TIME-DEPENDENT FAILURE IN LOAD-BEARING POLYMERS A ... · Time-Dependent Failure in Load-Bearing...

In: Degradable Polymers for Skeletal Implants ISBN 978-1- 60692-426-6 Editors: P.I.J.M. Wuisman and T. M. Smit, pp. © 2008 Nova Science Publishers, Inc. Chapter 2

TIME-DEPENDENT FAILURE IN LOAD-BEARING POLYMERS. A POTENTIAL HAZARD IN STRUCTURAL

APPLICATIONS OF POLYLACTIDES

Leon E. Govaert1, Tom A.P. Engels1, Serge H.M. Söntjens1, and Theo H. Smit2

1. Eindhoven University of Technology, Mechanical Engineering, Polymer Technology

2. VU Medical Centre, Amsterdam and Skeletal Tissue Engineering Group Amsterdam

ABSTRACT Polylactides are commonly praised for their excellent mechanical properties (e.g. a high

modulus and yield strength). In combination with their bioresorbability and biocompatibility, they are considered prime candidates for application in load-bearing biomedical implants.

Unfortunately, however, their long-term performance under static load is far from impressive. In a previous in vivo study on degradable polylactide spinal cages in a goat model it was observed that, although short-term mechanical and real-time degradation experiments predicted otherwise, the implants failed prematurely under the specified loads. In this chapter we demonstrate that this premature failure is attributed to the time-dependent character of the material used. The phenomenon is common to all polymers, and finds its origin in stress-activated segmental molecular mobility leading to a steady rate of plastic flow. The main conclusion is that knowledge of the instantaneous strength of a polymeric material is insufficient to predict its long-term performance.

INTRODUCTION

When skeletal structures or tissues fail due to trauma or disease, additional support is

required to take over their mechanical function. For example, in spinal diseases leading to degeneration, instability and/or severe deformations, fusion of one or more spinal segments may be indicated. Devices used for this purpose not only should maintain or restore the spinal anatomy, but also create the proper mechanical environment for bony fusion. As bones and implants must resist considerable loads, metal is a popular material for this purpose.

Although metal implants are routinely used and quite successful, there also are some drawbacks. In the first place: metals (and non-degradable polymers alike) are permanent materials and as such remain susceptible to long-term complications like wear [1], migration

Leon E. Govaert, Tom A.P. Engels, Serge H.M. Söntjens et al. 2

[2], and late foreign body reactions [3;4]. For this reason, some surgeons recommend to remove all metallic implants used for fixation [5]. Worldwide, the removal of the metallic hardware varies from a routine procedure in all patients (Germany, Australia), to selective removal only from patients with symptoms (e.g. Netherlands) [6]. In the USA, retrieval surgeries for the spine were reported in 25-40% of the patients [7-9]. A second disadvantage of metal implants is that they eclipse the fusion zone on radiological imaging. It is in fact impossible to determine whether healing has been achieved within a metal implant or not. In case of persistent back pain, this is a complicating factor to determine surgical success or failure. Finally, metal implants cause stress shielding over the fusion area, resulting in delayed unions. Obviously, these are undesired properties for fixation implants aiming at healing or fusion.

Skeletal fixation devices essentially have a temporary function: once healing is achieved, removal is desired both from the clinical and biomechanical point of view. Indeed, living bone itself is the optimal mechanical support, because living bone is a self-optimizing tissue through mechanical adaptations [10-12]. Furthermore, with permanent implants there always will remain a possible risk for long-term complications. These considerations motivated the development of degradable polymer implants [13-16], which have evident advantages over metal devices: their stiffness is comparable to that of bone; they do not interfere with radiography, computer tomography, or magnetic resonance imaging [17]; and they degrade over time and thus eliminate the necessity of retrieval surgeries. In addition, the healing process may be stimulated by the successive loss of their mechanical properties, thereby gradually increasing the loads on the healing tissues. This concept of degradable polymers for skeletal tissue regeneration has amply been described, but its practical implementation remains challenging, in particular for load-bearing implants as used in trauma or spine.

Although degradable polymers are interesting materials for surgical implants, there are some caveats. First, polymer degradation can cause a severe host tissue responses: late complications like osteolytic reactions have been reported with the use of different polyester implants [18-24]. Degradation and intensity of the inflammatory response are influenced by implant related factors (polymer type, purity, crystallinity, design, processing techniques), and environment related factors (implantation site, vascularization, micro-motion, dynamic loading) [25-27]. New implants thus should be carefully evaluated at their specific anatomic location before clinical introduction.

Mechanical strength is a second concern of degradable polymers: the skeleton -in particular the spine and long bones- is subject to relatively large amplitudes of dynamic loading. Polymers not only have limited strength as compared to metals, but they also appear to degrade faster under such conditions [25;28]. Early loss of mechanical strength of the implants destabilizes the spinal segment, thus causing non-unions and clinical failure. Another observation in pre-clinical studies is the plastic deformation of implants made of 70/30 PLDLLA [29]. Cages which apparently had sufficient strength for bearing spinal loads during at least eight months appeared to have been broken and deformed after only three months (Figure 1). It appeared in additional studies, that the mechanical strength of 70/30 PLDLLA was lower for lower loading rates, higher temperature, and higher humidity [30]. Thus, 70/30 PLDLLA appears to show strong time-and load-dependent behaviour which is typical for glassy polymers [31].

Time-Dependent Failure in Load-Bearing Polymers 3

Figure 1. A 70/30 PLDLLA cage after three and six months follow-up in a goat spine. Histology shows micro-cracks already after three months of implantation. Micro-MRI confirms that micro-cracks are formed and also shows some plastic deformation of the cage. After six months, severe deformation of the cage is typically seen, along with failed fusion [29].

