Abstract:
A method and an apparatus for predicting a score-line cracking propensity of a multi-ply substrate. The method includes the steps of: bending the multi-ply substrate; acquiring tensile load data from the multi-ply substrate during bending; and computing a material property of a top ply of the multi-ply substrate based on the acquired tensile load data. The material property must show a strong correlation to the score-line cracking propensity of the multi-ply substrate. The material property which is computed is the energy consumed in plastic deformation of the top ply during the fracture process. The measurement results can be used to predict score-line cracking propensity in multi-ply board systems, such as multi-ply paperboard.

Description:
FIELD OF THE INVENTION 
     This invention generally relates to the manufacture of paperboard products. In particular, the invention relates to methods and apparatus for predicting score-line cracking propensity in paperboard products having multiple plies. 
     BACKGROUND OF THE INVENTION 
     There have been available few tests for evaluating score-line cracking, for instance, the score cracking angle test disclosed by Whitsitt and McKee in “Investigation of Improved Device for Evaluating the Cracking Potential of Linerboard,” Institute of Paper Chemistry Summary Report, Project No. 1108-29 (1996). This test, first developed at the Institute of Paper Chemistry, fails to either measure a fundamental material property, or detect damage in a single ply. No meaningful correlations have thus been found over the years to score-line cracking performance in the field. 
     A recent test, disclosed by J. Gonzalez in “Score Cracking in Linerboard,” M. S. Dissertation (No. 6190-Research), Institute of Paper Science and Technology, Georgia (2000), is not so much a predictive test, but rather is a set-up that attempts to replicate, rather poorly, scoring. It does not scientifically measure any board property that may prove to correlate to score-line cracking propensity in the field. The test comprises two motor-driven horizontal metal wheels forming essentially a nip compression. A linerboard sample (25 cm×12 cm), manually folded in half and fed between the flat metal wheels, undergoes a nip-type compressive force. The cracking percent of the folded sample is then measured visually or using a microscope. 
     Experimental work carried out at International Paper&#39;s Corporate Research Center in the period February-May, 2000 has been instrumental in providing insight into the root causes of the propensity for score-line cracking in white-top linerboard (especially 69 lb.). The mechanistic basis for designing a score-line-crack-resistant two-ply linerboard is grounded in three (non-mutually exclusive) functional factors: (1) the ability of the top ply to undergo large plastic (irreversible) deformation prior to failure; (2) the ability of the base ply to compress elastically while the top ply is deforming (plastically); and (3) in order for (1) and (2) to simultaneously apply, the interlaminar (ply) bond must be low enough (but adequate to ensure against delamination) to allow the top ply to “slide” over the base ply. Achieving this requires the development of a testing method capable of predicting plastic deformations, or the fracture toughness, of the top ply alone, and able to correlate such a measurement with score-line cracking propensity in the field. 
     In materials science and engineering, the term “material” has a precise meaning. It refers to either a pure substance or an alloy that can be approximated as essentially homogeneous in composition. When more than one substance or material are combined, and when this combination has internal structural heterogeneity, the term “composite material” is used. According to this definition, wood fibers may be regarded as composite materials, or, specifically, composite tubes of cellulosic microfibrils embedded in an amorphous matrix of hemicellulose and lignin. Structurally, paper or board is, however, a network. On a microscopic scale, paper or board is a cellulosic network of crossing fibers filled with voids; macroscopically, it could be regarded as a continuum with inherent (micro)cracks and flaws being “smeared out” for the purpose of simplifying analysis. For practical issues related, for instance, to box construction, such as scoring, it may be deemed appropriate that linerboard be dealt with as a continuum whose material properties and structural analysis are determined relying on theories of elasticity and plasticity from the field of solid mechanics. Thus, two-ply linerboard constructs comprise two elastic-plastic sheet-like materials whose properties may be analyzed orthotropically. Safeguarding against, for instance, cracking in the top ply during scoring would necessitate attention principally to: i) the extent of (plastic) deformability in each ply; and ii) inter-ply stresses. 
     Linear elastic materials load and unload along the same path (see FIG.  1 ); crack growth in such a material can be represented graphically by the load-displacement curve depicted in FIG.  2 . The curve is linear up to the point of crack propagation, and the displacement is zero when the specimen is unloaded. The energy consumed in the fracture process is therefore equivalent to the area enclosed under the curve. The irreversible work consumed during elastic fracture is confined to thin boundary layers along the faces of the propagating crack. 
