Forum second debate

On 10/5/05 at 7pm EST.
The Forum will have its second debate.
The topic to be debated will be topical sealers and their role in the stone industry. Do your research get the facts and the myths.

You can take this time to register. Make sure you have access before Wednesday.
http://www.huligar.com/chat/

[srosen]

Jo thanks for the invite I will try and be there .

[Brian Briggs]

If I have time I will be there. The wife leaves for Canada Wednesday and I have kid duty.

[Yonkers]

Originally Posted by Brian Briggs

If I have time I will be there. The wife leaves for Canada Wednesday and I have kid duty.

I'll be sure and alert Canada Customs for you.

Jo, I doubt I'll be there as I am getting into too many video games.

[donnystoned]

i also have kid duty this wed. however if the little sob's behave , then i may be able to join. :lol:

[Gabe]

I also have kid duty, but if the kids behave, I will add what I can.

Gabe

[donnystoned]

i think this wed . is national dad gets kid duty day! :lol:

The following is an article which should help explain basic polymer chemistry...if anyone is interested


WHAT'S IN A FLOOR FINISH?

Understanding the Basic Ingredients Helps Avoid Floor Care Problems

by Roger McFadden

INTRODUCTION

Chemists and floor care professionals often speak different languages. The chemist talks about polymerization, melting points and monomers. And the floor care professional talks about durability, wet-look gloss and burnish response.

As a chemist specializing in floor finish development I have learned the importance of communicating and listening to floor care professionals. Professionals are the ones who use the floor finishes. It is their needs that we chemists must satisfy.

Floor care professionals are very cooperative in teaching us chemists about their floor finish procedures, application methods, and equipment. But most floor care experts that I know are as interested in learning more about the floor finishes they use as I am in learning about their techniques and procedures.

Two questions floor care professionals often ask are, 1) what is in a floor finish? and 2) why is it in there?. Let's look at the answers to these questions to better understand how to prevent and solve expensive floor care problems.

WHAT ARE FLOOR FINISHES?

A floor finish is a liquid which is applied to a resilient tile floor and dries to a hard, durable and smooth film. This film is about the thickness of waxed paper and is expected to protect and extend the life of the floor while providing an attractive appearance and slip resistant surface.

WHAT’S IN A FLOOR FINISH

High quality floor finishes may contain as many as twenty-five ingredients. Some of these ingredients evaporate while others remain on the floor after drying. The ingredients that evaporate are called, "volatile" components and the ingredients that stay on the floor are called, "non-volatile" components. The volatile ingredients assist in the film formation, drying and curing of the finish and then evaporate. The non-volatile ingredients are the solid materials which stay on the floor and make up the floor finish film.

The ingredients used to make floor finishes combine to produce a balanced blend of physical and performance characteristics. Some of these characteristics include: hardness, gloss, clarity, scuff

resistance, slip resistance, water and detergent resistance, buffability, removability, recoatability, and toughness.

There are five basic categories of floor finish ingredients, (1) polymer emulsions, (2) film formers, (3) modifiers, (4) preservatives and (5) water.

POLYMER EMULSIONS

A polymer is a giant molecule made from a large number of similar small molecules, called monomers, which are joined together chemically. The chemical process of making a polymer is called polymerization. When a polymer is made from two or more monomers, it is called a copolymer. Many polymers are named for the monomer from which they are made. For example, the polymer polyethylene is named for its monomer ethylene.

Chemists suspend the giant floor finish polymer in water, and they become polymer emulsions. Most floor finish manufacturers treat the monomers and processes used to make their polymer emulsions as a trade secret. However it is generally known that most floor finish polymer emulsions are made from acrylic or styrene type monomers.

The polymer emulsions are the workhorse of a floor finish. They are the backbone upon which all of the other ingredients are connected. There are virtually thousands of potential combinations of polymers which can be used to make floor finishes. The choice of the polymers used in floor finishes influences nearly every performance characteristic, including: durability, gloss, slip resistance, leveling, clarity, water and detergent resistance, recoatability, mark resistance, removability and powder resistance.

FILM FORMERS

Polymer emulsions without film formers would produce dry, loose crystals on the floor surface. Improper film formation can produce a variety of floor care problems including: poor adhesion and powdering, poor gloss, streaking, cratering, fisheyes, blushing, orange peeling and poor leveling. Some of the ingredients that contribute to proper film formation are coalescing agents, plasticizers, wetting and leveling agents and antifoamers.

