Joop Baltussen - Academia.edu (original) (raw)

Papers by Joop Baltussen

Research paper thumbnail of The Tensile Strength of Polymer Fibres

Polymeric and Inorganic Fibers

A theory of the tensile strength of oriented polymer fibres is presented. From an analysis of the... more A theory of the tensile strength of oriented polymer fibres is presented. From an analysis of the observed fracture envelope it is shown that the criterion for fracture of the fibre is either a critical shear stress or a critical shear strain. Owing to the chain orientation distribution in the fibre, the initiation of fracture is likely to occur in domains whose symmetry axes have orientation angles in the tail of this distribution. By considering the fibre as a molecular composite, the tensile strength is calculated as a function of the modulus. The results are compared to the observed values of PET, POK, cellulose II, PpPTA, PBO and PIPD fibres. In addition, the relation between the ultimate strength and the chain length distribution is investigated. By using the critical shear strain as a fracture criterion in the Eyring reduced time model, relations are derived for the fibre strength as a function of the load rate, as well as for the lifetime under constant load. Moreover, this model predicts the dependence of the strength on the temperature. The theoretical relations are compared to the experimental results on PpPTA fibres.

Research paper thumbnail of The viscoelastic extension of polymer fibres: complex loadings

Polymer, 2003

The response of oriented polymer fibres to complex loading patterns is investigated. It is shown ... more The response of oriented polymer fibres to complex loading patterns is investigated. It is shown that the creep and stress relaxation is nonlinear with the applied stress. The ratio of the creep rate and the stress-relaxation rate is given by the local slope of the tensile curve and not by the elastic modulus as predicted by linear viscoelastic theory. A consequence of this observation is that viscoelastic and yield deformations are coupled. By analysing the results of the step-creep and the strain-relaxation-strain experiments performed on poly(p-phenylene terephthalamide) fibres, it is shown that the linear superposition principle does not apply to the tensile deformation of polymer fibres above the yield point. Finally the various components of the tensile deformation that should be covered by a constitutive equation for polymer fibres are discussed.

Research paper thumbnail of The viscoelastic extension of polymer fibres: creep behaviour

Polymer, 2001

The continuous chain model developed for the description of the tensile deformation of fibres is ... more The continuous chain model developed for the description of the tensile deformation of fibres is extended to include the creep behaviour. The description of the viscoelastic extension of the fibre is based on the linear viscoelastic shear deformation of the domain. From the time dependent change of the chain orientation angle the creep strain of the fibre is derived. The

Research paper thumbnail of A model for the tensile curve with yield of a polymer fibre

Polymer Bulletin, 1996

A model is presented for the tensile curve of fibres made of linear extended polymers measured be... more A model is presented for the tensile curve of fibres made of linear extended polymers measured below the glass transition temperature. In this series model the parameters are the chain orientation distribution, the average modulus for shear between the chains, the chain modulus and a simple yield condition based on the critical resolved shear stress. A good agreement between the experimental tensile curves of poly(pphenylene terephthalamide) and poly(ethylene terephthalate) fibres and the theoretical curves has been obtained.

Research paper thumbnail of Yielding and hysteresis of polymer fibres

Polymer, 1995

The yielding phenomenon in the tensile curves of polymer fibres is explained by the onset of a se... more The yielding phenomenon in the tensile curves of polymer fibres is explained by the onset of a sequential and plastic orientation mechanism of the chains brought about by the resolved shear stress. The proposed simple theory shows that the yield strain in tension and compression varies from 0.5% for highly oriented fibres to about 2.2% for randomly oriented specimens, and

Research paper thumbnail of The elastic extension of polymer fibers in the glassy state: Experimental results

Journal of Rheology, 1997

ABSTRACT The results of the continuous chain model for the elastic deformation of polymer fibers ... more ABSTRACT The results of the continuous chain model for the elastic deformation of polymer fibers in the glassy state, which has been presented in the previous article, are compared to the results from experiments on poly(p-phenylene terephthalamide) (PpPTA), poly(ethylene terephthalate) (PET), cellulose, and PE fibers, and PpPTA and PET sheets. The calculated elastic stress versus strain curve is compared to the experimental curve of PpPTA fibers. The predicted relation between the elastic modulus versus strain curve and the orientation of the fiber during extension are compared to the results obtained by x-ray diffraction. The effect of plastic deformation on the experimental modulus versus strain curve is considered, and a new method for the experimental determination of the shear modulus g from the elastic modulus versus strain curve is presented. The calculated elastic modulus versus strain curves are compared to the experimental curves of PpPTA, PET, cellulose, and PE fibers with widely divergent values for their orientation parameter. The shear moduli for these fibers have been determined and are compared with literature values, the relation between the experimentally determined shear modulus and the structure of the fiber is discussed. The shear moduli of a series of PET fibers are compared to the values obtained by birefringence. The modulus of PpPTA and PET sheets are compared to the calculated values. Good agreement between the experimental and calculated results has been obtained