     Paper and board, however, are tough, ductile materials (the extent of which depends on furnish composition and papermaking conditions) whose yield stress is low (see FIG.  3 ). When such a material is strained, it yields not only at the point(s) of crack initiation, but away from these points too. Thus, irreversible deformation is no longer confined to the thin boundary layer along the faces of the propagated crack (as in elastic fracture), but is spread throughout the material. In addition to the work required in the crack tip process zone, significant irreversible work is consumed in the yielded regions away from the crack. It is important to recognize that the plastic deformation outside the fracture process zone is not essential to the process of fracture. Consequences of the plastic flow include curvature in the load-displacement curve on loading, and displacement irreversibilities upon unloading, both in a specimen without a crack (FIG. 3) and a specimen with a crack (FIG.  4 ). 
     The work done during loading, given by the area under the load-displacement curve in FIG. 4, represents the combined contribution to fracture and remote flow. These two works are difficult to separate experimentally. However, a methodology is needed to separate the elastic and plastic portions of the fracture energy consumed in deforming the top-ply of two-ply linerboard systems. This methodology should be designed so that the measured plastic contribution of the work done during the fracture process correlates well with predicting the propensity of linerboard to score-line cracking during converting operations. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a method and an apparatus for predicting a score-line cracking propensity of a multi-ply substrate. The method comprises the steps of: bending the multi-ply substrate; acquiring data from the multi-ply substrate during bending; and computing a material property of a top ply of the multi-ply substrate based on the acquired data. The material property must show a strong correlation to the score-line cracking propensity of the multi-ply substrate. In accordance with the preferred embodiment of the invention, the material property which is computed is the energy consumed in plastic deformation of the top ply during the fracture process. The measurement results can be used to predict score-line cracking propensity in multi-ply board systems. In accordance with the preferred embodiment, the substrate is paperboard. 
     Also in accordance with the preferred embodiment, the apparatus is implemented as a top-ply fracture tester designed to bend a sample of a multi-ply substrate and acquire data during bending from which the plastic energy consumption during the fracture process can be automatically computed. The tester comprises two clamps in which the sample is placed; one of the clamps is fixed, the other rotates the sample around a spindle. When bending the sample, it is under a net tensile force, which is recorded using a load cell. A computer receives inputs from the load cell and from a position detector which detects the position of the rotating clamp during the sample bending operation. The computer is programmed to compute the energy consumed during plastic deformation of the top ply of the multi-ply substrate. This top-ply fracture tester induces fracture in the top ply only, and allows the identification of elastic and plastic regions in a single ply. Score-line cracking resistance essentially emanates from the ability of the sheet to deform plastically (in the top ply). 
     The test and analysis methods in accordance with the preferred embodiment characterize failure in the outermost ply of a multi-ply linerboard system. The test method specifically measures cracking resistance, and correlates board functionality to field performance (converting operations), by accurately measuring the nonlinear, plastic deformation of the ply, or plastic fracture energy. 
     In accordance with the teaching of the invention, material changes in the board can be correlated with “damage” phenomena, occurring physically, which are relatively easily detectable. When a two-ply linerboard sample is tested as described above, an operator would visually notice three distinct phenomena taking place at three discrete intervals: (1) the development of a (macro)crack as the sample is bent around the spindle; (2) the opening up of the (macro)crack; and (3) the complete separation of the fibers, just prior to eventual failure and delamination of the top ply from the base ply. These stages are respectively referred to herein by the terms “crack,” “gap” and “flap.” These stages represent the entire zone of plastic deformation while subjecting the top ply to a net tensile state of stress. Plastic deformation in linerboard is thus characterized by two components: the energy consumed during the transition from crack to gap and that consumed during the transition from gap to flap. Each component, or both, may be optimized to improve certain aspects of the board&#39;s ability to deform plastically, and, in turn, resistance to cracking. 
