Fatigue performance of wood-based composites as upholstered furniture frame stock.
Edgewise edge·wise also edge·ways
1. With the edge foremost.
2. On, by, with, or toward the edge.
Adv. 1. bending fatigue performances of three wood-based composites (southern yellow pine plywood, oriented strandboard, and particleboard) were evaluated by subjecting them to zero-to-maximum constant amplitude and stepped cyclic cyclic /cyc·lic/ (sik´lik) pertaining to or occurring in a cycle or cycles; applied to chemical compounds containing a ring of atoms in the nucleus.
cy·clic or cy·cli·cal
1. bending loads. Results of zero-to-maximum constant amplitude cyclic load tests indicated that fatigue lives of 25,000 cycles each began at stress levels of 75 and 70 percent of modulus of rupture the measure of the force necessary to break a given substance across, as a beam, expressed by eighteen times the load which is required to break a bar of one inch square, supported flatwise at two points one foot apart, and loaded in the middle between the points of support.
- Rankine. (MOR MOR
MOR adj abbr (MUS) (= middle-of-the-road) → para el gran público
MOR adj abbr (Mus) (= ) values for the plywood and oriented strandboard evaluated in this study, respectively. Particleboard fatigue life did not reach 25,000 cycles until the stress level was reduced to 55 percent of its MOR value. Regression analysis In statistics, a mathematical method of modeling the relationships among three or more variables. It is used to predict the value of one variable given the values of the others. For example, a model might estimate sales based on age and gender. of S-N data (applied nominal stress versus log number of cycles to failure) indicated a linear relationship between applied nominal stress and the logarithm logarithm (lŏg`ərĭthəm) [Gr.,=relation number], number associated with a positive number, being the power to which a third number, called the base, must be raised in order to obtain the given positive number. of number of cycles to failure. It was observed that the S-N function relationship could be expressed with the form S = MOR (1 - H X [log.sub.10] [N.sub.f]). The constant H values in the equation were 0.05, 0.07, and 0.09 for plywood, oriented strandboard, and particleboard, respectively. It seems that the constant H is correlated to basic wood element sizes of composite raw material such as veneer veneer (vənēr`), thin leaf of wood applied with glue to a panel or frame of solid wood. The art of veneer developed with early civilization. and particles. Cyclic stepped load tests of full-size sofa back top rail specimens verified that the Palmgren-Miner rule is an effective method to estimate fatigue life of wood composites subjected to the edgewise cyclic stepped bending stresses using their S-N curves.
Strength design of upholstered furniture frames should take into account information about member material fatigue strength properties since most service failures of the frames appear to be fatigue related (Eckelman and Zhang 1995). As more plywood and engineered wood composites are used for furniture frame structural materials Structural materials
Construction materials which, because of their ability to withstand external forces, are considered in the design of a structural framework.
Brick is the oldest of all artificial building materials. , and furniture manufacturers continue to seek new materials in order to re-engineer their products, the information related to fatigue strength properties of various types of wood composites becomes increasingly essential.
In engineering, the term fatigue is defined as the progressive damage that occurs in a material subjected to cyclic loading (USDA USDA,
n.pr See United States Department of Agriculture. 1999). This loading may be repeated (stresses of the same sign, that is, always compression or always tension, for example, zero-to-maximum complete repeated stressing refers to cases with a zero stress ratio) or reversed (stresses of alternating compression and tension, that is, a non-zero stress ratio). The stress ratio, R, is defined as the ratio of minimum stress over maximum stress per cycle (Dowling 1999). The stress range is the difference between the maximum and the minimum stress values. Half the stress range is called the stress amplitude. Averaging the maximum and minimum values gives the mean stress. Fatigue life is the number of cycles that are sustained before failure, while fatigue strength is the maximum stress attained in the stress cycle determining fatigue life. Fatigue strength versus life is a stress-life curve, also called an S-N curve. The stress amplitude or nominal stress is commonly plotted versus the number of cycles to failure in metals. The stress level (the percentage of the static strength) versus the number of cycles to failure is commonly seen in wood and wood composites research publications (Kommers 1943, Cai et al. 1996). The fatigue limit Fatigue limit is a property of ferrous alloys and titanium alloys. It is the constant amplitude (or range) of cyclic stress that can be applied to a material without causing fatigue failure. , or endurance limit, is defined as the stress to which a specimen can be subjected an infinite number infinite number
a number so large as to be uncountable. Represented by 8, frequently obtained by 'dividing' by zero. of times with-out failure.
