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  • 1.
    Backlund, Hans-Olof
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Höglund, Hans
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Study of tangential forces and temperature profiles in commercial refiners2003Inngår i: 2003 International Mechanical Pulping Conference, 2003, s. 379-388Konferansepaper (Fagfellevurdert)
  • 2. Batchelor, W. J.
    et al.
    Westerlind, Bo.S.
    Hägglund, R.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Effect of test conditions on measured loads and displacements in zero and short span testing2003Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Single fibre mechanical properties play a critical role in determining sheet mechanical properties, but these mechanical properties are rarely measured due to the time-consuming nature of the tests. The zero span strength is commonly used as a measure for the strength of the fibres, but the results also can depend on the test conditions. Modelling has shown that the load displacement curves are influenced by the thickness to span ratio, as there is an in-homogenous stress-field in the thickness direction of the sample. This paper will present data on the effect of grammage and clamping pressure on the loads and displacements in zero/short span tests. Clamps were designed and made for a displacement controlled load frame made by Material Testing System (MTS). These clamps can test up to ten plies of papers with a span length from 0 to 3 mm. For the sake of comparison, tests were made using a commercial zero/short span tester, which is load controlled but is limited in span length and thickness of the tested material. Both machines were found to give comparable results. Isotropic 65 gsm handsheets, 36 gsm aluminium foil and 42 gsm greaseproof paper (MD and CD) were tested as functions of clamping pressure and grammage. An intrinsic zero-span strength was defined as the y-axis intercept of plot. A recently published procedure for determining the short span stress-strain curve from zero and short span testing was evaluated for the effect of grammage, clamping pressure and span on the calculated result. It was concluded that the method only gives results that are independent of the test conditions when the conditions are carefully selected.

  • 3.
    Batchelor, Warren J.
    et al.
    Monash University, Australia.
    Westerlind, B. S.
    SCA Graphic Research, Sundsvall.
    Hägglund, R.
    SCA Packaging Research, Sundsvall.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Effect of test conditions on measured loads and displacements in zero-span testing2006Inngår i: TAPPI Journal, ISSN 0734-1415, Vol. 5, nr 10, s. 3-8Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Single fiber mechanical properties play a critical role in determining sheet mechanical properties, but fiber mechanical properties are rarely measured, because of the time-consuming nature of the tests. Zero-span strength is commonly used as a measure of fiber strength, but the results can vary with the test conditions. Modeling has shown that the load displacement curves are influenced by the thickness-to-span ratio, as there is a heterogeneous stress field in the thickness direction of the sample.

    This paper presents data on the effect of grammage on the loads and displacements in zero-span tests. Clamps were designed and made for a displacement-control led load frame. These clamps can test up to 10 plies of papers with,a span length from 0 to 3 mm. For the sake of comparison, tests were made using a commercial zero-span tester, which is load controlled but limited in span length and thickness of the tested material. Both machines were found to give comparable results. Isotropic 65 g/m(2) handsheets, 36 g/m(2) aluminum foil, and 42 g/m(2) greaseproof paper were tested as functions of sheet grammage. An intrinsic zero-span strength was defined as the y-axis intercept of a plot of zero-span strength versus grammage.

    Application:This paper demonstrates that the measured zero-span strength is always less than the intrinsic zero-span strength. The results show that, for best results, the grammage of the material tested should be minimized to obtain a measured value that is as close to the intrinsic value as possible.

  • 4.
    Berg, Jan-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Effect of Temperature on Fracture of Spruce in Compression Using Acoustic Emissions1995Inngår i: AECM-5, Fifth International Symposium on Acoustic Emission From Composite Material, Columbus, OH, USA: The American Society for Nondestructive Testing, Inc. , 1995, s. 139-148Konferansepaper (Fagfellevurdert)
  • 5.
    Berg, Jan-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    A Micromechanical Model of the Deterioration of a Wood Fibre1999Inngår i: Journal of Pulp and Paper Science, ISSN 0826-6220, Vol. 25, nr 2, s. 66-71Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A simple analytical model is presented in this paper for the prediction of the stiffness degradation and the damage state in a wood fibre, loaded in uniaxial tension or shear. The model is based on an assumed displacement field together with the minimum total potential energy theorem. For the damage development, an energy criterion is employed. The model is applied to a specific example and the relevant stiffness coefficients are calculated as a function of the damage state. The damage development as a function of the applied loads is also given. The results from a specific example considered indicate that a tensile load affects the stiffness degradation to a larger extent than does a shear load.

  • 6.
    Berg, Jan-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Effect of Temperature on Fracture of Spruce in Compression, Investigated by Use of Acoustic Emission Monitoring2000Inngår i: Journal of Pulp and Paper Science (JPPS), ISSN 0826-6220, Vol. 26, nr 8, s. 294-299Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Acoustic Emission (AE) monitoring during compression of wood has been used to investigate the fracture history with specific emphasis on its dependence on temperature, moisture content, strain and loading direction. The wood was compressed in both the lateral and longitudinal directions in order to select preferred modes of deformation to achieve desired irreversible changes in the wood structure. The elastic modulus, the compressive strength and the cumulated number of AE events decreased with increasing temperature. It was concluded that the most efficient loading direction is longitudinal in order to introduce flaws in wood under compression and that a longitudinal compression of 24%, corresponding to a specific energy input of 3 kWh/ton, is needed in order to achieve substantial changes in the wood structure. The compression should be carried out at temperatures well below 120°C in order to introduce many failure sites.

