(A2) by the standard derivation of mathematical statistics. By defining A j + A 2 = A ', and assuming it has a distribution (p(A), the total load required is then P(h) = 2 KOD2A'j$P(A,r)(p(A)rdrdA (4-11) A r Now, A = A[ + A 2 - 2S(r/2) - h = A - h - 2S(r/2) where A - h is the overlap between the peaks of the pair of asperities considered. Because of misalignment, the peaks may overlap without being any contacts. Further, if we define the result of the r-integration as P 0 ( A - h ) = 2^y | J P ( A -h-2S(r/2),r)rdr (4-12) o then P(h) = oA j>0 (A - h)(p(A )dA (4-13) h In the same way, according to Greenwood and Tripp (1970-1971), if we write A0(A-h) = 2nco ™JA(A-h-2S(r/2),r)rdr (4-14) o the total contact area is A(h) = Q)A J A O ( A -h)(p(A)dA (4-15) h For simplicity, it was assumed that the surfaces are covered with paraboloidal asperities to conform to general Hertz approximation. The asperity shape is then z = S( X) = A 212R where R is the radius of curvature at the peak. Thus 2S(r/2) = r2/4R . Because of the misalignment, the Hertz theory for the contact of two paraboloids can be only approximately applied, since the normal load is not acting vertically and there must also be a tangential component. However, according to Greenwood and Tripp (1970-1971), the tangential component was generally 109 negligible due to the slopes of real surfaces. By applying Hertz's theory concerning the relationship between load and elastic modulus and radius of curvature for two contact bodies (Johnson 1985), Equation (4-12) becomes P 0 ( A '-h) = 2ma j>( A -h-2S(r/2),r)rdr = -KCOE*(—)2 r(A - h - - ^ - r ) 2 rdr .I 3 4R \6-j2 - -7tcoE*R*(A-h)2 (4-16) 15 Then the total load required is °° 1 fS F? 3 °° — P(h) = QJA fP0(A -h)

( 5 ) 6 ? 5 , in which

0, with a maximum contact area up to 1%. It was found that a>R o~ was reasonably constant with a value of around 0.05, and k was around 100 MPa for metal materials. For wood materials, as shown in Figure 4.1, the compression was generally up to the last stage with a negative separation or h h compression. When a negative separation occurs (—7 < 0), Fn(—7)can be solved by a h mathematical tool (Mathematica 2007). For example, when —r = -2, we have <7 F2(-2)=^L= {(s + 2)2

/?'cT )2F2(A)(100%) * 100% G The results demonstrate that the contact area is surface roughness dependent. Theoretically, in order to achieve a full 100% contact area, the amount of compression seems to be approximately 4.4 times of the surface equivalent RMS roughness (50 fim). Figure 4.5 shows the theoretical prediction of contact area in relation to nominal veneer-to-veneer compression. Based on this model, it seems that the contact area increased nonlinearly with increasing nominal compression. Due to the nature of an integration of normal distribution of asperity heights, the contact area seems to approach to its maximum value. Note particularly that using nominal compression in the model can successfully deal with the variation of veneer surface roughness for generic prediction whereas the compression ratio (CR), generally used in the manufacturing of wood composites, is essentially thickness and surface roughness dependent. Figures 4.6 shows how contact area changes in terms of veneer compression ratio (CR) and surface roughness based on the model prediction. Three veneer roughness grades were simulated, namely, smooth, medium rough and rough. Their three equivalent RMS roughness (cr ) values were based on the roughness measurement results in Chapter 3 (see Figure 3.8). In order to achieve an 80% or higher contact area, the CR required was about 5.0%, 7.0% and 10.0% for the smooth, medium rough and rough veneer, respectively. This implies that processing the rough 115 veneer will inevitably result in a lower material recovery when manufacturing into quality veneer products. As a result, it seems to be beneficial to sort veneer based on its surface roughness. For a typical plywood/LVL mill with an annual capacity of 250 million ft2 (on a 3/8" basis), every reduction of 1% CR will translate to about $300,000 savings. 4.5 Model Validation As shown in Figure 4.7, the comparison was made for the contact area between the measured and predicted in terms of nominal compression. In general, it was found that the real contact area measured from the glue coverage map, before it reached about 50%, was larger compared to the theoretical prediction. This is probably due to the fact that during compression, the glue could flow or move and veneers would experience some lateral expansion with a mixture of elastic and plastic deformation whereas in the theoretical model, only elastic deformation was assumed. With increasing nominal compression, the predicted contact area tended to be larger than the measured contact area. This is probably because: 1) the theoretical model assumed that all asperities had identical (parabolic) shapes, differing only in heights from their mean lines of the plane; and 2) in reality, roughness is not uniformly random as defined by the normal distribution in the model. As shown early in Figure 4.3, veneer surface roughness is more abnormal. Further research is needed to modify the model to consider veneer lateral expansion, plastic deformation and glue movement, and so on. 4.6 Conclusions Contact mechanics, classic Hertz theory and Greenwood and Tripp's theory were adopted to characterize contact area of the two nominally flat rough surfaces in relation to surface roughness parameters and nominal separation. To simulate veneer-to-veneer contacts which permit compression in both separation and compression (negative separation) modes, four stages of contacts between the two non-conforming wood surfaces were proposed in terms of the two surface roughness profiles and the separation between the two mean lines of planes. The Greenwood and Tripp's theory, generally used for generic metal materials, was extended to the stage of compression. In the meantime, the veneer-to-veneer contact area was experimentally investigated under different loads through an image analysis of glue coverage. Some key inputs to the modified Greenwood and Tripp's model were determined to predict the contact area during veneer compression. The model demonstrated that the contact area was mainly 116 determined by surface density of asperity peaks, average radius of the asperities, equivalent RMS surface roughness and nominal separation (or compression). Compared to the measured contact area, the predicted contact area was somehow underestimated before it reached about 50%, which could be mainly due to the fact that the model developed did not consider veneer plastic deformation, lateral expansion and glue transfer during compression. However, with increasing nominal compression, the predicted contact area tended to be larger than the measured contact area. Further research is warranted to modify the theoretical model for improved prediction of the contact area and resulting stress. 