Cliff J. Lissenden

3D Finite Element Analysis of Particle-Reinforced Aluminum

Abstract Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress–strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle volume fraction of the 3D models predicted the same macroscopic stress–strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45° from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.

Numerical modelling of damage development and viscoplasticity in metal matrix composites

Abstract Metal matrix composites can exhibit inelastic response due to matrix viscoplasticity as well as fiber/matrix interfacial damage. This paper presents a numerical procedure that can be used to implement a micromechanical model based on a periodic array of continuous fibers embedded in a metallic matrix. The model incorporates elastic-viscoplastic constitutive equations for the matrix and non-linear interfacial traction-displacement relations for the fiber/matrix interface. Generalized plane strain finite elements are formulated in such a way to allow the application of multiaxial loadings while only having to discretize a generic transverse plane. Non-linear lamination theory provides the link between the micro- and macro-level responses of laminated composites subjected to thermomechanical loading. Numerical results indicate that a relatively small number of elements are required to achieve mesh convergence. Also, the axial tensile response is independent of the condition of the fiber/matrix interface, while debonding significantly influences the transverse tensile and axial shear responses.

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

Abstract. Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility.

Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: Higher harmonic generation

A generalized approach is presented to analyze the nature of guided wave mode interactions in isotropic weakly nonlinear elastic plates. The problem formulation is carried out in terms of the displacement gradient, which facilitates systematic analysis of mode interactions in general and that of higher harmonic generation in particular. Only cumulative harmonics are analyzed; these (1) have nonzero power flow and (2) are phase matched. Results indicate that the interaction of Rayleigh-Lamb modes of the same nature (symmetric or antisymmetric) can generate only cumulative harmonics that are symmetric modes, while the interaction between modes of opposite nature can generate only cumulative harmonics that are antisymmetric modes. A methodology for assessing cumulative higher harmonic generation (e.g., the third harmonic) is also proposed.

Structural health monitoring of fatigue crack growth in plate structures with ultrasonic guided waves

Fatigue crack growth in plate structures is monitored with ultrasonic guided waves generated from piezoelectric transducers. Cracks initiate in the vicinity of fastener holes due to cyclic in-plane loading. Ultrasonic guided waves that are partially obstructed by the fastener holes are investigated. Since fatigue crack growth increases the obstruction, these waves are effective for monitoring fatigue crack growth in a pitch-catch mode. The transmission coefficient (TC), which is defined essentially as the current-to-baseline amplitude ratio, and the transmission coefficient ratio (TCR), which is based on amplitude ratios from a single wave, are signal features used for crack characterization. The TCR is well suited for structural health monitoring. The excellent agreement between experimental results and finite element analysis of wave propagation corroborates the experiments. A sparse array of transducers is shown to effectively monitor a multifastener joint. The approach using obstructed ultrasonic guided waves has strong potential for prognostics-based structural health management due to the linear relationship between crack size and the TC.

Nonlinear guided waves in plates: a numerical perspective.

Harmonic generation from non-cumulative fundamental symmetric (S0) and antisymmetric (A0) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.

Damage Detection by Piezoelectric Patches in a Free Vibration Method

An experimental program was undertaken to evaluate the feasibility of using piezoelectric patches for damage detection in composite materials. The fact that damage development can cause shifts in the natural frequencies of a structural component suggested an impulse-frequency response approach, in which free vibration was initiated by a single external mechanical pulse and was sensed by piezoelectric patches. Patches in both surface-bonded and embedded configurations were tried. The investigation was conducted on unidirectional glass fiber/epoxy laminated plates containing controlled levels of damage, present as interply delaminations. The data obtained from the piezoelectric patches showed the expected decrease in frequency of the natural vibrational modes with increase in damage. The attractiveness of this method lies in its convenience and its potential for use in the field.

Fiber–matrix interfacial constitutive relations for metal matrix composites

Abstract This article presents a three dimensional fiber–matrix debonding model for weakly bonded composites based on a modified Needleman [1] type cohesive zone model. In this model the fiber–matrix interface is fully described by its strength and ductility under normal and shear loading. Debonding initiates when a quadratic interaction of the interfacial tractions attains a critical value (the interfacial strength). Coulombic frictional forces resist sliding after debonding initiates. Complete interfacial separation occurs when the magnitude of the resultant interfacial displacement exceeds the ductility of the interface. The debonding model is implemented, along with the Bodner–Partom viscoplastic model, in the method of cells micromechanical model of Aboudi [2] to take advantage of the model’s computational efficiency. Model predictions for cyclic loading are observed to agree well with the experimentally obtained transverse tensile and axial shear responses of silicon carbide/titanium.

Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates

The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.

Second harmonic generation in composites: Theoretical and numerical analyses

Second harmonic generation in a transversely isotropic plate and a symmetric compositelaminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric compositelaminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric compositelaminates.