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Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates
Accepted Manuscript Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates Jerzy Smardzewski, Michał Słonina, Michał Maslej PII: DOI: Reference:
S0263-8223(16)32927-0 http://dx.doi.org/10.1016/j.compstruct.2017.02.047 COST 8268
To appear in:
Composite Structures
Received Date: Accepted Date:
21 December 2016 10 February 2017
Please cite this article as: Smardzewski, J., Słonina, M., Maslej, M., Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates, Composite Structures (2017), doi: http://dx.doi.org/ 10.1016/j.compstruct.2017.02.047
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Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates
Jerzy Smardzewski*, Michał Słonina, Michał Maslej Poznan University of Life Sciences Faculty of Wood Technology Department of Furniture Design Wojska Polskiego 38/42 60-637 Poznan Poland Tel: +48 61 848 74 75 Fax: +48 61 848 74 74 [email protected]
(*)
Corresponding author
Abstract Changes in air relative humidity and temperature exert a negative influence on hygroscopic wood based composites from which honeycomb sandwich panels are manufactured. Ready market globalisation causes that furniture from honeycomb sandwich panels manufactured in conditions of a dry climate are utilised in a tropical climate or are transported for several weeks through a tropical climate zone and then used in a dry climate. Water sorption and desorption processes by wood composites affect their loss of stiffness and strength. This study determined the impact of changes in ambient climatic conditions on the stiffness and strength of joints manufactured from honeycomb panels. A new method of numerical stiffness and strength modelling of joints subjected to changes in air relative humidity and temperature was developed. Key words: climate; experiment; FEM, honeycomb; joints; strength
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1. Introductioin Limited wood resources make it necessary to look for new, light honeycomb sandwich panels which could replace traditional particle boards (PB), Medium Density Fibreboard (MDF), High Density Fibreboard (HDF), Oriented Strand Board (OSB) as well as plywood (PW). Honeycomb panels are characterised by relatively high strength and stiffness at small mass [1] [2] [3] [4] [5] [6] [7] [8]. Their high strength quality in relation to density [9] [10] is particularly interesting. However, one of the major service problems is limited possibility of application of these honeycomb panels in construction of cabinet furniture utilised in different climatic zones. Furniture strength is determined by the strength of their corner joints. Furniture elements are commonly connected with the assistance of connecting links, which ensure unassisted assembly by end-users. So far, experiments were conducted to examine mechanical properties of such joints using typical wood composites such as: PB, MDF, HDF, OSB, PW, PB, MDF, HDF, OSB, PW, [11] [12] [13] [14] [15] [16] as well as new adhesives and connectors [17] [18] [19] [20] [21] [22]. On the other hand, there are few publications dealing with issues associated with the strength of corner joints from honeycomb panels. In the case of wood-based honeycomb sandwich panels, experiments were conducted regarding the effect of selected types of connectors and the method of their mounting on joint strength [23] [24] [25]. However, there is no information in the available literature on the subject concerning the influence of changes in climatic conditions on stiffness and strength of furniture joints. Ready market globalisation causes that furniture from honeycomb sandwich panels manufactured in conditions of a dry climate are utilised in a tropical climate or are transported for several weeks through a tropical climate zone and then used in a dry climate. In many places situated in the tropical zone, mean air relative humidity (in interiors) fluctuates from 62% to 85% and mean temperatures – from 22 ˚C to 29 ˚C. Similar climate change we can observe in Europeans kitchens and bathrooms. Mean air relative humidity in factory production shop floors manufacturing furniture from honeycomb panels amounts to 40% and temperature – to 26 ˚C. Such changes in air relative humidity and temperature expose furniture to water sorption from surroundings or sorption and later desorption of water to surroundings. Processes of water sorption and desorption from wood composites result in loss of their stiffness and strength. Determination of the impact of changes in ambient climatic conditions on the stiffness and strength of joints manufactured from honeycomb panels will make it possible to select proper ways of protecting furniture during transport as well as in the 2
place of end utilisation. Moreover, elaboration of a method of numerical modelling of joint stiffness and strength will allow cheap, virtual prototyping of furniture, which will be used in conditions of tropical climate. The aim of the study was numerical modelling and laboratory determination of the effect of changes in air relative humidity and temperature on the stiffness and strength of corner joints of honeycomb panels manufactured from wood composites.
2. Materials and methods 2.1. Test of joints For experiments, the authors prepared L-type corner joints with shapes and dimensions shown in Fig. 1. Arms of the experimental joints were made from 18 mm thick honeycomb sandwich panels faced with HDF of 3 mm nominal thickness. The panel core was made of 12 mm high paper honeycomb (Fig. 2). The honeycomb wall was 0.2 mm thick and corresponded to the thickness of paper. In the place where two neighbouring honeycombs were glued together, the wall thickness amounted to 0.4 mm. A single core cell formed a 20 mm long and 15 mm wide hexagon. The core was placed in such a way that the cell width was oriented parallel to the length of the joint. Outside the core, symmetrically, two cuboidal reinforcing elements (12 mm x 50 mm x width of joint) were placed made from PB (P2 - furniture boards for interior use). They were used to mount in them eccentric connecting links with a metal mandrel. The hexagonal core and reinforcements were glued to facings using FOLCO® LIT D 1932-MOD glue. It is an unfilled PVAc-based adhesive with cross-linkable groups. According to manufacturer’s information, its viscosity amounted to 12 000 mPa⋅s, pH = 3, density 1080 kg/m3, open time 8 – 10 min. The glue was applied to the surface of HDF in the amount of 120 g/m2. The assembly was pressed for 1 minute at the temperature of 70 ˚C and pressure of 0.4 MPa. The honeycomb sandwich panels obtained as described above served as arms of joint elements. In order to reproduce a typical protection of narrow surfaces of panel elements applied in furniture, they were glued along the circumference with an ABS rim 1 mm thick using for this purpose hot-melt adhesive Purmelt RS G 270/7 characterised by the following properties: viscosity 30 000 mPa⋅s, softening point (Kofler) 68 ˚C, curing time to final strength 2 – 5 days. After a two-week period of seasoning of elements in laboratory conditions (temperature 21 ˚C ± 1 ˚C, air relative humidity 65% ± 3%), appropriate holes were made in them to mount eccentric fasteners (Fig. 1, 2). A single fastener consisted of a metal eccentric of 14.7 mm diameter and 13 3
mm height and a 34 mm long threaded mandrel. The outer thread diameter equalled 6.1 mm, the core diameter – 4.9 mm, while the thread itself was 14.5 mm long. During joint mounting, mandrels were screwed in with a constant moment of 1.342 Nm and then the eccentric was turned pressing the panel elements together with a force of approximately 200 N. Joint mechanical properties, including their stiffness and strength, were determined in compression (Fig. 3a) and tension (Fig. 3b) tests. Tests were performed using a numerically controlled Zwick 1445 testing machine recording: force P with 0.01 N accuracy and displacement along the direction of DP load with 0.01 mm accuracy. Tests were terminated when the load decreased by 20 N or the displacement DP exceeded 20 mm. On the basis of measured DP values, in each test, the change in the value of the ∆f angle between joint arms was determined. Joint stiffness was determined on the basis of the mathematical model described in papers [22] [26].
Joint stiffness in the
compression test (Fig. 3a) was determined from the following equation: =
∆
[Nm/rad],
(1)
where: = , a’ = 0.481 m, length of the arm on which force P acts, while in the tension test (Fig. 4b) stiffness was determined from equation: =
∆
[Nm/rad],
(2)
where: = , e’ = 0.0594 m, length of the arm on which force P acts. The strength of joints was determined by comparing maximum bending moments causing joint destruction. In the case of joints subjected to compression, formula = was employed, whereas formula = was used for joints subjected to tension. In all, 72 joints were used in experiments (Table 1). Twenty four of them were seasoned in climatic conditions of a furniture factory. Air relative humidity in the company amounted to H = 41% and air temperature T = 26 ˚C. The remaining samples were subjected to seasoning in a climatic chamber where conditions: H = 85% and T = 28 ˚C. In this case, 24 joints were subjected to a successive period of seasoning in climatic conditions: H = 40% and T = 20 ˚C. After seasoning all samples were subjected to
4
compression and tension. Climatic conditions were determined based on: the experience of one of the largest factories producing for the Asian market and on the basis [27].
