Chemomechanics of Damage Accumulation and Damage-Recovery Healing in Bituminous Asphalt Binders

(1)

Chemomechanics of Damage Accumulation

and Damage-Recovery Healing in Bituminous

Asphalt Binders

(2)

(3)

Chemomechanics of Damage

Accumulation and Damage-Recovery

Healing in Bituminous Asphalt Binders

(4)

(5)

The research described in this thesis was performed in the section of Road and

Railway Engineering, Faculty of Civil Engineering and Geosciences, Delft

University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands. This

work was supported by the Delft Healing Consortium, Western Research Institute,

and the Federal Highway Administration, U. S. Department of Transportation

under Contract Nos. DTFH61-07-H-00009 and DTFH61-07-D-00005.

(6)

Chemomechanics of Damage Accumulation

and Damage-Recovery Healing in

Bituminous Asphalt Binders

PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof.ir. K.C.A.M. Luyben,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen op 3 Maart 2014 om 15:00 uur

door

Adam Troy PAULI

Bachelor of Science in Chemistry, University of Wyoming

(7)

Dit proefschrift is goedgekeurd door de promotoren

Prof. dr. A. Scarpas

Prof. dr. ir S. van der Zwaag

Samenstelling promotiecommissie:

Rector Magnificus

voorzitter

Prof. dr. A. Scarpas,

Technische Universiteit Delft, promotor

Prof. dr. ir. S. van der Zwaag,

Technische Universiteit Delft, promotor

Prof. dr. S.J. Picken

Technische Universiteit Delft

Prof. dr. D.L. Little

Texas A&M University, USA

Dr. M.L. Greenfield

University of Rhode Island, USA

Dr. J.P. Planche

Western Research Institute, USA

Prof.dr.ir. S.M.J.G. Erkens

Technische Universiteit Delft, reservelid

Published and distributed by:

Adam Troy Pauli

Copyright ©2014 by A.T. Pauli

Printed by Sieca Repro, Delft, The Netherlands

ISBN 978-94-6186-269-3

All rights reserved. No part of the material protected by this copyright notice

may be reproduced or utilized in any form or by any means, electronic or

mechanical, including photocopying, recording or by any information

storage and retrieval system, without written consent from the publisher.

(8)

(9)

(10)

Acknowledgements

I first had the pleasure of meeting Dr. Scarpas, Tom, in the fall of 2006 in Urbana-Champaign, Illinois. At the time I was a senior research scientist on staff at the Western Research Institute, Laramie, WY. I was on a business trip attending a Federal Highway Administration Expert Task Group (FHWA-ETG) meeting where I was presenting work related to structuring in asphalt binders at microscopic and nano-scopic scales via atomic force microscopy. Talking with Tom and his colleague Niki Kringos, a graduate student of his at the time, after the meeting, Tom proposed, or rather I should say “coined” the concept of “chemomechanics of damage and healing in asphalt binders”. This moment of eureka was based on his impressions of what I had presented regarding asphalt binder structuring as it could potentially relate to his team’s extensive work in mechanics, now focusing on bituminous materials. From this first meeting Tom invited me to collaborate with his group. From this collaboration I am very pleased to be submitting a thesis to a renowned European University, Delft University of Technology, for the title of Doctor of Philosophy in the field of civil engineering.

I had the pleasure of meeting Dr. Van der Zwaag, Sybrand, in the spring 2007, in Delft, the Netherlands on a second trip to Europe. At our first meeting I was honoured to accept a signed copy of his recently published book entitled “Self healing materials: an alternative approach to 20 centuries of materials”. This publication has since provided valuable insight and reference material for the present thesis. The following summer, my colleagues and I then had the pleasure of hosting Sybrand and his wife in the United States in my home state of Wyoming during the Annual Petersen Asphalt Research Conference, held in the city of Laramie. Initial preparation of the present thesis began at that time. I am thus very grateful to Dr. Scarpas and Dr. Van der Zwaag for their support in the advancement of this degree program.

I foremost would like to gratefully acknowledge and thank the Federal Highway Administration, U. S. Department of Transportation, for the Lion’s share of the financial support for this research effort which has lead to the present thesis, supported under Contract Nos. DTFH61-07-H-00009 and DTFH61-07-D-00005. Thus, I would like to thank personally Dr. Jack Youtcheff, Dr. Ernie Bastian and Eric Weaver of the Federal Highway Administration who have been strong supporters of this work for which I have had the opportunity to engage in over the past eight years at Western Research Institute. I would also like to thank the Delft Healing Consortium for their financial and technical support of this research. The Delft Healing Consortium consists of Nynas Bitumen AB, Shell Global Solutions, the Dutch Ministry of Public Works and Ooms Nederlands Holding for which this membership constitutes a great wealth of knowledge and expertise in the field of bituminous infrastructure material properties and design.

Development of the technical content of this thesis represents a strong and productive collaboration between both past and present colleagues from Western Research Institute and Delft University of Technology, and as such, I would like to acknowledge the Delft CAPA team, particularly Dr. Niki Kringos (now Associate Professor, KTH Sweden), Alexander Schmets

(11)

(Delft) and Cor Kasbergen (Delft) for their contribution to this thesis with regard to computational analyses of composite structure properties in bituminous asphalt binders. I would also like to thank Dr. Jan Branthaver, Dr. Ray Robertson, Dr. Fran Miknis, Dr. Shin Che Huang, Julie Miller, Will Grimes, James Beiswenger, Appy Beemer, Steve Salmans, and the rest of the Transportation Technology staff at WRI for both their technical and moral support.

I finally wish to acknowledge my family, my father Adam, my mother Joanne, my sisters and their families, for their ever continual moral and spiritual support, God Bless.

Troy Pauli

(12)

(13)

i

Chapter 1: Introduction

1.1 Background and Statement of Problem

Materials used in the fabrication of infrastructure, specifically roads and highways, like asphalt and concrete, are continually being engineered to offer greater resistance to performance failure. In modern material science a paradigm in engineering design has emerged in regard to self or autonomic healing properties, which may be innate in a material or designed into a material [Kessler 2007; Van der Zwaag 2007; Yuan et al. 2008]. Thus, utilization of "smart" material design principles (i.e., self-healing mechanisms) can improve failure resistance in infrastructure materials thus improving infrastructure sustainability. Bituminous asphalt pavement longevity as one example of a material pertinent to infrastructure sustainability continues to receive a great deal of attention in terms of both economics (durability and sustainability) and safety.

