FATIGUE CRACK GROWTH BEHAVIOUR OF SM45C STEEL UNDER CYCLIC MODE I WITH SUPERIMPOSED STATIC MODE II LOADINGS

Abstract— The practical applications of studies related to constant amplitude mode I loading are somewhat limited, since mode I crack growth is often influenced by mode II (sliding mode) or mode III (tearing mode) in industrial situations. For these cases, criteria, rules, and laws have to be worked out and verified by experiments. However, it is very difficult to evaluate mixed-mode fatigue cracking due to crack surface interference, crack closure, crack branching, etc. This paper, which defines the length of a branched crack as an effective slant crack with a length equal to the distance between the two crack tips, explains the influences of crack surface interference by introducing concepts of adhesive wear and scrutinizes some related researches on mixed-mode crack growth behaviour. Additionally an effective stress intensity factor range is described which considers crack closure and crack surface interference and is verified with crack growth tests under mode I fatigue loading and cyclic mode I with a superimposed static mode II loading.     

Fatigue damage in nickel and copper single crystals at nanoscale

Nanoscale fatigue damage simulations using molecular dynamics were performed in nickel and copper single crystals. Cyclic stress–strain curves and fatigue crack growth were investigated using a middle-tension (MT) specimen with the lateral sides allowing periodic boundary conditions to simulate a small region of material as a part of a larger component. The specimen dimensions were in the range of nanometers, and the fatigue loading was strain controlled under constant and variable amplitude. Four crystal orientations, [111], [100], [110] and [101] were analyzed, and the results indicated that the plastic deformation and fatigue crack growth rates vary widely from one orientation to another. Under increasing strain amplitude loading, nickel nanocrystals experienced a large amount of plastic deformation causing at least in one orientation, [101], out-of-plane crack deviation in a mixed mode I+ II growth. Under constant amplitude loading, the fatigue cracks were a planar mode I type. Double slip is observed for some orientations, while for others, many more slip systems were activated causing a more evenly distributed plastic region around the crack tip. A comparative analysis revealed that small cracks grow more rapidly in copper than in nickel single crystals.     

DD6单晶高温合金振动疲劳性能及断裂机理

研究[001]取向的DD6单晶高温合金的室温振动疲劳S-N曲线,并获得了其室温振动疲劳极限。利用体视显微镜、扫描电子显微镜、背散射衍射等手段对DD6单晶高温合金振动疲劳断裂机制进行分析。结果表明:采用S-N法估算得到的[001]取向的DD6单晶高温合金室温振动疲劳极限约为337.5MPa。振动疲劳裂纹断口呈现单个或多个沿{111}晶体学扩展平面组成的形貌特征,断口上分为疲劳源区和疲劳扩展区两个阶段,裂纹在应力最大截面处的表面或内部缺陷处萌生,呈单源特征,疲劳扩展区呈现类解理断裂特征,未出现典型的疲劳条带特征。说明沿{111}晶面滑移是DD6单晶高温合金室温振动疲劳断裂的主要变形机制,断口上的类解理扩展平面以及微观上类解理花样是DD6单晶高温合金室温振动疲劳断裂的主要特征。     

Fracture toughness of polycrystalline tungsten under mode I and mixed mode I/II loading

The fracture toughness of swaged polycrystalline tungsten was tested parallel and perpendicular to the swaging direction and under mixed mode I/mode II loading. The fracture mode is dominated by the microstructure and changed from all-transgranular cleavage in mode I to almost all-intergranular fracture in mode II. The mixed mode results can be related to two common failure criteria, the maximum tensile stress criterion (Maximum σ) and the maximum energy release rate criterion (Maximum G), but the large scatter in the data prohibits a clear distinction between the two criteria. Tests at 77 K show that the polycrystal is significantly tougher than the single crystal at this temperature. This is a consequence of the deflection of the crack into the grain boundaries and the imperfect texture (as compared to a single crystal) of the polycrystalline material.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