117 a) Before contact (separation h » 0 ) A A A A / A A A b) Start to contact (separation h>0) / f r i f t i i I c) Certain contacts with zero separation (separation h = 0) d) Fu l l contacts after compression (separation h < 0) Figure 4.1 Stages of the contact between two non-conforming body surfaces 118 r «— • Mean line of plane 2 Mean line of plane 1 £ Deformation or indentation: A = h - (Aj + A'2) Figure 4.2 Contacts of two nominally flat rough surfaces 119 E S i i o o d csi o (D O > X Veneer loose side: R = 39 um I I o o O csi o m o > X Veneer tight side: R = 32 jim Figure 4.3 Typical 2-D veneer surface roughness profiles at the loose side and tight side 120 CO a> n u a c o o 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 h Nominal compression veneer-to-veneer — (negative separation) 5.0 CO Q. S W (0 £ 4-* CO Figure 4.4 The relationship between contact area, stress and nominal veneer-to-veneer compression 121 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Nominal compression veneer-to-veneer — (negative separation) a Figure 4.5 The theoretical prediction of contact area in relation to nominal veneer-to-veneer compression 0 2 4 6 8 10 12 14 16 18 20 Compression ratio (%) Figure 4.6 The theoretical prediction of contact area in terms of veneer compression ratio (CR) and surface roughness 123 Figure 4.7 Comparison of predicted and measured contact area in relation to nominal veneer-to-veneer compression 4.7 Bibliography A S M E B46.1-2002. 2003. Surface texture (surface roughness, waviness, and lay). The American Society of Mechanical Engineers. Three Park Avenue, New York . N Y 10016-5990. U S A . Faust, T. D . and J. T. Rice. 1987. Effects of a variable glue application rate strategy on bond quality and resin consumption in the manufacture of southern pine plywood. Forest Prod. J. 37(7/8):64-70. Greenwood, J. A . 1967. On the area of contact between a rough surface and a flat. J. Lubric. Technology, Trans. A m . Soc. Mech. Engineers. 1, 81. Greenwood, J. A . , and J. H . Tripp 1970-1971. The contact of two nominally flat rough surfaces. Proc. Inst. Mech. Eng., V o l . 185. 625-633. Greenwood, J. A . and J. B . P. Will iamson. 1966. Contact of nominally flat surfaces. Proceedings, Royal Society, A295, 300. Johnson, K . L . 1985. Contact mechanics. Cambridge University Press. Mathematica® (Version 5.2). 2007. Wolfram Research, Inc. Campaign, U S A . Mitutoyo. 2004. SJ -400 — Surface roughness tester. User's Manual. Neese, J. L . , J. E . Reeb and J. W . Funck. 2004. Relating traditional surface roughness measures to gluebond quality in plywood. Forest Prod. J. 54 (l):67-73. 125 CHAPTER V MECHANICS OF VENEER COMPRESSION 5.1 Introduction As discussed in Chapters 3 and 4, the surfaces of wood veneers are rough to various degrees. Depending on the level of roughness, the stress-strain relationship during veneer transverse (radial) compression could be significantly different. At the early stage, a non-linear stress-strain relationship occurs for achieving progressive veneer-to-veneer contacts. Then elastic deformation prevails and if the applied pressure is discontinued, the veneer will largely recover to its original thickness. Once the yield point is exceeded, cell wall elastic buckling and plastic bending (yielding) or brittle fracture (crushing) start to occur depending on test conditions and the nature of the cell wall materials. A plastic plateau is subsequently reached where large deformation is possible with only a small increase in applied pressure, resulting in irreversible deformation (or strain hardening). This plateau ends where the densification zone starts, which coincides with the compression of the collapsed cell walls. Wood veneer is a cellular and porous material, which exhibits both viscoelastic (creep) and elasto-plastic (springback) behaviour during compression (Wolcott et al. 1990; Dai 2001). At the microscopic level, the relative thickness of the cell walls, thus the relative density, determines the mechanical properties of wood. Veneer compression Young's modulus (£) , determined by cell wall bending, varies generally as the density to the third power. In contrast, veneer compression strength (or yield stress), determined by the plastic bending (yielding) and/or buckling of the cell walls, varies as the square of the density (Gibson and Ashby 1997). The transverse compression properties of wood veneer play a key role in the plywood/LVL hot-pressing. During hot pressing, the multi-ply veneer assemblies are consolidated and then densified under a combination of changing temperature and moisture content (MC). Under a constant pressure, the creep-induced deformation occurs. In addition, the deformation from thermo-softening of individual veneer plies also results due to the coupled effect of temperature and M C on veneer compression E. As heat is transferred from the platen to the veneer assemblies, veneers closer to the platens will soften and deform more than those in the inner region. The inner region is generally stiffer and can generally resist more deformation. Thus, an initial density gradient forms across the panel thickness. Subsequently during press unloading, depending on the stage of veneer compression, different rates of springback result. Therefore, 126 two major steps in controlling final product thickness and density profile are the pressing stage when density profile is created from creep deformation and thermo-hydro softening and the springback as the panel unloads and exits the press. As discussed in Chapter 1, for oriented strand board (OSB) and particleboard made from discontinuous wood elements such as strands and particles, a high compression ratio (CR) (about 