Significant progress has been made, in terms of scientific and engineering investigations conducted over the past few decades [Kennedy et al. 1990; Bell 1989; Rao Tangella et al. 1990; Vinson et al. 1989; Sousa et al. 1991; Anderson et al. 1994; Branthaver et al. 1993; Petersen et al. 1994; Robertson et al. 2001], to understand the relationships between compositional and mechanical properties of the materials comprising asphalt pavements. Bituminous asphalt paving materials like all other "engineered” materials tend to fail over time. Hence, the need for comprehensive theories and models to relate material composition to mechanical response represents the bottleneck in current research pertaining to long term prediction of asphalt pavement performance with the introduction of new material design.

In early asphalt pavement research Hveem [1943] attributed asphalt pavement failure modes to the “chemical action” of the binder (asphalt bitumen). Specifically, four properties of the binder were identified as being critical to the quality of a pavement. These four properties were consistency, durability, curing rate and resistance to water. Consistency relates to the flow properties of the asphalt. Durability relates to the change in consistency of the asphalt, for example, the variation in viscosity as a function of temperature, or the change in material properties brought about by oxidative age hardening. Cure rate is associated with the resistance of an asphalt-aggregate mixture to “setting” during construction. Finally, moisture damage, often resulting in stripping of the pavement (i.e. destruction of the asphalt-aggregate bond), also impacts other failure modes such as fatigue and thermal cracking. In short, all modes of failure are coupled to each other to some degree, further complicating a comprehensive fundamental understanding of the system and its chemical-mechanical underpinnings.

The modes of failure in asphalt pavement research commonly cited are, aging and embrittlement due to oxidative age hardening [Bell 1989], fatigue cracking, due primarily to cyclic loading from traffic [Rao Tangella et al. 1990], permanent deformation due to the softening of the pavement resulting in rutting [Sousa et al. 1991], and thermal fatigue due to embrittlement and

(19)

2

binder material shrinkage at low temperatures [Vinson et al. 1989]. All of these modes of damage are further compounded by moisture. The mechanisms of permanent deformation, “rutting”, are currently better understood compared to other modes of failure and can usually be mitigated by polymer modification of an asphalt binder [Fontes et al. 2010; Doh et al. 2007; Masad et al. 2005; Tashman et al. 2005; Shen et al. 2005; Wong et al. 2004; Tayfur et al. 2007; Kettil et al. 2007]. Research endeavors are currently focused on investigating thermal and load related fatigue failure compounded by moisture invasion and its contribution to overall pavement performance.

A more common approach taken to study and model pavement fatigue behavior, particularly repeated loading fatigue, relies on utilizing continuum mechanics models and theories with input from testing of mechanical properties including cyclic loading experiments of representative sample systems. Little et al. [Little et al. 1998, 1999; Kim et al. 2001; Williams et al. 2001] have for example applied continuum-mechanics modeling with inputs from fatigue damage testing of mastics (i.e. asphalt binder plus aggregate fines) in order to predict pavement performance. In this modeling/experimental approach changes in the viscous, elastic and plastic behavior of mastics are attributed to thermo-mechanical properties derived based on non-equilibrium thermodynamic approaches originating from theories proposed by Schapery [1990]. A significant qualitative finding to come from this research is the observed propensity of asphalt mastics to exhibit "self-healing”. Little et al. [1998, 1999] observed that mastic test specimens subjected to cyclic loading conducted by dynamic mechanical analysis (DMA), regained strength when rest periods were introduced during the testing protocol. Healing as reported by these authors is defined in part by wetting/de-wetting mechanisms of micro-crack surfaces and mechanical crack closure.

Heavy oil residua including bituminous asphalt has been viewed by many investigators as colloidal in nature [Nellensteyn et al. 1933; Saal et al. 1939; Yen and Chilingarian 1994; Mullins et al. 2007]. Although this view is generally useful for explaining observed rheological properties a better understanding of chemical structuring is needed to establish the fundamental link between the chemical and physical properties of asphalt which most influence its mechanical properties in pavement systems. Asphalt chemistry at the molecular level may result in a variety of intermolecular associations (structuring). This structuring is largely responsible for the physical properties of asphalt, and is therefore particularly important with respect to the performance of asphalt pavements in terms of mechanical properties. Structuring occurs at various length scales ranging from molecular to macroscopic, but most asphalt researchers have concerned themselves with what has been called “microstructure”. Microstructure is commonly assumed to be a three-dimensional association of polar constituents variously distributed in a less polar liquid phase [Petersen et al. 1994].

Pauli et al. [2011] have recently suggested that the interaction between non-polar constituents present in asphalt, including crystallizing paraffin waxes, are responsible for the so-called bumble bee-structures, originally reported by Loeber [1996] and Jones and Germinario [1999],

(20)

3

that have been observed on the surface of asphalt thin-film samples imaged by AFM. The observed structuring was shown to occur in non-polar asphalt fractions (lacking polar species such as asphaltenes and resins) which contain most of the wax-type materials. Previous discussions of micro-structuring in asphalts focused mainly on polar/polar interactions. The authors concluded that the non-polar constituents of asphalt, specifically the “waxy” materials are responsible for the observed surface structuring on asphalt films, and that the appearance of the structuring was related to wax-type (e.g. mass or chain length).

Observations reported by Pauli et al. [2011] may be relevant to asphalt fracture and self-healing, in that, phase transition phenomena associated with wax structuring (crystallization) in many asphalt binders likely takes place at temperatures that are typically encountered under pavement service conditions. It is thus hypothesized that the processes of fracture and self-healing (macro scale phenomena), or more specifically, damage accumulation and damage recovery healing of the asphalt binder phase of a pavement (nano-, micro-scale phenomena), may be considered in terms of “chemomechanical” mechanisms that result in the redistribution of molecules and/or molecular “phases” originating from some pseudo-equilibrium state of structure when damage is imposed. Damage recovery healing then constitutes a return to another pseudo-equilibrium state via a healing or recovery process. The compositional (physicochemical) properties most likely to influence damage accumulation and damage recovery healing could then involve phase transitions related to wax structuring and colloidal interactions associated with asphaltenes which influence viscosity, flow and interfacial phenomena within the asphalt and asphalt-mastic particle phases of a pavement.