Research paper thumbnail of Kinetics of magnetic flocculation. II. Flocculation of coarse particles

Journal of Physics D: Applied Physics, 1990

In theoretical studies of flocculation kinetics one usually assumes that the flocculation process... more In theoretical studies of flocculation kinetics one usually assumes that the flocculation process reaches a steady state very rapidly. This assumption is invalid when a long-range attraction between the particles is present. In this paper we will show that such a situation occurs for magnetic flocculation, provided that the particles are not too small. A full mathematical description of such a process is very difficult. As an alternative, a modified version of von Smoluchowski's model for rapid flocculation is presented, which describes the qualitative features of our experimental observations of aqueous Mn,03 colloids with a particle diameter of about 0.8 um quite well. In particular this model suggests that the deviations from the 'steady state' predictions increase very rapidly with increasing particle size, making these results almost always incorrect for many practical applications of magnetic flocculation.

Research paper thumbnail of Kinetics of magnetic flocculation. I. Flocculation of colloidal particles

Journal of Physics D: Applied Physics, 1990

The magnetic dipoldipole interaction between magnetized colloidal particles can lead to particle ... more The magnetic dipoldipole interaction between magnetized colloidal particles can lead to particle aggregation (flocculation), when it is strong enough to outweigh the stabilizing forces of electro-chemical origin. An understanding of the timescale at which the magnetic flocculation process is developing is of essential importance for its practical use as a separation technique. Incorporation of the magnetic dipoledpole interaction between the particles into the well established Fuchs theory of flocculation kinetics is difficult, due to the fact that this magnetic interaction is not spherically symmetric. In this paper a numerical approach is presented, in which the basic equation for flocculation is solved allowing for a cylindrically symmetric interaction, such as due to the presence of induced magnetic moments in paramagnetic particles. Experimental observations on the flocculation kinetics of fine-particle (about 0.2 pm diameter) electrostatically stabilized Mnp03 colloids corroborate the predictions of our model calculations.

Research paper thumbnail of The tensile and compressive deformation of polymer and carbon fibers

Journal of Applied Polymer Science, 2001

An outline of the continuous chain model for the description of the tensile and compressive defor... more An outline of the continuous chain model for the description of the tensile and compressive deformation of polymer fibers below the glass transition temperature is presented. The basic mechanism is the contraction of the chain orientation distribution as a result of elastic, plastic, and viscoelastic shear deformation. The deformation of the fiber is calculated for finite strains and arbitrary values of the orientation parameter. The model explains the yield and the compressive strength of polymer fibers. The tensile curve, including yielding, is described in terms of the modulus for shear between the chains, the chain modulus, the chain orientation distribution, and a yield parameter. The response to complex time-dependent loading schemes can be calculated by introduction of the Eyring reduced time model. The elastic tensile deformation of carbon fibers is described in terms of the classical series aggregate model. It is shown that the modulus for shear between the graphitic planes and the orientation distribution of these planes govern the tensile and compressive properties of carbon fibers. The high values of the shear modulus are attributed to some covalent bonding between the graphitic planes. A survey of the various models for the strength of polymer fibers is presented and a new model is discussed, which explains the failure envelope of polymer fibers.

Research paper thumbnail of The Eyring reduced time model for viscoelastic and yield deformation of polymer fibres

Polymer, 2004

A model is proposed for the description of the viscoelastic and yield behaviour of polymer fibres... more A model is proposed for the description of the viscoelastic and yield behaviour of polymer fibres. It involves the introduction of activated transitions with relaxation times that are a function of the stress. This is analogous to the introduction of an Eyring reduced time. These transitions govern the shear deformation of a domain, being the building block of the continuous chain model for the tensile deformation of polymer fibres. The main features of the viscoelastic behaviour of fibres have been derived. They are the rate dependence of the yield stress, the transition from a concave creep curve for a stress below the yield stress to the logarithmic behaviour for stresses above the yield stress, the creep rate of a fibre, the disappearance of the yield for increasing temperatures and the response to complex loadings.

Research paper thumbnail of The stress and sonic modulus versus strain curve of polymer fibres with yield

Polymer, 1999

The stress vs. strain curve with yield and the sonic modulus vs. strain curve of fibres of linear... more The stress vs. strain curve with yield and the sonic modulus vs. strain curve of fibres of linear polymers below the glass transition temperature are modelled by the continuous chain model in combination with a simple yield model. It is supposed that yield of polymer fibres is due to shear deformation of the domains. The yield model is based on a critical shear yield strain. A good agreement between the experimental tensile and sonic modulus vs. strain curves and the theoretical curves has been obtained for a selection of poly(p-phenylene terephthalamide) and poly(ethylene terephthalate) fibres.

