Сraig. Dental Materials

less than 1500 per year. Because dental materials can be subjected to moderate stresses repeated a large number of times, it is important in the design of a restoration to know what stress it can withstand for a predetermined number of cycles. Restorations should be designed so the clinical cyclic stresses are below the fatigue limit. Many gold cast alloys, for example, can withstand from 1 million to 25 million flexures without fracture when a stress below the yield stress is applied.

Fatigue fractures develop from small cracks and propagate through the grains of a material. In general, the causes of cyclic failure in a material are inhomogeneities and anisotropy of the material. These imperfections lead first to the development of microcracks, which coalesce and ultimately lead to a macroscopic crack and failure. Areas of stress concentration, such as surface defects and notches, are particularly dangerous and can lead to catastrophic failure.

Fatigue properties do not always relate closely to other mechanical properties. Some parameters that influence fatigue are grain size and shape, composition, texture, surface chemistry and roughness, material history (i.e., fabrication and heat treatment), and environment. For example, in dental appliances made of resin the internal stresses developed during the molding and processing tend to subject the structure to fatigue failure.

Note that the environment a material is subjected to is a critical factor in determining fatigue properties. Any environmental agent that can degrade a material will reduce fatigue strength. Therefore elevated temperatures, humidity, aqueous media, biological substances, and pH deviations away from neutral can all reduce fatigue properties. As a result, fatigue data, which are typically presented based on tests in laboratory air at room temperature, are not always relevant to the service conditions in the oral cavity. The higher temperature, humidity, saline environment with proteins, and fluctuating pH all tend to reduce fatigue strength from its level in the laboratory.

In the previous discussions of the relationship between stress and strain, the effect of load application rate was not considered. In many metals and brittle materials, the effect is rather small. However, the rate of loading is important in many materials, particularly polymers and soft tissues. The mechanical properties of many dental materials, such as agar, alginate, elastomeric impression materials and waxes; amalgam, and plastics; dentin, oral mucosa, and periodontal ligaments, are dependent on how fast they are stressed. For these materials, increasing the loading (strain) rate produces a different stress-strain curve with higher rates giving higher values for the elastic modulus, proportional limit, and ultimate strength. Materials that have mechanical properties independent of loading rate are termed elastic. Materials that have mechanical properties dependent on loading rate are termed viscoelastic.In other words, these materials have characteristics of an elastic solid and a (viscous) fluid. The properties of an elastic solid were previously discussed in detail. Before viscoelastic materials and properties are presented, fluid behavior and viscosity are reviewed.

FLUID BEHAVIOR AND VISCOSITY

In addition to the many solid dental materials that exhibit some fluid characteristics, many dental materials, such as cements and impression materials, are in the fluid state when formed. Therefore (viscous) fluid phenomena are important. Viscosity (7) is the resistance of a fluid to flow and is equal to the shear stress divided by the shear strain rate. or

When a cement or impression material sets, the viscosity increases, making it less viscous and more solid-like. The units of viscosity are poise, p (1 p = 0.1 Pa s = 0.1 N s/m2), but often data are reported in centipoise, cp (100 cp = 1 p). Some typical values of viscosity for dental materials are

Temperature Viscosity

Material

Cements Zinc phos-

phate

Zinc polyacrylate

Endodontic sealers

Fluid denture resins

Impression materials Agar Alginate Impression

plaster Polysullide,

light Polysulfide,

heavy Silicone, syringe Silicone, regular

Zinc oxideeugenol

listed in Table 4-11. As a basis for comparison, the viscosity of water at 20" C is 1 cp.

Rearranging the equation for viscosity, we see that fluid behavior can be described in terms of stress and strain, just like elastic solids.

In the case of an elastic solid, stress (o)is proportional to strain (€1, with the constant of proportionality being the modulus of elasticity

(E). The above equation indicates an analogous

Fig. 4-20 Force versus displacement of a spring, which can be used to model the elastic response of a solid.

