FATIGUE BEHAVIOR AND DESIGN OF WOOD COMPOSITES AS FURNITURE COMPONENTS

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1 FATIGUE BEHAVIOR AD DESIG OF WOOD COMPOSITES AS FURITURE COMPOETS Li Dai, Grad Research Assistant, Jilei Zhang, Associate Professor, Dept. of Forest Products, Mississippi State University, Mississippi State, MS3976 Approved for publication as Conference Article o. FP 374 of the Forest and Wildlife Research Center, Mississippi State University Abstract This research project evaluated edge-wise bending fatigue behavior of selected wood composites as upholstered furniture frame stock. Edgewise bending fatigue behaviors of selected wood composites were evaluated by subjecting them to zero-to-maximum constant amplitude loads. Regression analysis of S- data (applied nominal stress versus log number of cycles to failure) indicated a linear relationship between applied nominal stress and the logarithm of number of cycles to failure. This relationship also can be expressed in the form of including material modulus of rupture, and constants E and H which were correlated to basic wood element sizes of composite raw material such as veneer, strand, and particles. The design moment value for a structural member subjected to stepped cycle bending moments in a sofa frame can be determined by multiplying a constant to the maximum fatigue moment level to which the member needs to resist without failure. These constants were 1.7,.0 and.5 for plywood, OSB, and PB, respectively. Introduction Strength design of upholstered furniture frames should take into account member material fatigue strength properties since most service failures of the frames appear to be fatigue related [10]. As more wood composites such as plywood, oriented strandboard (OSB), and particleboard (PB) are used as furniture frame stock, the information related to fatigue strength properties of various types of wood composites becomes more essential. Plywood is described as a flat panel built up of sheets of veneer called plies, united under pressure by a bonding agent to create a panel with an adhesive bond between plies [17]. OSB is an engineered structural-use panel manufactured from thin wood strands bonded together with waterproof resin under heat and pressure. Orientation of wood strands with a typical aspect ratio (that is, strand length divided by width) of at least three can produce a panel product with greater bending strength and stiffness in the oriented or aligned direction. PB is produced by mechanically reducing the material into small particles, applying adhesive to the particles, and consolidating a loose mat of the particles with heat and pressure into a panel product. Fatigue study results of wood and plywood subjected to repeated and reversed flat-wise bending stresses 1,790 cycles per minute [13] indicated that the S- curves (percentage of mean control static modulus of rupture versus the number of cycles to failure) for wood does not exhibit a knee as do the curves of ferrous metals. o endurance limits were established for tested wood specimens and the experimental data indicates that if an endurance limit for wood exists, it occurs above 50 million cycles. The fatigue strength for 50 million cycles of reversed stress is approximately 7 percent of the static modulus of rupture (MOR) for the species investigated (yellow birch, yellow-poplar, Sitka spruce, and Douglas fir) whether in the form of solid wood or plywood. The fatigue strength of solid Sitka spruce and Douglas fir at 50 million cycles of repeated stress is approximately 36 percent of their respective static modulus of rupture. The values of the endurance ratio for some species of solid wood, which is the ratio of endurance limit to ultimate static stress, are of the order one-quarter to one-third of the ultimate static stress [5]. The edge-wise fatigue bending resistance of medium density fiberboard (MDF), OSB, and PB was investigated [4] with the stress-based and matched piece approach. Experimental results indicated that all three materials would be expected to have fatigue lives of at least 00,000 cycles at the load stress levels of 40 percent of MOR or less.