There are three major approaches to analyzing and designing against fatigue failures: the stress-based approach, the strain-based approach, and the fracture mechanics Fracture mechanics is a method for predicting failure of a structure containing a crack. It uses methods of analytical Solid mechanics to calculate the driving force on a crack and those of experimental Solid mechanics to characterize the material's resistance to fracture. approach (Dowling 1999). The stress-based approach is to base analysis on the nominal (average) stresses in the region of the component being analyzed. The nominal stress that can be resisted under cyclic loading is determined by considering mean stresses and by making adjustments for the effects of stress raisers. The strain-based approach involves more detailed analysis of the localized yielding that may occur at stress raisers during cyclic loading. The fracture mechanics approach specifically treats growing cracks using the methods of fracture mechanics.
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 (MC), and specimen size (USDA 1999).
Creep, temperature rise, and loss of MC occur in tests of wood for fatigue strength (USDA 1999) at faster cyclic loading. Smaller rises in temperature would be expected for slower cyclic loading or lower stresses. Decreases in MC are probably related to temperature rise.
Fatigue study results of wood and plywood subjected to repeated and reversed flatwise bending stresses at 1,790 cycles per minute (Kommers 1943) indicated that the S-N curves (percentage of mean control static modulus of rupture [MOR] versus the number of cycles to failure) for wood does not exhibit a "knee" as do the curves of ferrous ferrous (fĕr`əs), iron in the +2 valence state.
Containing or having to do with iron. The difference between ferrous and ferric is the number of valence electrons they contain (ferrous contains two and ferric contains three), which metals. No endurance limits were established for tested wood specimens, and the experimental data indicate 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 27 percent of the static 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 the static MOR of the materials.
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 (Bodig and Jayne 1982).
The edgewise fatigue bending resistance of medium density fiberboard (MDF (1) (Main Distribution Frame) A wiring rack that connects outside lines with internal lines. It is used to connect public or private lines coming into the building to internal networks. ), oriented strandboard (OSB OSB
Order of Saint Benedict ), and particleboard has been investigated (Bao and Eckelman 1995) 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 200,000 cycles at the load stress levels of 40 percent of MOR or less. The study indicated that fatigue life amounted to over 1 million cycles when the stress level was 30 percent of MOR values. No mathematical representations were derived to approximate S-N curves of evaluated materials.
Shear fatigue properties of 23/32-inch-thick commercial OSB were investigated (Cai et. al 1996) under repeated sinusoidal sinusoidal /si·nus·oi·dal/ (si?nu-soi´dal)
1. located in a sinusoid or affecting the circulation in the region of a sinusoid.
2. shaped like or pertaining to a sine wave. loading using a five-point flatwise bending test. Regression of the fatigue data of stress-level (the percentage of the static shear strength For the shear strength of soil, see .
Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear. ) versus the log number of cycles-to-failure resulted in a linear S-N curve. The coefficients of variation (COVs) of the number of cycles-to-failure recorded for five tested specimen groups ranged from 97 to 185 percent.
A preliminary study of low-cycle fatigue of black spruce under parallel-to-grain compression (Gong and Smith 1999) indicated that residual strength Residual strength is the load or force (usually mechanical) that a damaged object or material can still carry without failing. of fatigue specimens could exceed static compressive strength Compressive strength is the capacity of a material to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed. Concrete can be made to have high compressive strength, e.g. . The effective modulus increases rapidly then decreases gradually with the number load cycles for a 95 percent peak stress level.
