Two-step Fatigue Tests Research Articles

Internal crack initiation characteristics and early growth behaviors for very-high-cycle fatigue of a titanium alloy electron beam welded joints

The very-high-cycle fatigue has become an important issue in recent years. The crack initiation mechanism and early crack growth behaviors of electron beam welded joints of TC21 titanium alloy were discussed. In order for the subsurface crack growth to be observed, a repeated two-step fatigue test was performed for the beach mark formation. Two kinds of initiation modes of microcracks could exist. One is the initiation from microvoids and the other results from the dislocation accumulation. During early growth, the microcrack path could deflect when it passed through the boundaries, leading to the FGA region formation. The crack closure could also occur during growth. By the Paris’ law integration, the crack propagation life was discovered to occupy only a small number of the fatigue life.

Small internal fatigue crack growth rate measured by beach marks

Internal fatigue crack growth rates were measured using the beach marks created by repeated two-step fatigue tests on a high-strength steel. This material revealed internal fractures originating from oxide-type inclusions whose sizes ranged from 14 to 40µm. Large and small beach marks were observed depending on the conditions under which the repeated two-step fatigue tests were carried out. Small beach marks indicated small internal cracks just after crack initiation, while large beach marks indicated internal cracks in the final stages. The small internal cracks showed extremely slow growth rates that were much smaller than the lattice length: the measured growth rates were very close to those calculated using fracture mechanics. The large internal cracks showed conventional growth rates, larger than the lattice length, and the border between the large and small internal cracks was almost equal to the threshold stress intensity range ΔKth. These results show the validity of evaluating the fatigue lives by calculating the crack propagation lives of the small internal cracks as in the Tanaka-Akiniwa model. However, it has been suggested that the Tanaka-Akiniwa model overestimates the effects of inclusion sizes, meaning that the Tanaka-Akiniwa model has room for improvement. To correct this problem, we propose a new model, based on a new crack growth law, in which the crack growth rate also depends on crack size. The new model generates more realistic predictions.

ビーチマーク法による内部疲労き裂伝ぱ速度の評価

Internal fatigue crack growth rate was measured by using beach marks resulting from repeated two-step fatigue tests for JIS-SCM440 low-alloy steel. This material showed internal fractures under stress ratio of R = 0, and the inclusion sizes of the internal fracture origins ranged from 14 to 40 μm. Two types of beach marks were observed: One was small beach marks indicating internal cracks at an initial stage of fatigue. The other was large ones indicating the internal cracks at a final stage. The internal crack shape at the initial stage was a half-ellipse and asymmetric, while that at the final stage were a circle and symmetric. The asymmetric internal crack shape requires three-dimensional modeling, and therefore, an extremely slow crack growth rate, smaller than the lattice length, is expected in two-dimensional modeling. The growth rate of the asymmetric internal crack was evaluated by d√area /dN instead of conventional da/dN. As the result, the asymmetric internal crack revealed the extremely slow crack growth rate, in spite of the conventional crack growth rate of the symmetric internal crack. The border of the two-types internal cracks was corresponding to conventional ΔKth. Moreover, the growth rate of the asymmetric internal crack showed good agreements with that estimated by Omata’s method based on the conventional fatigue test results. These results support validity of Tanaka-Akiniwa model for the internal crack growth. This research thus proved that gigacycle fatigue life of high-strength steel could be predicted by crack growth life based on Tanaka-Akiniwa model.

Visualization of internal small fatigue crack growth

Internal small fatigue crack growth caused by gigacycle fatigue of high-strength steel was successfully visualized using beach marks created by a repeated two-step fatigue test. The created beach marks were clear enough to visualize the initial stage of the internal fatigue crack growth. The beach marks indicated that the internal crack shape just after initiation from an inclusion was not a circle but a half-ellipse, suggesting that the early stage of the internal crack growth requires three-dimensional modeling, and therefore, an extremely slow crack propagation rate, smaller than the lattice length, is expected in two-dimensional modeling. Moreover, it was found that the crack propagation life exceeded 1.42×107 cycles. This meant that the minimum crack propagation rate per cycle in two-dimensional modeling was smaller than the lattice length.

Nonlinear Cumulative Fatigue Damage Model

Cumulative fatigue damage is an important consideration in determining the fatigue life of structures. A cumulative linear damage rule cannot provide a reasonable explanation for cumulative fatigue damage, but a damage curve method based on nonlinear cumulative fatigue damage model can give a reasonable explanation. In this paper, a specific mathematical model is put forward, which is based on the damage curve method. In the model, miner formula is modified properly and an exponent formula is give out to fit the damage accumulate. According to a two-step fatigue test of aluminum–alloy welded joint, the comparison between the calculated results and the testing results is less than 5%. It shows that the model is reasonable and accuracy.

The effects of grain boundary on dislocation development for cyclically deformed IF steel

Polycrystalline interstitial-free steels (IF steels) were cyclically deformed at constant total strain amplitude (Δ ɛ/2) in the range from 0.05% to 0.6%. The transformed speed of loop patches into dislocation cells and walls near grain boundary is faster than that in the grain interior while total strain amplitude is lower than 0.15%. However, the well-known dislocation-free zones (DFZs) near grain boundary are very hard to be found in this study. Additionally, dislocation cells tend to transform into loop-patch structure near grain boundary during high–low strain-controlled fatigue test (two-step fatigue test).

接触端部局所応力に基づくフレッティング疲労き裂成長限界条件の検討

It was reported previously by the author that the effect of various factors influencing the fretting fatigue limit could be evaluated based on the local stress at the contact edge. In this report, the meaning of the local stress in fretting fatigue was studied. The two-step fatigue test showed that the value of the local stress fatigue limit was nearly the same as the fatigue limit of an edge cracked specimen containing a non-propagating crack formed by the pre-fretting fatigue. The change of stress intensity factor due to the crack growth under fretting fatigue condition was calculated by FEM. The fretting fatigue limit was the condition at which a micro-crack generated by fretting remains as a non-propagating crack. The condition to form a non-propagating crack in fretting fatigue was evaluated on the basis of the threshold condition of short fatigue crack growth.

A statistical consideration of Miner's rule

Miner's rule regarding the fatigue behaviour of materials is discussed in statistical terms. The conditions required for both the parameters of the log-normal and Weibull distribution functions of fatigue life and the cumulative damage rule to satisfy the statistical Miner's rule are derived. For the case when the conditions obtained are not satisfied, the reliability of the population and the mean cumulative cycle ratio to failure are considered for two-step fatigue tests, and calculation examples are given. It is found that fatigue life scatter has a fairly large effect on the mean cumulative cycle ratio to failure.