2 The study indicated that fatigue life amounted to over one million cycles when the stress level was 30 percent of MOR values. o mathematical representations were derived to approximate S- curves of evaluated materials. Shear fatigue properties of 3/3 inch thick commercial OSB were investigated [6] under repeated sinusoidal loading using a five-point flat-wise bending test. Regression of the fatigue data of stress-level (the percentage of the static shear strength) versus the log number of cycles-to-failure resulted in a linear S- curve. The coefficients of variation of the number of cycles-to-failure recorded for five tested specimen groups ranged from 97 to 185 percent. Factors influencing fatigue strength and life of wood and wood composites are frequency of cycling, repetition or reversal of loading, stress ratio, temperature, moisture content, and specimen size [17]. Creep, temperature rise, and loss of moisture content, occur in tests of wood for fatigue strength at faster cyclic loading. Smaller rises in temperature would be expected for slower cyclic loading or lower stresses. Decreases in moisture content are likely related to temperature rise. The furniture procurement programs of the US government require that upholstered furniture manufacturers conduct the General Service Administration (GSA) performance test regimen FAE-80-14A [11]. Then provide furniture performance data to prove satisfaction of performance specifications suitable for use by the federal government. Performance tests are based on a zero-to-maximum cyclic stepped load (variable amplitude loading) method rather than static load or constant amplitude cycling load method [8, 9]. In this cyclic stepped load method, a given initial maximum load is applied to the furniture at a rate of 0 cycles per minute, for 5,000 cycles. After the prescribed number of cycles has been completed, the maximum load is increased by a given increment and the procedure is repeated. This process is continued until a desired load level has been reached or until the frame or its components suffer disabling damage [10]. The acceptance levels used by the GSA are light, medium, and heavy service. Strength and durability design of upholstered furniture frames, to satisfy performance test standards such as GSA performance test regimen needs information regarding fatigue strength properties of their components. However, the strength properties currently available for the design of upholstered furniture frames have primarily been determined by static load tests. Research to determine the fatigue properties of wood composites subjected to cyclic loads in furniture applications has been minimal. Although fatigue studies have been done extensively in the area of wood and wood composites as structural components of bridges, roofs, walls, and floors, information has not been systematically introduced into design of furniture required resisting repeated loads as structures. Research results are not in the form ready for engineers to design a furniture frame considering fatigue effects. This is especially pertinent since more plywood, OSB, and engineered wood composite products are currently being used for frame structural materials. The S- curves of glass-fiber-reinforce thermoplastics composites tested under zero-to-maximum tension or bending are approximated by a relationship of the form, S = u (1 0.1 log 10 f ) [1], where u is the ultimate tensile strength. The constant 0.1 determines the slope of the resulting straight line on a log-linear plot. The methods of Juvinall [1] or Shigley [16] are widely recommended as the procedures for estimating entire stresslife curves for engineering metals. The Palmgren-Miner rule [14, 15] can be employed to estimate the fatigue life of a machine component under a given variable loading condition based on its S- curve. The primary objective of this research was to evaluate the fatigue performance of wood composites as furniture frame stock. Then to develop experimental and design procedure for furniture frame engineering design while considering fatigue effects. Therefore, the secondary objectives included: 1) obtain experimental stress-life curves of selected wood composites, ) explore different methods of deriving estimated S- curves for wood composites, 3) estimate fatigue life of wood composite materials subjected to cyclic stepped loads, and 4) derive equivalent static moments and their ratios to applied fatigue moments for furniture frame design considering of fatigue effects.

