Shrinkage Stress Measurements Research Articles

Shrinkage stress evolution during photopolymerization: Theory and experiments

Photopolymerized materials are widely used for a broad range of industrial applications including coatings, three-dimensional (3D) printing, micro/nano-scale fabrications, restorative dentistry, etc. However, the service quality and life of these materials are dramatically impaired by polymerization shrinkage stress evolved during the photopolymerization process in practices. A theoretical model for mechanism exploration and accurate prediction of the shrinkage stress evolution is thus-far inaccessible and strategies for alleviating the stress based on existing studies are quite controversial. Herein, we develop a comprehensive theoretical model that can accurately capture the evolution of the shrinkage stress under various working conditions. The model is established by a time-incremental method based on 3D viscoelasticity theory coupling the evolutions of reaction kinetics and material properties during photopolymerization. Theoretical predictions of the shrinkage stress are then validated by groups of experimental measurements using a series of photopolymers and their composites under various testing conditions. We show that our model is able to correctly predict both the individual and combined effects of instrumental compliance, specimen geometry, material composition, and photocuring protocol on the shrinkage stress evolution, results of which well clarify the diverse conflicts existed in the literature. The magnitudes of the predicted stresses based on our model agree quantitatively with those of the experimental ones, far exceeding the prediction accuracy of all existing models. In addition, our model also successfully predicts the results measured in the literature using various testing devices, indicating that our model could be applied to existing setups for shrinkage stress measurement of bulk materials. Our theory-experiment-combined study not only provides a theoretical approach to accurately predict and thoroughly uncover the shrinkage stress evolution during photopolymerization, it will also guide further explorations on shrinkage stress reduction and material property optimization for photopolymers with improved service life. Additionally, the presented model on the shrinkage stress evolution paves a potentially new way for the derivation of material mechanical property evolutions and thus revealing the mechanical-chemical-coupled mechanisms during photopolymerization.

The two sides of the C-factor

ObjectiveThe aim of this paper is to investigate the effects on shrinkage strain/stress development of the lateral constraints at the bonded surfaces of resin composite specimens used in laboratory measurement. MethodsUsing three-dimensional (3D) Hooke’s law, a recently developed shrinkage stress theory is extended to 3D to include the additional out-of-plane strain/stress induced by the lateral constraints at the bonded surfaces through the Poisson’s ratio effect. The model contains a parameter that defines the relative thickness of the boundary layers, adjacent to the bonded surfaces, that are under such multiaxial stresses. The resulting differential equation is solved for the shrinkage stress under different boundary conditions. The accuracy of the model is assessed by comparing the numerical solutions with a wide range of experimental data, which include those from both shrinkage strain and shrinkage stress measurements. ResultsThere is good agreement between theory and experiments. The model correctly predicts the different instrument-dependent effects that a specimen’s configuration factor (C-factor) has on shrinkage stress. That is, for noncompliant stress-measuring instruments, shrinkage stress increases with the C-factor of the cylindrical specimen; while the opposite is true for compliant instruments. The model also provides a correction factor, which is a function of the C-factor, Poisson’s ratio and boundary layer thickness of the specimen, for shrinkage strain measured using the bonded-disc method. For the resin composite examined, the boundary layers have a combined thickness that is ∼11.5% of the specimen’s diameter. SignificanceThe theory provides a physical and mechanical basis for the C-factor using principles of engineering mechanics. The correction factor it provides allows the linear shrinkage strain of a resin composite to be obtained more accurately from the bonded-disc method.

Ester-free thiol–ene dental restoratives—Part B: Composite development

ObjectivesTo assess the performance of thiol–ene dental composites based on selected ester-free thiol–ene formulations. Further, to point out the benefits/drawback of having a hydrolytically stable thiol–ene matrix within a glass filled composite. MethodsComposite samples containing 50–65wt% of functionalized glass microparticles were prepared and photopolymerized in the presence of a suitable visible light photoinitiator. Shrinkage stress measurements were conducted as a function of the irradiation time. Degrees of conversion were measured by FT-IR analysis by comparing the double bond signals before and after photopolymerization. Mechanical tests were carried out on specimens after curing as well as after extended aging in water. Dynamic mechanical analysis was employed to track the changes in storage modulus near body temperature. The properties of the thiol–ene composites were compared with those of the BisGMA/TEGDMA control. ResultsDepending on the resin type, similar or higher conversions were achieved in thiol–ene composites when compared to the dimethacrylate controls. At comparable conversions, lower shrinkage stress values were achieved. Although exhibiting lower initial elastic moduli, the thiol–ene composites’ flexural strengths were found to be comparable with the controls. Contrary to the control, the mechanical properties of the ester-free thiol–ene composites were shown to be unaffected by extensive aging in water and at least equaled that of the control after aging in water for just five weeks. SignificanceEmploying non-degradable step-growth networks as organic matrices in dental composites will provide structurally uniform, tough materials with extended service time.