Research paper thumbnail of The Tensile Strength of Polymer Fibres

Polymeric and Inorganic Fibers

A theory of the tensile strength of oriented polymer fibres is presented. From an analysis of the... more A theory of the tensile strength of oriented polymer fibres is presented. From an analysis of the observed fracture envelope it is shown that the criterion for fracture of the fibre is either a critical shear stress or a critical shear strain. Owing to the chain orientation distribution in the fibre, the initiation of fracture is likely to occur in domains whose symmetry axes have orientation angles in the tail of this distribution. By considering the fibre as a molecular composite, the tensile strength is calculated as a function of the modulus. The results are compared to the observed values of PET, POK, cellulose II, PpPTA, PBO and PIPD fibres. In addition, the relation between the ultimate strength and the chain length distribution is investigated. By using the critical shear strain as a fracture criterion in the Eyring reduced time model, relations are derived for the fibre strength as a function of the load rate, as well as for the lifetime under constant load. Moreover, this model predicts the dependence of the strength on the temperature. The theoretical relations are compared to the experimental results on PpPTA fibres.

Research paper thumbnail of The viscoelastic extension of polymer fibres: complex loadings

Polymer, 2003

The response of oriented polymer fibres to complex loading patterns is investigated. It is shown ... more The response of oriented polymer fibres to complex loading patterns is investigated. It is shown that the creep and stress relaxation is nonlinear with the applied stress. The ratio of the creep rate and the stress-relaxation rate is given by the local slope of the tensile curve and not by the elastic modulus as predicted by linear viscoelastic theory. A consequence of this observation is that viscoelastic and yield deformations are coupled. By analysing the results of the step-creep and the strain-relaxation-strain experiments performed on poly(p-phenylene terephthalamide) fibres, it is shown that the linear superposition principle does not apply to the tensile deformation of polymer fibres above the yield point. Finally the various components of the tensile deformation that should be covered by a constitutive equation for polymer fibres are discussed.

Research paper thumbnail of The viscoelastic extension of polymer fibres: creep behaviour

Polymer, 2001

The continuous chain model developed for the description of the tensile deformation of fibres is ... more The continuous chain model developed for the description of the tensile deformation of fibres is extended to include the creep behaviour. The description of the viscoelastic extension of the fibre is based on the linear viscoelastic shear deformation of the domain. From the time dependent change of the chain orientation angle the creep strain of the fibre is derived. The

Research paper thumbnail of A model for the tensile curve with yield of a polymer fibre

Polymer Bulletin, 1996

A model is presented for the tensile curve of fibres made of linear extended polymers measured be... more A model is presented for the tensile curve of fibres made of linear extended polymers measured below the glass transition temperature. In this series model the parameters are the chain orientation distribution, the average modulus for shear between the chains, the chain modulus and a simple yield condition based on the critical resolved shear stress. A good agreement between the experimental tensile curves of poly(pphenylene terephthalamide) and poly(ethylene terephthalate) fibres and the theoretical curves has been obtained.

Research paper thumbnail of Yielding and hysteresis of polymer fibres

Polymer, 1995

The yielding phenomenon in the tensile curves of polymer fibres is explained by the onset of a se... more The yielding phenomenon in the tensile curves of polymer fibres is explained by the onset of a sequential and plastic orientation mechanism of the chains brought about by the resolved shear stress. The proposed simple theory shows that the yield strain in tension and compression varies from 0.5% for highly oriented fibres to about 2.2% for randomly oriented specimens, and

Research paper thumbnail of The elastic extension of polymer fibers in the glassy state: Experimental results

Journal of Rheology, 1997

ABSTRACT The results of the continuous chain model for the elastic deformation of polymer fibers ... more ABSTRACT The results of the continuous chain model for the elastic deformation of polymer fibers in the glassy state, which has been presented in the previous article, are compared to the results from experiments on poly(p-phenylene terephthalamide) (PpPTA), poly(ethylene terephthalate) (PET), cellulose, and PE fibers, and PpPTA and PET sheets. The calculated elastic stress versus strain curve is compared to the experimental curve of PpPTA fibers. The predicted relation between the elastic modulus versus strain curve and the orientation of the fiber during extension are compared to the results obtained by x-ray diffraction. The effect of plastic deformation on the experimental modulus versus strain curve is considered, and a new method for the experimental determination of the shear modulus g from the elastic modulus versus strain curve is presented. The calculated elastic modulus versus strain curves are compared to the experimental curves of PpPTA, PET, cellulose, and PE fibers with widely divergent values for their orientation parameter. The shear moduli for these fibers have been determined and are compared with literature values, the relation between the experimentally determined shear modulus and the structure of the fiber is discussed. The shear moduli of a series of PET fibers are compared to the values obtained by birefringence. The modulus of PpPTA and PET sheets are compared to the calculated values. Good agreement between the experimental and calculated results has been obtained