3 Materials and Methods Approach This research uses the stress-based approach to analyze fatigue behavior of simply supported wood-based composites subjected to edge-wise zero-to-maximum center cyclic loading. The S- curves were proposed to describe the fatigue behaviors of wood composites subjected to the zero-to-maximum repeated cyclic loading. First static bending strength of each of six wood-based composites was evaluated to obtain their individual mean values of MOR. This was followed by an investigation of a stress-life curve of each composite by subjecting specimens to different levels of zero-to-maximum constant amplitude cyclic loadings. These stress levels were percentage of the mean MOR value. Juvinall and Adkins methods [1] were utilized to derive the estimated S- curves for the composites. The Palmgren-Miner rule was applied to estimate the fatigue life of wood composites as upholstered furniture stock subjected to cyclic stepped loads. The dimension of a full size sofa frame member, back top rail, was estimated using the Palmgren-Miner rule based on its stepped load schedule and S- curves of materials. Materials Six wood composites were included in this study as shown in Table 1. The plywood was Frame 1 furniture-grade, 5-ply southern yellow pine plywood. The full-size sheet of plywood (4 8 ft) was constructed with the grade C center ply aligned parallel to the grade A/B face ply. The face plies were aligned parallel to the sheet eight foot direction. The two grade C core even-number plies were aligned perpendicular, and adjacent to the faces. A phenol-formaldehyde resin was used as the binder. OSB#1 was an aspen board with face strands oriented in the direction parallel to eight foot direction of 4 by 8-ft full-size sheets. The other three OSB materials were southern yellow pine board with face strands oriented in the direction parallel to the eight foot direction of 4 by 8-ft full-size sheets, and bonded with an isocyanate emulsion. PB was southern yellow pine board (4 8 ft), bonded with a urea-formaldehyde resin. Bending specimens in this study were fabricated from cutting full-size sheets of the plywood, OSB, and PB panels randomly selected from panel stacks supplied by manufacturers. All specimens were conditioned in an 8% equilibrium moisture content chamber prior to tests, and were randomly assigned to testing groups. Table 1 - Mean values of physical and mechanical properties of tested materials. a Moisture Modulus of Modulus Material type Thickness Content Density Rupture Elasticity (in.) (%) (pcf) (psi) ( 10 6 psi) of Plywood 3/4 7.8 (4) 4.0 (3) 6,600 (15) 0.99 (17) OSB#1 3/3 5.8 (4) 4.3 (5) 4,600 (10) 0.94 (5) OSB# 3/3 6.8 (5) 41.0 (5) 4,00 (16) 0.74 (8) OSB#3 3/3 6. (5) 41.5 (5) 3,600 (9) 0.63 (4) OSB#4 3/3 6.1 (4) 40.1 (5),800 (15) 0.5 (6) Particleboard 3/4 7.7 () 49.0 (3) 1,600 (10) 0.33 (10) a Values in parentheses are coefficients of variation in percent. Static tests Simply supported center-point loaded edge-wise bending tests were performed to obtain mean values of MOR for all composites. Specimens measured -inches wide by 40-inches long, with their length directions parallel to the full size sheet eight foot direction. Specimens were tested according to ASTM D4761 [] at a span to depth ratio of 18. Thirty replications were tested for each of the three materials evaluated. All static bending tests were conducted on a hydraulic SATEC universal-testing machine at a loading rate of 0.10 inch per minute. Loaddeflection data of the tested specimens were recorded. Also specimen moisture content and density were also measured [3]. Fatigue tests Specimens of constant amplitude cyclic tests measured inches wide by 40 inches long which was the same as the static test. Specimens were randomly picked from the same specimen sources in static tests. Constant amplitude cyclic tests were conducted on a specially designed air cylinder and pipe rack system as shown in

4 Figure 1. This set-up allowed 10 specimens to be tested simultaneously. The specimens were simply supported with a support span of 36 inches and tested edge-wise using center point loads. Figure 1 A specially designed air cylinder and pipe rack setup for constant amplitude cyclic tests. Specimens of plywood and OSB # were subjected to eight nominal stress levels. These stress levels were 90, 80, 75, 70, 65, 60, 55, and 50 percent of the mean MOR value of each material, respectively. Six nominal stress levels were applied to OSB #1, OSB #3, and OSB #4, respectively. They were 80, 75, 70, 65, 60, and 55 percent of the mean MOR value of each material. ominal stress levels applied to PB were 90, 80, 75, 70, 65, 60, 55, 50, 45, and 35 percent of its mean MOR value. Ten replications were tested for each cyclic load level of each material group. Zero-to-maximum cyclic loads were applied to specimens by air cylinders for each load level at a rate of 0 cycles per minute [11]. The fatigue cycle starts with zero loads, then the load reaches its maximum value for 0.75 second, drops to zero and retains zero for 0.75 second until the next load cycle starts. A programmable logic controller (PLC) and electrical re-settable counter system recorded the number of cycles to failure (fatigue life) completed. Limit switches actuated and stopped the test when the tested specimen completely broke into two parts. All specimens were tested in the lab room maintained at the temperature of 74 F and 50 percent relative humidity. Results and Discussion Static tests Table 1 summarizes the mean values of the physical and mechanical properties of evaluated materials. Mean values of MOR in column 5 were considered as the control strength for fatigue test specimens to determine fatigue load levels. S- curves Individual data points of applied nominal stress versus fatigue life, the number of cycles to failure, of each evaluated material were plotted on a linear-log coordinate system, as shown in Figures to 7. The COVs of fatigue life averaged 19, 109, 16, 113, 93, and 101 percent for plywood, OSB#1, OSB#, OSB#3, OSB#4, and PB, respectively. The linear-log plots indicated an approximately linear relationship between nominal stress and

