Micro-mechanical modelling of mechano-sorptive creep in paper

Transcription

1 Micro-mechanical modelling of mechano-sorptive creep in paper Johan Alfthan Licentiate Thesis Department of Solid Mechanics Royal Institute of Technology Stockholm 2002

2 Micro-mechanical modelling of mechano-sorptive creep in paper Johan Alfthan Licentiate Thesis no. 81, 2002 TRITA HFL-0311 Department of Solid Mechanics Royal Institute of Technology SE Stockholm, Sweden

3 Preface The work presented in this thesis has been carried out between February 1999 and April 2002 at the Department of Solid Mechanics, Royal Institute of Technology, Stockholm, Sweden. I would like to thank my supervisors Prof. Peter Gudmundson and Prof. Sören Östlund who initiated the project and provided excellent guidance and support during the work. I would also like to thank Dr. Joel Panek 1 and Prof. Christer Fellers at STFI for valuable discussions and support. The financial support from the Foundation for Strategic Research (SSF), through the Forest Products Industry Research College (FPIRC), from Jacob Wallenbergs Forskningsstiftelse and from Lars-Erik Thunholms Stiftelse för Främjande av Vetenskaplig Forskning is gratefully acknowledged. Finally I want to thank my colleagues for creating a stimulating atmosphere at the department. Stockholm in May 2002 Johan Alfthan 1 Now at Iggesund Paperboard, Workington, UK

4 This thesis consists of an introduction and the two appended papers: Paper A: J. Alfthan, P. Gudmundson and S. Östlund, A micro-mechanical model for mechanosorptive creep in paper, J. Pulp Paper Sci., 28(3): (2002) Paper B: J. Alfthan A simplified network model for mechano-sorptive creep in paper, Report 309, Department of Solid Mechanics, KTH, Stockholm (2002), submitted for international publication

5 Introduction Mechano-sorptive creep Paper packages must be designed to withstand loads for a long time. In this design creep deformation must be considered. Creep of paper is affected by humidity. Higher humidity, and therefore higher moisture content, means more creep. In addition, creep is accelerated by varying humidity, a phenomenon known as mechano-sorptive creep, or accelerated creep. The total deformation after a few humidity cycles exceeds the deformation at any constant humidity, see Fig x cyclic % RH constant 50 % RH constant 90 % RH total strain ε time [h] Fig. 1. Example of mechano-sorptive creep [1]. Results from compressive creep tests (specific stress knm/kg) in cyclic and constant relative humidity are shown. Mechano-sorptive creep was first discovered in wood in the early 1960s [2, 3]. For paper it was first reported in 1972 [4, 5]. There is no clear-cut way to separate creep and hygroexpansion, i.e. the superposition principle does not hold [6, 7]. Mechano-sorptive creep has also been observed in concrete [8], wool [9, 10] and some synthetic fibres [11, 12]. Modelling The most important load cases in packages are compression and bending, and many experimental results reflect this, e.g. the results in Fig. 1. The mechanical properties of paper are different in tension and compression, and this is true 1

