Nonclassical nonlinear elasticity of crystalline structures.

Hysteretic elastic nonlinearity has been shown to result in a dynamic nonlinear response which deviates from the known classical nonlinear response; hence this phenomenon was termed nonclassical nonlinearity. Metallic structures, which typically exhibit weak nonlinearity, are typically categorized as classical nonlinear materials. This article presents a material model which derives stress amplitude dependent nonlinearity and damping from the mesoscale dislocation pinning and breakaway to show that the lattice defects in crystalline structures can give rise to nonclassical nonlinearity. The dynamic nonlinearity arising from dislocations was evaluated using resonant frequency shift and higher order harmonic scaling. The results show that the model can capture the nonlinear dynamic response across the three stress ranges: linear, classical nonlinear, and nonclassical nonlinear. Additionally, the model also predicts that the amplitude dependent damping can introduce a softening-hardening nonlinear response. The present model can be generalized to accommodate a wide range of lattice defects to further explain nonclassical nonlinearity of crystalline structures.

Multiscale model to study dislocation dynamics in nonlinear resonance spectroscopy of crystalline solids.

This letter reports on a multi-scale model which captures the dislocation dynamics due to applied vibration stress and its influence on the bulk nonlinear response in a nonlinear resonance spectroscopy experiment. Due to dislocation dynamics, a sinusoidal variation in frequency shift could be observed at the low applied stress range, which was consistent with NRS experiments carried out on cold drawn steel. Using the model, NRS response to "Buck hook" phenomenon was also explored. The results showed that the frequency shift can exhibit three strain regions similar to non-classical nonlinear materials. Further discussions highlight the non-classical nonlinear nature of crystalline solids with lattice defects.

Influence of surface roughness on the measurement of acoustic nonlinearity parameter of solids using contact piezoelectric transducers.

The current article reports on the experimental study of the influence of surface roughness on the measurement of the acoustic nonlinearity parameter. The nonlinearity parameter was measured using contact piezoelectric transducers, which were calibrated using the reciprocity based technique. Aluminum and steel samples were chosen to study the influence of hardness of the sample on the measurement of the nonlinearity parameter. While, lower Ra value (average asperity height) aluminum samples were more susceptible to surface deformation and scratches from coupling the transducer to the sample, the same could not be observed for steel samples. Results demonstrate a large variation in nonlinearity parameter for aluminum (∼35%) compared to steel (∼2%) between two consecutive experiments, suggesting flattening of asperities after the first experiment. Experiments were also performed with 3 different setup configurations; (1) receiver and transmitter on rough sides, (2) receiver on smooth and transmitter on rough side and (3) receiver on rough and transmitter on smooth side. Results show that least variation in the measured nonlinearity parameter was observed when the receiver was placed on the smooth side, and a 10% variation was observed between the three setup configurations. Finally, a comparison of relative nonlinearity parameter calculated using current or voltage ratio and absolute nonlinearity parameter showed large discrepancies. Conclusions were drawn from the experimental observations.

Determination of acoustic nonlinearity parameter (ß) using nonlinear resonance ultrasound spectroscopy: Theory and experiment.

The present article investigates the possibility of using nonlinear resonance ultrasound spectroscopy to determine the acoustic nonlinearity parameter (ß) and third order elastic constant by developing an inverse problem. A theoretical framework was developed for nonlinear forced vibration of a cantilever beam using material nonlinearity (stress-strain nonlinearity). The resulting nonlinear equation was solved using method of multiple time scales to obtain the nonlinear frequency shifts. The present works focuses only on classical nonlinearity and, therefore, a diverse group of intact, classic nonlinear materials were chosen. The samples were tested using nonlinear resonance ultrasound spectroscopy, and the developed theory was used to invert the experimental frequency shifts to obtain the nonlinearity parameters. The third order elastic constants and ß were calculated using their analytical relationship with the nonlinearity parameter. The experimentally determined C111 and ß values for all various materials agree well with literature values. In addition to determining ß, determination of the sign, or phase of ß was also explored theoretically and experimentally.

Numerical study of Rayleigh wave propagation along a horizontal semi-infinite crack buried in half-space.

The present article investigates the propagation of Rayleigh waves along a horizontal semi-infinite crack, and its interaction with the crack tip. Finite element analysis was used to simulate wave propagation and study the interaction. An incident Rayleigh wave diffracts as bulk waves into the half-space upon interaction with the crack tip. It was observed that the diffracted bulk modes can interact with the half-space boundary, and mode converts into a Rayleigh wave traveling along the boundary. A qualitative analysis was performed to determine the effect of crack depth using transmission, reflection, and scattering coefficients. Moreover, the possibility of Lamb wave generation also arises since the crack face and boundary form a stress-free plate section. The source of the "turning" Lamb modes was also identified from the observations. The characteristics of the transmitted Rayleigh wave were also explored, and a certain degree of mode coupling between Rayleigh and shear waves was observed when the crack tip was farther away from the boundary.