  • 7.
    Berg, Jan-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Fibre wall crack development2009Inngår i: Proceedings - 2009 International Mechanical Pulping Conference, IMPC 2009, 2009, s. 340-343Konferansepaper (Fagfellevurdert)
    Abstract [en]

    An analytical model has been applied to calculate the energy to achieve a certain damage state in a softwood fibre wall by uniaxial tension or shear load. At conditions such as prevailing at the entrance of the gap between the plates in a refiner less energy was needed for earlywood compared to latewood fibres. The energy was lower for loading in shear compared to tension for both earlywood and latewood fibres with a low microfibril angle. This implies that it would be preferred to refine earlywood and latewood fibres separately.

  • 8.
    Berg, Jan-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gulliksson, Mårten E.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    On the energy consumption for crack development in fibre wall in disc refining - A micromechanical approach2009Inngår i: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 63, nr 2, s. 204-210Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An analytical model has been applied to calculate the acquired strain energy density in order to achieve a certain damage state in a softwood fibre by uniaxial tension or shear load. The energy density was found to be dependent on the microfibril angle in the middle secondary wall, the loading case, the thicknesses of the fibre cell wall layers, and conditions such as moisture content and temperature. At conditions, prevailing at the entrance of the gap between the plates in a refiner and at relative high damage states, more energy is needed to create cracks at higher microfibril angles. The energy density was lower for earlywood compared to latewood fibres. For low microfibril angles, the energy density was lower for loading in shear compared to tension for both earlywood and latewood fibres. Material parameters, such as initial damage state and specific fracture energy, were determined by fitting of input parameters to experimental data.

  • 9.
    Edvardsson, Sverker
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    On dissipative effects of paper web adhesion strength2011Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 48, nr 1, s. 24-30Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This work is concerned with the adhesion strength between a paper web and a metal roll surface, which is a common situation in paper machines world-wide. It is shown that the classic expression relating the work of adhesion to the peeling angle and web tension is, in general, insufficient. An improved model is suggested to take into account the energy dissipation due to elastic-plastic deformation behavior of wet paper materials. To judge the model, an industrially relevant example of wet newsprint and a mild steel surface is studied. It is found that the agreement between theory and experimental observations is excellent. A key result is that elastic-plastic material behavior must always be included for wet paper materials in peeling processes.

  • 10.
    Edvardsson, Sverker
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    A Note on Wet Paper Web Adhesion Strength2012Inngår i: Journal of Testing and Evaluation, ISSN 0090-3973, E-ISSN 1945-7553, Vol. 40, nr 4, s. 682-686Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This work is concerned with the determination of the adhesion strength between a paper web and an adhesive surface. Edvardsson et al. [Edvardsson, S., Gradin, P., and Isaksson, P., "On Dissipative Effects of Paper Web Adhesion Strength," Int. J. Solids Struct., Vol. 48(1), 2011, pp. 24-30] suggested recently a model that takes into account the energy dissipation caused by elastic plastic deformation in the bent structure of a paper specimen. This model is further developed and investigated in the present work. A linear relation in plastic dissipation is discovered facilitating a novel analysis of the peeling tension and a more convenient determination of the proper adhesion strength. Industrial relevant examples are made with wet newsprint and kraft stock. A straightforward experimental procedure for determining the consistent adhesion strength is suggested. It is found that the agreement between the model and the experimental observations is good.

  • 11.
    Engstrand, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kemiteknik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Hellström, Lisbeth
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Sandström, Peter
    SCA Reseach.
    Liden, Joar
    SCA Ortviken.
    Söderberg, Mats
    SCA Research.
    Mats, Egnell
    Andritz Iggesund Tools.
    Improved refining energy efficiency in thermo-mechanical pulping by means of collimated wood chipping – from solid mechanics to full scale evaluation2016Inngår i: PaperWeek Canada 2016 Conference February 1 to 5, 2016, Montreal: Technical Track Program / [ed] Greg Hay, 2016Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The wood chipping process was never optimized with regard to high yield pulping processes as thermomechanical pulping (TMP) and chemithermomechanical pulping (CTMP). It is generally believed that wood chips for pulping should be produced in such a way that the degree of damage is minimized and that the chip dimensional distribution should be as narrow as possible. Since the TMP and CTMP processes were developed in the 60-ies and 70-ies, compression screw as well as roll nip equipment have been developed to pretreat wood chips as a way to reduce refining energy consumption to given fiber and pulp properties and also in order to improve impregnation. The general conclusions are that a combination of shear and compression in the tangential or radial direction of the wood initiates cracks that later in the refiner will enhance and optimize fiber separation and also fiber property development. The idea with the collimated chipping technology is to utilize the wood chipper as a tool, combining cutting of wood logs to wood chips with a pretreatment of the chips by creating cracks that would enhance fiber separation, fiber surface development as well as chip-impregnation. In this case the compression is performed in the wood fiber direction, in which direction wood actually is weakest when it comes to compression induced cracking. The maximization of the amount of cracks in wood-chips is performed by optimizing the knife angle (or spout angle) in the chipper, to what we call collimated chipping (according to a patent owned by CCT AB). This presentation describes a theoretical background and two demonstration scale studies performed by SCA Forest Products at their Ortviken mill. One conclusion drawn, based on two-month test period with three weeks of collimated chipping, was that specific refining energy reduction was around 100 kWh/adt of the 1400 kWh/adt used in primary stage double disc refining. Most probably the potential is higher if the whole system is optimized. Tests were performed at constant production rate and energy was reduced by reducing power to constant freeness, leading to similar tensile and light scattering levels. The deliberately increased forces created in the wood chipper by means of an optimized (increased) edge angle caused more problems with knife holder equipment than normally, as well as increased vibrations. These problems will have to be solved for future long-term implementation of the technique.