Three-dimensional mixed mode I+II+III singular stress field at the front of a {\varvec{(}}\mathbf{111 }{\varvec{)}[}\bar{\mathbf{1 }}\bar{\mathbf{1 }}\mathbf 2 {\varvec{]}\times [}\mathbf 1 \bar{\mathbf{1 }}\mathbf 0 {\varvec{]}} crack weakening a diamond cubic mono-crystalline plate with crack turning and step/ridge formation

A heretofore-unavailable mixed Frobenius type series, in terms of affine-transformed x-y coordinate variables of the Eshelby–Stroh type, is introduced to develop a new eigenfunction expansion technique. This is used, in conjunction with separation of the z-variable, to derive three-dimensional mixed-mode I+II+III asymptotic displacement and stress fields in the vicinity of the front of a semi-infinite through-thickness $(111)[\bar{{1}}\bar{{1}}2]\times [1\bar{{1}}0]$ crack weakening an infinite diamond cubic mono-crystalline plate. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the diamond cubic mono-crystalline plate are exactly satisfied. Explicit expressions for the mixed mode I+II+III singular stresses in the vicinity of the front of the through-thickness crack, are presented. Most important mixed modes I+II+III response is elicited even though the far-field loading is only mode I or II or III or any combination thereof. Finally, atomistic modeling of cracks requires consideration of both the long range elastic interactions and the short range physico-chemical reactions, such as bond breaking. The Griffith-Irwin approach does not take the latter into account, and nano-structural details such as bond orientation must be accounted for. A new mixed-mode I+II+III crack deflection criterion elucidates the formation of steps and/or triangular ridges on the crack path. The planes of a multiply deflected crack are normal to the directions of broken bonds. Additionally, the mixed-mode (I+II+III) crack deflection and ridge formation are found to be strongly correlated with the elastic stiffness constants, ${c}^{\prime }_{14}$ and ${c}^{\prime }_{56}$ , of the diamond cubic single crystal concerned.     

复合型裂纹起裂角厚度效应的实验研究

完成了飞机结构铝合金LC4CS的2、4、8和14mm四种不同厚度试样在I+II复合加载条件下的复合型断裂实验,系统分析了厚度和复合载荷对裂纹起裂角的影响,揭示了常用复合型断裂准则的厚度适用范围,用三维断裂理论对结果进行了讨论。结果表明:复合型裂纹起裂角具有明显的厚度效应;最大周向应力准则能够准确预测薄试样和厚试样(厚度为2 mm 和14 mm)在各种复合加载条件下的起裂方向,但是不适用于中间厚度的试样,尤其是8 mm厚度的情况。最大三轴应力准则试图考虑裂纹尖端三维约束对裂纹起裂的影响,但是结果并不理想。最小应变能密度因子理论的预测结果与最大周向应力准则的预测结果非常接近,但同样不能预测8mm厚度试样的起裂方向。非常有必要建立一个普遍适用的三维复合型断裂准则。     

THE SIGNIFICANCE OF MEAN STRESS ON THE FATIGUE CRACK GROWTH THRESHOLD FOR MIXED MODE I + II LOADING

Abstract— The effect of mean stress on near threshold fatigue crack growth behaviour under mixed mode I+II loading has been studied in a structural steel BS4360 50D in laboratory air at room temperature. It was found that the branch crack threshold decreased significantly as R ratio ( P _min/ P _max) increased from 0.1 to 0.7. A simple model is proposed to predict the branch crack threshold behaviour for R -ratio sensitive materials. Further investigation is required to model the mode II dominant situations where the branch crack thresholds tend to converge on a high value.     

Investigation of Mixed Mode I/II Brittle Fracture Using ASCB Specimen

Using the asymmetric semi-circular bend specimen (ASCB) with vertical crack, a series of mixed mode I/II fracture tests were performed on two different rigid polyurethanes materials. The experimental results obtained for brittle fracture are compared with the theoretical predictions based on MTS and SED criteria. The results demonstrate that the SED criterion gives better results for mode II loading conditions, while for mode I and predominantly mode I both criteria are accurate.     