2.2. Numerical analysis The impact of changes in relative air humidity and temperature on joint stiffness and strength was determined using finite element method. Quality verification of calculations involved comparison of stiffness coefficients Kj determined numerically and experimentally. It was assumed that consistence of the examined displacements DP and angle deformations ∆f would ensure the quality of the developed numerical model and the quality of the calculation results. In all, 72933 eight-node cuboid “brick” type finite elements were used to model the construction of joints. The total of 27424 nodes was used. Two numerical models of joints were prepared. In each model, materials were assigned elastic properties determined in conditions of the hygroscopic equilibrium of the climate in which the joints were examined (Table 2 to 4). Joint models were supported and loaded in accordance with static conditions during experimental investigations for compression and tension tests (Fig. 3, 4). For numerical calculations, the authors chose the module of non-linear analysis. Joints were loaded with force P with the value corresponding to the maximum destructive force in laboratory tests. For each task, the load curve was selected individually on the basis of the curve run character , = ∆ in the experimental test of joint compression and tension. Contact surface was defined between joint arms adjacent to each other as a result of assembly. Contacts were also introduced between the surface of mandrel and the surface of hole formed in the support B made of particle board. A “bonded” type linkage was modelled between the mandrel thread and the hole in the second support. In order to reproduce assembly forces occurring in experimental samples, appropriate pairs of forces were applied in the numerical model (Fig. 4). A surface load of 200 N total value was applied to the hole side surface of the eccentric and to the end face of the mandrel. The direction of load vectors was parallel to the mandrel axis. A surface load of 200 N was applied to the side surface of the thread hole acting in the same direction as before but of opposite sense. Pairs of forces defined in this way reproduced the state of initial loading caused by the turn of the eccentric and axial shift of the mandrel. Results of numerical calculations also allowed determination of the influence of changes in air humidity and temperature on the change of the safety value coefficient of individual materials as well as the entire joint construction. 5
Stress limit of all joint elements depends on the applied materials and is presented as material yield point. The maximum reduced stress criterion σM, according to von Mises, is based on the von Mises-Hencky hypothesis. This hypothesis states that an elastic material begins to yield in a place where reduced stresses, according to von Mises, approach the yield point. If a particle board is characterised by a yield point of the order of 3.78 MPa, then each stress above this boundary will cause a permanent deformation of the structure. Therefore, if it is assumed that a joint is not to be permanently deformed by exceeding yield point (majority of cases), then the maximum permissible stress will amount to 3.78 MPa. So in majority of cases, the yield point is applied as the stress limit. On the basis of normal stresses σxx, σyy, σzz as well as tangential stresses τxy, τyz, τzx, the reduced stress, according to van Mises, is expressed as:
=
! ! ! √#
.
(3)
Therefore, employing the yield point, the authors decided to calculate safety factors for joints as coefficients of maximum permissible stress in relation to the equivalent stress (von Mises): $% =
&'. )
,
(4)
where: R0.2 - conventional yield point, σM – permissible stresses for a static and quasistatic loads (von Mises equivalent stresses). This coefficient must be higher than 1, if a joint is to be acceptable. Further on in the study, the authors decided to calculate acceptable equivalent stresses for the analysed joint constructions depending on the impact of changes in air humidity and temperature. Calculations were carried out using the Autodesk Simulation Mechanical 2015 program.
2.3. Test of materials It was assumed in the study that HDF would be used as facings of honeycomb sandwich panels, cores would be made from paper, supports – from PB, rims – from ABS, while the mandrel and eccentric - from aluminium. Studies of elastic properties and moisture 6
content of wood-based composites were carried out in accordance with standard requirements [28], [29]. In addition, the authors decided to assess the impact of changes in air humidity and temperature on elastic properties of individual wood-based materials. Mechanical properties of glue lines were not investigated on the assumption that in the numerical model “bonded” type joints corresponded sufficiently well to all adhesive joints in the analysed construction. Therefore, in the static bending test, modulus of elasticity (MOE) and modulus of rapture (MOR) of wood based composites were determined. In all, 72 samples – 36 for HDF and 36 for PB were prepared for experiments (Table 1). In order to determine conventional elasticity limit R0.02 and conventional yield point R0.2 for the employed wood composites as well as to ascertain the effect of changes in air humidity and temperature on these values, uniaxial tensile tests were conducted. Based on the stress-strain diagram, the authors determined: Young modulus MOE, conventional elasticity limit R0.02 and yield point R0.2. It was further assumed that the conventional elasticity limit R0.02
corresponded to the
proportionality limit RPR (Fig. 5). The linear elasticity modulus MOE was determined by measuring ∆t = t2 - t1 elongation corresponding to force ∆F = F2 – F1: , ,-
*+ = .
/ 01 1 -
,
(5)
where: F1 and F2 - values of loading forces, t1 and t2 - strain gauge indications and K – strain gauge standard constant. In the case of the applied MK3 strain gauge with a clock sensor of 0.01 mm measurement accuracy and measuring length L0 = 90 mm, K = 0.0000111. The conventional proportionality limit was determined graphically on the basis of the tangency point ordinate of the loading force FPR corresponding to the conventional proportionality limit (Fig. 5), which was calculated from the formula: 234 =
,56 ./
.
(6)
Conventional yield point R0.2 was determined using the loading method. The M point ordinate (Fig. 5) represents the value of the loading force F0.2 corresponding to the conventional yield point, which was calculated from the formula:
7
27.# =
,'. ./
.
(7)
In all, 72 samples were prepared for experiments, 36 samples for HDF and 36 for PB with shapes and dimensions as shown in Fig. 6 (Table 1). Twelve samples from each material were seasoned in conditions of a factory (H = 41%, T = 26 ˚C). The remaining samples were subjected to seasoning in a climatic chamber in conditions of H = 85% and T = 28 ˚C. After that 12 samples from each material were subjected to tensile test. The remaining samples were subjected to successive seasoning in climatic conditions of H = 40% and T = 20 ˚C. Samples seasoned in this way, once they attained constant mass, were also subjected to tensile test. For the study, a gray paper (weight 70g/m2, minimum breaking length of 6000 m) was used. Paper elastic properties were determined according [30]. Investigations were carried out for identical air climatic conditions, which were determined in the course of wood composite studies. The length of mounting was 180 mm. Mechanical properties of ABS and aluminium 1050-H14 were taken from manufacturers’ data.
3. Results 3.1.Properties of materials Fig. 7 presents HDF and PB moisture content following conditioning in air of changing humidity and temperature. Figures 8 and 9 illustrate MOE and MOR variability determined in the course of the bending test depending on changes in air relative humidity and temperature. Samples conditioned at H = 41% and T = 26 ˚C were treated as reference samples. It is evident from these Figures that following moistening of HDF to 14.56% moisture content, their MOE and MOR decreased by, respectively 47.5% and 42.5% in relation to values for reference samples. After successive drying of these boards to 5.9% moisture content, their MOE and MOR decreased, respectively, by 17.9% and 11.4% in relation to values for reference samples. In addition, it is also clear from these Figures that after moistening PB boards to 15.40% moisture content, their MOE and MOR decreased, respectively, by 53.5% and 44.8% in relation to values for reference samples. After their consecutive drying to 6.72% moisture content, their MOE and MOR decreased, respectively, by 37.2% and 35.3% in relation to values for reference samples. It is evident then, that following moistening and next drying of the examined wood-based materials, their mechanical properties deteriorated significantly, 8
This can exert a considerable effect on properties of honeycomb sandwich structures. In addition, particle boards are composites which are more sensitive to changes in air humidity and temperature in comparison with HDF. Tables 2, 3 and 4 collate mechanical properties of materials subjected to uniaxial tensile. These materials were seasoned in changing humidity and temperature conditions. The collated results were used as input data for numerical calculations. It is evident from these tables that, together with the increase of air humidity and temperature, elasticity constants of wood composites underwent deterioration (Table 3). After sample re-drying in H = 40% and T = 20 ˚C conditions, these properties improved slightly (Table 4); nevertheless they were significantly lower in comparison with properties of reference samples presented in Table 2.
3.2.Stiffness of joints On the basis of DP displacements measured in the direction of force P action as well as geometry of joints, angle ∆f increment (or loss) between arms of the joint was calculated. Stiffness coefficient Kj was calculated and its maximum values are collated in Table 5. It is evident from this Table that, together with the increase of air humidity and temperature, joint maximum stiffness Kj(max) decreased distinctly. Reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) showed the highest stiffness of 2.0 kNm/rad and 9.36 kNm/rad, respectively, for compression and tension. Following moistening of joints in H = 85% and T = 28 ˚C conditions, their stiffness decreased by 7% and 25%, respectively. Another drying process of joints in air humidity and temperature conditions of H = 40% and T = 20 ˚C resulted in a stiffness decline of compressed joints and increase of stiffness of joints subjected to tension. In this case, however the maximum joint stiffness was lower than the stiffness of reference joints, respectively by 25% and 4.4%. Fig. 10 shows joint stiffness in the loading function. It is clear from this Figure that in the case of small loads, up to 50 N, stiffness increased rapidly and afterwards, together with force increase, it approached asymptotically the maximum Kj(max) value. Once this value was reached, joint stiffness declined slowly. It is worth mentioning that reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C), attained their highest stiffness at loads of 275 N and 487 N, respectively, for compression and tension. For joints subjected to moistening in conditions H = 85% and T = 28˚C, the maximum stiffness occurred at 76 N and 258 N, respectively. The process of joint drying in the air characterised by humidity of H = 40% and temperature T = 20 9
˚C caused that maximum stiffness of compressed joints became apparent at the load of 106 N, while that of stretched joints – at the force of 323 N. Moreover, it is quite apparent from Table 5 and Fig. 10 that joints subjected to compression exhibited distinctly poorer stiffness in all climatic conditions. Quantitatively speaking, stiffness of compressed joints was from 3.77 to 5.96 times lower in comparison with stretched joints. Table 5 and Fig. 10 also collate results of numerical calculations for identical joints. It is evident from Table 4 that maximum stiffness of joints subjected to compression amounted to 2.47 kNm/rad and 1.6 kNm/rad, respectively, for (H = 40%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. The difference of calculation results in relation to the laboratory measurements amounted, respectively, to +23.5% and -13.9%. On the other hand, maximum stiffness of joints subjected to tension amounted to 15.44 kNm/rad and 7.64 kNm/rad, respectively for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. Therefore, the difference of calculation results in relation to the laboratory measurements amounted to, respectively, +64.9% and +8.8%.