  • 12.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Acoustic emission monitoring during mechanical-loading of paper: State of the art2004Rapport (Annet vitenskapelig)
  • 13.
    Gradin, Per A
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Nyström, Staffan K
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Graham, D
    Kao, D
    Knight, B
    Acoustic Emission applied to mechanically loaded Paper2004Inngår i: EWGAE (European Working Group on Acoustic Emission) 2004 proceedings, 2004, s. 423-431Konferansepaper (Fagfellevurdert)
  • 14.
    Gradin, Per A.
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Johansson, Ola
    Sunds Defibrator AB.
    Berg, Jan-Erik
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Nyström, Staffan
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Measurement of the Power Distribution in a Single Disc Refiner1999Inngår i: Journal of Pulp and Paper Science, ISSN 0826-6220, Vol. 25, nr 11, s. 384-387Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A vital parameter in the production of mechanical pulp through refining is the energy consumption. Until recently, the pulping industry has focused on the total energy consumed, without a full understanding of how this energy is distributed in the refiners. In this paper two methods are suggested by which it is possible to estimate the energy supplied at an arbitrary point along the disc radius on refiner segments. The methods are based on instrumented bar with strain gauges. In the first method, a bar is slotted so that the sensor can be viewed as consisting of a number of cantilever beams separated by slots. In the second method, the sensor consists of one continuous bar along the disc radius. The sensors are calibrated such that influence coefficients are obtained for the slotted case and an influence function is obtained for the continuous one. The tangential forces are obtained directly in the first method, while in the second they are given by an integral equation which can be solved numerically. From the knowledge of the tangential force the power distribution can be calculated. Experimental results from the use of the slotted sensor are also given.

  • 15.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för informationsteknologi och medier.
    Backlund, Hans-Olof
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    New sensors for measurement of tangential force distribution in mill-scale TMP chip refinersManuskript (Annet vitenskapelig)
  • 16.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Berg, Jan-Erik
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Nyström, Staffan
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Measuring forces in a refiner plate gap2011Inngår i: Proceedings of International Mechanical Pulping Conference, 2011, s. 81-83Konferansepaper (Fagfellevurdert)
  • 17.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Berg, Jan-Erik
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kemiteknik.
    Nyström, Staffan
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kemiteknik.
    Measuring Tangential Forces in a Pulp Refiner: A Novel Approach2016Inngår i: Experimental techniques (Westport, Conn.), ISSN 0732-8818, E-ISSN 1747-1567, Vol. 40, nr 2, s. 789-793Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    To get some insight into the processes that are active during the refining of wood, the tangential force distribution in the plate gap is of interest. Over the years several designs of force sensors have been developed for this purpose. One drawback with these designs is that each sensormeasures forces over quite a small area such that in order to cover the whole disc with a reasonably good resolution, many sensors have to be used. Also, there are problems to protect the active parts of the sensors from the harsh environment in the plate gap. In this paper a different concept is presented, in that the sensor is continuous and consists of a hollow radial bar equipped with strain gages on the inside. The force sensor was calibrated before mounting by loading it with a known load in the tangential direction and in different positions while measuring the strains in the points where the gages are located. This makes it possible to determine the so-called influence (or Green) functions. Knowing these it is possible to determine the tangential force distribution from strain values measured during operation of the refiner. Guidelines for doing this are presented together with a detailed description of the load sensor and some experimental results.

  • 18.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Graham, D
    University of Greenwich, UK.
    Nygård, P
    Paper and Fibre Research Institute, Norway.
    Vallen, H
    Vallen-Systeme GmbH, Germany.
    The use of acoustic emission monitoring to rank paper materials with respect to their fracture toughness2008Inngår i: Proceedings of the Society for Experimental Mechanics, Inc., Society for experimental mechanics , 2008, Vol. 65, s. 133-137Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this study, a simplified Acoustic Emission (AE) equipment, in essence an AE signal conditioner and a USB (Universal Serial Bus) data acquisition system, is used to study what happens in paper structures during mechanical loading. By the use of such equipment, some parameters that can be extracted are e.g. the stress and strain at onset of AE, the stress and strain at the onset of rapid AE defined as some numerical factor (larger then one) times the initial emission rate, the emission rate at the first stage of loading and the stress and strain at final failure i.e. when the specimen loses its load carrying ability.In this study however, the interest is focused on one particular parameter i.e. the elastic strain energy density Wc at onset of AE. This is a parameter with a clear physical meaning and in this study, the correlation between this parameter and a fracture toughness measure, is investigated.The conclusion is that when nine different paper materials (with a large span regarding properties) are considered, there is a correlation (however not linear) between these two parameters.

  • 19.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Graham, D
    Nygård, P
    Vallen, H
    The Use of Acoustic Emission Monitoring to Rank Paper Materials With Respect to their Fracture Toughness2008Inngår i: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 48, nr 1, s. 133-137Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this study, simplified Acoustic Emission (AE) equipment, in essence an AE signal conditioner and a USB (Universal Serial Bus) data acquisition system, are used to study what happens in paper structures during mechanical loading. By the use of such equipment, some parameters that can be extracted are e.g. the stress and strain at onset of AE, the stress and strain at the onset of rapid AE (defined in some appropriate way), the emission rate at the first stage of loading and the stress and strain at final rupture. In this study however, the interest is focused on one particular parameter i.e. the elastic strain energy density Wc at onset of AE. This is a parameter with a clear physical meaning and in this study, the correlation between this parameter and a fracture toughness measure, is investigated. The conclusion is that when nine different paper materials (with a large span regarding properties) are considered, there is a correlation (however not linear) between these two parameters.