     In accordance with the preferred method, the operator records the visual detection of the crack, gap and flap by pressing a pre-specified alphanumeric key (on the computer keypad) for each event. The computer is programmed to detect these specific key depressions. Once the test is complete, the computer program computes the (elastic and plastic) energies consumed from inception to failure of the single ply. Generally, the following is determined from a specimen&#39;s load-elongation curve: (1) energy consumed during elastic deformation (up to crack initiation); (2) energy consumed during the crack-to-gap transition (the first plastic component); (3) energy consumed during the gap-to-flap transition (second plastic component); and (4) energy consumed during the crack-to-flap transition (total plastic contribution, or sum of energy components (2) and (3)). The computer is also preferably programmed to compute the standard deviations, which may further help indicate two things: operator&#39;s precision (the larger the standard deviation, the worse is the operator&#39;s accuracy for identifying crack, gap and flap) and sample variability (for instance, the standard deviation tends to be higher for recycle furnishes owing to inherent variability in pulp quality and, hence, mechanical properties of the board). 
     Thus the top-ply fracture tester disclosed herein enables one to instantaneously obtain a load-displacement curve for each ply of a multi-ply linerboard system, or any similar multi-ply structure. From the individual load-elongation curve, each ply&#39;s elastic and plastic components are computed and analyzed. For white-top linerboard, it is shown that the top ply is characterized by a two-component plastic zone of deformation, which are respectively referred to herein as the “crack-to-gap” and the “gap-to-flap” components. An unequivocal correlation has been shown between the energy consumed during the crack-to-flap transition (the whole plastic zone) and the propensity for score-line cracking in the field. The plastic zone characterization also serves as a litmus test, which would be useful for proposing ways to improve the board&#39;s mechanical performance under varying papermaking conditions, furnish type and board structural configuration. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a graph showing a stress-strain curve for a linear elastic material. 
     FIG. 2 is a graph showing a load-displacement curve for crack propagation in a linear elastic material. 
     FIG. 3 is a graph showing a stress-strain curve for an elastic-plastic material. 
     FIG. 4 is a graph showing a load-displacement curve for crack propagation in an elastic-plastic material. 
     FIG. 5 is a schematic representation of load versus deformation to show the principles of fracture as applied to deforming the top ply in a two-ply linerboard construct: A), the elastic region until crack initiation; B) the crack-to-gap transition; C) the gap-to-flap transition; B+C) crack-to-flap transition. 
     FIGS. 6-9 are photographs showing crack initiation and propagation to failure in the top ply of a two-ply linerboard construction. These side views respectively depict: an intact sample (FIG.  6 ); crack initiation (FIG.  7 ); further crack propagation to the gap stage (FIG.  8 ); and ultimate failure of the top ply, i.e., the flap stage (FIG.  9 ). 
     FIG. 10 is a schematic showing a front view of a top-ply fracture tester in accordance with the preferred embodiment of the invention. 
     FIG. 11 is a schematic showing a top view of the top-ply fracture tester in accordance with the preferred embodiment of the invention. The rotating arm is shown in its initial and final positions. 
     FIG. 12 is a block diagram generally depicting the electrical and some mechanical components of the top-ply fracture tester in accordance with the preferred embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In accordance with the preferred embodiment of the invention, a predictive tester for score-line cracking was developed which is able to measure the energy consumed in causing cracks to initiate and propagate in each ply of a multi-ply board. The energy consumption necessarily relates to the ability of the board to deform plastically. The tester achieves this goal by measuring a fundamental material property, which may then be correlated with field performance, i.e., converting operations. 
     Existing techniques for measuring fracture toughness (the essential work of fracture technique or the J-integral technique) would yield an overall number for the combined board that obfuscates the true fracture toughness value of the single ply. Hence, a measurement as such is rendered unhelpful to predicting, and subsequently minimizing, the cracking propensity of the top ply in a two-ply linerboard. 
     The top-ply fracture tester disclosed herein provides an accurate measure of the energy consumed in deforming the top ply on its own. This capability allows one to investigate score-line cracking phenomena occurring in the top ply of the linerboard. The top-ply fracture tester induces fracture in the top ply only, and allows the identification of elastic and plastic regions in a single ply, as shown in FIG.  5 . In the graph shown in FIG. 5, the term “crack” refers to observable discontinuities in the outermost ply under observation; the term “gap” refers to the propagation of macro-cracks leading to their opening up; and the term “flap” refers to the increase in the gap, or crack opening, and ultimate delamination of the ply (under observation) upon further load application. These terms are further illustrated in the photographs presented in FIGS. 6-9, which represent crack initiation and propagation to failure in the top ply of a two-ply linerboard construct. In particular, FIGS. 6-9 are side views which respectively depict: an intact sample (FIG.  6 ); crack initiation (FIG.  7 ); further crack propagation to the gap stage (FIG.  8 ); and ( d ) ultimate failure of the top ply, i.e., the flap stage (FIG.  9 ). 
