Authors: Isao Ishimoto, Masahiro Endo

Abstract: A unified method is presented for the prediction of the fatigue strength of steel components containing small holes and being subjected to combined loading. Materials investigated were an annealed 0.37% carbon steel and a quenched and tempered Cr-Mo steel. Combined axial and torsional fatigue loading tests were carried out using specimens containing a small hole, which was introduced into the surface by drilling. The diameter of holes equaled the depth and was either 100µm
or 500µm. The non-propagating cracks emanating in the radial direction from the holes were observed at the fatigue limit. When the loading condition is the same, they were on a plane that inclined at the same angle with respect to the specimen axis, regardless of the size of holes. This result suggested that the fatigue strength would be controlled by the Mode I threshold condition for propagation of a crack initiated on a critical plane. A criterion connecting uniaxial fatigue strength with multiaxial fatigue strength was proposed based upon the assumption that at the threshold level, the variation of the stress intensity factor of a Mode I crack initiated under combined loading equaled that under uniaxial loading. The predictive method proposed based upon this criterion is practical in that no fatigue test is necessary in making predictions. For the various conditions of in-phase and out-of-phase fatigue loadings with an imposed mean or static load, experimental results agreed well with predictions.

1929

Authors: Alain Franz Knorr, Michael Marx

Abstract: One problem of the quantitative description of small fatigue crack propagation is the fluctuating crack growth rate induced by obstacles like grain or phase boundaries. Sometimes cracks stop completely for a large number of cycles sometimes cracks only decelerate, both resulting in an additional number of life time cycles. However, so far it is not clear, what actually determines the resistance of a grain boundary against fatigue cracks. Therefore we investigate small crack propagation through grain boundaries systematically by in-situ imaging in the scanning electron microscope and focused ion beam (FIB) crack initiation. By this unique technique, artificial stage I cracks with constant crack parameters can be observed while interacting with different grain boundaries which gives detailed information on the interaction mechanisms. We identified different useful aspects of the interaction between microcracks and microstructural barriers on the microscopic scale. 3D-tomographs revealed by serial sectioning and FIB give information about the transition process from the initial grain to the neighbouring one. The resulting purely geometrical consideration leads to a quantitative description of the blocking effect of grain boundaries and can be used to calculate the probability of a crack transfer from the orientation data of two neighboring grains only.

929

Abstract: The threshold stress intensity factor (ΔKth) of small crack is affected by various factors, especially by material hardness, stress ratio and crack size. Test results showed that harder material had higher ΔKth and smaller crack had lower ΔKth. The crack closure measurement on a very small crack was done to make clear the root cause of those effects. Most of those effects could be explained by the peculiar behavior of crack closure for crack deeper than 100µm. However, everything could not be understood only by the crack closure behaviour. In addition to the difference in crack closure, (ΔKeff)th itself was also dependent on crack size when the crack depth was shallower than 100µm. Another remarkable phenomenon was experienced in this study. Unusual decrease in ΔKth was found in some case. The large decrease of ΔKth occurred under the conjunction of three factors, that is,
extremely high stress ratio (R) higher than 0.8, small crack and hard material. This kind of large reduction in ΔKth in high R region is of much importance in turbo machinery that operates under high mean stress with small vibratory stress.

89

Authors: Satoshi Muramoto, Hisao Matsunaga, Shigeaki Moriyama, Masahiro Endo

Abstract: Semi-elliptical shear-mode fatigue cracks were promoted in the axial direction of round
specimens of SAE52100 bearing steel by fully-reversed cyclic torsion tests under a static axial
compressive stress. Non-propagating cracks smaller than 1 mm were obtained in two ways; (i)
stress amplitude decreasing tests of notched specimens, or (ii) constant stress amplitude tests of
smooth specimens. The threshold stress intensity factor ranges, (KIIth and (KIIIth, showed a crack
size dependency.

449

Authors: Jin Quan Guo, Fen Lan Ou, Jian Feng Zhong, Shun Cong Zhong, Xiao Xiang Yang, Li Gang Yao

Abstract: For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

817

Authors: Naoya Shomura, Keiji Yanase, Hisao Matsunaga, Masahiro Endo

Abstract: The near-threshold fatigue behavior of small, semi-elliptical surface cracks in a bearing steel was investigated under cyclic shear-mode loading in ambient air. Fully-reversed cyclic torsion was combined with a static axial compressive stress to obtain a stable shear-mode crack growth in the longitudinal direction of cylindrical specimens. Shear stress amplitude was gradually decreased with an increase in crack length and the crack finally became non-propagating. Abrasive wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. Further, it was found that these effects resulted in a significant decrease in the crack growth rate. In this study, we shed light on the important role of the crack size and crack face interference on the crack growth behavior.