The continued study of the failure mechanism of black spruce under parallel-to-grain compression (Gong and Smith 2000) indicated that fatigue damage develops from both existing kinks, which are formed during the first load cycle, and newly formed kinks due to the load cycling. The failure process of wood under sustained loads can be divided into three separate stages: 1) kink initiation; 2) kink growth; and 3) macroscopic macroscopic /mac·ro·scop·ic/ (mak?ro-skop´ik) gross (2).
mac·ro·scop·ic or mac·ro·scop·i·cal
1. Large enough to be perceived or examined by the unaided eye.
The furniture procurement programs of the U.S. federal government require that upholstered furniture manufacturers conduct the General Service Administration (GSA (1) (Global mobile Suppliers Association, Sawbridgeworth, U.K., www.gsacom.com) A membership organization of suppliers of GSM products and services. Its goal is to promote GSM as the worldwide mobile communications standard. See GSM Association and GSM. ) performance test regimen FNAE-80-214A (GSA 1998), and 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 (R = 0) cyclic stepped load (variable amplitude loading) method rather than static load or constant amplitude cycling load method (Eckelman 1988a, 1988b). In this cyclic stepped load method, a given initial maximum load is applied to the furniture at a rate of 20 cycles per minute, for 25,000 cycles. After the prescribed number of cycles has been completed, the maximum load is increased by a given increment To add a number to another number. Incrementing a counter means adding 1 to its current value. , 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 dis·a·ble
tr.v. dis·a·bled, dis·a·bling, dis·a·bles
1. To deprive of capability or effectiveness, especially to impair the physical abilities of.
2. Law To render legally disqualified. damage (Eckelman and Zhang 1995). The acceptance levels used by the GSA are light, medium, and heavy service.
Strength design of upholstered wood furniture frames, to satisfy durability performance test standards such as the 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 mostly 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 the design of furniture requiring resisting repeated loads as structures. Research findings are not in the form ready for furniture engineers to design a furniture frame considering fatigue effects. This is especially pertinent now as more plywood, OSB, and engineered wood composite products are being used as frame structural materials.
The S-N curves of glass-fiber-reinforced thermoplastic A polymer material that turns to liquid when heated and becomes solid when cooled. There are more than 40 types of thermoplastics, including acrylic, polypropylene, polycarbonate and polyethylene. composites tested under zero-to-maximum tension or bending are approximated by a relationship of the form, S = [[sigma].sub.u] (1 - 0.1 X [log.sub.10] [N.sub.f]) (Adkins 1988), where [[sigma].sub.u] is the ultimate tensile strength tensile strength
Ratio of the maximum load a material can support without fracture when being stretched to the original area of a cross section of the material. When stresses less than the tensile strength are removed, a material completely or partially returns to its . The constant 0.1 determines the slope of the resulting straight line on a log-linear plot. The methods of Juvinall (Juvinall and Marshek 1991) or Shigley (Shigley and Mischke 1989) are widely recommended as the procedures for estimating entire stress-life curves for engineering metals. The Palmgren-Miner rule (Palmgren 1924, Miner 1945) can be employed to estimate the fatigue life of a machine component under a given variable loading condition based on its S-N (stress versus the number of cycles-to-failure) curve.
[FIGURE 1 OMITTED]
Very limited application and verification studies using those methods have been found in the area of wood structures and their components, especially in estimating the fatigue life of furniture frame components subjected to cyclic stepped loads. Development of a method for estimating the fatigue life of furniture frame components will form the basis for incorporating material fatigue data into the furniture engineering design process to take this important factor into consideration.
The primary objective of this research was to evaluate the fatigue performance of wood-based composites as furniture frame stock and to develop an experimental and design procedure for furniture frame engineering design considering the fatigue effects. Therefore, the secondary objectives included: 1) obtain stress-life curves of wood composite materials; 2) estimate fatigue life of wood composite materials subjected to cyclic stepped loads; and 3) explore different methods of deriving estimated S-N curves for wood composites as upholstered furniture frame stock.
Materials and methods
This research uses the stress-based approach to analyze fatigue behavior of simply supported wood-based composites subjected to edgewise zero-to-maximum (R = 0) center cyclic loading. The S-N curves (applied nominal stress versus the number of cycles to failure) were proposed to describe the fatigue properties of wood composites subjected to the zero-to-maximum repeated cyclic loading.
Static bending strength properties of wood composites were evaluated first to obtain mean values of MOR, followed by an investigation of stress-life curves of wood composites subjected to zero-to-maximum constant amplitude cyclic loading. The methods of Juvinall (Juvinall and Marshek 1991) and Adkins (1988) were proposed to derive the estimated S-N curves for wood composites.
The Palmgren-Miner rule was proposed 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 See rules based. on its stepped load schedule and S-N curves of materials. Fatigue tests of simply supported full size back top rail specimens were performed under zero-to-maximum cyclic stepped load schedules to validate the Palmgren-Miner rule.
