Elastic properties and strain-to-crack-initiation of calcium phosphate bone cements: Revelations of a high-resolution measurement technique

Abstract

Calcium phosphate cements (CPCs) should ideally have mechanical properties similar to those of the bone tissue the material is used to replace or repair. Usually, the compressive strength of the CPCs is reported and, more rarely, the elastic modulus. Conversely, scarce or no data are available on Poisson's ratio and strain-to-crack-initiation. This is unfortunate, as data on the elastic response is key to, e.g., numerical model accuracy. In this study, the compressive behaviour of brushite, monetite and apatite cements was fully characterised. Measurement of the surface strains was done using a digital image correlation (DIC) technique, and compared to results obtained with the commonly used built-in displacement measurement of the materials testers. The collected data showed that the use of fixed compression platens, as opposed to spherically seated ones, may in some cases underestimate the compressive strength by up to 40%. Also, the built-in measurements may underestimate the elastic modulus by up to 62% as compared to DIC measurements. Using DIC, the brushite cement was found to be much stiffer (24.3 ± 2.3GPa) than the apatite (13.5 ± 1.6GPa) and monetite (7.1 ± 1.0GPa) cements, and elastic moduli were inversely related to the porosity of the materials. Poisson's ratio was determined to be 0.26 ± 0.02 for brushite, 0.21 ± 0.02 for apatite and 0.20 ± 0.03 for monetite. All investigated CPCs showed low strain-to-crack-initiation (0.17-0.19%). In summary, the elastic modulus of CPCs is substantially higher than previously reported and it is concluded that an accurate procedure is a prerequisite in order to properly compare the mechanical properties of different CPC formulations. It is recommended to use spherically seated platens and measuring the strain at a relevant resolution and on the specimen surface.

Experimentally Achievable Accuracy Using a Digital Image Correlation Technique in measuring Small-Magnitude (<0.1%) Homogeneous Strain Fields

“…Although they should mimic the mechanical behavior of bone tissue, their mechanical properties are still far from optimal. In fact, CPCs are brittle [ 2 , 3 , 4 ], and the limited data available in the literature suggests that this material can only withstand small strain levels (range 0.1–0.2%) before failure [ 5 , 6 ]. Therefore, new CPC formulations are still under development [ 7 ].…”

A novel strategy to enhance interfacial adhesion in fiber-reinforced calcium phosphate cement

“…Although the bending strength values reported for CPCs are typically in the range of 5-15 MPa (Martin & Brown 1995;Ginebra et al 2001), close to that of trabecular bone (estimated between 10 and 20 MPa) (Barinov 2010), their strain to failure is much lower . The brittleness of CPCs has recently been highlighted in a report on their strain-to-crack-initiation, which amounted to a mere 0.2% in compression (Ajaxon et al 2017). An improvement of the mechanical performance of these materials, and particularly a mitigation of their brittle behavior, would significantly extend the applicability of CPCs.…”

Combining multi-scale 3D printing technologies to engineer reinforced hydrogel-ceramic interfaces

“…It has been mentioned in the literature that mechanical properties of self-setting ceramics are lower than high-temperature sintering ceramics [ 56 ]. Nevertheless, the scaffolds from this study still showed values in the physiological range reported for trabecular bone [ 54 , 55 ]. While sintering may further improve the mechanical strength of the constructs, this would prevent the direct incorporation and anchoring of lowmelting point thermoplastic polymers as presented in this study as a strategy to improve bone-to-soft tissue interfaces.…”

“…Tangent modulus, ultimate strength and energy to failure were characterized by performing unconfined compression tests and calculated from the stress-strain curves ( figure 4(B) , supple-mentary figures S4(A) and (B) ). Importantly, all formulations and pore designs exhibited compressive properties in the range of cancellous bone [ 54 , 55 ]. Tangent modulus, ultimate strength and energy to failure of scaffolds made from both NC-PCaP and C-PCaP gradually decreased with increasing porosity, as expected ( figures 4(B), (D) and supplementary figure S4(C) ).…”

“… Mechanical properties: (A) representative PCaP scaffold, (B) representative engineered stress-strain curves of C-PCaP scaffolds, (C) tangent modulus, (D) ultimate strength of NC-PCaP paste (grey) and C-PCaP paste (blue) scaffolds with different porosities. (Greyish-filled area showing range of tangent modulus of cancellous bone [10–5000 MPa [ 54 ]] (B) and ultimate strength [2–45 MPa [ 55 ]] (C)). …”