Coalescing Agents

Coalescing agents such as glycol ethers, glycol ether esters and ester-alcohols allow the polymer molecules suspended in the emulsion to coalesce (come together) into a continuous film without flaws or imperfections on the floor (See Figure 3). Coalescing agents stay behind for a short time after the water has evaporated to soften and bring the polymer molecules together into a continuous and tough film.

A precise amount of coalescing agent is needed for proper film formation. For this reason it is important for floor care professionals to minimize evaporation by keeping floor finish containers and mop buckets, covered or closed when not in use. Floor care problems associated with a loss of these coalescing agents include: poor adhesion, low gloss and poor durability.

Plasticizers

Floor finish polymers would crack and break without plasticizers to make them flexible and impact resistant. Chemists are careful to design floor finishes with accurate amounts of plasticizer. "Over plasticized" floor finishes can produce tackiness, poor soil resistance and plasticizer migration. "Under plasticized" floor finishes can create powdering, low gloss, slippery floors and recoatability problems.

Leveling and wetting agents

The polymers in floor finishes are bulky and have high surface tension which prevent proper flowing and leveling of the finish. Leveling and wetting agents lower the surface tension of the finish allowing it to spread and flow over the floor surface uniformly and evenly. Tiny amounts of these surface active agents provide big benefits by preventing the finish from pulling apart and puddling during the drying process.

Antifoaming Agents

Water based floor finishes contain small amounts of surfactants and emulsifiers which can produce bubbles and foam in the dried film. These surface flaws, sometimes described as craters and fisheyes, destroy the smooth and reflective appearance of the dried film. Antifoaming agents are added to floor finishes to rapidly break these bubbles and stop them from producing ugly imperfections.

MODIFIERS

The polymer emulsions selected for floor finishes meet a broad range of performance requirements. But chemists have found non-volatile ingredients which can be added to the polymer emulsion to modify and improve the performance of the floor finish. For instance, gloss, clarity, hardness, buffability, scuff and scratch resistance, slip resistance and durability can all be improved when modifiers like resins, wax emulsions, urethanes, ultraviolet absorbers and metal crosslinkers are added.

Alkali Soluble Resins

There are three primary alkali soluble resins which are used in floor finishes. They include, (1) rosin, (2) acrylic and (3) styrene-maleic anhydride resins. These resins are added to floor finishes primarily to improve leveling, clarity and gloss. However, they also affect many other properties including removability, detergent resistance, color, recoatability and water resistance.

Wax Emulsions

The wax emulsions added to floor finishes are synthetic polyethylene or polypropylene waxes which have replaced natural waxes because of their improved consistency in color, performance and availability. Their major contribution to the floor finish is improved slip resistance, durability, toughness and high speed buffability.

Waterborne Urethanes

These are used in floor finishes where chemical and water resistance, impact resistance, and flexibility are required. When combined with polymer emulsions, they also provide improved adhesion to old and worn floor surfaces. Three objections often mentioned when high levels of waterborne urethanes are used in floor finishes are their cost, tendency to discolor and removability.

Ultraviolet Stabilizers

The effect of ultraviolet radiation on synthetic polymers is similar to its effect on the human skin. The ultraviolet radiation can cause yellowing and drying out of the finish. Floor finishes contain tiny amounts of stabilizers to prevent yellowing and discolorations caused by ultraviolet radiation.

Crosslinkers

Crosslinkers connect the different polymer chains in the floor finish emulsion. Their primary purpose is to provide both durability and removability of the floor finish film. Zinc compounds commonly are used to crosslink acrylic polymer floor finishes.

PRESERVATIVES

Some of the ingredients in floor finishes are sensitive to attack by microorganisms. These attacks can destroy the floor finish and cause discolorations, destruction of the floor finish emulsion and unpleasant odors. Formaldehyde has been the primary antimicrobial agent used in floor finishes for over 20 years. But most modern floor finishes now contain new replacements, due to health issues raised by formaldehyde.

Antimicrobial agents are added to protect the finish by preventing the growth of microorganisms during manufacturer and storage. However, the amount of antimicrobial agent in a floor finish is usually not sufficient to protect against cross contamination during use. This is why floor care professionals should keep their finishing equipment clean, and insist on never pouring used finish into new finish.

Another type of preservative added to floor finishes is the antifreeze agent, which provides freeze-thaw stability.

WATER

Floor finishes are made with deionized water to provide a stable and friendly environment for all the floor finish ingredients. The use of deionized water assures that colorful impurities found in some water systems do not dry into the floor finish film causing slight discolorations or reductions in gloss or clarity.