A paradoxical conundrum to this hypothesis is that one type of structuring which leads to embrittlement of asphalt binder likely also involves the crystallization of paraffin and microcrystalline waxes. One specific and well studied mechanical response influenced by this type of structuring phenomenon is referred to as isothermal physical (reversible) age hardening. Physical hardening is thought to contribute to thermal cracking of pavements constructed in cold climates [Bahia and Anderson 1992]. This type of response, originally observed by rheological measurements of sub-ambient isothermal changes in asphalt creep compliance, led to speculation by researchers as to the compositional nature of the asphalt which directly or indirectly contributes to this phenomenon. Bahia and Anderson [1992] originally suggested that that a collapse of free volume in the asphalt composition (changes in intermolecular configurations), analogous to polymer microphase rearrangements, as pavement temperatures approached the asphalt's glass transition temperature, was responsible for the observed hardening effect. Claudy et al. [1992], in the same time period, reported that differential scanning calorimetry (DSC) and thermo-microscopic (optical) methods supported the hypothesis that wax and/or other crystallizing moieties in asphalt were at least partially responsible for the hardening phenomena observed by Bahia [1991] and Bahia and Anderson [1992].

(21)

4

1.2 Research Aim and Thesis Objectives

The principal motivation of the present thesis is to aid in the effort by the Asphalt Research Consortium [ARC 2008] in the development of mutli-scale multi-physics approaches to model pavement performance by developing a theoretical “chemomechanical” framework based on thermodynamics to understand the mechanisms of damage accumulation and damage recovery healing in the bituminous asphalt binder phase of asphalt pavements. Damage accumulation and damage recovery healing of asphalt binder is defined in the present thesis at nano- and micro-scale as a change in the local density of a material and redistribution of compositional phases to account for linear and non-linear viscoelastoplastic flow properties and phase transition phenomena associated with these types of materials. Compositional phases in the present case may be represented by the colloidal dispersion of asphaltenes dispersed in a maltene continuous phase and/or the distribution of nano-scopic and microscopic wax crystals in the bulk asphalt and at free-surfaces undergoing melt-recrystallization with thermal and mechanical variation.

Damage-healing evolution rate laws based on fundamental thermodynamic principles have historically provided logical modeling approaches to derive dissipative functions based on entropy production to describe damage accumulation and damage recovery healing mechanisms in bituminous asphalt pavement systems. As such, the studies present are inspired by Hveem’s [1943] concept of the “chemical action” of the binder as a working hypothesis that damage accumulation and damage recovery healing in the binder phase of an asphalt pavement system may be described by a chemomechanical mechanism that assumes that both chemical and mechanical mechanisms provide driving forces for damage and healing.

• The principle objective of this study is to develop a theoretical framework, based on fundamental scientific theories and principles to describe damage accumulation and damage recovery healing in complex materials like bituminous asphalt binders applicable to asphalt pavements. The theoretical framework that is developed constitutes a non-equilibrium thermodynamics based model which treats damage accumulation and damage recovery healing as chemomechanical processes.

• To accomplish the objectives of this study, models and experimental methodologies derived or referenced from relevant theories of physics, chemistry and mechanics are considered to show commonality as to how the composition of a material like bituminous asphalt binder drives the mechanical response as this relates to performance of infrastructure systems constructed with this material.

• A prominent theme of this thesis relies on the development of a hierarchical approach to derive ansatz net entropy production expressions in terms of the principal flux-force terms to define damage accumulation and damage recovery healing mechanisms in the asphalt binder phase of asphalt pavement systems.

(22)

5

• It is anticipated that the theoretical and modeling approaches considered in this thesis will contribute directly to the advancement of multi-scale multi physics models of asphalt binder which describe chemical-to-mechanical behavior (chemomechanical mechanisms) in order to aid in the design of new "smart"-materials with improved material property characteristics.

1.3 Methodology

1.3.1 Composition and Physicochemical Properties

Chromatographic separation and physico-chemical characterization of bituminous asphalt and asphalt fractions are employed to determine a host of material compositional properties, including distribution in molecular mass by HP-GPC (high-performance gel permeation chromatography), characterization of thermal properties, melting and vaporization temperature by TGA (thermo gravimetric analysis), and surface free energy.

1.3.2 Rheological and Mechanical Properties

Rheological and mechanical properties of bituminous asphalt and asphalt chromatographic fractions are considered throughout this thesis. Temperature dependent DSR (dynamic shear rheometry) is used to quantify flow activation energy, viscosity/fluidity, and moduli. Thermal fatigue behavior is investigated through testing with the Asphalt Binder Cracking Device, (ABCD).

1.3.3 Morphology

AFM (atomic force microscopy) images collected at various temperatures are used to study morphological changes in asphalt binder thin- films prepared on glass substrates. AFM images show morphological changes related to phase transition temperatures (e.g. wax appearance and disappearance temperatures).

1.3.4 Computational Modeling

Micro finite element simulations are utilized to quantify mechanical response of materials which exhibit multiphase compositional characteristics.

1.3.5 Field Studies and Model Validation

Experimental and computational results are finally validated by comparison to pavement performance data derived from comparative test site data where asphalt material is available for testing.

(23)

6

1.4 Thesis Overview

In chapter 2 an irreversible non-equilibrium thermodynamic framework is proposed to define “chemomechanical” mechanisms to describe damage accumulation and damage recovery healing phenomena potentially operative in asphalt binder materials. An ansatz net entropy production expression is developed which is expounded upon in subsequent chapters.

Chapters 3 and 4 consider the physicochemical nature of interfacial and flow properties, respectively, of asphalt binders as each applies to the rheological and mechanical response of the material alone and the material in the mastic state. Correlations are developed to relate material composition (physicochemical) properties to rheological properties commonly tested for in these materials. Chapter 3 specifically relates the asphalt composition to surface free energy while chapter 4 relates asphalt composition to flow properties. Correlations are then developed to relate both compositional and rheological properties of asphalt binders to fatigue and self-healing behavior of mastics where it is observed that the flow property directly contributes to the healing propensity of asphalt binders.

