Extending the annular in-plane torsional shear test specimen to applications at high strain rates

In-plane torsional shear testing is a well-established material testing technique in the metal forming community. The corresponding specimen is designed to be machined from sheet metal with a continuous annular shear zone intended to deform in simple shear. Consequently, there are no geometric discontinuities or “edge-effects” to induce volumetric changes or instabilities with the result that large true plastic strains up to 1.0 can be achieved. This paper presents an extension of the in-plane torsional shear test to the dynamic regime. Dynamic experiments were performed using a torsional split Hopkinson bar (TSHB) on specimens manufactured from Al 1050 H14. The experimental results show that the adopted technique can be used to determine the material behavior accurately and reliably in the dynamic regime.

Vibration of porous functionally graded plates with geometric discontinuities and partial supports

Vibrational study of the porous functionally graded plate with geometric discontinuities and partial supports has been presented in the present paper. The kinematics of functionally graded plate is based on the refined exponential shear deformation theory. The displacement field has been refined by dividing the in-plane and out of the plane displacements into bending and shear components. The theory accounts for the nonlinear transverse shear stress variation along with the thickness with only four unknowns. The closed-form solution (Navier’s solution), as well as FEM-based solution, have been used for the vibration analysis of functionally graded plate. The geometric discontinuities have been incorporated in terms of a circular cut-out of different sizes at the center of the plate. Modified rule of mixtures, modified sigmoid law, and trigonometric law have been used to compute the effective material properties of the functionally graded plate. A C0 continuous iso-parametric FEM formulation has been used to attain the results in the case of FEM solution, and the efficacy of the present solution is demonstrated by comparing the results with the available literature. The results reflect that the porosity inclusion, circular cut-out, and position of the boundary constraints have a notable influence on the fundamental frequency of the functionally graded plate. It is also concluded that after a specific radius of circular cut-out, the vibration response of functionally graded plate exhibits nonlinearity in nature.

Macro-Scale Geometric Voids to Alter Stress Wave Propagation in Solids

Structural discontinuities, such as voids or inclusions in otherwise uniform, solid materials have previously been successfully implemented to alter the propagation of various types of waves through a range of materials and structures. Much of this work has focused on micro-scale features and low energy waves. The disruption of waves carrying larger amounts of energy currently relies mainly on large material deformation, typically with a layer of the structure becoming permanently damaged in order to protect other portions. However, the ability to disrupt, alter, direct, and control higher energy waves without significant damage to the material or structure can be desirable. Microscale features can disperse wave fronts, scattering their energy and reducing the potentially damaging effects of the concentrated loads carried in these waves. However, the control of the distribution of these microscale features throughout the material and structure can be difficult, limiting the ability to use these materials to control the dispersion of the wave energy or direct it to more desirable regions in the structure. Macro-scale features can be more easily formed into patterns and arrangements which can be designed for specific wave-controlling or directing properties. Additionally, materials and structures with macro-scale discontinuities can result in a greater change in energy per inclusion and a greater spatial range of their effects throughout the domain of the material. Therefore, they have the potential to be used to address input waves of higher energy. The use of macro-scale features may provide added manufacturing-based benefits, particularly with the more widespread development and use of advanced manufacturing methods, such as additive manufacturing. This study examines the feasibility of the use of arrays of macro-scale features to direct and control input stress waves. The effect of the shape and arrangement of macro-scale geometric features is studied under a range of orders of magnitudes of the incident stress wave. Methods are developed in this work to predict the propagation of the stress waves through the material and to quantitatively assess the effects of these included arrays of structural, geometric discontinuities. The results of this study are used to evaluate the feasibility of the use of these geometric macro-scale arrays to control the propagation of stress waves in structures while limiting gross material deformation and damage to the overall structure.

Probabilistic Risk Assessment of Aging Layered Pressure Vessels

The National Aeronautics and Space Administration (NASA) operates approximately 300 aging layered pressure vessels that were designed and manufactured prior to ASME Boiler and Pressure Vessel (B&PV) code requirements. In order to make decisions regarding the continued fitness-for-service of these non-code carbon steel vessels, it is necessary to perform a relative risk of failure assessment for each vessel. However, risk assessment of these vessels is confounded by uncertainties and variabilities related to the use of proprietary materials in fabrication, missing construction records, geometric discontinuities, weld residual stresses, and complex service stress gradients in and around the welds. Therefore, a probabilistic framework that can capture these uncertainties and variabilities has been developed to assess the fracture risk of flaws in regions of interest, such as longitudinal and circumferential welds, using the NESSUS® probabilistic modeling software and NASGRO® fracture mechanics software. In this study, the probabilistic framework was used to predict variability in the stress intensity factor associated with different reference flaws located in the head-to-shell circumferential welds of a 4-layer and 14-layer pressure vessel. The probabilistic studies predict variability in flaw behavior and the important uncertain parameters for each reference flaw location.

A numerical approach to determine fiber orientations around geometric discontinuities in designing against failure of GFRP laminates

Purpose Determining fiber orientations around geometric discontinuities is challenging and simultaneously crucial when designing laminates against failure. The purpose of this paper is to present an approach for selecting the fiber orientations in the vicinity of a geometric discontinuity; more specifically round holes with edge cracks. Maximum stresses in the discontinuity region are calculated using Classical Lamination Theory (CLT) and the stress concentration factor for the aforementioned condition. The minimum moment to cause failure in a lamina is estimated using the Tsai–Hill and Tsai–Wu failure theories for a symmetric general stacking laminate. Fiber orientations around the discontinuity are obtained using the Tsai–Hill failure theory. Design/methodology/approach The current research focuses on a general stacking sequence laminate under three-point bending conditions. The laminate material is S2 fiber glass/epoxy. The concepts of mode I stress intensity factor and plastic zone radius are applied to decide the radius of the plastic zone, and stress concentration factor that multiplies the CLT stress distribution in the vicinity of the discontinuity. The magnitude of the minimum moment to cause failure in each ply is then estimated using the Tsai–Hill and Tsai–Wu failure theories, under the aforementioned stress concentration. Findings The findings of the study are as follows: it confirms the conclusions of previous research that the size and shape of the discontinuity have a significant effect on determining such orientations; the dimensions of the laminate and laminae not only affect the CLT results, but also the effect of the discontinuity in these results; and each lamina depending on its position in the laminate will have a different minimum load to cause failure and consequently, a different fiber orientation around the geometric discontinuity. Originality/value This paper discusses an important topic for the manufacturing and design against failure of Glass Fiber Reinforced Plastic (GFRP) laminated structures. The topic of introducing geometric discontinuities in unidirectional GFRP laminates is still a challenging one. This paper addresses these issues under 3pt bending conditions, a load condition rarely approached in literature. Therefore, it presents a fairly simple approach to strengthen geometric discontinuity regions without discontinuing fibers.

The numerical analysis of the interaction between the low-order Lamb wave modes and surface breaking cracks

Lamb waves, as one of the types of guided waves, are extensively used for inspecting large structures as well as for structure health monitoring applications. One of the biggest benefits of guided waves is their ability to travel over long distances without much attenuation. Lamb waves are often used for inspection of piping systems and similar geometries where the dimension in the third direction is significantly smaller than the other two. No wonder that the study of the interaction of Lamb waves with particular types of geometric discontinuities is a frequent topic of research. The main aim of the proposed paper is to present the findings related to the numerical study of the interaction between low-order Lamb wave modes and surface breaking crack oriented at different angles relative to the free surface.