Normalization of cohesive laws for quasi-brittle materials. (1st June 2017) - Tryding, Johan; Ristinmaa, Matti
Highlights: For traction-separation laws of the form, T / T 0 = f ( ( δ / δ N / x c ) 1 / c ), it is shown that x c is a function of c . The parameter c represents the characteristic form of the traction-separation laws. The length δ N is defined by the ratio of the strength T 0 to the maximum slope of the curve, N max . The length δ N is shown to be related to the length δ N = Γ 0 / T 0, where Γ 0 is the fracture energy. Data normalized with Γ 0 and δ N indicate an independence of material directions, moisture and size. Abstract: Analytical relations to describe experimentally measured traction-separation laws are often expressed in dimensionless quantities. The traction and the separation are commonly normalized using the cohesive strength and a length measure, respectively. The ratio between the fracture energy and the cohesive strength is often used as a length measure. An alternative length measure is the ratio between the cohesive strength and the maximum slope of the traction-separation law. A relation between these two length measures are established. To illustrate the implications on cohesive laws, three existing cohesive laws are rewritten using the alternative normalization. As a result it is shown that the number of unknown material parameters can be reduced. One of the derived dimensionless cohesive law is validated against experimental uniaxial tension and compression load-deformation data of different sample sizes and different quasi-brittle materials, i.e. concrete and paperboard. A good fit of the cohesive law is shown to all the investigated data. These findings indicate that the derived normalized cohesive law is independent of material directions, moisture contents and sample size.