CHEMISTRY AND CARE COMBINE

The ingredients described here are a good cross-section of what many floor finishes contain, but they are not the only ones. You can get more information about the finishes you use by contacting your sanitary supply distributor or the finish manufacturer.

Teamwork between chemists and floor care professionals has produced modern finishes far superior to those of the past. But it takes more than a superior finish to defend against the abrasive soils tracked into buildings. It also takes a well-planned and well-executed floor care program that is designed to do the job right. Knowing the ingredients in a finish and why they are used can help cleaning managers select the proper finish and prevent expensive floor care problems.



About the Author: Roger McFadden is Technical Director and Senior Chemist at Paulsen & Roles Laboratories in Portland, OR, a maker and distributor of products for commercial and industrial cleaning.

Hear is a link that may shed some more light on this topic.
http://www.phy.bme.hu/~van/Publ/VanVas01p.pdf

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1 INTRODUCTIONIn continuum physical theories the complexmechanical properties of material are described byconstitutive functions. One of the basic constructionmethods to get reasonable constitutive functions isbased on the Second Law of thermodynamics. Thematerial equations have to be compatible with theSecond Law in every system where dissipationoccurs, including fracture and failure of rockmaterials, too. Here (of course) thermodynamics isunderstood not only as a theory to deal with thermalphenomena and temperature changes, but as thetheory dealing with the stability of materials. In thisrespect Second Law is understood as a requirementof stability, restricting the possible materialequations of all media.In rock mechanics the pure mechanical propertiesare modeled by continuum mechanical methods, andeven the violations of material stability areunderstood in most cases as pure mechanicalphenomena using fracture mechanics as modelingtool. Fracture mechanics deals with holes (cracks)and discontinuities embedded in an ideal mechanicalcontinuum. Several works use statistical methods tounderstand the interaction and interlocking of cracksin the mechanical continuum. In rocks damageprocesses include not only microcracking andinterlocking of cracks but several other differentmechanisms, therefore the applicability of this kindof statistical considerations is questionable. Tounderstand the appearing broad range of differentphenomenarequirestoapplydifferentphenomen ological methods and to understand, inwhat sense could be the different approachesunified. Some new developments in modernnonequilibrium thermodynamics give a hope todeepen our understanding of the role of the SecondLaw in mechanical modeling and to extend theexisting models to give simple descriptions ofseveral related phenomena.Failure and change of elastic properties aretreated as independent phenomena in mechanics.The situation is similar in the theories of plasticity,where the yield criteria is considered to beindependent on elastic properties of the material (butnot independent on the Second Law). Continuumdamage mechanics (see e.g. Krajcinovic 1996) is atheory motivated by the need of unification offailure and nonlinear elasticity. The original idea isthat growing damage can lead to failure. However,after some initial attempt the researchers in damagemechanics gave up to find a theoretical connectionand nowadays the damage surfaces(criticaldamage) are given independently on the change ofmechanic properties.In this short paper we will show that a connectioncan be found, if the foundations of the underlyingnonequilibriumthermodynamictheoriesarein vestigated. Failure and fracture can be consideredas a kind of material instability. Moreover, we canuse similar concepts and methods to the case ofphase transitions in fluid and gaseous bodies. Asparticular applications we will show how theclassical Griffith concept (and all the so calledenergy methods) includes thermodynamic instabilitySecond Law of thermodynamics and the failure of rock materialsP. VánBudapest University of Technology and Economics, Department of Chemical PhysicsB. VásárhelyiBudapest University of Technology and Economics, Department of Engineering GeologyABSTRACT:The relation of nonequilibrium thermodynamics to some failure and fracture theories of rock mechanics isinvestigated. The basic concepts are given to connect failure to the properties of material equations describingthe elastic properties. The resulted in thermodynamic conditions are proved to be compatible with classicallocalization and failure theories of solid materials. Compatibility with experiments and some empirical, ad-hoc failure criteria of rocks is also demonstrated.