40-60%) is generally required to remove the void space that separates the individual wood elements, thereby providing contacts between strands or particles and promoting bonding (Dai and Steiner 1993; Lang and Wolcott 1996a). By comparison, for plywood and L V L , the key is to bring continuous veneer elements into adequate contacts by overcoming surface irregularities such as roughness for bonding development. The panel structure after hot pressing is still dictated by the two distinct elements: veneer and glueline. For such products, a high CR is generally not required (Wellons et al. 1983). The normal CR ranges are only from 3 to 15%. Indeed, in the plywood/LVL manufacture, the amount of veneer compression, veneer creeping and springback behaviour are closely related to panel performance and material recovery. The knowledge on how veneers deform across the panel thickness is essential to determine the platen pressure required to achieve the target thickness. So far, only a few researchers have investigated the creep and stress relaxation of wood strands (fibers) and mats at ambient conditions (von Haas 1998; Dai et al. 2000; Dai 2001; Carvalho et al. 2001), and non-linear behaviour of strands and particles during compression of OSB and particleboard under isothermal or cold pressing (Dai and Steiner 1993; Lenth and Kamke 1996; Lang and Wolcott 1996a; Lang and Wolcott 1996b; Wang and Winistorfer 2000). The resulting models simulated the stress-strain behaviour of OSB and particleboard by separating the effect of temperature and M C on the mechanical properties of wood from the general deformation behaviour of wood. Although the effect of temperature and M C gradients on the mechanical properties of wood was studied, the springback behaviour of wood was not considered in these studies (Harless et al. 1987; Suo and Bowyer 1994; Zhou and Dai 2004). Dai et al. (2000) analyzed the implications of the mat elasto-plasticity on formation of vertical density profile, and concluded that the springback due to resin pre-cure was the main reason for the low density surface. Godbille (2002) investigated both compression and springback behaviour of wood to simulate the mechanical behaviour of particleboard during hot pressing. The general approach was to use a modified Hooke's law, as discussed in Chapters 1 and 3, to describe the stress-strain relationship for whole range of wood transverse compression, 127 and use a single non-linear strain function to determine the wood deformation during hot pressing. This strain function can be obtained from compression tests scaled by the corresponding compression Young's modulus E, which is the function of veneer temperature (T) and M C . In the case of unloading, the strain function was approximated to a linear term to take strain hardening into consideration (Godbille 2002). While the strain function derived generally fitted with the experimental data with a reasonable accuracy, a large discrepancy was found for the strain level up to the yield point (approximately 20%) (Godbille 2002; Zhou and Dai 2004). This could be acceptable for non veneer-based wood composites such as OSB and particleboard due to their higher level of compression required and significant number of constituent elements used in the mats. However, for veneer-based wood composites such as plywood and L V L , veneer surface roughness affects the initial non-linear stress-strain relationship; the compression in the veneer assemblies is generally from the early stage of progressive contact to the stage of plastic deformation (plateau) with a majority of compression being in the linear elastic stage. As a result, the modified Hooke's law may not be adequate to describe the veneer stress-strain relationship. Compared to discontinuous wood elements such as strands and particles which are randomly deposited in the mat, veneer plies are rather large and continuous which are assembled in a more controlled manner. For OSB and particleboard, the effect of wood density is more or less averaged or masked. When the modified Hooke's law was applied, a single strain function could generally be accepted for a wide range of wood density. In contrast, for plywood and L V L , veneer sheets are sometime classified into distinct density groups especially when different species are used and/or stress grading is performed. Note that wood density not only significantly affects veneer compression E and yield stress but the strain function as well, since the latter is determined by the cell structure. If the modified Hooke's law is used, various strain functions may be needed over a wide range of density. To better describe the veneer compression stress-strain relationship, it seems essential to determine the effect of wood density on veneer compression behaviour in conjunction with M C and temperature, and use a model to describe the stress-strain relationship at different stages of compression. This could help develop a solid understanding of the mechanics of veneer compression, which forms the main topic of this Chapter. 128 So far, no information has been available to describe the mechanical behaviour of wood under the initial stage of progressive contact; and no work has been performed concerning the time-dependent creep and springback behaviour of wood veneer. Meanwhile, no models have been developed to describe the mechanical behaviour of the veneer during hot pressing. In this work, extensive experiments were conducted to investigate the effect of wood density, temperature and M C on veneer transverse compression behaviour. A regression model based on a response surface methodology (RSM) was established for veneer compression E and yield stress. As well, creep tests were conducted to investigate the deformation of the veneer under the predetermined pressures. In addition, veneer specimens were loaded to different stages of compression to ascertain the springback behaviour, thickness recovery and dimensional stability. Furthermore, loading and unloading tests were conducted to examine the springback behaviour of the veneer. Based on the results, an analytical model was developed to describe the mechanical and deformation behaviour of the veneer during transverse (radial) compression, and was further used in developing the panel densification module for plywood/LVL hot pressing. 