**2.3 The typical ratio**

The typical value for both stationary and non-stationary low-cycle loading is the ratio between limit deflections for single and repeated loading ( \* *w* and \*\* *w* , respectively). The

Interrelation Between Failure and

**specimen with edge notch** 

Fig. 6. Test scheme

capacity, *iii*) the average value of them.

its length is less than the notch width.

in Fig. 6. The field of view is outlined by dashed line.

Damage Accumulation in the Pre-Fracture Zone Under Low-Cycle Loading 413

**3. Development of fatigue crack under low-cycle tension conditions of a plain** 

Tests on a plain specimen loaded in tension with the narrow edge notch were conducted. During the test, direct observation of fatigue crack propagation was performed using a digitized microscope with the resolution of 22500 pixel/mm2. The testing scheme is shown

The specimens were made from D16T alloy preliminary heat-treated at 500ºС to give more plastic material. Plain specimens with notches of different lengths (1–3 mm) were used. The minimum load was the same in every cycle, the maximum load was chosen such that three different loading types were provided: *i*) near yield strength, *ii*) near the limit of load

Photographs in Fig. 7 illustrate stages of crack propagation near crack-like defect in two

In the case of continuous tension, the following stages may be observed. First, intense plastic deformation ahead of the notch tip occurs and two zones of strain localization are formed with a delta-shaped area between these zones. The area we term as a pre-fracture zone since further it will define the crack extension direction. At this stage, several focuses of fatigue crack initiation are formed, which are located at notch angles as it is seen in the photograph (a.1). The pre-fracture zone is formed not by a prospective crack, but by the notch itself and its shape is unclear. Further (a.2), one of microcracks develops as a crack propagating within the zone of plastic strain localization irrespective of the pre-fracture zone specified by the notch. This zone becomes more structured and its tip is separated from the crack tip. Here the pre-fracture zone tip starts to shift towards the developing crack. At the next stage (a.3), crack branching takes place, the branches being formed just as near the crack, so at its faces. This evidences the significant extent of material embrittlement in the vicinity of crack extension. The angle at the pre-fracture zone tip starts to decrease. Then (a.4) the branch nearest to the pre-fracture zone tip has some advantages and defines the final direction of crack extension. When the crack tip joins the pre-fracture zone tip (a.5), the critical state is achieved after which the crack starts to extend very fast. The final failure of a specimen is preceded by a short stage (a.6), at which the angle at the pre-fracture zone crack becomes similar to the crack opening angle and one of pre-fracture zone edges defines a path of the subsequent crack extension unambiguously. The crack is very short before the critical state:

Under repeated low-cycle loading conditions, the pre-fracture zone created by a notch plays no noticeable role especially in the cases when cycle loading starts at insignificant plastic

cases *i*) continuous tension with constant rate, *ii*) low-cycle tension.

tests show that this ratio for material is constant when different schemes of stationary and non-stationary loading are applied (Kornev et al., 2010). This allows one to use this ratio for comparison of results obtained on specimens with various geometrical dimensions and for different loading regimes. For duralumin, we have \* \*\* *w w*≥ .

### **2.4 Preliminary inelastic strain**

Preliminary inelastic strain of a material, from which the specimens have been made, essentially influences material resistance to cyclic fracture. As an example, Fig. 5 displays the experimental diagrams with curves of *w* versus *P* (Fig. 5 (a)) and the *δw*(*N*) diagram (Fig. 5 (b)) for D16Т duralumin with various degrees of preliminary stretching: diagram **1** for original materials, diagram **2** for materials stretched by 5%, and diagram **3** for materials stretched by 10%. All the specimens were loaded for the same *P*max value, but in Fig. 5 (a), diagrams for three tests are displaced, for convenience, from each other along the horizontal axis.

Fig. 5. (a), (b). Low-cycle loading of aluminum alloy after preliminary plastic deformation for D16T alloy

In Fig. 5(b), the area under the curve characterizes the limit deflection \*\* *w* , which decreases as preliminary stretching increases. However, the decrease in \*\* *w* is followed by the decrease in δ*w* . This leads to increase of the limiting number of loading cycles.

### **2.5 Variation in the notch depth**

Comparison of tests conducted on beams with notches of different depths has shown that if δ *w N*( ) diagrams have been plotted for some notch depth *l*, the diagrams can be used to obtain analogous diagrams for other *l* values. Assume that δ *w N*( ) diagrams have been plotted for the notch depth 1*l* , and for the notch depth 2*l* there is the only diagram with curves of *w* versus *P* for single loading. The value of maximum applied force *P P* max 1 = corresponds to some deflection *w w*= 1 for 1 *l* under single loading, the limit deflection of cyclic loading for this notch depth being \*\* \*\* *w w*= <sup>1</sup> , and the limit deflection of the single loading being \* \* *w w*= <sup>1</sup> . In this case, the curve of damage accumulation *f*<sup>1</sup> (*N*) for *P P* max 1 <sup>=</sup> , <sup>1</sup> *l l* = can be used to obtain the curve *f*<sup>2</sup> (*N*) for *P P* max 2 = , 2 *l l* = . Here *P*2 is the force for which a specimen with the notch depth 2*l* has the deflection *w w*= 2 such that

$$\frac{w\_1}{w\_1^{\*\*}} = \frac{w\_2}{w\_2^{\*\*}} \text{, where } \frac{w\_2^{\*\*}}{w\_2^{\*\*}} = \frac{w\_1^{\*\*}}{w\_1^{\*\*}} \Rightarrow w\_2^{\*\*} = \frac{w\_1^{\*\*} w\_2^{\*\*}}{w\_1^{\*\*}} \cdot 1$$