Building on chapters 3 and 4, chapter 5 considers in some depth the modes of embrittlement of asphalt binders based on bitumen composition and rheological flow properties. Specifically, asphalt binder oxidation and low temperature thermal fatigue are considered to be two primary modes of embrittlement. Oxidation of the asphalt binder phase of a pavement system is taken into consideration as a major contributor to load related fatigue and as a primary contributor to the determination of healing capacity. The physicochemical properties of unaged asphalt binders, specifically the molecular weight distribution of the oil phase of bitumen, are also considered in terms of their tendency to dictate the low temperature rheological properties of the bitumen. Here it is observed that high molecular weight chemically “neutral” oils correlate to thermal fatigue damage response. The mechanical response attributed to damage in this case constitutes the thermal contraction of the asphalt binder as the pavement is subjected to low temperatures.

Chapter 6 considers recent studies of the morphology of bitumen asphalt as this relates to chemical composition. Findings discussed in chapter 6 lead directly to the observation that bituminous asphalt binders exhibit multi-phase characteristics at micron-scale. The structuring of crystalline phases that are observed by atomic force microscopy to take place in the temperature range corresponding to the service life temperature of in-place pavements. It is currently speculated and demonstrated experimentally that the structuring observed is directly related to paraffin wax commonly found to be present in a majority of heavy crude oils and detectable in weight percent range of 0.1% to as high as 5%, as determined by wax crystallization enthalpies via differential scanning calorimetry.

Chapter 7 constitutes the final technical chapter of this thesis. In this chapter computational and experimental data are presented and discussed to support a chemomechanical theory of asphalt

(24)

7

binder damage accumulation originating from the observed phase transition phenomena of waxes discussed in chapter 6. Here results from micro finite element modeling are presented for simulated damage accumulation in biphasic systems under monotonic and cyclic loading conditions. Damage parameters including work to yield (monotonic loading) and permanent displacement (cyclic loading) are correlated with compositional properties, or more precisely, morphological variations among the biphasic systems studied. It is observed that variations in simulated damage response for a set of biphasic systems which vary in terms of morphological properties may be “back” correlated with mechanical response determined by laboratory testing of asphalt binders which vary in a similar trend to biphasic systems in terms of their morphological properties.

Finally, chapter 8 presents conclusions of findings presented throughout the thesis emphasizing the development of the chemomechanical framework to describe damage accumulation and damage recovery healing phenomena in asphalt pavements.

(25)

8

Chapter 2: Thermodynamics of Damage and Healing Processes:

Mathematical Formulation

2.1 Introduction

2.1.1 Damage-Healing Material Design Principles

Materials used in the fabrication of transportation infrastructure, asphalt pavements specifically, are continually being engineered to offer greater resistance to failure. In response to demands to improve the useful lifespan of these types of materials a paradigm in engineering design has emerged in regard to self or autonomic healing properties, which, in some cases may be innate in a particular material or, in other cases may be designed into materials [Kessler 2007; Van der Zwaag 2007; Yuan et al. 2008]. Kessler [2007] and Yuan et al. [2008] have recently published review papers on the topic of self-healing material systems. In these publications the authors consider state-of-the-art research conducted to improve the physical and mechanical properties of predominately polymer and polymeric coating materials by incorporating self-healing mechanisms into current material designs.

Yuan et al. [2008] adopt the terms extrinsic and intrinsic to describe self-healing processes with and without the addition of “pre-embedded” healing agents, respectively. Intrinsic self-healing is then defined as being an innate property of the material which requires a stimulus (usually heating) to activate the healing or repair process. Upon “stimulation” of the damaged material, physical and/or chemical interactions take place to repair damage. A few key examples of these interactions include surface rearrangements, diffusion, wetting, hydrogen bonding or other chemical reactivity, melting/crystallization, and so forth. Extrinsic healing, on the other hand, may involve identical types of interactions, but in this case materials are tailored by incorporating or “pre-embedding” a healing agent (e.g. epoxy glue) into the material matrix. A more detailed exposition on the topic of self-healing materials may be found in Van der Zwaag [2007] and Ghosh [2009]. A key concept to emerge from these works is the importance of the mechanism(s) involved in damage/self-healing processes in biological materials, polymers, metals, concrete and bituminous asphalt. Van der Zwaag [2007] for example has considered current design principles, namely the “damage prevention” approach and a self-healing inspired “damage management” approach. Each design principle is described by a damage function

[

( , )

]

d m _ρ t dtdefined in the present case by a change in material strength  of a material mass element ( , )m _ρ t changing as a function of density and time

[

( , )

]

0, 0 0, n i i t t t d m t t t t dt ρ _+Δ ≥ < <   = _< _{< <}     (2.1)

(26)

9

Here, the rate of change in damage with respect to time is necessarily specified as a positive slope suggesting that damage progresses forward with time, while healing, comparatively is specified as a negative slope suggesting that healing is a restoration of damage restored to a previous point in time relative to the damage timeline. In the damage prevention design approach, damage can remain constant at zero (i.e., never damages), or continues to sustain damage throughout its life cycle to time t . With the damage management design approach, on _n the other hand, damage may actually decrease over a designated time interval t_i_+Δ_t. Van der Zwaag [2007] further points out that material strength may actually decrease at the expense of improving the self-healing properties of newly designed materials. In theory both types of design principles should be considered together in material design, in that, both strengthening the material while also improving the healing propensities of the material should result in optimum material performance.

A commonly desired property to improve upon when taking these two design principles into consideration is the healing efficiency,

[

]

[

]

0 0( , ) η = ( , ) n i m t m t ρ ρ   (2.2)

where ₀

[

m₀( , )_ρ t

]

defines the initial mechanical state of the system and _n

[

m_i( , )_ρ t

]

defines the material state after damage accumulation and damage recovery healing have taken place. The remainder of this section considers recent studies which identify common healing processes in different types of materials, while also considering how physicochemical and mechanical properties of a material contribute to a particular healing process. Hence, understanding compositional properties of a material as this relates to the various healing processes should lead to better design of material properties and thus improve healing efficiency.

