Sridhar Santhanam

An algorithm for determining the optimal blank shape for the deep drawing of aluminum cups

Abstract In the deep drawing of cups, the earing defect is caused by planar anisotropy in the sheet and friction between the blank and punch/die. In the past, several incomplete research efforts have been directed toward predicting an optimal blank shape that will avoid the formation of ears. In this paper, we consider the problem of optimal blank design for deep drawing, including the effects of anisotropy and friction. The material considered for the simulations is aluminum 2048. A planar anisotropic yield function proposed by Barlat is used. The initial blank shape chosen is circular. A finite element analysis is performed to simulate the deep-drawing process. An error metric, to measure the amount of earing, is constructed for the resulting cup. This error metric is then used to re-design the initial blank shape. The cycle is repeated until the error metric satisfies a preset convergence criterion. This iterative design process leads to an optimal blank shape. Several different test problems are considered, including flanged and flangeless circular and square cups. Simulation results are very encouraging with reasonable number of iterations to arrive at the optimal blank shape.

Reflection of Lamb waves obliquely incident on the free edge of a plate

The reflection of obliquely incident symmetric and anti-symmetric Lamb wave modes at the edge of a plate is studied. Both in-plane and Shear-Horizontal (SH) reflected wave modes are spawned by an obliquely incident in-plane Lamb wave mode. Energy reflection coefficients are calculated for the reflected wave modes as a function of frequency and angle of incidence. This is done by using the method of orthogonal mode decomposition and by enforcing traction free conditions at the plate edge using the method of collocation. A PZT sensor network, affixed to an Aluminum plate, is used to experimentally verify the predictions of the analysis. Experimental results provide support for the analytically determined results.

Reflection and transmission of fundamental Lamb wave modes obliquely incident on a crack in a plate

Lamb waves are increasingly being used for structural health monitoring of plate-like structures. In order to take advantage of Lamb waves, it is important to have a good understanding of how they interact with defects such as cracks. In this study, the scattering of the fundamental S0 Lamb mode by a part-through transverse symmetric crack in an isotropic plate is examined. The modal decomposition technique coupled with the method of collocation is used to determine the energy reflection coefficients of reflected and transmitted waves. These coefficients are shown to depend on the crack depth and the incident frequency. Experiments were conducted to verify the analytical results. Two different crack depths and frequencies were used. The experimental results follow the trends seen in the analytical results.

Multimodal sparse reconstruction in Lamb wave-based structural health monitoring

Lamb waves are utilized extensively for structural health monitoring of thin structures, such as plates and shells. Normal practice involves fixing a network of piezoelectric transducers to the structural plate member for generating and receiving Lamb waves. Using the transducers in pitch-catch pairs, the scattered signals from defects in the plate can be recorded. In this paper, we propose an l1-norm minimization approach for localizing defects in thin plates, which inverts a multimodal Lamb wave based model through exploitation of the sparseness of the defects. We consider both symmetric and anti-symmetric fundamental propagating Lamb modes. We construct model-based dictionaries for each mode, taking into account the associated dispersion and attenuation through the medium. Reconstruction of the area being interrogated is then performed jointly across the two modes using the group sparsity constraint. Performance validation of the proposed defect localization scheme is provided using simulated data for an aluminum plate.

Multimodal sparse reconstruction in guided wave imaging of defects in plates

Abstract. A multimodal sparse reconstruction approach is proposed for localizing defects in thin plates in Lamb wave-based structural health monitoring. The proposed approach exploits both the sparsity of the defects and the multimodal nature of Lamb wave propagation in plates. It takes into account the variation of the defects’ aspect angles across the various transducer pairs. At low operating frequencies, only the fundamental symmetric and antisymmetric Lamb modes emanate from a transmitting transducer. Asymmetric defects scatter these modes and spawn additional converted fundamental modes. Propagation models are developed for each of these scattered and spawned modes arriving at the various receiving transducers. This enables the construction of modal dictionary matrices spanning a two-dimensional array of pixels representing potential defect locations in the region of interest. Reconstruction of the region of interest is achieved by inverting the resulting linear model using the group sparsity constraint, where the groups extend across the various transducer pairs and the different modes. The effectiveness of the proposed approach is established with finite-element scattering simulations of the fundamental Lamb wave modes by crack-like defects in a plate. The approach is subsequently validated with experimental results obtained from an aluminum plate with asymmetric defects.

