Selección de Procesos y Subprocesos para la valoración cualitativa

The application o f ceramic materials as surgical implants requires an understanding o f the mechanical properties. The load a ceramic must withstand under physiological conditions depends on the structural nature and microstructural characteristics inherent to it. It is commonly known that ceramics are hard but brittle materials, properties that are influenced by the nature o f the ionic and covalent bonding. In contrast, metals and polymers can exhibit ductile behaviour and differ altogether in their structural nature from ceramics. It is therefore important to address the various physical properties that form the basis o f the techniques used for mechanical testing.

2.10.1 Elasticity

Elasticity is a term that refers to the extent o f deformation as a consequence o f applying a load on a material and reflects the slight change in atomic spacing. The atomic bond strength o f the material, the stress, and the temperature influence the deformation o f the material. Deformation can also be referred to as strain s, and the load defined in terms o f stress a. When stress is applied to a material it undergoes a level o f strain up to a point known as the limit o f proportionality. Prior to this point the strain is reversible, that is, any deformation in shape and change in atomic spacing that occurs can be reversed thus returning the material to its original state. This behaviour is known as elastic deformation which can be expressed by the following relationship, where E is the modulus o f elasticity or Young’s modulus

D evelopm ent o f G lass R einforced H ydroxyapatite for H ard Tissue Surgery G eorge G eorgiou Where <7 E 8 E e stress elastic modulus strain

(Tensile stress) E q uation 21

Similarly, an expression can also be given for shear stress, a form o f loading that is applied on a plane o f unit area:

Where T G G y : shear stress : Shear modulus : strain E q uation 22 Brittle fracture Stress — Elastic Strain

F igu re 37. Graph showing elasticity on the linear portion o f the stress-strain curve.90

At certain temperatures ceramics will behave elastically until they reach a level o f stress that causes fracture, this is known as brittle fracture (Figure 37). Beyond a certain stress

D evelopm ent o f G lass R einforced ] lydrox.yapaiiie for Hard Tissue Surgery G eoriie G eorgiou

materials behave plastically, this term refers to materials that undergo permanent deformation and do not return to their original state (Figure 38). This behaviour can also be denoted as plastic deformation or plastic strain and is a characteristic seen in metals.^^’^®^ Plastic behaviour can occur in different ways, in aluminium for instance the transition from elastic strain to plastic strain is smooth (Figure 38(a)). However, in other materials the initial plastic strain is discontinuous and can be described as a region beyond the elastic limit where the stress increases the strain until a yield point where the stress drops a little as the sample is stretched slightly (Figure 38(b)). Further stretching increases the stress from a lower yield point.

Stress Yield strength Tensile strength Tensile Breaking Plastic strength Elastic Strain a _strength Yield point Stress Breaking strength Plastic Elastic Strain (a)

(b)

F igure 38. Graphs illustrating plastic as well as elastic behaviour.90

The brittle behaviour does not hold true for all ceramics. Ceramics having the rock salt structure display plastic deformation, this is primarily due to the dislocations that occur within the cubic structure. At room temperature and under sustained loading ceramics such as LiF, NaCl and MgO belonging to this cubic symmetry undergo plastic deformation.^®

D evelopm ent o f Glass R einforced Hydroxyapatite for Hard Tissue S urgery G eorge G eorgiou

2.10.2 Modulus o f elasticity

Having established that the modulus o f elasticity E represents the proportional region o f a stress-strain curve and more specifically the amount o f stress cj required to produce a unit elastic strain E = — E q u ation 23 S Where B : elastic modulus CJ : stress c : strain

It is therefore essential to consider the structural aspects, in terms o f the atomic bonds, that contribute to the magnitude o f the elastic modulus.

Materials that possess a high modulus o f elasticity reflect the strength o f the atomic bonding. An increase in the inter-atomic spacing requires a greater amount o f stress for materials that have strong atomic bonding, hence they exhibit a greater modulus o f e l a s t i c i t y . T h e modulus o f elasticity for materials that have weak ionic bonds compared to those with strong covalent bonds differ. NaCl adopts the cubic structure that contains weak ionic bonds, therefore a low modulus o f elasticity is expected. This is measured at 44.2GN.m‘^ for NaCl. Diamond, however, possessing strong covalent bonds has a significantly greater modulus o f about 1035GN.m'^. This trend is much the same for metals as it is for ceramics or other materials.^®

D evelopm ent o f G lass R einforced MydroKyapatite for Hard Tissue Surgery G eorge G eorgiou

Different crystallographic directions have shown to vary in bond strength and hence in modulus o f elasticity. Materials posses anisotropy, this is simply a difference in bond strength in a given orientation. An example o f this anisotropy can be shown for a single crystal o f iron belonging to the body centred cubic structure. The elastic modulus is shown to differ for two planes o f orientation, the [1 1 1] direction and the [1 0 0] direction which

display values o f 283GN.m'^ and 124GN.m'^ respectively. The higher value shown in one direction represents those atoms that are most closely packed and also the greater density o f the [1 1 1] direction compared to the [1 0 0] direction.^^

Polycrystalline ceramics, though, contain many crystals in random orientation. Polycrystalline ceramics have a single elastic moduli that is obtained from the average o f the elastic moduli for various crystallographic directions from individual crystals. However, the anisotropy must be taken into careful consideration when selecting a ceramic because it presents a degree o f internal stress to the material and does have an effect on the application o f the material. ^

Thermal expansion, which occurs as a consequence o f heating the ceramic, causes a decrease in the modulus o f elasticity and corresponds to an increase in the inter-atomic

90

spacing.

Materials consisting o f more than one composition have an elastic modulus that is the sum o f the moduli o f the constituent phases and can be estimated using the law o f mixtures:

D evelopm ent o f G lass Rem forced HydroKyapatite for Hard Tissue Surgery G eorge G eorgiou

E

EaVa + EyVb

: Elastic moduli o f a and b respectively : Volume fraction o f a and b respectively

E q u ation 24

Examples o f such materials include glass or carbon-reinforced organics and glass-bonded ceramics.

A relationship for the effect o f porosity on the elastic moduli can also be given. This assumes that the presence o f porosity in a material always gives a decrease in modulus:

Where

Eo

P