(From Park JB: Biomaterials science and engineering, New York, 1984, Plenum Press, p 26.)

situation for a viscous fluid, where the (shear) stress is proportional to the strain rate and the constant of proportionality is the viscosity. The stress is therefore time dependent because it is a function of the strain rate, or rate of loading. To better comprehend the concept of strain rate dependence, consider two limiting cases-rapid and slow deformation. A material pulled extremely fast (dt -+ 0) results in an infinitely high stress, whereas a material pulled infinitesimally slow results in a stress of zero.

The behavior of elastic solids and viscous fluids can be understood from simple mechanical models. An elastic solid can be viewed as a spring (Fig. 4-20). When the spring is stretched by a force, 4 it displaces a distance, x.The applied force and resultant displacement are proportional, and the constant of proportionality is the spring constant, k. Therefore

Note that this relation is equivalent to

Also note that the model of an elastic element does not involve time. The spring acts instanta-

Strain rate (dddt)

Fig. 4-21 Stress versus strain rate for a dashpot, which can be used to model the response of a viscous fluid.

(From Park JB: Biomaterials science and engineering, New York, 1984, Plenum Press, p 26.)

neously when stretched. In other words, an elastic solid is independent of loading rate.

A viscous fluid can be viewed as a dashpot, or a shock absorber with a damping fluid

tional to the stress (z) and the constant of proportionality is the viscosity of the fluid (7).

Although the viscosity of a fluid is proportional to the shear rate, the proportionality differs for different fluids. Fluids may be classified as Newtonian, pseudoplastic, or dilatant depending on how their viscosity varies with shear rate, as shown in Fig. 4-22. The viscosity of a Newtonian liquid is constant and independent of shear rate. Certain dental cements and impression materials are Newtonian. The viscosity of a pseudoplastic liquid decreases with increasing shear rate. Several endodontic cements are pseudoplastic, as are monophase rubber impression materials. When subjected to low shear rates during spatulation or while an impression is made in a tray, these impression materials have a high viscosity and possess "body" in the tray. These materials, however, can also be used in a syringe, because at the higher shear rates encountered as they pass through the syringe tip, the viscosity decreases by as much as tenfold. The viscosity of a dilatant

Shear rate

Fig. 4-22 Shear diagrams of Newtonian, pseudoplastic, and dilatant liquids. The viscosity is shown by

the slope of the curve at a given shear rate.

liquid increases with increasing shear rate. Examples of dilatant liquids in dentistry include the fluid denture-base resins.

Two additional factors that influence the viscosity of a material are time and temperature. The viscosity of a non-setting liquid is typically independent of time and decreases with increasing temperature. Most dental materials, however, begin to set after the components have been mixed, and their viscosity increases with time, as evidenced by most dental cements and impression materials. A notable exception is a zinc oxideeugenol material that requires moisture to set. On the mixing pad, these materials maintain a constant viscosity that is described clinically as a long working time. Once placed in the mouth, however, the zinc oxide-eugenol materials show rapid increases in viscosity because exposure to heat and humidity accelerates the setting reaction.

In general, for a material that sets, viscosity increases with increasing temperature. However, the effect of heat on the viscosity of a material that sets depends on the nature of the setting reaction. For example, the initial viscosities of a zinc phosphate cement (material A) and a zinc

polycarboxylate cement (material B) are compared at three temperatures in Fig. 4-23. The setting reaction of A is highly exothermic, and mixing at reduced temperatures results in a lower viscosity than when mixed at higher temperatures. The setting reaction of B is less affected by temperature. Clinically, additional working time is achieved for these cements by the use of coolor frozen-slab mixing techniques.