Research paper thumbnail of Kinetics of magnetic flocculation. II. Flocculation of coarse particles

Journal of Physics D: Applied Physics, 1990

In theoretical studies of flocculation kinetics one usually assumes that the flocculation process... more In theoretical studies of flocculation kinetics one usually assumes that the flocculation process reaches a steady state very rapidly. This assumption is invalid when a long-range attraction between the particles is present. In this paper we will show that such a situation occurs for magnetic flocculation, provided that the particles are not too small. A full mathematical description of such a process is very difficult. As an alternative, a modified version of von Smoluchowski's model for rapid flocculation is presented, which describes the qualitative features of our experimental observations of aqueous Mn,03 colloids with a particle diameter of about 0.8 um quite well. In particular this model suggests that the deviations from the 'steady state' predictions increase very rapidly with increasing particle size, making these results almost always incorrect for many practical applications of magnetic flocculation.

Research paper thumbnail of Kinetics of magnetic flocculation. I. Flocculation of colloidal particles

Journal of Physics D: Applied Physics, 1990

The magnetic dipoldipole interaction between magnetized colloidal particles can lead to particle ... more The magnetic dipoldipole interaction between magnetized colloidal particles can lead to particle aggregation (flocculation), when it is strong enough to outweigh the stabilizing forces of electro-chemical origin. An understanding of the timescale at which the magnetic flocculation process is developing is of essential importance for its practical use as a separation technique. Incorporation of the magnetic dipoledpole interaction between the particles into the well established Fuchs theory of flocculation kinetics is difficult, due to the fact that this magnetic interaction is not spherically symmetric. In this paper a numerical approach is presented, in which the basic equation for flocculation is solved allowing for a cylindrically symmetric interaction, such as due to the presence of induced magnetic moments in paramagnetic particles. Experimental observations on the flocculation kinetics of fine-particle (about 0.2 pm diameter) electrostatically stabilized Mnp03 colloids corroborate the predictions of our model calculations.

Research paper thumbnail of The tensile and compressive deformation of polymer and carbon fibers

Journal of Applied Polymer Science, 2001

An outline of the continuous chain model for the description of the tensile and compressive defor... more An outline of the continuous chain model for the description of the tensile and compressive deformation of polymer fibers below the glass transition temperature is presented. The basic mechanism is the contraction of the chain orientation distribution as a result of elastic, plastic, and viscoelastic shear deformation. The deformation of the fiber is calculated for finite strains and arbitrary values of the orientation parameter. The model explains the yield and the compressive strength of polymer fibers. The tensile curve, including yielding, is described in terms of the modulus for shear between the chains, the chain modulus, the chain orientation distribution, and a yield parameter. The response to complex time-dependent loading schemes can be calculated by introduction of the Eyring reduced time model. The elastic tensile deformation of carbon fibers is described in terms of the classical series aggregate model. It is shown that the modulus for shear between the graphitic planes and the orientation distribution of these planes govern the tensile and compressive properties of carbon fibers. The high values of the shear modulus are attributed to some covalent bonding between the graphitic planes. A survey of the various models for the strength of polymer fibers is presented and a new model is discussed, which explains the failure envelope of polymer fibers.

Research paper thumbnail of The Eyring reduced time model for viscoelastic and yield deformation of polymer fibres

Polymer, 2004

A model is proposed for the description of the viscoelastic and yield behaviour of polymer fibres... more A model is proposed for the description of the viscoelastic and yield behaviour of polymer fibres. It involves the introduction of activated transitions with relaxation times that are a function of the stress. This is analogous to the introduction of an Eyring reduced time. These transitions govern the shear deformation of a domain, being the building block of the continuous chain model for the tensile deformation of polymer fibres. The main features of the viscoelastic behaviour of fibres have been derived. They are the rate dependence of the yield stress, the transition from a concave creep curve for a stress below the yield stress to the logarithmic behaviour for stresses above the yield stress, the creep rate of a fibre, the disappearance of the yield for increasing temperatures and the response to complex loadings.

Research paper thumbnail of The stress and sonic modulus versus strain curve of polymer fibres with yield

Polymer, 1999

The stress vs. strain curve with yield and the sonic modulus vs. strain curve of fibres of linear... more The stress vs. strain curve with yield and the sonic modulus vs. strain curve of fibres of linear polymers below the glass transition temperature are modelled by the continuous chain model in combination with a simple yield model. It is supposed that yield of polymer fibres is due to shear deformation of the domains. The yield model is based on a critical shear yield strain. A good agreement between the experimental tensile and sonic modulus vs. strain curves and the theoretical curves has been obtained for a selection of poly(p-phenylene terephthalamide) and poly(ethylene terephthalate) fibres.