Role of filler and functional group conversion in the evolution of properties in polymeric dental restoratives

ObjectivesTo examine effects of shrinkage and modulus on the dynamic development of shrinkage stress as a function of methacrylate conversion and filler loading in a model photocurable dimethacrylate-based resin with a silanized barium glass filler. MethodsBisGMA/TEGDMA samples with filler loading levels of 0–70wt% were evaluated. Irradiation times and intensities were varied to achieve a wide range of conversion. Shrinkage stress measurements were accompanied with real-time conversion monitoring, while shrinkage and modulus measurements were made at different static conversion points. ResultsShrinkage increased nearly linearly with respect to conversion, while for a given value of conversion, it decreased proportionally with increasing filler content. Modulus advanced in an exponential fashion with conversion and also increased incrementally with filler content; however, modulus values rose disproportionately rapidly for the highest filler loading. At either high or low filler loading levels, stress at limiting conversion, which was inversely proportional to the filler load, was high while at an intermediate filler content, a minimum in stress was observed due to the combined effects of filler based shrinkage reduction, restricted limiting conversion and only moderately enhanced modulus. The level of polymerization stress predicted from the conversion-indexed shrinkage and modulus measurements over-estimated the experimental stress states as modulus evolved due to system compliance that to some degree mimics the clinical situation presented by photocuring bonded composite restorations.Significance Measurement of monomer conversion provides a common basis by which different material properties can be rationally compared.

Shrinkage stress development in dental composites—An analytical treatment

ObjectivesThe aim of this paper is to develop a comprehensive mathematical model for shrinkage stress development in dental composites that can account for the combined effect of material properties, specimen geometry and external constraints. MethodsA viscoelastic model that includes the composite's elastic, creep and shrinkage strains, and their interaction with the sample's dimensions and the external constraint is developed. The model contains two dimensionless parameters. The first one represents the compliance of the external constraint relative to that of the composite sample, and the second controls the rate of shrinkage stress decay through creep. The resulting differential equation is solved for two special cases: zero compliance and zero creep. Predictions for shrinkage stress measurements are then made using the analytical solutions for instruments with different compliances, samples with different thicknesses and composites with different filler fractions. ResultsThe model correctly predicts how shrinkage stress increases with time, its dependence on the interaction between the entire system's compliance and the material properties, and the effect of the filler fraction on its maximum value. Comparisons with reported shrinkage stress measurements have provided very good agreement between theory and experiments. SignificanceThe results provided by the model can help to resolve most, if not all, of the seemingly conflicting experimental observations reported in the literature. They can also provide some useful guidelines for optimizing the mechanical performance of dental composite restorations. The compliance ratio, a new parameter derived from the model, represents a fuller description of the constraints of the system.

Polymerization shrinkage stress measurement for a UV-curable resist in nanoimprint lithography

A simple method was developed to obtain the polymerization shrinkage stress exerted on the sidewalls of resist/stamp interface in ultraviolet nanoimprint lithography. This method is based on the measurements of demolding force which is the sum of adhesion and friction forces. The mean polymerization shrinkage stress on the sidewalls can readily be decoupled from overall demolding force by independently measuring the friction coefficient, adhesion force and geometries of stamp structures. The polymerization shrinkage stress on the sidewalls is overall larger than adhesion and increases by adding more cross-linking agent to the resist composition. This indicates that in addition to lowering the adhesion at the resist/stamp interface, development of resists with low degrees of shrinkage during UV curing is critical to reducing demolding force. It was also found that the shrinkage stress depends not only on the resist composition but also the stamp structure. A pillar structured stamp leads to a larger stress than a stamp with gratings with identical depth and width.