This chapter addresses this typical mechanical behaviour of glassy polymers. First, the phenomenology of delayed failure in glassy polymers is discussed. The problem is in fact quite well-known in non-degradable polymers like polycarbonate. Subsequently, the time-dependent behaviour of three amorphous polylactides is quantified in a series of short- and long-term loading experiments. It will be shown that the time-dependency of glassy polylactides is so strong, that early failure under static loading conditions can be explained.

DELAYED FAILURE IN POLYMERS

Phenomenology

Let us first illustrate the problem at hand. In Figure 2a the stress-strain curve of

polycarbonate (PC), a ductile glassy polymer, is shown, measured at a constant strain rate of 10-2 s-1 in uniaxial extension. Initially the material displays a linear region, where the stress increases proportionally with strain. At higher stresses the response becomes non-linear and subsequently reaches a maximum; the so-called yield stress. This maximum marks the onset of plastic deformation, and soon after the material displays necking, a strain-localization phenomenon [32]. In this process a localized plastic deformation zone is formed that subsequently propagates along the entire length of the specimen whereas the applied force


Figure 2. Deformation behavior of polycarbonate in uniaxial extension. a) Tensile test at a constant strain-rate of 10-2 s-1. b) Creep test under a constant load of 55 MPa.

remains almost constant. Upon further straining the material breaks at a stress level that depends strongly on molecular weight [33,34]. Please note, from a mechanical point of view, the moment of neck initiation is where the material is regarded to fail as this is the point where it loses it mechanical integrity.

We are now confronted with the question whether the information in the stress-strain curve in Figure 2a (short-term), can be used to determine the maximum load level that can be sustained without failure over the lifetime of our product: the design strength. In the case of construction metals, this is usually the yield strength, as static loads below this level will only induce macroscopic elastic deformations. In other words: for metals any static load below the yield strength can be endured almost indefinitely1.

Unfortunately, the situation is more complicated in case of polymers. To illustrate this we perform an experiment were we load an identical sample, with the same strain rate, to a stress value of 55 MPa, about 15% below the yield stress. Subsequently this load is kept constant over time. The material’s response to this excitation is shown in Figure 2b. Under the applied static stress the polymer displays a time-dependent mechanical response. The deformation of the sample is observed to increase gradually in time, and after a short while it deforms at a constant rate of strain. At longer loading times the deformation rate increases and the material subsequently fails after being loaded for only 9 hrs. The observed mode of failure is very similar to that observed in the short-term tensile test; necking. For this reason the phenomenon is sometimes referred to as delayed yielding [35,36].

The time-scale on which polycarbonate fails, proves to depend strongly on the level of the applied load. This is illustrated in Figure 3a, which gives the creep response of polycarbonate for three different stress levels. The higher the stress level, the faster the material deforms and fails. The stress-dependence of the time-to-failure is shown in Figure 3b. A semi-logarithmic relation is observed where a decrease in stress of approximately 3 MPa leads to an increase in lifespan by an order of ten. This brings us to the remarkable insight that, in the case of polymers, it is not the question whether the material will fail under static load, but rather when it will fail under the specified load.

1 This does not hold for cyclic loading where fatigue failure may occur.

b a


Figure 3. a) Deformation of polycarbonate under various constant stress levels. The markers indicate the point where necking occurs (ductile failure). b) Stress dependence of the time-to-failure, taken from (a).

Origin

Let us now examine the physical background of the observed time-dependent failure

process. Amorphous polymers consist of long, covalently-bonded molecules that are randomly distributed throughout the material. Each molecule has the ability to change its spatial conformation by rotation over covalent bonds that form the back-bone of the chain, and in its equilibrium state a random coil will be the most probable conformation. The rate at which a chain can change its conformation depends strongly on temperature. At high temperature conformational changes are fast and the chains can move freely with applied deformation (rubberlike behavior). At low temperature (below the glass transition temperature), chain mobility decreases drastically and the material virtually “vitrifies” [37] (becomes glass-like). Here it is essential to realize that changes in chain conformation are still feasible! However, due to the extremely low mobility of the chains, these conformational amendments are generally not observable within practical experimental time scales. This situation changes drastically upon the application of stress. Similar to temperature, applied stress enhances main-chain mobility and, as a result, the effects of changes in chain conformations become visible.

To demonstrate the profound influence of applied stress and temperature on chain mobility we take a closer look at the deformation behavior of a polymer glass around the yield point. In Figure 4a the stress-strain curves of PC are presented for 2 temperatures at various strain rates. The yield stresses determined from these experiments (maxima of the curves), are plotted in Figure 4b as a function of the applied strain rate. Typically, the yield stress is observed to increase with increasing strain rate and decreasing temperature [38].

In the initial stage of loading, where the stress is still low, chain mobility will be negligible, and the modulus is determined by the intermolecular interactions between

a b


individual chains. With increasing stress, the chain mobility increases and changes in chain conformation gradually start to contribute to the deformation of the material. This contribution progressively increases, until it reaches a stress level where the plastic strain rate resulting from chain mobility exactly matches the one experimentally applied; the yield stress. In other words, applied stress induces a state of enhanced molecular mobility that stimulates a dynamic rearrangement of molecular segments, resulting in a steady rate of plastic flow. The magnitude of this plastic flow rate depends on the applied stress and temperature.

For further illustration we consider the deformation of PC under static stress; the creep curves in Figure 3a. From this figure we determine the evolution of strain rate as a function of strain, a so-called Sherby-Dorn plot [39] (Figure 5a).