  • 20.
    Gradin, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A Note on the Co-linearity of forces and Displacements in an Elastic Structure2011Inngår i: Journal of Applied Fluid Mechanics, ISSN 1735-3572, E-ISSN 1735-3645, Vol. 78, nr 6, s. Art. no. 4003912-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Theconditions under which force vectors and corresponding displacement vectors becomeco-linear are investigated under the assumption of a linear elasticstructure and for an arbitrary number of loading points. Itis shown that there exist an infinite number of directionsalong which the load and displacement vectors in each loadingpoint coincide. Moreover, the problem of co-linearity is analogous tothe problem of finding the extreme values of the workperformed on an elastic structure under the constraint that eachforce has a given magnitude. The result for a finitenumber of loading points is extended to a continuous loaddistribution on the boundary of an elastic structure, i.e., itis possible to find an infinite number of load distributionssuch that the displacement in a point on the boundaryis co-linear with the boundary stress vector in that samepoint.

  • 21.
    Hellström, Lisbeth
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Engstrand, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gregersen, Øyvind
    Department of chemical engineering, NTNU, Norway.
    Collimated chipping technology in order to reduce the energy consumption in mechanical pulping2011Inngår i: Proceeding for International Mechanical Pulping Conference, Xi'an, P.R. of China, 2011, s. 457-460Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    It has recently been shown that it is possible to improve the energy efficiency during first stage TMP (thermomechanical pulp) refining by utilizing a modified chipping method (collimated chipping). A patent application regarding this method has been filed and is pending. The modification consists in that the spout angle i.e. the angle between the fibre direction of the wood specimen and the cutting plane, is increased. This paper reports the differences in properties of IMP refined from chips produced at two different spout angles i.e. 30 and 50 with and without the addition of sodium bisulphite (NaHSO3) to the dilution water. It was found that the specific energy input for a certain CSF (Canadian Standard Freeness) value was lower for chips produced at spout 50 but that the addition of chemicals to the dilution water had no influence on the specific energy value for a given CSF value. However, the tensile index and specific light scattering coefficient was substantially higher for handsheets made of the pulp refined from chips produced at spout angle 50 and with NaHSO3 added compared to handsheets from pulp made from 30 and 50 chips without chemicals added.

  • 22.
    Hellström, Lisbeth
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Engstrand, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för tillämpad naturvetenskap och design.
    Gregersen, Øyvind
    Department for Chemical Engineering, NTNU, Norway.
    Evaluation Of Collimated Chipping Technology For Reducing Energy Consumption In Mechanical Pulping2012Inngår i: Journal of Science & Technology for Forest Products and Processes, ISSN 1927-6311, E-ISSN 1927-632X, Vol. 2, nr 3, s. 6-9Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    It has recently been shown that the energy efficiency during first-stage TMP (thermo-mechanical pulp) refining can be improved using amodified chipping method (collimated chipping), where the angle between the fibre direction of the wood specimen and the cutting plane is increased. This paper reports the differences in properties of TMP refined from wood chips produced at two different spout angles, 30° and 50°, with and without the addition of sodium bisulphite (NaHSO3) to the dilution water. It was found that the specific energy input for a certain CSF (Canadian Standard Freeness) value was lower for chips produced at spout 50°, but that the addition of chemicals to the dilution water had no influence on the specific energy value for a given CSF value. However, the tensile index and specific light-scattering coefficient were substantially higher for handsheets made from the pulp refined from chips produced at spout angle 50° and with NaHSO3 added compared to handsheets from pulp made from 30° and 50° chips without chemicals added.

  • 23.
    Hellström, Lisbeth
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Strain Distribution in Wood During Chipping2007Inngår i: International Mechanical Pulping Conference 2007, TAPPI, 2007, Vol. 1, s. 251-255Konferansepaper (Fagfellevurdert)
    Abstract [en]

    To be able to understand more in detail what actually happens during chipping, the strain field in a chip during chipping was studied by means of the Digital Speckle Photography (DSP) technique. In addition to recording the strain field, the load on and displacement of the chipping tool was also recorded. The equipment used in this study was a DSP system, an MTS servo hydraulic testing machine and a specially developed chipping device. Displacement controlled testing was performed with a crosshead speed of 1.0 mm/s. The results are promising but needs some improvement regarding resolution of the digital images in a vicinity of the knife-edge. The cutting speed in this investigation is low in comparison to normal industrial cutting speeds and since wood in general exhibits a viscoelastic material behaviour this might give a slightly different strain field as compared to an industrial chipping process. However, it is believed that using DSP as a tool for studying the deformations during chipping, even under quite restricted conditions, will increase the understanding of the chipping process. The present study is a part of a larger project aimed at a better understanding of the chip formation and wear mechanisms of wood chipping knifes.