The wood-based materials included in this study were southern yellow pine plywood, OSB, and particleboard. The plywood was Frame 1 furniture-grade, 0.75-inch-thick 5-ply southern yellow pine plywood. The full-size sheet of plywood (4 by 8 ft.) was constructed with the grade C center ply (mathematics, data) ply - 1. Of a node in a tree, the number of branches between that node and the root.
2. Of a tree, the maximum ply of any of its nodes. aligned parallel to the grade A/B face plies plies 1
Third person singular present tense of ply1.
Plural of ply1. . The face plies were aligned parallel to the sheet 8 foot direction. The two grade C core even-number plies were aligned perpendicular, and adjacent to the faces. A phenol-formaldehyde resin was utilized as binder. The OSB was 0.75-inch-thick southern yellow pine board with face strands oriented in the direction parallel to the 8-foot direction of 4 by 8-foot full-size sheets. The adhesive was an isocyanate i·so·cy·a·nate
Any of a family of nitrogenous chemicals that are used in industry and can cause respiratory disorders, especially asthma, if inhaled. emulsion emulsion: see colloid.
Mixture of two or more liquids in which one is dispersed in the other as microscopic or ultramicroscopic droplets (see colloid). Emulsions are stabilized by agents (emulsifiers) that (e.g. . Particleboard was 0.75-inch-thick southern yellow pine boards (4 by 8 ft.), bonded with a urea-formaldehyde resin u·re·a-for·mal·de·hyde resin
Any of various thermosetting resins made by combining urea and formaldehyde and widely used to make molded household and industrial objects.
Noun 1. . The particleboard product selected for this study was at the extreme low end of industrial particle-board grades based on its average MOR value of 1,600 psi. Specimens in this study were fabricated fab·ri·cate
tr.v. fab·ri·cat·ed, fab·ri·cat·ing, fab·ri·cates
1. To make; create.
2. To construct by combining or assembling diverse, typically standardized parts: from cutting full-size sheets of the plywood, OSB, and particleboard panels randomly selected from panel stacks supplied by manufacturers. All specimens were conditioned in an 8 percent equilibrium MC chamber prior to tests, and were randomly assigned to testing groups.
Static bending test
Simple support center-point load edgewise bending tests were performed to obtain mean values of MOR and modulus of elasticity modulus of elasticity
The ratio of the stress applied to a body to the strain that results in the body in response to it. The modulus of elasticity of a material is a measure of its stiffness and for most materials remains constant over a range of stress. of the three composites. Specimens measured 0.75 inch thick by 2 inches wide by 40 inches long, with their length directions parallel to the full size sheet 8-foot direction. Specimens were tested referencing ASTM ASTM
American Society for Testing and Materials D 4761 (ASTM 2001a) 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 SATEC Sino-American Technology and Engineering Conference
SATEC Scarborough Academy for Technological, Environmental, and Computer Education universal-testing machine at a loading rate of 0.10 inch per minute. Load-deflection data of the tested specimens and their failure modes were recorded. Specimen MC and density were also measured (ASTM 2001b).
Constant amplitude cyclic tests. -- Specimens of constant amplitude cyclic tests measured 2 inches wide by 40 inches long. Specimens were randomly picked from the same specimen sources in static tests.
Constant amplitude cyclic tests were conducted on a specially designed air cylinder air cylinder can mean:-
rack - framework for holding objects system as shown in 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 edgewise using centerpoint loads.
Specimens of plywood and OSB were subjected to eight nominal stress levels by applying zero-to-maximum constant amplitude cyclic loads to obtain their stress-life curves (S-N curves). These stress levels were 90, 80, 75, 70, 65, 60, 55, and 50 percent of their mean MOR strength values obtained from previous static bending tests. Ten nominal stress levels of zero-to-maximum constant amplitude cyclic loads were applied to particleboard specimens to obtain S-N curves. Those stress levels were 90, 80, 75, 70, 65, 60, 55, 50, 45, and 35 percent of its mean MOR strength value.
Ten replications were considered for each cyclic load level of each material group. Eighty specimens were evaluated for plywood and OSB, respectively, and 100 specimens were tested for particleboard.
