STRENGTH, TOUGHNESS, FAILURE AND FRACTURE MORPHOLOGY
There are two fundamentally different approaches to the concept of strength and failure. The first is the classical strength of materials approach, attempting to understand strength and failure of timber in terms of the strength and arrangement of the molecules, the fibrils, and the cells by thinking in terms of a theoretical strength and attempting to identify the reasons why the theory is never satisfied.
The second and more recent approach is much more practical in concept since it considers timber in its current state, ignoring its theoretical strength and its microstructure and stating that its performance will be determined solely by the presence of some defect, however small, that will initiate on stressing a small crack; the ultimate strength of the material will depend on the propagation of this crack.
Many of the theories have required considerable modification for their application to the different fracture modes in an anisotropic material such as timber. Both approaches are discussed below for the more important modes of stressing.
Tensile strength parallel to the grain: Over the years a number of models have been employed in an attempt to quantify the theoretical tensile strength of timber. In these models it is assumed that the lignin and hemicelluloses make no contribution to the strength of the timber; in the light of recent investigations, however, this may not be valid for some of the hemicelluloses.
One of the earliest attempts modelled timber as comprising a series of endless chain molecules, and strengths of the order of 8000 MPa were obtained. More recent modelling has taken into account the finite length of the cellulose molecules and the presence of amorphous regions.
Calculations have shown that the stress needed to cause chain slippage is generally considerably greater than that needed to cause chain scission, irrespective of whether the latter is calculated on the basis of potential energy function or bond energies between the links in the chain; preferential breakage of the cellulose chain is thought to occur at the C–O–C linkage. These important findings have led to the derivation of minimum tensile stresses of the order of 1000–7000 MPa (Mark, 1967).
The ultimate tensile strength of timber is of the order of 100 MPa, though this varies considerably between species. This figure corresponds to a value between of 0.1 and 0.015 of the theoretical strength of the cellulose fraction. Since this accounts for only half the mass of the timber and since it is assumed, perhaps incorrectly, that the matrix does not contribute to the strength, it can be said that the actual strength of timber lies between 0.2 and 0.03 of its theoretical strength.
In attempting to integrate these views of molecular strength with the overall concept of failure, it is necessary to examine strength at the next order of magnitude, namely the individual cells. It is possible to separate these by dissolution of the lignin–pectin complex cementing them together.
Using specially developed techniques of mounting and stressing, it is possible to determine their tensile strengths. Much of this work has been done on softwood tracheids, and mean strengths of the order of 500 MPa have been recorded by a number of investigators. The strengths of the latewood cells can be up to three times those of the corresponding earlywood cells. Individual tracheid strength is therefore approximately five times greater than that of solid timber.
Softwood timber also contains parenchyma cells, which are found principally in the rays and lining the resin canals, and which are inherently weak. Many of the tracheids tend to be imperfectly aligned and there are numerous discontinuities along the cell, consequently it is to be expected that the strength of timber is lower than that of the individual tracheids.
Nevertheless, the difference is certainly substantial and it seems doubtful whether the features listed above can account for the total loss in strength, especially when it is realised that the cells rupture on stressing and do not slip past one another. When timber is stressed in tension along the grain, failure occurs catastrophically with little or no plastic deformation at strains of about 1%. Visual examination of the sample usually reveals an interlocking type of fracture that can be confirmed by optical microscopy.
However, the degree of interlocking is considerably greater in the latewood than in the earlywood. Whereas in the former, the fracture plane is essentially vertical, in the latter the fracture plane follows a series of shallow zigzags in a general transverse plane; it is now thought that these thin walled cells contribute very little to the tensile strength of timber. Thus, failure in the stronger latewood region is by shear, while in the earlywood, though there is some evidence of shear failure, most of the rupture appears to be transwall or brittle.
Examination of the fracture surfaces of the latewood cells by electron microscopy reveals that the plane of fracture occurs either within the S1 layer or, more commonly, between the S1 and S2 layers. Since shear strengths are lower than tensile strengths these observations are in accord with comments made previously on the relative superiority of the tensile strengths of individual fibres compared with the tensile strength of timber.
