED that is more forgiving since it accounts for both the stress and strain effects, in contrast to the SIF model that leaves out the strain and the mean stress. Since the principle of least variance refers to the average of the R-integrals, the results based on the linear sum (LS) and root mean square (RMS) will differ quantitatively, but not qualitatively. The obvious mismatch of the fatigue load used to determine the material property and that for the bridge design can be adjusted and absorbed into the appropriate choice for the load frequency, a compensating factor not realized up to now. To this end, the weighted functions in the R-integrals further emphasize long run effects of the least variance reliability analysis. Attention is called to Changeability in addition to determinability and probability for predicting the time to failure. That is to better anticipate the change in the fatigue load frequency, to which the assistance of health monitoring should provide.     

Electric-field-induced fatigue crack growth in ferroelectric ceramics

Electric-field-induced fatigue crack growth in pre-cracked PZT ferroelectric ceramics is experimentally investigated in this work. It is found that the crack open and close under an alternating electric field is a major mechanism of crack propagation. The experimental results also show that the frequency, waveform, as well as the amplitude ratio, of the electric loading, play important roles in electric-field-induced fatigue cracking. Empirical formulations of fatigue crack propagation rates are obtained based on the experimental results. It is revealed that the crack grows at a nearly constant rate when the loading frequency is below 100 Hz. However, with the increase of the loading frequency over 125 Hz, the crack propagation rate diminishes rapidly.     

Fatigue life enhancement of structures using shape optimisation

The paper proposes a new approach for shape optimisation with fatigue life as the design objective. Conventional designs often incorporate stress optimisation that aims at reducing stress concentrations around a structural boundary by minimising the peak stress. However, this is only an effective and sufficient measure for an ‘ideal’ or ‘flaw-less’ structure. It is a well-known fact that flaws (cracks) are inevitably present in most structures. This emphasises the need to investigate the influence of cracks on optimised shapes. Numerical modelling of cracks using the Finite Element Method requires a fine mesh to model the singularity at crack tips, which makes fracture calculations computationally expensive. Furthermore, for a damage tolerance based optimisation, numerous cracks are to be considered at various arbitrary locations in a structure, and fatigue life evaluation needs to be repeated for each crack at every iteration. This makes the optimisation process extremely computationally inefficient for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, there has been inadequate research to consider fracture parameters, such as fatigue life, in the optimisation objective. To address this, the paper presents an approach for the shape optimisation of damage tolerant structures with fatigue life as the design constraint.The damage tolerance based optimisation was performed using a number of nonlinear programming algorithms, namely the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method, the Fletcher Reeves (Conjugate Direction) method, and the Sequential Unconstrained Minimisation Technique (SUMT). These methods were extended for optimising the fatigue life in the presence of numerous surface cracks. A significant enhancement in fatigue life was achieved for various crack cases consisting of different initial and final crack sizes. It is shown that the fatigue life optimised shapes can be considerably different from the corresponding stress optimised solution. This emphasises the need to explicitly consider fatigue life as a distinct design objective when optimising damage tolerant structures. A fatigue life optimisation leads to the generation of a ‘near uniform’ fatigue critical surface. The design space near the ‘optimal’ region was found to be relatively flat. This means that the precise identification of the local/global optimum solution is not critical, because a significant structural performance enhancement can be achieved in the ‘near’ optimal region. An additional benefit of fatigue life optimisation is that the resulting optimised shapes may even be lighter than the stress optimised designs. To verify the optimal solutions obtained using the nonlinear programming algorithms, the results were compared with those obtained using a heuristic optimisation method (Biological algorithm). The solutions predicted by both the methods, employing inherently different (gradient-based and gradient-less) algorithms, were found to agree very well.     

FGHxx粉末高温合金疲劳损伤行为表征、评价与展望

FGHxx系列结构材料是我国近年来成功开发的损伤容限型粉末高温合金,由FGH95到FGH99系列,主要是通过材料的化学成分、制粉工艺及后续的热处理工艺参数等优化措施,达到提高在役温度下的强度、韧性性能,改善疲劳裂纹扩展阻力等目的。相比于材料工艺力学的现有研究成果,该系列材料在固体力学相关的疲劳损伤表征、寿命评价、微结构对疲劳裂纹萌生行为的研究存在显著滞后,尤其在损伤容限相关的关键科学问题以及工程关注的安全评估手段等有待深入探究。本文基于作者们对现有的FGHxx系列粉末高温合金疲劳损伤研究现状和关键科学问题的掌握和理解以及对应的部分实验研究结果,从材料微结构特征、疲劳数据分散特点、宏微观疲劳裂纹扩展行为、SEM原位测试、疲劳寿命预测模型、疲劳损伤安全区（三维K-T关系图）的建立等进行了评述和展望。     

交变载荷下含两孔洞的铝合金长条的五种疲劳破坏型式

通过试验发现交变载荷下含两孔洞的铝合金长条,由于两孔洞的方位不同,至少有五种疲劳裂纹引起的破坏型式.在五种不同的破坏情况下,疲劳裂纹初始寿命和疲劳裂纹扩展寿命均不同,必须分阶段评估,这也直接影响到整体疲劳寿命的预计;此时常规的、经典的疲劳裂纹扩展理论难以直接应用.     