Stepped cyclic load test. -- Full-size member fatigue tests were performed under the stepped cyclic loading schedule to validate the Palmgren-Miner rule in estimating fatigue life of frame structural members subjected to cyclic stepped loads based on known S-N curves. The 80-inch-long back top rails of a full-size three-seat sofa frame were considered. Therefore, the cyclic stepped load schedule of the frame performance test "Top Rails-Front to Back" (GSA 1998) was selected to fatigue full-size specimens simply supported. Three identical loads, P, were applied at the centerpoint and at points 1/6 the span, L, from each end, respectively, using an air cylinder and pipe rack system similar to that shown in Figure 1. Up to three specimens were tested simultaneously. Therefore, the maximum bending [M.sub.j] at the centerpoint for each fatigue level in Table 1 can be calculated with the formula [M.sub.j] = 5PL/12. The span between two end supports was 72 inches. Table 1 gives the stepped cyclic loading schedule for fatigue evaluation of full-size back top rails, and corresponding maximum bending moments of each fatigue load level. The test began at a load level of 75 pounds per cylinder. Loads increased in increments of 25 pounds per cylinder after 25,000 cycles had been completed at each load level. Tests continued until specimens broke.
Table 2 gives specimen depths of three composites that satisfied passing stresses corresponding to GSA performance test acceptance levels: light-, medium-, and heavy-service acceptance levels. Depths were estimated using the Palmgren-Miner rule based on experimental stress-life curves resulting from constant amplitude cyclic tests and the cyclic stepped load schedule (Table 1). Six replications were considered for each combination of material type by performance-acceptance level.
General methods of tests. -- Zero-to-maximum (R = 0) cyclic loads were applied to specimens by air cylinders for each load level at a rate of 20 cycles per minute (GSA 1998). The fatigue cycle starts with zero load, 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 See PLC.
(hardware) Programmable Logic Controller - (PLC) A device used to automate monitoring and control of industrial plant. Can be used stand-alone or in conjunction with a SCADA or other system. and electrical re-settable counter system recorded the number of cycles completed. Limit switches actuated ac·tu·ate
tr.v. ac·tu·at·ed, ac·tu·at·ing, ac·tu·ates
1. To put into motion or action; activate: electrical relays that actuate the elevator's movements.
2. and stopped the test when the tested specimen broke completely into two parts.
All specimens were tested in the lab room maintained at the temperature of 74 [+ or -] 2[degrees]F and 50 [+ or -] 2 percent relative humidity relative humidity
The ratio of the amount of water vapor in the air at a specific temperature to the maximum amount that the air could hold at that temperature, expressed as a percentage. . All tests were run until specimens were broken, and failure modes were recorded.
Results and discussion
Table 3 summarizes the mean values of the physical and mechanical properties of evaluated materials. Mean values of MOR from static tests were considered as the control strength for the test specimens subjected to constant amplitude cyclic loading.
Failure modes of three tested materials were summarized in Table 4. Four types of failure modes occurred in static and fatigue bending tests. They were simple tension, splintering tension, brash brash (brash) heartburn.
water brash heartburn with regurgitation of sour fluid or almost tasteless saliva into the mouth. tension, and twist.
Constant amplitude cyclic tests. -- Table 5 summarizes range, mean values, and COVs of fatigue life (number of cycles to failure) of each material subjected to each of the edgewise, zero-to-maximum, constant amplitude, and center cyclic loading tests. Individual data points of nominal stress versus fatigue life of each tested material were plotted on a linear-log coordinate system coordinate system
Arrangement of reference lines or curves used to identify the location of points in space. In two dimensions, the most common system is the Cartesian (after René Descartes) system. in Figure 2.
Plywood members had average fatigue lives of 34,754; 61,044; and 118,339 cycles when pine plywood members were subjected to nominal stress equal to 75, 70, and 65 percent of their MOR values, respectively. This could suggest that light-, medium-, and heavy-service acceptance levels (Table 1) could be met when pine plywood members were designed as back top rails to resist constant amplitude cyclic stresses equal to 75, 70, and 65 percent of their respective averaged MOR values.
[FIGURE 2 OMITTED]
For OSB as back top rails, below 70 percent of their MOR values, average fatigue life could pass the light-service acceptance level when they are subjected to constant amplitude cyclic loading. For particleboard used as back top rails, the averaged maximum stress allowed will be below 55 percent of its MOR value to pass the light-service acceptance level.