Figure 4. a) Stress-strain curves for polycarbonate at various strain rates (10-4, 10-3 and 10-2 s-1) and temperatures. b) Yield stress as a function of strain rate for various temperatures.

Figure 5. a) Evolution of strain rate during creep at various loads (derived from the data in Figure 2a). b) Stress as a function of strain rate. Tensile experiments (open symbols), creep experiments (closed symbols).

a b

b a


Figure 6. Intrinsic deformation behavior of PC in uniaxial compression (a) at a constant compressive strain rate of 10-2 s-1, (b) under a constant true compressive stress of 64 MPa.

In this plot we can observe that, at each load, the strain rate initially decreases (primary creep) until it reaches a steady state of flow, where the strain rate remains more or less constant (secondary creep). It was first demonstrated by Bauwens-Crowet et al. [40] that the steady state obtained in static loading is identical to that obtained at the yield stress in a constant strain rate experiment. This is demonstrated in Figure 5b, that presents the steady state values of stress and strain rate obtained from tensile tests at constant strain rate and creep tests under static load. Both yield exactly the same curve.

In summary: we now established that applied stress induces a state of enhanced molecular mobility in polymer glasses that results in a steady rate of plastic flow. The question that remains is: how does this lead to strain localization and subsequent failure?

Intrinsic Deformation Behavior To understand the reason for strain localization, we have to study the stress-strain

response in an experimental set-up in which a sample can deform homogeneously up to large plastic deformations. Examples of such techniques are uniaxial compression tests [41,42] or video-controlled tensile tests [43], and the stress-strain curves thus obtained are generally referred to as the intrinsic stress-strain response. An illustrative example is presented in Figure 6a, which shows the intrinsic response of PC in an uniaxial compression test at a constant rate of strain. In contrast to the behavior in uniaxial extension, the sample does not display necking but deforms homogeneously over the entire strain range covered. After the yield point, the intrinsic stress-strain response of polymer glasses displays two characteristic phenomena: strain softening, the initial decrease of true stress with strain, and strain hardening, the subsequent upswing of the true stress-strain curve (Figure 6a). Strain hardening is generally interpreted as the result of a stress contribution of the orienting molecular network [41,42,44] A similar picture is observed for the response to a constant true compressive stress (Figure 6b). Comparable to figure 1b, the static load induces a steady rate of plastic flow. Plastic deformation accumulates steadily, until, at a critical level of plastic

a b


strain, strain softening sets in and the deformation rapidly increases until it is stabilized by strain hardening [45].

Figure 7. Intrinsic deformation behavior of PC in uniaxial compression (a) influence of applied strain rate, (b) influence of physical aging.

Regarding the intrinsic mechanical response of glassy polymers, there are two time-dependencies that need to be considered [31]. The first one we already encountered: it is the time-dependence of the mechanical properties itself. The influence of strain rate on the intrinsic behavior of polycarbonate is presented in Figure 7a. With increasing strain rate the yield stress increases similarly to the observations in Figure 3a,b. Moreover, an identical effect is observed in the post-yield region, where the curves shift upwards by the same amount as the yield stress.

The second time-dependency that is of importance is the influence of the age of the material. Polymer glasses are generally not in thermodynamic equilibrium and, as a result, display a persistent drive towards it (physical aging), leading to a gradual change in mechanical properties over time [46,47]. This process can be accelerated by storing the material at an elevated temperature below its glass transition temperature; a heat-treatment called annealing. In Figure 7b, the intrinsic response of an annealed sample of PC is compared to that of a rapidly cooled sample (quenched). It is clear that physical aging results in an increase of both modulus and yield stress, but upon plastic deformation the differences between the curves disappear and eventually they fully coincide at a strain of approximately 0.2. Apparently all influence of thermal history is erased at that strain and both samples are transformed to a similar, mechanically ‘rejuvenated’ state [31,48].

From Figure 7b it is obvious that an increase of yield stress, due to a thermal treatment, will directly imply an increase in strain softening. The influence of molecular weight on the intrinsic response is usually small and negligible [31], which makes thermal history the key factor in influencing the intrinsic properties of a specific polymer glass. A change in thermal history will also reflect in the long-term failure behavior of polymer glasses [45]. This is demonstrated for PC in Figure 8a,b. Figure 8a presents the yield stress vs. strain rate in uniaxial extension for quenched and annealed PC. As a result of annealing the yield stress increases, but the kinetics (slope of the curve) remain unchanged. As can be witnessed in Figure 8b, the increase in yield stress is accompanied by an improvement in the life-time under constant stress. Depending on the effectiveness of the treatment, the improvement may be by orders of magnitude [45]. The second point of interest is that the slope of applied stress

a b


versus the logarithm of time to failure is the same for both thermodynamic states. Moreover, the absolute value of this slope is virtually identical to that observed for the yield stress versus the logarithm of strain rate [40,45] (Figure 8a).

With respect to the mode of failure, it is in particular the post-yield characteristics of the polymer, i.e. strain softening and strain hardening, that play a determining role [48,49]. In the vicinity of stress concentrations, strain softening will inevitably lead to the formation of localized plastic deformation zones (DZ’s). The initial size and evolution of the DZ is determined by a subtle interplay between the amount of strain softening and the amount of strain hardening. If the strain hardening is sufficiently strong, the DZ’s are stabilized and expand in a controlled fashion to the bulk of the material. Typical examples of such ductile behavior are shear band formation and necking. In the case of insufficient strain hardening, on the other hand, the material will be inclined to deform plastically by crazing, extremely localized zones of plastic deformation that act as a precursor for cracks and thus induce a brittle failure mode [48,49].

