Characterisation Methods for VSs

With reference to the bone ingrowth requirements listed in Chapter 2, the porosity, pore size distribution and uni-axial compressive strength of the porous structures had to be determined. The measurements of these characteristics are detailed in the follow sections.

3.4.1. Porosity of Porous Material

The porosity of a porous material is determined by measuring the amount of void space inside the structure and determining what percentage of the total volume of the material is made up of void space. The porosity can be found using equation ( 3-2 ): 𝜌 ( 3-2 )

Where mass was measured by a balance (Adam Equipment, UK) with an accuracy of ±0.01g, the volume was measured by digital callipers with an accuracy of ±0.02mm.

3.4.2. Porosimetry

Mercury porosimetry was used to measure the pore size distribution. If mercury (non wetting liquid) is placed in contact with an open pore, the surface tension of the mercury acts along the line of contact with the pore which is equal to the perimeter of the pore. This surface tension creates a force to resist the mercury entry. The magnitude of this force is proportional to the length of the contact ( ), the surface tension ( ) of mercury, and the cosine of the contact angle ( ) as shown in Figure 3-17.

Figure 3-17 Liquid-solid contact angle for wetting and non wetting liquid.

If a circular pore is present at the surface, the force to resist the entry of mercury can be expressed as:

( 3-3 )

When external pressure is applied sufficiently, it forces the mercury over the interface of the pore and bridges the pore. The externally applied force, therefore, is the product of the pressure ( ) and area ( ) over which the pressure is applied. If a circular pore is at the surface, the externally applied force can be expressed as:

( 3-4 )

Liquid-solid contact angle Θ>90°

Porous structure material

Wetting liquid Non wetting liquid

When just before the force resisting the mercury entry is overcome, an equation is given as:

( 3-5 )

Therefore, for a given pressure, the mercury can intrude into a pore whose diameter is greater than:

( 3-6 )

By measuring the volume of mercury that intrudes into the porous material with each pressure change, the volume of the pore in the corresponding size is known. However, this technology cannot measure the blind pores and closed pores as shown in Figure 3-18. Even the open pore in cross-linked pores and though pores cannot be measured properly because the technique measures the largest entrance to a pore rather than the actual inner size of the pore. It therefore determines the largest connection from the sample surface to the pore rather than the pore.

Figure 3-18 Pore classifications .

In order to overcome the limitation involved in mercury porosimetry, a new method was provided by Bhattacharya [173] with quoted accuracy greater than 99.9% was used. This method is based on a digital porous structure model which can be obtained by various methods such as CT scanning. However large computing power

Blind pore

Closed pore

and memory are required in the new method. A revised method was provided to minimise the computation of the pore size distribution and is detailed in Chapter 4.

3.4.3. Uni-axial Compressive Stress and Strain Test

Uni-axial compressive testing is the most common method for determining the mechanical properties of bone ingrowth structures [77]. The bone ingrowth structure needs to be strong enough to support the applied loads in normal use without deformation. The cylindrical samples with dimensions of Ø15mm x 30mm (±0.1mm) were used for uni-axial compressive testing. In order to avoid edge effects, a height-to-thickness ratio of at least 1.5 and at least 7 cells in each direction was used. An Instron 4505 test machine with lubricated platens, to reduce the effect of frication was used with a cross-head speed of 25.4mm/min and a total displacement of 10mm [174,175]. From the resultant graph shown in Figure 3-19, the compressive strength was determined either at the intersection between the two red lines drawn along the initial loading slope and the stress plateau or the

initial peak stress if there was one following the procedure of Ashby [174].

Figure 3-19 Determination of the compressive strength for components that do not exhibit an initial peak stress.

0 20 40 60 80 100 120 0 5 10 15 20 25 30 35 St ress, 𝜎 , (M P a) Strain, ε, (%) Load cell 50KN

Cross-head speed 25.4mm/min Total displacement 10mm

3.5.

Summary

The software packages for designing the new custom software are listed in Table 3-1 and the software packages for creating, manipulating, repairing and slicing the solid model are summarised in Table 3-2. By using this software, the CAD data was converted into a version suitable for AM fabrication.

Table 3-1 Software packages

Programming language package Python 2.7

Scientific computing package Numpy 1.6.2

2D plot package Matplotlib 1.1.1

Visualization package VTK 5.6.0

GUI programming package PySide 1.1.2

PC performance profile package Psutil 0.6.1

Custom software distribution package Py2exe 0.6.9

Table 3-2 Software packages used in creating, manipulating, repairing and slicing the solid model.

Creating solid model with close surface Pro Engineer Wildfire 4 Manipulating and repairing a solid model in STL format Magics

Slicing a solid model and hatching close contours Realizer built-in software

The MCP SLM Realizer 100 was chosen to fabricate samples by laser melting the CpTi (average particle size 45µm) powder layer by layer. Before the fabrication, the parameters were developed and are listed in Table 3-3. The used powder was recycled and the samples were cleaned based on the method provided by Stryker Orthopaedics. The porosities of these samples were measured by gravimetric analysis and the pore size distribution was measured by mercury porosimetry. Finally uni-axial compressive testing to ASTM E9 was performed on the samples.

Table 3-3 Parameters for fabricating VSs.

Laser focus 1515 Laser input power 80W

CHAPTER 4