The mechanical properties of many dental materi- als, such as alginate, elastomeric impression mate- rials, waxes, amalgam, polymers, bone, dentin, oral mucosa, and periodontal ligaments, depend on how fast they are loaded. 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 ulti- mate strength. Materials that have mechanical prop- erties independent of loading rate are termed elastic.
In these materials, strain occurs when the load is applied. Other materials exhibit a lag in response when a load is applied. This time lag is referred to as a viscous response. Materials that have mechanical properties dependent on loading rate and exhibit both elastic and viscous behavior are termed visco- elastic. 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 their properties are presented, fluid behavior and viscosity are reviewed in the following section.
Fluid Behavior and Viscosity
In addition to the many solid dental materials that exhibit some fluid characteristics, many dental mate- rials, such as cements and impression materials, are in the fluid state when formed. Therefore fluid (vis- cous) phenomena are important. Viscosity (η) is the resistance of a fluid to flow and is equal to the shear stress divided by the shear strain rate, or:
η =τ/ dε/dt
When a cement or impression material sets, the viscosity increases, making it less viscous and more solidlike. 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).
Rearranging the equation for viscosity, we see that fluid behavior can be described in terms of stress and strain, just like elastic solids.
τ = η dε/dt
In the case of an elastic solid, stress (σ) is pro- portional to strain (ε), with the constant of propor- tionality being the modulus of elasticity (E). The aforementioned equation indicates a similar situ- ation for a viscous fluid, where the stress (shear) 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 lim- iting cases: rapid and slow deformation. A material pulled extremely fast (dt → 0) results in an infinitely Strain -
Strong Tough Stiff Ductile
Stress -
1
Strong Stiff Brittle
Strain - Flexible
Ductile Strong
Resilient Strong
Resilient Ductile Weak Flexible
Brittle
Flexible
Stress -
5 6 7
Flexible Brittle
8 2
Weak Stiff Ductile
3
Weak Stiff Brittle
4
Weak
FIG. 4.12 Stress-strain curves for materials with vari- ous combinations of properties.
high stress, whereas a material pulled infinitesi- mally slow results in a stress of zero. This concept will be important in understanding stress relaxation and delayed gelation phenomena, explored later in this chapter. The behavior of elastic solids and vis- cous fluids can be understood from studying simple mechanical models. An elastic solid can be viewed as a spring (Fig. 4.13). When the spring is stretched by a force, F, it displaces a distance, x. The applied force and resultant displacement are proportional, and the constant of proportionality is the spring constant, k.
Therefore, according to Hooke’s law:
F=kx
Note that this relation is equivalent to the equa- tion presented in the Stress-Strain Curves section of this chapter:
σ=Eε
Also note that the model of an elastic element does not involve time. The spring acts instantaneously when stretched. In other words, an elastic solid is independent of loading rate.
A viscous fluid can be viewed as a dashpot, or a piston moving through a viscous fluid (Fig. 4.14).
When the fluid-filled cylinder is pulled, the rate of strain (dε/dt) is proportional to the stress (τ) and the constant of proportionality is the viscosity of the fluid (π).
Although the viscosity of a fluid is proportional to the shear rate, the proportionality differs for different fluids. Fluids may be classified as newtonian, pseudo- plastic, or dilatant depending on how their viscosity varies with shear rate, as shown in Fig. 4.15. The viscos- ity of a newtonian fluid is constant and independent of shear rate. Some dental cements and impression mate- rials are newtonian. The viscosity of a pseudoplastic fluid decreases with increasing shear rate. Monophase
elastomeric impression materials are pseudoplastic.
When subjected to low shear rates during spatulation or while an impression material is loaded in a tray in preparation of placing it into the mouth, these impres- sion materials have a high viscosity and stay in place without flowing. 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. This charac- teristic is sometimes referred to as thixotropy, although that term actually describes the change in viscosity of a material with time. The tomato-based food condiment ketchup is also pseudoplastic, which makes it difficult to remove from a bottle. Shaking the bottle or rapping the side of the bottle increases its shear rate, decreases its viscosity, and improves its pourability. The viscosity of a dilatant fluid increases with increasing shear rate.