To illustrate this we compare the mechanical responses of PC and polystyrene (PS). Most striking here is the difference in macroscopic failure behavior of PC, which shows a ductile failure mode (necking) and PS, which fails in a fully brittle fashion (Figure 9a).

Figure 8. a) Yield stress vs. strain rate in uniaxial extension for annealed and quenched PC. b) Time-to-failure vs. applied stress for annealed and quenched PC.

a b

b a


Figure 9. a) Mode of failure of PC (ductile) and PS (brittle). b) Comparison of the intrinsic deformation behavior of PC and PS.

This can be rationalized by the differences in the intrinsic stress-strain curves of PC and PS presented in Figure 9b. In uniaxial compression, both polymers behave ductile and can be deformed to high compressive strains. Polystyrene exhibits pronounced strain softening and only a weak contribution of the strain hardening. In uniaxial extension, strain localizations cannot be stabilized and evolve almost without limits. As a result this extreme strain localization leads to the initiation of crazes, and, ultimately, macroscopic failure. Polycarbonate, on the other hand, displays only a moderate amount of strain softening and a much stronger contribution of the strain hardening. Localized plastic deformation zones, induced by strain softening, are now stabilized and spread out to other regions in the material. As a result a larger volume participates in the deformation and shear yielding and stable necking are observed. Nevertheless, also polycarbonate will initiate crazes if a more severe localization is introduced by changing the geometry of the test, e.g. by adding a notch [34,50].

As we explained above, the amount of strain softening can be altered by thermal treatments, like annealing. Even small changes in yield stress can have major consequences for the macroscopic deformation behavior. For instance, a subtle increase in strain softening induced by annealing, leads to severe localization of strain and brittle fracture in low-molecular weight polycarbonate [45, 49]. On the other hand, by removing strain softening through mechanical pre-conditioning [51], PS becomes ductile and can be deformed in uniaxial extension up to strains of 30%. These experiments clearly indicate the dominant role of strain softening in localization and failure of glassy polymers.

Predictability of Failure So far, we have established that applied stress induces a state of enhanced molecular

mobility in polymer glasses that stimulates a dynamic rearrangement of molecular segments, resulting in a steady rate of plastic flow. The deformation can propagate at this steady pace until strain softening sets in, accelerating the rate of deformation initiating a localized plastic deformation zone; catastrophic failure occurs.

A successful prediction of time-dependent failure under static and dynamic excitations can be obtained by application of a constitutive model able to capture the intrinsic deformation characteristics of glassy polymers [45,52] (Figure 7ab). However, this method requires a substantial investigation of the mechanical performance of the polymer glass. If we limit ourselves to a single loading geometry (uniaxial compression or tension) the approach is rather straight forward. In the physical picture described above, a logical first step towards lifetime prediction is the prediction of the plastic flow rate as a function of applied stress and temperature ( , )pl Tε σ . In most cases the kinetics can be captured excellently by a simple

Eyring flow rule [53]. Subsequently, it is hypothesized that strain softening always sets in at the same critical

plastic strain εcr. The lifetime under load tfail can then be estimated by:


( , )ε

ε σ= cr

failpl

tT

(1)

Figure 10. a) Compressive stress-strain curves of PLLA, PDLLA, and PLDLLA at a strain rate of 10-3s-1. b) Compressive stress-strain curves of PLDLLA at strain rates of 10-4, 10-3 and 10-2 s-1; influence of applied strain rate.

In this straightforward approach the kinetics of failure under static stress are directly linked, and therefore identical, to the kinetics of plastic flow. This is exactly what is observed in practice (see Figure 8a, b), and consequently the approach proved very successful in predicting time-dependent failure of PC and PVC in long-term static loading [54,55]. Equivalent expressions were also successfully applied to predict failure in static and dynamic loading conditions for other polymers [56-58].

Delayed Failure of Polylactides

Materials In this study we set out to capture the deformation behavior of amorphous

polylactides. In the field of biomedical resorbable implants used as structural fixation components in the spine, mostly amorphous PLDLLA is used [59-64]. This choice is related to the fact that degradation times of semi-crystalline PLA are longer than needed and that unfavorable inflammatory responses can occur when highly crystalline debris is left after degradation of the amorphous phase [23,65]. Since we use observations on amorphous PLDLLA resorbable spinal cages as a starting point [29,30], this investigation will be restricted to amorphous PLA’s.

From the available polylactides, we chose three different materials: a homochiral poly(L,L-lactide) (PLLA) with a glass transition temperature of 58°C, a racemic co-polymer poly(D,L-lactide) (PDLLA) with a glass transition temperature of 42°C, and a 70:30 copolymer of L-lactide and D,L-lactide (PLDLLA) with a glass transition temperature of 52°C. All materials were studied in the fully amorphous state. For this purpose PLLA was rapidly quenched from the melt to avoid crystallization. The other two are amorphous by nature.

a b


Mechanical Evaluation The intrinsic mechanical responses of all three materials, measured in uniaxial

compression at a constant strain rate, are presented in Figure 10a. The differences between the three materials appear only minor. The main difference is the value of the yield stress; i.e. PDLLA (78 MPa), PLDLLA (71 MPa), and subsequently PLLA (81 MPa). Please note, these data were obtained on dry samples, in wet conditions the yield stress will be substantially lower [30].

Figure 11. a) Yield stress vs. strain rate in uniaxial compression for PLLA, PLDLLA and PDLLA. b) Time-to-failure vs. applied stress in uniaxial compression for PLLA, PLDLLA and PDLLA.

