Heating during shearing and opening dominated dynamic fracture of polymers

The heat generated from dissipative mechanisms during shearing and opening dominated dynamic fracture of polymethyl methacrylate and polycarbonate was measured with a remote sensing technique that utilizes the detection of infrared radiation. Significant heating was detected for both materials and both modes of fracture. In the shear dominated experiments, the temperature increase at the crack tip in polymethyl methacrylate was 85 K, the approximate increase necessary to reach the glass transition temperature. An adiabatic shear band followed by a dynamically propagating crack were observed during the shear dominated experiments using polycarbonate. The recorded shear band temperature increase was 45 K. This was followed by an additional 100 K temperature increase from the ensuing crack, raising the temperature above glass transition. The maximum temperature increase recorded for the opening mode experiments was 55 K for polymethyl methacrylate and 105 K for polycarbonate. The results of this study show that temperature effects are significant during the dynamic fracture of polymers. The effects are especially important in the shear dominated case where local temperatures approach or exceed the polymer glass transition temperature.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Experimental determination of cohesive failure properties of a photodegradable copolymer

In this paper we present a methodology to measure the material traction-separation relation for a poly(ethylene carbon monoxide) copolymer, ECO. This material exhibits a ductile-to-brittle transition when subjected to ultraviolet irradiation and undergoes a change of failure mechanism, from shear yielding to crazing, in the process. Single edge notched tension specimens of ECO irradiated for 50 h were used to generate slow-speed stable crack growth, predominantly from material crazing. Full-field measurements of the in-plane deformation around the growing crack tip were performed using the optical technique of digital image correlation. A multicamera setup was used in which simultaneous measurement of both the far-field displacement and that directly surrounding the craze was performed. The far-field results were used to obtain a value of the energy release rate supplied to the crack tip region. The near-tip results were used to extract a material traction-separation law in the regime of steady-state crack growth. A softening traction-separation relation was measured. The area under the traction-separation curve was then compared with the simultaneous far-field measurements and the agreement was very good (within 6.5%) validating the experimental methodology used.     

Crack Path Selection in Microstructurally Tailored Inhomogeneous Polymers

In this work the photodegradation of a polyethylene co-polymer, ECO, is exploited to generate inhomogeneous arrangements of model “granular” media that aids in the experimental study of crack path selection problems. The advantage of our approach is that the well-known sensitivity of ECO’s properties to ultraviolet (UV) light allows knowledge of both grain and grain boundary response a priori to performing the experiments. A model granular arrangement with identical grain structure and of three different levels of grain boundary strength was constructed. Each microstructure was loaded in uniaxial tension, and the resulting strain fields were recorded using digital image correlation (DIC). Depending on the applied load and the local microstructure, crack initiation and growth occurred differently: either one main crack developed and became responsible for failure, or an initial crack formed but arrested, and a host of secondary cracks appeared at different critical locations, including grain boundaries and grain interiors. Thus, the experimental configuration can be used to produce controllable amounts of intergranular vs. transgranular failure. The DIC results were correlated with global load–displacement measurements and were compared to finite element models using ABAQUS that simulated the configurations tested in each case. A von Mises and Tresca yield criterion was used to illustrate areas where failure was possible, and the results were favorably compared with the experimental failure initiation sites in each case.     

A Hybrid Experimental/Numerical Investigation of the Response of Multilayered MEMS Devices to Dynamic Loading

In order to probe the mechanical response of microelectromechanical systems (MEMS) subjected to dynamic loading, a modified split Hopkinson pressure bar was used to load MEMS devices at accelerations ranging from 10³–10⁵  g. Multilayer beams consisting of a PZT film sandwiched between two metal electrodes atop an elastic layer of silicon dioxide were studied because of their relevance to active MEMS devices. Experiments were conducted using the modified split Hopkinson pressure bar to quantify the effects of dynamic loading amplitude, duration, and temporal profile on the failure of the multilayered cantilever beams. Companion finite element simulations of these beams, informed by experimental measurements, were conducted to shed light into the deformation of the multilayered beams. Results of the numerical simulations were then coupled with independent experimental measurements of failure stress in order to predict the material layer at which failure initiation occurred, and the associated time to failure. High-speed imaging was also used to capture the first real-time images of MEMS structures responding to dynamic loading and successfully compare the recorded failure event with those predicted numerically.     

Analysis of coherent gradient sensing (CGS) by fourier optics

A coherent laser beam reflected or transmitted from a deforming plate specimen acquires an optical path difference (phase change) which is related to the deformation and stress field. The optical method of Coherent Gradient Sensing (CGS) uses two parallel grating plates to displace (shear) and recombine the distorted light beam emerging from the specimen. Fringes are produced on the image plane by the interference of the shifted and unshifted beams. The fringe pattern is related to the spatial difference of the phase in the shearing direction. If the shearing distance is small enough, the spatial difference of the phase approximates to its gradient. Each fringe in the image represents a locus of equal gradient component of the phase in the shearing direction. The technique is interpreted by means of wave optics, using the Fraunhofer approximation and the paraxial theory of lenses. The assumptions made in earlier analyses have been removed here. A more precise analysis based on Fourier optics is presented. The simplicity of the optical setup and variable resolution of the technique have led to its frequent use in the area of solid mechanics, including fracture mechanics. Some examples are discussed in the second half of this paper.     

Evidence of a natural boundary and nonintegrability of the mixmaster universe model

Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically, we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence on initial conditions.     

Digital Image Correlation for Improved Detection of Basal Cell Carcinoma

Border detection is a critical aspect during removal of a basal cell carcinoma tumor. Since the tumor is only 3% to 50% as stiff as the healthy skin surrounding it, strain concentrates in the tumor during deformation. Here we develop a digital image correlation (DIC) technique for improved lateral border detection based upon the strain concentrations associated with the stiffness difference of healthy and cancerous skin. Gelatin skin phantoms and pigskin specimens are prepared with compliant inclusions of varying shapes, sizes, and stiffnesses. The specimens with inclusions as well as several control specimens are loaded under tension, and the full-field strain and displacement fields measured by DIC. Significant strain concentrations develop around the compliant inclusions in gelatin skin phantoms, enabling detection of the tumor border to within 2% of the actual border. At a lower magnification, the lateral border between a pigskin/inclusion interface is determined within 23% of the border. Strain concentrations are identified by DIC measurements and associated with the lateral edges of the compliant inclusions. The experimental DIC protocol developed for model specimens has potential as a tool to aid in more accurate detection of basal cell carcinoma borders.     

Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium

Using a focal plane array infrared camera, the heat generated during large strain compression (at a rate of 1 s⁻¹) is used to study the characteristics of plastic flow for hcp zirconium. Heat generation during plastic flow in a reference material, copper, was seen to develop uniformly both at the lower (40 μm/pixel) and higher (8 μm/pixel) magnifications used in this study. The thermomechanical response of Zr, however, was seen to depend on the loading direction with respect to the specimen texture. Highly textured zirconium compressed along nonbasal oriented grains results in a homogeneous thermal response at both scales. However, compression along basal (0001) oriented grains shows evidence of inhomogeneous deformation at small strains that lead to macroscale localization and failure at large strains. The conversion of plastic work into heat is observed to be a dynamic process, both in the time-dependent nature of the energy conversion, but also in the passage of waves and ‘bursts’ of plastic heating. Basal compression also showed evidence of small scale localization at strains far below macroscale localization, even below 10%. These localizations at the lower strain levels eventually dominate the response, and form the shear band that is responsible for the softening of the macroscopic stress–strain curve.