Fracture mechanical modelling of embossed paper
Sammanfattning: This thesis consists of two scientific papers on strength and fracture of embossed tissue paper. In Paper A an experimental study of embossed tissue paper is presented. The mechanical properties of most soft tissue paper are to a large extent governed by the creping and subsequent embossing process. The objective is to study the in-plane fracture mechanical properties of different creped tissue paper products having different embossing patterns. In order to reproduce the embossing process patterned metal plates were used to imprint patterns in paper sheets. Fracture toughness was obtained by tensile testing of paper samples containing pre-fabricated cracks. The fracture process occurring in a sample having a periodic embossing pattern was studied by the aid of a computer controlled CCD-camera system. Inspection of the damage evolution of samples containing a pre-fabricated cracks indicates that damage occur in indentation rows parallel to the crack plane, near the tip of the main crack. This suggests that the stresses at the tip of the crack is shielded by neighbouring rows of indentation; energy dissipation may occur not only at the tip of the main crack, but in several indentation rows parallel to the main crack. Furthermore, below a certain crack lengths, the pre-fabricated crack failed to localise damage. Additionally, it was observed that the stress-strain response of creped tissue paper exhibits a pronounced non-linear behaviour in cross-direction. However, tensile tests of an embossed 2-ply tissue paper made from the same base paper exhibits surprisingly an almost linear behaviour up to failure in cross-direction. In Paper B a model is presented which aims at describing the crack tip shielding effect occurring in an embossed tissue paper material having a periodic indentation pattern. The material is analysed as consisting of representative unit cells. One major objective of homogenising, is the possibility to circumvent the complexity associated with detailed modelling of the periodic geometry of the embossed paper sheet. The effective damage behaviour of a unit cell is determined. This is accomplished by homogenising the cohesive behaviour of the unit cell, based on which an effective cohesive law is established. The result is used to describe the damage behaviour of the body. Additionally, the effective elastic properties of a unit cell are determined. The crack tip of an embossed tissue paper undergoing damage may be visualised to consist of three regions: (i) a fracture process zone ahead of the main crack developing in the direction of the crack (ii); the region immediately outside the crack plane where damage localises to the edges of the round embossing imprints(iii);an entirely elastic undamaged region outside the damage region where no damage and consequently no energy dissipation takes place. The shielding effect may be quantified by means of the shielding ratio WS,/ WMain where WMain is the energy dissipated in the fracture process zone in the plane of the main crack and WS is the energy dissipated outside the plane of the main crack. Both WMain and WS were estimated by the aid of the effective cohesive law determined for the unit cell. The shielding effect is computed and observed to be governed by the density of the indentations and relative size of the indentation.
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