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper, we construct a model for prediction of fatigue crack initiation based on the material’s microstructure. In order to do so, the energy of a persistent slip band (PSB) is monitored and an energy balance approach is taken, in which cracks initiate and the material fails due to stress concentration from a PSB (with respect to dislocation motion). These PSBs are able to traverse low-angle grain boundaries (GB), thus belonging to clusters of grains. As a consequence of the ongoing cyclic slip process, the PSBs evolve and interact with high-angle GBs, the result of which leads to dislocation pile-ups, static extrusions in the form of ledges/steps at the GB, stress concentration, and ultimately crack initiation. Hence, this fatigue model is driven by the microstructure, i.e. grain orientations, widely distributed grain sizes, precipitates, PSB-GB interactions, as well as the affect of neighboring grains. The results predict that cracks initiate near twin boundaries from PSBs spanning a single large grain with a favorable orientation or multiple grains connected by low-angle GBs. Excellent agreement is shown between model predictions and experimental data.     

表面直接氟化改性对有机玻璃弯曲疲劳性能的影响

本文使用表面直接氟化改性来改善有机玻璃的弯曲疲劳性能。测试了改性前后有机玻璃的断裂韧性与弯曲强度，重点研究了不同缺口形式的有机玻璃在改性前后的弯曲疲劳性能变化并分析了疲劳裂纹扩展过程。弯曲疲劳寿命的测定结果表明有机玻璃的疲劳性能在表面直接氟化改性后得到明显改善，表面氟化层的结构约束效应是有机玻璃疲劳寿命提高的主要原因。此外，在疲劳断裂面上观察到规律性的条纹带形貌，疲劳条纹带的形成与裂纹尖端银纹区的产生具有一定的联系。表面直接氟化改性后疲劳条纹带扩展速率的降低也充分证明了有机玻璃疲劳寿命的提高。研究结果证明，表面直接氟化改性修复是一种提高有机玻璃疲劳性能的可行方法，对有机玻璃的工业使用具有指导意义。     

Microstructure-sensitive modeling of polycrystalline IN 100

A rate dependent, microstructure-sensitive crystal plasticity model is formulated for correlating the mechanical behavior of a polycrystalline Ni-base superalloy IN 100 at 650 °C. This model has the capability to capture first order effects on the stress–strain response due to (a) grain size, (b) γ′ precipitate size distribution, and (c) γ′ precipitate volume fraction. Experimental fatigue data with variable strain rates are used to calibrate the model for several distinct IN 100 microstructures (grain size, precipitate size distributions and volume fractions) obtained from thermomechanical processing. Physically based hardening laws are employed to evolve the dislocation densities for each slip system, taking into consideration the dislocation interaction mechanisms.     

A novel method for measuring and characterizing dynamic fracture-initiation toughness of elastic-plastic materials

The characterization and testing methods of the dynamic fracture initiation toughness of elastic-plastic materials under tensile impact are studied. By using the self-designed bar-bar tensile impact apparatus, a novel test method for studying dynamic fracture-initiation has been proposed based on the one-dimensional test principle. The curve of average loadv. s. displacement is smooth until unstable crack propagation, and the kinetic energy which does not contribute to the crack growth can be removed from total work done by external-force to the specimen. The fracture-initiation point is determined by compliance-changing rate method. The results show that these methods are feasible and effective. Through the analysis of the conversion between work and energy of a fracture specimen, the dynamicJ-integral is adopted as a characteristic parameter for elastic-plastic materials under impact loading. TheJ-integral is calculated from and curves by using the formula proposed, by Rice. TheJ-integral at fracture initiation is employed to describe the dynamic fracture-initiation toughness of elastic-plastic materials and the experimental results indicate thatJ _ID can be regarded as a material constant.     

焊接金属疲劳裂纹萌生寿命估算方法的研究

疲劳裂纹萌生阶段在整个疲劳破坏过程中占有极为重要的地位，而萌生阶段的裂纹体损伤规律用长裂纹断裂力学方法是无法确定的．以萌生阶段中塑性滞回能作为控制参量，根据实验数据拟合出疲劳损伤的连续曲线，得到裂纹萌生寿命估算公式．     

Rate dependent critical strain energy density factor of Huanglong limestone

Critical strain energy density of rock can be defined as a fundamental parameter in rock fracture mechanics, an intrinsic material property related to resistance to crack initiation and propagation. By means of the three-point bending experiments, the critical strain energy density factor of Huanglong limestone was measured over a wide range of loading rates from 8.97 × 10⁻⁴ MPam^1/2 s⁻¹ to 1.545 MPam^1/2 s⁻¹. According to the approximate relationship between static and dynamic critical strain energy density factor of Huanglong limestone, relationship between the growth velocity of crack and magnitude of load is obtained. The main conclusions are summarized as follows: (1) when the loading rate is higher than 0.0279 MPam^1/2 s⁻¹, the critical strain energy density factor of rock increased markedly with increasing loading rate. However, when loading rate is lower than 0.0279 MPam^1/2 s⁻¹, the critical strain energy density factor slightly increased with an increase in loading rate. It is found from experimental results that the critical strain energy density factor is linear proportional to the exponential expression of loading rate, (2) for Huanglong limestone, when the growth velocity of crack is lower than 100 m/s, value of the maximum load was nearly a constant. However, when the growth velocity of crack is higher than 1000 m/s, value of the maximum load dramatically increases with increasing the crack growth velocity, and (3) the critical SED of Huanglong limestone is higher as the loading rate is higher.     

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.