Influences of annealing treatments proved minimal, which could be related to the fact that, close to Tg, glassy polymers can obtain the equilibrium state with the result that the treatment will induce no further changes [66,67]. The intrinsic responses display a very pronounced strain softening, more than a factor of 2 for PLLA (even more than PS, see Figure 9b), and a rather weak strain hardening. This intrinsic response is in full accordance with the fact that amorphous PLA’s are very brittle in tension or bending, similar to PS fracturing through a crazing mechanism [68,69]. Of course, this also makes the material extremely sensitive for stress concentrations, e.g. the stress-concentration induced by the thread root of a screw will act as a crack initiation site [70]. By plasticization, blending, co-polymerization and/or rubber toughening the toughness of the material can be improve [71-75], but also orientation of the polymer chains, e.g. by cold- and hot drawing, is a route to improvement [69,76].

The strain rate-dependence of PLDLLA is presented in Figure 10b. Remarkable is the rather strong strain-rate dependence of the yield stress; approx. 13 MPa per decade of strain rate. It is also clear that the strain rate dependence in the strain hardening region is much lower; approx. 4 MPa/decade. As a result the amount of strain softening has a quite strong strain-rate dependence which will make the material more brittle at higher strain rates.

The strain-rate dependence of the yield stress is presented in figure 11a for all 3 PLA’s. It can be observed that the deformation kinetics (slope of the curve) are identical for all three materials. The curves of the individual materials appear shifted vertically with respect to one

a b


another, with PLLA on the top position and PLDLLA at the bottom. The vertical shift between these two extremes is approximately 11 MPa. The lifetime under constant stress is presented in Figure 11b. The picture here compares well to that of the strain rate dependence

Figure 12. a) Yield stress vs. strain rate in uniaxial compression for PLLA and PC. b) Time-to-failure vs. applied stress in uniaxial compresson for PLLA and PC.

of the yield stress. The three materials show identical kinetics, but appear shifted vertically with respect to one another.

Also in this case, the absolute slope of applied stress versus the logarithm of time to failure (Figure 11b) is virtually identical (13 MPa/decade) to that observed for the yield stress versus the logarithm of strain rate (Figure 11a).

Long-Term Performance of PLA’s Vs other Glassy Polymers

From a qualitative point of view, the deformation behaviors of the three PLA’s are similar to that of other glassy polymers. From a quantitative point of view, however, there are some major differences. As an illustration, Figure 12 compares the strain-rate dependence of the yield stress and the stress-dependence of the time to failure of PLLA with that of PC. For a standard tensile test (strain rate 10-3 s-1) the yield stress of PLLA is approximately 100 MPa (Figure 12a), considerably higher than that of PC (65 MPa). However, the most striking difference is that in the slopes of yield stress versus the logarithm of strain rate. For an increase in strain rate by a factor of ten the yield stress increases 13 MPa for PLLA, but only 3 MPa for PC. Apparently the plastic flow rate is much more stress-dependent in PC than in PLLA. This difference can also be observed in the slopes of applied stress versus time to failure (Figure 12b), where the same kinetics apply. This implies that an decrease in applied stress by 13 MPa leads to an increase in lifetime by a factor of 10 for PLLA, whereas the same reduction in stress would result in an increase of over a factor of 10.000 for PC.

Despite the excellent short term properties of PLLA, its lifetime under a static stress of 50 MPa (50% of the short term strength) is only little more than a single day. In comparison, the lifetime of PC under the same load of 50 MPa (76% of the short term strength) is over 3 months! This is actually the expected lifetime of PLLA at a static load of only 25% of its short term strength. From a quantitative point of view it is quite clear that the long-term performance of PLLA is worrying. Taking into account that the example given here relates to its performance under dry conditions, at room temperature, the picture becomes even more disturbing.

b a


Figure 13. a) The maximum load of the PLDLLA cage as a function of loading speed (displacement rate), temperature, and humidity. b) Time-to-failure for dry cages at 37ºC. The dotted line is a prediction for the time-to-failure of the wetted cages, based on a decrease by 0.5 kN as determined in Figure 13a.

To illustrate this, Figure 13 presents some mechanical data on the PLDLLA spinal cage which displayed premature failure in a goat study [29]. Figure 13a shows the dependence of cage strength as a function of loading speed, temperature and humidity [30]. The dependence on loading speed presents a similar picture to the data presented in Figure 12a.

In general, the cage appears to be stronger at higher loading velocity, lower temperature, and under dry conditions. An increase in loading velocity by a factor 10 increases the cage strength by 0.86 kN. Taking into account the cross-sectional area of the spinal cage (70 mm2), this would imply an increase of yield stress of 12.3 MPa/decade, which compares well to the slope observed in Figures 11a and 12a. The cage strength, determined according to ASTM D695 at a loading rate of 1.3 mm.min-1, is 7.1 kN. An increase in temperature from 23ºC (room temperature) to 37ºC (body temperature) substantially decreases the cage strength by 1.5 kN. An extra decrease in strength of 0.5 kN is observed when the cage is tested after being soaked in water for 24 hrs. This influence of temperature and humidity is equal for all loading velocities, i.e. the slope of the curve remains unchanged.

