By the end of this chapter you will have developed a conceptual foundation of the reasons for fracture of restorative materials and a basic framework of design features that will enhance your ability to increase the fracture resistance of restorative materials in the oral environment. This knowledge will allow you to differentiate the potential causes of clinical failures that may be attributed to material deficiencies, design features, dentist errors, technician errors, or patient factors such as diet, biting force magnitude, and force orientation. However, a familiarity with the key terms is essential to understand the principles involved in the load-versus-deformation behavior of dental biomaterials.
Stress intensity (stress intensity factor)—Relative increase in stress at the tip of a crack of given shape and size when the crack surfaces are displaced in the opening mode (also Fracture Toughness).
Elastic solids may be stiff or flexible, hard or soft, brittle or ductile, and fragile or tough. However, these are qualitative mechanical properties that do not describe how similar or dissimilar dental materials of the same type may be. Mechanical properties are defined by the laws of mechanics—that is, the physical science dealing with forces that act on bodies and the resultant motion, deformation, or stresses that those bodies experience. This chapter focuses primarily on static bodies—those at rest—rather than on dynamic bodies, which are in motion. However, fatigue properties, determined from cyclic loading, are also important for brittle materials, as discussed later. Mechanical properties of importance to dentistry include brittleness, compressive strength, ductility, elastic modulus, fatigue limit, flexural modulus, flexural strength, fracture toughness, hardness, impact strength, malleability, percent elongation, Poisson’s ratio, proportional limit, shear modulus, shear strength, tensile strength, torsional strength, yield strength, and Young’s modulus.
All mechanical properties are measures of the resistance of a material to deformation, crack growth, or fracture under an applied force or pressure and the induced stress. An important factor in the design of a dental prosthesis is strength, a mechanical property of a material, which ensures that the prosthesis serves its intended functions effectively and safely over extended periods of time. In a general sense, strength is the ability of the prosthesis to resist induced stress without fracture or permanent deformation (plastic strain). Plastic deformation occurs when the elastic stress limit (proportional limit) of the prosthesis material is exceeded. Although strength is an important factor, it is not a reliable property for estimating the survival probabilities over time of prostheses made of brittle material because strength increases with specimen size and stressing rate, decreases with the number of stress cycles, and is strongly affected by surface processing damage. Thus, strength is not a true property of a material compared with fracture toughness, which more accurately describes the resistance to crack propagation of brittle materials.
Why do dental restorations or prostheses fracture after a few years or many years of service? The simplest answer is that the mastication force exerted by the patient during the final mastication cycle (loading and unloading) has induced a failure level of stress in the restoration. But why did the fracture not occur during the first month or year of clinical service? One can assume that the stress required to fracture a restoration must decrease somehow over time, possibly because of the very slow propagation of minute flaws to become microcracks through a cyclic fatigue process. The failure potential of a prosthesis under applied forces is related to the mechanical properties and the microstructure of the prosthetic material. Mechanical properties are the measured responses, both elastic (reversible upon force reduction) and plastic (irreversible or nonelastic), of materials under an applied force, distribution of forces, or pressure. Mechanical properties are expressed most often in units of stress and/or strain. The stressing rate is also of importance since the strength of brittle materials increase with an increase in the rate at which stress is induced within their structures. They represent measures of (1) elastic or reversible deformation (e.g., proportional limit, resilience, and modulus of elasticity); (2) plastic or irreversible deformation (e.g., percent elongation and hardness); or (3) a combination of elastic and plastic-deformation (e.g., toughness and yield strength). To discuss these properties, one must first understand the concepts of stress and strain and the differences between force, pressure, and stress.
When a force or pressure is exerted on an elastic solid, the atoms or molecules respond in some way at and below the area of loading, but the applied force has an equal and opposite reaction at the area at some other point in the structure (e.g., an area that supports the solid and resists its movement). Although we assume for simplicity that the stress induced in the material structure is uniform between the loaded surface and the resisting surface, this is clearly not the case. In fact, the stress induced near the surface decreases with distance from the loading point and increases as the supporting surface is approached. This pattern is called a stress distribution or stress gradient.