The
results of numerical calculations also revealed the regularity, mentioned earlier, of a rapid stiffness increase for small loads. In this case, joints attained maximum stiffness for the load of 100 N. Once this load was achieved, stiffness decreased considerably. Also in this case, it was demonstrated that the stiffness of compressed joints was from 4.77 to 6.25 times lower in comparison with the stiffness of stretched joints. Similar regularities in deformations and rigidities were also reported by [11] [13] [18].
3.3.Strength of joints The authors also determined strength of the experimental joints on the basis of laboratory results. For this purpose, they calculated the bending moment (MC and MT, respectively, for compression and tension). It is evident from Fig. 11 that together with the increase of air humidity and temperature, joint maximum strength decreased visibly. Reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) showed the highest strength of 19.8 Nm and 48.0 Nm for compression and tension, respectively. Following moistening of joints in H = 85% and T = 28 ˚C conditions, their strength decreased by 41.4% and 29.2%, respectively. Another joint drying process in air humidity and temperature conditions of H = 40% and T = 20 ˚C resulted in an increase of joint strength. However, in this case, maximum stiffness of joints was smaller than that of reference joints by 18.2% and 18.8%, respectively. Fig. 12 presents strength 10
changes of joints in the function of the angle deformation ∆f. It is clear from this Figure that, together with the increase of angle deformations, the strength curve asymptotically approached the maximum value MC(max) or MT(max). Once this value was achieved, the joints were usually destroyed. It can be mentioned here that reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) reached the highest strength at deformations of 0.013 rad and 0.009 rad, respectively, for compression and tension. For joints subjected to moistening in conditions H = 85% and T = 28 ˚C, the maximum strength occurred at 0.011 rad and 0.007 rad, respectively. The process of joint drying in the air characterised by humidity of H = 40% and temperature T = 20 ˚C caused that maximum strength of compressed joints became apparent at 0.020 rad, while that of stretched joints – at 0.009 rad. Moreover, it is quite clear from Table 5 and Fig. 12 that joints subjected to compression exhibited distinctly worse strength in all climatic conditions. Quantitatively speaking, the strength of compressed joints was from 2.40 to 2.93 times lower in comparison with stretched joints. A similar regularity was also reported [19] [21] [31]. Table 5 and Fig. 12 also present results of numerical calculations for the examined joints. It is evident from the table that maximum strength of joints subjected to compression amounted to 20.8 Nm and 46.0 Nm, respectively, for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. The difference of calculation results in relation to the laboratory measurements amounted, respectively, to +5.1% and +43.1%. On the other hand, maximum strength of joints subjected to tension amounted to 46.0 Nm and 32.0 Nm, respectively, for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. Therefore, the difference of calculation results in relation to the laboratory measurements amounted to, respectively, -4.2% and -5.9%. The results of numerical calculations also revealed the regularity mentioned earlier of a rapid strength increase for small increases in deformations. Joints attained maximum strength for maximum values of angle deformations. Once these values were reached, a destruction process followed which was mild and manifested itself in a continuous decline of bending moment values. Also in this case, it was demonstrated that the strength of compressed joints was from 2.21 to 1.92 times lower than the strength of stretched joints. The results of performed numerical calculations also provided information about the distribution of reduced von Mises stresses as well as about safety factors Xe for these joints (Fig. 13, 14). Figures 13a and 14a present von Mises reduced stresses and the 11
safety factor of joints subjected, respectively, to compression and tension, seasoned in air humidity of 41% and temperature of 26 ˚C. It is evident from these Figures that the highest reduced stresses concentrated in holes under the threaded part of the mandrel made in supports from particle boards. The developing stresses were caused by the pressure of the mandrel on the side surface of the hole. The maximum value of these stresses (for maximum loads) reached 10.25 MPa and 11.34 MPa, respectively for compressed and stretched joints. Also, in places of pressure of the mandrel on the hole side surface, the lowest values of the safety factor were determined and reached 0.395 and 0.357, respectively. Such low values of the safety factor Xe indicate that permanent damages occurred in these places, which reduced stiffness and strength of joints. Figures 13b and 14b present von Mises reduced stresses and safety factor of joints subjected to compression and tension, seasoned in conditions of air humidity of 85% and temperature of 26 ˚C. It is evident also from these Figures that the highest reduced stresses concentrated under the threaded part of the mandrel in holes made in particle board supports. These stresses were caused by the pressure of the mandrel against the side surface of the hole. The maximum value of these stresses attained 8.23 MPa and 9.57 MPa for compressed and stretched joints, respectively. In places where the mandrel pressed against the hole side surface also the lowest values of the safety factor occurred, which – for these joints – amounted to 0.28 and 0.24, respectively. From the comparison of calculated safety factor values, it is evident that for compressed and stretched joints seasoned in H = 41%, T = 26 ˚C conditions, safety factors were, respectively, by 41% and 48% higher in relation to safety factor values of joints seasoned in H = 85%, T = 28 ˚C conditions. Typical damages of arms illustrated in Fig. 15 caused by joint compression or tension corresponded with the results of numerical calculations indicating the same places of failure. It is worth mentioning that numerically calculated pressures on the hole in the support caused by the mandrel always concentrated on the side which underwent damage. It should be noted that in case of compression (Fig.15a), a part above the mandrel has been delaminated. But in case of tension, section below the mandrel (Fig.15b). These type of destructions dominate outside the scope of linear elasticity of joints. Comparing the illustration from the Figure 15a with stress distribution on the Figure 13, we will notice some regularity. The greatest stress are concentrated in the upper part of the hole. This means that with increasing of load, they contribute to delamination of the core and 12
facing panels. From the figures 14 we can observed that higher stresses are concentrated below of the mandrel under tension. Therefore, for loads larger than those from the linear elasticity range, delamination of panels will be below the connector (Fig. 15b). Tables 6 and 7 show the results of correlation analysis between the measuring results of the bending moment MC, MT and angle of rotation of joint arms ∆f determined in the laboratory and numerically. Input data for Spearman’s R correlation analysis derived from Fig. 12. It is evident from this collation that the determined correlation coefficients were significant with p < .05. This means that the elaborated numerical models simulated correctly the effect of changing air temperature and humidity on stiffness and strength of L-type corner joints manufactured from honeycomb sandwich wood composites.
