Jerarquía de procesos

The mechanical properties of any foam are related to its structure and the

properties of the material of which the cell walls are made. Important

structural features of a foam are its relative density, the degree to which its

cells are open or closed and the anisotropy of the foam. Crucial cell wall

properties are the solid density, Young’s Modulus, yield strength, fracture

strength and creep parameters of the solid material.

As mentioned previously conventional methods of mechanical testing are

unsuitable when applied to porous materials due to the difficulties

encountered with machining and gripping the test pieces. Compression

testing has been successfully employed for the characterisation of

cancellous bone and has also been adopted for the testing of porous

hydroxyapatite.

Porosity within ceramics can be described as either micro or macro and open

or closed. Micro porosity generally involves pores measuring 1pm and less

and macropores as anything above that.

Gibson et al (1997) have successfully predicted the mechanical behaviour of

cellular solids and highly porous materials, by modelling the structure as an

elastic brittle foam (see figure 6.3). From the relationship between ultimate

Production and characterisation of porous hydroxyapatite Suzanne Calicut either open or closed cell models (equation 6.7). Mechanical properties of

low-density structures such as porous ceramics and cancellous bone can

also be modelled to their relative density by equation 6.7

o — Cl

T

Equation 6.7 Where

a = Ultimate compressive strength

— = Relative density p *

p = Apparent density

p*= Real density

Where X=2 in an open celled isotropic foam, and x=1 for a closed cell

isotropic foam. C^ is the proportionality constant and is dependent on the

structure of the strut material, Whitehouse and Dyson (1974) found the

proportionality constant to be reduced when closed porosity formed during

processing was present within the ceramic struts.

Porous ceramics when under a compressive stress will generally deform by

Production and characterisation of porous hydroxyapatite ___________________________________________________ Suzanne Calicut Linear elasticity at low strain rates is generally controlled by cell wall bending

which is followed by a collapse plateau controlled by the brittle crushing of

the individual cells followed by a region of densification controlled by the

crushing of the solid cell walls, in which the stress rises steeply. Increasing

the relative density of the foam will increase the Young’s Modulus, raise the

plateau stress and reduce the strain at which densification starts.

Linear elastic

Densification Collapse plateau

Q .

Strain

Figure 6.3 Stress-strain relationship of an elastic brittle foam

Liu (1997) investigated the influence of porosity and pore size on the

compression strength of porous hydroxyapatite produced using burn out

techniques involving polyvinyl butyral particles. The author found that the

compressive strength correlated linearly with macropore size and that

ceramics with smaller macropores gave higher compressive strength results

than those with larger pores. However, Lange and Miller (1987) found the

Production and characterisation of porous hydroxyapatite ___________________________________________________ Suzanne Calicut using reticulated foam technology to be independent of cell size. They also

found that there was a large scatter in data, which appeared to be related to

the processing variations and defects such as cracks within the cell struts

and specimen density variations.

Le Huec et al (1995) studied the influence of porosity on the mechanical

strength of calcium phosphate ceramics. The samples had open porosity

with total volumes of between 20-60% and pore sizes between 5 and 400pm.

The authors found that there was a decrease in compressive strength with

increased porosity, which was related to a decrease in the quantity of solid

material present in each specimen. It was also noted that the larger pores

had a greater influence upon the compressive strength than the micropores,

this observation is concurrent with the findings of Griffiths (1920) on the

rupture of ceramic materials, who found that the maximum theoretical stress

at rupture is inversely proportional to the dimensions of the fissure. The

authors concluded that there was a marked decrease in compressive

strength with increased porosity and that not only total porosity but also pore

size have to be optimised to optimise the compressive strength.

Goretta et al (1990) studied the mechanical behaviour of porous open cell

alumina at room and at high temperatures, they found that at room

temperature the foam's mechanical properties obeyed the relationships

predicted by Gibson and Ashby based on failure by bending of individual

Production and characterisation of porous hydroxyapatite ___________________________________________________ Suzanne Calicut from the model and these deviations were attributed to microstructural

irregularities such as broken or spilt struts or closed cells. They also found

that the mechanical strengths and fracture toughness values were improved

when tested at 900°C but were significantly poorer at 1200°C, this was

attributed to creep deformation.

Hing et al (1999) characterised porous commercially produced

hydroxyapatite (Endobon®) in terms of its mechanical properties, macro and

microstructure. All of the specimens were found to fail in an elastic brittle

type mechanism. However, individual specimens mechanical properties were

highly dependent on their apparent density, this relationship between the

strength and apparent density of isotropic specimens was best described by

a quadratic relationship and in anisotropic specimens by a linear relationship.

It was found that an increase in apparent density from 0.38 to 1.25g cm'^

Production and characterisation of porous hydroxyapatite Suzanne Calicut

Chapter 7