Cyclic Deformation and Fatigue Damage Behavior of Cu Monocrystals, Bicrystals and Tricrystals

1.IntroductionMostofmechanisticstudiesoncyclicdeformationhavebeencarriedoutonCucrystalsinsingle-slipori-entations.ThereareseveralexcellentreviewarticleswhichemphasizeddifferentaspectsofthesubjectI1~6].Whenawell-annea1edCucrystalsuitablyorientedforsingleslipissubjectedtocyclicdeformationbetweenconstantplasticstrainamplitudelimits7platroomtemperatureinair,itwillhardenundertheactionofcyclicstraining.Thepeakstressincreasesrapidlyatfirstandthenmoreslowly,approachingavalue,thesaturationstressTs.Ap…     

Fatigue life prediction of copper single crystals using a critical plane approach

A critical plane multiaxial fatigue criterion was employed to predict the fatigue life of copper single crystals. The detailed stress-strain response was obtained through the constitutive modeling using a newly developed crystal plasticity theory. The constitutive model was capable of capturing the major deformation features of copper single crystals under cyclic loading including the cyclic stress-strain curves, cyclic hardening behavior, and the evolution of the hysteresis loops with increasing number of loading cycles. Fatigue life prediction of the single crystal copper was conducted based upon the stress-strain response obtained from the cyclic plasticity model. The fatigue criterion takes into account the plastic strain localization within a single crystal. The critical plane (cracking plane) was identified as the material plane where the fatigue damage accumulation first reached a critical value. For copper single crystals with the crystal orientations being within the standard crystallographic triangle, the fatigue criterion can predict both fatigue life and cracking direction consistent with the experimental observations. More importantly, the constants used in the fatigue criterion were found to be identical to those used for the pure polycrystalline copper with different grain sizes and texture.     

FATIGUE CRACKING POSSIBILITY ALONG GRAIN BOUNDARIES AND PERSISTENT SLIP BANDS IN COPPER BICRYSTALS

In this paper, the fatigue cracking possibility in different kinds of copper bicrystals with large-angle grain boundaries (GBs) and copper multicrystals containing some low-angle GBs are compared. The results showed that the fatigue cracks, in the copper bicrystals, always nucleated firstly along GBs no matter whether the GBs are perpendicular or parallel to the stress axis. Whereas, for the copper multicrystals containing low-angle GBs, the persistent slip bands (PSBs) are always the preferential sites to initiate fatigue cracks no matter whether low-angle GBs are perpendicular or parallel to the stress axis.
Additionally, the fatigue lives of the GBs, and the [1¯23] and [3¯35] grains in the [1¯23] ⊥ [3¯35] and [5¯913] ⊥ [5¯79] bicrystals were measured at different cyclic stresses and strain amplitudes. The results show that intergranular fracture always occurred prior to transgranular fracture in those bicrystals. The fatigue lives increased in the order of the GB, the [1¯23] and the [3¯35] grains in the [1¯23] ⊥ [3¯35] bicrystal under cyclic tension–tension loading. On the other hand, the fatigue life of the GB in the [5¯913] ⊥ [5¯79] bicrystal is about two to three times higher than that in the [1¯23] ⊥ [3¯35] bicrystal. Based on these experimental results from the copper bicrystals and multicrystals, it is indicated that the possibility of fatigue cracking increased in the order of low-angle GBs, PSBs and large-angle GBs. It is suggested that both the PSB–GB mechanism and the step mechanism required for GB fatigue cracking were questionable, and the interaction modes of PSBs with GBs may be more important for intergranular fatigue cracking.     

