An empirical model for estimating fracture toughness using the DCDC geometry

The double cleavage drilled compression (DCDC) geometry is useful for creating large cracks in a material in a controlled manner. Several models for estimating fracture toughness from DCDC measurements have been proposed, but each is suitable for a subset of geometries and material properties. In this work, a series of finite element fracture simulations are performed over a range of sample widths, hole sizes, heights, Young's moduli, Poisson's ratios, critical stress intensity factors, and boundary conditions. Analyzing the simulation results, fracture toughness is found to be a simple function of sample width, hole size, and an extrapolated stress at zero crack length obtained from a linear fit of the data. Experimental results in the literature are found to agree with this simple relationship. © 2014 Springer Science+Business Media Dordrecht

Phononic layered composites for stress-wave attenuation

The aim is to design a layered metamaterial with high attenuation coefficient and high in-plane stiffness-to-density ratio using homogenization to calculate and optimize the dynamic effective stiffness and mass density of layered periodic composites (phononic layers) over a broad frequency band. This is achieved by: (1) minimizing the frequency range of the first pass band, (2) maximizing the frequency range of the stop band, and (3) creating local resonance over the second pass band. To verify the theoretical calculation, laboratory samples were fabricated and their attenuation coefficient were measured and compared with the theoretical results. It is observed that over 4-20 kHz frequency range the attenuation per unit length in the optimally designed composite can exceed 500 dB/m; which increases with increasing frequency. A dynamic Ashby chart, depicting attenuation coefficient vs. in-plane stiffness-to-density ratio, is presented for various engineering materials and is compared with the fabricated metamaterial to show the significance of our design. This method can be used in variety of applications for stress wave management, e.g., in addition to match the impedance of the resulting composite to that of its surrounding medium to minimize (or essentially eliminate) stress wave reflection

Ultrasonic properties of fly ash/polyurea composites

An experimental study has been conducted to determine the mechanical properties of fly-ash/polyurea composites by measuring their longitudinal and shear wave velocities, and attenuations at various fly ash volume fractions, using ultrasonic. The complex-valued longitudinal and shear moduli were computed from these measurements at various temperatures. It was observed that a 30% volume fraction addition of fly ash has increased the longitudinal storage and loss moduli and shear storage and loss moduli by up to 22%, 141%, 298% and 125%, respectively. The complex bulk modulus and Poisson's ratio of the composites at 1. MHz were also estimated. Additionally, a computational model based on the method of dilute-randomly-distributed inclusions was created to estimate the dynamic mechanical properties of the composites. The experimental and computational results were compared and showed good agreement

Experimentally-based relaxation modulus of polyurea and its composites

Polyurea is a block copolymer that has been widely used in the coating industry as an abrasion-resistant and energy-dissipative material. Its mechanical properties can be tuned by choosing different variations of diamines and diisocyanates as well as by adding various nano- and micro-inclusions to create polyurea-based composites. Our aim here is to provide the necessary experimentally-based viscoelastic constitutive relations for polyurea and its composites in a format convenient to support computational studies. The polyurea used in this research is synthesized by the reaction of Versalink P-1000 (Air Products) and Isonate 143L (Dow Chemicals). Samples of pure polyurea and polyurea composites are fabricated and then characterized using dynamic mechanical analysis (DMA). Based on the DMA data, master curves of storage and loss moduli are developed using time–temperature superposition. The quality of the master curves is carefully assessed by comparing with the ultrasonic wave measurements and by Kramers–Kronig relations. Based on the master curves, continuous relaxation spectra are calculated, then the time-domain relaxation moduli are approximated from the relaxation spectra. Prony series of desired number of terms for the frequency ranges of interest are extracted from the relaxation modulus. This method for developing cost efficient Prony series has been proven to be effective and efficient for numerous DMA test results of many polyurea/polyurea-based material systems, including pure polyurea with various stoichiometric ratios, polyurea with milled glass inclusions, polyurea with hybrid nano-particles and polyurea with phenolic microbubbles. The resulting viscoelastic models are customized for the frequency ranges of interest, reference temperature and desired number of Prony terms, achieving both computational accuracy and low cost. The method is not limited to polyurea-based systems. It can be applied to other similar polymers systems

Determining the shear relaxation modulus and constitutive models for polyurea and polyurea-based composite materials from dynamic mechanical testing data

Polyurea and polyurea-based composite materials are widely used due to their excellent mechanical properties. In order to facilitate large-scale computational studies for this group of materials, a robust and standard method is needed to extract their viscoelastic constitutive parameters. In this study, frequency-domain master curves which cover a wide range of frequencies are developed using the data of dynamic mechanical analysis through time-temperature superposition (TTS). The quality of the master curves is assessed both by Kramers-Kronig relations and by comparing with the ultrasonic wave testing data. Then the time-domain relaxation modulus is obtained by the high-resolution Prony series approximated from the relaxation spectrum. To reduce computational cost, 4 to 8-term Prony series are then fitted from the time-domain relaxation modulus for a limited frequency range of interest. Both the high and low-resolution Prony series are converted back to frequency domain to compare with the master curves developed by TTS and show good agreements. This method is not limited to polyurea and polyurea-based composites and it can be applied to other similar polymer systems as well

Phononic layered composites for stress-wave attenuation

The aim is to design a layered metamaterial with high attenuation coefficient and high in-plane stiffness-to-density ratio using homogenization to calculate and optimize the dynamic effective stiffness and mass density of layered periodic composites (phononic layers) over a broad frequency band. This is achieved by: (1) minimizing the frequency range of the first pass band, (2) maximizing the frequency range of the stop band, and (3) creating local resonance over the second pass band. To verify the theoretical calculation, laboratory samples were fabricated and their attenuation coefficient were measured and compared with the theoretical results. It is observed that over 4-20 kHz frequency range the attenuation per unit length in the optimally designed composite can exceed 500 dB/m; which increases with increasing frequency. A dynamic Ashby chart, depicting attenuation coefficient vs. in-plane stiffness-to-density ratio, is presented for various engineering materials and is compared with the fabricated metamaterial to show the significance of our design. This method can be used in variety of applications for stress wave management, e.g., in addition to match the impedance of the resulting composite to that of its surrounding medium to minimize (or essentially eliminate) stress wave reflection