15

Authors: Won Beom Kim, Jeom Kee Paik, Hiroshi Yajima

Abstract: In this research, corrosion fatigue crack initiation tests using 13 Cr stainless steel were
conducted in synthetic seawater to investigate the corrosion fatigue crack initiation life (Nc). In
addition, a corrosion fatigue crack initiation and propagation model was suggested also. Until now,
corrosion fatigue crack initiation life was treated ambiguously. The important point of this model is
the suggestion of the moment of the corrosion fatigue crack initiation life at which the critical size
of the corrosion pit changes to the crack. As the crack which emanates from the pit is usually small,
accordingly it is treated as a small crack. In addition, the observation of the corrosion fatigue
fracture surfaces using SEM were conducted. And the fracture mechanics analysis using an intrinsic
crack model was conducted for the treatment of the small crack. Finally, the following were
obtained. In the case without a clear stress concentration point which seems to fall into a corrosion
fatigue crack initiation, as the meaning to define the number of cycles, at which the fatigue crack
propagation rate becomes faster than the corrosion pit growth rate so that the fatigue crack initiates
from the pit and its propagation starts in earnest, as the reasonable and universal corrosion fatigue
crack initiation life (Nc) has been clarified.

1007

Abstract: This paper offers some new calculating equations on the small crack growth rate for describing the elastic-plastic behavior of materials under symmetric or un-symmetric cyclic loading. And it yet suggests the estimating formulas of the life relative to varied small crack size aoi at each loading history. The method is to adopt the ratio e p e e D D / by plastic strain range to elastic strain
range as a stress-strain parameter, using some staple material parameters as the material constants in damage calculating expression. And it gives out a new concept of the composite material constant, that it is functional relation with each staple material constants, average stress，average strain and critical loading time. The calculated results are accordant with the Landgraf’s equation, so could avoid unnecessary fatigue tests and will be of practical significance to stint times, manpower and capitals, the convenience for engineering applications.

79

Authors: Yoshimasa Takahashi, Hiroaki Yoshitake, Takahiro Shikama, Hiroshi Noguchi, Masanori Takuma

Abstract: The giga-cycle property of a newly developed Al alloy, which contains 0.5wt.% excess Mg solute compared to a standard age-hardened 6061 alloy (6061-T6), was investigated by using smooth specimens subjected to ultrasonic fatigue. The fatigue strength of the new alloy was higher than that of a normal 6061 alloy particularly at relatively low stress amplitude level. Several analyses (surface crack observation, fractography, FIB cross-sectioning, etc.) were also conducted to reveal the micro-mechanism of the observed strength properties. The following results were obtained: i) No fatigue limit was confirmed for both 6061 and new alloy. ii) Total life (*N*_{f}) of 6061 and new alloys was determined by a single fatigue crack initiated from a surface PSB crack. iii) Crack initiation resistance defined by *N*_{25 }(number of cycles to reach ρ = 25 mm^{-2}, where ρ is the PSB crack number density) for new alloy was higher than that of 6061. iv) The higher fatigue strength of new alloy was explained by the effect of excess Mg solute which increased the resistance against the formation of PSB cracks.

293

Authors: Masayuki Kamaya, Takayuki Kitamura

Abstract: Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic property of each crystal influences on the local stress field ahead of a crack tip if the crack size is not large enough in comparison with the grain diameter. This brings about the change in the crack driving force (CDF) such as stress intensity factors. In the present study, in order to investigate the cause and magnitude of the change in the CDF, the finite element analysis is performed. The calculations are carried out for a single crystal model, a bi-crystal model, and a polycrystal model containing a transgranular or an intergranular semi-circular crack. The results implied that the magnitude of CDF is dependent not only on the crystal orientation but also on the deformation-constraint caused by the difference in elastic modulus of grains near the crack tip. The statistical scatter of CDF due to the random crystal orientation in a polycrystal is examined by a Monte Carlo simulation. The variation in the SIF becomes small as the crack size increases.

1165