Gluing wood is one of a few methods of inseparable and stiff connecting wooden elements. Usually, these connections are done in a method that allows the use of the greatest shearing strength of the created glue-line, and during designing, they are placed in such locations of the construction in which axial and transverse forces dominate, avoiding places subject to bending and torsional loads.
Constructions of wood joinery and skeletal furniture belong to the group of 2-D or 3-D systems. From the strength point of view structural nodes are located in irrational places, in corners. Of course this method are used for hundreds of years, ensuring technology of assembly and aesthetics of implementation. In spite of how furniture is used, glue-lines are subject to damage even before the state of stresses in wooden elements reaches acceptable values. Therefore, the correct design of the construction requires conducting destructive strength tests each time. The conclusions and guidelines resulting from them are the basis for modernising implemented or developing new constructions. These types of methods of design are not the fastest and certainly not the cheapest. That is why, the leading role in designing should be played by strength calculation of wooden glue-lines. Unfortunately, the methods of these calculations are not, as yet, recognised well and described. In many analyses of the strength of wooden joints, a continuity and homogeneity of the glue-line is assumed. Such an assumption is very convenient from the analytical point of view, however, for practical reasons, too risky. In the process of bonding structural elements, there are often deficiencies relative to the technological assumptions, which leads to:
• the formation of loosenesses, that is heterogeneities, in which the adhesive occurs in a state that is not completely hard, due to the inaccurate mixing of its ingredients,
• the occurrence of gas pockets in cohesive layers, often as a result of too vigorous mixing of finished adhesives or all of its ingredients,
• the formation of unglued areas, when the gas pockets applied with the adhesive begin to move in an unhardened glue-line towards the adherent, where they join air contained in micropores, open fibres or wood vessels,
• the formation of adhesive spills as a result of applying too much adhesive on the surfaces of connectors joined together.
In several works of analytical character, the issue of heterogeneity has already been undertaken, limiting it to the properties attributed to glue-line connecting metal adherents. Apalak and Davies (1994) designed angular joints of metal elements connected with epoxy adhesives, taking into account the sizes and form of hardened excesses of glue, hereinafter called spills. On the basis of the studies conducted, they claimed that spills significantly reduce tensions in glue-line and increase the strength of the joints. Kuczmaszewski (1995) came to similar conclusions on the basis of studies of metal lap joints, who in his studies took into account the discontinuity of a glue-line visible in the form of gas pockets and unglued areas. The heterogeneity of glue-line was also the subject of studies of Francis and Gutierrez-Lemini (1984), who, using the finite element method, modelled cracks and gas pockets in the glue-line, stating the concentration of stresses around the source of discontinuity of the glue-line.
This chapter will describe the issues related to the influence of heterogeneity of glue-line of wooden joints on the distribution of tangential stresses in the glue-line, and, in particular, with the importance of gas pockets and unglued areas.
In the solutions of Wnuk (1981) and L^czkowski (1988), concerning nonlinear models of the mechanics of cracking, it was assumed that around the gas pocket with a radius R under the influence of load, a gap is formed in the shape of a circular ring with a radius R and (R + c). The front of the gap is surrounded by a plastic area with a radius rp1 (Fig. 6.48).
Fig. 6.48 The calculation scheme of energy balance—gas pocket
By treating the area of spheres with a radius R + c + rpl as isolated, they presented the balance of energy processes taking place during cracking in the following form:
U = Uo-Uod + Up + Upl, (6.143)
where
Uo elastic energy of the homogeneous centre,
Uod offload energy released after the crack has been created,
Up surface energy, constituting residues of offload energy,
Upl work of structural deformation, constituting a part of offload energy.
Offload energy for gas pocket with the module E = 0 amounts to:
and surface energy:
where
0 proper surface energy.
The difficulty associated with identifying the radius of the plastic area rp1 was solved by Kuczmaszewski (1995), by adopting, after Wnuk (1981), the equation:
where
Rek plasticity limit of the glue, r normal stress.
Therefore, the energy of plastic deformation has been calculated from the equation:
where
ee relative structural elongation
By entering the obtained equations to the equation of energy balance, the final form is obtained:
(6.148)
To determine the critical value of the radius of the gas pocket Rkr, at which the initiation of a crack gap takes place, the first derivative of the balance equation should be compared to zero and c substituted by zero. As a result of these calculations, the following equation is obtained:
By assuming of surface energy, plastic elongation spi and other elastic features, on the basis of characteristics a = f(s), the variability of critical radius, which initiates a process of cracking in the glue-lines of wooden joints can be specified.
Under the influence of load impact a, the radius of unglued area R increases to R + c (Fig. 6.49). By adopting the assumption that deformations at the border of phases are the same, Kuczmaszewski (1995) assumed after Wnuk (1981) that loaded energy now takes the form: the calculation scheme of energy balance is as follows:
Fig. 6.49 The calculation scheme of energy balance—unglued area
where
Ex, Ek elasticity modules of the adherent and glue-line.
Due to the clear difference of phases between the glue and the adherent on wooden joints, the ingredient of surface energy in the balance equation was replaced by work needed to separate these phases, that is, work of adhesion Ws on the surface of the circular ring with a radius R and R + c. Therefore,
energy of plastic deformation:
ek
and the energy equation takes the form:
|
Rek |
3 |
‘1 г |
+ Ws • n • |
(R + c)2—R2 |
|
IVRk — |
[Ex Es |
|
U = Uo—— — • (R + c)3 |
|
R, |
|
2 |
|
ek |
|
•(Rex + Rek). |
+ £e • n2 (R + c)
ek
(6.153)
where
Rex plasticity limit of the adherent.
Like before, the critical value of the radius of heterogeneity (unglued areas) is obtained after differentiating the energy equation U with respect to R + c and the corresponding transformations:
Assuming a work of adhesion Ws, for different materials (Proszyk et al. 1997), and a elastic characteristics of adherents, the variability of the critical radius which initiates the process of cracking in the glue-lines of wooden joins can be determined.
The process of destroying adhesive joints is generally violent by nature, regardless of the elastic characteristics of the glue. Hardened glue in the form of a glue-line stiffened additionally through elements of connectors shows greater stiffness than the same glue hardened in the form of a sample for studying the shear module of elasticity (Smardzewski and Dzi^gielewski 1994; Dzi^gielewski and Wilczynski 1990). Due to the fact that processes of decohesion begin within the ends of the glue-line, where the greatest tangential stresses occur, the existence of heterogeneity in this area can only facilitate the process.
Gas pockets present in glue-line contribute to an increase in stresses around the source of heterogeneity. This phenomenon initiates the process of decohesion, thus reducing the strength of the connection. Unglued areas, such as gas pockets, constitute a potential source for initiating the processes of friable cracking and decrease the strength of the connection. Increasing the value of stresses in glue-line to the limit of plasticity of the glue suddenly decreases the critical radius value of heterogeneity, which reaches values many times smaller than the thickness of the glue-line. In such conditions, even the smallest type of heterogeneity in the form of a gas pocket, unglued area or looseness constitutes the source of friable cracking. Due to the significant influence of heterogeneity of the adhesive on the strength of joints, the processes of preparing adhesive mass and elements meant for gluing should be done with extreme care.
