A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

Growth of short cracks during low and high cycle fatigue in a duplex stainless steel

Damage evolution during low- and high-cycle fatigue in an embrittled duplex stainless steel is characterized in this paper. Moreover, scanning electron microscopy observations (SEM) in combination with electron backscattered diffraction (EBSD) measurements and transmission electron microscopy (TEM) were employed in order to analyze microcracks formation and propagation. During low-cycle fatigue, microcracks initiate the ferrite phase either along slip planes with the highest Schmid factor (SF) inside the grains or at the α/α grain boundary. Then, microcracks propagation take place in ferrite or austenite grains with the highest SF. An analysis of the dislocation structure in the near-surface and in ferritic grains in the bulk of the specimen has shown that dislocation microbands are associated with microcrack initiation.In the high-cycle fatigue regime, damage generally initiates in the austenite by slip band formation followed by crack initiation either at an α–α boundary or at an α–γ boundary in the intersection of slip bands in the austenite. The microstructure in the austenite consists of a low density of dislocation pile-ups while the ferrite is practically inactive or develops only micro-yielding at boundaries.Despite the differences in both fatigue regimes, phase boundaries are an effective barrier against crack propagation because they delay the advance of the crack tip.     

AFM evidence of surface relief formation and models of fatigue crack nucleation

Atomic force microscopy and high resolution scanning electron microscopy were used to find the true surface relief corresponding to persistent slip markings emerging from persistent slip bands on fatigued polycrystalline austenitic and ferritic stainless steels. The persistent slip markings are formed by extrusions and intrusions. The shape of extrusions and intrusions was documented and the kinetics of the extrusion growth was studied in both steels. The experimental data were discussed and compared with the predictions of the recent models of fatigue crack nucleation.     

The effects of texture and grain morphology on the fracture toughness and fatigue crack growth resistance of nanocrystalline platinum films

The fracture toughness and fatigue crack growth resistance of nanocrystalline materials are significantly affected by the thickness of the specimen. In this work we relate the mechanical properties of nanocrystalline platinum films to their texture and grain morphology. Tensile, creep and fatigue testing of annealed, ∼1 μm films resulted in mechanical properties similar to the as-received films (yield strength of ∼1.2 GPa, fracture toughness ∼17.8 MPa √m, and a fatigue crack growth power law exponent of ∼4.2). However, the breakdown of the initially columnar grain morphology had a marked effect on the transition point from an intergranular to transgranular fatigue cracking mode. Finite element modeling suggests that cyclic (fatigue) grain coarsening and the transition from inter- to transgranular cracking modes are a result of the relative importance of dislocation slip accommodation on in-plane and through-thickness oriented slip directions.     

Experimental and FEM study of thermal cycling induced microcracking in carbon/epoxy triaxial braided composites

The microcrack distribution and mass change in T700s/PR520 and T700s/3502 carbon/epoxy braided composites exposed to thermal cycling was evaluated experimentally. Acoustic emission was utilized to record the crack initiation and propagation under cyclic thermal loading between −55 °C and 120 °C. Transverse microcrack morphology was investigated using X-ray computed tomography. The differing performance of two kinds of composites was discovered and analyzed. Based on the observations of microcrack formation, a meso-mechanical finite element model was developed to obtain the resultant mechanical properties. The simulation results exhibited a decrease in strength and stiffness with increasing crack density. Strength and stiffness reduction versus crack densities in different orientations were compared. The changes of global mechanical behavior in both axial and transverse loading conditions were studied. By accounting for the obtained reduction of mechanical properties, a macro-mechanical finite element model was utilized to investigate the influence of microcracking on the high-speed impact behavior.     

The influence of microstructure on fatigue crack propagation in polyoxymethylene

An analysis of the influence of crystalline microstructure on fatigue crack propagation in poly-oxymethylene is presented. A series of test specimens containing a variety of diverse micro-structures was prepared through controlled thermal treatments of plaques from four different lots of polyoxymethylene. Extensive characterization of the crystalline microstructure was carried out in order to permit a direct comparison between the fatigue behaviour and crystalline microstructure. The degree of crystallinity and tie molecule density were both found to have a significant affect on fatigue crack propagation rate while average spherulite size did not appear to influence fatigue behaviour. Additionally, the fatigue fracture surfaces of many of the test specimens were examined. Three distinct surface topographies were observed and found to correlate with different stages of crack growth. In the region near the end of fatigue crack propagation, closely spaced surface markings that resemble fatigue striations were observed.     

Cyclic deformation and lifetime of Alloy 617B during isothermal low cycle fatigue

Isothermal low cycle fatigue tests are carried out on the nickel-base Alloy 617B in the solution-annealed, stabilized and long-term aged conditions at temperatures between room temperature and 900 °C. In addition, fatigue microcrack growth is measured using the replica technique. Transmission electron microscopy studies suggest that the observed differences in cyclic hardening between the different heat treatments result from the precipitation of fine carbides. Scanning electron microscope observations indicate a change in fracture mode for the solution-annealed and long-term aged material with temperature. The Chaboche model is able to describe the time and temperature dependent cyclic plasticity of the three material conditions. The measured lifetimes and crack growth rates can be described using a fracture mechanics based lifetime model. However, the data for room temperature and for temperatures above 400 °C fall into two different scatter bands due to differences in crack growth rates.     

