L.R. Francis Rose

The martensitic transformation in ceramics — its role in transformation toughening

This paper reviews the current knowledge and understanding of martensitic transformations in ceramics - the tetragonal to monoclinic transformation in zirconia in particular. This martensitic transformation is the key to transformation toughening in zirconia ceramics. A very considerable body of experimental data on the characteristics of this transformation is now available. In addition, theoretical predictions can be made using the phenomenological theory of martensitic transformations. As the paper will illustrate, the phenomenological theory is capable of explaining all the reported microstructural and crystallographic features of the transformation in zirconia and in some other ceramic systems. Hence the theory, supported by experiment, can be used with considerable confidence to provide the quantitative data that is essential for developing a credible, comprehensive understanding of the transformation toughening process. A critical feature in transformation toughening is the shape strain that accompanies the transformation. This shape strain, or nucleation strain, determines whether or not the stress-induced martensitic transformation can occur at the tip of a potentially dangerous crack. If transformation does take place, then it is the net transformation strain left behind in the transformed region that provides toughening by hindering crack growth. The fracture mechanics based models for transformation toughening, therefore, depend on having a full understanding of the characteristics of the martensitic transformation and, in particular, on being able to specify both these strains. A review of the development of the models for transformation toughening shows that their refinement and improvement over the last couple of decades has been largely a result of the inclusion of more of the characteristics of the stress-induced martensitic transformation. The paper advances an improved model for the stress-induced martensitic transformation and the strains resulting from the transformation. This model, which separates the nucleation strain from the subsequent net transformation strain, is shown to be superior to any of the constitutive models currently available

Mindlin plate theory for damage detection: Imaging of flexural inhomogeneities

The scattering of plate waves by localized damage or defects that can be modeled as flexural inhomogeneities is examined within the framework of Mindlin plate theory. These inhomogeneities are characterized by variations in one or more of the four plate-theory parameters: the bending stiffness, shear stiffness, rotary inertia, and transverse inertia. It is shown that the Born approximation for the scattered field leads to a plate-theory analog of the Fourier diffraction theorem, which relates the far-field scattering amplitude to the spatial Fourier transform of the inhomogeneity variations. The application of this result is illustrated by using synthetic data derived for an idealized model of a delamination as a flexural inhomogeneity, ignoring mode coupling effects. A computationally efficient implementation of the filtered back-propagation algorithm, based on the eigensystem of the scattering operator, is employed for image reconstruction. The implications for in-situ imaging of structural damage in plate-like structures are briefly discussed, and some directions for further work are indicated.

Modelling mechanical properties of core–shell rubber-modified epoxies

Abstract Experiments have been carried out to quantify the effects of rubber content and strain rate on the elastic and plastic deformation behaviour of core–shell rubber-modified epoxies. Both the Youngs modulus and the yield stress were found to be slightly dependent on strain rate, but very sensitive to the volume fraction of rubber particles. Finite element analyses have also been performed to determine the influences of rubber content on the bulk elasticity modulus and the yield stress. By comparing with experimental results, it is found that the Youngs modulus of rubber-toughened epoxies can be accurately estimated using the Mori–Tanaka method, provided that the volume fraction of rubber particles is appropriately evaluated. A yield function is proposed to quantify the effects of hydrostatic stress on the plastic yielding behaviour of rubber-modified epoxies. Agreement with experimental results is good. Also, a viscoplastic model is developed to simulate the strain-rate-dependent stress–strain relations.

An extended diffraction tomography method for quantifying structural damage using numerical Green's functions

Existing damage imaging algorithms for detecting and quantifying structural defects, particularly those based on diffraction tomography, assume far-field conditions for the scattered field data. This paper presents a major extension of diffraction tomography that can overcome this limitation and utilises a near-field multi-static data matrix as the input data. This new algorithm, which employs numerical solutions of the dynamic Greens functions, makes it possible to quantitatively image laminar damage even in complex structures for which the dynamic Greens functions are not available analytically. To validate this new method, the numerical Greens functions and the multi-static data matrix for laminar damage in flat and stiffened isotropic plates are first determined using finite element models. Next, these results are time-gated to remove boundary reflections, followed by discrete Fourier transform to obtain the amplitude and phase information for both the baseline (damage-free) and the scattered wave fields. Using these computationally generated results and experimental verification, it is shown that the new imaging algorithm is capable of accurately determining the damage geometry, size and severity for a variety of damage sizes and shapes, including multi-site damage. Some aspects of minimal sensors requirement pertinent to image quality and practical implementation are also briefly discussed.