Effect of shrinkage strain, modulus, and instrument compliance on polymerization shrinkage stress of light-cured composites during the initial curing stage

Objectives The aim of this study was to investigate the influence of shrinkage strain, modulus, and instrument compliance on the polymerization shrinkage stress measurement of light-cured composites, and to determine whether the silorane-based low-shrinkage composite shows a low-polymerization shrinkage stress. Methods A universal hybrid; Z250 (Z2), a flowable; Z350 (Z3), and a silorane-based; P90 (P9) composite was examined. A modified “bonded disc method” was used to measure the axial shrinkage strain of the composite. For the measurement of the initial modulus development of composites during light curing, a dynamic oscillatory shear test was undertaken using a custom-made oscillation rheometer. A frequency of 6 Hz and strain amplitude of 0.0091 rad for 20 s was employed and the complex shear modulus ( G *) was determined. A newly designed stress–strain analyzer was made to measure the shrinkage stress of the composites with two modes: (1) high compliance, or (2) low compliance. The shift between the two modes was controlled by an On–Off switch of a negative feedback circuit. Theoretical shrinkage stress was calculated from the shrinkage strain and modulus measured above, and compared with experimentally measured stress. Data were analyzed with one-way ANOVA and Tukey's post hoc test ( α = 0.05), and correlation analysis was done to investigate the relationship between measured stress and shrinkage strain, modulus, and theoretical stress. Results The shrinkage strain of Z3 (4.12%) at 10 min was the highest, followed by Z2 (2.31%) and P9 (0.77%). At 10 s after light curing, Z2 showed the highest modulus (466.2 MPa), Z3 (154.1 MPa), and P9 the lowest (130.7 MPa). The measured stresses with low compliance were much higher than those with high compliance. With high compliance, the contraction stress of Z3 was the highest (2.75 MPa), followed by Z2 (1.54 MPa) and P9 (0.48 MPa). In low-compliance mode, the stresses of Z3 (7.93 MPa) and Z2 (7.48 MPa) were similar ( p = 0.323) while the stress of P9 (3.23 MPa) was much lower. A strong correlation was observed between the theoretical stress and the measured stress with low compliance ( R = 0.996). In high-compliance mode, the shrinkage strain also showed a near-linear relationship with the stress measured ( R = 0.937), but the modulus showed a low correlation with the measured stress ( R = 0.398). Significance Depending on the instrument compliance, polymerization shrinkage stress showed significant differences for each material. In high-compliance shrinkage strain played a greater role, while in low-compliance shrinkage strain and elastic modulus contributed comparably in determining the shrinkage stress. The low-shrinkage silorane-based composite demonstrated considerable reduction in shrinkage strain and stress.

Effect of instrument compliance on polymerization shrinkage stress measurements of composites

Effect of instrument compliance on polymerization shrinkage stress measurements of composites

Effect of instrument compliance on the polymerization shrinkage stress measurements of dental resin composites

compliance 유무가 복합레진의 중합수축응력의 측정에 미치는 영향 The purpose of this study was to evaluate the effect of instrument compliance on the polymerization shrinkage stress measurements of dental composites. The contraction strain and stress of composites dur- ing light curing were measured by a custom made stress-strain analyzer, which consisted of a displacement sensor, a cantilever load cell and a negative feedback mechanism. The instrument can measure the poly- merization stress by two modes: with compliance mode in which the instrument compliance is allowed, or without compliance mode in which the instrument compliance is not allowed. A flowable (Filtek Flow: FF) and two universal hybrid (Z100: Z1 and Z250: Z2) composites were stud- ied. A silane treated metal rod with a diameter of 3.0 mm was fixed at free end of the load cell, and other metal rod was fixed on the base plate. Composite of 1.0 mm thickness was placed between the two rods and light cured. The axial shrinkage strain and stress of the composite were recorded for 10 minutes during polymerization, and the tensile modulus of the materials was also determined with the instrument. The statistical analysis was conducted by ANOVA, paired t-test and Tukey's test (α <0.05). There were significant differences between the two measurement modes and among materials. With com- pliance mode, the contraction stress of FF was the highest: 3.11 (0.13), followed by Z1: 2.91 (0.10) and Z2: 1.94 (0.09) MPa. When the instrument compliance is not allowed, the contraction stress of Z1 was the highest: 17.08 (0.89), followed by FF: 10.11 (0.29) and Z2: 9.46 (1.63) MPa. The tensile modulus for Z1, Z2 and FF was 2.31 (0.18), 2.05 (0.20), 1.41 (0.11) GPa, respectively. With compliance mode, the mea- sured stress correlated with the axial shrinkage strain of composite; while without compliance the elastic modulus of materials played a significant role in the stress measurement.(J Kor Acad Cons Dent 34(2):144-152, 2009)