Conclusions The objective of this study involved modelling and laboratory determination of the impact of changes in air humidity and temperature on the stiffness and strength of corner joints of honeycomb panels manufactures from wood composites. The performed laboratory experiments proved that the increase in air humidity and temperature deteriorated joint stiffness even by 25% and their strength – by up to 40%. For this reason, furniture manufactured and packed in dry climate and utilised in the tropical climate will be characterised by considerably lower quality, worse stiffness and strength. Drying joints (furniture) in climatic conditions similar to original ones will improve significantly their stiffness and strength. However, these properties will be worse in comparison with reference products. Therefore, articles manufactured from wood composites transported through the tropical zone to countries with dry climate should be specially protected against moisture. The elaborated methodology of numerical stiffness and strength modelling of joints is correct. It can be used in designing offices for virtual simulation of the quality of products manufactured from wood-based honeycomb sandwich composites subjected to changing parameters of air humidity and temperature
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[14] Malkoçoğlu A, Yerlikaya NÇ, Çakiroğlu FL. Effects of Number and Distance Between Dowels of Ready-To-Assemble Furniture on Bending Moment Resistance of corner joints. Wood Research 2013;58:671–80. [15] Yerlikaya N, Aktaş A. Enhancement of load-carrying capacity of corner joints in case-type furniture. Materials and Design 2012;37:393–401. doi:10.1016/j.matdes.2012.01.010. [16] Tankut AN, Tankut N. Evaluation the effects of edge banding type and thickness on the strength of corner joints in case-type furniture. Materials and Design 2010;31:2956–63. doi:10.1016/j.matdes.2009.12.022. [17] Atar M, Ozcifci A, Altinok M, Celikel U. Determination of diagonal compression and tension performances for case furniture corner joints constructed with wood biscuits. Materials and Design 2009;30:665–70. doi:10.1016/j.matdes.2008.05.023. [18] Kureli I, Altinok M. Determination of mechanical performances of the portable fasteners used on case furniture joints 2011;6:4893–901. doi:10.5897/AJAR11.284. [19] Altinok M, Taş HH, Çimen M. Effects of combined usage of traditional glue joint methods in box construction on strength of furniture. Materials and Design 2009;30:3313–7. doi:10.1016/j.matdes.2008.12.004. [20] Yerlikaya N. Effects of glass-fiber composite, dowel, and minifix fasteners on the failure load of corner joints in particleboard case-type furniture. Materials and Design 2012;39:63–71. doi:10.1016/j.matdes.2012.02.024. [21] Tankut AN, Tankut N. Investigations the effects of fastener, glue, and composite material types on the strength of corner joints in case-type furniture construction. Materials and Design 2009;30:4175–82. doi:10.1016/j.matdes.2009.04.038. [22] Smardzewski J, Rzepa B, Kilic H. Mechanical Properties of Externally Invisible Furniture Joints Made of Wood-Based Composites. BioResources 2016;11:1224– 39. [23] Koreny A, Simek M, Eckelman CA, Haviarova E. Mechanical properties of knock-down joints in honeycomb panels. BioResources 2013;8:4873–82. [24] Petutschnigg AJ, Koblinger R, Pristovnik M, Truskaller M, Dermouz H, Zimmer B. Leichtbauplatten aus Holzwerkstoffen?Teil I: Eckverbindungen. Holz Als Roh- Und Werkstoff 2004:405–10. doi:10.1007/s00107-004-0526-6. [25] Petutschnigg AJ, Koblinger R, Pristovnik M, Truskaller M, Dermouz H, Zimmer 15
B. Leichtbauplatten aus Holzwerkstoffen. Teil II: Untersuchung zum Schraubenausziehwiderstand. Holz Als Roh - Und Werkstoff 2005;63:19–22. doi:10.1007/S00107-004-0540-8. [26] Smardzewski J, Imirzi HO, Lange J, Podskarbi M. Assessment method of bench joints made of wood-based composites. Composite Structures 2015;123:123–31. doi:10.1016/j.compstruct.2014.12.039. [27] EN 318: 2002. Wood-based panels. Determination of dimensional changes associated with changes in relative humidity. n.d. [28] EN 310: 1993. Wood-based panels: Determination of modulus of elasticity in bending and of bending strength. n.d. [29] EN 322: 1993. Wood-based panels – Determination of moisture content. n.d. [30] PN-EN ISO 1924-2: 2010 Paper and board - Determination of tensile properties Part 2: Constant rate of elongation method (20 mm/min). n.d. [31] Ta HH. Strength properties of L-profiled furniture joints constructed with laminated wooden panels 2010;5:545–50.
16
List of figures Fig. 1. L-type corner joint Fig. 2. Structure of one element of joint: A – ABS rim 1 mm thick, B – particle board 12 mm thick, C – paper core of hexagonal cells (12 mm high walls) Fig. 3. Method of joint analysis: a) compression, b) tension Fig. 4. Joint loading with forces of initial assembly Fig. 5. Diagram used to determine conventional proportionality limit and yield point Fig. 6. A sample for measurements of elasticity limit and yield point of wood-based materials Fig. 7. Absolute moisture content of HDF and PB Fig. 8. Modulus of linear elasticity (MOE): a) HDF b), PB in static bending test Fig. 9. Static bending strength: a) HDF, b) PB Fig. 10. Change of joint stiffness in the function of force: a) compression, b) tension Fig. 11. Strength of joints Fig. 12. Stiffness of joints in: a) compression, b) tension Fig. 13. Von Mises stresses and safety factors of joints subjected to compression, seasoned in conditions of: a) air humidity of 41% and temperature of 26 ˚C, b) air humidity of 85% and temperature of 28 ˚C Fig. 14. Von Mises stresses and safety factor of joints subjected to tension, seasoned in conditions: a) air humidity 41% and temperature 26 ˚C, b) air humidity 85% and temperature 28 ˚C Fig. 15. Typical damage of joints during: a) compression, b) tension
17
Fig. 1
18
Fig. 2
19
Fig. 3
20
Fig. 4
21
Fig. 5
22
Fig. 6
23
Fig. 7
24
Fig. 8
25
Fig. 9
26
Fig. 10
27
Fig. 11
28
Fig. 12
29
Fig. 13
30
Fig. 14
31
Fig. 15
32
Table 1. Number of samples Type of samples
Type of test
L-type joints
Compression Tension
Beam PB Beam HDF Dumbbell PB Dumbbell HDF
Bending Tensile
Climatic conditions / number of samples H = 85%, T = 28 ˚C / 48 After drying to: H = 41%, T = 26 ˚C H = 85%, T = 28 ˚C H = 40%, T = 20 ˚C 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
Table 2. Properties of materials seasoned in H = 41% and T = 26 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1907/214*
4.60/0.40*
1.65/0.18*
3.78/0.33*
0.35
680/8.1*
HDF
4112/401*
26.83/1.41*
4.05/0.30*
14.49/0.68*
0.30
870/31*
Paper
5100/87*
89.43/6.20*
6.42/0.87*
16.80/1.25*
0.35
725/7.3*
ABS
2495
-
5.97
58.61
0.31
1150
Aluminum
68900
370
103
270
0.33
2705
1050-H14
* StD - Standard deviation
Table 3. Properties of materials seasoned in H = 85% and T = 28 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1141/186*
2.88/0.32*
1.00/0.17*
2.31/0.26*
0.32
732/10*
HDF
1498/102*
7.55/0.44*
1.34/0.09*
4.34/0.18*
0.30
921/27*
Paper
1430/78*
43.35/7.32*
2.83/0.21*
6.72/0.09*
0.33
786/16*
* StD - Standard deviation
33
Table 4. Properties of materials seasoned in H = 40% and T = 20 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1521/125*
3.74/0.21*
1.25/0.06*
3.05/023*
0.34
704/16*
HDF
2604/108*
15.01/0.97*
2.58/0.12*
8.40/0.15*
0.31
879/24*
Paper
3946/86*
67.34/6.54*
3.75/0.32*
16.80/0.12*
0.34
703/13*
* StD - Standard deviation
Table 5. Joint stiffnesses and strengths Test
Properties
Unit
FEM
H-41%,
H-85%,
H-40%,
H-41%,
H-85%,
T-26 ˚C
T-28 ˚C
T-20 ˚C
T-26 ˚C
T-28 ˚C
Compression P(max)
N
411
241
337
431
345
MC(max)
Nm
19.8
11.6
16.2
20.8
16.6
Kj(max)
kNm/rad
2.00
1.86
1.50
2.47
1.60
Tensile P(max)
N
812
577
657
900
540
MT(max)
Nm
48.0
34.0
39.0
46.0
32.0
Kj(max)
kNm/rad
9.36
7.02
8.95
15.44
7.64
34
Table 6. Correlation of bending moments MC and MT determined in the laboratory and numerically Compression
Average
StD
H-41%, T-26C
H-41%, T-26C
10.49810
6.469393
1.000000
FEM H-41%, T-26C
10.46022
6.506904
0.999790
Tensile
H-41%, T-26C
H-41%, T-26C
7.748247
5.146004
1.000000
FEM H-41%, T-26C
7.583780
4.865064
0.983080
Compression
H-85%, T-28C
H-85%, T-28C
16.33787
11.66430
1.000000
FEM H-85%, T-28C
15.83354
11.22623
0.999047
Tensile
H-85%, T-28C
H-85%, T-28C
16.02417
11.79860
1.000000
FEM H-85%, T-28C
16.03718
11.54809
0.999082
Marked correlation coefficients are significant with p <.05
Table 7. Correlation of angle of rotation of joint arms ∆f determined in the laboratory and numerically Compression
Average
StD
H-41%, T-26C
H-41%, T-26C
0.006510
0.002645
1.000000
FEM H-41%, T-26C
0.005969
0.003436
0.999071
Tensile
H-41%, T-26C
H-41%, T-26C
0.002205
0.000948
1.000000
FEM H-41%, T-26C
0.001526
0.000981
0.996621
Compression
H-85%, T-28C
H-85%, T-28C
0.007078
0.004292
1.000000
FEM H-85%, T-28C
0.007812
0.004663
0.888785
Tensile
H-85%, T-28C
H-85%, T-28C
0.003957
0.003561
1.000000
FEM H-85%, T-28C
0.004234
0.003651
0.981127
Marked correlation coefficients are significant with p <.05
35
S0263-8223(16)32927-0 http://dx.doi.org/10.1016/j.compstruct.2017.02.047 COST 8268
To appear in:
Composite Structures
Received Date: Accepted Date:
21 December 2016 10 February 2017