  • 24.
    Hellström, Lisbeth
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Engstrand, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gregersen, Øyvind
    Department for Chemical Engineering, NTNU, Trondheim, Norway.
    Properties of wood chips for thermomechanical pulp (TMP) production as a function of spout angle2011Inngår i: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 65, nr 6, s. 805-809Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Spruce woodchipswere produced under well-controlled conditions in a laboratory woodchipper at spout angles of 30°, 40°, and 50° at a cutting rate of 20 m s-1 and with a nominalchip length of 25 mm. Thechips were then refined under thermomechanical pulp (TMP) conditions in a pilot refiner plant. The pulpproperties such as freeness, average fiber length, and shives content were determined and evaluated as a function of specific energy consumption. For a first stage refining and for a freeness value of 350 ml, a decrease in specific electrical energy consumption could be achieved by performing thewood chipping at a spout angle of 50° as compared to 30° which is the spout angle commonly used. A patent application regarding this method has been filed and is pending. It is realized that a freeness value is not directly indicative of any quality measure, such as, for example tensile index and light scattering coefficient but the obtained results can be interpreted to be promising. Further studies are needed regarding the impact of the modified chipping process.

  • 25.
    Hellström, Lisbeth
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gulliksson, Mårten
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A laboratory wood chipper for chipping under realistic conditions2011Inngår i: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 51, nr 8, s. 1309-1316Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In order to be able to study the damage mechanisms and in general the mechanisms active when a wood chip is created during the wood chipping process, it is crucial to have access to an experimental equipment in which chips can be produced under realistic conditions. In this paper is presented a laboratory chipper, which has been developed to admit chipping at rates that can be varied in a large interval i.e. at rates ranging from zero to 50 m/s. The knife used to cut the chips is mounted in a knife holder, which is instrumented in such a way that forces in three orthogonal directions can be measured. Since the actual force and the measured force differs due to inertia effects, a simple mathematical model is developed and used to evaluate the force acting on the knife. Some results are shown from the force measurements and it is concluded that the laboratory chipper is a versatile tool in the process of increasing the understanding of the chipping process.

  • 26.
    Hellström, Lisbeth M.
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Biller, Sven-Olov
    Andritz Iggesund Tools AB, Iggesund, Sweden.
    Edvardsson, Sverker
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    A theoretical and experimental study of the circular sawing process2014Inngår i: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 68, nr 3, s. 307-312Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    To gain further insight into the energy dissipation during the wood sawing process, a theoretical model has been developed. The model is based on the assumption that there are two basic causes for energy dissipation during sawing: the creation of a new surface and the compression of material below a saw tooth. It is assumed that both contributions can be dependent on the cutting angle (the angle between the fiber direction and the tangent to the path followed by a saw tooth) because a saw tooth changes its angle of attack during its way through a log. To determine this dependence of the dissipation on the cutting angle, a series of experiments with pine plank sawing were performed by means of different feeding rates and cutting angles while the electrical power supplied to the saw was measured. The parameters in the theoretical model were derived from the experimental findings. Finally, two tests were carried out under different conditions with respect to thickness and cutting angles and the validity of the model was confirmed concerning the prediction of the electrical power consumption.

  • 27.
    Hellström, Lisbeth M
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A device for studying wood chipping under realistic conditions2009Inngår i: Proceedings - 2009 International Mechanical Pulping Conference, IMPC 2009, 2009, s. 252-254Konferansepaper (Fagfellevurdert)
    Abstract [en]

    It seems to be a consensus in the papermaking society that chip quality is very much a matter of a narrow thickness distribution. Much effort has been spent on studying the influence of certain process parameters on the thickness distribution of chips. However, when these studies have been performed in a laboratory environment, the conditions have been far from realistic when it comes to for instance cutting rates. In this paper a laboratory chipper is presented, which has been developed to admit chipping at rates used in the industry. The knife holder is instrumented in such a way that moments and forces in three directions can be measured. Results from tests, where the cutting rate is varied, is presented and it is concluded that the laboratory chipper is a versatile tool in the process of increasing the understanding of the chipping process.

     

     

  • 28.
    Hellström, Lisbeth M
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A Method for Experimental Investigation of the Wood Chipping Process2008Inngår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 23, nr 3, s. 339-342Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    SUMMARY: To be able to formulate criteria’s for determining the onset of the creation of a wood chip; it is desirable to be able to study the deformation fields in a vicinity of the edge of the chipping tool. To that end, an experimental setup has been developed in which the chipping can be performed under very well defined conditions. In this setup it is possible to control the rate of indentation of the chipping tool and also to measure the force on the tool. The setup admits also that the angle of the wood specimen with respect to the cutting plane can be varied in both a horizontal and a vertical plane. To determine the deformations, a Digital Speckle Photography (DSP) equipment is used, which together with image processing software makes it possible to determine the strain field on the surface of the wood specimen. One observation that can be made in these studies is that prior to the creation of a chip, there is a localization of strains in a thin region starting from the edge of the tool and directed parallel to the grain. Another observation made during the experimental work is that there exist different types of fracture processes, each giving different chip thicknesses.

  • 29.
    Hellström, Lisbeth M
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Eriksson, Kjell
    Luleå University of Technology.
    An Analytical and Numerical Study of some aspects of the Wood Chipping Process2009Inngår i: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 24, nr 2, s. 225-230Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    SUMMARY: In order to model the wood chipping process, the primary process parameters have been identified and their first order interaction studied. The model is analytical and incorporates, in particular, the influence of sliding friction between the wood chipping tool and the log. To estimate the accuracy of the analytical model, a Finite Element (FE) analysis of the problem considered was also performed. The analytical model and the FE analysis are both restricted to small deformations and linear elastic orthotropic material behaviour. The most severe limitation with both the analytical and the FE model is the assumption of linearly elastic material. On the other hand, it is felt that existing models of anisotropic plasticity in metals are lacking too much of physical relevance, if applied to wood. The analytical model predicts the normal and shear strain distribution in the crack-plane prior to crack initiation. The analytical distributions are in reasonable agreement with the corresponding distribution of the FE analysis. Based on experimental findings, it is suggested that the stress field over the entire crack-plane, in conjunction with the stress field close to the tip of the chipping tool, are critical for chip creation, rather than just the latter.

