PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 97–105 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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observed in Fig. 6 that the strain energy release rate increases with increasing of α / l 1 ratio which is due to the decrease of the modulus of elasticity in the beam cross-section in which the crack tip is located. The curves in Fig. 6 indicate that the strain energy release rate increases with increasing of l / l 1 ratio (this is explained by the increase of the bending moment in the beam portion between the supports).

Fig. 6. The strain energy release rate in non-dimensional form plotted against α / l 1 ratio (curve 1 – at l / l 1 =0.3, curve 2 – at l / l 1 =0.5 and curve 3 – at l / l 1 =0.7).

4. Conclusions

An analytical study of lengthwise fracture in a continuously inhomogeneous beam whose upper surface is in contact with aggressive environment is performed. The material is continuously inhomogeneous along the height and length of the beam. Due to the contact with the aggressive environment, a damage zone appears in the beam. The depth of the damage zone increases with the time. The beam is loaded by two transverse forces applied at the ends of the beam. A lengthwise crack is located symmetrically with respect to the mid-span. The fracture is analyzed in terms of the strain energy release rate. A time-dependent solution to the strain energy release rate is derived by applying the compliance method. The fracture is studied also by using the J -integral approach. The fact that the strain energy releases rate is equal to the value of the J -integral is a verification of the analysis developed in the present paper. The change of the strain energy release rate with the time is evaluated. It is found that the strain energy release rate increases with the time which is due to the increase of the damage zone depth. The effect of crack location along the height of the beam is investigated. The calculations indicate that the strain energy release rate decreases with increasing of h 1 /2 h ratio. This finding is explained by increase of the bending stiffness of the lower crack arm (the upper crack arm is free of stresses). The effect of the crack length on the fracture behaviour is investigated too. The investigation shows that the strain energy release rate increases with increasing of α / l 1 ratio (this ratio characterizes the crack length). The increase of l / l 1 ratio leads to increase of the strain energy release rate (this finding is attributed to increase of the bending moment in the beam portion between supports). Concerning the effect of continuous material inhomogeneity, the analysis reveals that the strain energy release rate decreases with increasing of f and g . The fact that the appearance of damage zone as a result of the contact of the beam with aggressive environment leads to increase of the strain energy release indicates that the influence of the damage zone has to be taken into account in lengthwise fracture analysis of continuously inhomogeneous beam configurations.

References

Druyanov, B, Nepershin, R., 1990. Theory of plasticity, Engineering. EL-Wazery, M.S., EL-Desouky, A.R., 2015. A review on functionally graded ceramic-metal materials, Material Environment Science, 6, 1369 1376. Gasik, M.M., 2010. Functionally graded materials: bulk processing techniques. International Journal of Materials and Product Technology 39, 20-29. Hirai, T., Chen, L., 1999. Recent and prospective development of functionally graded materials in Japan. Mater Sci. Forum 308-311, 509-514.