Initiation and propagation of fatigue cracks in cast IN 713LC superalloy

Fatigue life, initiation and propagation of cracks at 800 °C in a cast Ni-base superalloy IN 713LC were experimentally studied in high-cycle fatigue region. Load symmetrical cycling and cycling with high tensile mean load were applied. Both crystallographic crack initiation resulting in long Stage I crack growth and non-crystallographic Stage II propagation were observed. High scatter of fatigue life data was explained by: (i) variability in microstructural conditions for crystallographic crack initiation and propagation and by (ii) influence of casting defect size distribution. The fractographic observation supports the slip band decohesion mechanism of crack initiation and an important role of cyclic slip localization in persistent slip bands.     

金属陶瓷热冲击疲劳裂纹形成机制

研究了金属陶瓷热冲击疲劳特性, 重点探讨了裂纹的形成机制。试验结果表明, 随着循环温度的增高, 裂纹形核孕育期缩短, 裂纹扩展速率增大; 随着金属陶瓷中金属相含量的增加, 裂纹扩展速率降低。热冲击疲劳裂纹的形成与微孔洞的形核、长大和连通有关。研究还发现, 金属陶瓷热冲击疲劳断口中存在疲劳条纹。      

Computer simulation of fatigue crack initiation

Results of a Monte Carlo simulation of the initiation stage of fatigue failure of aluminum alloys are described. Initiation processes simulated are: (1) nucleation of cracks at particles at or near the alloy surface; (2) early growth of microcracks with lengths on the order of the grain size; and (3) microcrack coalescence. Analytic models which describe nucleation and microcrack growth form the basis of the simulation, and relate the fatigue failure processes to the alloy microstructure. Two types of simulation outputs are obtained: (1) predictions of microscopic cracking parameters such as crack density, length and closure stress; (2) predictions of the mean and scatter in alloy fatigue lifetimes. Examples of both types of predictions are shown for selected aluminum alloys, and are compared to experimentally determined values.     

Initiation and short crack growth in austenitic–ferritic duplex steel‐effect of positive mean stress

The effect of the mean stress on the crack initiation and short crack growth of austenitic–ferritic duplex steel has been studied. High mean stresses and stress amplitudes result in appreciable mean strain relaxation and long‐term hardening. Mean stress produces unidirectional slip bands and slip steps that serve as nuclei for persistent slip bands and persistent slip markings. It leads to the acceleration of the crack initiation and production of a high density of cracks. Crack linkage contributes to the growth of short cracks. The concept of equivalent crack was used to describe the crack growth. The kinetics of short crack growth with positive mean stress is similar to that in symmetric loading, that is, exponential growth is observed. Positive mean stress results in earlier crack initiation and in the acceleration of the crack growth rate. Both factors contribute to the decrease of the fatigue life.     

Damage mechanisms of fatigue fracture in a metastable beta Ti-15-3 alloy

The mechanism of crack tip deformation in metastable beta Ti-15-3 alloy under fatigue loading has been examined. In spite of the small thickness of the test specimens (1 mm), the plastic zone revealed plane strain conditions which was transformed to a plane stress zone when its size became 0.25 of the crack length. Slip processes whose density increased with crack length were the dominant microscopic feature of crack tip plasticity. Microcracks emanating from the main crack appeared as a result of extensive slip damage. Transmission electron microscopy (TEM) and X-ray evidence indicate the absence of twinning or phase transformation and that dislocation processes constitute the microstructural origin of crack propagation resistance in the alloy. Energy calculations show that the specific energy of slip, 20 MJ m⁻³, exceeds that of microcracking by three orders of magnitude.     

A MICRO-MECHANICS ANALYSIS FOR SHORT FATIGUE CRACK GROWTH

Crack initiation and early growth of fatigue cracks in a fully annealed 0.4% carbon steel was investigated using plastic replicas and torsion loading. In a structure consisting of a 70/30 mixture of pearlite and ferrite the cracks are seen to develop and grow initially along slip bands in the ferrite phase. Energetic considerations lead to the formulation of a model which, while characterizing short crack growth rate, also considers those microstructural variables relevant to fatigue crack initiation and early crack growth. The driving force for crack growth is provided by the energy of the slip band; correspondingly crack growth per cycle is proportional to the strength of the slip band. In the short fatigue crack region, cracks grow initially at a fast rate but deceleration occurs quickly and, depending on the stress level, they either arrest or are temporarily halted at a critical length. This critical length is shown to coincide with the value of the threshold length for crack growth under LEFM conditions.     