Failing in shear implies that the shear strength of the wall layers is lower than the shear strength of the lignin–pectin material cementing together the individual cells. Confirmation of these views is forthcoming from the work of Mark (1967), who calculated the theoretical strengths of the various cell-wall layers and showed that the direction and level of shear stress in the various wall layers are such as to initiate failure between the S1 and S2 layers.
Mark’s treatise received a certain amount of criticism on the grounds that he treated one cell in isolation, opening it up longitudinally in his model to treat it as a two dimensional structure; nevertheless, the work marked the beginning of a new phase of investigation into elasticity and fracture and the approach has been modified and subsequently developed.
The extension of the work has explained the initiation of failure at the S1–S2 boundary, or within the S1 layer, in terms of either buckling instability of the microfibrils, or the formation of ruptures in the matrix or framework giving rise to a redistribution of stress.
Thus, both the microscopic observations and the developed theories appear to agree that failure of timber under longitudinal tensile stressing is basically by shear unless density is low, in which case trans-wall failure occurs. However, under certain conditions the pattern of tensile failure may be abnormal. Firstly, at temperatures in excess of 100°C, the lignin component is softened and its shear strength is reduced.
Consequently, on stressing, failure will occur within the cementing material rather than within the cell wall. Secondly, trans-wall failure has been recorded in weathering studies where the mode of failure changed from shear to brittle as degradation progressed; this was interpreted as being caused by a breakdown of the lignin and degradation of the cellulose, both of which processes would be reflected in a marked reduction in density (Turkulin and Sell, 1997).
Finally, in timber that has been highly stressed in compression before being pulled in tension, it will be found that tensile rupture will occur along the line of compression damage which, as will be explained below, runs transversely. Consequently, failure in tension is horizontal, giving rise to a brittle type of fracture. In the literature a wide range of tensile failure criteria is recorded, the most commonly applied being some critical strain parameter, an approach that is supported by a considerable volume of evidence, though its lack of universal application has been pointed out by several workers.
Compression strength parallel to the grain: Few attempts have been made to derive a mathematical model for the compressive strength of timber. One of the few, and one of the most successful, is that by Easterling et al. (1982). In modelling the axial and transverse compressive strength of balsa, these authors found that their theory – which related the axial strength linearly to the ratio of the density of the wood to the density of the dry cell wall material, and the transverse strength to the square of this ratio – was well supported by experimental evidence. It also appears that their simple theory for balsa may be applicable to timber of higher density.
Compression failure is a slow-yielding process in which there is a progressive development of structural change. The initial stage of this sequence appears to occur at a stress of about 25% of the ultimate failing stress (Dinwoodie, 1968), though Keith (1971) considers that these early stages do not develop until about 60% of the ultimate.
There is certainly a very marked increase in the amount of structural change above 60%, which is reflected by the marked departure from linearity of the stress– strain diagram. The former author maintains that linearity here is an artefact resulting from insensitive testing equipment and that some plastic flow has occurred at levels well below 60% of the ultimate stress.
Compression deformation assumes the form of a small kink in the microfibrillar structure, and because of the presence of crystalline regions in the cell wall, it is possible to observe this feature using polarisation microscopy (Fig. 1). The sequence of irreversible anatomical changes leading to failure originates in the tracheid or fibre wall at that point where the longitudinal cell is displaced vertically to accommodate the horizontally running ray.
As stress and strain increase, these kinks become more prominent and increase numerically, generally in a preferred lateral direction, horizontally on the longitudinal–radial plane and at an angle to the vertical axis of from 45° to 60° on the longitudinal–tangential plane. These lines of deformation, generally called a crease and comprising numerous kinks, continue to develop in width and length; at failure, defined in terms of maximum stress, these creases can be observed by eye on the face of the block of timber (Dinwoodie, 1968).
At this stage there is considerable buckling of the cell wall and delamination within it, usually between the S1 and S2 layers. Models have been produced to simulate buckling behaviour, and calculated crease angles for instability agree well with observed angles (Grossman and Wold, 1971).
Dinwoodie (1974) has shown that, the angle at which the kink traverses the cell wall (Fig. 1) varies systematically between earlywood and latewood, between different species, and with temperature. Almost 72% of the variation in the kink angle could be accounted for by a combination of the angle of the microfibrils in the S2 layer and the ratio of cell-wall modulus of elasticity in longitudinal and horizontal planes. Attempts have been made to relate the size and number of kinks to the amount of elastic strain or the degree of viscous deformation.
