PSI - Issue 65

Prokopyev L.A. et al. / Procedia Structural Integrity 65 (2024) 170–176 Prokopyev L.A., , Andreev Ya.M., Semenov S.O., Lukin E.S. / Structural Integrity Procedia 00 (2024) 000–000

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The data shown in Figure 1 approximately shows the increase in yield strength with decreasing temperature for several materials. This increase can cause a significant decrease in the size of the plastic zone at the crack tip. In mechanics, this phenomenon can become one of the causes of brittle fracture, the parameters of which can be used to predict the type of fracture.

3. Theory and calculation

The work uses the well-known equations of linear fracture mechanics to describe the yield zone at the crack tip Ошибка! Источник ссылки не найден. : 3 cos 1 sin sin 2 2 2 2 3 cos 1 sin sin 2 2 2 2 3 sin cos cos 2 2 2 2 I xx xx I yy I xy K T r K r K r                                           (2) The components of Ϭ zz , depending on the type of stress state, are given in equation 3 Ошибка! Источник ссылки не найден. . As in other investigations, the von Mises criterion was used to approximate the shape and size of the yield zone at the crack tip. Equation Ошибка! Источник ссылки не найден. shows the expression for the Mises criterion in terms of principal stresses:       2 2 2 2 1 2 2 3 3 1 2 Y              (4) Substituting (2) and (3) into (4), we obtain an approximate estimate of the change in the size of the plastic zone with temperature changes. This difference is obtained by using the temperature dependence of the yield stress shown earlier (1). For selected materials, the approximate dimensions of the plastic zone were calculated for a plane stressed state and a plane-strain state at temperatures t=20 ℃ , t=-60 ℃ (Figure 2). For this case, the stress intensity factor was chosen as a constant. As can be seen from Figure 2, the plastic zone of steel “A 107” is expected to be most susceptible to low temperatures. On the contrary, aluminum is almost unaffected by low temperatures. A quantitative assessment of the change in the size of the plastic zone with temperature changes is proposed. To do this, the size of the plastic zone in the direction of the crack continuation line was calculated. A dimensionless value has been determined equal to the ratio of the size of the plastic zone at low temperatures to the size of the plastic zone at t=20 ℃ . This is the modified value of the radius of the plastic zone, calculated for several materials and presented in Figure 3.         0       zz zz xx yy  plane strain plane strain (3)