  • 30.
    Hellström, Lisbeth Maria
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Carlberg, Torbjörn
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    A Study of Fracture processes in Wood Chipping2008Inngår i: 6th Fundamental Mechanical Pulp Research Seminar, Espoo: KCL Oy Keskuslaboratorio - Centrallaboratorium AB , 2008Konferansepaper (Fagfellevurdert)
  • 31.
    Holmgren, Sven-Erik
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Svensson, Birgitta A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Lundberg, B
    An Encapsulated Split Hopkinson Pressure Bar for Testing of Wood at Elevated Strain Rate, Temperature and Pressure2008Inngår i: Experimental techniques (Westport, Conn.), ISSN 0732-8818, E-ISSN 1747-1567, Vol. 32, nr 5, s. 44-50Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents a device, based on a split Hopkinson pressure bar (SHPB) setup, by which it is possible to obtain stress vs. strain for a wood specimen at high deformation rate, high temperature and high steam pressure. The need for determining the mechanical properties of wood not only at high deformation rate but also at high temperature and pressure is motivated by the need to model the wood chip refining process in mechanical pulp-ing. At mechanical chip refining, e.g. in thermomechanical pulping processes, preheated wood chips together with added water are fed into the centre of a refiner which in essence consists of two circular discs. Most often one disc is stationary and the other is rotating. The wood chips are transported radially between the discs due to inertia. On their way, due to impacts from radial bars on the discs, they are eventually broken down to individual fibres and fibre fragments. The device presented here is an SHPB set-up, modified so that the bars and the specimen are encapsulated in a pressure vessel within which the temperature is constant. In this way effects of temperature gradients in the bars are avoided. Pilot tests have been carried out which verify the intended per-formance of the device.

  • 32.
    Hägglund, R
    et al.
    SCA Packaging Research, Sundsvall S 851 21, Sweden.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Tarakameh, D
    Some Aspects on the Zero-span tensile test2004Inngår i: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 44, nr 4, s. 365-374Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we present some analytical and numerical results concerning the zero-span testing method, frequently used for quality control of cellulose fiber for papermaking. Of particular interest is the relationship between an apparent modulus obtained from the zero-span testing method and the elastic properties of the fibers. The apparent elasticity modulus is estimated using two energy theorems in elasto-statics in which the role of span length is explored. Analytical results, derived under the assumption that slippage between specimen and clamps does not occur, clearly show that the apparent modulus strongly depends on the span length. This is verified by the numerical results obtained using the finite element method. In addition to the above analysis, the effect of slippage is investigated, also by utilizing the finite element method, and it is found that for a specific case, the contribution from slippage to the total displacement depends strongly on the length of the span. Tensile tests at nominal zero span were conducted in an effort to further validate the analysis with relevant experimental data and it was concluded that there is qualitative agreement between the experimental results and the result of the analysis.

  • 33.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Shear buckling in the core of a corrugated board structure2009Inngår i: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 88, nr 4, s. 610-614Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In some situations, a corrugated board package can experience loading of such a kind so that the corrugated core, or as it is most often referred to, the fluting, is loaded in transverse shear. This might cause the fluting to collapse and through this, cause a decrease in the bending stiffness. In this paper, an exact solution for the elastic instability of an infinite linear elastic strip with an initial curvature and loaded in pure in-plane shear is given. The solution is a modification of an existing solution for an isotropic strip. To experimentally investigate the accuracy of the model, a special device has been developed in which paper strips are loaded in pure in-plane shear to observe the buckling behavior. According to the experiments performed, the model seems to quantitatively well capture the main buckling behavior and lends some confidence to the theory. With use of the model it is easy to judge which deformation process most likely will occur, shear buckling or plastic deformation, and thereby allows one to structurally optimize the geometric ratio, i.e. the ratio between thickness and height of the fluting, when designing the corrugated core structure. Finally, it is illustrated that going below a certain critical thickness of the fluting may cause the structural strength of the board panel to decrease drastically.

  • 34.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    A bending specimen for constant energy release rate under controlled displacement conditions2005Inngår i: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 72, nr 11, s. 1770-1775Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A bending specimen to give a constant energy release rate under given displacement conditions is developed. The specimen is shown by experiments to give a, in essence, constant energy release rate.

  • 35.
    Isaksson, Per
    et al.
    Uppsala Univ, Angstrom Lab, SE-75121 Uppsala, Sweden.
    Gradin, Per A.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    Hellström, Lisbeth M.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för naturvetenskap.
    A numerical and experimental study regarding the influence of some process parameters on the damage state in wood chips2013Inngår i: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 67, nr 6, s. 691-696Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The specific energy consumption during mechanical refining operation can be reduced by choosing the optimal process parameters in the wood chipping process such that a beneficial pretreatment is obtained. In the case of the utilization of a larger knife-edge angle, which is one such process parameter, the energy reduction is presumably due to the increased compressive loading parallel to the wood fibers. In the present article, a chip damage parameter D of spruce is in focus, which is relevant for cracking parallel to the fibers. D is defined and its dependence on the chip length and edge angle of the chipping knife is analyzed numerically by means of finite element analyses (FEA). The cutting force was measured in a pilot wood chipper for a number of knife-edge angles. There is a good correlation between the experimental results and those of FEA.