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and show, how other specific rock mechanicalfailure criteria can be understood as violation ofthermodynamicstability.Attheendathermodynamic improvement of the empiricalcriteria of Lade is given using the ideas above and asimple particular model.2 DYNAMIC AND THERMODYNAMICSTABILITYIn nonequilibrium thermodynamics the Second Lawintroduces the entropy function as the manifestationand theoretical tool to deal with the stability ofequilibrium. There are two different aspects to beconsidered here:Thermodynamic stability; the convexity ofentropy function. This is a static stabilityrequirement that ensures the stability of equilibriumstates of matter in case of small externalperturbationsofthethermodynamicstate,indep endently of the particular dynamic equations.Phase boundaries appear where thermodynamicstability is violated.Dynamic stability of thermodynamic equilibrium;positive entropy production, where particulardynamic equations of matter are considered. Theconnection between the two stability concepts isclear in case of the so called ‘equilibrium’ systems,where the state variables and the relations betweenthem are those that can be measured in equilibrium.Thermodynamic and dynamic stability togetherrestrict the possible functional form of theconstitutive functions to give the asymptotic stabilityof specific equilibrium states (Glansdorff andPrigogine 1971, Gurtin 1975). For homogeneous(discrete) systems this idea was developed in detailgiving a remarkable conceptual background of theSecond Law (Matolcsi 1992, 1996a, b).The situation is more involved in nonequilibriumsystems where the hypotheses of local equilibrium isviolated, the ‘equilibrium’ state variables areinadequate to characterize the processes (Ván 1995).For systems with internal variables (an importantclass of nonequilibrium systems) the firstrequirement, the thermodynamic stability results inthe desired theoretical tool to describe materialinstability of mechanical origin. Let us consider asimple mechanical system, where the traditionalextensive state variables the specific entropy s anddeformationεare supplemented by a set of internalvariables=(αi, i=1,…,n). Each internal variablecan be a tensor of any order. Different variable setsand thermodynamic potential functions are used inthese kind of investigations. In mechanicstraditionally we can meet the Helmholtz free energyφ(T, , ) and the Gibbs free energyψ(T, , ), too.The corresponding variables are the temperature T,deformation and stressandrespectively. Thetwo free energies and the internal energy e(s, , )are related by partial Legendre transformations::++=+=TsTseψφ,where s is the entropy.The thermodynamic stability appears as therequirement of concavity of the entropy function. Aconcave entropy results in conditions for the otherthermodynamic potentials, too. In case of puremechanical processes, when temperature is constant,concave entropy gives a convex Helmholtz freeenergy. The requirement of a convexity in therelevant variables for a two times differentiableHelmholtz free energy can be written as=⋅⋅),(),(2ddDddφ0),(),(222222>⋅∂∂∂∂∂∂∂∂∂∂⋅=ddddφφφφ(1)for every (d , d ). Here a notation from themechanical literature is applied where d and dare arbitrary vectors from the linear spaces wherethe deformation and internal variables are definedrespectively. D2φdenotes the second derivativeφ.To investigate the inequality (1) Sylvester conditionfor symmetric matrices can be applied. It issupposed that the functional form of the entropy(and the free energies consequently) does notcontain differential or integral operators. However,the process dependence of the correspondingequations is considered through the introducedinternal variables. Therefore the resulted stress-strain relations will be rate dependent, but a rateform notation is not necessary and could even bemisleading.A (partially) convex Helmholtz free energy givesrequirements for the Gibbs free energy, but theserequirements cannot be expressed as a simpleconcavity or convexity for all variables (one can saythat Gibbs free energy is convex in the internalvariables and concave in the other ones), thereforesometimes a conversion to Helmholtz free energycan be useful for thermodynamic stabilitycalculations.The subset of the state space where the conditionsof thermodynamic stability are satisfied determinesthe static stability domain of the material. Outsidethis domain the material is unstable, without furtherconstraint fails. From a physical point of view thesituation is analogous to phase boundaries in case offluid bodies but in solid bodies the observedphenomena can be qualitatively different. Herefailure changes the properties of the material and theinternal interactions (for example the cohesionvanishes and dry friction will be the dominatingdissipation mechanism). Moreover, in this case all of
