Research Paper
Time-dependent failure of amorphous poly-d,l-lactide: Influence of molecular weight

https://doi.org/10.1016/j.jmbbm.2012.04.014Get rights and content

Abstract

The specific time-dependent deformation response of amorphous poly(lactic acid) (PLA) is known to lead to rapid failure of these materials in load-bearing situations. We have investigated this phenomenon in uniaxial compression on P(L)DLLA samples with various molecular weights. The experiments revealed a strong dependence of the yield stress on the applied strain rate. Lower molecular weights showed identical deformation kinetics as higher molecular weights, albeit at lower stress values. This dependence on molecular weight was incorporated into an Eyring-equation by introducing mobility through a virtual temperature that is shifted by the deviation of the Tg from Tg,∞. Stress-dependent lifetime of polymer constructs was described by the use of this modified Eyring-equation, combined with a critical plastic strain. This model proves useful in predicting the molecular weight dependence of the time to failure, although it slightly overestimates life time at low stress levels for a material with very low molecular weight. The versatility of the model is demonstrated on e-beam sterilized PLDLLA, where the resulting reduction in molecular weight induces a substantial decrease in lifetime. A single Tg measurement provides sufficient information to predict the decrease in lifetime.

Introduction

Polylactic acid (PLA) fibers have been used successfully as resorbable suture materials for many years (Gupta et al., 2007). Recently, these materials (Middleton and Tipton, 2000) have also gained interest for use in orthopedic applications such as bone screws (Brkaric et al., 2007), plates (Athanasiou et al., 1998) and spinal cages (Smit et al., 2007, Smit et al., 2008). The main difference between these two situations is that in sutures—a soft tissue application—the material is generally not under substantial mechanical load, whereas in orthopedic applications the loads can be significant. These large loads may lead to rapid failure of polymer constructs, even when their magnitude is well below the instantaneous mechanical strength of the material (Ender and Andrews, 1965, Matz et al., 1972, Narisawa et al., 1978, Teoh and Cherry, 1984). As a result of the difference in stress states, the lifetime of a suture depends largely on the rate of hydrolytic degradation, whereas, in the case of an orthopedic implant, the time-dependent deformation of the material is also expected to play a significant role. It is moreover, not inconceivable that the deformation kinetics are influenced by the changes occurring in the material due to (hydrolytic) degradation, i.e. an increase in end-group concentration and a reduction in chain length. This degradation may be induced during use, but also during sterilization, potentially leading to significant differences in strength between sterilized and unsterilized constructs. Such an effect was recently observed by Smit et al. (2007), who found more rapid failure of e-beam sterilized spinal cages, compared to unsterilized constructs, under physiologically relevant loads. To more generally evaluate the applicability of polylactides as a construction material for medical implants, we investigated the intrinsic mechanical properties of the material as a function of molecular weight, and subsequently attempted to construct a model with predictive power for the lifetime at a specific applied load, taking changes in molecular weight into account.

Considerable effort has been directed towards the development of models that allow prediction of the intrinsic time-dependent deformation (Boyce and Arruda, 1990, Buckley and Jones, 1995, Haward and Thackray, 1968, Klompen et al., 2005a) and enabled a quantitative analysis of short-term and long-term failure in glassy polymers. The focus in this research area has largely been on glassy polymers and has been successful for e.g. polycarbonate (PC) (van Breemen et al., 2011, Boyce and Arruda, 1990, Klompen et al., 2005a, Klompen et al., 2005b), polystyrene (PS) (Wu and Buckley, 2004, van Melick et al., 2003a, van Melick et al., 2003b), and poly(methyl methacrylate) (PMMA) (Arruda et al., 1995, van Breemen et al., 2009), but also proved to be applicable to semi-crystalline polymers (van Erp et al., 2009) and composites (Govaert and Peijs, 2000, Govaert et al., 2001). These models do not incorporate a dependence of the intrinsic deformation kinetics on molecular weight of the polymer. It has, however, been argued that when the molecular weight of polylactides decreases, changes in kinetics may occur, leading to unexpectedly rapid failure (Smit et al., 2007). A promising starting point for describing such behavior is the observation by Fox and Flory (1950) that the glass transition temperature of a polymer drops rapidly when the molecular weight drops below a threshold value. Since both deformation kinetics and glass transitions are governed by segmental motion of the polymer chain it is reasonable to assume that there is a connection between them. Wu and Buckley previously proposed this concept and incorporated changes in average molecular weight into their model by incorporating the influence of chain ends on the Vogel temperature, thus allowing accurate prediction of the molecular weight dependence of the yield stress of polystyrene (Wu and Buckley, 2004). We propose a similar approach by incorporation of the influence of chain ends on mobility by including the shift in glass transition directly into the deformation kinetics.

Section snippets

Materials

The polymers used to determine the Fox-Flory parameters for poly-d,l-lactides were either standards purchased from Polysource in (0.95, 2.3, 4.12, and 7.6 kg mol–1) or commercial samples provided by Purac Biomaterials in Gorinchem, the Netherlands (3.88, 10.7, 56.5, and 209 kg mol–1). The average molecular weights (Mn) of the materials from Purac were calculated from the inherent viscosity in chloroform, as provided by the manufacturer, using the technique described by Solomon and Ciuta (1962) and

The model

The stress-activated flow of (highly) viscous liquids can be described with the Eyring flow equation as proposed by Henry Eyring in 1936 (Eyring, 1936)ε̇pl(σ,T)=ε̇0exp(ΔURT)sinh(σVkBT)where ε̇pl is the plastic flow rate, ε̇0 a reference rate constant, ΔU the activation energy, R the gas constant, T the ambient temperature, σ the applied stress, V the activation volume and kB Boltzmann's constant. This approach proves very useful for the prediction of the strain rate- and temperature

Conclusions

We have proposed a model that incorporates the effect of molecular weight, and molecular degradation, on the creep rupture performance of glassy PLA. The approach is based on the hypothesis that the main-chain segmental mobility of the chain is governed by the relative undercooling with respect to Tg. Hence, the increased mobility caused by a molecular-weight induced decrease in Tg should be equivalent to the that of an infinitely long chain at a virtual temperature T˜, which is defined as the

Acknowledgment

This work is part of the Research Program of the Dutch Polymer Institute DPI, Eindhoven, the Netherlands, project number #614.

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