Further examination of the criterion for crack initiation under mixed-mode I+III loading

Mixed-mode fracture presents spectacular, scale-independent, pattern formation in nature and engineering applications. The criteria for crack initiation and growth under such mixed mode loading, however, are not well established. This work is aimed at exploring the failure criteria and the pattern formation under combined modes I and III. Specific designs of specimens based on boundary element simulations are considered with the aim of examining crack path selection at nucleation, threshold behavior of crack front fragmentation and, spacing of fragmentation. Experimental investigations with these specially designed geometries show that there does not exist a threshold ratio of \(K_{III}^{\infty }/K_{I}^{\infty }\) below which a crack will propagate smoothly without fragmenting into facets. The crack front is shown to fragment immediately as soon as it is perturbed by a small amplitude mode III loading. The experimental results show further that spacing of the fragmentation is set not by any intrinsic length scale of the material, but by the characteristic dimension of the driving crack and the global loading.     

MIXED MODE (I + III) FATIGUE THRESHOLDS IN A FORGING STEEL

Abstract— The results of mixed mode (I + III) fatigue tests on a low pressure steam turbine rotor steel are presented. Tests were performed on a uniaxial servohydraulic fatigue machine fitted with a torsion-bending loading frame. The onset of failure was marked by fatigue facets which grew perpendicular to the maximum principal stress direction. A criterion for mixed mode (I + III) fatigue thresholds based on the orientation and the crack opening displacement of fatigue cracks is proposed.     

Study of Fatigue Behavior of Epoxy‐Carbon Composites under Mixed Mode I/II Loading

This paper presents an experimental assessment of the initiation and propagation of interlaminar cracks under mixed mode I/II dynamic fracture loading of a composite material with an MTM45‐1 epoxy matrix and unidirectional IM7 carbon‐fiber reinforcement. The aims of the experimental program developed for this purpose are to determine, on the one hand, the initiation curves of the fatigue delamination process, understood as the number of load cycles needed to generate a fatigue crack, and on the other, the crack growth rate (delamination rate) for different percentages of static Gc, in both cases for two mode mixities (0.2 and 0.4) and for a tensile ratio R = 0.1. All this with the goal of quantifying the influence of the degree of mode mixity on the overall behavior of the laminate under fatigue loading. The results show that the energy release rate increases with increasing loading levels for both degrees of mode mixity and that the fatigue limit is located around the same percentages. However, crack growth rate behavior differs from one degree of mode mixity to the other. This difference in the behavior of the material may be due to the varying influence of mode I loading on the delamination process.

     

A REVIEW OF FATIGUE CRACK GROWTH IN STEELS UNDER MIXED MODE I AND II LOADING

The majority of methods for predicting the direction of propagation of mixed mode cracks have assumed that they branch to grow as mode I cracks. However, under some circumstances mode II crack growth occurs. Rolling contact fatigue cracks are one example of an industrial problem where cracks appear to grow under predominantly mode II loading without branching. This paper reviews the available models and the experimental studies in the literature on mixed mode I and II loading, and discusses the parameters that affect the mode of crack growth.     

VECTOR CTD CRITERION APPLIED TO MIXED MODE FATIGUE CRACK GROWTH

Abstract— This work is aimed at developing a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behaviour, especially in the near threshold region. Being a mechanisms-related parameter, the vector crack tip displacement (CTD) is defined as a vector summation of CTOD and CTSD_c which act, respectively in the directions of mode I and mode II fatigue crack growth. The basic assumption is that both direction and rate of mixed mode fatigue crack growth are governed by the vector ΔCTD, which represents the resultant of the "driving force"at the crack tip. The analytical predictions obtained by using the vector ΔCTD are in good agreement with the reported experimental results of mixed mode I and II fatigue cracks.     

