Issue 35

Š. Major et alii, Frattura ed Integrità Strutturale, 35 (2016) 379-388; DOI: 10.3221/IGF-ESIS.35.43 383 Distribution of the von Mises stress obtained for elastic deformation of thread area of screw is shown in Fig.6. In this figure is clearly visible local maximum of stress concentration at the bottom of thread (lower diameter of thread). The crack initiates in this region. The evolution of normal stress along the crack path is displayed in Fig. 7, for four different loads. For analysis of crack propagation phase is necessarily calculate the stress intensity factor at the bottom of thread, respectively at the forehead of crack. For this calculation second finite element model was prepared. For this model semieliptical crack is assumed. It is assumed, that the crack initiates on te lower diameter of thread and subsequently grows along the bottom of the thread (crack grows along the helix, with inclination 14.5°, which corresponds to the thread pitch) and propagates into core of the screw, see Fig. 8. The crack is characterized by two axes a and b , these two axis define the ellipse. The major axis is tangential to the thread and the secondary axis is perpendicular to the axis of the helix, respectively to the axis of screw. Figure 7 : The evolution of normal stress along the crack path, for four different loads (200 N, 300 N, 400 N, 500 N). When the diameter of crack is smaller then 50 μm, it is assumed that the crack flat. This assumption cannot be used for crack diameter greater then 50 μm. For greater crack is necessarily use submodelling, becose the number of elements is too large. The calculation of stress-intensity factor at the front of crack was based on J -integral method. For calculation was assumed that the material can be characterized by linear elastic deformation. Stress-intensity factor is a function of crack length a . This relations is can be determined by repeated simulations. The lenght of crack at the start of simulation was 5 μm. This length is much smaller than the initial crack length for the propagation phase. With Paris' Law, a relationship n S S D D K a a K           (2) can be obtained where Δa S and Δa D are increments of crack on surface and deepest poit of crack. The ΔK S and ΔK D are appropriate increments of stress-intensity factors and n is exponent in Paris law. With new increment of Δa S , crack length at the surface changed and a new finite element model can be solved and the stress-intensity factor calculated. This process is repeated by software until the final length of crack is reached. The shape changes in the process of crack growth can be described by the ratio a / b , where a and b are values corresponding to the lengths axis of the ellipse. Relations between ratio a / b and the length of crack is shown in Fig. 9. A sharp decline in the ratio a / b (see Fig. 9) indicates that the crack propagates faster along the helix (around the circumference of the screw cylinder) then into body of material. The following figure shows realitions between crack intensity factor (at the bottom of the thread) and crack length. Gradient of stress-intensity factor is is much greater at the