Session U30: Focus Session: Mechanical Properties: Deformation, Rupture and Failure

Shock Wave Theory for Rupture of Rubber

The rupture of rubber differs from conventional fracture. It is supersonic, and the speed is determined by strain levels ahead of the tip rather than total strain energy as for ordinary cracks. Dissipation plays a very important role in allowing the propagation of ruptures, and the back edges of ruptures must toughen as they contract, or the rupture is unstable. In this talk I will review the experimental evidence for these claims. I will present several levels of theoretical description of the phenomenon: first, a numerical procedure called mesoscopic particle modeling, which is capable of incorporating large extensions, dynamics, and bond rupture; second, a simple continuum model that can be solved analytically, and which reproduces several features of elementary shock physics; and third, an analytically solvable discrete model that accurately reproduces numerical and experimental results, and explains the scaling laws that underly this new failure mode. Rupture speeds compare well with experiments, although opening angles of the rupture are not captured especially well. Some additional interesting topics that may be encountered along the way include the question of how to model sound dissipation in disordered solids, and a numerical instability that is suggestive of the phenomenon of strain crystallization.   

Tuning the Adhesion of Soft Elastomers with Topographic Patterns

Nature (e.g. gecko and jumping spider) utilizes surface patterns to control adhesion. The primary mechanism of adhesion for these systems can be sufficiently described by linear elastic fracture mechanics theory and material-defined length scales. Based upon these natural inspirations, similar mechanisms can be used to control the adhesion of elastic polymers. For viscoelastic polymers, patterns tune adhesion through additional mechanisms that have not been previously observed. Here, we illustrate the effects of topographic patterns in tuning the adhesion for soft, elastic or viscoelastic, elastomers. Contact adhesion tests based on Johnson, Kendall and Roberts (JKR) theory are used to characterize the adhesion of patterned poly(dimethyl siloxane) as well as poly(n-butyl acrylate) elastomers. We demonstrate that patterns can be utilized to control the adhesion of these polymers by: 1) controlling the balance of initiation and propagation for local separation process, 2) controlling the local crack velocity to alter the global viscoelastic response, and 3) altering the local separation mode through modification of a polymer layer's lateral confinement.   

Finite Element Calculations Using a New Constitutive Model for the Chemical Aging of Rubber

We have developed a constitutive model for rubber networks undergoing simultaneous crosslinking and scission reactions. This model is a modification of the independent network hypothesis that includes the coupling between strain history and chemical reactions. This coupling occurs because formation of networks in the strained state is greatly affected by the networks that were already present. Even when early networks scission, the overall material response shows some memory of the initial networks (i.e., some later stage networks act as earlier stage networks). We account for this effect using stress transfer functions. The model has been tested on microscopic molecular dynamics simulations. We will present results using this constitutive model in finite element calculations showing the large effect that the coupling of strain history and chemical reaction has.   

Effect of chain bridging on mechanical properties of lamellae-forming block copolymers

We report studies on solid-state mechanical properties of lamellae-forming block copolymers composed of poly(cyclohexylethylene) (C) and poly(ethylene) (E). Specifically, we have investigated the effect of bridging conformations in the semicrystalline E block. We studied CEC, ECEC, and ECECE architectures and found that tensile properties of C/E block copolymers are extremely sensitive to the fraction of ``soft'' E chains tethered between glassy C domains. While the CEC polymer has a strain-to-failure of $\sim $300{\%}, the ECEC and ECECE polymers fail at $\sim $1{\%} strain. By employing ECEC/CEC and ECECE/CEC blends, we have come up with a molecular parameter that describes a sharp brittle-to-ductile transition and captures the tensile properties of a broad range of C/E block copolymer architectures having equal sized E blocks. In another set of experiments, increasing the ``middle-to-loose'' E block length ratio was found to toughen the ECECE block copolymers. We propose that these effects are related to a critical concentration of bridged E chains that governs the failure mechanisms in glassy-semicrystalline block copolymers.   