Influence of instrument compliance and specimen thickness on the polymerization shrinkage stress measurement of light-cured composites

Objectives The aim of our study was to investigate the effects of instrument compliance and specimen geometry on the polymerization shrinkage stress measurements of composites. Methods A custom designed stress–strain analyzer was made using a linear variable differential transformer probe and a cantilever load cell. A sandblasted glass rod was fixed at the free end of the load cell, and another glass rod was located on a base plate. A composite was placed between the two rods and light cured. The end displacement of the load cell during polymerization was recorded for 10 min. A flowable (Filtek Flow), a universal hybrid (Z100), and a packable (P60) composite were studied. To investigate the effect of specimen geometry and instrument compliance, specimen thickness was varied between 0.5, 1.0, and 2.0 mm, and three load cells with maximum capacities of 20, 100, and 500 kgf were used. Ten maxillary premolars were prepared with two sizes of MOD cavities; the bucco-lingual widths and depths of the cavities were 1.5 mm × 2 mm and 3 mm × 2 mm, and the cusp compliance and deflection were measured before and during composite polymerization. Results The measured polymerization stress decreased in the order of Filtek Flow, Z100, and P60 for all measurement conditions. As the specimen thickness was increased, the shrinkage stress per unit thickness (mm) decreased. The measured stress decreased with increasing instrument compliance. The cusp compliance (3.32 μm/N) of the 3 mm × 2 mm cavities was similar to that of instrument with a 20 kgf load cell (3.34 μm/N). Significance For determining the most clinically relevant values for shrinkage stress of dental composites, the instrument compliance should closely match that of the tooth walls in the cavity geometry to be tested.

Probing the origins and control of shrinkage stress in dental resin-composites: I. Shrinkage stress characterization technique*

The accurate and reliable characterization of the polymerization shrinkage stress is becoming increasingly important, as the shrinkage stress still is a major drawback of current dimethacrylate-based dental materials and restricts its range of applications. The purpose of this research is to develop a novel shrinkage stress measurement device to elucidate the shrinkage stress evolution of dental restorative composites while allowing for controlled sample deformation during the polymerization. Furthermore, the device is designed to mimic the clinically relevant cusp-to-cusp displacement by systematically adjusting the instrument compliance, the bonded surface area/unbonded area by sample geometry, and the total bonded area by sample diameter. The stress measurement device based on the cantilever beam deflection theory has been successfully developed and characterized using a commercial dental composite. It was shown that this device is a highly effective, practical and reliable shrinkage stress measurement tool, which enables its facile applications to the investigation of shrinkage stress kinetics of both commercial and experimental composites, as well as for probing various aspects that dictate shrinkage stress development.

Probing the origins and control of shrinkage stress in dental resin composites. II. Novel method of simultaneous measurement of polymerization shrinkage stress and conversion.

This study probes the interrelationships between polymerization shrinkage stress development and the polymerization progress with a novel experimental technique. This technique is capable of real time, simultaneous measurement of double-bond conversion and shrinkage stress with the use of a noninvasive near-infrared fiber-optic system, along with a cantilever beam-based tensometer. The results from both filled and unfilled bis-GMA/TEGDMA (70:30 mass ratio) systems showed that the shrinkage stress buildup was concentrated in the latter stages of polymerization, with its dramatic increase linked to the asymptotic approach of conversion to its limiting value. The monotonic increase of shrinkage stress with conversion in the vitrified state is attributed to the dramatic increase of the sample's elastic modulus during the vitrification stage and a certain amount of cooling stress as the sample cools down from the temperature rise caused by the exothermic polymerization and light absorption. Excellent reproducibility of both the polymerization kinetics assessment and the shrinkage stress measurement has been achieved.