Please cite this article as: Smardzewski, J., Słonina, M., Maslej, M., Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates, Composite Structures (2017), doi: http://dx.doi.org/ 10.1016/j.compstruct.2017.02.047
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Stiffness and failure behaviour of wood based honeycomb sandwich corner joints in different climates
Jerzy Smardzewski*, Michał Słonina, Michał Maslej Poznan University of Life Sciences Faculty of Wood Technology Department of Furniture Design Wojska Polskiego 38/42 60-637 Poznan Poland Tel: +48 61 848 74 75 Fax: +48 61 848 74 74 [email protected]
(*)
Corresponding author
Abstract Changes in air relative humidity and temperature exert a negative influence on hygroscopic wood based composites from which honeycomb sandwich panels are manufactured. Ready market globalisation causes that furniture from honeycomb sandwich panels manufactured in conditions of a dry climate are utilised in a tropical climate or are transported for several weeks through a tropical climate zone and then used in a dry climate. Water sorption and desorption processes by wood composites affect their loss of stiffness and strength. This study determined the impact of changes in ambient climatic conditions on the stiffness and strength of joints manufactured from honeycomb panels. A new method of numerical stiffness and strength modelling of joints subjected to changes in air relative humidity and temperature was developed. Key words: climate; experiment; FEM, honeycomb; joints; strength
1
1. Introductioin Limited wood resources make it necessary to look for new, light honeycomb sandwich panels which could replace traditional particle boards (PB), Medium Density Fibreboard (MDF), High Density Fibreboard (HDF), Oriented Strand Board (OSB) as well as plywood (PW). Honeycomb panels are characterised by relatively high strength and stiffness at small mass [1] [2] [3] [4] [5] [6] [7] [8]. Their high strength quality in relation to density [9] [10] is particularly interesting. However, one of the major service problems is limited possibility of application of these honeycomb panels in construction of cabinet furniture utilised in different climatic zones. Furniture strength is determined by the strength of their corner joints. Furniture elements are commonly connected with the assistance of connecting links, which ensure unassisted assembly by end-users. So far, experiments were conducted to examine mechanical properties of such joints using typical wood composites such as: PB, MDF, HDF, OSB, PW, PB, MDF, HDF, OSB, PW, [11] [12] [13] [14] [15] [16] as well as new adhesives and connectors [17] [18] [19] [20] [21] [22]. On the other hand, there are few publications dealing with issues associated with the strength of corner joints from honeycomb panels. In the case of wood-based honeycomb sandwich panels, experiments were conducted regarding the effect of selected types of connectors and the method of their mounting on joint strength [23] [24] [25]. However, there is no information in the available literature on the subject concerning the influence of changes in climatic conditions on stiffness and strength of furniture joints. Ready market globalisation causes that furniture from honeycomb sandwich panels manufactured in conditions of a dry climate are utilised in a tropical climate or are transported for several weeks through a tropical climate zone and then used in a dry climate. In many places situated in the tropical zone, mean air relative humidity (in interiors) fluctuates from 62% to 85% and mean temperatures – from 22 ˚C to 29 ˚C. Similar climate change we can observe in Europeans kitchens and bathrooms. Mean air relative humidity in factory production shop floors manufacturing furniture from honeycomb panels amounts to 40% and temperature – to 26 ˚C. Such changes in air relative humidity and temperature expose furniture to water sorption from surroundings or sorption and later desorption of water to surroundings. Processes of water sorption and desorption from wood composites result in loss of their stiffness and strength. Determination of the impact of changes in ambient climatic conditions on the stiffness and strength of joints manufactured from honeycomb panels will make it possible to select proper ways of protecting furniture during transport as well as in the 2
place of end utilisation. Moreover, elaboration of a method of numerical modelling of joint stiffness and strength will allow cheap, virtual prototyping of furniture, which will be used in conditions of tropical climate. The aim of the study was numerical modelling and laboratory determination of the effect of changes in air relative humidity and temperature on the stiffness and strength of corner joints of honeycomb panels manufactured from wood composites.
2. Materials and methods 2.1. Test of joints For experiments, the authors prepared L-type corner joints with shapes and dimensions shown in Fig. 1. Arms of the experimental joints were made from 18 mm thick honeycomb sandwich panels faced with HDF of 3 mm nominal thickness. The panel core was made of 12 mm high paper honeycomb (Fig. 2). The honeycomb wall was 0.2 mm thick and corresponded to the thickness of paper. In the place where two neighbouring honeycombs were glued together, the wall thickness amounted to 0.4 mm. A single core cell formed a 20 mm long and 15 mm wide hexagon. The core was placed in such a way that the cell width was oriented parallel to the length of the joint. Outside the core, symmetrically, two cuboidal reinforcing elements (12 mm x 50 mm x width of joint) were placed made from PB (P2 - furniture boards for interior use). They were used to mount in them eccentric connecting links with a metal mandrel. The hexagonal core and reinforcements were glued to facings using FOLCO® LIT D 1932-MOD glue. It is an unfilled PVAc-based adhesive with cross-linkable groups. According to manufacturer’s information, its viscosity amounted to 12 000 mPa⋅s, pH = 3, density 1080 kg/m3, open time 8 – 10 min. The glue was applied to the surface of HDF in the amount of 120 g/m2. The assembly was pressed for 1 minute at the temperature of 70 ˚C and pressure of 0.4 MPa. The honeycomb sandwich panels obtained as described above served as arms of joint elements. In order to reproduce a typical protection of narrow surfaces of panel elements applied in furniture, they were glued along the circumference with an ABS rim 1 mm thick using for this purpose hot-melt adhesive Purmelt RS G 270/7 characterised by the following properties: viscosity 30 000 mPa⋅s, softening point (Kofler) 68 ˚C, curing time to final strength 2 – 5 days. After a two-week period of seasoning of elements in laboratory conditions (temperature 21 ˚C ± 1 ˚C, air relative humidity 65% ± 3%), appropriate holes were made in them to mount eccentric fasteners (Fig. 1, 2). A single fastener consisted of a metal eccentric of 14.7 mm diameter and 13 3
mm height and a 34 mm long threaded mandrel. The outer thread diameter equalled 6.1 mm, the core diameter – 4.9 mm, while the thread itself was 14.5 mm long. During joint mounting, mandrels were screwed in with a constant moment of 1.342 Nm and then the eccentric was turned pressing the panel elements together with a force of approximately 200 N. Joint mechanical properties, including their stiffness and strength, were determined in compression (Fig. 3a) and tension (Fig. 3b) tests. Tests were performed using a numerically controlled Zwick 1445 testing machine recording: force P with 0.01 N accuracy and displacement along the direction of DP load with 0.01 mm accuracy. Tests were terminated when the load decreased by 20 N or the displacement DP exceeded 20 mm. On the basis of measured DP values, in each test, the change in the value of the ∆f angle between joint arms was determined. Joint stiffness was determined on the basis of the mathematical model described in papers [22] [26].
Joint stiffness in the
compression test (Fig. 3a) was determined from the following equation: =
∆
[Nm/rad],
(1)
where: = , a’ = 0.481 m, length of the arm on which force P acts, while in the tension test (Fig. 4b) stiffness was determined from equation: =
∆
[Nm/rad],
(2)
where: = , e’ = 0.0594 m, length of the arm on which force P acts. The strength of joints was determined by comparing maximum bending moments causing joint destruction. In the case of joints subjected to compression, formula = was employed, whereas formula = was used for joints subjected to tension. In all, 72 joints were used in experiments (Table 1). Twenty four of them were seasoned in climatic conditions of a furniture factory. Air relative humidity in the company amounted to H = 41% and air temperature T = 26 ˚C. The remaining samples were subjected to seasoning in a climatic chamber where conditions: H = 85% and T = 28 ˚C. In this case, 24 joints were subjected to a successive period of seasoning in climatic conditions: H = 40% and T = 20 ˚C. After seasoning all samples were subjected to
4
compression and tension. Climatic conditions were determined based on: the experience of one of the largest factories producing for the Asian market and on the basis [27].