A self-consistent approximation for crack bridging by elastic/perfectly plastic ligaments

Abstract In several contexts where the effectiveness of crack-bridging reinforcements degrades when the static or cyclic stress transmitted by the reinforcements exceeds a threshold value, the reinforcements can be idealized as elastic/perfectly plastic springs with the yield stress corresponding to the threshold stress for degradation. A self-consistent procedure is proposed for estimating the net crack tip stress intensity factor k tip for a given applied stress, crack length and length of unbridged zone. Plausible analytical representations are postulated for the crack profile over the intervals where the crack-bridging springs respond elastically. The representations involve k tip as a scaling factor, and lead to implicit formulae for k tip . When the applied stress exceeds the threshold for degradation, further simplifications yield explicit formulae for k tip . The best results obtained from these formulae agree closely over much of the parameter space with those obtained more laboriously by solving a non-linear integral equation. The approximations can be used to assess the influence of cyclic debonding on the effectiveness of externally bonded repairs, or of fiber reinforcement in metal laminates and metal-matrix composites. One of the approximations is an upper bound for k tip and can therefore offer conservative estimates for the effectiveness of the bonded repair or fiber reinforcement.

Imaging Damage Using Mixed Passive and Active Sensors

Existing damage imaging techniques rely on the use of active sensors, such as piezoelectric actuators, that can both transmit and receive guided waves. This paper presents a new time-reversal imaging approach to enable the use of passive sensors, such as optical fibre sensors and strain gauges, to augment active sensors for imaging structural damage. Computational simulations have revealed that damage size and severity can be accurately determined from the scattered wave using as few as six sensors: one active sensor and five passive sensors.

Scattering of the Fundamental Symmetric Wave Mode Incident at a Defect on the Blind Side of a Weep Hole in an Isotropic Plate

The scattering of a fundamental symmetric wave mode by a notch on the blind side of weep hole is described in this paper. It will report on findings obtained from computational simulations to determine the effect and interaction of the impinging waves with the defect on the open hole located on the blind side of the incident wave. The finite element simulation results showed mode conversions of fundamental modes, leaky edge waves on the circumferential surface and source-like diffractions radiating from the tip of the notch and hole. These findings highlight the potential of applying this wave phenomenon to quantify defect located hard-to-inspect areas by positioning actuator and sensor in accessible regions of metallic structures and is relevant to the development and improvement of current techniques in non-destructive inspection of metallic structures

Modified time reversal imaging of a closed crack based on nonlinear scattering

A recent variant of time reversal imaging is used to detect and characterize a closed crack based on both the fundamental and the second harmonic components of the scattered waves in the presence of Contact Acoustic Nonlinearity at the crack interface. A Finite Element model, which includes unilateral contact with Coulomb friction to account for contact between the crack faces, is used to compute the scattered field resulting from the interaction between incident longitudinal plane waves and the crack. The knowledge of the scattering for multiple incident angles constitutes the input for the imaging algorithm. Good reconstruction of the crack is obtained from both harmonic sources, and second harmonic based images also enables one to identify the location of the second harmonic sources along the crack. This first imaging based on the second harmonic also offers potential baseline free detection of closed cracks.

Scattering Phenomena of Edge Guided Waves at and around Notches

This work presents a computational investigation into the scattering of edge guided waves travelling by a notch. To establish a good understanding of this scattering phenomenon, the analysis was conductedon a range of length scales. The finite element analysis indicate that the edge guided surface waves are scattered by the presence of a notch which resulted in a SH0-like appearance wave radiating into the medium. This can be mistaken as a mode conversion of the fundamental lamb modes or even a source at notch tips. The phenomenon becomes harder to notice at higher frequency as increasing the frequency decreases the speed and both the bulk and surface waves travel at identical speeds. A clear understanding of this interaction furthers our knowledge in one of the most prominent interaction in the study of acoustic waves for structural health monitoring.

Comparative evaluation of in situ stress monitoring with Rayleigh waves

The in situ monitoring of stresses provides a crucial input for residual life prognosis and is an integral part of structural health monitoring systems. Stress monitoring is generally achieved by utilising the acoustoelastic effect, which relates the speed of elastic waves in a solid, typically longitudinal and shear waves, to the stress state. A major shortcoming of methods based on the acoustoelastic effect is their poor sensitivity. Another shortcoming of acoustoelastic methods is associated with the rapid attenuation of bulk waves in the propagation medium, requiring the use of dense sensor networks. The purpose of this article is twofold: to demonstrate the application of Rayleigh (guided) waves rather than bulk waves towards stress monitoring based on acoustoelasticity, and to propose a new method for stress monitoring based on the rate of accumulation of the second harmonic of large-amplitude Rayleigh waves. An experimental study is conducted using the cross-correlation signal processing technique to increase the accuracy of determining Rayleigh wave speeds when compared with traditional methods. This demonstrates the feasibility of Rayleigh wave–based acoustoelastic structural health monitoring systems, which could easily be integrated with existing sensor networks. Second harmonic generation is then investigated to demonstrate the sensitivity of higher order harmonics to stress-induced nonlinearities. The outcomes of this study demonstrate that the sensitivity of the new second harmonic generation method is several orders of magnitude greater than the acoustoelastic method, making the proposed method more suitable for development for online stress monitoring of in-service structures.