Twin boundary: Controllable interface to fatigue cracking

Twin boundaries(TBs) are key factors influencing the mechanical properties of crystalline materials. We have investigated the intrinsic fatigue cracking mechanisms of TBs during the past decade. The effects of TB orientations on the fatigue cracking mechanisms were revealed via cyclic deformation of a series of grown Cu bicrystals with a sole TB. Furthermore, the combined effects of crystallographic orientation and stacking fault energy(SFE) on the fatigue cracking mechanisms were clarified through cyclic deformation of polycrystalline Cu and Cu alloys. Both developments were reviewed in this report which will provide implications to optimize the interfacial design for the improvement of fatigue performance of metallic materials.     

The development of grain-orientation-dependent residual stressess in a cyclically deformed alloy

There have been numerous efforts to understand and control the resistance of materials to fracture by repeated or cyclic stresses. The micromechanical behaviours, particularly the distributions of stresses on the scale of grain size during or after mechanical or electrical fatigue, are crucial to a full understanding of the damage mechanisms in these materials. Whether a large microstress develops during cyclic deformation with a small amount of monotonic strain but a large amount of accumulated strain remains an open question. Here, we report a neutron diffraction investigation of the development of intergranular stresses, which vary as a function of grain orientations, in 316 stainless steel during high-cycle fatigue. We found that a large intergranular stress developed before cracks started to appear. With further increase of fatigue cycles, the intergranular stress decreased, while the elastic intragranular stored energy continued to grow. One implication of our findings is that the ratio between the intergranular and intragranular stored energies during various stages of fatigue deformation may validate the damage mechanism and can be used as a fingerprint for monitoring the state of fatigue damage in materials.     

铜单晶体循环应力应变曲线的平台行为的取向效应

系统讨论和总结了单滑移,双滑移和多滑移取向铜单昌体循环形变中呈现的不同平台行为。分析结果表明,晶体取强烈影响双滑移和多滑移铜晶体的循环变行为,平台区的出现与否及平台应力的高低,不仅与闰错反应模式和强度有关。     

Surface roughness evolution under constant amplitude fatigue loading using crystal plasticity

Crystallographic plasticity has been applied to study the initiation of microcracks on the smooth surface of polycrystals under a uniform applied stress. Even under a uniform external stress, due to the different crystallographic orientations of the grains in the polycrystals, there is non-uniform stress distribution and the deformation is also not uniform. Under the fatigue loading, the roughness increases with the number of fatigue cycles, and deformation will localize in some places, where microcracks form.     

铜单晶体在循环形变中形成的形变带

系统研究了循环形变铜单昌体中宏观形变带的产生规律和特征及相应的位错结构,并对其形成机制进行了综合探讨。结果表明,在不同取向铜单昌体的循环形变中,形变带ＤＢＩ近似沿主滑移面发展。而ＤＢⅡ的惯习面接近传统的扭折面｛１０１｝,两者成严格的正交分布。     

晶体取向对铜单晶体循环硬化行为的影响

研究了不同取向铜单晶体的循环硬化行为.结果表明,晶体取向对双滑移和多滑移取向铜单晶体的循环硬化行为有强烈的影响.不同取向铜单晶体的初始循环硬化率θ0.2与晶体中的位错反应模式、强度以及交滑移机会密切相关.临界双滑移晶体在循环硬化初始阶段呈现出独特的应变突发行为.     

Half-cycle slip activity of persistent slip bands at different stages of fatigue life of polycrystalline nickel

The slip activity of persistent slip bands (PSBs) in polycrystalline nickel was studied using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The half-cycle slip activity as well as the local shear strain amplitudes was investigated after half-cycle deformation at different numbers of cycles in the domain of stress saturation. Moreover, the fraction of grains containing cumulated PSBs and the accumulated volume fraction of PSBs was estimated depending on the number of cycles during fatigue life. The volume fraction of active PSBs during half-cycle deformation is significantly lower than the cumulated PSB volume and decreases with increasing number of cycles. Additionally, an increasing localization of cyclic plastic strain within the PSBs was observed. However, with increasing number of cycles the average local shear strain amplitude remains almost unchanged. Thus, PSBs in polycrystals are subjected to a life history which is characterized by active and inactive periods of their half-cycle slip activity during cyclic deformation at different stages of the saturation state.     

