PSI - Issue 28

G. Clerc et al. / Procedia Structural Integrity 28 (2020) 1761–1767 Gaspard Clerc/ Structural Integrity Procedia 00 (2020) 000–000

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Keywords: Fracture Mechanics, Wood Adhesive

1. Introduction Most of the engineering design nowadays is based on a stress/stiffness approach, meaning that the resistance of a structural member is estimated according to the maximum stress occurring in the structural element. To estimate the strength of the structural member its stiffness is obtained which is generally well correlated with the strength. This approach is relatively simple and robust. However, it fails to describe accurately the influence of defects such as cracks or delaminations. Indeed, in a stress/stiffness approach the structural member is simplified as a continuum with homogenous properties, however this is rarely the case. To take as example timber, cracks can be present in the timber due to the drying process and/or delamination can occur due to ambient humidity change. In a stress/stiffness approach those defects are generally considered using a strength reduction factor. This approach cannot accurately describe the complexity of the presence of defects and fails to predict for example if the size of a given defect is critical or not and if this defect will propagate or not. Also, it is generally too conservative. To answer these specific questions, another approach should be used. The theory of fracture mechanics was developed by Griffith (1921) and can be used to predict the material resistance to failure. Two main approaches can be used, a stress intensity factor approach and an energy based approach. Barret and Foschi (1977) investigated the stress intensity factor approach. In this paper only the energy based approach is investigated as it is more suited to anisotropic and heterogenous material such as bonded wood, and as the derivation of the main equation is less dependent on the sample geometry. Fracture mechanics is often used in material testing with samples having well defined properties. It is however rarely used in engineering design with structural members of arbitrary geometry. In timber construction standards, there are few design problems which require a fracture mechanic approach. One example of fracture mechanics in timber construction is found in Eurocode 5 (EC5), where the design of connections loaded perpendicular to the grain are done according to Linear Elastic Fracture Mechanics (LEFM) (Jockwer and Dietsch, 2018). (Gustafsson et al., 2001) proposed a design approach based on fracture mechanics for the design of glued-in-rods. This approach is however not yet implemented in design standards. Other authors (Bengtsson and Johansson, 2002), (Gustafsson, 1987) proposed to use fracture mechanics for the design of bonded glue line instead of using strength/stiffness criteria. The general issue with fracture mechanic based design is that despite a more sound physical basis, it is complex to acquire reliable Energy Release Rate values. This is due to the difficulty to determine such values, to the relatively scant available literature on the topic compared to strength values and to the larger scatter in material morphology and fracture properties. Another, difficulty, which is examined in this paper, is the complexity of deriving the crack-growth equation for arbitrary geometry. These points are summarized in table 1.

Table 1: Comparison between Stress/Stiffness and Fracture Mechanics approach for structure design

Stress/Stiffness Approach

Fracture mechanics Approach Material values are rarely available and more difficult to obtain Application more complicated (derivation of crack growth equation) Can be used to predict the crack propagation for specific loading situation

Material characteristic values are widely available

Simple design approach

Difficulty to deal with defects and their propagation in material

In this paper, the difficulty of applying fracture mechanics to arbitrary sized structural member is investigated. First the main steps to derive the fracture mechanics equation are shown for a well-known sample geometry (3 point End Notched Flexure sample, 3-ENF). Then these main steps are applied to a new sample geometry, the 3 points central crack flexure sample (3-CCF). This geometry was designed to investigate the effect of a specimen upscaling on the crack propagation. The size of the sample was however limited by the available testing machine. For the 3-CCF