2.2. Numerical analysis The impact of changes in relative air humidity and temperature on joint stiffness and strength was determined using finite element method. Quality verification of calculations involved comparison of stiffness coefficients Kj determined numerically and experimentally. It was assumed that consistence of the examined displacements DP and angle deformations ∆f would ensure the quality of the developed numerical model and the quality of the calculation results. In all, 72933 eight-node cuboid “brick” type finite elements were used to model the construction of joints. The total of 27424 nodes was used. Two numerical models of joints were prepared. In each model, materials were assigned elastic properties determined in conditions of the hygroscopic equilibrium of the climate in which the joints were examined (Table 2 to 4). Joint models were supported and loaded in accordance with static conditions during experimental investigations for compression and tension tests (Fig. 3, 4). For numerical calculations, the authors chose the module of non-linear analysis. Joints were loaded with force P with the value corresponding to the maximum destructive force in laboratory tests. For each task, the load curve was selected individually on the basis of the curve run character , = ∆ in the experimental test of joint compression and tension. Contact surface was defined between joint arms adjacent to each other as a result of assembly. Contacts were also introduced between the surface of mandrel and the surface of hole formed in the support B made of particle board. A “bonded” type linkage was modelled between the mandrel thread and the hole in the second support. In order to reproduce assembly forces occurring in experimental samples, appropriate pairs of forces were applied in the numerical model (Fig. 4). A surface load of 200 N total value was applied to the hole side surface of the eccentric and to the end face of the mandrel. The direction of load vectors was parallel to the mandrel axis. A surface load of 200 N was applied to the side surface of the thread hole acting in the same direction as before but of opposite sense. Pairs of forces defined in this way reproduced the state of initial loading caused by the turn of the eccentric and axial shift of the mandrel. Results of numerical calculations also allowed determination of the influence of changes in air humidity and temperature on the change of the safety value coefficient of individual materials as well as the entire joint construction. 5
Stress limit of all joint elements depends on the applied materials and is presented as material yield point. The maximum reduced stress criterion σM, according to von Mises, is based on the von Mises-Hencky hypothesis. This hypothesis states that an elastic material begins to yield in a place where reduced stresses, according to von Mises, approach the yield point. If a particle board is characterised by a yield point of the order of 3.78 MPa, then each stress above this boundary will cause a permanent deformation of the structure. Therefore, if it is assumed that a joint is not to be permanently deformed by exceeding yield point (majority of cases), then the maximum permissible stress will amount to 3.78 MPa. So in majority of cases, the yield point is applied as the stress limit. On the basis of normal stresses σxx, σyy, σzz as well as tangential stresses τxy, τyz, τzx, the reduced stress, according to van Mises, is expressed as:
=
! ! ! √#
.
(3)
Therefore, employing the yield point, the authors decided to calculate safety factors for joints as coefficients of maximum permissible stress in relation to the equivalent stress (von Mises): $% =
&'. )
,
(4)
where: R0.2 - conventional yield point, σM – permissible stresses for a static and quasistatic loads (von Mises equivalent stresses). This coefficient must be higher than 1, if a joint is to be acceptable. Further on in the study, the authors decided to calculate acceptable equivalent stresses for the analysed joint constructions depending on the impact of changes in air humidity and temperature. Calculations were carried out using the Autodesk Simulation Mechanical 2015 program.
2.3. Test of materials It was assumed in the study that HDF would be used as facings of honeycomb sandwich panels, cores would be made from paper, supports – from PB, rims – from ABS, while the mandrel and eccentric - from aluminium. Studies of elastic properties and moisture 6
content of wood-based composites were carried out in accordance with standard requirements [28], [29]. In addition, the authors decided to assess the impact of changes in air humidity and temperature on elastic properties of individual wood-based materials. Mechanical properties of glue lines were not investigated on the assumption that in the numerical model “bonded” type joints corresponded sufficiently well to all adhesive joints in the analysed construction. Therefore, in the static bending test, modulus of elasticity (MOE) and modulus of rapture (MOR) of wood based composites were determined. In all, 72 samples – 36 for HDF and 36 for PB were prepared for experiments (Table 1). In order to determine conventional elasticity limit R0.02 and conventional yield point R0.2 for the employed wood composites as well as to ascertain the effect of changes in air humidity and temperature on these values, uniaxial tensile tests were conducted. Based on the stress-strain diagram, the authors determined: Young modulus MOE, conventional elasticity limit R0.02 and yield point R0.2. It was further assumed that the conventional elasticity limit R0.02
corresponded to the
proportionality limit RPR (Fig. 5). The linear elasticity modulus MOE was determined by measuring ∆t = t2 - t1 elongation corresponding to force ∆F = F2 – F1: , ,-
*+ = .
/ 01 1 -
,
(5)
where: F1 and F2 - values of loading forces, t1 and t2 - strain gauge indications and K – strain gauge standard constant. In the case of the applied MK3 strain gauge with a clock sensor of 0.01 mm measurement accuracy and measuring length L0 = 90 mm, K = 0.0000111. The conventional proportionality limit was determined graphically on the basis of the tangency point ordinate of the loading force FPR corresponding to the conventional proportionality limit (Fig. 5), which was calculated from the formula: 234 =
,56 ./
.
(6)
Conventional yield point R0.2 was determined using the loading method. The M point ordinate (Fig. 5) represents the value of the loading force F0.2 corresponding to the conventional yield point, which was calculated from the formula:
7
27.# =
,'. ./
.
(7)
In all, 72 samples were prepared for experiments, 36 samples for HDF and 36 for PB with shapes and dimensions as shown in Fig. 6 (Table 1). Twelve samples from each material were seasoned in conditions of a factory (H = 41%, T = 26 ˚C). The remaining samples were subjected to seasoning in a climatic chamber in conditions of H = 85% and T = 28 ˚C. After that 12 samples from each material were subjected to tensile test. The remaining samples were subjected to successive seasoning in climatic conditions of H = 40% and T = 20 ˚C. Samples seasoned in this way, once they attained constant mass, were also subjected to tensile test. For the study, a gray paper (weight 70g/m2, minimum breaking length of 6000 m) was used. Paper elastic properties were determined according [30]. Investigations were carried out for identical air climatic conditions, which were determined in the course of wood composite studies. The length of mounting was 180 mm. Mechanical properties of ABS and aluminium 1050-H14 were taken from manufacturers’ data.
3. Results 3.1.Properties of materials Fig. 7 presents HDF and PB moisture content following conditioning in air of changing humidity and temperature. Figures 8 and 9 illustrate MOE and MOR variability determined in the course of the bending test depending on changes in air relative humidity and temperature. Samples conditioned at H = 41% and T = 26 ˚C were treated as reference samples. It is evident from these Figures that following moistening of HDF to 14.56% moisture content, their MOE and MOR decreased by, respectively 47.5% and 42.5% in relation to values for reference samples. After successive drying of these boards to 5.9% moisture content, their MOE and MOR decreased, respectively, by 17.9% and 11.4% in relation to values for reference samples. In addition, it is also clear from these Figures that after moistening PB boards to 15.40% moisture content, their MOE and MOR decreased, respectively, by 53.5% and 44.8% in relation to values for reference samples. After their consecutive drying to 6.72% moisture content, their MOE and MOR decreased, respectively, by 37.2% and 35.3% in relation to values for reference samples. It is evident then, that following moistening and next drying of the examined wood-based materials, their mechanical properties deteriorated significantly, 8
This can exert a considerable effect on properties of honeycomb sandwich structures. In addition, particle boards are composites which are more sensitive to changes in air humidity and temperature in comparison with HDF. Tables 2, 3 and 4 collate mechanical properties of materials subjected to uniaxial tensile. These materials were seasoned in changing humidity and temperature conditions. The collated results were used as input data for numerical calculations. It is evident from these tables that, together with the increase of air humidity and temperature, elasticity constants of wood composites underwent deterioration (Table 3). After sample re-drying in H = 40% and T = 20 ˚C conditions, these properties improved slightly (Table 4); nevertheless they were significantly lower in comparison with properties of reference samples presented in Table 2.
3.2.Stiffness of joints On the basis of DP displacements measured in the direction of force P action as well as geometry of joints, angle ∆f increment (or loss) between arms of the joint was calculated. Stiffness coefficient Kj was calculated and its maximum values are collated in Table 5. It is evident from this Table that, together with the increase of air humidity and temperature, joint maximum stiffness Kj(max) decreased distinctly. Reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) showed the highest stiffness of 2.0 kNm/rad and 9.36 kNm/rad, respectively, for compression and tension. Following moistening of joints in H = 85% and T = 28 ˚C conditions, their stiffness decreased by 7% and 25%, respectively. Another drying process of joints in air humidity and temperature conditions of H = 40% and T = 20 ˚C resulted in a stiffness decline of compressed joints and increase of stiffness of joints subjected to tension. In this case, however the maximum joint stiffness was lower than the stiffness of reference joints, respectively by 25% and 4.4%. Fig. 10 shows joint stiffness in the loading function. It is clear from this Figure that in the case of small loads, up to 50 N, stiffness increased rapidly and afterwards, together with force increase, it approached asymptotically the maximum Kj(max) value. Once this value was reached, joint stiffness declined slowly. It is worth mentioning that reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C), attained their highest stiffness at loads of 275 N and 487 N, respectively, for compression and tension. For joints subjected to moistening in conditions H = 85% and T = 28˚C, the maximum stiffness occurred at 76 N and 258 N, respectively. The process of joint drying in the air characterised by humidity of H = 40% and temperature T = 20 9
˚C caused that maximum stiffness of compressed joints became apparent at the load of 106 N, while that of stretched joints – at the force of 323 N. Moreover, it is quite apparent from Table 5 and Fig. 10 that joints subjected to compression exhibited distinctly poorer stiffness in all climatic conditions. Quantitatively speaking, stiffness of compressed joints was from 3.77 to 5.96 times lower in comparison with stretched joints. Table 5 and Fig. 10 also collate results of numerical calculations for identical joints. It is evident from Table 4 that maximum stiffness of joints subjected to compression amounted to 2.47 kNm/rad and 1.6 kNm/rad, respectively, for (H = 40%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. The difference of calculation results in relation to the laboratory measurements amounted, respectively, to +23.5% and -13.9%. On the other hand, maximum stiffness of joints subjected to tension amounted to 15.44 kNm/rad and 7.64 kNm/rad, respectively for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. Therefore, the difference of calculation results in relation to the laboratory measurements amounted to, respectively, +64.9% and +8.8%.