Figure 13b presents the time-to-failure for dry cages at 37ºC under various compressive forces below its instantaneous strength. Also here the general observation corresponds with that presented in Figures 11b and 12b. Time-to-failure was generally short and strongly dependent on the applied load. The long term performance of wet cages was estimated here by shifting the fit through the “dry” data by 0.5 kN, as determined from the compression experiments in Figure 13a. Under a compression load of 50% of the short-term strength (ASTM D695), wet cages are expected to collapse after less than one hour of loading. At 25% of the cage strength the lifetime is approximately one month.

a b


Influence of Molecular Degradation In the case of degradable polymers, like the PLA’s studied here, the molecular weight

steadily decreases over the course of time. It seems justified to question the possible influence of degradation on the failure kinetics. An important indication for a relation between molecular weight and mechanical performance is the reduction in cage strength that is observed during in-vitro degradation of ETO and E-beam sterilized PLDLLA spinal cages [77]. Similar results were found in a recent study on the influence of molecular weight on the mechanical performance of PDLLA [78]. Nevertheless, combined modeling of molecular degradation and time-dependent failure seems to indicate only a very minor acceleration of failure at very low stress levels. At higher stresses time-dependent failure will occur before there is sufficient degradation to influence flow kinetics [78].

CONCLUDING REMARKS We have established that glassy polymers can best be regarded as highly viscous fluids.

Upon application of stress a state of enhanced molecular mobility is induced, that stimulates a dynamic rearrangement of molecular segments, resulting in a steady rate of plastic flow. This deformation can propagate at this steady pace until strain softening sets in, accelerating the rate of deformation initiating a localized plastic deformation zone; failure occurs. This implies that under static load the implant will always fail, the main question being when.

This specific type of failure mechanism clearly requires a new approach to the design of load-bearing polymer constructs. It is clearly demonstrated in Figure 13, that, even if we consider only a single loading geometry, it is difficult to speak of the strength of an implant. With predictive models becoming available, the long-term performance of a degradable construct can in principle be estimated in early stages of design. Since mechanical testing protocols for interbody devices, like ASTM-F2077, currently do not consider long-term failure under static loading, it seems most appropriate to reconsider the standardized testing protocols for load-bearing constructs when these are made of polymers like amorphous PLA’s.

REFERENCES

[1] Togawa D, Bauer TW, Brantigan JW et al. Bone graft incorporation in radio-graphically successful human intervertebral body fusion cages. Spine 2001;26:2744-50.

[2] Taneichi H, Suda K, Kajino T et al. Unilateral transforaminal lumbar interbody fusion and bilateral anterior-column fixation with two Brantigan I/F cages per level: clinical outcomes during a minimum 2-year follow-up period. J Neurosurg.Spine 2006;4:198-205.

[3] Togawa D, Bauer TW, Lieberman IH et al. Lumbar intervertebral body fusion cages: histological evaluation of clinically failed cages retrieved from humans. J.Bone Joint Surg.Am. 2004;86-A:70-9.


[4] Ohlin A, Karlsson M, Duppe H et al. Complications after transpedicular stabilization of the spine. A survivorship analysis of 163 cases. Spine 1994;19:2774-9.

[5] Mueller M, Allgoewer M, Schneider R et al. Manual of internal fixation. Techniques recommended by the AO Group. 2nd ed. New York: Springer, 1979.

[6] Chapman M, Woo S. Principles of Fracture Healing. In: Chapman M, Madison M, eds. Operative Orthopaedics. Philadelphia: JB Lippincott Company, 1988:115-23.

[7] Brantigan JW, Steffee AD, Lewis ML et al. Lumbar interbody fusion using the Brantigan I/F cage for PLIF and the VSP pedicle screw system: two year results of a FDA IDE clinical trial. In: Husson J, LeHuec J, eds. In Intersomatique du Rachis Lumbaire. Montpellier: Sauramps Medical, 1996.

[8] Ray CD. Threaded fusion cages for lumbar interbody fusions. An economic comparison with 360 degrees fusions. Spine1997;22:681-5.

[9] Bjarke CF, Stender HE, Laursen M et al. Long-term functional outcome of pedicle screw instrumentation as a support for posterolateral spinal fusion: randomized clinical study with a 5-year follow-up. Spine 2002;27:1269-77.

[10] Smit TH, Odgaard A, Schneider E. Structure and function of vertebral trabecular bone. Spine 1997;22:2823-33.

[11] Huiskes R, Ruimerman R, van Lenthe GH et al. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 2000;405:704-6.

[12] Smit TH, Muller R, van DM et al. Changes in bone architecture during spinal fusion: three years follow-up and the role of cage stiffness. Spine 2003;28:1802-8.

[13] van Dijk M, Smit TH, Burger EH et al. Bioabsorbable poly-L-lactic acid cages for lumbar interbody fusion: three-year follow-up radiographic, histologic, and histomorphometric analysis in goats. Spine 2002;27:2706-14.

[14] Wuisman PI, van DM, Smit TH. Resorbable cages for spinal fusion: an experimental goat model. J.Neurosurg. 2002;97:433-9.

[15] van Dijk M, Tunc DC, Smit TH et al. In vitro and in vivo degradation of bioabsorbable PLLA spinal fusion cages. J.Biomed.Mater.Res. 2002;63:752-9.

[16] van Dijk M, Smit TH, Arnoe MF et al. The use of poly-L-lactic acid in lumbar interbody cages: design and biomechanical evaluation in vitro. Eur.Spine J. 2003;12:34-40.

[17] Cordewener FW, Bos RR, Rozema FR et al. Poly(L-lactide) implants for repair of human orbital floor defects: clinical and magnetic resonance imaging evaluation of long-term results. J.Oral Maxillofac.Surg. 1996;54:9-13.

[18] Rokkanen PU, Bostman O, Hirvensalo E et al. Bioabsorbable fixation in orthopaedic surgery and traumatology. Biomaterials 2000;21:2607-13.

[19] Partio EK, Bostman O, Hirvensalo E et al. Self-reinforced absorbable screws in the fixation of displaced ankle fractures: a prospective clinical study of 152 patients. J Orthop.Trauma 1992;6:209-15.