For the elastic solid in question, the atoms may be compressed in such a way that their interatomic equilibrium distances are decreased temporarily until the force is decreased or eliminated. However, if the force is increased further, it is possible that the atoms will be displaced permanently or their bonds ruptured. Dental restorations should be designed such that permanent displacement of atoms or rupture of interatomic bonds does not occur except possibly at surface areas where normal wear may occur.
The physical process by which atoms or molecules become displaced from their equilibrium positions under the application of an external force or pressure is related to yielding or plastic deformation on a broader scale. Stress is the force per unit area acting on millions of atoms or molecules in a given plane of a material. Except for certain flexural situations, such as four-point flexure, and certain nonuniform object shapes, stress typically decreases as a function of distance from the area of the applied force or applied pressure. Thus, stress distributions in an elastic solid are rarely uniform or constant. However, for purposes of determining mechanical properties, we assume that the stresses are uniformly distributed.
For dental applications, there are several types of stresses that develop according to the nature of the applied forces and the object’s shape. These include tensile stress, shear stress, and compressive stress. The strength of a material is defined as the average level of stress at which it exhibits a certain degree of initial plastic deformation (yield strength) or at which fracture occurs (ultimate strength) in test specimens of the same shape and size. Strength is dependent on several factors, including the (1) stressing rate, (2) shape of the test specimen, (3) size of the specimen, (4) surface finish (which controls the relative size and number of surface flaws), (5) number of stressing cycles, and (5) environment in which the material is tested. However, the clinical strength of brittle materials (such as ceramics, amalgams, composites, and cements) is reduced when large flaws are present or if stress concentration areas exist because of improper design of a prosthetic component (such as a notch along a section of a clasp arm on a partial denture). Under these conditions a clinical prosthesis may fracture at a much lower applied force because the localized stress exceeds the strength of the material at the critical location of the flaw (stress concentration).
When one chews a hard food particle against a ceramic crown, the atomic structure of the crown is slightly deformed elastically by the force of mastication. If only elastic deformation occurs, the surface of the crown will recover completely when the force is eliminated. Elastic stresses in materials do not cause permanent (irreversible) deformation. On the other hand, stresses greater than the proportional limit cause permanent deformation and, if high enough, may cause fracture. For brittle materials that exhibit only elastic deformation and do not plastically deform, stresses at or slightly above the maximal elastic stress (proportional limit) result in fracture. These mechanical properties of brittle dental materials are important for the dentist to understand in designing a restoration or making adjustments to a prosthesis.
Based on Newton’s third law of motion (i.e., for every action there is an equal and opposite reaction), when an external force acts on a solid, a reaction occurs to oppose this force which is equal in magnitude but opposite in direction to the external force. The stress produced within the solid material is equal to the applied force divided by the area over which it acts. A tensile force produces tensile stress, a compressive force produces compressive stress, and a shear force produces shear stress. A bending force can produce all three types of stresses, but in most cases fracture occurs because of the tensile stress component. In this situation, the tensile and compressive stresses are principal axial stresses, whereas the shear stress represents a combination of tensile and compressive components.
When stress is induced by an external force or pressure, deformation or strain occurs. As an illustration, assume that a stretching or tensile force of 200 newtons (N) is applied to a wire 0.000002 m2 in cross-sectional area. The tensile stress (σ), by definition, is the tensile force per unit area perpendicular to the force direction:
The SI unit of stress or pressure is the pascal, which has the symbol Pa, that is equal to 1 N/m2, 0.00014504 lbs/in2 in Imperial units, or 9.9 × 10−6 atmospheres. Because the wire has fractured at a stress of 100 megapascals (MPa), its tensile strength is 100 MPa, where 1 MPa = 1 N/mm2 = 145.04 psi.
In the English or Imperial system of measurement, the stress is expressed in pounds per square inch. However, the megapascal unit is preferred because it is consistent with the SI system of units. SI stands for Systéme Internationale d’ Unités (International System of Units) for length, time, electrical current, thermodynamic temperature, luminous intensity, mass, and amount of substance.
