Viscoelastic Deformation in Timber
Timber is neither truly elastic in its behaviour nor truly viscous, but rather a combination of both states; such behaviour is usually described as viscoelastic and, in addition to timber, materials such as concrete, bitumen and the thermoplastics are also viscoelastic in their response to stress.
Viscoelasticity implies that the behaviour of the material is time dependent; at any instant in time under load its performance wilI be a function of its past history. Now if the time factor under load is reduced to zero, a state that we can picture in concept, but never attain in practice, the material will behave truly elastically, and we have seen in former articles how timber can be treated as an elastic material and how the principles of orthotropic elasticity can be applied.
However, where stresses are applied for a period of time, viscoelastic behaviour will be experienced and, while it is possible to apply elasticity theory with a factor covering the increase in deformation with time, this procedure is at best only a first approximation.
In a material such as timber, time dependent behaviour manifests itself in a number of ways, of which the more common are creep, relaxation, damping capacity and the dependence of strength on duration of load. When the load on a sample of timber is held constant for a period of time, the increase in deformation over the initial instantaneous elastic deformation is called creep, and Fig. 1 illustrates not only the increase in creep with time, but also the subdivision of creep into a reversible and an irreversible component – of which more will be said in a later section.
Most timber structures carry a considerable dead load and the component members of these will undergo creep; the dip towards the centre of the ridge of the roof of very old buildings bears testament to the fact that timber does creep. However, compared with thermoplastics and bitumen, the amount of creep in timber is appreciably lower.
Viscoelastic behaviour is also apparent in the form of relaxation, where the load necessary to maintain a constant deformation decreases with time; in timber utilisation this has limited practical significance and the area has attracted very little research. Damping capacity is a measure of the fractional energy converted to heat compared with that stored per cycle under the influence of mechanical vibrations; this ratio is time dependent. A further manifestation of viscoelastic behaviour is the apparent loss in strength of timber with increasing duration of load.
Creep in Timber
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Modelling of Deformation Under Variable
Moisture content: Mathematical modelling of viscoelastic creep has been described in the above pharagraphs. The requirement for a model of mechano-sorptive creep was originally set out by Schniewind (1966) and later developed by Grossman (1976) and Mårtensson (1992).
More recently, the list of requirements that must be satisfied for such a model has been reviewed and considerably extended by Hunt (1994); aspects of sorption were included on the list. Many attempts have been made over the last three decades to develop a model for mechano-sorptive behaviour. A few of these models have been explanatory or descriptive in nature, seeking relationships at the molecular, ultrastructural or microscopic levels.
Most of them, however, have been either purely mathematical, with the aim of producing a generalised constitutive equation, or partly mathematical, where the derived equation is linked to some physical phenomenon, or change in structure of the timber under stress.
More information on the parameters that have been included in these mathematical models as well as the types of models that have been developed over the years are to be found in Ranta-Maunus (1973, 1975), Tong and Ödeen (1989b), Hunt (1994), Morlier and Palka (1994) and Hanhijärvi (1995).
It may be recalled that it is fifty years since the concept of mechano-sorptive deformation was first established (Armstrong and Kingston, 1960). Since then, the concept of mechano-sorptive deformation – which is primarily a function of the amount of moisture change and associated dimensional changes – has been clearly separated from that of viscoelastic creep, which is present under both constant and changing levels of moisture and which is primarily a function of time.
However, in complex cases involving environmental changes, there appears in certain circumstances to be a small interaction between viscoelastic creep and mechano-sorptive creep, albeit that this is probably not a common mechanism (Hanhijärvi and Hunt, 1998; Matar and Hunt, 2003). Hunt (1999) employed a new way to characterise wood creep by plotting data in the form of strain rate against strain; solution of this differential equation led to the more normal relation of strain against time.
It was then found that normalisation of both the ordinate and abscissa resulted in a single master creep curve for both juvenile and mature wood from a single sample and, more important, approximately also for all test humidities. The traditional approach to the quantitative modelling of creep under variable humidity conditions incorporated four separate components, three of which relate to mechano-sorptive behaviour, while the fourth component deals with viscoelastic creep.
However, owing to the difficulty of analysing the three separate components of mechano-sorptive creep, some workers have resorted to a different approach by taking only two components, one reversible and one irreversible, which are then added to the viscoelastic component to quantify total creep (Matar and Hunt, 2003).
It should be appreciated that such a model is based almost entirely on the convenience of handling of the experimental data. Using their new model, Matar and Hunt regard the gradually decreasing increments of additional mechano-sorptive creep during humidity changes as the irreversible component (while the sample is still under load) and this component can then be quantified by an exponential-decay type of equation. Such analysis implies that there is an eventual creep limit, a conclusion that is not shared by many workers (e.g. Navi et al., 2002).
The remaining creep/recovery component in Matar’s and Hunt’s new model is treated as reversible, and the term pseudocreep is applied to it since this component is not a creep component, but rather a differential expansion or shrinkage component, the magnitude of which depends on the level of strain (Hunt, 2004). The real merit of such a model is that it allows the estimation of a practical upperbound value for creep in Service Classes 1 and 2 of Eurocode 5.
Equally important, the amount of mechano-sorptive limiting creep was nearly the same at 63 and 90% relative humidity. This implies that the mechano-sorptive creep occurs mainly at low and intermediate rather than high moisture contents; its importance, therefore, is that it correlates with swelling and shrinkage, which are also greater at lower moisture contents. This is a very significant conclusion.
Following on from the theoretical explanation of mechano-sorptive behaviour mentioned earlier, the idea has been developed of using the concept of physical ageing developed for polymers to explain mechano-sorptive effects in timber (Hunt and Gril, 1996).
Thus it is argued that the effects of humidity changes require the additional measurement of the increased activity associated with the molecular destabilisation and its relaxation-time constraint associated with the physical ageing phenomenon (thermodynamic equilibrium); the application of this concept suggests that the speed of moisture change might be important in mechano-sorptive deformation.
This concept has been taken up and developed by Ishimaru and others in Japan (Ishimaru, 2003). In a further quest to refine the modelling of creep, especially in its relationship to the anatomy of the wood, Hunt and Gril (2006) have recently focused attention on the anomalies that take place during swelling and shrinkage and of the dangers in assuming that these processes can be characterised by a single value.
From modelling, it was demonstrated that the restraint produced by the S1 layer of the cell wall is most important and that the level of this restraint relaxes with time and with changes in moisture content.
Such findings complement the work of Esteban et al. (2004), who found that repeated moisture cycling resulted in a considerable reduction in moisture sorption and rate of shrinkage in various species, a phenomenon that they termed swelling fatigue, and is a further example of the physical ageing process.
Although much work has been undertaken to try to understand and model mechano-sorptive creep, especially in trying to increase the accuracy of the model, much still remains to be done.
While the primary variables have been identified, great difficulty arises in quantifying how these vary with the number and magnitude of the changes that take place in moisture content and their associated effects on the physical and chemical structure of wood.