Varley et al. [Varley and Van der Zwaag 2008; Varley et al. 2010] have considered thermo-mechanical properties of self-healing ionomers (i.e. poly(ethylene-co-methacrylic) acid, EMAA) by observing healing rates after ballistics testing at macroscopic and microscopic levels. These studies showed that local frictional heating induced a thermally activated healing process. Both viscous and elastic properties of the polymer and variables associated with the ballistics testing (e.g. bullet grain and velocity of impact) are said to contribute to variations in the healing propensity of the systems examined in their studies. The authors specifically show how inner and outer zones of damage are identified for the damage hole which results after ballistics testing. Changes in outer region morphology are related to elastic recovery, something akin to a shape-memory effect, while changes in the morphology of the inner region relate to viscous effects where frictional heating is localized.

Varley et al. [2010], as an example of how changes in material composition affect healing propensities, observed that the healing properties could be manipulated with changes to the

(27)

10

composition of a specific polymer-blend. If, for example, carboxylic acids were used to modify the polymer blend, elastic recovery was reduced, thus enhancing the elastomeric healing mechanism. Clustering of the ionomeric moieties of the polymer blends was shown to be related to elastic recovery. By adding ions to certain blends, healing efficiency was reduced due to more extensive clustering of the ionomer phase, thus increasing elastic behavior of the material. In addition to observational approaches, mechanical testing, including mechanical spectroscopy, tensile load testing to yield, and differential scanning calorimetry, was employed. Results from the mechanical testing demonstrated that differences in material properties for different blends under loading could be related back to results derived from observational approaches.

Yufa et al. [2009] considered healing in polymers, specifically, diblock copolymer films damaged by nano-lithography, i.e., an atomic force microscopy (AFM) technique employed as a wear testing approach. In this study thin-film polymer sample surfaces (i.e. poly(styrene-b-methylmethacrylate), PSMMA diblock copolymer) were scratch damaged “scarred” by AFM- lithography then monitored via AFM imaging over time. With small scratches, in particular, the investigators could observe changes in ordering in morphology of the scratch and the pile-up of material on the surface of the film as a function of temperature. Partial healing was observed at 373 K over a 30-min period while complete healing was observed at 398 K over the same time period, which is a slightly higher temperature than the glass transition of the material, which was determined to be 383 K. Considering the difference in healing propensities below and above the material glass transition temperature healing properties in these materials were speculated to be attributed to viscoelastic and plastic flow behavior.

Other types of materials, for example the glass/ceramic sealants used in the production of solid oxide fuel cells, [Liu et al. 2008; Zhang et al. 2011], exhibit self-healing behavior which has been attributed to thermally activated processes. The composition of these materials being calcium aluminosilicate-based, calcium borate-based, or other, allows the possibility of coexisting amorphous and crystalline phases. Upon heating of these materials, the crystalline phase of the glass, rich in calcium borate, begins to melt and exhibits viscoelastic flow while at much lower temperatures amorphous phases exhibit brittle behavior. Crystallization/melting in this case occur at high temperatures, 700-900°C, near the operational temperature of the solid oxide fuel cell.

Materials used in transportation infrastructure, concrete for example, have been investigated by several researchers in terms of self-healing properties [Yang et al. 2009; Homma et al. 2009]. Yang et al. [2009] provides a good reference for studies involving self-healing in cementitous composites. These researchers site several mechanisms identified in the self healing of concrete, including further hydration of un-reacted cement with contact with water, expansion of the cement to induce crack closure, crystallization of calcium carbonate, and crack closure by introduction of solid impurities (mineral content found in hard water for example) introduced by water. Of these various mechanisms, crystallization of calcium carbonate is considered to be the principal mechanism of self healing in cementitous systems. Initial crack width was also thought

(28)

11

to be a strong contributing factor to efficient self healing, in that beyond a limiting width of crack, the system will no longer heal. Reinforcement in the form of embedded fibers, which are frequently added to concrete, where shown to help limit the nominal crack width.

In each of the case studies considered, the mechanisms associated with flow, elastic-plastic behavior and phase transition tendencies at specified temperature ranges each contribute to the healing propensity differently for different material types. Hence, several researchers have considered constitutive modeling approaches which consider material properties related to flow, elastic-plastic behavior and phase transition phenomena to describe and formulate self healing mechanisms [Barbero et al. 2005; Xu and Li 2010; Voyiadjis et al. 2010].

By exploiting the utility of modeling damage and self-healing mechanisms in bituminous asphalts based on continuum thermodynamic principles, the present thesis considers damage accumulation and damage recovery self-healing in terms of a constitutive equation which defines the net entropy production rate

: : : 0 d p h d p h net d p h S ψ _ζ ψ _ζ ψ _ζ ζ ζ ζ ∂ ∂ ∂ = + + ≥ ∂ ∂ ∂     _(2.3)

more generally expressed by

1 : 0 r net S _αα α α= ψ ζζ ∂ = ≥ ∂



  _(2.4)

Here ∂

ψ

α ∂

ζ

α represents the derivative in work or free energy _ψ per (not defined here) thermodynamic variable or structure parameter _ζ relating to processes α = p d h, , ,... defining d-damage, p-plastic flow, h-healing, etc. where

ζ

α = ∂ ∂

ζ

t defines the time rate of change in the thermodynamic variable (structure parameter). The remaining two sub-sections present a review of current literature which considers constitutive modeling in viscoelastic materials and entropy production in damage-healing processes.

2.1.2 Work Potential and Entropy Production

The mechanical behavior of viscoelastic media, specifically in regard to fatigue fracture and healing of asphalt pavements, has been considered by Little et al [Little et al. 1999; Lytton et al. 2001; Kim et al. 2001] in terms of approaches originally proposed by Schapery [1990]. Schapery’s [1990] approach relates work (or energy) to internal state variables representing damage-healing processes. Schapery has shown that virtual work of a mechanical process,dW '

is defined in terms of generalized forces Q_j and virtual displacements d , for q_j q j_j( ₌1,2,..., )J

(29)

12 ' _j _j

W =Q q

d d (2.5)

The virtual work is shown to be a function of generalized displacement (q j_j =1, 2,..., )J and structure parameters, or state variables (s m_m =1, 2,...,M). Generalized forces, in turn, are defined in terms of the work potential,

( ) ( , ) j j j m j Q q W q s q ∂ = ∂ (2.6)

As with molecular thermodynamic state variables (e.g.dG T P( , )_{= ∂ ∂}

(

G T

)

_PdT _{+ ∂ ∂}

(

G P dP

)

_T ) Schapery shows that

( , )_j _m _j _m _j _j _m _m j m W W dW q s dq ds Q dq f ds q s ∂ ∂ = + = − ∂ ∂ (2.7) where m m W f s ∂ − = ∂ (2.8) is a thermodynamic force.