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our previous implicit assumptions on thehomogeneous representative volume elements canbecome meaningless. In solid materials we cannotspeak unambiguously of an other homogeneousphase after the loss of thermodynamic stability, in acontinuum description the phases are immediatelylocalized. This is best seen if we give a closer lookat the condition of stability loss and recognize that(1) can be interpreted as a generalization of theclassical Hadamard-Hill localization condition ofshear banding. Using purely mechanical argumentsand investigating jump surfaces in the velocity fieldshear banding appears in the direction n if0)det(=⋅⋅nCn,(2)where C is the fourth order stiffness tensor, that canbe given as the second partial derivative of theHelmholtz free energy22:C∂∂=φ.(Hadamard 1903, Hill 1962, Asaro & Rice 1977)We can see that C is the (1,1) submatrix in ourgeneral thermodynamic stability condition (1). Anecessary condition of this submatrix to be positivedefinite is closely related to the mentioned classicallocalization condition of Hadamard and Hill, thelater gives the boundary of the stability domainwhen equality holds. A more general requirement ofpositive definite elastic moduli can be derived fromenergetic-stability considerations resulting in alocalization condition. This general energeticlocalization condition considers shear-banding andcleavage type localization instabilities, too (see e.g.Krajcinovic 1996 and Broberg 1999). Our condition(1) can be considered as a generalization of theseclassicalrequirements(allenergetictypeconside rations can be interpreted as disguisedthermodynamic train of thoughts).Therefore the loss of thermodynamic stability, atleast in some cases, does not result in ahomogeneous change in the material but indicatesthe appearance of some localized patterns, forexample shear bands. Hence the analogy with phasetransitions can be misleading, instead of phasetransitions we can call the related process as phasebreaking. Of course more developed localizationmodels considering the thickness of shear bands andother gradient dependent nonlocal effects can also beintroduced.Internal variables give the basic theoreticalconcept to thermodynamic motivated approaches ofplasticity, damage mechanics or rheology. In thiscase the fundamental Helmholtz relation expressedby the Gibbs free energyψ(T, ,) for ahomogeneous representative volume element can bewritten asA ddsdTd⋅−−−=:ψ,(3)where T is the temperature,andare the stressand the deformation respectively, the double dotdenotes the trace of the product of the two tensorsand A is the affinity conjugated to the internalvariablesThis relation is a short and physicallyinterpretable version of the potential property of thefree energy. That property can be expressed alsowith partial derivativesTs∂∂−=ψ,∂∂−=ψε,A∂∂−=ψ.(4)Before continuing to discuss the consequences ofthermodynamic stability and other static phenomena,we give some hint on the dynamics emerging fromthermodynamic considerations. The other part of theSecond Law beyond the thermodynamic stability isthe requirement of positive entropy production. Thatpostulate results in prescriptions and some veryparticular forms of the possible dynamic equations.For solid bodies with small deformations theproduction of entropy multiplied by the temperatureand written in terms of Gibbs free energy reads as0:122≥⋅∂∂+∂∂+∂∂=−&&ψψψsTP.(5)Here the dot above the quantities denotessubstantial time derivatives. It is easy to identifythermodynamic currents and forces in the aboveexpressionand give explicit relations for thedynamics of the different introduced quantities. Onthe other hand additional physical restrictions seemto be reasonable in most of the practical situations inmechanics. One of them that the mechanicalequilibration is faster than the evolution of theinternal variables (the terminal velocity of crackpropagation in ideal elastic materials is not morethan the half of the sound velocity). In this case wecan suppose a mechanical equilibrium∂∂−=ψ.(6)The dynamics of the internal variables isdetermined as follows (as a first approximation)),(∂∂=ψL&,where L is a material parameter, characterizing thespeed of the damage propagation.To investigate the theoretical and experimentalrelevance of this kind of dynamics is not the subjectof this short paper. We remark here that typicaldamaging and failure mechanisms observed forbrittle rocks (Bieniawski 1967 or Martin andChandler 1994) can be modeled by a single vectorialinternal variable (supposing that microcracking is
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the dominating internal mechanism) and fewmaterial parameters.A SIMPLE MODEL FOR BRITTLE FAILUREIn this section a simple model of brittle material issuggested and the static stability properties areinvestigated. For brittle materials the microstructureis formed by microcracks, that are growing andinterlocking with increasing pressure. In case ofbrittle rocks with grains the structure of microcracksis not so simple as for homogeneous materials.According to the compressive stresses they can beintergranular and also can be formed inside thegrains. The mode of failure depends on the directionof the loading for slow and also for fast processes.Therefore, it seems to be reasonable to introduce asingle vectorial internal variable that incorporatesthe average properties of microstructure. In this casewe can interpret it as the average of the microcrackvectors and we will call it as damage.To deal with the static properties of particularmaterials a reasonable form of one of the potentialfunctions is necessary. According to the experienceand traditions a second order polynomial issuggested for the Gibbs free energy. Using thesymmetry requirements for isotropic materials wecan get the following functional form.2)(21))((212()(2),(22222⋅⋅⋅++⋅⋅+++++++++=γβ λµδςψβλµδTrkTrkkTrk(7)Due to the isotropy only ten material constantsappear and only five of them can be considered asnew. All the terms can be interpreted physically andmeasurement methods can be suggested for thematerial constants. There are some clues for theinterpretation (a more detailed treatment is given inVán 2000).