5.2 Experimental 5.2.1 Materials The source of veneer materials was the same as described in Chapter 3. Among a total of 150 (3.2 mm thick) rotary-cut random aspen dried veneer sheets (1.2 x 1.2 m), 120 veneer sheets were taken and then visually separated into the three roughness groups for the compression tests performed in Chapter 3. The remaining 30 veneer sheets were used to cut 1) 900 specimens (30 x 30 -mm) for the compression tests with 30 specimens from each sheet, and 2) 90 specimens (30 x 30 -cm) for the creep test with 3 specimens from each sheet. These 900 specimens were kept in plastic bags for compression tests. The average veneer M C was about 3% on an oven-dry basis. The 5-point thickness and weight of each specimen were measured to calculate veneer density. For each of these 90 (30 x 30 -cm) specimens, the 9-point thickness and weight were measured. They were wrapped in a plastic bag for the creep test. 5.2.2 Veneer Compression as Affected by Surface Roughness and Density The experimental results were obtained from the compression tests as described in Chapter 3. In those tests, fifteen 30 x 30 -mm dried aspen veneer specimens were randomly selected from the three roughness groups with known roughness and density. These specimens were compressed at 129 the ambient temperature (20°C) to a maximum load of 975 kg to record the load-displacement curve for each specimen. Subsequently, based on the area and thickness of each veneer specimen, the stress-strain relationship was plotted. 5.2.3 Veneer Compression in Terms of Veneer Density, MC and Temperature To investigate the effect of wood density, M C and temperature on veneer transverse (radial) compression, a response surface methodology (RSM) was used. This method has been widely used to evaluate veneer yield and quality (Warren and Hailey 1980) and optimize pulping processes (Khun and Cornell 1996; Jimenez et al. 2000; Rosli et al. 2003). A second-order central composite design (CCD) was adopted to design the experiment, which involves devising the composition of the experimental conditions and subsequently developing a regression model. This design consists of factorial design points with eight (2k, k = 3) runs, two center points and six axial or star points to estimate the first- and second-order interaction terms of a polynomial, which meets the general requirements that every variable in the mathematical model can be estimated from a fairly small number of experiments. In this study, three independent veneer variables were selected as: veneer density (Xi), M C (X2) and temperature (X3), whereas the two dependent variables were veneer compression modulus (£) and yield stress. Table 5.1 shows the 16 experimental runs of veneer compression tests dealing with the three levels of each variable. Each variable was normalized from -1 to +1 in order to facilitate direct comparison of the coefficients and visualization of the effects of the individual independent variables on the response (or dependent) variable. This normalization approach also results in more accurate estimates of the regression coefficients as it reduces interrelationships between linear and quadratic terms. For veneers with actual values of density (p*), M C (MC*) and temperature (T*), their respective coded values, namely, p, M C and T, can be calculated as follows: p = - l + £ *-0.35 0.075 (5-1) M C = -1 + MC*-0.5 4.5 (5-2) T = -1 + r*-20 65 (5-3) 130 Table 5.2 compares the actual value of each variable with its coded value. Note that the middle level of each variable was chosen as the average value whereas the upper and lower levels of each variable generally covered the range of variation for aspen veneer in the p l y w o o d / L V L manufacturing. Before the test, veneer specimens were pre-selected based on the three density levels specified in Table 5.2. For each experimental run, three replicates were used. In total, forty-eight 30 x 30 -mm veneer specimens were compressed under the different combinations of density, temperature and M C . Experimental results were fitted to the following second-order polynomial: where Xx, X2 and X 3 are the three independent variables which influence the response Y ; anda 0 , at (i = 1-3), bi (i = 1-3) and ctj (i = 1-3; j = 1-3; i < j) are unknown coefficients. The experimental set up for the compression test was described early in Figure 3.2. Attachments for an Instron universal tester were designed to allow testing of the veneer in compression at various levels of temperatures. The attachments consisted of two identical aluminium blocks (15.2 x 15.2 -cm) equipped with an electric heater and a thermocouple probe connected to a controller so that the mechanical properties of the veneer can be measured at different temperatures. Veneer specimens (30 x 30 -mm) were first seasoned to the three designated M C levels in an environmental chamber then placed between the two preheated blocks in the tester. The controlled temperature of the heating block was set according to the experimental run. Before starting the test, a load level of about 2.5 kg was applied onto each specimen and the L V D T extensometer was zeroed. Based on the readings from the probe, the temperature of the veneer specimen would reach the target in about 10 to 20 s. After that, isothermal compression testing started with a loading rate of 2 mm/min (0.08 in/min). The M C of the veneer specimen was measured upon completion of each experiment to account for the loss during its preheating between the two heated blocks. In order to limit vapourization during compressing at 150°C which is higher than the boiling point of water, veneer specimens were wrapped in a thin foil of aluminium for the testing. 