In the modeling of viscoelastic response in asphalt mastic systems Little et al. [Little et al. 1999; Lytton et al. 2001; Kim et al. 2001] simplify their analyses by replacing generalized displacement variables with pseudo-variables, pseudo-strain R

ij

ε for example, where

( , )R j R ij m ij Q W _ε s ε ∂ = ∂ (2.9)

given the definition of pseudo-strain in terms of a convolution integral 1 ( ) t _ij R ij R d E t d E d ε ε τ τ τ −∞ =



− (2.10)

Here _ε_ij is the actual physical strain, E is the reference modulus, and _R E t is a relaxation ( ) modulus. This approach effectively reduces the “viscoelastic” responses of a system to that of an elastic system, which simplifies both computation and empirical analyses.

Based on this approach, Kim et al [Kim et al. 2001] defined a damage evolution rate law for viscoelastic behavior with changing microstructure in asphalt-mastic systems undergoing damage-healing, generally expressed by

(30)

13 ( ) m R m m m m ds W A s dt s α _−∂  =  _∂   _ (2.11) where R R( , )R m

W ≡W _ε s is the pseudo strain energy density function, A s is a function of _m( )_m

m

s , and _α_m is a regression constant. The work potential then defines the dissipation of energy due to fracture propagation in viscoelastic media in terms of a damage entropy production rate

1 0 m damage m _damage ds W S T s dt _∂   = _∂   ≥       _(2.12)

A similar “generalized” expression should apply to healing, 1 0 h h m healing h m _healing W ds S T s dt _∂   =  _∂   ≥       _(2.13)

In chapter 3, experimental and computational studies conducted by Little et al. [Little et al. 1999; Lytton et al. 2001; Kim et al. 2001] are examined in more detail where asphalt binder surface free energy as it relates to damage and healing is discussed. In the remaining sections of the present chapter, entropy production in damaging/self-healing systems will be developed in terms of diffuse interface theory as a means of incorporating “damage and healing rates” into constitutive modeling endeavors.

2.1.3 Entropy Production in Damage-Healing Processes

To expand on the concept of entropy production in damage-healing phenomena, Nosonovsky et al. [Nosonovsky 2010; Nosonovsky et al. 2009; Nosonovsky and Bhushan 2010] suggest that the net entropy production in damage-healing “tribosystems” (i.e. tribiological surface wear systems) may be considered in terms of the sum of entropy production terms for all damage and healing processes. The net entropy production rate of a damage-healing system S is then defined by _net

net damage healing

S =S +S (2.14)

Entropy production in a non-equilibrium thermodynamic process is defined by the sum of the “flux-force” conjugate-pairs of thermodynamic variables [Demirel 2007], as

1 0 N j j j j S J X = =



≥  _, _(2.15)

(31)

14

where generalized fluxes J , and thermodynamic forces _j X , define conjugate pairs of _i thermodynamic variables (e.g. temperature-entropy, pressure-volume, chemical potential-number of particles, stress-strain, etc.). Each flux is said to couple with all other thermodynamic forces (and vice-versa), expressed by

( )

1 N i i ij i j J X L X = =



(2.16)

where L_ij kinetic coupling coefficients are derived based on Onsager’s reciprocal relationships [Demirel 2007]. The net entropy production rate of a coupled process is then expressed by

1 1 0 N N ij ij i j i j S L X X = = =



≥  _(2.17)

Nosonovsky et al. [2010] suggests that a net entropy production rate in a damage-healing process is coupled,

/

d h _i i i d d h h

S =



X J = X J +X J (2.18)

where _{X J and}_d _d X J_{h h} are damage (subscript-d) and healing (subscript-h) flux-force terms, which couple as d dd d dh h J =L X +L X (2.19) and h hd d hh h J =L X +L X (2.20)

respectively, where, according to Onsager’s reciprocal relations Ldh=Lhd. The net entropy

production rate is expressed by

(

)

(

)

( )

2

( )

2 2 d dd d dh h h hd d hh h dd d dh d h hh h S X L X L X X L X L X L X L X X L X = + + + = + +  (2.21)

Nosonovsky et al. [2010] also suggests that the net entropy production rate in damage-healing processes follows the scaling rule

/

net macro meso micro nano

S =S +S +S (2.22)

(32)

15

( )

2 macro dd d S =L X (2.23) / 2 meso micro dh d h S = L X X (2.24)

( )

2 nano hh h S =L X (2.25)

which states that nano-scopic fluxes associated with the “actions” of molecules which contribute to healing in a damaged system couple with macroscopic fluxes associated with damage the process resulting in an intermediate scaling term?

2.2 Thermodynamic Derivation of Damage-Healing Processes 2.2.1 Entropy Production in Damage Processes

Drawing on the engineering design principles discussed by Van der Zwaag [2007], and thermodynamic formulations of damage/self-healing processes developed in the work of Schapery [1990] and Nosonovsky et al. [Nosonovsky 2010; Nosonovsky et al. 2009; Nosonovsky and Bhushan 2010], a theoretical framework is developed in the present chapter to define micro- and nanoscale damage accumulation and damage recover healing in bituminous asphalt binder materials.

In microscale damage processes the entropy production rate is defined by both the processes of micro crack initiation [Helrich, 2009] and micro crack propagation [Rice 1978],

damage initiation crack

S ₌S ₊S (2.26)

where

ε 1

σ ij

initiation elastic plastic ji

d S S S T dt = + =    _(2.27) and

(

2

)

0 plastic a crack da da S T dt T dt γ − = = ≥    _(2.28)

given the effective strain rate _ε_ij ₌d_ε_ij dt, which is subject to both elastic “e” and plastic “p” responses defined by strain components,

ε

ij

= +

ε

eij

ε

ijp. Here, entropy production of a dissipative

process is defined in terms of a stress-strain rate couple _{σ ε}_{ji ij} , where V is a unit volume and a

is the strain energy. Strain energy is defined by the rate of change in potential energy dU_a per change in crack opening da

(33)

16 2 plastic a a dU dU da da γ = = +  (2.29)

where the total strain energy  is defined by the sum of the plastic strain _plastic and work of cohesion W_coh ₌2

_γ

, given the surface energy _γ, expressed as ₌2

_γ

₊_plastic.

