Abstract: Two procedures to evaluate fracture resistance of notched components are proposed in this contribution: the Strain Energy Density (SED) over a control volume and the Cohesive Zone Model (CZM). With the aim to simplify the application of the two fracture criteria, the concept of the ‘equivalent local mode I’ is presented. The control volume of the SED criterion and the cohesive crack of the CZM, have been rotated along the notch edge and centered with respect to the point where the elastic principal stress is maximum. Numerical predictions are compared with experimental results from U and V shaped notches under three point bending with notch root radius ranging from 0.2 to 4.0 mm. In parallel the loading conditions vary, from pure mode I to a prevailing mode II. All specimens were made of PMMA and tested at -60°C. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.
How to cite this paper
Berto, F & Gomez, G. (2017). Notched plates in mixed mode loading (I+II): a review based on the local strain energy density and the cohesive zone mode.Engineering Solid Mechanics, 5(1), 1-8.
Atzori, B., & Lazzarin, P. (2001). Notch sensitivity and defect sensitivity under fatigue loading: two sides of the same medal. International Journal of Fracture, 107(1), 1-8. Bazant, Z. P., & Planas, J. (1997). Fracture and size effect in concrete and other quasibrittle materials (Vol. 16). CRC press. Berto, F., Lazzarin, P., Gómez, F. J., & Elices, M. (2007). Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’concept. International Journal of Fracture, 148(4), 415-433. Carpinteri, A. (1987). Stress-singularity and generalized fracture toughness at the vertex of re-entrant corners. Engineering Fracture Mechanics, 26(1), 143-155. Dini, D., & Hills, D. A. (2004). Asymptotic characterisation of nearly-sharp notch root stress fields. International Journal of Fracture, 130(3), 651-666. Elices, M., Guinea, G. V., Gomez, J., & Planas, J. (2002). The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics, 69(2), 137-163. Gogotsi, G. A. (2003). Fracture toughness of ceramics and ceramic composites. Ceramics International, 29(7), 777-784. Gómez, F. J., & Elices, M. (2003). Fracture of components with V-shaped notches. Engineering Fracture Mechanics, 70(14), 1913-1927. Gómez, F. J., Elices, M., & Valiente, A. (2000). Cracking in PMMA containing U‐shaped notches. Fatigue & Fracture of Engineering Materials & Structures, 23(9), 795-803. Gómez, F. J., Elices, M., & Planas, J. (2005). The cohesive crack concept: application to PMMA at− 60 C. Engineering Fracture Mechanics, 72(8), 1268-1285. Gómez, F. J., Elices, M., Berto, F., & Lazzarin, P. (2007). Local strain energy to assess the static failure of U-notches in plates under mixed mode loading. International Journal of Fracture, 145(1), 29-45. Knésl, Z. (1991). A criterion of V-notch stability. International Journal of Fracture, 48(4), R79-R83. Lazzarin, P., & Zambardi, R. (2001). A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches. International journal of fracture, 112(3), 275-298. Lazzarin, P., & Berto, F. (2005). Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches. International Journal of Fracture, 135(1-4), 161-185. Leguillon, D., & Yosibash, Z. (2003). Crack onset at a v-notch. Influence of the notch tip radius. International Journal of Fracture, 122(1-2), 1-21. Nui, L. S., Chehimi, C., & Pluvinage, G. (1994). Stress field near a large blunted tip V-notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials. Engineering Fracture Mechanics, 49(3), 325-335. Planas, J., & Sancho, J. M. (2007). Computational orientated finite elements. COFE. Internal report. JP0501. Departamento de Ciencia de los Materiales. Universidad Politécnica de Madrid. Seweryn, A. (1994). Brittle fracture criterion for structures with sharp notches. Engineering Fracture Mechanics, 47(5), 673-681. Seweryn, A., & Łukaszewicz, A. (2002). Verification of brittle fracture criteria for elements with V-shaped notches. Engineering Fracture Mechanics, 69(13), 1487-1510. Strandberg, M. (2002). Fracture at V-notches with contained plasticity. Engineering Fracture Mechanics, 69(3), 403-415. Taylor, D. (2004). Predicting the fracture strength of ceramic materials using the theory of critical distances. Engineering Fracture Mechanics, 71(16), 2407-2416. Yosibash, Z., Bussiba, A., & Gilad, I. (2004). Failure criteria for brittle elastic materials. International Journal of Fracture, 125(3-4), 307-333. Yosibash, Z., Priel, E., & Leguillon, D. (2006). A failure criterion for brittle elastic materials under mixed-mode loading. International Journal of Fracture, 141(1-2), 291-312.