3 ( i< j ) (5-4) 131 The load-displacement curves of aspen veneer were obtained at different combinations of veneer density, temperature and M C . Then, based on the area and thickness of each specimen, the stress-strain relationship was established to compute the veneer compression modulus (E) and estimate the yield stress. Average compression E and yield stress were calculated for each experimental run. 5.2.4 Veneer Creeping Tests Under a constant platen pressure, veneers will exhibit viscoelastic (creep) behaviour. For general viscoelastic materials, the basic constitutive equation between applied stress and strain according to the definition is (Christensen 1971): de a = | X ^ (5-5) where ev is viscous strain, t is pressing time, | i is viscous coefficient of the veneer reflecting the relationship between strain ev and pressing time t, and a is the pressure applied. Equation (5-5) is a first order linear ordinary differential equation. To solve it, an initial condition is needed such that ev is equal to zero when time t is zero. So we can obtain the solution for the creep strain as follows: ev = — t (5-6) However, | i changes with pressing time, which causes complexity to determine creep strain. Instead, an experimental approach is generally used to determine the creep strain with time by curve fitting (Bodig and Jayne 1982). To understand the time-dependent viscoelastic behaviour of aspen veneer under a constant applied pressure, experiments were conducted by suddenly applying and maintaining different levels of pressures (stresses) onto 30 x 30 -cm aspen veneer specimens. By the time of testing, veneer average M C was 5%. The tests were conducted with a 96 x 96 -cm computer controlled press at an ambient temperature (20°C). At each stress level, three replicates were used. The veneer specimens were pre-selected to have identical thickness (3.25 mm) and density (0.425 g/cm3) to eliminate the potential effect of veneer density. According to the literature, the highest creep strain was associated with the cell-wall yield point where wood starts buckling. The creep in both the linear range and the highly densified range was considerably lower than that in the 132 cell-wall buckling and yielding range (Dai 2001). In this study, three stress loading levels were selected as 1.21 MPa (175 psi), 1.38 MPa (200 psi) and 1.55 MPa (225 psi), which were normally used in aspen plywood and L V L manufacturing. The time of holding was set to 17 min. A high stress level for achieving cell wall buckling and yielding at the ambient temperature (20°C) was not pursued due to the hydraulic pressure limitation of the press. Of the large number of methods used to portray creep and relaxation behaviour of composite materials, empirical curve fitting is among the simplest, which requires that an appropriate equation be chosen to describe the data. Among a number of equations used to describe the creep behaviour of composites, a parabolic representation can be effectively used to demonstrate the empirical approach to creep behaviour. The equation takes the following form according to Bodig and Jayne (1982): £y = ea+j3tm (5-7) where ea is instantaneous (elastic) strain, t is time and /3 and m are constants. Rearranging and taking logarithms gives log( £y-£a) = \ogp + m log t (5-8) By plotting log( £ - ea) as a function of log?, the parameters ft and m can be determined. 5.2.5 Veneer Compression and Springback Tests To investigate the elasto-plastic (springback) behaviour of aspen veneer during transverse (radial) compression, the compression tests were first conducted under the following four different temperatures: 20°C, 50°C, 100°C and 150°C. Ten replicates were used for each temperature level. Veneer M C was approximately 6%. For each veneer specimen (30 x 30 -mm), the weight was first measured, and then eight spots on edges plus one spot in the center were marked for thickness measurement. Subsequently, the average veneer thickness and density were determined. The apparatus described in Section 5.2.3 was used and same procedures were followed. The veneer compression tests were started and stopped until the maximum load reached approximately 650 kg. At this load level, all veneer specimens reached the stage of cell wall densification at different temperatures. After unloading, the thickness and weight of each veneer specimen were measured. Irrecoverable strain was determined for each specimen. Subsequently, all specimens were soaked in the cold water for 2 h. The thickness of each specimen was measured again at the same spots to determine the 2-h thickness swell. 133 Assuming original veneer thickness is to, at the end of the compression, the veneer thickness is reduced to tc. During and after unloading, the veneer thickness bounces back to ts. Subsequently, after 2-h cold water soaking, final wet thickness of veneer is tw. Hence the thickness recovery after compression (R t) before soaking can be calculated as: R t=-^*100% (5-9) The compression strain (e) is defined as: 8 = - ^ ^ - (5-10) The irrecoverable strain after compression (sp) is computed as: s p = = 1 - R t (5-11) As well, the springback ratio (St) can be calculated as: S,= -^—^*100% = ( 1 - - ^ £ - ) * 1 0 0 % (5-12) ~*c h ~ h Furthermore, the 2-h veneer thickness swell (TS2h) can be determined as: T S 2 h = - ^ - ^ * 100% (5-13) t.. Finally, the irrecoverable strain after compression (ep) can be calculated based on compression strain (s) and springback ratio (St) as follows: e p = ( l - S , ) * 8 (5-14) Therefore, if the compression strain and the springback ratio are known, the irrecoverable strain can be determined. To compare the thickness recovery and springback ratio between the first stage of progressive contact and the second stage of linear elastic, compression tests of veneer specimens (30 x 30 -mm) were conducted at the ambient temperature (20°C). Ten replicates were used. For each veneer specimen (30 x 30 -mm), the weight was first measured, and then eight spots on edges plus one spot in the center were marked for thickness measurement. Subsequently, the average 134 veneer thickness and density were determined. Veneer average M C was approximately 6%. For the progressive contact, the compression tests were stopped prior to the start of the linear elastic stage based on the shape of load-displacement curve. During compression, the maximum strain was recorded. After unloading, the thickness of each specimen was measured again from the same spots to calculate the irrecoverable strain. To further investigate the springback behaviour of aspen veneer, loading and unloading tests were conducted at different levels of strain. The purpose of the tests is to determine the amount of springback at the end of compression. The apparatus and procedures described in Section 5.2.3 were again used and adopted. The following four temperature levels were used: 20°C, 50°C, 100°C and 150°C. Two