Under conditions of prolonged loading, total strain and the ratio of creep strain to elastic strain (relative creep) appear to provide the most sensitive guide to the occurrence of cell-wall deformation; the gross creases appear to be associated with strains of 0.33% (Keith, 1972). The number and distribution of kinks depend on temperature and moisture content.
Increasing moisture content, though resulting in a lower strain to failure, results in the production of more kinks, although each is smaller in size than its ‘dry’ counterpart; these are to be found in a more even distribution than they are in dry timber. Increasing temperature results in a similarly wider distribution of the kinks.
Static bending: In the bending mode timber is subjected to compression stresses on the upper part of the beam and tensile on the lower part. Since the strength of clear timber in compression is only about one third that in tension, failure will occur on the compression side of the beam long before it will do so on the tension side. In knotty timber, however, the compressive strength is often equal to and can actually exceed the tensile strength. As recorded in the previous section, failure in compression is progressive and starts at low levels of stressing.
Consequently, the first stages of failure in bending in clear straight-grained timber will frequently be associated with compression failure, and as both the bending stress and consequently the degree of compression failure increase, so the neutral axis will move progressively downwards from its original central position in the beam (assuming uniform crosssection), thereby allowing the increased compression load to be carried over a greater crosssectional area. Fracture occurs when the stress on the tensile surface reaches the ultimate strength in bending.
Toughness: Timber is a tough material, and in possessing moderate to high stiffness and strength in addition to its toughness, it is favoured with a unique combination of mechanical properties emulated only by bone which, like timber, is a natural composite. Toughness is generally defined as the resistance of a material to the propagation of cracks. In the comparison of materials it is usual to express toughness in terms of work of fracture, which is a measure of the energy necessary to propagate a crack, thereby producing new surfaces.
In timber the work of fracture, a measure of the energy involved in the production of cracks at right angles to the grain, is about 104 J/m2 ; this value is an order of magnitude less than that for ductile metals, but is comparable with that for the manmade composites. Now the energy required to break all the chemical bonds in a plane cross section is of the order of 1–2 J/m2 , that is, four orders of magnitude lower than the experimental values. Since pull-out of the microfibrils does not appear to happen to any great extent, it is not possible to account for the high work of fracture in this way (Gordon and Jeronimidis, 1974; Jeronimidis, 1980).
One of the earlier theories to account for the high toughness of timber was based on the work of Cook and Gordon (1964), who demonstrated that toughness in fibrereinforced materials is associated with the arrest of cracks made possible by the presence of numerous weak interfaces. As these interfaces open, so secondary cracks are initiated at right angles to the primary, thereby dissipating the energy of the original crack.
This theory is applicable to timber, but it is doubtful whether the total discrepancy in energy between experiment and theory can be explained in this way. Subsequent investigations have contributed to a better understanding of toughness in timber (Gordon and Jeronimidis, 1974; Jeronimidis, 1980).
Prior to fracture it would appear that the cells separate in the fracture area, and on further stressing these individual and unrestrained cells buckle inwards, generally assuming a triangular shape. In this form they are capable of extending up to 20% before final rupture thereby absorbing a large quantity of energy. Inward buckling of helically wound cells under tensile stresses is possible only because the microfibrils of the S2 layer are wound in a single direction.
Observations and calculations on timber have been supported by glass-fibre models, and it is considered that the high work of fracture can be accounted for by this unusual mode of failure. It appears that increased toughness is possibly achieved at the expense of some stiffness, since increased stiffness would have resulted from contrawinding of the microfibrils in the S2 layer.
So far, we have discussed toughness in terms of only clear timber. Should knots or defects be present, timber will no longer be tough and the comments made earlier as to viewpoint are particularly relevant here. The material scientist sees timber as a tough material, but the structural engineer will view it as a brittle material because of its inherent defects.