Influence of laminate sequence and fabric type on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of influence of laminate sequence and fabric type on the baseline acoustic nonlinearity of fiber-reinforced composites. Nonlinear elastic wave techniques are increasingly becoming popular in detecting damage in composite materials. It was earlier observed by the authors that the non-classical nonlinear response of fiber-reinforced composite is influenced by the fiber orientation [Chakrapani, Barnard, and Dayal, J. Acoust. Soc. Am. 137(2), 617-624 (2015)]. The current study expands this effort to investigate the effect of laminate sequence and fabric type on the non-classical nonlinear response. Two hypotheses were developed using the previous results, and the theory of interlaminar stresses to investigate the influence of laminate sequence and fabric type. Each hypothesis was tested by capturing the nonlinear response by performing nonlinear resonance spectroscopy and measuring frequency shifts, loss factors, and higher harmonics. It was observed that the laminate sequence can either increase or decrease the nonlinear response based on the stacking sequence. Similarly, tests were performed to compare unidirectional fabric and woven fabric and it was observed that woven fabric exhibited a lower nonlinear response compared to the unidirectional fabric. Conjectures based on the matrix properties and interlaminar stresses were used in an attempt to explain the observed nonlinear responses for different configurations.

Finite element simulation of core inspection in helicopter rotor blades using guided waves.

This paper extends the work presented earlier on inspection of helicopter rotor blades using guided Lamb modes by focusing on inspecting the spar-core bond. In particular, this research focuses on structures which employ high stiffness, high density core materials. Wave propagation in such structures deviate from the generic Lamb wave propagation in sandwich panels. To understand the various mode conversions, finite element models of a generalized helicopter rotor blade were created and subjected to transient analysis using a commercial finite element code; ANSYS. Numerical simulations showed that a Lamb wave excited in the spar section of the blade gets converted into Rayleigh wave which travels across the spar-core section and mode converts back into Lamb wave. Dispersion of Rayleigh waves in multi-layered half-space was also explored. Damage was modeled in the form of a notch in the core section to simulate a cracked core, and delamination was modeled between the spar and core material to simulate spar-core disbond. Mode conversions under these damaged conditions were examined numerically. The numerical models help in assessing the difficulty of using nondestructive evaluation for complex structures and also highlight the physics behind the mode conversions which occur at various discontinuities.

Influence of fiber orientation on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of non-classical nonlinear response of fiber-reinforced composites. Nonlinear elastic wave methods such as nonlinear resonant ultrasound spectroscopy (NRUS) and nonlinear wave modulation spectroscopy have been used earlier to detect damages in several materials. It was observed that applying these techniques to composites materials becomes difficult due to the significant inherent baseline nonlinearity. Understanding the non-classical nonlinear nature of the composites plays a vital role in implementing nonlinear acoustic techniques for material characterization as well as qualitative nondestructive testing of composites. Since fiber reinforced composites are orthotropic in nature, the baseline response variation with fiber orientation is very important. This work explores the nature of the inherent nonlinearity by performing nonlinear resonant spectroscopy (NRS) in intact unidirectional carbon/epoxy samples with different fiber orientations with respect to major axis of the sample. Factors such as frequency shifts, modal damping ratio, and higher harmonics were analyzed to explore the non-classical nonlinear nature of these materials. Conclusions were drawn based on the experimental observations.

The interaction of Rayleigh waves with delaminations in composite laminates.

In the present work, the interaction of Rayleigh waves with a delamination in a fiber reinforced composite plate was analyzed. Rayleigh waves, upon interacting with delamination mode, convert into Lamb waves in the delamination zone. These guided Lamb modes have the capability to mode convert back into Rayleigh modes when they interact with the edge of the delamination. A unidirectional glass/epoxy laminate with a delamination of known size was fabricated and tested using air-coupled ultrasonics. Finite element models were developed to understand the mode conversions occurring at various sections of the delamination. Particle displacements along with numerical and experimental velocities were considered to identify each mode. Conclusions were drawn based on the velocity analysis.

Nondestructive evaluation of helicopter rotor blades using guided Lamb modes.

This paper presents an application for turning and direct modes in a complex composite laminate structure. The propagation and interaction of turning modes and fundamental Lamb modes are investigated in the skin, spar and web sections of a helicopter rotor blade. Finite element models were used to understand the various mode conversions at geometric discontinuities such as web-spar joints. Experimental investigation was carried out with the help of air coupled ultrasonic transducers. The turning and direct modes were confirmed with the help of particle displacements and velocities. Experimental B-Scans were performed on damaged and undamaged samples for qualitative and quantitative assessment of the structure. A strong correlation between the numerical and experimental results was observed and reported.