Examples of dilatant fluids in dentistry include the fluid denture base resins.
Slope (k) x
F Displacement (x)
Force (F)
F FIG. 4.13 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:
Plenum Press; 1984:26.)
x Slope ()
Newtonian fluid cylinder
Strain rate (d/dt)
Stress ()
F F
FIG. 4.14 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:
Plenum Press; 1984:26.)
Shear rate
Shear stress
Pseudoplastic Newtonian
Dilatant
FIG. 4.15 Shear diagrams of newtonian, pseudoplastic, and dilatant liquids. The viscosity is shown by the slope of the curve at a given shear rate.
Viscoelastic Materials
For viscoelastic materials, the strain rate can alter 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. Alginate impressions should there- fore be removed from the mouth quickly to improve their tear resistance. Another example of strain-rate dependence is the elastic modulus of dental amal- gam, which is 21 GPa at slow rates of loading and 62 GPa at high rates of loading. A viscoelastic mate- rial therefore may have widely different mechanical properties depending on the rate of load application, 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 relax- ation 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 deforma- tion are important in the evaluation of orthodontic elastic bands. The decrease in load (or force) with time for rubber and plastic bands of the same size at a constant extension of 95 mm is shown in Fig.
4.16. The initial force was much greater with the plastic band, but the decrease in force with time was much less for the rubber band. Therefore plastic bands are useful for applying high forces, although the force decreases rapidly with time, whereas rubber bands apply lower forces, but the force decreases slowly with time in the mouth;
rubber bands are therefore useful for applying more sustained loads.
The importance of creep can be seen by interpre- tation of the data in Fig. 4.17, which shows creep curves for low- and 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. The high creep behavior of low-copper amalgam contrib- uted to its decline in popularity.
Creep Compliance
A creep curve yields insight into the relative elas- tic, viscous, and inelastic 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, vis- cous, and inelastic elements. Creep recovery curves are produced from data collected during removal of a load (Fig. 4.18). In such a curve, after the load 500
400 300 200 100
12 3 4 56 7 8 1 5 10 15 20 Hours
Load (g)
Days
Latex Plastic
FIG. 4.16 Decrease in load of latex rubber and plas- tic bands as a function of time at a constant extension of 95 mm. (From Craig RG, ed. Dental Materials: A Problem- Oriented Approach. St. Louis: Mosby; 1978.)
Conventional allo y
High-performance alloy 0.24
0.16
0.08
2 4 8 12
Time (hours)
16 20 24
Strain
FIG. 4.17 Creep curves for conventional (low-copper) and high-performance (high-copper) amalgams. (From O’Brien WJ. Dental Materials: Properties and Selection.
Chicago: Quintessence; 1989:25.)
Remove load Apply load
Time
Strain A
C B
FIG. 4.18 Creep recovery curve showing (A) elastic, (B) anelastic, and (C) viscous strain.
is removed, there is an instantaneous drop in strain and slower strain decay to some steady-state strain value, which may be nonzero. The instantaneous drop in strain represents the recovery of elastic strain. The slower recovery represents the inelastic strain, and the remaining, permanent strain repre- sents the viscous strain. A family of creep curves can be determined by using different loads. A more use- ful way of presenting these data is by calculating the creep compliance. Creep compliance (Jt) 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. 4.19 is characterized by the following equation:
Jt=J0+JR+ t/η
where J0 is the instantaneous elastic compliance, JR
is the retarded elastic (inelastic) compliance, and t/η represents the viscous response at time t for a viscosity η. The strain associated with J0 and JR is completely recoverable after the load is removed;
however, the strain associated with JR is not recov- ered immediately but requires some finite time. The strain associated with t/η is not recovered and rep- resents 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. In this case, the vis- coelastic qualities can be described concisely by a single curve.
The creep compliance curve therefore permits an estimate of the relative amount of elastic, inelastic, and viscous behavior of a material. J0 indicates the flexibility and initial recovery after deformation, JR the amount of delayed recovery that can be expected, and t/η the magnitude of permanent deformation to be expected. Creep compliance curves for elasto- meric impression materials are shown in Chapter 12, Fig. 12.17.