VISCOELASTIC MATERIALS

For viscoelastic materials, altering the strain rate alters the stress-strain properties. The tear strength of alginate impression material, for example, is increased about four times when.the rate of loading is increased from 2.5 to 25 cm/ min. Another example of strain-rate dependence is the elastic modulus of dental amalgam, which is 21 GPa at slow rates of loading and 62 GPa at high rates of loading. A viscoelastic material therefore may have widely different mechanical properties depending on the rate of load appli-

cation, and for these materials it is particularly important to specify the loading rate with the test results.

Materials that have properties dependent on the strain rate are better characterized by relating stress or strain as a function of time. Two properties of importance to viscoelastic materials are stress relaxation and creep. Stress relaxation is the reduction in stress in a material subjected to constant strain, whereas creep is the increase in strain in a material under constant stress.

As an example of stress relaxation, consider how the load-time curves at constant deformation are important in the evaluation of orthodontic elastic bands. The decrease in load (or force) with time for a latex and a plastic band of the same size at a constant extension of 95 mm is shown in Fig. 4-24. The initial force was much greater with the plastic band, but the decrease in force with time was much less for the latex band. Therefore plastic bands are useful for applying high forces, although the force decreases rapidly with time, whereas latex bands apply lower

Fig. 4-25 Creep curves for conventional (low copper) and high-performance(high copper) amalgams.

(From O'BrienWJ: Dental materials: properties and selection, Chicago, 1989, Quintessence, p 25.)

forces, but the force decreases slowly with time in the mouth; latex bands are therefore useful for applying more sustained loads.

The importance of creep can be seen by interpreting the data in Fig. 4-25, which shows creep curves for lowand high-copper amalgam. For a given load at a given time, the low-copper amalgam has a greater strain. The implications and clinical importance of this are that the greater creep in the low-copper amalgam makes it more susceptible to strain accumulation and fracture, and also marginal breakdown, which can lead to secondary decay. Note that low-copper amalgam is no longer commonly used in dentistry.

MECHANICAL MODELS O F VlSCOELASTlClTY

Because a viscoelastic material may be viewed as a material exhibiting characteristics of both a solid and a fluid, we may also understand the behavior of a viscoelastic material in terms of combinations of the simple mechanical models of a spring and dashpot, introduced previously. Strain as a function of time for the various combinations is shown in Fig. 4-26. When a constant load is applied (at time to) to a spring (an ideal elastic element), an instantaneous strain occurs and the strain remains constant with time; when the load is removed (at time t,), the strain instantaneously decreases to zero. When a constant

,ldeal elastic element

ldeal viscous element

3

t

.C-

E I tj

load is applied to an ideal viscous element, the strain increases linearly with time, and when the load is removed, no further increase or decrease in strain is observed. The elastic element reacts instantaneously (changes strain) to a change in load, and the viscous element reacts after a finite time.

The relative time-course of spring and dashpot reactions is observed when the two ideal elements are combined. When a spring and viscous element are in series (a Maxwell model) and a fixed load is applied, a rapid increase in strain occurs and is followed by a linear increase in strain with time. The resultant strain, often referred to as the viscoelastic strain, represents a combination of elastic and viscous responses. The rapid increase in strain represents the elastic portion of the strain (i.e., response of the elastic spring), whereas the linear increase represents the viscous portion of the strain (i.e., response of the viscous component). When the load is removed an instantaneous recovery of the elastic strain occurs, but the viscous strain remains.

A constant load applied to a spring and viscous element in parallel (a Kelvin or Voigt model)

causes a nonlinear increase in strain with time as a result of the viscous element and reaches a constant value as a result of the spring. On removal of the load, the spring acts to decrease the strain to zero. However, the strain does not instantaneously diminish to zero because of the action of the dashpot. Note that real materials exhibit more complex behavior than these simple models predict, and modeling the strain-time properties requires a combination of the elements described. Impression materials such as agar, alginate, polysulfide, and silicone have been modeled by a Maxwell model in series with a Kelvin model.

An example of the importance of viscoelasticity lies with impression materials. Because these materials are viscoelastic, they d o not immediately lose their strain when a load is removed. Therefore on removal from the mouth, these materials remain stressed, and thus time is required for the material to recover before a die can be poured.

