PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127 Author name / Structural Integrity Procedia 00 (2019) 000–000

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It is interesting to compare the lengthwise fracture behaviour of the beam at the four cross-section geometries (isosceles triangle, antiparallelogram, T-shape and circle) assuming that they have the same area. Such comparison is presented in Fig. 13 where the strain energy release rate in non-dimensional form is plotted against a l / ratio for the four beam cross-section geometries assuming that the base of the isosceles triangle, antiparallelogram and T shape is b r 2  , the upper base of the antiparallelogram is b r  1 , the thicknesses of the flange and the stem of the T-shape are p b 0.2  and q b 0.2  , respectively.

Fig. 13. The strain energy release rate in non-dimensional form plotted against a l / ratio (curve 1 – at circular cross-section, curve 2 – at triangular cross-section, curve 3 – at trapezoidal cross-section and curve 4 – at T-shape cross-section). The heights of the isosceles triangle, antiparallelogram and T-shape are determined under the condition of equality of their areas to the area of a circle of radius, r . The material has the same moduli of elasticity in tension and compression. It can be observed in Fig. 13 that the strain energy release rate is highest for the beam of circular cross-section. The lowest strain energy release rate is obtained for a beam of T-shape cross-section. This finding shows that the T-shape cross-section (among the four cross-section geometries considered in the present paper) is the most efficient for improving the fracture performance of the beam. 4. Conclusions The effects of the geometry of the beam cross-section on the lengthwise fracture behaviour of inhomogeneous linear-elastic beam configurations are analyzed. The beams under consideration exhibit continuous material inhomogeneity in both height and length directions. The lengthwise fracture is analyzed in terms of the strain energy release rate. For this purpose, a methodology for calculation of the strain energy release rate is developed. The case when the beams have different behaviour in tension and compression is also considered. The methodology is applied to investigate lengthwise fracture in simply supported inhomogeneous beam. The compliance method is used for verification of the strain energy release rate. The external loading consists of one vertical force applied at the lower crack arm. The continuous distribution of modulus of elasticity along the height and the length of the beam is described by applying a power law. The effects of the geometry of four cross-sections (isosceles triangle, antiparallelogram, T-shape and circle) on the lengthwise fracture behaviour of the inhomogeneous beam configuration are evaluated. For the case when the beam cross-section is an isosceles triangle, it is found that the strain energy release rate decreases with increasing of h b / and s a / ratios (the later ratio characterizes the loading conditions). The analysis reveals that when the beam cross-section is an antiparallelogram, the increase of b b / 1 and h b / ratios leads to decrease of the strain energy release rate. For a beam of a T-shaped cross-section,