5 log fatigue life. Therefore, the following equation was employed to fit individual data points using the least square regression (LSR) method for each material data set: S = C - D log 10 f... (1) where S = applied nominal stress (psi.); f = number of cycles to failure; C, D = fitting constants %low limit LSR line Cycles t o failure Figure Individual data points and regression S- curves of plywood were plotted on linear-log coordinate system LSR line 5% low limit ominal Stress (psi) Cycles to failure Figure 3 Individual data points and regression S- curves of OSB #1 were plotted on linear-log coordinate system.

6 5%Low limit LSR line Cycles t o failure Figure 4 Individual data points and regression S- curves of OSB # were plotted on linear-log coordinate system % low limit LSR line 300 ominal Stress (psi) Cycles to failure Figure 5 Individual data points and regression S- curves of OSB #3 were plotted on linear-log coordinate system.

7 3000 LSR line 5% low limit 500 ominal Stress (psi) Cycles to failure Figure 6 Individual data points and regression S- curves of OSB #4 were plotted on linear-log coordinate system. 5%low limit LSR line Cycles to failure Figure 7 Individual data points and regression S- curves of PB were plotted on linear-log coordinate system. Table gives the regression fitting constant values of C and D, and coefficient of determination r values of derived equations for each of the materials. The Juvinall method was proposed to derive estimated equations of S- curves of wood composites using fatigue strengths, m u and m u, at two specified numbers of cycles, cycle and cycle, respectively. The reduction factor at 1000-cycle is m, which is calculated based on the fatigue strength at 1000-cycle divided by ultimate bending strength (MOR), u. The reduction factor at cycle is m, which is calculated based on the fatigue strength at cycle divided by ultimate bending strength, u. Also, m values show that fatigue strengths were 56, 5, and 40 percent of MOR values for plywood, OSB, and PB, respectively, at one million cycles. PB tends to show lower values for m and m values than plywood and OSB.

8 Table Constants of estimated S- curve equations derived based on all data points, and expressed with different methods. Regression Juvinall Adkins Material type MOR C D r m m E H (psi) Pine plywood 6,600 5, OSB OSB#1 4,600 4, OSB# 4,00 3, OSB#3 3,600 3, OSB#4,800, Avg. = Particleboard 1,600 1, The Adkins method was applied. Therefore, the estimated S- curves of wood composites including, u, were derived accordingly based on equation (1). The equation had the following format: S = u (E - H log 10 f )... () where S = applied nominal stress (psi.); u = ultimate bending strength (MOR), (psi); f = number of cycles to failure; E = C/ u ; H = D/ u. The resulting constants E and H were given in Table in the Adkins columns. The constant, E, was 0.88, 0.9, and 0.96, and the constant, H, was 0.05, 0.07, and 0.09 for plywood, OSB, and particleboard, respectively. These indicated that the constants are correlated to the sizes of basic wood elements composing of each material such as veneer, strand, and particleboard. Low limit regression lines at 95% were derived for the materials. For each of the applied load levels of each tested material, the corresponding number of cycles to failure at the low 5% point was calculated based on mean and standard deviation of the ten sample points at each load level. Then the equation (1) was employed to fit these individual data points, i.e., one data point for each applied load level of each material. Table 3 shows the constant results, C and D for regression, and E and H for Adkins method. Results of derived constants E and H values in Table 3 might suggest that for practical design purposes of considering fatigue effects the S- curves of wood composites evaluated in this study could be approximated by equation (), where the constant E value is 0.85, and the constant H values were 0.06, 0.08, and 0.10, for plywood, OSB, and particleboard, respectively. Figures to 7 show these S- curves for each of six materials. Table 3 Constants of estimated S- curve equations derived based on 5% low limit data points, and expressed with different methods. Regression Juvinall Adkins Material type MOR C D r m m E H (psi) Pine plywood 6,600 5, OSB OSB#1 4,600 4, OSB# 4,00 3, OSB#3 3,600 3, OSB#4,800, Avg. = Particleboard 1,600 1,