– The first term represents the energy attributeddirectly to the cracks.− The second term is related to the hydrostaticenergy conservation of the material.δcharacterizes the damage independent andδkthe damage dependent part. Pore fluidpressure can be a physical mechanism in thebackground. (All of the parameters candepend on temperature and density of thematerial.)− The next two terms are the usual elastic freeenergy contributions whereµandλare wellknown elastic coefficients related to theYoung modulus E and Poisson ratioνbyµ=(1+ν)/E and λ=µ/E. kµand kλcharacterizetheir damage dependence.−⋅ ⋅is the deformation in the direction ofthe crack surface, therefore the sixth termconsiders the opening of the cracks.− The last term contains the square of thesubstantial crack vector, therefore it means anenergy contribution necessary for turning thecracks with the deforming media.Another clue to the interpretation of the materialparameters can be given by the equation of themechanical equilibrium (6) calculating the damagestrain (the residual strain due to the growingdamage).I0oβδδ++==)(),((20k.Here I is the second order unit tensor and thecircleois the usual notation of the tensorial productin continuum mechanics.With this particular free energy we caninvestigate the stability thresholds suggested in thecondition (1). Calculating the (1,1) submatrix,related to the localization we can get that in case ofzero damageµ>0 andµ+ν>0.. Calculation of thedamage related (2,2) submatrix we can get therequirement of thermodynamic stability in case ofzero deformation isζ>0. On the other hand severaldifferent explicit upper limits can also be calculatedfor the damage parameter in case of specific loadingconditions.This particular Gibbs free energy function can beconsidered as a direct generalization of the ideas ofGriffith in two different ways, applying the twoconditions given in his original paper Griffith 1924.One of them is if we accept the interpretation ofRice 1978 and Lawn 1993 and assume that theenergy condition is connected directly to the freeenergy. Therefore the free energy governing theevolution of crack extension is the reversible workW minus the surface energy (related to the energyrelease rate G) necessary for the crack separation.More properly, in two dimensions for uniaxialtensile loading and a crack perpendicular to theloading axis we can write111112),(),(αασασψGW−=(8)whereα1is the length of the crack,σ1is the tensilestress, W is the reversible work component and thelast term is the specific surface energy. For perfectlyelastic materials we can give the work in a morespecific formEEW212121112),(απσσασ+−=.Here the first term is the pure elastic work, whilethe second is the work necessary for the reversiblecrack extension (see e.g. the original work Griffith
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1924). The expression (8) above is a special form ofthe free energy function (7) for this particularsituation, where for exampleµ=1/2E, kµ=πand theother material parameters are zero.The thermodynamic stability condition (1) withthe previous simple Gibbs free energy gives a threedimensional failure criteria. To check the validity itis reasonable to consider experiments with similargeneral loading conditions, or the related empiricalfailure criteria.The damage (failure) surface of brittle materials(rocks, ceramics, etc..) has a particular threedimensional shape in the stress space as one can seequalitatively on Figure 1. Let us observe the roundedtriangle shape on the octahedral plane (cross sectionperpendicular to the hydrostatic pressure line).The rate dependence of the failure strengthobserved in experiments makes doubt that this formexpresses real material properties (Martin andChandler 1994), but here we accept it as anexperimental evidence of the time independentstrength surface of brittle materials.Most of the strength criteria for rocks weresuggested for special loading conditions and onlysome of them applies to explain the particular formof the failure surface. The first and oldest one is theoriginal two dimensional Griffith criterion based ontheoretical calculations for single cracks embeddedin an elastic domain. Later it was generalized tothree dimension by Murell extending some expectedproperties of the failure surface from two into threedimensions (Murell 1963, Jaeger and Cook 1971).This criteria suggests a parabolic failure