The
results of numerical calculations also revealed the regularity, mentioned earlier, of a rapid stiffness increase for small loads. In this case, joints attained maximum stiffness for the load of 100 N. Once this load was achieved, stiffness decreased considerably. Also in this case, it was demonstrated that the stiffness of compressed joints was from 4.77 to 6.25 times lower in comparison with the stiffness of stretched joints. Similar regularities in deformations and rigidities were also reported by [11] [13] [18].
3.3.Strength of joints The authors also determined strength of the experimental joints on the basis of laboratory results. For this purpose, they calculated the bending moment (MC and MT, respectively, for compression and tension). It is evident from Fig. 11 that together with the increase of air humidity and temperature, joint maximum strength decreased visibly. Reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) showed the highest strength of 19.8 Nm and 48.0 Nm for compression and tension, respectively. Following moistening of joints in H = 85% and T = 28 ˚C conditions, their strength decreased by 41.4% and 29.2%, respectively. Another joint drying process in air humidity and temperature conditions of H = 40% and T = 20 ˚C resulted in an increase of joint strength. However, in this case, maximum stiffness of joints was smaller than that of reference joints by 18.2% and 18.8%, respectively. Fig. 12 presents strength 10
changes of joints in the function of the angle deformation ∆f. It is clear from this Figure that, together with the increase of angle deformations, the strength curve asymptotically approached the maximum value MC(max) or MT(max). Once this value was achieved, the joints were usually destroyed. It can be mentioned here that reference joints obtained in conditions of factory (H = 41% and T = 26 ˚C) reached the highest strength at deformations of 0.013 rad and 0.009 rad, respectively, for compression and tension. For joints subjected to moistening in conditions H = 85% and T = 28 ˚C, the maximum strength occurred at 0.011 rad and 0.007 rad, respectively. The process of joint drying in the air characterised by humidity of H = 40% and temperature T = 20 ˚C caused that maximum strength of compressed joints became apparent at 0.020 rad, while that of stretched joints – at 0.009 rad. Moreover, it is quite clear from Table 5 and Fig. 12 that joints subjected to compression exhibited distinctly worse strength in all climatic conditions. Quantitatively speaking, the strength of compressed joints was from 2.40 to 2.93 times lower in comparison with stretched joints. A similar regularity was also reported [19] [21] [31]. Table 5 and Fig. 12 also present results of numerical calculations for the examined joints. It is evident from the table that maximum strength of joints subjected to compression amounted to 20.8 Nm and 46.0 Nm, respectively, for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. The difference of calculation results in relation to the laboratory measurements amounted, respectively, to +5.1% and +43.1%. On the other hand, maximum strength of joints subjected to tension amounted to 46.0 Nm and 32.0 Nm, respectively, for (H = 41%, T = 26 ˚C) and (H = 85% , T = 28 ˚C) climatic conditions. Therefore, the difference of calculation results in relation to the laboratory measurements amounted to, respectively, -4.2% and -5.9%. The results of numerical calculations also revealed the regularity mentioned earlier of a rapid strength increase for small increases in deformations. Joints attained maximum strength for maximum values of angle deformations. Once these values were reached, a destruction process followed which was mild and manifested itself in a continuous decline of bending moment values. Also in this case, it was demonstrated that the strength of compressed joints was from 2.21 to 1.92 times lower than the strength of stretched joints. The results of performed numerical calculations also provided information about the distribution of reduced von Mises stresses as well as about safety factors Xe for these joints (Fig. 13, 14). Figures 13a and 14a present von Mises reduced stresses and the 11
safety factor of joints subjected, respectively, to compression and tension, seasoned in air humidity of 41% and temperature of 26 ˚C. It is evident from these Figures that the highest reduced stresses concentrated in holes under the threaded part of the mandrel made in supports from particle boards. The developing stresses were caused by the pressure of the mandrel on the side surface of the hole. The maximum value of these stresses (for maximum loads) reached 10.25 MPa and 11.34 MPa, respectively for compressed and stretched joints. Also, in places of pressure of the mandrel on the hole side surface, the lowest values of the safety factor were determined and reached 0.395 and 0.357, respectively. Such low values of the safety factor Xe indicate that permanent damages occurred in these places, which reduced stiffness and strength of joints. Figures 13b and 14b present von Mises reduced stresses and safety factor of joints subjected to compression and tension, seasoned in conditions of air humidity of 85% and temperature of 26 ˚C. It is evident also from these Figures that the highest reduced stresses concentrated under the threaded part of the mandrel in holes made in particle board supports. These stresses were caused by the pressure of the mandrel against the side surface of the hole. The maximum value of these stresses attained 8.23 MPa and 9.57 MPa for compressed and stretched joints, respectively. In places where the mandrel pressed against the hole side surface also the lowest values of the safety factor occurred, which – for these joints – amounted to 0.28 and 0.24, respectively. From the comparison of calculated safety factor values, it is evident that for compressed and stretched joints seasoned in H = 41%, T = 26 ˚C conditions, safety factors were, respectively, by 41% and 48% higher in relation to safety factor values of joints seasoned in H = 85%, T = 28 ˚C conditions. Typical damages of arms illustrated in Fig. 15 caused by joint compression or tension corresponded with the results of numerical calculations indicating the same places of failure. It is worth mentioning that numerically calculated pressures on the hole in the support caused by the mandrel always concentrated on the side which underwent damage. It should be noted that in case of compression (Fig.15a), a part above the mandrel has been delaminated. But in case of tension, section below the mandrel (Fig.15b). These type of destructions dominate outside the scope of linear elasticity of joints. Comparing the illustration from the Figure 15a with stress distribution on the Figure 13, we will notice some regularity. The greatest stress are concentrated in the upper part of the hole. This means that with increasing of load, they contribute to delamination of the core and 12
facing panels. From the figures 14 we can observed that higher stresses are concentrated below of the mandrel under tension. Therefore, for loads larger than those from the linear elasticity range, delamination of panels will be below the connector (Fig. 15b). Tables 6 and 7 show the results of correlation analysis between the measuring results of the bending moment MC, MT and angle of rotation of joint arms ∆f determined in the laboratory and numerically. Input data for Spearman’s R correlation analysis derived from Fig. 12. It is evident from this collation that the determined correlation coefficients were significant with p < .05. This means that the elaborated numerical models simulated correctly the effect of changing air temperature and humidity on stiffness and strength of L-type corner joints manufactured from honeycomb sandwich wood composites.