Probing the Contact and Sliding of Elastomer/Polymer Interfaces

In this study, we have designed a novel approach to couple interface sensitive infrared-visible sum frequency generation (SFG) spectroscopy with adhesion and friction experiments. This provides a direct probe of the interfacial structure in terms of orientation and density of molecules during contact and sliding which is important in understanding the molecular origin of adhesion and friction. Here, we show that the friction forces between poly(dimethyl siloxane) (PDMS) lens and glassy poly(styrene) (PS) are $\approx $4 times higher than PDMS sliding on surfaces of crystalline alkyl side chain comb polymers. This cannot be explained by the differences in adhesion energy or hysteresis. The in-situ SFG measurements indicate local interdigitation during contact, which is evident from the decrease in the number of oriented phenyl groups at the interface. The local penetration is unexpected at room temperature (T$_{R})$ that is much below the T$_{g}$ of PS. For comparison, we have also studied poly(n-butyl methacrylate) and poly(n-propyl methacrylate) having T$_{g}$ above and below T$_{R}$, respectively. Both of these polymers show similar adhesion and friction forces as PS. The SFG results indicate that local changes in interfacial structure affect friction, regardless of the bulk T$_{g. }$ These results also show that the adhesion energy and hysteresis are not sufficient to predict friction, which makes the characterization of the molecular structure during contact and sliding essential.   

Mesoscopic Random Lattice Models of Rupture in Rubber

In an earlier work, Marder illustrated how rupture in rubber differs from conventional fracture. Dissipation and toughening of the back edges of ruptures are critical for the propagation of stable ruptures. In this earlier work, mesoscopic models were arrived at by approximating the Mooney-Rivlin theory of rubber by a finite difference scheme on a triangular lattice. From this perspective, qualitatively the lattice sites are considered to be crosslinkers and the bonds are polymers. We extend this work by considering the crosslinkers to be randomly distributed throughout the material rather than being ordered. For both random and ordered lattices, without rupture, there are many different ways to construct free energy functionals that reproduce the continuum theory. However, not all of the constructions are numerically stable. We explore the physical consequences of the disorder and the physical interpretations of the observed numerical instabilities.   

Annealing History Dependence of Young's Modulus in Thin Polymer Films Using an Axi-symmetric Peel Test Apparatus

We present a study of chain relaxation in thin spincast films above the glass transition temperature. We employ a novel axi-symmetric peel test, which uses the deformation of a thin spincast polymer film brought into contact with a flat substrate. The use of a thin membrane minimises uncertainty in the contact radius while the use of spincast films provides very smooth surfaces by means of a very simple method. The experimental profile of the deformed membrane shows good agreement with the expected logarithmic profile. While this agreement allows measurement of the Young's modulus and solid-solid work of adhesion in thin films, this study will focus on the dependence of the Young's modulus on the annealing history in thin films. The thermal history dependence shows that for short annealing times Young's modulus is larger than expected, suggesting that the chains are oriented during spincasting. For longer times, Young's modulus reaches literature values.   

Contributions to the Adhesion of Glassy Polymers from Radical Recombination and Segmental Interpenetration at Elevated Temperatures

We study two examples of adhesive interactions between glassy polymers that occur when the polymers are heated to elevated temperatures. First set is the adhesion between thin films of poly(phenylene oxide) (PPO). The samples are brought into contact at an elevated temperature and cooled to room temperature prior to measuring the fracture energy by using the contact mechanics approach based on JKR (Johnson, Kendall and Roberts) theory. Very little adhesion is observed at temperatures below about 130C, which enables us to perform a second set of experiments, where adhesion is due to radical recombination across the interface. Polystyrene (PS) is synthesized by anionic polymerization, and terminated by an end-capped nitroxide radical group. Nitroxide mediated polymerization is used to attach a poly (\textit{tert-}butyl acrylate) (tBA) block to the PS chains. These block copolymers are added to the PPO films that are brought into contact with one another. Nitroxide radicals become uncapped at elevated temperatures, with subsequent radical recombination providing another potential mechanism for the formation of bonds across the interface.   

Adhesion and Spatial Distribution of Water in the Presence of Moisture: Surface Chemistry Affects.