The COVs of fatigue life averaged 129, 126, and 101 percent for plywood, OSB, and particleboard, respectively. It seems that the COVs tended to decrease as the stress level decreased.
The S-N curves were proposed to describe the fatigue behavior of wood composites subjected to zero-to-maximum constant amplitude cyclic loading. Linear-log plots of individual data points of applied nominal stress, S, versus fatigue life and the number of cycles to failure [N.sub.f] of each tested material (Fig. 2) indicated an approximately linear relationship between nominal stress and log fatigue life. Therefore, the following equation was employed to fit individual data points using the least square regression method to obtain a mathematical representation of the curve for each set of data:
S = C - D X [log.sub.10] [N.sub.f] 
S = applied nominal stress (psi)
[N.sub.f] = number of cycles to failure
C, D = fitting constants
Linear least-squares fit of the individual data points resulted in three regression equations for pine plywood, pine OSB, and particleboard. Table 6 gives the regression fitting constant values of C and D, and coefficient of determination Coefficient of determination
A measure of the goodness of fit of the relationship between the dependent and independent variables in a regression analysis; for instance, the percentage of variation in the return of an asset explained by the market portfolio return. Also known as R-square. [r.sup.2] values of derived equations for each of the three materials.
The method of Juvinall was proposed to derive estimated equations of S-N curves of wood composites using fatigue strengths, m'[[sigma].sub.u] and m[[sigma].sub.u], at two specified numbers of cycles, 1,000 cycles and [10.sup.6] cycles, respectively. The reduction factor at 1,000 cycles is m', which is calculated based on the fatigue strength at 1,000 cycles divided by ultimate bending strength (MOR), [[sigma].sub.u]. The reduction factor at [10.sup.6] cycles is m, which is calculated based on the fatigue strength at [10.sup.6] cycles divided by ultimate bending strength, [[sigma].sub.u]. Table 6 and Figure 2 show the resulting values for m and m' for three tested material curves. The 1,000-cycle point reduction factor, m', ranged from 0.68 to 0.74, and the fatigue limit reduction factor, m, ranged from 0.40 to 0.56.
Also, the Adkins' method was applied. Therefore, the estimated S-N curves of wood composites including [[sigma].sub.u] were derived accordingly based on Equation . The equation had the following format:
S = [[sigma].sub.u](E - H X [log.sub.10] [N.sub.f]) 
S = applied nominal stress (psi)
[[sigma].sub.u] = ultimate bending strength (MOR) (psi)
[N.sub.f] = number of cycles to failure
E = C/[[sigma].sub.u]
H = D/[[sigma].sub.u]
The resulting fitting constants E and H were given in Table 6 in the Adkins columns. The constant E ranged from 0.9 to 1.0, and the constant H was 0.05, 0.07, and 0.09 for plywood, OSB, and particleboard, respectively. Results of derived constants E and H values might suggest that S-N curves of wood composites could be approximated by Equation , where the constant E value is 1, and the constant H values were 0.05, 0.07, and 0.09 for plywood, OSB, and particleboard, respectively.
Stepped cyclic load test. -- The Palmgren-Miner rule was proposed to estimate the fatigue life of full-size composite members subjected to cyclic stepped loads based on their estimated stress-life curves. The Palmgren-Miner rule states unity summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) of life fraction:
[[N.sub.1]/[N.sub.f1]] + [[N.sub.2]/[N.sub.f2]] + [[N.sub.3]/[N.sub.f3]] + ...... = [summation] [[N.sub.j]/[N.sub.fj]] = 1 
[N.sub.j] = number of cycles applied to a member at the bending moment A bending moment exists in a structural element when a moment or torque is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have units such as newton.metres (N.m) and foot.pounds (ft.lb). [M.sub.j]
[N.sub.fj] = number of cycles to failure from the member material S-N curve for the bending moment [M.sub.j]
The estimation equation indicates that for a given stepped-load regimen and a known S-N curve, material fatigue failure is expected when the life fractions sum to unity, that is, when 100 percent of the life is exhausted. The fatigue life of a frame member under a given stepped bending load regimen could be estimated based on its material S-N curve.
Back top rail depths for meeting the heavy-service acceptance level were calculated to illustrate steps for estimating member sizes based on known S-N curves and fatigue load schedules.