The pound-force (lbf) is not an SI unit of force or weight. It is equal to a mass of 1 pound multiplied by the standard acceleration of gravity on earth (9.80665 m/s2). The newton (N) is the SI unit of force, named after Sir Isaac Newton. To illustrate the magnitude of 1 MPa, consider a McDonald’s quarter-pound hamburger (0.25 lbf or 113 g before cooking) suspended from a 1.19-mm-diameter monofilament fishing line. The stress per unit area within the line is 1 N/mm2, or 1 MPa. If the line is 1.0 m long and if it stretches 0.001 m under the load, the strain (ε) is the change in length, Δl, per unit original length, lo, or
We can conclude that the line reaches a stress of 1 MPa at a tensile strain of 0.1%. Note that although strain is a dimensionless quantity, units such as meter per meter or centimeter per centimeter are often used to remind one of the system of units employed in the actual measurement. The accepted equivalent in the English system is inch per inch, foot per foot, and so forth.
Burnishing of a cast metal margin is a process sometimes used to reduce the width of a gap between the crown margin and the tooth surface. For a metal with relatively high ductility and moderate yield strength, application of a high pressure against the margin will plastically deform the margin and reduce the gap width. However, because elastic deformation has also occurred, the margin will spring back as elastic strain decreases during the decrease in pressure. Thus, burnishing the margin will close the gap only to the extent of the plastic deformation (strain) that is induced during burnishing.
Strain, or the change in length per unit length, is the relative deformation of an object subjected to a stress. Strain may be either elastic, plastic, elastic and plastic, or viscoelastic. Elastic strain is reversible. The object fully recovers its original shape when the force is removed. Plastic strain represents a permanent deformation of the material; it does not decrease when the force is removed. When a prosthetic component such as a clasp arm on a partial denture is deformed past the elastic limit into the plastic deformation region, elastic plus plastic deformation has occurred, but only the elastic strain is recovered when the force is released. Thus, when an adjustment is made by bending an orthodontic wire, a margin of a metal crown, or a denture clasp, the plastic strain is permanent but the wire, margin, or clasp springs back a certain amount as elastic strain recovery occurs.
Viscoelastic materials deform by exhibiting both viscous and elastic characteristics. These materials exhibit both properties and a time-dependent strain behavior. Elastic strain (deformation) typically results from stretching but not rupturing of atomic or molecular bonds in an ordered solid, whereas the viscous component of viscoelastic strain results from the rearrangement of atoms or molecules within amorphous materials.
Stress is described by its magnitude and the type of deformation it produces. Three types of “simple” stresses can be classified: tensile, compressive, and shear. Complex stresses, such as those produced by applied forces that cause flexural or torsional deformation, are discussed in the section on flexural stress.
A tensile stress is always accompanied by tensile strain, but it is very difficult to generate pure tensile stress in a body—that is, a stress caused by a load that tends to stretch or elongate a body. The reason is that if a slight amount of bending (flexure) occurs during tensile loading, the resulting stress distribution will consist of tension, compression, and shear components. The microtensile test is designed to load a test specimen along its long axis and the testing machine fixtures often have a toggle or freely rotating attachment that minimizes the misalignment of loaded specimen with the loading axis of the testing machine.
There are few pure tensile stress situations in dentistry. However, a tensile stress can be generated when structures are flexed. The deformation of a bridge and the diametral compression of a cylinder described later represent examples of these complex stress situations. In fixed prosthodontics clinics, a sticky candy (e.g., Jujube, a sticky/gummy candy) can be used to remove crowns by means of a tensile force when patients try to open their mouths after the candy has mechanically bonded to opposing teeth or crowns. However, tensile, compressive, and shear stresses can also be produced by a bending force, as shown in Figure 4-1 and as discussed in the following sections. Because most dental materials are quite brittle, they are highly susceptible to crack initiation in the presence of surface flaws when subjected to tensile stress, such as when they are subjected to flexural loading. Although some brittle materials can be strong, they fracture with little warning because little or no plastic deformation occurs to indicate high levels of stress.
When a body is placed under a load that tends to compress or shorten it, the internal resistance to such a load is called a compressive stress. A compressive stress is associated with a compressive strain. To calculate compressive stress, the applied force is divided by the cross-sectional area perpendicular to the axis of the applied force.
This type of stress tends to resist the sliding or twisting of one portion of a body over another. Shear stress can also be produced by a twisting or torsional action on a material. For example, if a force is applied along the surface of tooth enamel by a sharp-edged instrument parallel to the interface between the enamel and an orthodontic bracket, the bracket may debond by shear stress failure of the resin luting agent. Shear stress is calculated by dividing the force by the area parallel to the force direction.