驻留滑移带与晶界和孪晶界的交互作用

对含有退火孪晶的多晶铜进行了不同塑性应变幅下的应变疲劳实验,利用扫描电镜及其电子通道衬度技术（SEM-ECC）观察了表面滑移形貌、疲劳裂纹和位错组态,研究了驻留滑移带与晶界和孪晶界的交互作用．结果表明,在晶界附近和远离晶界处观察到位错组态分布的不均匀现象．这种不均匀性导致多晶铜中疲劳裂纹首先沿着普通大角晶界开裂,在孪晶界处由于应变相容性较好而难以产生疲劳裂纹．     

CYCLIC DEFORMATION OF A1-4%Cu ALLOY POLYCRYSTALS CONTAINING θ" PRECIPITATES

The cyclic deformation of polycrystalline A1-4%Cu alloy containing θ precipitates was investigated by strain controlled tests, and compared to monocrystalline cyclic behavior. The cyclic deformation of the polycrystals was found to depend on the grain size, and in coarse-grained material (grain diameter = 1 mm) a definite plateau was observed in the cyclic stress-strain (CSS) curve. In order to explore the relationship of cyclic behavior between single crystals and polycrystals, three available orientation factors were examined. This relationship can be interpreted by selection from the different types of orientation factors (Taylor factor, Sachs factor and Maximum Schmid factor), which operate to different degrees depending on the magnitude of the strain amplitude and the grain size.     

FATIGUE DAMAGE IN AUSTENITIC-FERRITIC DUPLEX STAINLESS STEELS

Fatigue damage in two austenitic-ferritic duplex stainless steels, with the structure of a natural composite and different levels of nitrogen content, was studied in low-cycle fatigue. Both steels show initial cyclic hardening followed by softening and a long stabilisation period. The cyclic stress-strain curve increases with the nitrogen content while Manson-Coffin curves of both steels intersect at medium fatigue lives. The study of the surface relief reveals intensive slip markings both in ferrite and in austenite. Their density is influenced by the nitrogen content. Both the intensity and density of the persistent slip band (PSB) markings are higher in the ferrite. Crack initiation was found to appear predominantly in PSBs in the ferritic grains at the low strain amplitudes, and in the ferritic and austenitic grains at the highest strain amplitudes. The level of the cyclic stress-strain response and the fatigue lives are discussed in terms of the cyclic strain localisation and of the effect of texture and nitrogen content on the strength and fatigue damage. The increased strength of the austenitic phase, due to high nitrogen alloying, results in cyclic slip localisation in the ferrite, and the decrease of fatigue life, compared with the steel with the lower nitrogen content.     

一个特殊单滑移取向铜单晶疲劳位错结构研究

为了更细致地揭示面心立方金属单晶体的循环变形机制,利用扫描电镜电子通道衬度(SEM-ECC)技术观察研究了Schmid因子为0.5的[41841]单滑移取向铜单晶体的循环饱和位错结构.实验表明,在单滑移铜单晶体中,胞结构除了在高应变幅下的循环变形中出现外,还可能出现在循环应力-应变(CSS)曲线平台区的较低塑性应变幅下.驻留滑移带(PSBs)会随应变幅的增大而在试样表面聚集成内部含有位错胞的粗滑移带,带内的位错胞结构被认为是由于带内滑移阻力增大引起的应变集中所致形成的.此外,CSS曲线高应变幅区起始部分对应的循环饱和位错结构观察揭示出迷宫结构和胞结构是由PSBs逐渐演变而成的.     

Simulation of deformation and lifetime behavior of a fcc single crystal superalloy at high temperature under low-cycle fatigue loading

This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.     