MIXED MODE SMALL CRACK GROWTH

Abstract— The fatigue crack growth behavior of small part-through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated. Experiments were performed on thin-wall tubular specimens loaded in tension, torsion and combined tension torsion. Crack sizes analyzed ranged from 20 μm to 1 mm and growth rates ranged from 10^-7 to 10^-4 mm/cycle for 1045 steel and from 10^-5 to 10^-2 mm/cycle for Inconel. Nucleation and the early growth of cracks occurs on planes of maximum shear strain amplitude for both of these materials even in tensile loading. An equivalent strain based intensity factor was employed to correlate the crack growth rate under mixed mode loading conditions In loading conditions other than torsion, a transition from mode II to mode I was observed for 1045 steel. Principal strains were used to analyze mode I cracks. Cracks in Inconel 718 grow in mode II for the majority of the fatigue life. The maximum shear strain amplitude and the tensile strain normal to the maximum shear strain amplitude plane were used to calculate the strain based intensity factor for mixed mode loading.     

ANALYSIS OF CRACK TIP HYDROGEN DISTRIBUTION UNDER I/II MIXED MODE LOADS

Abstract— The distribution of hydrogen in the vicinity of a crack tip was studied using SIMS (Secondary Ion Mass Spectrometry) under different ratios of I/II mixed mode loads. Modified WOL specimens with kinked slits were employed in the course of the experimental work. Spectrographic measurements show that under I/II mixed mode loading, both in the HIC and in the r ^max_p directions, there are two hydrogen accumulation peaks ahead of the crack tip, corresponding to the location of the maximum hydrostatic stress and maximum equivalent plastic strain, respectively. Based on results obtained over a range of loading conditions from mode I to a high K_II/ K_I, ratio, it is shown that the mode II component has a clear influence on both peaks. The conditions for hydrogen redistribution are discussed in terms of crack tip stress-strain fields.     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

CRACK PROPAGATION UNDER MIXED MODE (I + III) LOADING

Abstract— In this paper are presented the results of fatigue crack propagation tests on angled-slit, three point bend mixed-mode (I + III) specimens manufactured from a low pressure steam turbine rotor forging. The path of crack propagation has been studied for two mixed mode (I + III) loading conditions. It has been observed that crack growth occurs by a mode I mechanism and a model has been developed to correlate crack growth rates in mixed mode (I + III) specimens with data from pure mode I fatigue tests.     

Fatigue striation formation in an Fe–3%Si alloy—effects of crystallographic orientation and neighbouring grains

In order to know the criterion of fatigue striation formation, fatigue fracture surfaces and crack paths were investigated in Fe–3%Si single and bicrystals having various crystallographic orientations. On single crystals, striations were formed when the loading direction was close to a 〈110〉 direction. In this direction, the crack grew perpendicular to the loading direction. When the loading direction was near a 〈111〉 direction and the crack grew along an inclined plane, no striations were observed. Even in this orientation, when the crack grew perpendicular by necessity using bicrystals, striations were observed. This suggests that striations are not formed on a special crystallographic plane, but are formed when the fatigue crack plane is perpendicular to the loading direction regardless of crystallographic orientation.     

Mixed mode I/II fracture of 2024-T3 friction stir welds

For the first time, a series of mixed mode I/II fracture experiments have been performed on both base material and three families of friction stir welds (FSWs) in 6.4 mm thick, 2024-T351 aluminum plate; the FSW joints are designated hot, medium and cold due to the level of nominal weld energy input per unit weld length (specific weld energy) during the joining process.Results from the fracture tests indicate that the measured critical crack opening displacement (COD) at a fixed distance behind the crack tip properly correlates both load-crack extension response and microstructural fracture surface features for both the base metal and all FSWs, providing measure of a quantitative fracture toughness. The COD values also indicate that transition from mode I to mode II dominant crack growth occurs at lower loading angles for FSW joints having higher specific weld energy input, with a truly mixed mode I/II COD measured during crack growth in the medium FSW joint. Using results from recent detailed FSW metallographic studies, specific features in the fracture process are correlated to the FSW microstructure. Finally, the observed ductile crack growth path in all three welds tends to exit the under-matched FSW weld region as the far-field applied shear loading is increased, with the medium FSW being the only case where the flaw remained within the FSW region for all combinations of shear and tensile loading.