     The instrument in accordance with the preferred embodiment is programmed to report each of three values for each replicate and then give the average and standard deviation of each value after the last replicate is run. The reported values are the following: (1) The area under the stress-strain curve up to the point of crack initiation in the outermost ply. The area under the stress-strain curve represents the energy consumed, in this case up to crack initiation. (2) The area under the stress-strain curve from the crack to the gap. This area represents the energy consumed during the process following crack initiation and before the inception of gap formation, or crack opening. (3) The area under the curve from the gap to the flap. This area represents the energy consumed during the process of gap formation, or crack opening, and ultimate delamination within the same ply. 
     A preferred embodiment of the top-ply fracture tester is depicted in FIGS. 10-12. To allow for the gradual material “degradation”, i.e. cracking, within the outermost ply, the top-ply fracture tester mechanism has been designed to bend any multi-ply film- or sheet-like structure S, e.g. linerboard, around a ⅛-inch vertical (fixed) spindle  2  (refer to FIG. 10) supported by a spindle support structure  4 . In so doing, the sample S will experience a net resultant tensile force. The sample (e.g., 1 inch wide and 5.75 inch long) is firmly held between two air (pneumatic) clamps  6  and  8 . The opposing surfaces of the jaws of these air clamps have transverse grooves to ensure no slippage of the paperboard sample S during bending. Air is supplied to the clamps from a pressurized source via air lines  32  by operation of an air supply switch  35 . 
     In accordance with the preferred embodiment, air clamp  6  is fixedly coupled to a load cell  10  via a rod  12 . The rod  12  is vertically supported by a mounting bracket  24  attached to the base  30 . The load cell  10  is attached to an L-shaped bracket  26 , the latter also being mounted to the base  30 . The load cell  10  is thus coupled to the air clamp  6  via rod  12  and measures the sample load response during bending. 
     The other air clamp  8  is mounted to one end of a rod  16 . The other end of rod  16  has a spring housing  18  mounted thereto. The rod  16  is slidably supported by a mounting bracket  22  attached to the base  30 . Thus the assembly of the air clamp  8 , the spring housing  18  and the rod  16  is axially slidable as a unit. A spring  14  is installed inside the spring housing  18  and couples the assembly to a fixed rod  17  which has a radial flange at one end. The spring  14  applies a tensile load to the sample. The rod  17  is fixedly supported by a mounting bracket  20 . The rod  17  and a hole in the mounting bracket  20  are both threaded to allow adjustment of the axial position of the rod  17 , which in turn allows the operator to adjust the tension applied by spring  14  depending on the basis weight of the material being tested. 
     The brackets  20  and  22  are both mounted to a rotating or turning arm  28 . The turning arm is rotatable about the axis of spindle  2 , preferably to a maximum of about 160 degrees. As the turning arm swings, it carries the air clamp  8 , causing the latter to rotate about the spindle axis, which in turn causes the sample S to bend around the spindle  2 . In FIG. 11, the turning arm  28  is shown in the starting position A and in a rotated position B. As is best seen in FIG. 10, the spindle support structure  4  is mounted to the top of base  30 . The turning arm  28  is rotatably mounted to base  30  by means of a bearing (not shown). 
     Further components of the top-ply fracture tester in accordance with the preferred embodiment are shown in FIG.  12 . The turning arm  28  is rotated under the control of a computer  34 , which is preferably incorporated in the test stand (as seen in FIG.  10 ). The computer  34  supplies the appropriate command to a motor controller  36  in response to depression of a “run” key on an operator interface  38 . In response to the “run” command from the computer, the motor controller activates an electric motor  40 . The electric motor  40  has an output shaft (not shown) which is coupled to the turning arm  28  via a drive train (e.g., a gear assembly)  42 . The arm  28  can be set to rotate at varying speeds; for example, successful tests have been conducted with the arm rotational speed set at 1 degree/second. Testing requiring faster rates of elongation may be accommodated by varying the speed of the rotating arm. 
     As the turning arm  28  rotates, a position detector  44  detects the angular position of the arm and outputs an analog signal. This analog signal is converted to a digital signal by an analog-to-digital converter  46 , which sends a digital signal representing arm angular position to the computer  34 . At the same time, the load cell  10  measures the tensile force or load being applied to the sample during rotation of the turning arm  28  and outputs an analog signal. This analog signal is converted to a digital signal by another analog-to-digital converter  48 , which sends a digital signal representing tensile load to the computer  34 . Thus the computer simultaneously acquires tensile load data and angular position (i.e., displacement) data. The computer is programmed to generate a characteristic, real-time load-elongation curve (e.g., of the type shown in FIG. 5) for display on a display monitor  50 . 