envelope incase of pressure loading and a constant limit stress incase of tensile loading (see Griffith 1924).Figure 1. Failure surface in the stress space according toexperimental evidence (Lade 1993).Another three dimensional generalization of thecriterion of Griffith was used by Theocaris 1987 inhis Elliptic Paraboloid Failure Criterion. Thiscriterion suggests an elliptic paraboloid open fromthe hydrostatic axis as initial failure surface in thestress field. It has been proved to be useful todescribe the failure of anisotropic materials andresults in a better fitting than the criterion ofGriffith-Murell (Theocaris 1999). Here the failureloci are given by the next equation at the stress space1:::=+ bB.where B and b are fourth and second order tensorsrespectively.Theyaretobedeterminedexperimen tally. The parameters should be given in away that the failure loci form a paraboloid whoseaxis is the hydrostatic pressure line. Theocaris givesexperimental procedures and calculation methods todetermine the failure loci from the experiments. Letus remark that the anisotropic property introduced inthis criterion is not necessarily a materialcharacteristics, because it can arise from an initiallyanisotropic damage distribution in case of originallyand materially isotropic base continuum, too. On theother hand, the smooth paraboloid seems to be astrong simplification for tensile loadings. It is easyto see that the criteria of Theocaris can beconsidered as a special case of our thermodynamiccondition in case of constant damage andconsidering only the (1,1) submatrix of (1).As a third possibility, the best fitting to themeasured failure surfaces can be achieved by thecriteria of Lade. It is simple and easy to apply,because contains only three material parameters m,η1, a and given by the next function in the stressspace1133127η=−mapIII(9).where I1= Tr and I3= det are the first and thirdinvariants of the stress tensor and pais theatmospheric pressure. Moreover, because the normalstresses contain a translation in the stress spacealong the hydrostatic axis, the mean stressesiinthe formula (9) should be replaced withi=i+ apa,where i=1,2,3. The corresponding materialparameters has been calculated for several rocksfrom the available (three dimensional) experimentaldata (Lade 1993).All the three criteria are empirical, they weresuggestedwithoutanyserioustheoreticaljustifica tion. In the following we will see that thethermodynamic stability condition of our simplemodel with one vectorial internal variable can give acomparable fitting, moreover, it has a strong
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theoretical background as a direct thermodynamicgeneralization of Griffith criteria in threedimensions.To demonstrate the differences a simple exampleis given here, based on the experimental data ofBrown performed on Wombeyan marble in biaxialexperiments with brush plattens (Brown 1974).According to biaxial experiments, contrary to Mohrassumptions, not only the difference of the biggestand lowest principal stresses determine the strengthof the rock: the influence of intermediate stresses isnot negligible. Lade fitted his criteria with theexperimental data of Brown (Lade 1993).Figure 2. Biaxial experimental data, criterion of Lade andthermodynamic failure envelope.Figure 2 shows the results of biaxial experiments,the corresponding fitted failure surface of Lade andthe failure surface proposed by the thermodynamicstability condition. The empty dots denote theexperimental results and the broken line is thethreshold of the criterion of Lade with the parametervalues m=1.162,η1=601500 and a=38.0. Thethermodynamic criterion results in the three ellipticcurves. Their internal hull gives the boundaries ofthermodynamic stability an denoted by the thickestline on the figure. The parameters areδ=0,kδ=10.9976,µ=50000, kµ=0.03,λ=0.14, kλ=0,ζ=100,β=11.2156, kβ= 0 andγ= 0.0353352. Onlythree parameters are used for the fitting, the othernon-zero parameters are calculated from the knownproperties of the material or estimated suitably. Theinitialdamagevectorischosenas=(0.003,0.003,0.00 3),supposingauniformdirectional distribution. The chosen particular valuesare not too important, because the failure surface isindependent on the damage if it is sufficiently small.It can be seen on the figure that the thermodynamiccondition gives a piecewise continuous failurethreshold.Let us observe some important qualitativedifferences between the empirical and thethermodynamic criteria. The thermodynamic failuresurface is a cross section of several surfaces,therefore it has some vertices. One of the vertices ison the hydrostatic axis for tensile stresses. It issimilar to the construction of the Griffith-Murellcriteria, where also some cross sectional surface wasproposed (a very special one). The published data onthis experiment of Brown is not sufficient todetermine all of the thermodynamic parameters (forthe fitting we have chosen a suitable parameter set,consideringsomephysicalmechanisms).Measurement s to determine the material parametersfor a brittle