In the mouth, shear failure is unlikely to occur for at least four reasons: (1) Many of the brittle materials in restored tooth surfaces generally have rough, curved surfaces. (2) The presence of chamfers, bevels, or changes in curvature of a bonded tooth surface would also make shear failure of a bonded material highly unlikely. (3) To produce shear failure, the applied force must be located immediately adjacent to the interface, as shown in Figure 4-2, B. This is quite difficult to accomplish even under experimental conditions, where polished, flat interfaces are used. The farther away from the interface the load is applied, the more likely it is that tensile failure rather than shear failure will occur because the potential for bending stresses would increase. (4) Because the tensile strength of brittle materials is usually well below their shear strength values, tensile failure is more likely to occur.
Examples of flexural stresses produced in a three-unit fixed dental prosthesis (FDP) and a two-unit cantilever FDP are illustrated in Figures 4-1, A, and 4-1, B, respectively. These stresses are produced by bending forces in dental appliances in one of two ways: (1) by subjecting a structure such as an FDP to three-point loading, whereby the endpoints are fixed and a force is applied between these endpoints, as in Figure 4-1, A; and (2) by subjecting a cantilevered structure that is supported at only one end to a load along any part of the unsupported section, as in Figure 4-1, B. Also, when a patient bites into an object, the anterior teeth receive forces that are at an angle to their long axes, thereby creating flexural stresses within the teeth.
As shown in Figure 4-1, A, tensile stress develops on the tissue side of the FDP, and compressive stress develops on the occlusal side. Between these two areas is the neutral axis that represents a state with no tensile stress and no compressive stress. For a cantilevered FDP such as that shown in Figure 4-1, B, the maximum tensile stress develops within the occlusal surface area since it is the surface that is becoming more convex (indicating a stretching action). If you can visualize this unit bending downward toward the tissue, the upper surface becomes more convex or stretched (tensile region) and the opposite surface becomes compressed. As explained in the section on stress concentration, these areas of tension represent potential fracture initiation sites in most materials, especially in brittle materials that have little or no plastic deformation potential.
Shown in Figure 4-2 is a bonded two-material system with the white atoms of material A shown above the interface and the shaded atoms of material B shown below the interface. The atoms are represented over six atomic planes, although dental structures have millions of atomic planes. However, the principles of stress and strain apply in both cases. In the upper section of Figure 4-2, A, a shear force is applied at distance d/2 from interface A-B. As this force increases in magnitude, it first produces an elastic shear strain (lower section of Figure 4-2), which will return to zero strain when the shear force is removed. As shown in Figure 4-2, B, if the shear force on the external surface is increased sufficiently, a permanent or plastic deformation will be produced.
For the case in Figure 4-2, B, the force is applied along interface A-B and not at a distance away, as shown in Figure 4-2, A. Because of this application of force along the interface, pure shear stress and shear strain develop only within the interfacial region. Because atoms have been displaced at near-neighbor locations, localized plastic deformation has also occurred. In the lower section of Figure 4-2, B, the force has been released and a permanent strain of one atomic space has occurred. For Figure 4-2, A, the stress induced is not pure shear since the force is applied at a distance from the interface. This is the reason why most shear bond tests do not actually measure shear strength but a tensile component of bending stress. These strength values are reported erroneously as shear strength rather than “apparent shear strength,” which indicates that pure shear was unlikely.
Mechanical properties and parameters that are measures of the elastic strain or plastic strain behavior of dental materials include elastic modulus (also called Young’s modulus or modulus of elasticity), dynamic Young’s modulus (determined by the measurement of ultrasonic wave velocity), shear modulus, flexibility, resilience, and Poisson’s ratio. Other properties that are determined from stresses at the highest stress end of the elastic region of the stress-strain graph or within the initial plastic deformation region (proportional limit, elastic limit, and yield strength) are described in the following section on strength properties.