[20] Bergsma EJ, Rozema FR, Bos RR et al. Foreign body reactions to resorbable poly(L-lactide) bone plates and screws used for the fixation of unstable zygomatic fractures. J Oral Maxillofac Surg 1993;51:666-70.

[21] Bostman OM. Osteoarthritis of the ankle after foreign-body reaction to absorbable pins and screws: a three- to nine-year follow-up study. J Bone Joint Surg.Br. 1998;80:333-8.


[22] Bostman OM, Pihlajamaki HK. Late foreign-body reaction to an intraosseous bioabsorbable polylactic acid screw. A case report. J Bone Joint Surg.Am. 1998;80:1791-4.

[23] Bergsma JE, de Bruijn WC, Rozema FR et al. Late degradation tissue response to poly(L-lactide) bone plates and screws. Biomaterials 1995;16:25-31.

[24] Bostman OM, Pihlajamaki HK. Adverse tissue reactions to bioabsorbable fixation devices. Clin.Orthop.Relat Res. 2000;216-27.

[25] Middleton JC, Tipton AJ. Synthetic biodegradable polymers as orthopedic devices. Biomaterials 2000;21:2335-46.

[26] Bostman O, Pihlajamaki H. Clinical biocompatibility of biodegradable orthopaedic implants for internal fixation: a review. Biomaterials 2000;21:2615-21.

[27] Vert M. Poly(lactic acid)s. In: Wnek GE, Bowlin GL, eds. Encyclopedia of Biomaterials and Biomedical Engineering. New York: Marcel Dekker, inc., 2004:1254-64.

[28] Athanasiou KA, Agrawal CM, Barber FA et al. Orthopaedic applications for PLA-PGA biodegradable polymers. Arthroscopy 1998;14:726-37.

[29] Krijnen MR, Mullender MG, Smit TH et al. Radiographic, histologic, and chemical evaluation of bioresorbable 70/30 poly-L-lactide-CO-D, L-lactide interbody fusion cages in a goat model. Spine 2006;31:1559-67.

[30] Smit TH, Engels TAP, Wuisman PI et al. Time-dependent mechanical strength of 70/30 Poly(L, DL-lactide): shedding light on the premature failure of degradable spinal cages. Spine 2008;33:14-8.

[31] Klompen ETJ, Engels TAP, Govaert LE, Meijer HEH, Modeling of the postyield response of glassy polymers: influence of thermomechanical history. Macromolecules 2005;38:6997-7008.

[32] Vincent PI, Necking and cold drawing, Polymer 1960:1:7-19. [33] Flory PJ, Tensile strength in relation to molecular weight of high polymers, J. Amer.

Chem. Soc. 1945:67:2048-50. [34] Vincent PI, The tough-brittle transition in thermoplastics, Polymer 1960:1:425-44. [35] Matz DJ, Guldemond WG, Cooper SL, Delayed yielding in glassy polymers, J. Polym.

Sci., Polym. Phys. Ed. 1972:10:1917-30. [36] Narisawa I, Ishikawa M, Ogawa H, Delayed yielding of polycarbonate under constant

load, J. Polym. Sci., Polym. Phys. Ed. 1978:16:1459-70. [37] McKenna GB, Glass formation and glassy behavior, In Comprehensive Polymer

Science, Vol. 2:Polymer Properties; Booth C, Price C, Eds., Pergamon: Oxford, 1989; Ch. 10, pp 311–362.

[38] Bauwens-Crowet C, Bauwens J-C, Homès G, Tensile yield-stress behavior of glassy polymers, J. Polym. Sci., A-2 1969:7:735-42.

[39] Sherby OD, Dorn JE, Anelastic creep of PMMA, J. Mech. Phys. Solids 1954:6:145-62. [40] Bauwens-Crowet C, Ots J-M, Bauwens J-C, The strain-rate and temperature

dependence of yield of polycarbonate in tension, tensile creep and impact tests. J. Mater. Sci. Let. 1974:9:1197-1201.

[41] Arruda EM, Boyce MC, Evolution of plastic anisotropy in amorphous polymers during finite straining, Int. J. Plast. 1993:9:697-720.

[42] van Melick HGH, Govaert LE, Meijer HEH, On the origin of strain hardening in glassy polymers, Polymer 2003:44:2493-2502.


[43] G’Sell C, Hiver JM, Daoun A, Souahi A, Video-controlled tensile testing of polymers and metals beyond the necking point, J. Mater. Sci. 1992:27:5031-39.

[44] Tervoort TA, Govaert LE, Strain-hardening behavior of polycarbonate in the glassy state, J. Rheol. 2000:44:1263-77.

[45] Klompen ETJ, Engels TAP, van Breemen LCA, Schreurs PJG, Govaert LE, Meijer HEH, Quantitative prediction of long-term failure of polycarbonate. Macromolecules 2005;38:7009-17.

[46] Struik LCE, Physical aging in amorphous polymers and other materials. Amsterdam: Elsevier, 1978.

[47] Hutchinson JM, Physical aging of polymers, Prog. Polym. Sci. 1995:20:703-60. [48] Meijer HEH, Govaert LE, Mechanical performance of polymer systems: the relation

between structure and properties, Prog. Polym. Sci. 2005:30:915-938. [49] van Melick HGH, Govaert LE, Meijer HEH, Localisation phenomena in glassy

polymers: influence of thermal and mechanical history, Polymer 2003:44:3579-91. [50] Fraser RAW, Ward IM, The impact fracture behaviour of notched specimens of

polycarbonate, J. Mater. Sci. 1977:12:459-68. [51] Govaert LE, van Melick HGH, Meijer HEH, Temporary toughening of polystyrene

through mechanical pre-conditioning, Polymer 2001:42:1271-4. [52] Janssen RPM, de Kanter D, Govaert LE, Meijer HEH, Fatigue life predictions for

glassy polymers: a constitutive approach, Macromolecules 2008:41:2520-30. [53] Eyring H, Viscosity, plasticity, and diffusion as examples of absolute reaction rates, J.

