Semi-analytical estimation of the effective plastic zone size at U-notch neighborhood in thin sheets under mixed mode I/II loading

• Published in: Engineering fracture mechanics 2020-11, Vol.239, p.107323, Article 107323
• Main Authors: Torabi, A.R., Shahbazian, B.
• Format: Article
• Language: English
• Subjects: Aluminum; Effective plastic zone size; Elastic-plastic finite element analysis; Finite element method; Formulations; Irwin’s model; Metal sheets; Mixed mode I/II loading; Neighborhoods; Notches; Numerical methods; Plastic zones; Stress distribution; U-notch; Yield criteria
• ISSN: 0013-7944; 1873-7315
• DOI: 10.1016/j.engfracmech.2020.107323

•Irwin’s approach is extended to U-shaped notches to predict the plastic zone size.•Tresca and Von-Mises criteria are used as the yielding criteria for the material.•Analytical expressions of the elastic stress field around blunt notches are used.•Analytical estimations are well verified by conducting elastoplastic FE analyses.•Extended Irwin’s model is successful in predicting the effective plastic zone size. In an effort to semi-analytically estimate the effective plastic zone size around U-shaped notches under mixed mode I/II loading by using the Tresca and Von-Mises yield criteria, explicit formulas of the elastic stress field at the neighborhood of such notches and the extended Irwin’s model are employed. Since the formulations are proposed under plane-stress conditions, they are useful to be used for thin sheets with elastic-plastic behavior. For verification of the proposed formulas, elastic-plastic finite element analyses are done on thin U-notched aluminum sheets and the corresponding numerical results are compared with the semi-analytical estimations. For the most cases, it is shown that the effective plastic zone size, which is crucial for determining the type of ductile failure, can be successfully estimated by using the proposed semi-analytical formulas. Furthermore, due to lack of precision of the analytical stress fields used in this study, the shapes of the plastic zones obtained by the semi-analytical and numerical methods are not the same. This research also reveals that instead of the complicated and time-consuming numerical elastic-plastic solutions, by using the semi-analytical method based on the linear elastic solution, the effective plastic zone size at the neighborhood of U-notches under mixed mode I/II loading can be determined simply and rapidly.