Numerical material testing for discontinuous fiber composites using statistically similar representative volume elements.

A computational method is proposed in order to predict mechanical properties of discontinuous fiber composites (DFCs) based on computational homogenization with statistically similar representative volume elements (SSRVEs). The SSRVEs are obtained by reducing the complexity of real microstructures based on statistical measures. Specifically, they are constructed by minimizing an objective function defined in terms of differences between the power spectral density of target microstructures and that of the SSRVEs. In this paper, an extended construction method is proposed based on the reformulation of the objective function by integer design variables. The proposed method is applied to the representation of a real material, namely glass fiber reinforced nylon 6. The results show that the mechanical properties computed by numerical material tests using the SSRVEs agree with experimental results. Therefore, it is found that the nonlinear mechanical properties of the DFC can be suitably predicted by the proposed method without any special calibration to experiments performed on the composites.

Nonlinear acoustic response through minute surface cracks: FEM simulation and experimentation.

The second harmonic of a Rayleigh wave passing through a minute surface crack has been numerically analyzed by semi-explicit FEM including special elements which account for a nonlinear stress-strain relation at crack surfaces. Minute cracks perpendicular to a free, flat surface close under compressive stress when width of the crack opening is less than the longitudinal amplitude of the Rayleigh wave. Thereafter, compressive and shear stresses are partially transmitted through the closed cracks, whereas tensile and shear stresses are not transmitted through cracks that remain open. This leads to marked nonlinear ultrasonic response. Calculation was performed for an aluminum block having a surface crack. The transverse component of the Rayleigh wave propagating through the cracks shows distorted waveforms, making the second harmonic amplitude clearly noticeable. In an experiment, the second harmonic component of the leaky Rayleigh wave was detected for a simple crack model consisting of two aluminum blocks, by use of a PVDF line-focused transducer. The results of the experiment show that the second harmonic amplitude is a second-order function of the fundamental wave amplitude, and is more pronounced for low compressive stress applied to close the crack surfaces.