average M C levels, namely 3% and 6%, were selected. The strain levels were selected to represent different stages of the compressive stress-strain relationship, namely, LI (linear elastic), L2 (early plastic, right crossing the yield point), L3 (plastic, plateau) and L4 (cell wall densification). A full factorial design was conducted with 32 experiments (3 replicates each). Before conducting loading and unloading tests, for each veneer specimen (30 x 30 -mm), the weight was first measured, and then eight spots on edges plus one spot in the center were marked for thickness measurement. Subsequently, the average veneer thickness and density were determined. Following the shape of the load-displacement curve, the compression stages can be easily determined. For each specimen, the compression test was started until the maximum strain level reached the predetermined stage and then the load was entirely removed. After unloading, the thickness of each specimen was measured from the same spots. 5.3 Results and Discussion 5.3.1 Veneer Stress-Strain Relationship in Terms of Surface Roughness and Density As shown in Figure 5.1, veneer surface roughness has a substantial effect on the initial stage of veneer transverse (radial) compression, namely progressive contact. The stress-strain relationship exhibited a non-linear (exponential) pattern. The fit of an exponential equation to the experimental data was found to be very good for different levels of veneer roughness. For these veneer specimens compressed at the ambient temperature (20°C) and 3% M C , the threshold pressure was about 1.31 MPa. The rougher the veneer surface, the larger the strain level prior to the start of the linear-elastic stage. Based on the measurements from the representative veneer 135 specimens, the initial strain level prior to the start of the linear elastic stage was found to range from 0.05 to 0.12 depending on veneer surface roughness. Figure 5.2 shows the effect of veneer density on the compressive stress-strain relationship. In general, the deformation of wood is non-uniform and occurs by the progressive collapse of cells from the surface inwards, although the unit step is still the plastic collapse of a cell (Gibson and Ashby 1997). Five specimens were classified into the two density groups: high (0.51 - 0.53 g/cm3) and medium (0.42 - 0.43 g/cm3). Veneer density mainly affected the linear-elastic stage of veneer transverse compression. The higher the veneer density, the steeper the slope. As well, for the two compression curves at the same density level of 0.42 g/cm3, the slopes seemed to be identical but the two strain levels prior to the start of the linear elastic stage were quite different due to their different levels of surface roughness. Furthermore, the shape of stress-strain relationship appeared to be different between the high density veneer and medium density veneer. 5.3.2 Effect of Veneer Density, MC and Temperature on Compression Modulus and Yield Stress Table 5.3 summarizes the experimental results for the 16 runs of the compression tests. The veneer compression modulus (£) was calculated based on the stress-strain relationship at the linear elastic stage. Using a statistical software program (JMP 2000), a second-order RSM model for the effect of wood density, temperature and M C on veneer compression E was developed as follows: E = 30.21 + 19.89 p - 6.07 M C - 12.95 T - 3.29 p * M C - 5.14 p * T - 1.34 M C * T + 11.94 p 2 + 1 . 9 4 M C 2 +2.94 T 2 (5-15) As well, a second-order RSM model for the effect of veneer density, temperature and M C on yield stress was developed as follows: o~Y = 3.12 + 0.74 p -0.27 M C - 1.01 T - 0.10 p * M C + 0.15 p * T + 0.1 M C * T + 0.19 p 2 - 0 . 1 6 M C 2 +0.54 T 2 (5-16) The results concerning analysis of variance for veneer compression E are shown in Table 5.4. The empirical regression model for veneer compression E gave an R 2 of 0.986 and a standard 136 error of estimate (SEE) of 4.06. Based on Table 5.4, the model fitted the experimental data very well. In Equation (5-15), all three variables use coded values from -1 to 1. Similarly, the results concerning analysis of variance for yield stress are shown in Table 5.5. The empirical regression model for the yield stress gave an R 2 of 0.940 and a standard error of estimate (SEE) of 0.43. Based on Table 5.5, the model also fitted the experimental data very well. In Equation (5-16), all three variables use coded values from -1 to 1. Based on the regression models, veneer compression E and yield stress can be predicted at any combination of veneer density, M C and temperature with a high accuracy. As an example, for veneers with dry density 0.40 g/cm3 and 5% M C at 85°C, the coded value for density, M C and temperature are -0.333, 0 and 0, respectively. Based on Equations (5-15) and (5-16), the predicted veneer compression E and yield stress are 24.9 MPa and 2.8 MPa, respectively. Figure 5.3 shows the prediction profiler of the three variables in terms of the veneer compression E and yield stress. The significance level of each variable was determined by the maximum difference (absolute value) in the veneer compression E or yield stress at the three designated levels of the variable. In general, the larger the difference, the more important the variable. It was evident that for the veneer compression E, the wood density had the largest effect, followed by veneer temperature and M C within the range tested; In contrast, for yield stress, the temperature had the largest effect, followed by veneer density and M C within the range tested. Both veneer compression E and yield stress notably decreased with decreasing veneer density and increasing veneer temperature and M C . Figure 5.4 shows the response of the veneer compression E in relation to M C and temperature when veneer dry density is 0.40 g/cm (a) and 0.45 g/cm (b). At each density level, the response appeared to be a curvilinear pattern with some interactions existing between M C and temperature. 