The viscoelasticity of the oral tissues also has important clinical implications. The palatal mucosa has little resistance to loading compared

Fig. 4-27 Displacement versus force for denture baseplates suppolted by six teeth and by mucosa alone. Loading rate was 4 Nisec.

(Adapted from Wills DJ, Manderson RD: J Dent 5:310, 1977.)

with the periodontal ligament. Thus denture baseplates supported by palatal mucosa show substantially more displacement as a function of load than those supported by teeth (Fig. 4-27). The creep of the palatal mucosa under load is sustained and recovery is prolonged and variable because the mechanism of deformation and recovery is controlled by physiological and physical factors. Making an impression of the mucosal tissues in their resting state therefore requires that the tissues be allowed to recover free of the denture for several hours. Teeth, on the other hand, will recover from load within minutes. Recording the mucosal tissues under load will result in recoil of these tissues, initially displacing the denture base and artificial teeth to a position superior to the natural teeth. However, the tissues will return to their displaced state on loading of the denture.

CREEP COMPLIANCE

A creep curve yields insight into the relative elastic, viscous, and anelastic response of a viscoelastic material; such curves can be interpreted in

terms of the molecular structure of the associated materials, which have structures that function as elastic, viscous, and anelastic elements. On removal of a load, a creep recovery curve can be obtained (Fig. 4-28). In such a curve, after the load is removed there is an instantaneous drop in strain and a slower strain decay to some steadystate strain value, which may be nonzero. The instantaneous drop in strain represents the recovery of elastic strain. The slower recovery represents the anelastic strain, and the remaining, permanent strain represents the viscous strain. A family of creep curves can be determined by using different loads. A more useful way of presenting these data is by calculating the creep compliance. Creep compliance (J,j is defined as strain divided by stress at a given time. Once a creep curve is obtained, a corresponding creep compliance curve can be calculated. The creep compliance curve shown in Fig. 4-29 is characterized by the equation

where Jo is the instantaneous elastic compliance, J, is the retarded elastic (anelastic) compliance, and t/q represents the viscous response at time t for a viscosity 11.The strain associated with Jo and JR is completely recoverable after the load is removed; however, the strain associated with J, is not recovered immediately but requires some finite time. The strain associated with t/q is not recovered and represents a permanent deformation. If a single creep compliance curve is calculated from a family of creep curves determined at different loads, the material is said to be linearly viscoelastic. Then the viscoelastic qualities can be described concisely by a single curve.

The creep compliance curve therefore permits an estimate of the relative amount of elastic, anelastic, and viscous behavior of a material. Jo indicates the flexibility and initial recovery after deformation, J, the amount of delayed recovery that can be expected, and t/q the magnitude of permanent deformation to be expected. Creep compliance curves for elastomeric impression materials are shown in Chapter 12, Fig. 12-25.

Time

Fig. 4-29 Creep compliance versus time for a viscoelastic material.

(Adapted from Duran RL, Powers JM, Craig RG: J Dent Res

%:I 801, 1979.)

mine dynamic modulus and a torsion pendulum used for impact testing, have been used to study viscoelastic materials such as dental polymers. Ultrasonic techniques have been used to determine elastic constants of viscoelastic materials such as dental amalgam and dentin. Impact testing has been applied primarily to brittle dental materials.

DYNAMIC MODULUS

The dynamic modulus (%)is defined as the ratio of stress to strain for small cyclical deformations at a given frequency and at a particular point on the stress-strain curve. When measured in a forced oscillation instrument, the dynamic modulus is computed by

Although static properties can often be related to the function of a material under dynamic conditions, there are limitations to using static properties to estimate the properties of materials subjected to dynamic loading. Static testing refers to continuous application of force at slow rates of loading, whereas dynamic testing involves cyclic loading or loading at high rates (commonly referred to as impact). Dynamic methods, including a forced oscillation technique used to deter-

where m is the mass of the vibrating yoke, q is the height divided by twice the area of the cylindrical specimen, and p is the angular frequency of the vibrations.