2.2.2 Entropy Production in Healing Processes

The entropy production rate terms in healing processes are less obvious compared to damage response. If the healing capability of different materials differs due to their variation in molecular composition, then, under similar environmental conditions different materials should be expected to heal by different mechanisms. An understanding of the compositional (physicochemical) properties of materials which differ in their composition (e.g. asphalt which differs from concrete, for example) is then required in order to define potential mechanisms which explain self healing propensities. The physicochemical properties which drive a material’s mechanical properties may also define the available “actions” of healing unique to that particulate material. Materials may for example exhibit viscoelastic flow, mixing/phase separation and/or crystallization and melting.

The entropy production rate of healing is likely defined by the sum of entropy production rates of the processes involved

healing

S S_α

α =



 __(2.30)

One potential healing process may involve crystallization. As an example, crystallization of polymer from solution [Turi 1981] is driven by the change in chemical potential in species-“i” in going from a solution state to the crystalline state expressed by

0

sln cryst

i i i

μ μ μ

Δ ≡ − = (2.31)

This chemical potential change may be defined in terms of the free energy of mixing that occurs,

(

)

0 0 0

( )

eq cryst m

i mix i cryst cryst

m m T T T G n G H H T T μ Δ − Δ ≡ ∂ ∂ = Δ = −Δ = −Δ (2.32)

given n , the number of moles in species-i, _i 0

m

T , the equilibrium melting temperature, and the enthalpy of crystallization ΔH_cryst. The free energy of mixing _ΔG_mix, may further be derived based on the Flory-Huggins expression

(34)

17

(

)

2 ln ln seg mix i i j j i j i j V G RT n n n RT ϕ ϕ ϕ δ δ    Δ = _ + +  − _     (2.33)

given the volume fraction of material phases

ϕ

_i and _ϕ_j where,

(

j j

)

j j j i i n V n V n V ϕ = + (2.34)

Here, V_{i j}_, are partial molar volumes, n_{i j}_, are number of moles,

δ δ

_i, _j are the solubility parameters of species-i,j, and Vsegis the volume per segregated strand of a polymer. In the case

of asphalt molecular composition, to be discussed in detail in chapter 6, a likely molecular species with polymer-like characteristics which undergoes phase separation and crystallization, are paraffin (i.e. “polymethylene”) waxes.

Combining terms from equations 2.32, 2.33 and 2.34 results in an expression for the melting point depression

( )

0 j m cryst RTf T T H ϕ Δ = − Δ (2.35)

where the function f

( )

ϕ , is expressed by

( )

(

)

(

) (

2

)(

)

2 ln (1 ) 1 seg 1 j j j j i i i j j i j V f V V n V V RT ϕ =_ ϕ + −ϕ − +  δ δ−  −ϕ _     (2.36)

The net entropy production rate of a crystallization processes from solution is defined by the entropy flux and internal or local entropy production rate

e i

net

dS d S d S

dt = dt + dt (2.37)

where the entropy flux is expressed by

1 q qj e i d d S d dt T dt dt   =  +    (2.38)

and internal entropy production rate [Nosonovsky 2010] is expressed by

1 cryst 1

i dH

d S dn

(35)

18

given the heat fluxes qd _i dt and qd _j dt for species-i,j, the crystallization enthalpy ΔH_cryst, the equilibrium melting temperature 0

m

T , and the particle flux dn dt. Under adiabatic isotherm conditions of the system with its environment the entropy flux (heat transfer) may be ignored so thatS_net ₌S_i.

A second example of a healing process may involve flow. Here the entropy production rate for energy dissipation due to flow processes [Helrich 2009] is expressed by

1_τ_: _v

flow

S ₌T− _∇ _(2.40)

where τ defines the viscous stress tensor and ∇vdefines the gradient in the viscous flow field. In Cartesian coordinates the viscous dissipation function is expressed by

(

)

2 2 3 3 2 1 , 2 : μ μ μ 3 τ v xi xj xi v i xi j i xi xj υ υ υ = ∂   ∂ ∂   ∇ =  _∂  + _ _∂ + _∂ _ − ∇ ⋅    



(2.41)

for xi, xj, xk = x, y, z, and the coefficient of viscosity μ.

The net rate of entropy production of a self-healing process which then exhibits both crystallization and flow would be defined by

1 _τ_: _v ₀

healing cryst flow

dn S S S T dt μ −   = + = Δ + ∇ ≥      _(2.42)

This type of formulation constitutes an ansatz net rate of entropy production derivation for damage-healing processes S , which utilizes flux-force terms _{d h}_/ J X from equations 2.26 _j _j through 2.29 and 2.42. The ansatz net rate of entropy production S defining the type of d h/ damage-healing processes considered here is expressed by

(

)

(

)

{

}

1 / σ ε ε 2 τ: v 0 e p d h ji ij ij a _d h dn S T a dt γ μ −     =  + + − + Δ + ∇  ≥      _ _ _ _ _(2.43)

Equation 2.43 defines damage in terms of entropy production attributed to stress-strain and micro crack processes and healing process explicitly defined by flow and phase change in the material.

2.2.3 Diffuse Interface Theory and Healing

Phase-field formulations may be conveniently utilized to describe phase transformation phenomena (including crystallization) applicable for healing processes. The Cahn-Hilliard equation [Cahn and Hilliard 1958, 1959a, 1959b; Cahn 1965], which defines a rate law for phase

(36)

19

transition phenomena for solution mixture problems can be conveniently exploited to define the rate laws governing phase transition phenomena, including solidification of metals and crystallization in polymers [Guenthner and Kyu 2000; Kyu et al. 2000; Mehta et al. 2004a, 2004b; Xu et al. 2005; Yue et al. 2006; and Zhou et al. 2000, 2010].