6 for mechano-sorptive creep as well [1, 7]. This probably arises from the structural properties of the fibre network. The compressive load case involves more structural mechanisms. The models presented in this thesis are therefore first and foremost aimed at explaining mechano-sorptive creep in tension. The reasons for modelling mechano-sorptive creep are to be able design packages and predict their life-time and to be able optimise the material. There is no straightforward way to model mechano-sorptive creep. Several models and mechanisms have been suggested for mechano-sorptive creep. None of these models have been generally accepted. Most of them include a special mechanism to explain mechano-sorptive creep. As early as 1965 it was suggested that moving water disrupts hydrogen bonds [13], but later it was shown that a steady state flow of water does not produce accelerated creep [14]. It has been suggested that the moisture content changes themselves accelerate creep [15 18]. These models are phenomenological, and do not provide a physically based explanation for mechano-sorptive creep. Their strength is that they are relatively easy to apply as they treat the material as a continuum. Mechano-sorptive creep has also been connected to aging and the free volume of the material [19, 20], and to slip planes and dislocations [7, 21, 22]. Habeger and Coffin [23] suggested that mechano-sorptive creep is a result of inhomogeneous hygroexpansion and non-linear creep, which in this context means that an increase in stress causes an increase in creep rate that is larger than proportional to the stress change. Due to heterogeneous hygroexpansion, a moisture content change will give rise to a stress distribution in the material. The volume average of these stresses is zero. When these internal stresses are added to a stress state caused by external mechanical loads, the resulting stresses will be higher in some parts of the material and lower in others, giving higher and lower creep rates. If the creep rates depend non-linearly on stress the average creep rate will however be larger than the average stresses suggest. The uneven stress distribution will disappear over time as relaxation takes place during creep, and the moisture content has to change again to maintain the the accelerated creep. Similar models have been suggested for drying concrete [8] and metal-matrix composites during temperature cycling [24, 25]. The major advantage in comparison to other models is that accelerated creep turns out to be a natural consequence of regular creep and not a completely new phenomenon. The models presented in this thesis are based on this mechanism. An appropriate length scale for modelling must be chosen, see Fig. 2. At the largest scale, a box is considered. Few, if any, models for mechano-sorptive creep uses this length scale. Continuum models [15 18] can be used to model the material, in this case the corrugated board or liner. The model of Habeger and Coffin constitute an intermediate step between continuum and the fibre network, as some kind of heterogeneity is needed. Slip plane models [7, 21, 22] are based 2

7 on a smaller scale, fibre network or fibres, while the hydrogen-bond model [13] and free volume model [19, 20] fall on the molecular level. Box Corrugated board, liner Fibre network Fibres, fibrils Molecules Fig. 2. Different length scales, going from the box at the top down to molecules. An appropriate level must be chosen for modelling. The fibre network seems like a suitable level for modelling of mechano-sorptive creep. Continuum models for corrugated board or liner do not explain the physics behind mechano-sorptive creep. Models on fibre level or below are probably not necessary as neither the fibres themselves nor pure cellulose exhibit significant accelerated creep [26 28]. In this work, the hygroexpansion heterogeneity at the bonds is assumed to drive the accelerated creep. Summary of appended papers Paper A: A micro-mechanical model for mechano-sorptive creep in paper In this paper, stresses created at bonds due to anisotropic swelling during absorption and desorption of moisture, in combination with non-linear creep, are proposed to be the cause for mechano-sorptive creep. Two simplified models are first discussed in order to demonstrate the suggested mechanism. A three-dimensional fibre network model composed of elastic fibres and inelastic bonds is then studied by finite element calculations. The relative sliding in the bonds is described by a non-linear creep model which in combination with anisotropic fibre hygroexpansion results in accelerated creep of the network. 3

8 Paper B: A simplified network model for mechano-sorptive creep in paper A simplified network model for mechano-sorptive creep is presented. The model resembles Cox s model for fibrous materials, but creep and influence of bonds are included in addition to the elastic behaviour of the fibres. Three different creep laws describing the creep of individual fibres are applied in the simulations of creep of the network. Results from simulations using the model are presented. The influence of the amplitude of moisture content changes is discussed. It is shown that the model may produce macroscopic strains that are linear in stress, even though the creep of the fibres is non-linear. This may explain why both regular creep and mechanosorptive creep at small loads appear to be linear in stress. References 1. C. Fellers and J. Panek. Effect of relative humidity cycling on mechanosorptive creep. In Moisture and creep effects on paper, board and containers: 5th international symposium, Marysville, Victoria, Australia, L. D. Armstrong and R. S. T. Kingston. Effect of moisture changes on creep in wood. Nature, 185(4718): , L. D. Armstrong and G. N. Christensen. Influence of moisture changes on deformation of wood under stress. Nature, 191(4791): , V. L. Byrd. Effect of relative humidity changes during creep on handsheet paper properties. Tappi, 55(2): , V. L. Byrd. Effect of relative humidity changes on compressive creep response of paper. Tappi, 55(11): , H. W. Haslach, M. G. Pecht, and X. Wu. Variable humidity and load interaction in tensile creep of paper. In 1991 International Paper Physics Conference, pages , Kona, Hawaii, C. Söremark and C. Fellers. Mechano-sorptive creep and hygroexpansion of corrugated board in bending. J. Pulp Paper Sci., 19(1):J19 J26, G. Pickett. The effect of change in moisture-content of the creep of concrete under a sustained load. J. Amer. Concrete Inst., 13(4): ,