In conjunction with the dynamic modulus, values of internal friction and dynamic resilience can be determined. For example, cyclical stretching or compression of an elastomer results in irreversibly lost energy that manifests itself as heat. The internal friction of an elastomer is compara-

ble with the viscosity of a liquid. The value of internal friction is necessary to calculate the dynamic resilience,which is the ratio of energy lost to energy expended.

The dynamic modulus and dynamic resilience of some dental elastomers are listed in Table 4-12. These properties are affected by temperature (-15" to 37" C) for some maxillofacial elastomers, such as plasticized polyvinylchloride and polyurethane, but not so much for silicones. As shown in Table 4-12, the dynamic modulus decreases and the dynamic resilience increases as the temperature increases. As a tangible example, the dynamic resilience of a polymer used for an athletic mouth protector is a measure of the ability of the material to absorb energy from a blow and thereby protect the oral structure. Once the mouth protector has been worn, however, deterioration in properties is observed.

IMPACT STRENGTH

A material may have reasonably high static strength values, such as compressive, tensile, and shear strengths, and even reasonable elongation, but may fail when loaded under impact. Materials such as fused glasses, cements, amalgam, and some plastics have low resistance to breakage when a load is applied by an impact. Such a

sudden blow might correspond to the energy of impact resulting from an accident to a person wearing a restoration or from dropping the restoration on a floor.

The impact resistance of materials is determined from the total energy absorbed before fracture when struck by a sudden blow. Often a bar of material is supported as a beam and struck either at one end or in the middle with a weighted pendulum. A test specimen in an impact instrument is shown in Fig. 4-30. The energy absorbed by the blow can be determined by measuring the reduction in swing of the pendulum compared with the swing with no specimen present. The values are usually reported in joules, J (1J = 1 N m), for a specimen of a specific shape. Some substances offer relatively little resistance to the shock, whereas others of different composition may not fracture under the same impact. For example, the Charpy impact strength of unnotched specimens of denture resins ranges from 0.26 J for a conventional denture acrylic to 0.58 J for a rubber-modified acrylic resin.

TEAR STRENGTH AND TF$R

Tear strength is a measure of the resistance of a material to tearing forces. Tear strength is an

Fig. 4-30 Impact-testing instrument.

important property of dental polymers used in thin sections, such as flexible impression materials in interproximal areas, maxillofacial materials, and soft liners for dentures. Specimens are usually crescent shaped and notched. The tear strength of the notched specimen is calculated when the maximum load is divided by the thickness of the specimen, and the unit of tear strength is N/m.

Because of the viscoelastic nature of the materials tested, tear strength depends on the rate of loading. More rapid loading rates result in higher values of tear strength. Clinically, the rapid (or snap) removal of an alginate impression is recommended to maximize the tear strength and also to minimize permanent deformation. Typical values of tear strength are listed in Table 4-13 for some dental materials. The table indicates that the elastomeric impression materials have superior values of tear strength compared with agar and alginate hydrocolloids.

The tear energy (T) is a measure of the energy per unit area of newly torn surface and is deter-

mined from the load (F) required to propagate a tear in a trouser-shaped specimen by

where t is the specimen thickness and h is an extension ratio. Typical values of tear energy determined for some dental impression materials and maxillofacial materials are listed in Table 4-14.

Many materials used in dentistry are not homogeneous solids but consist of two or more essentially insoluble phases. There may be one continuous phase and one or more dispersed phases, or there may be two or more continuous phases, with each of these phases containing one or more dispersed phases. These materials are called composites. A composite can be generally defined as a combination of two or more different materials still present as separate entities in the final material. Although composites take advantage of selected properties of each material, the physical and mechanical properties of the composites are different from those of the