  • 36.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Kulachenko, Artem
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Acoustic Emission applied to mechanically loaded Paper ??Manuskript (Annet vitenskapelig)
  • 37.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Östlund, Sören
    Solid Mechanics, KTH.
    A simplified treatise of the Scott bond testing method2007Inngår i: Proceedings of the 2007 International Paper Physics Conference, May 6-11, 2007, Gold Coast, Qld, Australia, 1-6, 2007, 2007Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    The Scott bond test method has been used extensively in the paper industry over the years as a mean to assess the bond strength of paper. The method has been a subject of some controversy lately since it does not always correlate to the sensitivity of the material to fracture by delamination.

     

    To gain some further insight into which parameters govern the fracture process in a Scott bond test a simplified approach has been chosen in order to formulate an analytical mathematical/mechanical model of the test. The model is dynamic in the sense that inertia effects are included. The material model utilised is a simple cohesive theory that assumes a linear behaviour between stress and crack opening when the material has started to degrade. This choice of material model makes the mathematical model very nonlinear. In fact, a system of three coupled nonlinear second order partial differential equations have to be solved and adjusted to the correct initial conditions.

     

    The material parameters needed for the model are the elastic modulus in the thickness direction, the transverse shear (elastic) modulus, the tensile strength (in the thickness direction) and the fracture work (per unit area) for a delamination crack.

     

    To investigate the ability of the model, a Scott bond testing apparatus have been equipped with a piezoelectric load sensor. The load cell was mounted on the apparatus' pendulum so that the load acting on the sample holder could be recorded during the whole impact stage. This was done for a number of different initial velocities of the pendulum and it is found that the model gives a fair prediction of the contact load.

  • 38.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap, teknik och matematik.
    Östlund, Sören
    KTH, Hållfasthetslära.
    A simplified treatise of the Scott bond testing method2010Inngår i: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 50, nr 6, s. 745-751Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Scott bond test method has been used extensively in the paper industry over the years as a means to assess the bond strength of paper. The method has been a subject of some controversy lately since it does not always correlate to the sensitivity of the material to fracture by delamination. To gain some further insight into which parameters govern the fracture process in a Scott bond test a simplified approach has been chosen in order to formulate an analytical mathematical/mechanical model of the test. The model is dynamic in the sense that inertia effects are included. The material model utilised is a simple cohesive theory that assumes a linear behaviour between stress and crack opening when the material has started to degrade. This choice of material model makes the mathematical model very nonlinear. In fact, a system of three coupled nonlinear second order partial differential equations have to be solved and adjusted to the correct initial conditions. The material parameters needed for the model are the elastic modulus in the thickness direction, the transverse shear (elastic) modulus, the tensile strength (in the thickness direction) and the fracture work (per unit area) for a delamination crack. To investigate the ability of the model, a Scott bond testing apparatus have been equipped with a piezoelectric load sensor. The load cell was mounted on the apparatus’ pendulum so that the load acting on the sample holder could be recorded during the whole impact stage. This was done for a number of different initial velocities of the pendulum and it is found that the model gives a fair prediction of the contact load.

  • 39.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Hägglund, R
    Gradin, P
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    A continuum damage elastic-plastic model for packaging paper2003Inngår i: 2003 International Paper Physics Conference. Proceedings, 2003, s. 207-210Konferansepaper (Fagfellevurdert)
  • 40.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Hägglund, R
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Continuum damage mechanics applied to paper2004Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, nr 16-17, s. 4731-4755Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The mechanical behavior of two packaging paper materials subjected to tensile loading up to complete breakage has been investigated. A model for isotropic strain hardening elastic anisotropic plasticity, coupled to anisotropic damage, is discussed. The constitutive relations, including a gradient enhanced damage model, are developed within a thermodynamical framework. The Helmholtz free energy in the continuum is assumed to depend not only on the strain and stress components but also on the damage in the material.The model has been analyzed in a non-linear finite element procedure. The capability of the model to properly capture and simulate the failure of a paper material subjected to tensile loading is demonstrated by means of several numerical examples that are compared to, and verified with, experiments on packaging paper specimens of varying geometry.

  • 41.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Krusper, Aleksandra
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Shear correction factors for corrugated core structures2007Inngår i: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 80, nr 1, s. 123-130Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Because of the high computational cost involved when modeling a corrugated panel (in e.g., finite element analyses) the corrugated core sandwich is in this investigation homogenized and the panel is transformed to an equivalent continuous homogenous layer with effective equal properties. Mathematically, the corrugated board panel is divided into an arbitrary number of thin virtual layers. For each virtual layer, unique effective elastic modules are calculated. Then, the elastic properties in all layers are assembled together in order to be able to analyze a corrugated board as a continuous structure having equivalent mechanical properties to a real structure. It is shown that by using shear correction factors derived from an equilibrium stress field, improvements in the calculated stiffness and deflections can be achieved in circumstances when a corrugated board panel is subjected to bending. Following the algorithm outlined, the shear correction factors are easy to calculate and become a valuable tool when performing mechanical analyses of corrugated boards. The capability of the model to properly capture and simulate the mechanical behavior of corrugated boards subjected to plate bending as well as three-point-bending has been demonstrated by means of several numerical examples, which are compared to experiments on corrugated board panels of varying geometry.

