Issue34

P.O. Judt et alii, Frattura ed Integrità Strutturale, 34 (2015) 208-215; DOI: 10.3221/IGF-ESIS.34.22 214 corrected M - and L -integrals are plotted vs. the simplified theoretical size of the plastic zone according to Eq. (12). The values are normalized with respect to the maximum values max 288 M  N and max p 4.4 r  mm of the mode-I loading case. In Fig. 4(b) it is obvious that the M -integral increases as the region of the plastic deformation around the crack increases. The mixed-mode crack opening provides negligible values in L compared to M which even remain zero for the mode-I and mode-II crack openings. Nevertheless, the L -integral may serve as an additional condition describing the distribution of the material forces in the plastically deformed region. These first results seem promising with respect to a new application of the M - and L -integrals, separating the crack driving force and the plastic deformation driving forces in a similar manner as the separation of the J k -integrals of two interacting cracks [14]. (a) (b) Figure 4 : (a) DCB specimen with applied loads F 1 and F 2 and crack length a = 40mm, (b) normalized global M - and L -integrals with a linear elastic-perfectly plastic material model vs. the normalized plastic zone size max p p / r r from Eq. (12). C LOSURE ath-independent integrals are introduced applying remote integration contours along the external boundaries of the model. This global approach is beneficial compared to a local approach, where small integration contours around the crack tip are applied, as no special requirements regarding the crack tip meshing have to be considered and crack tips approaching interfaces can be appropriately handled. Additional integrals along crack faces, material interfaces and internal boundaries are calculated providing path-independence. It is emphasized, that the integration along material interfaces is important for both, the J k - and I k -integral for the accurate calculation of the crack tip loading. Crack paths at material interfaces are predicted accurately and compared to experimental findings. Next to the fracture toughness anisotropy, the boundary conditions at a material interface have a strong impact on crack paths. Based on global M - and L -integrals, a new approach for the separation of the crack driving force and forces inducing plastic deformation at the crack tip is motivated. A CKNOWLEDGEMENT he authors would like to acknowledge the financial support of the “Landes-Offensive zur Entwicklung Wissenschaftlich-ökonomischer Exzellenz (LOEWE)” Research Funding Program “Safer Materials”. R EFERENCES [1] Eshelby, J.D., The force on an elastic singularity. Phil. Trans. A, 244 (1951) 87-112. P T