     As in tensile testing regimes and the like, the sample&#39;s strain rate is critical to the fundamental material properties being recorded. While the board&#39;s plastic component of deformation is, for instance, an inherent material property, and hence will be true in all (correct) testing conditions, values will vary for significantly different strain rates. For the preferred top-ply fracture tester design, the strain rate is affected by three factors: the spring load, the arm rotational speed and the gauge length [the distance between the two free edges of the clamps]. It is thus imperative that all measured values be quoted with corresponding rate of elongation, or arm speed. For the example where the sample width was 1 inch wide, sample length was 5.75 inch long, and the arm speed was 1 degree/second, the gauge length was fixed at 4 inches. When in operation, a characteristic, real-time load-elongation curve is obtained. The testing operation and relevant calculations are controlled via a computer program. The test results are displayed on the display monitor and can be output to a printer in response to a print command input via the operator interface. 
     Using the present invention, an operator is able to correlate material changes in a multi-ply board with “damage” phenomena occurring physically, which are, relatively speaking, easily detectable. When a two-ply linerboard sample is tested as described above, the operator would visually notice three distinct phenomena taking place at three discrete intervals: (1) the development of a (macro)crack as the sample is bent around the spindle; then (2) the opening up of the (macro)crack; and finally (3) the complete separation of the fibers, just prior to eventual failure and delamination of the top ply from the base ply. These crack, gap and flap stages represent the entire zone of plastic deformation while subjecting the top ply to a net tensile state of stress. Plastic deformation in linerboard is thus characterized by two components: the energy consumed during crack-to-gap and that consumed during gap-to-flap (see FIG.  5 ). Each component, or both, may be optimized to improve certain aspects of the board&#39;s ability to deform plastically, and, in turn, resistance to cracking. 
     The visual detection of the crack, gap and flap is recorded by pressing a respective pre-specified alphanumeric key on the user interface  38 , e.g., a keypad, for each event. Once the test is complete, the computer program computes the (elastic and plastic) energies consumed from inception to failure of the single ply. Generally, the following is determined from a specimen&#39;s load-elongation curve: (1) energy consumed during elastic deformation (up to crack initiation); (2) energy consumed during crack-to-gap (the first plastic component); (3) energy consumed during gap-to-flap (second plastic component); and (4) energy consumed during crack-to-flap [total plastic contribution, or sum of (2) and (3)]. All of these values are computed along with the standard deviations, which may further help indicate two things: operator&#39;s precision (the larger the standard deviation, the worse is the operator&#39;s accuracy for recording crack, gap and flap) and sample variability (for instance, the standard deviation tends to be higher for recycle furnishes owing to inherent variability in pulp quality and, hence, mechanical properties of the board). Crack propagation is observed in real-time in the top ply, and as material degradation continues, in the base ply (or succeeding plies, as the case may be). 
     In accordance with one test procedure, fifteen replicates were tested for each sample. The samples were generally conditioned overnight in a controlled environment of 23±2°C. and 50±5% relative humidity. Testing should preferably be performed in a similarly controlled environment. 
     In accordance with a further preferred embodiment of the invention, the detection of crack, gap and flap can be automated by the use of acoustics. The working assumption is that each stage of damage accumulation is characterized by a particular pattern of crack propagation, with which is associated a specific rate of bond breakage and/or number of fiber breaks. Technical efforts must concentrate on eliminating noisy activities from regions other than those of interest (i.e., where cracks are propagating), while being able to accurately detect relative sound changes arising at the three distinct stages of damage. 
     Top-ply fracture testing in accordance with the method disclosed above was performed on a large number of samples of two-ply linerboard. This test data was initially used to validate the inherent properties measured by the top-ply fracture tester vis-à-vis the linerboard&#39;s score-line cracking performance in the field. Subsequently, having established the robustness and efficacy of the test, the top-ply fracture tester was utilized as the cornerstone behind improving the functionality (score-line cracking resistance) of a two-ply linerboard. Table 1 summarizes representative results and the concomitant trends. 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 To 
                   