Chem. Phys. 1936:4:283-91. [54] Visser HA, Bor TC, Wolters M., Engels TAP, Govaert LE, Life-time assessment of

load bearing polymer glasses: Application to polymer pipes under internal, Macromol. Mater. Eng., submitted.

[55] Visser HA, Bor TC, Wolters M., Engels TAP, Govaert LE, A new engineering approach to predict the hydrostatic strength of uPVC pipes, Proc. PPS07 EA, Göthenburg, Sweden, 2007.

[56] Coleman BD, Application of the theory of absolute reaction rates to the creep failure of polymeric filaments, J. Polym. Sci. 1956:20:447-55.

[57] Coleman BD, Knox AG, The interpretation of creep failure in textile fibers as a rate process, Text. Res. J. 1957:27:393-9.

[58] Janssen RPM, Govaert LE, Meijer HEH, An analytical method to predict fatigue life of thermoplastics in uniaxial loading: sensitivity to wave type, frequency and stress amplitude, Macromolecules 2008:41:2531-40.

[59] Lowe TG, Coe JD. Bioresorbable polymer implants in the unilateral transforaminal lumbar interbody fusion procedure. Orthopedics 2002; 25: S1179-S1183.

[60] Lowe TG, Tahernia AD. Unilateral transforaminal posterior lumbar interbody fusion. Clin Orthop 2002; 394: 64-72.

[61] Austin RC, Branch CL, Jr., Alexander JT. Novel bioabsorbable interbody fusion spacer-assisted fusion for correction of spinal deformity. Neurosurg Focus 2003; 14: E11 .

[62] Kuklo TR, Rosner MK, Polly DW, Jr. Computerized tomography evaluation of a resorbable implant after transforaminal lumbar interbody fusion. Neurosurg Focus 2004;16: E10.


[63] Couture DE, Branch CL, Jr. Posterior lumbar interbody fusion with bioabsorbable spacers and local autograft in a series of 27 patients. Neurosurg Focus 2004; 16: E8.

[64] Coe JD, Vaccaro AR, Instrumented transforaminal lumbar interbody fusion with bioresorbable polymer implants and iliac crest autograft. Spine 2005; 30: S76-S83.

[65] Park MC, Tibone JE, False magnetic resonance imaging persistence of a biodegradable anterior cruciate ligament interference screw with chronic inflammation after 4 years in vivo. Arthroscopy 2006; 22: 911e1-911-e4.

[66] Engels TAP, Govaert LE, Peters GWM, Meijer HEH, Processing-induced properties in glassy polymers: application of structural relaxation to yield stress development. J. Polym. Sci. B 2006:44:1212-25.

[67] Bauwens-Crowet C, Bauwens J-C, Annealing of polycarbonate below the glass transition, Polymer 1982:23:1599-1604.

[68] Grijpma DW, Pennings AJ. (Co)polymers of L-lactice,2 Mechanical properties. Macromol. Chem. Phys. 1994: 195: 1649-1663.

[69] Grijpma DW, Altpeter H, Bevis MJ, Feijen J. Improvement of the mechanical properties of poly(D,L-lactide) by orientation. Polym. Int. 2002; 51: 845-851.

[70] Brkaric M, Baker KC, Israel R, Harding T, Montgomery DM, Herkowitz HN, Early failure of bioabsorbable anterior cervical fusion plates, J. Spinal Disord. Tech. 2007:20:248-54.

[71] Jacobsen S, Fritz HG. Plasticizing polylactide – The effect of different plasticizers on the mechanical properties. Polym. Eng. Sci. 1999; 39: 1303-1310.

[72] Martin O, Avérous L. Poly(lactic acid): plasticization and properties of biodegradable multiphase systems. Polymer 2001; 42: 6209-6219.

[73] Shibata M, Teramoto N, Inoue Y. Mechanical properties , morphologies, and crystallization behavior of plasticized poly(L-lactide)/poly(butylene succinate-co-L-lactate) blends. Polymer 2007; 48: 2768-2777.

[74] Li Y, Shimizu H. Toughening of polylactide by melt blending with a biodegradable poly(ether)urethane elastomer. Macromol. Biosci. 2007; 7: 921-928.

[75] Grijpma DW, Hofslot DA van, Supèr H, Nijenhuis AJ, Pennings AJ. Rubber toughening of poly(lactide) by blending and block copolymerization. Polym. Eng. Sci. 1994; 34:1674-1684.

[76] Grijpma DW, Penning JP, Pennings AJ. Chain entanglement, mechanical properties and drawability of poly(lactide). Colloid. Polym. Sci. 1994; 272: 1068-1081.

[77] Smit TH, Thomas KA, Hoogendoorn RJW, Strijkers GJ, Helder MN, Wuisman PIJM, Sterilization and strength of 70-30 polylactise cages, Spine 2007:32:742-7.

[78] Söntjens SHM, Engels TAP, Smit TH, Govaert LE, Influence of molecular weight on the deformation and failure kinetics of PDLLA constructs, Biomaterials, in preparation.

TIME-DEPENDENT FAILURE IN LOAD-BEARING POLYMERS A ... · Time-Dependent Failure in Load-Bearing...

Documents

Transcript of TIME-DEPENDENT FAILURE IN LOAD-BEARING POLYMERS A ... · Time-Dependent Failure in Load-Bearing...