Many polymer adhesive bonds experience a complete loss of adhesion above a critical threshold relative humidity value. The adhesion loss from water exposure does not generally correlate with moisture solubility of the polymer; instead the surface layer of the polymer appears to be the controlling factor in the adhesion. Here, the adhesion and spatial distribution of water of a series of PMMA-Al adhesive samples in the presence of moisture is measured with neutron reflectivity, while the adhesive strength of the joint is measured using the shaft-loaded blister test. The role of changing surface chemistry was examined to determine their effect on this interfacial moisture content. The loss of adhesive strength upon exposure to moisture correlates directly with the interfacial water content. Surface modification methods that decrease the interfacial water content are used to tune the adhesive strength in moist environments. Minimization of the interfacial water concentration does not however result in the best adhesion in moist environments as interplay between the dry adhesion and water content exists.   

Quantifying Ballistic Armor Performance: A Minimally Invasive Approach

Theoretical and non-dimensional analyses suggest a critical link between the performance of ballistic resistant armor and the fundamental mechanical properties of the polymeric materials that comprise them. Therefore, a test methodology that quantifies these properties without compromising an armored vest that is exposed to the industry standard V-50 ballistic performance test is needed. Currently, there is considerable speculation about the impact that competing degradation mechanisms (e.g., mechanical, humidity, ultraviolet) may have on ballistic resistant armor. We report on the use of a new test methodology that quantifies the mechanical properties of ballistic fibers and how each proposed degradation mechanism may impact a vest's ballistic performance.   

Measurement of the Viscoelastic Bulk Modulus

A new piston-cylinder type pressurizable dilatometer has been developed to measure the time-dependent bulk modulus of viscoelastic materials. The PVT behavior and the glass transition temperature of a polystyrene have been measured as a function of pressure. Preliminary measurements of the time-dependent bulk modulus have also been made. The isothermal bulk modulus is important because its magnitude is directly related to isotropic residual stress development in curing thermoset-reinforced composites; in addition, by comparing the bulk and shear responses, proposed differences in the molecular origins can be explored.   

Influence of Physical Aging on the Mechanical Properties of a Random Polypropylene-Polyethylene Copolymer

Spontaneous aging of a random polypropylene-polyethylene copolymer was studied at 50 $^{o}$C above its glass transition temperature using differential scanning calorimetry, wide (WAXS) and small (SAXS) angle X-ray scattering, and dynamic mechanical relaxometry. Both the melting temperature and melting enthalpy of the copolymer increased with physical aging time at room temperature suggesting increased crystallinity. WAXS measurements also indicated an increase in crystallinity along with coexistence of $\gamma$ and $\alpha$ forms for highly aged samples. Dynamic mechanical measurements showed that the shear storage modulus increased uniformly at all frequencies of measurement from 0.1 Hz to 20 Hz. Furthermore a direct correlation was observed between the storage modulus and the melting enthalpy of the copolymer. Conversely, the change in shear loss modulus was frequency dependent, with larger changes at 20 Hz than at 0.1 Hz. This suggests that there are changes in the relaxation time spectra with aging. The aging process will be explored in more detail using both the SAXS and stress relaxation data.   

Fracture versus cavitation in probe-tack geometry: theory and experiments

We perform traction experiments on viscous liquids highly confined between parallel plates, a geometry known as the probe-tack test in the adhesion community. Direct observation during the experiment coupled to force measurement shows the existence of several mechanisms for releasing the stress. Bubble nucleation and instantaneous growth had been observed in a previous work. Upon increasing further the traction velocity or the viscosity, the bubble growth is progressively delayed. At even higher velocities, fractures at the interface between the plate and the liquid are observed before the bubbles have grown to their full size. We present a theoretical model that describes these regimes, using a Maxwell fluid as a model for the actual fluid. We present the resulting phase diagram for the different force peak regimes. It remarkably accounts for the data. Our results show that in addition to cavitation, interfacial fractures, commonly thought to be characteristic of soft viscoelastic solids like adhesives are already encountered in \emph{liquid} materials.