137 5.3.3 Veneer Creeping Behaviour during Compression Figure 5.5 shows the experimental results regarding the aspen veneer thickness change with time at the three stress (pressure) levels. At the ambient temperature (20°C) and 5% M C , the first stress (pressure) level situates at the end of the first stage of non-linear progressive contact (right prior to the linear elastic stage). The second and third stress levels represent linear elastic stage of the compressive stress-strain relationship. Figure 5.6 plots the creep strain with time. Note that the instantaneous strain is the sum of strain from eliminating surface roughness and strain from elastic deformation. Veneer surface roughness had a significant effect on the instantaneous strain. In general, the higher the pressure applied, the greater the reduction of thickness at the initial stage up to 1 min and in turn the instantaneous strain. During this stage, the effect of veneer surface roughness was largely eliminated. Obviously, the actual creep started after the surface was ironed out. It seemed that the low stress (pressure) level of 1.21 MPa resulted in the lowest instantaneous strain but the highest creep strain rate compared to the other two stress (pressure) levels. This is probably due to the effect of residual roughness. Recall that from Figure 5.1, at a threshold pressure level of approximately 1.31 MPa, the linear elastic stage starts with elimination of the major effect of veneer surface roughness. On average, for these aspen veneer specimens tested (mill peeled), surface roughness-induced strain was found to be equal or greater than 0.10. The difference in strain rates between 1.38 MPa and 1.55 MPa stress (pressure) levels seemed to be very small. Overall, the strain level due to veneer creeping was about 0.015-0.020. By fitting the experimental data, the following parameters were yielded as shown in Table 5.6. The parameter m was more stable with a value of about 0.30 whereas the parameter /? changed from 0.007 to 0.009 with the stress level from 1.21 MPa to 1.55 MPa. 5.3.4 Behaviour of Veneer after Compression Figure 5.7 shows the compressive stress-strain relationship of aspen veneer with the following four stages of transverse compression: progressive contact, linear elastic, plastic and cell wall densification. The tests were conducted at the four different temperatures, namely 20°C, 50°C, 100°C and 150°C with an average veneer M C level of 3%. In general, the linear-elastic stage 2 exhibited the compression behaviour from cell wall bending. The plastic stage 3 was controlled by the non-uniform plastic yielding of the cells, which generally starts at the surface of the loading platen and propagating inwards through the veneer thickness (Gibson and Ashby 1997). 138 Note that all specimens were pressed to the stage of cell wall densification. When veneer specimens are pressed beyond the elastic region, the maximum strain imposed on the specimens generally determines the amount of irrecoverable deformation. As shown in Figure 5.8, the springback ratios with different compression strains are dramatically different. The springback ratio reduced from about 85% to 30% with a range of compression strain from 0.3 to 0.8. Figure 5.9 shows the change of irrecoverable strain with regard to compression strain. Their relationship appeared to be an exponential pattern. In general, the higher the compression strain, the higher the irrecoverable strain. However, this level of irrecoverable strain was not stabilized or fixed in the wet environment. As shown in Figure 5.10, 2-h cold water soaking tests after compression demonstrated that there was a strong relationship between the thickness swell (TS) and irrecoverable strain level. The higher the irrecoverable strain after the compression, the higher the TS. This type of dimensional instability will impact the engineered applications of veneer-based composite products. In general, higher compression strain not only causes lower material recovery but also poorer dimensional stability. Since the maximum compression strain in plywood/LVL products is generally situated between the linear-elastic stage and the early plastic stage, the information on springback behaviour of veneer compression at different stages is essential to help improve material recovery and product performance. 5.3.5 Springback Behaviour of Veneer at Different Compression Stages Figure 5.11 compares the thickness recovery and springback ratio between the first stage of progressive contact and the second stage of linear elastic. On average, at ambient temperature (20°C) and 3% M C , when the maximum compressive strain was at the first stage (<=10%) with an average of 7.5%, the average springback ratio was about 75% and the thickness recovery was about 98%. In contrast, when the maximum compressive strain was at the second linear-elastic stage (between 10 and 18%), the average springback ratio was about 95% and the thickness recovery was about 99%. The results indicated that the first stage of progressive contact exhibited mixed behaviour of plasticity and elasticity. Typical representations of loading and unloading curves of aspen veneer are shown in Figures 5.12 and 5.13. The tests were conducted under 150°C temperature and 6% M C . Note that the 139 density of veneer specimens was 0.42 and 0.43 g/cm , respectively, for loading and unloading at the linear elastic stage (stage 2) and early plastic stage (right crossing the yield point). There was a significant difference in both thickness recovery and springback ratio between the linear elastic stage and the early plastic stage. The springback ratio was 63% for the compression at the linear stage compared to 57% for the compression at the early plastic stage. The irrecoverable strain with the maximum compression strain below the yield point was about 0.082 (thickness recovery 91.8%) whereas this strain with the maximum strain at the early plastic stage was about 0.202 (thickness recovery 81.8%). The difference in the irrecoverable strain was about 0.12. In the case of linear elastic, the irrecoverable strain was caused by veneer surface roughness and plasticity from thermo-softening. In contrast, in the case of early plastic stage, the irrecoverable strain was caused by veneer surface roughness and plasticity from cell wall buckling and yielding and thermo-softening. At the temperature of 150°C, a large proportion of the compression strain beyond the yield point was not recoverable. This indicates that to effectively enhance the densification, the compression strain should exceed the yield point. However, the detrimental effect of this