The word stiffness should come to mind upon reading one of these three terms in the dental literature. Elastic modulus describes the relative stiffness or rigidity of a material, which is measured by the slope of the elastic region of the stress-strain graph. Shown in Figure 4-3 is a stress-strain graph for a stainless steel orthodontic wire that has been subjected to a tensile force. The ultimate tensile strength, yield strength (0.2% offset), proportional limit, and elastic modulus are shown in the figure. This figure represents a plot of true stress versus strain because the force has been divided by the changing cross-sectional area as the wire was being stretched. The straight-line region represents reversible elastic deformation, because the stress remains below the proportional limit of 1020 MPa, and the curved region represents irreversible plastic deformation, which is not recovered when the wire fractures at a stress of 1625 MPa. However, the elastic strain (approximately 0.52%) is fully recovered when the force is released or after the wire fractures. We can see this easily by bending a wire in our hands a slight amount and then reducing the force. Assuming that the induced stress has not exceeded the proportional limit, it straightens back to its original shape as the force is decreased to zero.
This principle of elastic recovery is illustrated in Figure 4-4 for a burnishing procedure of an open metal margin (top, left), where a dental abrasive stone is shown rotating against the metal margin (top, right) to close the marginal gap as a result of elastic plus plastic strain. However, after the force is removed, the margin springs back an amount equal to the total elastic strain. Only by removing the crown from a tooth or die can total closure be accomplished. Because we must provide at least 25 µm of clearance for the cement, total burnishing on the tooth or die is usually adequate since the amount of elastic strain recovery is relatively small.
Shown in Figure 4-5 is a stress-strain graph for enamel and dentin that have been subjected to compressive stress. These curves were constructed from typical values of elastic moduli, proportional limit, and ultimate compressive strength reported in the scientific literature. If the tensile stress below the proportional limit in Figure 4-3 or the compressive stress (below the proportional limit) in Figure 4-5 is divided by its corresponding strain value, that is, tensile stress/tensile strain or compressive stress/compressive strain, a constant of proportionality will be obtained that is known as the elastic modulus, modulus of elasticity, or Young’s modulus. These terms are designated by the letter E. The units of E are usually expressed as MPa for highly flexible materials or GPa for most stiffer restorative materials. The slope of the straight-line region (elastic range) of the stress-strain graph is a measure of the relative rigidity or stiffness of a material. Although the stiffness of a dental prosthesis can increase by increasing its thickness, the elastic modulus does not change. The elastic modulus has a constant value that describes a material’s relative stiffness as determined from a stress-strain graph, which compensates for differences in cross-sectional area and length by plotting force per unit area by the relative change in dimension, usually length, relative to its initial value.
Variations in values of proportional limit, elastic modulus, and ultimate compressive strength have been reported for enamel and dentin relative to the area of the tooth from which the test specimens were obtained. Note that the proportional limit, ultimate compressive strength, and elastic modulus of enamel are greater than the corresponding values for dentin (Figure 4-5). In fact, the elastic modulus of enamel is about three times greater than that of dentin and, depending on the study considered, it can be as much as seven times higher. Dentin is capable of sustaining significant plastic deformation under compressive loading before it fractures. Thus, enamel is a stiffer and more brittle material than dentin and unsupported enamel is more susceptible to fracture. Conversely dentin is more flexible and tougher.
Because the elastic modulus of a material is a constant, it is unaffected by the amount of elastic or plastic stress induced in the material. It is independent of the ductility of a material, since it is measured in the linear region of the stress-strain plot. Thus, elastic modulus is not a measure of its plasticity or strength. Materials with a high elastic modulus can have either high or low strength values. Although a compressive test was selected to measure the properties of tooth structures in Figure 4-5, the elastic modulus can also be measured by means of a tensile test.
Because the elastic modulus represents the ratio of the elastic stress to the elastic strain, it follows that the lower the strain for a given stress, the greater the value of the modulus. For example, if one wire is much more difficult to bend than another of the same shape and size, considerably higher stress must be induced before a desired strain or deformation can be produced in the stiffer wire. Such a material would possess a comparatively high modulus of elasticity. A polyether impression material has a greater stiffness (elastic modulus) than all other elastomeric impression materials. Thus, a greater force is needed to remove an impression tray from undercut areas in the mouth. The modulus of elasticity of most dental biomaterials is given in units of giganewtons per square meter (GN/m2), also referred to as gigapascals (GPa). This property is indirectly related to other mechanical properties. For example, two materials may have the same proportional limit but their elastic moduli may differ considerably.