Fatigue life of a back top rail subjected to the stepped cyclic load schedule in Table 1 can be estimated using the Palmgren-Miner rule of Equation :
[25,000/[N.sub.f1]] + [25,000/[N.sub.f2]] + [25,000/[N.sub.f3]] + [25,000/[N.sub.f4]] = 1
For OSB, the S-N curve equation is: S = 3,959 - 287 X [log.sub.10] [N.sub.fj] (Table 6). For a rectangular cross-section beam subjected to a bending moment, stress and moment have the following relationship:
S = [6[M.sub.j]]/[b[h.sup.2]]
[M.sub.j] = nominal applied moment (lb.-in.), in Table 1
b = beam member width (in.)
h = beam member depth (in.)
Substituting the stress-moment equation into the S-N curve equation yielded the following relationship:
[N.sub.fj] = [10.sup.(C/D - [[6[M.sub.j]]/[Db[h.sup.2]]])]
Then, substituting [N.sub.fj] into the Palmgren-Miner rule Equation  yielded the following equation:
[25,000/[10.sup.(C/D - [[6[M.sub.1]]/[Db[h.sup.2]]])]] + [25,000/[10.sup.(C/D - [[6[M.sub.2]]/[Db[h.sup.2]]])]] + [25,000/[10.sup.(C/D - [[6[M.sub.3]]/[Db[h.sup.2]]])]] + [25,000/[10.sup.(C/D - [[6[M.sub.4]]/[Db[h.sup.2]]])]] = 1
For a given rail member thickness of 0.75 inch, a minimum rail depth of 3.656 inches results. Therefore, the depths of the specimens subjected to stepped load schedules were calculated using the above described calculation procedure.
Table 7 summarizes fatigue life results of back top rail specimens as observed cycles. Mean cycles and their COVs were calculated based on six replications. Mean differences between the estimated and observed fatigue life values were determined and expressed as a percentage of estimated cycles.
The Palmgren-Miner rule provided a reasonable estimation of fatigue life for plywood and OSB at medium- and heavy-service acceptance levels, and particleboard at light- and medium-service acceptance levels. It tended to provide a more conservative estimation of fatigue life for plywood and OSB members at a light-service acceptance level, and for particleboard at the heavy-service acceptance level. Considering applied stress (or stress level) to fatigue members as a linear function of logarithm of number of cycles to failure to the base 10, these cycle estimations with a relatively higher percentage of differences are reasonable.
This research project evaluated edgewise bending fatigue performances of three wood-based composites (southern yellow pine plywood, OSB, and particleboard) as upholstered furniture frame stock.
Results of zero-to-maximum constant amplitude cyclic load tests indicated that a fatigue life of 25,000 cycles started at stress levels of 75 and 70 percent of MOR values for plywood and OSB evaluated in this study, respectively. Particleboard fatigue life did not reach 25,000 cycles until the stress level was reduced to 55 percent of its MOR value.
The COVs of fatigue life averaged 129, 126, and 101 percent for plywood, OSB, and particleboard, respectively. It was observed that the COVs tended to decrease as stress levels decreased.
Regression analysis of S-N data concluded that the functional relationship between the fatigue stress and the log number of cycles to failure could be expressed with the linear equation S = C - D X [log.sub.10] [N.sub.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-N curves of wood composites could be approximated by S = MOR (1 - H X [log.sub.10] [N.sub.f]). The constant H values in the equation were 0.05, 0.07, and 0.09 for plywood, OSB, and particleboard, respectively. This equation reflects the relationship between material static strength and fatigue life. It seems that the constant H is correlated to basic wood element sizes of composite raw material such as veneer and particles.
Cyclic stepped load tests of full-size back top rail specimens verified that the Palmgren-Miner rule was an effective method to estimate fatigue life of wood composites subjected to edgewise cyclic stepped bending stresses using their S-N curves.