9 9. B. H. Mackay and J. G. Downes. The effect of the sorption process on the dynamic rigidity modulus of the wool fiber. J. Appl. Polym. Sci., 2(4):32 38, P. Nordon. Some torsional properties of wool fibers. Text. Res. J., 32: , J. Z. Wang, D. A. Dillard, M. P. Wolcott, F. A. Kamke, and G. L. Wilkes. Transient moisture effect in fibers and composite materials. J. Compos. Mater., 24: , J. Z. Wang, V. Davé, W. Glasser, and D. A. Dillard. The effects of moisture sorption on the creep behavior of fibers and composite materials. In C.E. Harris and T.S. Gates, editors, High Temperature and Environmental Effects on Polymeric Composites, volume 1174 of ASTM STP, pages ASTM, E. J. Gibson. Creep of wood: Role of water and effect of a changing moisture content. Nature, 206(4980): , L. D. Armstrong. Deformation of wood in compression during moisture movement. Wood Sci., 5(2):81 86, A. Ranta-Maunus. The viscoelasticity of wood at varying moisture content. Wood Sci. Technol., 9: , A. Mårtensson. Mechano-sorptive effects in wooden material. Wood Sci. Technol., 28: , T. J. Urbanik. Hygroexpansion-creep model for corrugated fiberboard. Wood Fiber Sci., 27(2): , S. Ormarsson, O. Dahlblom, and H. Petersson. A numerical study of the shape stability of sawn timber subjected to moisture variation. part 1: Theory. Wood Sci. Technol., 32(5): , Z. V. Padanyi. Mechano-sorptive effects and accelerated creep in paper. In 1991 International Paper Physics Conference, pages , Kona, Hawaii, Z. V. Padanyi. Physical aging and glass transition: Effects on the mechanical properties of paper and board. In Products of Papermaking, volume 1, pages , Oxford,

10 21. P. Hoffmeyer and R. W. Davidson. Mechano-sorptive creep mechanism of wood in compression and bending. Wood Sci. Technol., 23: , P. Hoffmeyer. Nonlinear creep caused by slip plane formation. Wood Sci. Technol., 27: , C. C. Habeger and D. W. Coffin. The role of stress concentrations in accelerated creep and sorption-induced physical aging. J. Pulp Paper Sci., 26(4): , S. M. Pickard and B. Derby. The deformation of particle reinforced metal matrix composites during temperature cycling. Acta Metall. Mater., 38(12): , D. C. Dunand and B. Derby. Creep and thermal cycling. In S. Suresh, A. Mortensen, and A. Needleman, editors, Fundamentals of metal-matrix composites, chapter 11. Butterworth-Heinemann, Boston, K. M. Sedlachek. The effect of hemicelluloses and cyclic humidity on the creep of single fibers. PhD thesis, Institute of Paper Science and Technology, Atlanta, Georgia, D. W. Coffin and S. B. Boese. Tensile creep behaviour of single fibers and paper in a cyclic humidity environment. In Moisture and creep effects on paper, board and containers: 3rd international symposium, pages 39 52, T. Jackson and I. Parker. Accelerated creep in rayon fibres. In Moisture and creep effects on paper, board and containers: 3rd international symposium, pages 53 67,