Loss of toughness, however, can arise not only on account of the presence of defects and knots, but also through the effects of acid, prolonged elevated temperatures, fungal attack, or the presence of compression damage with its associated development of cell-wall deformations; these result from overstressing within the living tree, or in the handling or utilisation of timber after conversion (Dinwoodie, 1971; Wilkins and Ghali, 1987). Under these abnormal conditions the timber is said to be brash and failure occurs in a brittle mode.
Fatigue: Fatigue, is usually defined as the progressive damage and failure that occur when a material is subjected to repeated loads of a magnitude smaller than the static load to failure; it is, perhaps, the repetition of the loads that is the significant and distinguishing feature of fatigue.
In fatigue testing the load is generally applied in the form of a sinusoidal or a square wave. Minimum and maximum stress levels are usually held constant throughout the test, though other wave forms, and block or variable stress levels, may be applied. The three most important criteria in determining the character of the wave form are:
- the stress range, Δs, where Δs = σmax – σ min
- the R-ratio, where R = σmin/σmax, which is the position of minimum stress (σmin) and maximum stress (σmax) relative to zero stress. This will determine whether or not reversed loading will occur. It is quantified in terms of the R-ratio, e.g. a wave form lying symmetrically about zero load will result in reversed loading and have an R-ratio of -1
- the frequency of loading. The usual method of presenting fatigue data is by way of the S–N curve, where log N (the number of cycles to failure) is plotted against the mean stress S; a linear regression is usually fitted.
Using test pieces of Sitka spruce, laminated Khaya and compressed beech, Tsai and Ansell (1990) carried out fatigue tests under load control in four point bending. The tests were conducted in repeated and reversed loading over a range of five R-ratios at three moisture contents (Fig. 2).
Fatigue life was found to be largely independent of species when normalised by static strength, but was reduced with increasing moisture content and under reversed loading. The accumulation of fatigue damage was followed microscopically in test pieces fatigued at R = 0.1 and was found to be associated with the formation of kinks in the cell walls and compression creases in the wood.
In related work Bonfield and Ansell (1991) investigated the axial fatigue in constant-amplitude tests in tension, compression and shear in both Khaya and Douglas fir using a wide range of R-ratios, and confirmed that reversed loading is the most severe loading regime.
Fatigue lives measured in all-tensile tests (R = 0.1) were considerably longer than those in all-compression tests (R = 10), a result that they related to the lower static strength in compression relative to tension. S–N data at different R-ratios yielded a set of constant lifelines when alternating stress was plotted against mean stress; these lifelines possessed a point of inflection when loading became all compressive. More information on fatigue in timber is to be found in Dinwoodie (2000).
Engineering Approach to Strength and Fracture
Fracture mechanics, provides a second approach to the concept of strength and failure. This is a more practical one and is based on the premise that all materials contain flaws or minute cracks, and that performance is determined solely by the propagation of cracks arising from these defects.
The largest flaw will become self-propagating when the rate of release of strain energy exceeds the rate of increase of surface energy of the propagating crack. The application of fracture mechanics to timber did not take place until as late as 1961. Part of the reason is due to the modelling of wood as an orthotropic material, and consequently there are six values of the fracture toughness for each of the three principal modes of crack propagation.
In timber, however, macroscopic crack extension almost always occurs parallel to the grain even though it is initiated in a different plane, thereby giving rise to a mixed-mode type of failure. The value of fracture toughness (Kc) depends not only on orientation (as implied above), but also on the opening mode, orientation, timber density, moisture content, specimen thickness, and crack speed (see e.g. Dinwoodie, 2000).
Thus, the value of KIc (Kc in mode I) in the four weak parallel-to-the-grain systems is about one-tenth that in the two tough across-the-grain systems. Kc increases with increasing density and with increasing specimen thickness.
Fracture mechanics has been applied to various aspects of timber behaviour and failure, e.g. the effect of knots, splits and joints, and good agreement has been found between predicted values using fracture mechanics and actual strength values. Examples are to be found in Dinwoodie (2000).
STRUCTURAL DESIGN IN TIMBER
Timber, like many other materials, is graded according to its anticipated performance in service, but because of its inherent variability distinct grades of material must be recognised. The grading of timber for structural use may be carried out visually or mechanically.
Visual grading, as the title implies, is a visual assessment of the quality of a piece of structural timber, and is carried out against the permissible defects limits given in BS EN 14081-1. However, visual grading is a laborious process since all four faces of the timber should be examined.