9 Full-size Frame Member Estimation The Palmgren-Miner rule was proposed to estimate the fatigue life of a full-size member in a sofa frame subjected to cyclic stepped loads. The Palmgren-Miner rule states unity summation of life fraction: 1 f 1 f 3 f 3... j fj 1...(3) where j = number of cycles applied to a member at the bending moment M j ; fj = number of cycles to failure from the member material S- curve for the bending moment M j. The depth of a 7-inch long back top rail of a three seat sofa frame for meeting the heavy-service acceptance level were calculated to illustrate steps for estimating member sizes based on known S- curves and fatigue load schedules. The cyclic stepped load schedule (Table 4) of the frame performance test, Top Rails-Front to Back (General Service Administration 1998) was selected as external fatigue loads applied to simply supported back top rails. Three identical loads, P, are applied at the center-point and at points 1/6 the span, L, from each end, respectively. Therefore, the maximum bending M j at the center point for each fatigue level can be calculated with the formula M j = 5PL/1. Table 4 Stepped cyclic loading schedule for 7-inch-long back top rails and maximum moment in back top rails for each fatigue load level under the simple-support boundary condition. umber of j P (lb.) loads Cumulative cycles Serviceacceptance level M j (lb.-in.) ,000 Light-Service, ,000 Medium-Service 3, ,000 3, ,000 Heavy-Service 4,500 Fatigue life of a back top rail subjected to the stepped cyclic load schedule can be estimated using the Palmgren- Miner rule of equation (3): 5,000 5,000 5,000 5, (4) f 1 f f 3 f 4 For plywood, the S- curve equation is, S = 6,600 ( log 10 fj ). For a rectangular cross-section beam subjected to a bending moment, stress and moment has the following relationship: S 6M bh j...(5) where M j = nominal applied moment (lb.-in.) in Table 4; b = beam member width (in.); h = beam member depth (in.). Substituting the stress-moment equation into the S- curve equation yielded the following relationship: fj 10 C 6M j D Dbh...(6) Then, substituting fj into the Palmgren-Miner rule equation [3] yielded the following equation:

