Modeling of the competition between shear yielding and crazing in glassy polymers Estevez, R.; Tijssens, M.G.A.; van der Giessen, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractFracture in amorphous glassy polymers involves two mechanisms of localized deformations: shear yielding and crazing. We here investigate the competition between these two mechanisms and its consequence on the material's fracture toughness. The mechanical response of the homogeneous glassy polymer is described by a constitutive law that accounts for its characteristic softening upon yielding and the subsequent progressive orientational strain hardening. The small scale yielding, boundary layer approach is adopted to model the local finite-deformation process in front of a mode I crack. The concept of cohesive surfaces is used to represent crazes and the traction-separation law incorporates craze initiation, widening and breakdown leading to the creation of a microcrack. Depending on the craze initiation sensitivity of the material, crazing nucleates at the crack tip during the elastic regime or ahead of the crack. As the crazes extend, plasticity develops until an unstable crack propagation takes place when craze fibrils start to break down. Thus, the critical width of a craze appears to be a key feature in the toughness of glassy polymers. Moreover, the opening rate of the craze governs the competition between shear yielding and brittle failure by crazing.

A novel cohesive surface model for crazing in polymers is developed. The model incorporates the initiation, growth and breakdown of crazes based on micromechanical considerations. The initiation of crazes is controlled by the stress state, in particular by the hydrostatic stress and cohesive surface normal traction. The widening of a craze is based on a rate-dependent viscoplastic formulation and failure of the craze occurs when the ®brils reach a material-dependent maximum extension. Crazing is simulated using a high density of cohesive surfaces immersed in the continuum. The ®nite element method is used to discretize both cohesive surfaces and continuum separately. The capabilities of the method to describe multiple crazing is demonstrated with an example.

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.

Crazing in amorphous polymers under mode I loading conditions is simulated using the concept of embedded cohesive surfaces with a recently proposed model. The dependence of the predicted crack growth resistance on the crazing material parameters is studied. In general, for constant loading rate, a lower fracture toughness is predicted for shorter craze lengths. However, since the widening of the craze is of a viscoplastic nature, this trend can be reversed for increasing loading rate. The parameter variations indicate that the perfectly plastic Dugdale cohesive zone model is not applicable to crazing. Mesh sensitivity with respect to length and orientation of the cohesive surface elements is also studied. Convergence of crack growth resistance and crack path predictions can only be expected for very ®ne, randomly oriented meshes.

Simulation of fracture of cementitious composites with explicit modeling of microstructural features Tijssens, M.G.A.; Sluys, B.L.J.; van der Giessen, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. AbstractFracture of cementitious composites is analyzed numerically using the cohesive surface methodology. The presence of aggregates in the cement matrix is explicitly accounted for. The composite is modeled in two dimensions as a threephase material, the third phase being the weak interfacial transition zone in between aggregates and cement matrix. The bulk material is regarded as elastic and fracture is described with cohesive surfaces. The cohesive surface constitutive model is motivated by experimental observations regarding the loading-rate sensitivity of cementitious composites and analytical studies regarding fracture of planar microcracks. The model predicts the important toughening mechanism of crack face bridging occurring in cementitious composites. Ó