  • 42.
    Isaksson, Per
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Kulachenko, Artem
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    The onset and progression of damage in isotropic paper sheets2006Inngår i: International Journal of Solids and Structures, ISSN 0020-7683, Vol. 43, nr 3-4, s. 713-726Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The validity of existing criteria and relations for the onset and evolution of damage in paper is investigated and it is found that a non - local theory has to be utilized.

  • 43.
    Krusper, Aleksandra
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Isaksson, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Modelling of out-of-plane compression loading of corrugated paper board structures2007Inngår i: Journal of engineering mechanics, ISSN 0733-9399, E-ISSN 1943-7889, Vol. 133, nr 11, s. 1171-1177Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A simple analytical model for calculating the nonlinear deformations of a corrugated core (fluting) during out-of-plane compression is developed. The results from the analytical model are compared to a more comprehensive finite-element model and to experiments. A connection between the boundary conditions and the damage state of the corrugated board is discussed. Including a modified set of boundary conditions gives an almost perfect match of the initial stiffness to the experimental results, indicating that the core might be significantly damaged as a result of the manufacturing process. Possibly, the strength of corrugated boards might be increased about 20% if one could avoid damaging the fluting during the manufacturing process.

  • 44.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Uesaka, Tetsu
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Basic mechanisms of fluting2006Inngår i: 92nd Annual Meeting Preprints-Book A, 7 Feb. 2006 , Canada, Que., Canada: Pulp and Paper Technical Association of Canada , 2006, s. 161-173Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation consistent with all field observations. The present paper reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding the fluting. The fluting formation has been considered as a post-buckling phenomenon which is analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale strain variations, which in turn are caused by the moisture variations created during fast convection drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, suggesting the presence of other mechanisms of fluting retention.

  • 45.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Uesaka, Tetsu
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Basic mechanisms of fluting formation and retention in paper2006Rapport (Annet vitenskapelig)
  • 46.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per A
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Westerlind, B
    Analysis of Paper Web Tension Profiles2005Inngår i: Journal of Graphic Technology, ISSN 1544-9599, E-ISSN 1544-9602, nr 2, s. 72-81Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The tension profiles of paper webs are very important for determining the runnability in printing presses. Uneven tension profiles, with lower web tension toward the edges, develop in the paper machine due to many factors such as moisture content, residual strains related to drying and draw conditions, fibre orientation etc. This study presents some simple relations regarding the initial strain distribution, but also a method for adjusting the tension profile by choosing an appropriate moisture distribution. The method is verified on web tension and moisture measurements in a pressroom.

  • 47.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Kuivurova, H.
    University of Oulu, Finland.
    Modelling the dynamical behaviour of a paper web: Part I2007Inngår i: Computers and Structures, ISSN 0045-7949, Vol. 85, nr 3-4, s. 131-147Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A new shell element has been proposed for geometrically non-linear, finite element analyses of axially moving paper web. Web instability problems of paper travelling in a printing system, such as wrinkling and fluttering, pose special challenges in the numerical analyses. For examples, these are finite bending stiffness (as opposed to membrane), orthotropy, and non-uniform distributions of mechanical and hygro-properties (in different length scales). The new formulation has accounted for paper transport velocity and paper bending stiffness based on a mixed Lagrangian-Eulerian description of the motion. A natural coordinate system has been employed in the analytical and finite element formulations. Benchmarking with different finite elements in various tests showed that the proposed element is indeed more stable and reliable for the chosen application than existing elements. The usability of the shell element has been successfully demonstrated by two example problems: wrinkling of stretched isotropic and orthotropic membranes, and the vibration of a web showing a speed-tensioning effect above a critical web transport velocity.

  • 48.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Kuivurova, H.
    University of Oulu, Finland.
    Modelling the dynamical behaviour of a paper web: Part II2007Inngår i: Computers and Structures, ISSN 0045-7949, Vol. 85, nr 3-4, s. 148-157Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid-solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called "edge-flutter" is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.

  • 49.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Uesaka, Tetsu
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Basic mechanisms of fluting formation and retention in paper2007Inngår i: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 39, nr 7, s. 643-663Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation and retention which is consistent with all field observations. This paper first reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding fluting. The fluting formation has been considered as a post-buckling phenomenon which has been analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with the ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale hygro-strain variations, which in turn are caused by the moisture variations created during fast convection (through-air) drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, but that high drying temperatures promote inelastic (irreversible) deformations in paper and this may itself preserve fluting.

  • 50.
    Kulachenko, Artem
    et al.
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Gradin, Per
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.
    Uesaka, Tetsu
    Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
    Tension wrinkling and fluting in heatset web offset printing process: post buckling analysis2005Inngår i: Advances in Paper Science and Technology: Transactions of the 13th fundamental research symposium, Vols 1-3, 2005, s. 1075-1099Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Geometrically non-linear, large scale post-buckling analyses were carried out to investigate the influence of different parameters on residual waviness (fluting) after printing in a heat set web offset printing press. Mixed implicit-explicit finite element techniques were used in the analyses. The numerical procedure was verified by experimentally acquired data. Results show that when the paper web is perfectly flat before printing, fluting patterns after drying and moisture recovery generally have higher wavelength than those typically observed in fluted samples. Initial cockles of imprinted sheets were found to have impacts on the fluting patterns and amplitudes. Among the factors investigated, ink thickness and hygroexpansivity had significant influences on fluting: increasing these factors increased fluting amplitudes.

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