Effects of Moisture on the Biaxial Strength of Wood-Based Composites
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EFFECTS OF MOISTURE ON THE BIAXIAL STRENGTH OF WOOD-BASEDCOMPOSITES J. C. Suhling* J.M. Considine ** K. C. Yeh* * Department of Mechanical Engineering Auburn University Auburn, AL36849-5341 ** U.S.D.A. Forest Products Laboratory One Gifford Pinchot Drive Madison,WI 53705-2398 ABSTRACT applications such as corrugated containers where it is subjected to complicated biaxial stress states, In the present work, the effects of moisture on including shear. At present, lack of accurate the biaxial strength of wood-based composite materials constitutive relations and reliable strength has been examined. Experiments have been performed on predictions under biaxial loading and variable paperboard to measure the uniaxial and biaxial input environments hampers analysis of such problems. parameters of the tensor polynomial criterion at Therefore, it has been common practice in the paper several levels of relative humidity. With these data, industry to use trial and error, and empirical the dependence of the zero shear biaxial failure approaches for optimizing the designs of paperboard envelope on humidity level has been predicted and products. The current lack of technology limits trends have been observed. creative design improvements which could curtail the excess use of materials and energy. Accurate predictions of material strength under 1. INTRODUCTION general biaxial normal loading plus shear are needed by the design engineer when considering typical Unlike laminated fiber-reinforced composite structural applications of paperboard. Examples of materials, paper (paperboard) is a multiphase important current applications where biaxial stress composite composed of moisture, fibers, voids, and states exist in paperboard include the quality control possibly chemical additives. The fibers in paperboard burst test (bulged plate), material handling are typically organic with cellulose fibers from wood operations during the papermaking process, and stacked being the chief material. Since cellulose fibers are corrugated containers. Controlled testing of paper self-binding, no matrix material is needed. Wood over a wide range of combined stress states is itself may be thought of as a natural composite difficult and expensive. Also, few industry consisting of cellulose fibers interconnected by a laboratories have the necessary experimental primarily lignin binder. Paper is by far the oldest equipment. Therefore, simple mathematical failure and most economically significant wood fiber criteria which yield accurate results are of great composite. importance. The three-dimensional physical structure of Numerous biaxial strength criteria have been paperboard is basically an assembly of discrete fibers proposed for orthotropic materials [1], and several of bonded together into a complex network. If the fibers these have been applied to paperboard. Prud'homme and were oriented randomly throughout the sheet, the Robertson [2] applied both the Tsai-Hill and Liu- material behavior would be isotropic. The actual Stowell (maximum stress) criteria to highly oriented nonrandom (anisotropic) arrangement of the fiber paper sheets and found the former to agree with network is caused by hydrodynamic forces which occur experiment. The results of several recent in the papermaking machine. A single preferred investigations have demonstrated that the tensor orientation of the fibers results which is called the polynomial failure criterion (often called the Tsai-Wu machine direction (MD). The in-plane direction Theory) can adequately predict plane stress biaxial perpendicular to the preferred direction is called the failure states of paperboard [3-7]. This theory cross-machine direction (CD). These directions of requires six experimentally measured input parameters material symmetry allow for paper to be modeled macroscopically as an orthotropic solid. for general utilization. Typically, these are the Paper materials tend to exhibit nonlinear tensile and compressive strengths in the machine and mechanical behavior which is affected significantly by cross-machine directions, the pure shear strength, and slight changes in the surrounding environmental a single piece of biaxial failure data. conditions. In addition, most papers are capable of All previous research on paperboard biaxial demonstrating every known rheological phenomenon. failure has been carried out in environmental rooms Current uses of paperboard provide several challenging which strive to maintain TAPPI standard conditions of problems in engineering mechanics. For example, temperature and relative humidity (73° F, 50% RH). It paperboard is often utilized in structural is well-known that the most critical quantity 602 influencing the characteristic mechanical response of a specific paper is its current and past history of moisture content. The moisture content or regain of (2) an element of material is defined as the ratio of the difference between current weight and dry weight to For a particular sample of paper, the are the unique components of the stress tensor. the dry weight. Fi, moisture content is determined predominately by the F , F , etc. are components in the (x,y,z) chemical and structural characteristics of its ij ijk component fibers and the relative humidity (RH) of the coordinate system of strength tensors of second, surrounding atmosphere. It is also affected to a fourth, sixth, and higher orders, respectively. In lesser degree by temperature, state of stress, and this work, tensorial criteria with only linear and past histories of stress, temperature, and humidity. quadratic terms will be considered. Additional higher Several experimental studies have been made on order terms may be retained in eq. (1). However, this the effects of relative humidity on paper behavior in tends to be impractical from an operational standpoint uniaxial stress states. Kolseth and de Ruvo [8] have because the number of coefficients to be surveyed several experimental investigations in this experimentally determined increases significantly. area. Moisture contents of test specimens have been Such tensorial strength predictions were first adjusted primarily by controlling the relative proposed by Malmeister [18] and subsequently by Tsai humidity of the surrounding atmosphere while and Wu [19]. Although not written in the same form, maintaining a constant temperature. In some studies the tensorial criterion given by Gol'denblat and the actual dependence of a material property on Kopnov [20] is operationally equivalent to eq. (1). moisture content was calculated by performing The latter authors seem to be the first to recognize additional experiments to determine the characteristic that a strength theory should be independent of sorption curve relating relative humidity to coordinate system. paperboard moisture content. Being invariant, eq. (1) is valid in all Extensive measurements of uniaxial tensile coordinate systems (x,y,z) once it is established in a stress-strain curves of paper at several humidity single coordinate system. For orthotropic materials levels have been performed by Andersson and Berkyto such as paperboard, the coordinate axes are normally [9], and Benson [10]. The latter author also related aligned with the directions of material symmetry (× = tensile properties directly to moisture content. The MD, y = CD). After components of the strength tensors effects of the level of relative humidity on the are obtained in this specially orthotropic coordinate initial elastic modulus of paper have been examined by system, components may be established in additional de Ruvo, et a1 [11], and Salmen and Back [12]. rotated coordinate systems by utilizing tensorial Okushima and Robertson [13] have noted the dependence transformation laws. Use of other sets of coordinate of the tensile stress-strain curve on strain rate at axes is usually unnecessary with single-ply or several different levels of humidity. Other uniformly laminated materials such as paper. researchers have reported on the influence of relative Under plane-stress conditions where the humidity on paperboard creep behavior [14], stress coordinate axes are aligned with the axes of material relaxation [15], and impact properties [16]. Humidity symmetry, eq. (1) reduces to and strain rate effects on the uniaxial compressive stress-strain curves of paperboard have been measured recently at the U.S.D.A. Forest Products Laboratory by Gunderson, Considine, and Scott [17]. (3) The literature shows no experimental data or analytical results which relate the moisture content of a paperboard sheet to its mechanical response under biaxial loading. In this work the effects of the where subscripts 1 and 2 on stresses level of moisture content on the zero-shear biaxial exclusively denote the MD and CD, respectively failure envelope of paperboard have been examined. (directions of material symmetry). Terms with The tensor polynomial criterion was used for coefficients F16, F26, F6, are absent in eq. (3) predicting paperboard biaxial strength. At zero because symmetry conditions require these coefficients shear, the input parameters to this theory are the to vanish in the specially orthotropic coordinate uniaxial tensile and compressive strengths in the MD system. The failure surface described by eq. (3) is and CD, respectively, and a single piece of biaxial an ellipsoid provided the following three restrictions failure data. Experiments have been performed to are satisfied measure these parameters at several levels of relative humidity, With these data,