Determination of cohesive laws for materials exhibiting large scale damage zones: from R-curves for wedge loaded DCB specimens to cohesive laws

摘要

Large cohesive zones have been experimentally observed in the crack wakes of various non-homogeneous materials, such as continuous-fibre composites, short-fibre composites, paper materials and adhesively joined structures. Traditionally, fracture resistance curves (R-curves) have been used to characterize this class of materials. Since the cohesive zones are comparable in size with test specimen dimensions, the R-curve behaviour can not be used as a material property (Suo et al., 1992). Instead, a cohesive law may be deduced as a material property. This law relates the crack surface traction to the opening displacement. Since a lot of experimental data exist in the form of R-curves, it would be useful to develop an approach, where this data could be used to extract cohesive laws. In the present study, means to acquire the cohesive law from conventional R-curve data are presented. The double cantilever beam (DCB) specimen with applied wedge forces is a widely used test method to obtain R-curves from load and crack length measurements. The purpose of the present study is to develop an approach that enables the cohesive law to be derived from a single DCB R-curve data set. A semi-analytical weight-function approach is employed, and the obtained cohesive laws may be used to predict crack growth for other geometries and load conditions. Microstructural parameters can be extracted from the cohesive law. Experimental observations of damage mechanisms suggest that micromechanical models may be developed to identify these parameters, e.g. fibre-matrix interfacial shear strengths in pull-out of crack-bridging fibres in composites. For example, fibre cross-over bridging in delamination of unidirectional composites can be modelled (Spearing and Evans, 1992), and related to results from macroscopic delamination tests (SΦrensen and Jacobsen, 1998). Even if fibre bridging does not physically take place, the inelastic processes may be described by cohesive laws that incorporate damage accumulation, e.g. in concrete (Hillerborg et al., 1976), paper material (Ostlund et al., 1999) and short-fibre composites (Lindhagen et al., 2000). Another potential of cohesive-zone modelling and micromechanics is design against notch sensitivity.