Conclusions The objective of this study involved modelling and laboratory determination of the impact of changes in air humidity and temperature on the stiffness and strength of corner joints of honeycomb panels manufactures from wood composites. The performed laboratory experiments proved that the increase in air humidity and temperature deteriorated joint stiffness even by 25% and their strength – by up to 40%. For this reason, furniture manufactured and packed in dry climate and utilised in the tropical climate will be characterised by considerably lower quality, worse stiffness and strength. Drying joints (furniture) in climatic conditions similar to original ones will improve significantly their stiffness and strength. However, these properties will be worse in comparison with reference products. Therefore, articles manufactured from wood composites transported through the tropical zone to countries with dry climate should be specially protected against moisture. The elaborated methodology of numerical stiffness and strength modelling of joints is correct. It can be used in designing offices for virtual simulation of the quality of products manufactured from wood-based honeycomb sandwich composites subjected to changing parameters of air humidity and temperature
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[14] Malkoçoğlu A, Yerlikaya NÇ, Çakiroğlu FL. Effects of Number and Distance Between Dowels of Ready-To-Assemble Furniture on Bending Moment Resistance of corner joints. Wood Research 2013;58:671–80. [15] Yerlikaya N, Aktaş A. Enhancement of load-carrying capacity of corner joints in case-type furniture. Materials and Design 2012;37:393–401. doi:10.1016/j.matdes.2012.01.010. [16] Tankut AN, Tankut N. Evaluation the effects of edge banding type and thickness on the strength of corner joints in case-type furniture. Materials and Design 2010;31:2956–63. doi:10.1016/j.matdes.2009.12.022. [17] Atar M, Ozcifci A, Altinok M, Celikel U. Determination of diagonal compression and tension performances for case furniture corner joints constructed with wood biscuits. Materials and Design 2009;30:665–70. doi:10.1016/j.matdes.2008.05.023. [18] Kureli I, Altinok M. Determination of mechanical performances of the portable fasteners used on case furniture joints 2011;6:4893–901. doi:10.5897/AJAR11.284. [19] Altinok M, Taş HH, Çimen M. Effects of combined usage of traditional glue joint methods in box construction on strength of furniture. Materials and Design 2009;30:3313–7. doi:10.1016/j.matdes.2008.12.004. [20] Yerlikaya N. Effects of glass-fiber composite, dowel, and minifix fasteners on the failure load of corner joints in particleboard case-type furniture. Materials and Design 2012;39:63–71. doi:10.1016/j.matdes.2012.02.024. [21] Tankut AN, Tankut N. Investigations the effects of fastener, glue, and composite material types on the strength of corner joints in case-type furniture construction. Materials and Design 2009;30:4175–82. doi:10.1016/j.matdes.2009.04.038. [22] Smardzewski J, Rzepa B, Kilic H. Mechanical Properties of Externally Invisible Furniture Joints Made of Wood-Based Composites. BioResources 2016;11:1224– 39. [23] Koreny A, Simek M, Eckelman CA, Haviarova E. Mechanical properties of knock-down joints in honeycomb panels. BioResources 2013;8:4873–82. [24] Petutschnigg AJ, Koblinger R, Pristovnik M, Truskaller M, Dermouz H, Zimmer B. Leichtbauplatten aus Holzwerkstoffen?Teil I: Eckverbindungen. Holz Als Roh- Und Werkstoff 2004:405–10. doi:10.1007/s00107-004-0526-6. [25] Petutschnigg AJ, Koblinger R, Pristovnik M, Truskaller M, Dermouz H, Zimmer 15
B. Leichtbauplatten aus Holzwerkstoffen. Teil II: Untersuchung zum Schraubenausziehwiderstand. Holz Als Roh - Und Werkstoff 2005;63:19–22. doi:10.1007/S00107-004-0540-8. [26] Smardzewski J, Imirzi HO, Lange J, Podskarbi M. Assessment method of bench joints made of wood-based composites. Composite Structures 2015;123:123–31. doi:10.1016/j.compstruct.2014.12.039. [27] EN 318: 2002. Wood-based panels. Determination of dimensional changes associated with changes in relative humidity. n.d. [28] EN 310: 1993. Wood-based panels: Determination of modulus of elasticity in bending and of bending strength. n.d. [29] EN 322: 1993. Wood-based panels – Determination of moisture content. n.d. [30] PN-EN ISO 1924-2: 2010 Paper and board - Determination of tensile properties Part 2: Constant rate of elongation method (20 mm/min). n.d. [31] Ta HH. Strength properties of L-profiled furniture joints constructed with laminated wooden panels 2010;5:545–50.
16
List of figures Fig. 1. L-type corner joint Fig. 2. Structure of one element of joint: A – ABS rim 1 mm thick, B – particle board 12 mm thick, C – paper core of hexagonal cells (12 mm high walls) Fig. 3. Method of joint analysis: a) compression, b) tension Fig. 4. Joint loading with forces of initial assembly Fig. 5. Diagram used to determine conventional proportionality limit and yield point Fig. 6. A sample for measurements of elasticity limit and yield point of wood-based materials Fig. 7. Absolute moisture content of HDF and PB Fig. 8. Modulus of linear elasticity (MOE): a) HDF b), PB in static bending test Fig. 9. Static bending strength: a) HDF, b) PB Fig. 10. Change of joint stiffness in the function of force: a) compression, b) tension Fig. 11. Strength of joints Fig. 12. Stiffness of joints in: a) compression, b) tension Fig. 13. Von Mises stresses and safety factors of joints subjected to compression, seasoned in conditions of: a) air humidity of 41% and temperature of 26 ˚C, b) air humidity of 85% and temperature of 28 ˚C Fig. 14. Von Mises stresses and safety factor of joints subjected to tension, seasoned in conditions: a) air humidity 41% and temperature 26 ˚C, b) air humidity 85% and temperature 28 ˚C Fig. 15. Typical damage of joints during: a) compression, b) tension
17
Fig. 1
18
Fig. 2
19
Fig. 3
20
Fig. 4
21
Fig. 5
22
Fig. 6
23
Fig. 7
24
Fig. 8
25
Fig. 9
26
Fig. 10
27
Fig. 11
28
Fig. 12
29
Fig. 13
30
Fig. 14
31
Fig. 15
32
Table 1. Number of samples Type of samples
Type of test
L-type joints
Compression Tension
Beam PB Beam HDF Dumbbell PB Dumbbell HDF
Bending Tensile
Climatic conditions / number of samples H = 85%, T = 28 ˚C / 48 After drying to: H = 41%, T = 26 ˚C H = 85%, T = 28 ˚C H = 40%, T = 20 ˚C 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
Table 2. Properties of materials seasoned in H = 41% and T = 26 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1907/214*
4.60/0.40*
1.65/0.18*
3.78/0.33*
0.35
680/8.1*
HDF
4112/401*
26.83/1.41*
4.05/0.30*
14.49/0.68*
0.30
870/31*
Paper
5100/87*
89.43/6.20*
6.42/0.87*
16.80/1.25*
0.35
725/7.3*
ABS
2495
-
5.97
58.61
0.31
1150
Aluminum
68900
370
103
270
0.33
2705
1050-H14
* StD - Standard deviation
Table 3. Properties of materials seasoned in H = 85% and T = 28 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1141/186*
2.88/0.32*
1.00/0.17*
2.31/0.26*
0.32
732/10*
HDF
1498/102*
7.55/0.44*
1.34/0.09*
4.34/0.18*
0.30
921/27*
Paper
1430/78*
43.35/7.32*
2.83/0.21*
6.72/0.09*
0.33
786/16*
* StD - Standard deviation
33
Table 4. Properties of materials seasoned in H = 40% and T = 20 ˚C conditions Material
MOE
Tensile
Elastic
Yield point
Poisson’s
strength
limit R0.02
R0.2
ratio
Density kg/m3
MPa PB
1521/125*
3.74/0.21*
1.25/0.06*
3.05/023*
0.34
704/16*
HDF
2604/108*
15.01/0.97*
2.58/0.12*
8.40/0.15*
0.31
879/24*
Paper
3946/86*
67.34/6.54*
3.75/0.32*
16.80/0.12*
0.34
703/13*
* StD - Standard deviation
Table 5. Joint stiffnesses and strengths Test
Properties
Unit
FEM
H-41%,
H-85%,
H-40%,
H-41%,
H-85%,
T-26 ˚C
T-28 ˚C
T-20 ˚C
T-26 ˚C
T-28 ˚C
Compression P(max)
N
411
241
337
431
345
MC(max)
Nm
19.8
11.6
16.2
20.8
16.6
Kj(max)
kNm/rad
2.00
1.86
1.50
2.47
1.60
Tensile P(max)
N
812
577
657
900
540
MT(max)
Nm
48.0
34.0
39.0
46.0
32.0
Kj(max)
kNm/rad
9.36
7.02
8.95
15.44
7.64
34
Table 6. Correlation of bending moments MC and MT determined in the laboratory and numerically Compression
Average
StD
H-41%, T-26C
H-41%, T-26C
10.49810
6.469393
1.000000
FEM H-41%, T-26C
10.46022
6.506904
0.999790
Tensile
H-41%, T-26C
H-41%, T-26C
7.748247
5.146004
1.000000
FEM H-41%, T-26C
7.583780
4.865064
0.983080
Compression
H-85%, T-28C
H-85%, T-28C
16.33787
11.66430
1.000000
FEM H-85%, T-28C
15.83354
11.22623
0.999047
Tensile
H-85%, T-28C
H-85%, T-28C
16.02417
11.79860
1.000000
FEM H-85%, T-28C
16.03718
11.54809
0.999082
Marked correlation coefficients are significant with p <.05
Table 7. Correlation of angle of rotation of joint arms ∆f determined in the laboratory and numerically Compression
Average
StD
H-41%, T-26C
H-41%, T-26C
0.006510
0.002645
1.000000
FEM H-41%, T-26C
0.005969
0.003436
0.999071
Tensile
H-41%, T-26C
H-41%, T-26C
0.002205
0.000948
1.000000
FEM H-41%, T-26C
0.001526
0.000981
0.996621
Compression
H-85%, T-28C
H-85%, T-28C
0.007078
0.004292
1.000000
FEM H-85%, T-28C
0.007812
0.004663
0.888785
Tensile
H-85%, T-28C
H-85%, T-28C
0.003957
0.003561
1.000000
FEM H-85%, T-28C
0.004234
0.003651
0.981127
Marked correlation coefficients are significant with p <.05
35