Table 1. -- Stepped cyclic loading schedule for full-size back top rail fatigue tests and calculated maximum moments in back top rails for each fatigue load level under the simple-support boundary condition. j P Cumulative cycles Service acceptance level Mj (lb.) (lb.-in.) 1 75 25,000 Light service 2,250 2 100 50,000 Medium service 3,000 3 125 75,000 3,750 4 150 100,000 Heavy service 4,500 Table 2. -- Depths of full-size back top rail specimens subjected to stepped load schedule. Service acceptance level Material type Light Medium Heavy Plywood 2.052 2.370 2.902 OSB 2.582 2.983 3.656 Particleboard 4.526 5.231 6.415 Table 3. -- Mean values of physical and mechanical properties of tested materials. (a) Material type MC Density MOR MOE (pcf) (psi) (X [10.sup.6] psi) Plywood 7.8 (4) 42 (3) 6,600 (15) 0.99 (17) OSB 6.8 (5) 41 (5) 4,200 (16) 0.74 (8) Particleboard 7.7 (2) 49 (3) 1,600 (10) 0.33 (10) (a) MOE = modulus of elasticity. Values in parentheses are coefficients of variation in percent. Table 4. -- Percentage distribution of failure modes for each of three tested materials in this study. Material type Simple tension Splintering tension Brash tension (%) Static Plywood 0 53 45 OSB 60 0 40 Particleboard 0 0 100 Fatigue Plywood 0 56 42 OSB 0 17 83 Particleboard 0 0 100 Material type Twist % Static Plywood 2 OSB 0 Particleboard 0 Fatigue Plywood 2 OSB 0 Particleboard 0 Table 5. -- Results of fatigue life (number of cycles to failure) at each of applied stress levels for each material subjected to zero-to- maximum constant amplitude cyclic loading. Pine plywood Pine OSB Stress levels Range Mean COV Range (%) (%) 90 572 to 1 60 299 1,677 to 1 80 2,138 to 1 284 241 8,731 to 116 75 68,943 to 269 34,754 72 8,423 to 54 70 168,114 to 1,711 61,044 122 75,399 to 144 65 256,418 to 3,645 118,339 69 310,716 to 1,458 60 689,172 to 41,455 248,701 89 216,788 to 1,457 55 1,644,794 to 64,563 490,984 101 721,356 to 5,933 50 1,598,718 to 357,816 821,914 42 1,352,107 to 56,478 45 35 Avg. 129 Pine OSB Particleboard Stress levels Mean COV Range Mean COV (%) (%) (%) 90 191 274 14 to 1 5 92 80 1,858 138 432 to 1 137 130 75 2,504 116 1,295 to 2 347 126 70 23,469 111 1,788 to 10 365 150 65 70,104 127 4,071 to 64 1,612 113 60 90,564 66 14,831 to 401 5,461 82 55 216,687 121 82,031 to 5,789 26,303 85 50 741,158 58 129,391 to 7,061 41,320 95 45 268,974 to 10,929 95,160 100 35 655,904 to 101,615 497,282 36 Avg. 126 101 Table 6. -- Constants of estimated equations for composite S-N curves. Regression Juvinall Adkins Material type MOR C D [r.sup.2] m' m E H (psi) Pine plywood 6,600 5,775 344 0.74 0.72 0.56 0.9 0.05 OSB 4,200 3,959 287 0.76 0.74 0.53 0.9 0.07 Particleboard 1,600 1,534 149 0.85 0.68 0.40 1.0 0.09 Table 7. -- Comparisons between estimated and observed mean fatigue life of full-size back top rail specimens for each combination of material type and service acceptance level. (a) Material type Plywood Service acceptance level Estimated Observed Difference (%) Light 25,000 39,406 (31) -57.6 Medium 50,000 54,166 (19) -8.3 Heavy 100,000 95,915 (27) 4.1 Material type OSB Particleboard Service acceptance level Observed Difference Observed (%) Light 37,753 (27) -51.0 30,033 (14) Medium 46,866 (40) 6.3 69,410 (16) Heavy 127,731 (16) -27.7 162,079 (9) Material type Particleboard Service acceptance level Difference (%) Light -20.1 Medium -38.8 Heavy -62.1 (a) Values in parentheses are coefficients of variation in percent.
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See also: Mechanics 12(3):A159-164.
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Steven R. Daniewicz
The authors are, respectively, Associate Professor and Graduate Student, Forest Prod. Lab., Mississippi State Univ., Mississippi State, MS 39762-9820; and Associate Professor, Mechanical Engineering Dept., Mississippi State Univ. Approved for publication as Journal Article No. FP 305 of the Forest and Wildlife Research Center, Mississippi State Univ. This paper was received for publication in February 2004. Article No. 9832.
*Forest Products Society Member.