densification is the reduced material recovery, lowered shear strength and increased thickness swell as demonstrated in Chapter 3. Similarly, as shown in Figure 5.13, there was also a significant difference in both thickness recovery and springback ratio between the 3 r d plastic stage and the 4 t h cell wall densification stage. Note that the density of veneer specimens were 0.43 g/cm3 for the compression at the 3 r d plastic stage and 0.46 g/cm3 for the compression at the densification stage. The difference in density caused the different slops at the linear elastic stage. The springback ratio was 52% for the plastic stage compared to 33% for the compression at the densification stage. The irrecoverable strain with the maximum compression at the plastic stage was about 0.261 (thickness recovery 73.9%) compared to about 0.450 (thickness recovery 55.0%) for the maximum strain at the cell wall densification. In comparison with Figure 5.12, at the third plastic stage (plateau), the level of compression had a significant effect on thickness recovery and springback ratio. Figures 5.14, 5.15, 5.16 and 5.17 show the relationship of compression strain and irrecoverable strain (strain retained after compression) with regard to the following four temperature levels: namely, 20°C, 50°C, 100°C and 150°C. The average veneer M C was 3%. The irrecoverable strain increased with increasing compression strain and temperature. Note that compared to the 140 compression at the linear elastic stage, compression at the early plastic stage (right crossing the yield point) resulted in a significant increase in both irrecoverable strain. Figures 5.18 and 5.19 show the springback ratio of aspen veneer at 3% M C and 6% M C , respectively. First, at both M C levels, veneer compression strain, demonstrated by the compression stage, had a significant effect on the springback ratio. Secondly, compression strain at the linear elastic stage resulted in the largest springback ratio. Compression at the early plastic stage (right crossing the yield point) resulted in a lower springback ratio, leading to a higher thickness loss compared to compression at the linear elastic stage. In addition, the springback ratio decreased with increasing veneer temperature. Furthermore, with the increase of veneer M C , the springback ratio decreased with the largest reduction being in the early plastic stage. At 3% M C , the springback ratio was only reduced slightly from 20°C to 50°C but was reduced more when temperature rose to 100°C or above. In contrast, at 6% M C ; the springback ratio decreased noticeably at the four different temperature levels. Figure 5.20 shows the prediction profiler from the statistical analysis of experiments with the full factorial design. It demonstrated that the compression stage had the largest effect on both springback ratio and thickness recovery, followed by temperature and M C . When temperature was increased from TI (20°C) to T2 (50°C), both springback ratio and thickness recovery only reduced slightly. When veneer temperature was greater than 50°C, the reduction of springback ratio and thickness recovery became more pronounced. 5.4 Analysis of Veneer Compressive Stress-Strain Relationship The experimental approach serves two purposes: 1) to determine the veneer basic properties; and 2) to characterize the material behaviour of the veneer during compression. For example, one needs to know veneer density and M C , and the creep behaviour of the veneer under a constant platen pressure in order to predict the creep deformation in addition to that caused by thermo-hydro softening. As well, one needs to know the springback ratio of the veneer in terms of veneer temperature, M C and the maximum compression strain. In contrast, an analytical analysis or theoretical modeling can further advance our understanding of the mechanisms of veneer compression. So far, modeling of veneer transverse (radial) compression has been limited to the application of the modified Hooke's law and use of a strain function to describe the stress-strain 141 relationship over the whole range of transverse compression. In the case of the veneer, the strain function cp (e) derived from the modified Hooke's law can be better expressed as: 9(£) = a / [ e * £ ( p , T , M C ) ] (5-17) where a is the applied stress, e is strain, and E is the veneer compression modulus, which is a function of veneer density (p), temperature (T) and moisture content (MC). If the first stage of progressive contact is ignored, cp(£) will be 1 at the linear elastic stage. However, if the first stage of non-linear progressive contact is considered, as shown in Figure 5.21, (p(e) will gradually increase with a maximum value being smaller than 1 at the end of the linear elastic stage. This phenomenon was mainly caused by the delayed elasticity from surface irregularities (roughness) of veneer specimens. As described in Section 5.3.4, the compressive stress-strain curve can be divided into four stages. Figure 5.22 only shows the first three compression stages, which is believed to be sufficient for simulating veneer compression in plywood and L V L manufacturing. At the second linear elastic stage, the stress-strain relationship can be described as: o- = £ ( e - e 0 ) (5-18) where 8o is the strain intercepting with the axis of strain, which mainly depends on veneer surface roughness. Hence, the strain function at the linear elastic stage can be expressed as: (p (e) = a / (E*e) = 1- ^ < 1 (5-19) e The rougher the surface, the larger the strain eo, hence the smaller the (p(e) at the linear elastic stage. This roughness-dependent strain function drastically increases the complexity of determining veneer deformation in which a single strain function needs to be derived. As a result, the strain function was not pursued in this study. Instead, a modeling approach was attempted to describe the mechanics and compression behaviour of the veneer at the first three compression stages. As shown in Figure 5.22, for the first stage, namely non-linear progressive contact, we have 0 < e < eR and 0 < a < aR (5-20) The subscript R means surface roughness. As described in Chapter 3, at the threshold pressure (stress), veneer surface roughness can be characterized. For the second stage, namely linear elastic, we have eR < e < eY and