rock and the compatibility with thepredictions on the dynamics are under way.CONCLUSIONS AND DISCUSSIONIn this paper a theoretical concept ofnonequilibrium phase breaking is proposed as a toolto extend the frames of the phenomenologicalthermodynamic modeling. As an application of thisidea a particular phenomena, the microcrack induceddamage is investigated in detail. A simple internalvariable theory is suggested, using a single vectorialinternal variable and based on the most generalsecond order approximation of the Gibbs freeenergy. We have seen that the model can beconsidered as a generalizations of the classicalenergetic Griffith model of failure. The boundary ofthe domain of thermodynamic stability is proved tobe a generalization of traditional mechanicallocalization criteria. A comparison with empiricalfailure criteria showed that this simple model withthermodynamic stability results in the best fitting tothe available experimental data in a threedimensional stress space.The concept of failure deserves some attentionfrom an experimental point of view. The materialcan be kept together even when its internal structureis completely destroyed. First it was pointed out byOrowan 1960 analyzing the classical experiments ofvon Kármán with Carrara marble. The marblebecame powdered, chalk like with large lateralpressures, which indicates a change in the internalstructure. In this case the phase breaking is closelyrelated to a real phase transition, and supposedlyanother free energy can be introduced to characterizethe powdered, frictional state.The dynamical properties of the phenomena arenot investigated in this paper, but it is clear that oursimple model can be considered only as a firstσ1σ2
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approximation. The orientation sensitivity of theKaiser effect, the fact that the microcracking isinitiated separately in different orientations is surelynot included in our model with a single averagingtype internal variable. However, the present studydemonstrates, that a nonequilibrium thermodynamicapproach to the description of the evolution of thewhole microcrack distribution seems to bepromising.ACKNOWLEDGEMENTSThis research was supported by OTKA F22620 andFKFP 0287/1997. Mathematica 3.0 made most ofthe calculations.REFERENCESAsaro, R.J. & Rice, J.R. 1977. Strain localization in ductilesingle crystals. J. of Mech. Phys. Sol., 25:309-338.Bieniawski, Z.T. 1967. Mechanism of brittle fracture of rocks,CSIR Report, MEG 580, Series ME/TH/21, ReferenceME/MR/4271, Pretoria, South Africa, National MechanicalEngineering Research Institute.Broberg, K.B. 1999. Cracks and Fracture, New York-etc.:Academic Press.Brown, E.T. 1974. Fracture of rock under uniform biaxialcompression. In Proc. of the 3th Int. Cong. of Rock Mech.,V2: 111-117. Denver.Glansdorff, P. & Prigogine, I. 1971. Thermodynamic Theory ofStructure, Stability and Fluctuations, London-etc.: Wiley-Interscience.Griffith, A.A. 1924. The theory of rupture. Trans. First Intl.Cong. Appl. Mech. Delft, 55-63.Gurtin, M.E. 1975. Thermodynamics and Stability. Arch. ofRat. Mech. Anal., 59:63-96.Hadamard, J. 1903. Leçons sur la Propagation des Ondes et lesEquations de l’Hydrodynamique. Chapter 6. Paris:Hermann.Hill, R. 1962. Acceleration waves in solids. J. of Mech. Phys.Sol., 10:1-10.Jaeger,, J.C. and Cook, N.G.W. 1971. Fundamentals of RockMechanics. London: Chapman and Hall.Krajcinovic, D. 1996. Damage Mechanics, Amsterdam-etc.:Elsevier.Lade, P.V. 1993. Rock strength criteria: The theories and theevidence. In E. T. Brown (ed.), Comprehensive Rockengineering I. Fundamentals: chapter 11:255-284, Oxford-etc.: Pergamon.Lawn,B. 1993. Fracture of brittle solids, Cambridge:Cambridge University Press.Martin, C.D. & Chandler, N.A. 1994, The progressive fractureof Lac du Bonnet granite, Int. J. of Rock Mech. and MiningSci. and Geomech. Abst., 31(6):643-659.Matolcsi T. 1992. Dynamic Laws in thermodynamics, PhysicsEssays, 8(4):457-465.Matolcsi T. 1996a. On the classification of phase transitions,ZAMP, 47:837-857.Matolcsi T. 1996b. On the dynamics of phase transitions,ZAMP, 47:858-879.Murell, S.A. F. 1963. A criterion for brittle fracture of rocksand concrete under triaxial stress and the effect of porepressure on the criterion. In C. Fairhurst (ed.), , Int. J. ofRock Mech. and Mining Sci. and Geomech. Abst.,31(6):643-659.Orowan, E. 1960. Mechanism of seismic faulting, In D. Griggsand J. Handin (ed.), Rock Deformation, 323-345.Rice, J. R. 1978. Thermodynamics of the quasi-static growth ofthe Griffith cracks J. of Mech. Phys. Sol., 26:61-78.Theocaris, P.S. 1987. Failure characterization of anisotropicmaterials by means of the Elliptic Paraboloid FailureCruterion. Adv. Mech. 10(3):83-101.Theocaris, P.S. 1999. Failure loci of some igneous andmetamorphic rocks. Rock Mech. Rock Eng., 32(4):267-290.Ván P. 2000, Internal thermodynamic variables and failure ofmicrocracked materials, submitted to J. Non-Equ. Therm.

[David Lauder]

Jo -

It will be midnight here in the UK and I will be bashing out lots of zzzzzzzzzzzzz's - enjoy your debating.

Regards