Furthermore, it does not separate naturally weak from naturally strong timber and hence it has to be assumed that pieces of the same size and species containing identical defects have the same strength. Such an assumption is invalid and leads to a most conservative estimate of strength. The permissible defects limits are set out in BS 4978 and BS 5756 if using the national (British) system of grading and the various visual grade and species combinations are attributed to strength classes in BS EN 1912. If adopting a European approach, the permissible defects limits are set out in BS EN 14081-1, and the various visual grade and species combinations are again attributed to strength classes in BS EN 1912.
Many of the disadvantages of visual grading can be removed by machine grading, a process that was introduced commercially in the 1970s with the use of bending machines that either placed the timber under a constant load and measured deflection or subjected the timber to a constant deflection and measured the load that had to be applied. The principle underlying this process is the high correlation that has been found to exist between the moduli of elasticity and rupture.
Grading machines based on this relationship usually provide higher yields of the higher grades than are achieved by visual grading. Since the above relationship varies among different species, it is necessary to set the grading machine for each species or species group and its geographical location (see below). Over the last decade a number of different types of machine have been developed to assess the measurable parameters that can be related to timber strength.
Some of these are based on X-rays or stress waves, either acoustical or vibrational in origin. For each of the machine types mentioned above, includindg the original bending machine, BS EN 14081 requires that the relationship between timber strength and the machine-indicated parameters (which is used to derive the settings to operate the machine in grading) is appropriate for the species of timber and the geographical region in which the tree was growing (BS EN 14081-1 and BS EN 14081-2).
Europe is now divided into four geographical regions for this purpose. Each region has been responsible for producing machine settings for the timber species that grow in that region and are used structurally in that region. The machine settings from the four regions are set out in BS EN 14081-4 while additional requirements for factory production control are presented in BS EN14081-3.
We should note in passing that the moisture content of the timber has a marked influence on the selection of grading machine. Thus while dry timber can be graded by all machine types, X-ray and stress-wave machines are normally limited to a timber moisture content of around 20%. Grading of green timber can currently only be done on bending machines, as the larger sectional size of green timber conveniently offsets the lower modulus.
Under the new European system the grade mark will include the specification number used in the grading (BS EN 14081):
- the species or species group
- the timber condition (green or dry)
- the strength class (see below)
- the grader or company name
- the company registration number
- the certification body (logo).
Graded timber is assigned to the strength classes contained in BS EN 338, a standard that provides the characteristic values for each of the strength properties and density for each of the eighteen strength classes of timber. A reduced version of Table 1 of BS EN 338, containing only six of the strength classes, is given in Table 1 to illustrate the type of data presented.
The formation of the European Union as a free trade area and the production of the Construction Products Directive (CPD) led automatically to the introduction and implementation of new European standards and the withdrawal of conflicting national standards. Such an approach has much merit, but as far as the UK is concerned, it has led to changes in both the derivation and use of working stresses.
First, test results are now expressed in terms of a characteristic value expressed in terms of the lower 5th percentile, in contrast to the former use in the UK of a mean value and its standard deviation. Second, in the design of timber structures the new Eurocode 5 is written in terms of limit state design in contrast to the former UK use of permissible stress design. Third, the number of strength classes in the new European system is greater than in the UK system, thereby giving rise to mismatching of certain timbers.
As noted above, the design of timber structures must now be in accordance with Eurocode 5 (BS EN 1995-1-1:2004). The characteristic values for timber given in BS EN 338 must be reduced according to the period of loading and service class (defined in terms of level of humidity). Values of Kmod (duration of load and service class) and Kdef (creep and service class) are set out in Eurocode 5 for each of the three service classes.
It is understood that although BS 5268-2:2007 is likely to be withdrawn officially at the end of October 2012, it is most likely that permissible stress design using the grade stresses for the various strength classes set out in BS 5268-2:2007 will continue for at least another decade in certain quarters of the industry employing where relevant Parts 1 and 2 of BS 5268-6. Certain grades of the various wood-based panels may be used for structural purposes. The characteristic values are calculated according to BS EN 1058 and are listed in BS EN12369-1 and BS EN 12369-2.