Simulating damage growth in a [90/0]s composite laminate using quasi-two-dimensional finite element methods

A computationally efficient numerical method is described for predicting the details of damage growth in cross-plied and angle-plied fiber composite laminates. Separate two-dimensional plane stress meshes are used to represent each layer. Element boundaries are aligned along primary crack paths (parallel to fibers). Element corners in separate layers which share the same planar coordinates are attached to a single through-thickness node. Cracking of a layer parallel to fibers is modeled by combinations of releasing element nodal connections in the layer, creating new nodes, and/or modifying element elastic properties, depending on whether or not the layer is attached to or delaminated from one or both of its neighbors. Delaminations are modeled by releasing nodal connections between layers and creating new nodes. The essential three-dimensional character of the process, which is necessary to incorporate the effects of stacking sequence, is maintained by casting mixed-mode delamination fracture mechanics in terms of interlaminar nodal forces, and including adjacent layer constraint on the fracture mechanics of cracks in layers. Choice of element size is important to the method and has resulted in simplifications to crack propagation and fiber fracture prediction methodologies. Results to-date of predicted static damage growth in notched cross-plied carbon composites are described.

An elastic-viscoplastic constitutive model for the hot-forming of aluminum alloys

Under hot-forming conditions characterized by high homologous temperatures and strain-rates, metals usually exhibit rate-dependent inelastic behavior. An elastic-viscoplastic constitutive model is presented here to describe metal behavior during hot-forming. The model uses an isotropic internal variable to represent the resistance offered to plastic deformation by the microstructure. Evolution equations are developed for the inelastic strain and the deformation resistance based on experimental results. A methodology is presented for extracting model parameters from constant true strain-rate compression tests performed at different temperatures. Model parameters are determined for an Al-1Mn alloy and an Al-Mg-Si alloy, and the predictions of the model are shown to be in good agreement with the experimental data.

Analysis of toughening mechanisms in the Strombus gigas shell.

A finite element analysis of the fracture mechanisms in the Strombus gigas conch shell is presented in this work. The S. gigas shell has a complex microarchitecture that consists of three main macroscopic layers of calcium carbonate: the inner, middle, and outer layers. Each layer is composed of lamellae of calcium carbonate, held together by a cohesive organic protein. As a result of this elaborate architecture, the S. gigas shell exhibits a much greater damage tolerance than the calcium carbonate by itself, with a work of fracture reported to be three magnitudes of order greater. The two main energy dissipating factors that contribute to this are multiple, parallel cracking along first-order interfaces in the inner and outer layers and crack bridging through the second-order interfaces of the middle layer. Finite element analysis was conducted to simulate and replicate flexural strength and work-of-fracture results obtained in the literature for both dry and wet physical bend test specimens. Several parameters were varied including protein strength and fracture toughness, initial protein damage, and the relative heights of macroscopic layers in order to create a model that predicted published, experimental results. The simulations indicate that having some initially weakened protein interfaces is key to matching the parallel cracking in the inner layer of the physical specimens. The wet models exhibit significantly higher work of fracture compared to the dry specimens in large part due to a crack growth resistance behavior in the middle layer, which was successfully modeled. The parametric studies that have been performed on the finite element models provide guidelines for manufacturing the ideal S. gigas-inspired, biomimetic composite.

Multimodal exploitation and sparse reconstruction for guided-wave structural health monitoring

The presence of multiple modes in guided-wave structural health monitoring has been usually considered a nuisance and a variety of methods have been devised to ensure the presence of a single mode. However, valuable information regarding the nature of defects can be gleaned by including multiple modes in image recovery. In this paper, we propose an effective approach for localizing defects in thin plates, which involves inversion of a multimodal Lamb wave based model by means of sparse reconstruction. We consider not only the direct symmetric and anti-symmetric fundamental propagating Lamb modes, but also the defect-spawned mixed modes arising due to asymmetry of defects. Model-based dictionaries for the direct and spawned modes are created, which take into account the associated dispersion and attenuation through the medium. Reconstruction of the region of interest is performed jointly across the multiple modes by employing a group sparse reconstruction approach. Performance validation of the proposed defect localization scheme is provided using simulated data for an aluminum plate.

Processing and characterization of silicon nitride nanofiber paper

Papers of silicon nitride nanofibers were synthesized by a carbothermal reduction process. These nanofiber papers were synthesized in situ and did not require a secondary processing step. The process utilized silica nanopowders and silica gel as the precursor material. Processing geometry played a crucial role in regulating the growth of the nanofiber papers. Characterization of the nanofiber papers indicated that the nanofibers were of the alpha silicon nitride phase. Both mechanical stiffness and strength of the nanofiber papers were measured. Thermal conductivity and specific heat of the papers were also measured and were found to be lower than many common thermal insulation materials at much smaller thicknesses and were comparable to those values that are typically reported for carbon-nanotube-based buckypaper. Results of the mechanical and thermal characterization indicate that these silicon nitride nanofiber papers can be utilized for specialized thermal insulation applications.