Thermally stimulated structural changes in highly oriented glassy poly(ethylene terephthalate)

Glassy poly(ethylene terephthalate) (PET) structures with an extraordinarily large chain orientation have been prepared from isotropic and X-ray amorphous initial film strips by applying a cold-drawing procedure with well defined parameters. Under annealing conditions, the resulting changes of the supermolecular structure and the thermomechanical behaviour are investigated. Differential scanning calorimetric studies have revealed a starting crystallization of the highly anisotropic and glassy PET structures at temperatures as low as 56°C. In situ two-dimensional wide-angle X-ray scattering (WAXS) experiments have been performed to describe the formation of the crystalline order with temperature. Synchrotron WAXS investigations focusing on the (0 1 0), (Ī1 0) and (1 0 0) reflections show a fast crystallization process. The final crystal structure at each temperature above 120°C is reached within less than 7.5 min. Dynamic mechanical thermal analysis, shrinkage strain and shrinkage stress measurements are discussed with respect to the relaxation of local molecular orientation as well as crystallization processes.

Tensile drawing of poly(aryl ether ether ketone): 1. Birefringence, infra-red dichroism and shrinkage-stress measurements

Birefringence, infra-red dichroism and shrinkage-stress data of poly(aryl ether ether ketone) (PEEK) uniaxially drawn above the glass transition have been analysed in the framework of the theory of rubber elasticity. It is shown that PEEK chains having a molecular weight M n ≈ 13000 only contain three entangelements per chain on average. The very low level of shrinkage stress of the samples having a draw ratio below the threshold of strain-induced crystallization is perfectly consistent with a weakly entangled network. The birefringence versus stress curve discloses an orientation-dominated regime at low strains and a deformation-dominated regime starting from the onset of the strain-induced crystallization. The length of the random link, L= 1.8 nm, is in very good agreement with the one that can be theoretically predicted for the stiff-chain polymer relatives, poly(ethylene terephthalate), polycarbonate and poly(phenylene oxide). A value for the intrinsic birefringence of the amorphous phase, Δn° a = 0.38±0.04, is also reported.

Changes in crystal structure parameters and thermal mechanical properties of poly(p‐phenylene terephthalamide) fibers under different annealing conditions

AbstractAs‐spun poly(p‐phenylene terephthalamide) (PPTA) fibers have been annealed by three different methods: (1) the relaxation mode; (2) the constant temperature mode; and (3) the constant tension mode. Wide‐angle x‐ray diffraction (WAXD) was used with all three modes to characterize the changes in three crystal structure parameters: the degree of crystal orientation, the apparent crystal size, and the lattice strain along the c‐axis of the crystal unit cell. It was found that internal stresses in the fibers, which are frozen‐in during either the fiber spinning process or in later annealing, is the key factor causing these structure parameter changes. Our thermal shrinkage stress measurements may reasonably represent the fiber's internal stresses. The thermal shrinkage modulus and the tensile modulus of the PPTA fibers under these annealing modes have been determined. Based on a serial model, quantitative structure–property relationships can be established. The effects of annealing temperature and applied tension on both the microscopic crystal structures and the macroscopic properties are also discussed.

The yield and thermoelastic properties of oriented poly(methyl methacrylate)

Oriented sheets of poly(methyl methacrylate) were prepared by drawing to different draw ratios at a range of temperatures near the glass transition temperature. The degree of molecular orientation in these materials was characterized by measuring birefringence, and specimens prepared for measurements of tensile yield stress and shrinkage stress at elevated temperature. The shrinkage stress measurements were carried out by holding specimens at constant length above the glass transition temperature and determining the resulting stress as a function of time. The peak value of stress was found to be a function of birefringence only, independent of draw ratio or draw temperature. The function was linear for a substantial range of birefringence. A further series of specimens was used to measure the tensile yield stress (in the orientation direction) as a function of temperature and strain rate. At each testing temperature it was found that the yield stress correlated uniquely with the birefringence. These results for shrinkage stress and yield stress can both be interpreted through the concept of a frozen-in molecular network, and a semi-quantitative relationship proposed which relates to the anisotropy of the yield stress to the frozen-in network stress. This provides a molecular explanation for the Bauschinger effect observed in oriented polymers.

A study of the drawing behavior of poly(ethylene terephthalate)

AbstractCold‐drawn and hot‐drawn samples of poly(ethylene terephthalate) were studied by means of measurements of shrinkage stress, birefringence and differential scanning calorimetry (DSC). The values of shrinkage stress were comparable for both types of sample, implying that the deformation of a molecular network is important for both cold drawing and hot drawing. The DSC results indicate that substantial crystallization occurs in hot drawing for other than the lowest draw ratios, and this crystallization gives rise to an additional peak in the shrinkage stress measurements. In addition to temperature, strain rate is also an important variable, and changes in strain rate caused significant changes in both hot‐drawn and cold‐drawn samples.