A stored energy criterion for fatigue crack nucleation in polycrystals

A series of microstructurally-differing, large-grained, notched, polycrystal BCC ferritic steel bend test samples have been analysed to extract the experimentally observed sites of fatigue crack nucleation together with the numbers of cycles to cause crack nucleation. The samples have been modelled with explicit representation of both grain morphologies and crystallographic orientations using crystal plasticity which has enabled a detailed assessment to be made of key microstructure-level quantities such as accumulated slip, slip rate, and densities of both statistically stored and geometrically necessary dislocations local to the experimentally observed sites of crack nucleation. These quantities when considered independently have not been found to correlate with experimentally observed cycles to nucleation.A new criterion for fatigue crack nucleation has been introduced in which a critical stored energy density, G_c, is argued to be necessary in order for crack nucleation. The rate of stored energy density determined at the sites of crack nucleation has been shown to correlate well with experimental measurement of cycles to nucleation, and the number of cycles to cause fatigue crack nucleation, for the samples for which such measurements are available, is well predicted. The criterion enables prediction of cycles to crack nucleation for all of the experimental samples and has been shown to demarcate correctly the crack nucleation lives observed over the range of differing experimental microstructures.     

A mathematical equation relating low cycle fatigue data to fatigue crack propagation rates

A mathematical equation is derived to predict fatigue crack growth rates on the basis of a J integral analysis from the fatigue fracture behaviour of low cycle fatigue samples. According to this equation, the fatigue crack propagation curves can be predicted if low cycle fatigue data and an initial microcrack size are available. The results obtained from this study show that the predicted fatigue crack propagation rates for Ti-24V, Ti-6Al-4V and Al-6Zn-2Mg alloys are very close to experimental values.     

Microstructural influence on small fatigue cracks in a ferritic–martensitic steel

Microstructure effects on fatigue crack initiation and propagation in ferritic–martensitic dual phase steel were investigated. Slip bands were formed in ferrite grains after several thousand cycles with ensuing crack initiation due to dislocation pile-up. Subsurface observations using a focused ion beam (FIB) and crystallographic analyses using electron backscatter diffraction (EBSD) measurements showed that crack initiation occurred as a result of the activation of a slip system having a high Schmid factor. Surface crack nucleation occurred quite frequently at ferrite/martensite and ferrite/ferrite boundaries, with crack propagation in the ferrite grains. This initiation mode can be attributed to the mismatch stresses at ferrite/martensite phase boundaries and at high angle grain boundaries.     

Fatigue crack growth behavior of X2095 Al–Li alloy

Microstructures and micro-textures of X2095 Al–Li alloy in as-received/superplastic state were characterized by means of SEM/BDS, X-ray diffraction and orientation imaging microscopy (OIM). It was observed that the microstructure of the alloy was typical of a particulate-reinforced composite material, consisting of aluminum matrix and homogeneously distributed T_B(Al₇Cu₄Li) particles with a volume fraction of about 10%. Brass-type texture was the dominant texture component. Both constant amplitude and near-threshold fatigue crack growth rates of the alloy in the L–T and T–L orientations were determined at different stress ratios. Particular attention was paid to the role of the T_B phase in the fatigue crack growth. When a fatigue crack approached a T_B particle, the crack basically meandered to avoid the particle. The T_B particles thus provided a strong resistance to the propagation of fatigue crack by promoting crack deflection and the related crack closure effects. The fatigue crack propagation behavior has been explained by the microstructural features, micro-textures, cracking characteristics and crack closure effects.     

Statistical description of the effect of Zr addition on the behavior of microcracks in Cu–6Ni–2Mn–2Sn–2Al Alloy

As possible substitutes for high-strength Cu–Be alloys, Cu–6Ni–2Mn–2Sn–2Al alloys have been developed. To clarify the physical background of the effect of trace Zr on the fatigue strength of such alloys, the initiation and propagation behavior of a major crack that led to the fracture of the tested specimens was monitored. When the stress amplitude was less than σ _a = 350 MPa, the fatigue life of the alloys with Zr was about 2–2.5 times larger than that of the alloy without Zr. When σ _a > 350 MPa, the effect of Zr addition on the fatigue life dramatically decreases as the stress amplitude increases. The increased fatigue life due to Zr addition resulted from an enhancement of the crack initiation life and microcrack growth life. The enhanced crack initiation life was mainly attributed to the strengthening of grain boundaries due to the precipitation of SnZr compounds. A statistical analysis of the behavior of multiple cracks was made to quantitatively evaluate the scatter in fatigue behavior. The statistical analysis supported the conclusions obtained from the behavior of a major crack.     

Fatigue crack propagation in aluminum nitride ceramics under cyclic compression

Room temperature fatigue crack growth characteristics under cyclic compressive loads were investigated in pure and 3 wt % yttria doped hot pressed aluminum nitride ceramics. A single edge-notch specimen geometry was used to induce a stable Mode I fatigue crack under cyclic compressive loads. The fatigue crack growth occurred in three stages, where the first stage is dominated by microcrack nucleation, coalescence and slow growth within the notch root. During the second stage, the crack growth is accelerated and finally, the crack growth deceleration and arrest occurred in third stage. The fatigue crack growth occurred predominantly by intergranular fracture. Insights gained from the experimental results and microscopic observations are discussed.