10 10 5,000 5,000 C 6M D Dbh 10 5,000 C 6M 3 D Dbh 10 5,000 C M 4 D Dbh 10 C 6M1 6 D Dbh 1...(7) For a given rail member thickness of 0.75 inch, a minimum rail depth of 3.05 inches results. Table 5 summarizes rail depths calculated for each material if it was used for a 7-inch-long back top rail in a sofa frame. Table 5 Estimated depths of 7-inch-long back top rails satisfying the heavy-service acceptance level for using different materials. Equivalent Material type Applied Moment Depth Moment Ratio (lb.-in.) (in.) (lb.-in.) Plywood 4, , OSB#1 4, ,095.0 OSB# 4, ,094.0 OSB#3 4, ,095.0 OSB#4 4, ,095.0 Particleboard 4, ,56.5 Equivalent Static Moment Based on the depth values in Table 5 calculated for considering fatigue effects, equivalent maximum static moment values, M u, could be calculated using the stress-moment relation by setting maximum bending stress MOR b h M u equal to the MOR value of the material used, which yields moments, 6. Therefore, with the given beam width and calculated depth h of each member in Table 5, the corresponding equivalent static moments for each material can be calculated as shown in column 4. The ratio of the equivalent static moment value to the corresponding fatigue moment was 1.7,.0 and.5 for plywood, OSB, and PB, respectively. These values suggest that for design of a sofa frame member to satisfy a specified fatigue moment level of its stepped cyclic load schedule, a static design moment value could be determined by multiplying a constant by the fatigue moment to which the member was subjected. The ratios calculated from this study also show that these constants are different among different types of wood composites. Conclusions This research project evaluated edge-wise bending fatigue behavior of selected wood composites as upholstered furniture frame stock. Regression analysis of S- data concluded that the functional relationship between the fatigue stress and the log number of cycles to failure could be expressed as S = C - D log 10 f for wood composites evaluated in this study. By incorporating MOR into the stress and log fatigue life equation, it was found that the S- curves of wood composites could be approximated by S = MOR (E H log 10 f ). This equation reflects the relationship between material static strength and fatigue life. The constant E, was 0.88, 0.9, and 0.96, and the constant, H, was 0.05, 0.07, and 0.09 for plywood, OSB, and particleboard, respectively. It seems that the constant E and H values were correlated to basic wood element sizes of composite raw material such as veneer, strand, and particles. The design moment value for a structural member subjected to stepped cycle bending moments in a sofa frame can be determined by multiplying a constant to the maximum fatigue moment level to which the member needs to resist without failure. These constants are different among different types of wood composites. They were 1.7,.0 and.5 for plywood, OSB, and PB, respectively, based on results from this study.

11 Literature Cited 1. Adkins, D. W. and R. G. Kander. Fatigue performance of glass reinforced thermoplastics. Paper o , Proceeding of the 4th Annual Conference on Advance Composites, September 1988, Dearborn, MI. Sponsored by ASM International, Materials park, OH American Society for Testing and Materials. Standard test methods for mechanical properties of lumber and wood-base structural material. ASTM D ASTM, West Conshohocken, PA American Society for Testing and Materials. Standard test methods for specific gravity of wood and wood-based material. ASTM D ASTM, West Conshohocken, PA Bao, Z. and C. A. Eckelman. Fatigue Life and Design Stresses for Wood Composites Used in Furniture. Forest Prod. J. 45(7/8): Bodig, J. and B. A. Jayne. Mechanics of Wood and Wood Composites. Van ostrand Reinhold Company Inc. ew York. pp Cai, Z, J. P. Bradtmueller, M. O. Hunt, K. J. Fridley, and D. V. Rosowsky. Fatigue behavior of OSB in shear. Forest Prod. J. 46(10): Dowling,. E. Mechanical Behavior of Materials. Prentice-Hall, Inc. ew Jersey. Pp Eckelman, C. A. Performance testing of furniture. Part I. Underlying concepts. Forest Prod. J. 38(3): Eckelman, C. A. Performance testing of furniture. Part II. A multipurpose universal structural performance test method. Forest Prod. J. 38(4): Eckelman, C. A. and J. Zhang. Uses of the General Service Administration performance test method for upholstered furniture in the engineering of upholstered furniture frames. Holz als Roh- und Werkstoff 53: General Service Administration. FAE-80-14A. Upholstered furniture test method. Furniture Commodity Center, Federal Supply Services. Washington. D. C Juvinall, R. C. and K. M. Marshek.Fundamentals of machine component design, nd ed., John Wiley, ew York, Y Kommers, W.J. The fatigue behavior of wood and plywood subjected to repeated and reversed bending stresses. o USDA Forest Service, Forest Products Laboratory, Madison, WI Miner, M. A. Cumulative damage in fatigue. J. of Applied Mechanics 1(3): A Palmgren, A. Die lebensdauer von kugallagern. Ver. Deut Ingr. 68: Shigley, J. E. and C. R. Mischke. Mechanical engineering design, 5th ed., McGraw-Hill, ew York, Y USDA Forest Service. Wood Handbook: Wood as an engineering material. Forest Prod. Soc., Madison, WI