Cyclic fatigue of hot isostatically pressed silicon nitride at elevated temperatures

Cyclic fatigue properties of a hot isostatically pressed silicon nitride were investigated at 1150, 1260 and 1370 °C in ambient air. The uniaxial tensile tests were conducted under various cyclic loading wave forms and frequencies. The correlation of stress-life relations between cyclic and static fatigue results was evaluated. At 1150–1370 °C, cyclic loading caused less damage than static loading, as evidenced by the longer failure time under cyclic loading versus static loading with the same maximum applied stresses. The cyclic loading effect was more pronounced in high frequency tests at 1260 and 1370 °C and might be related to the viscoelastic behaviour of the intergranular phase. Microstructural analyses and macroscopic cyclic stress-strain and strain-time relations indicated that cyclic loading/unloading may inhibit the normal accumulation of creep damage.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

Fatigue limit and crack growth in ultra-fine grain metals produced by severe plastic deformation

The experimental results on fatigue resistance of ultra-fine grain metals produced by severe plastic deformation (SPD) are reviewed with regard to two major characteristics of cyclic damage initiation and failure—fatigue limit and fatigue crack growth rate. The fatigue limit benefits considerably from grain refinement down to submicrocrystalline scale. Factors affecting the fatigue limit are discussed in the light of SPD-processing and resultant ultra-fine grain structure. Contrasting with the fatigue limit, the fatigue crack growth threshold deteriorates after SPD in comparison to that of ordinary polycrystals. Possible mechanisms of fatigue crack initiation and propagation are discussed and the guidelines for manufacturing are provided towards enhancement and optimization of fatigue performance.     

Fatigue crack growth behaviour of A533B steel in pressurized water at 288 and 28 °C

Fatigue crack growth behaviour of A533B steel was investigated in pressurized water at 288 °C using specimens machined from four different orientations. When inclusions were oriented along the direction of crack propagation, fatigue crack growth rate (FCGR) was enhanced compared to when they were perpendicular to the direction of crack propagation. At low ΔK levels FCGR in ambient water was slightly higher than that in 288 °C water. This may be attributed to the occurrence of intergranular cracking in ambient water tested specimen. Though mainly ductile striations were observed on the fracture surfaces, isolated intergranular facets (in a specimen tested in ambient water) and fan shaped features were also present. Hydrogen induced damage was clearly evident in the ambient water tested specimen in the form of isolated intergranular facets.     

Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals

This work reviews and critically discusses the current understanding of two scaling laws, which are ubiquitous in the modeling of monotonic plastic deformation in face-centered cubic metals. A compilation of the available data allows extending the domain of application of these scaling laws to cyclic deformation. The strengthening relation tells that the flow stress is proportional to the square root of the average dislocation density, whereas the similitude relation assumes that the flow stress is inversely proportional to the characteristic wavelength of dislocation patterns. The strengthening relation arises from short-range reactions of non-coplanar segments and applies all through the first three stages of the monotonic stress vs. strain curves. The value of the proportionality coefficient is calculated and simulated in good agreement with the bulk of experimental measurements published since the beginning of the 1960s. The physical origin of what is called similitude is not understood and the related coefficient is not predictable. Its value is determined from a review of the experimental literature. The generalization of these scaling laws to cyclic deformation is carried out on the base of a large collection of experimental results on single and polycrystals of various materials and on different microstructures. Surprisingly, for persistent slip bands (PSBs), both the strengthening and similitude coefficients appear to be more than two times smaller than the corresponding monotonic values, whereas their ratio is the same as in monotonic deformation. The similitude relation is also checked in cell structures and in labyrinth structures. Under low cyclic stresses, the strengthening coefficient is found even lower than in PSBs. A tentative explanation is proposed for the differences observed between cyclic and monotonic deformation. Finally, the influence of cross-slip on the temperature dependence of the saturation stress of PSBs is discussed in some detail. This works takes into account current discussions on the microstructural aspects of cyclic deformation and highlights further work that is required for fully understanding the physical origin of the two scaling laws.