                 Crack- 
                 Gap-to- 
                 Crack- 
                 Percent 
               
               
                   
                 Crack 
                   
                 to-Gap 
                 Flap 
                 to-Flap 
                 Field 
               
               
                 Sample 
                 (lb-deg) 
                 S.D. 
                 (lb-deg) 
                 (lb-deg) 
                 (lb-deg) 
                 Cracking 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 1,591 
                 183 
                 415 
                 511 
                 926 
                 6.1 
               
               
                 2 
                 1,728 
                 246 
                 424 
                 593 
                 1,017 
                 9.3 
               
               
                 3 
                 1,860 
                 404 
                 664 
                 2,102 
                 2,766 
                 0 
               
               
                 4 
                 1,654 
                 218 
                 615 
                 2,611 
                 3,227 
                 0 
               
               
                   
               
             
          
         
       
     
     S.D. is the standard deviation of the energy consumed up to crack initiation. The test data in Table 1 show a clear trend how the propensity for cracking (as quantified by the percent field cracking, which is the crack length percent relative to the length of the score line) correlates with energy consumed during the crack-to-flap transition, or the total energy consumed during plastic deformation. The following factors were found to affect the sheet&#39;s ability to plastically deform: the furnish type (virgin versus recycle), furnish quality (e.g. pulp viscosity), degree of fiber development (refining), inter-ply bonding and top-ply coverage. The interacting effects between each, or several of the above factors, result in the development of larger plastic zones of deformation in the top ply. 
     In conclusion, the top-ply fracture tester disclosed herein measures fundamental properties that show reproducible, accurate correlation with field performance. Using the top-ply fracture tester, one would be able to develop tools that enable the prediction of cracking propensity in terms of inherent material parameters (energy consumption during plastic deformation, or crack-to-flap) and papermaking conditions (that ultimately affect the board&#39;s material properties). By balancing the magnitudes of the two plastic components (crack-to-gap and gap-to-flap), one will also be better able to understand the limits to which the papermaking conditions and structural parameters (e.g., top-ply coverage) could be changed if the basic fiber properties (e.g., pulp furnish and/or quality) change, so as to produce optimal cracking-resistant linerboard. 
     It should also be noted that capabilities to predict score-line cracking propensity must intrinsically be associated with measuring energy absorption in the subject material, specifically, the energy consumed during plastic deformation. Routine mechanical measures (such as tensile strength, TEA, etc.) have been shown not to correlate, as expected from a theoretical standpoint). 
     While the invention has been described with reference to preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation to the teachings of the invention without departing from the essential scope thereof. Therefore it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.