In diffuse interface theory the change in free energy between different material phases in a mixture is considered identical to changes in free energy between two different states of matter (i.e. vapor condensing to liquid is modeled like unmixed to mixed solutions). A liquid to solid phase transition, for example, can be described by the free energy functional,

[

f0( ),ϕ ϕ,...

]

= ∇

  (2.44)

This functional is a composite functional of a “local” free energy term f₀( )

_ϕ

and a gradient “penalty” free energy term _{∇ representing the “diffuseness” of the transitional interface.}_ϕ For a generalized solidification process Emmerich [2010] defines the free energy functional for the tracking of a liquid-solid diffuse interface by

2 2 1 1 { ( ), } ( , ) 2κ 2κc r c f c _ϕ c d ϕ  ϕ ϕ  Φ =  + ∇ + ∇   



 (2.45)

given the free energy density term

[

]

1 2 1 2 1 4 ( , ) ln (1 ) ln(1 ) ( ) ( ) 2 2 4 m T f c u c c c c T c T ϕ = + − − + Δ −_α β − _Φϕ − ϕ + ϕ   (2.46)

whereΔ ≡T (T T− _m) T_m . In equations 2.45 and 2.46 T_m is the melting temperature, c is the conserved order parameter (a concentration field, dimensionless, 0_{≤ ≤ ),}c 1 _ϕ is the non-conserved phase-field order parameter (dimensionless, ₋1.5_{≤ ≤}_ϕ 1.5), κ_c and κ_ϕ are the corresponding mobility tensors, and α, _β, and _{u are phenomenological parameters determined} based on experimental phase diagrams. Finally, the variable Φ( )ϕ is referred to as the phase-field variable expressed by

3 5 4 2 ( ) 2 3 5 ϕ ϕ ϕ ϕ Φ = − + (2.47)

Figures 2.2.3.1 and 2.2.3.2 depict surface plots of Emmerich’s [2010] free energy density function expressed in equation 2.46

(37)

20

Figure 2.2.3.1. Surface plots of f( , ,_ϕ c T

{

₌300 ,K T T₌ _m ₌328 ,K T ₌400 ,K u_{= = =}_{β α} 1 )

}

from equation 2.46, for three different temperatures.

The rates of change in both conserved and non-conserved phase-field variables are expressed by

2 2 _κ 2 c c c c f c t c c ∂ ₌ _∇ ∂ ₌ _∇  _{∇ −}∂    ∂ ∂  ∂     (2.48) and 2 κ f t ϕ ϕ ϕ ϕ _ϕ ϕ ϕ   ∂ _{= −} ∂ _{= −} _{∇ −} ∂   ∂ ∂  ∂     (2.49)

respectively, where the chemical potential _μ is defined as

(

2

)

c

c κ c f c

μ= ∂ ∂ = ∇ − ∂ ∂ .

Figure 2.2.3.2. Surface plots of f( , ,_ϕ T c

{

₌0.05 )

}

from equation 2.46, plotted at constant c. ϕ c f(ϕ,c)

T>T

m

T=T

m

T<T

m

f(

ϕ,T)

ϕ

T

(38)

21

Consistency between non-equilibrium thermodynamics and phase-field formulations has been established [Sekerka 2011]. Sekerka [2011] has defined a Helmholtz free energy density expression for a crystallization process,

f u T s

Δ = Δ − Δ (2.50) where the change in local free energy is expressed by

ln 1 ( ) ( ) 2 f V V V m m W T T f c T c T L p g T T ϕ ϕ     Δ = Δ −  +  −  +     (2.51)

given the local change in the internal energy density

( ) ( ) 2 u V V W u c T L p _ϕ g _ϕ Δ = Δ + + (2.52)

and change in entropy density

ln ( ) ( ) 2 V s V m m L W T s c p g T T ϕ ϕ   Δ =  + +   (2.53) where f u s W ₌W TW₋ (2.54)

Here cV and LV are the heat capacity and latent heat per unit volume, and Tm is the melting

temperature. A double well potential is defined by the empirical functions

(

)

3 2 ( ) 10 15 6 p _{ϕ ϕ}₌ ₊ _ϕ₊ _ϕ (2.55) and

(

)

2 2 ( ) 1 g _{ϕ ϕ}₌ ₋_ϕ (2.56)

(39)

22

Figure 2.2.3.3. Surface plots of Δf( , )_ϕ T utilizing equation 2.51, for c_V ₌L_V ₌W_f ₌1.

Based on inspection of the variation of shape of these surfaces, variation in the potential energy surface function defined by equation 2.51 is more sensitive to variation in temperature around the melting temperature as compared to variations in the potential energy surface function defined equation 2.46. Unlike equation 2.46, equation 2.51 does not specifically define a conserved order parameter such as concentration.

The kinetic rate expressions, or “phase field equations”, derived from evaluating a free energy functional of the form

2 1 {( ), } ( , ) 2κ T f T _ϕ dV ϕ = _ ϕ + ∇ϕ _  



 (257) are expressed as 2 2 1 1 ( ) ( ) 2 κ f f V m W dp dg L t T T d T d T ϕ ϕ ϕ τ ϕ ϕ ϕ   ∂ =_∂  −  − + ∇   (2.58) and 2 2 2 ( ) ( ) 2 κ u V V u W T p g c L k T t t ϕ t ϕ _{ϕ ϕ} ϕ ∂ ₊ ∂ _{= ∇ +} _{∇ −} ∂ ∂ ∂  ∂ (2.59)

Given the set of functions 2.46-2.56, Sekerka [2011] defines the entropy production of the crystallization process by 2 q _κ2 _n ₀ sub c prod s d S d x dt T ϕϕ ϕ   = + _ + ∇ ⋅ ≥_  



  _  _  (2.60)

Here _ is a volume element functional defined by

1.0 0.5 0.5 0.25 0.0 -0.5 0.0 -1.0 -0.25 -0.5 320 325 330 335 0.5 0.25 0.0 -0.25 -0.5 335 330 0.5 -1.0 0.25 -0.5 0.0 325 0.0 -0.25 0.5 -0.5 320 1.0 T f(ϕ,T) f(ϕ,T) f(ϕ,T) ϕ ϕ T

Chemomechanics of Damage Accumulation and Damage-Recovery Healing in Bituminous Asphalt Binders