Variation Of Elastic Anisotropy Research Articles

Nonintrusive estimation of anisotropic stiffness maps of heterogeneous steel welds for the improvement of ultrasonic array inspection.

It is challenging to inspect austenitic welds nondestructively using ultrasonic waves because the spatially varying elastic anisotropy of weld microstructures can lead to the deviation of ultrasound. Models have been developed to predict the propagation of ultrasound in such welds once the weld stiffness heterogeneity is known. Consequently, it is desirable to have a means of measuring the variation in elastic anisotropy experimentally so as to be able to correct for deviations in ultrasonic pathways for the improvement of weld inspection. This paper investigates the use of external nonintrusive ultrasonic array measurements to construct such weld stiffness maps, representing the orientation of the stiffness tensor according to location in the weld cross section. An inverse model based on a genetic algorithm has been developed to recover a small number of key parameters in an approximate model of the weld map, making use of ultrasonic array measurements. The approximate model of the weld map uses the Modeling of anIsotropy based on Notebook of Arcwelding (MINA) formulation, which is one of the representations that has been proposed by other researchers to provide a simple, yet physically based, description of the overall variations of orientations of the stiffness tensors over the weld cross section. The choice of sensitive ultrasonic modes as well as the best monitoring positions have been discussed to achieve a robust inversion. Experiments have been carried out on a 60-mm-thick multipass tungsten inert gas (TIG) weld to validate the findings of the modeling, showing very good agreement. This work shows that ultrasonic array measurements can be used on a single side of a butt-welded plate, such that there is no need to access the remote side, to construct an approximate but useful weld map of the spatial variations in anisotropic stiffness orientation that occur within the weld.

Internal bone remodeling induced by metallic pin fitted into medulla of a long bone having cylindrical anisotropy: Theoretical predictions

Metallic implants are routinely used in orthopedic and dental surgery where implant-bone loosening is known as a major concern of failure, regardless of whether the implants are used in a temporary or permanent way (Cimerman et al., 2005; Goodacre et al., 2003; Herberts and Malchau, 2000). The problem of metallic pin fitted into medulla of a long bone as part of prosthetic device, previously studied by Cowin and van Buskirk (1978), is revisited in this contribution by considering bone material having cylindrical anisotropy. Indeed, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology (Orias et al., 2009). This work offers improved results and new highlights with respect the original work, such as interfacial pressure evolution with respect to the degree of anisotropy α as well as stress–strain distributions during the remodeling process. Our results are quantitatively compared with those in the reference work dealing with homogenous long bone treated as a transversely isotropic material (Cowin and van Buskirk, 1978).

Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p<0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p<0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C11) from the mid-diaphysis toward the epiphyses (p<0.05), since differences in the circumferential (C22) and longitudinal (C33) elastic constants were not statistically significant (p>0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p<0.0001, R2>0.46), as expected, but was only weakly correlated with C33/C11 (p<0.05, R2=0.04) and not significantly correlated with C33/C22 and C11/C22.

Phase-Field Simulation on Coarsening of the γ'Phase Particles in Ni-Based Superalloys Considering Elastic Inhomogeneity

A phase-field simulation is performed to examine the effect of elastic inhomogeneity between the  and ’ phases on coarsening of the ’ phase in Ni-based superalloys. In the calculation of elastic strain energy, the mechanical equilibrium equation in elastically inhomogeneous system is solved by an iterative-perturbation scheme. On the basis of the elastic constants of a practical Ni-based superalloy, a series of simulations is performed in which both elastic anisotropy and shear modulus are varied independently. The variation of elastic anisotropy gives significant effect on both morphology and size distribution function of the ’ particles, whereas the variation of shear modulus gives little effect on them. Furthermore, it is found that the coarsening rate constant of the cubic growth raw changes and increases with increasing the standard deviation of the ’ size distribution.

Ultrasonic Characterization of Elastic Anisotropy in Composites: Case Study of CFRP

Abstract Combined measurements of bulk and plate wave velocities are used to infer the complete matrix of elastic constants for orthotropic CFRP laminates. A direct estimate of Young's moduli in principal axes of the composite is deduced from the low-frequency values of the s 0-wave velocities in these directions. The non-contact ultrasonic evaluation of the in-plane anisotropy of Young's modulus in CFRP is implemented by air-coupled measurements of the a 0-wave dispersion extrapolated to a static case. A strong variation of elastic anisotropy as a function of frequency is measured for both s 0- and a 0-waves. A simple phenomenology presented enables a rapid quantification of frequency variation of plate wave anisotropy in composites. The relation between elastic wave anisotropies and inherent material elasticity is discussed for bulk, surface, and plate waves.

Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur

Experimental investigations for anatomic variation in the magnitude and anisotropy of elastic constants in human femoral cortical bone tissue have typically focused on a limited number of convenient sites near the mid-diaphysis. However, the proximal and distal ends of the diaphysis are more clinically relevant to common orthopaedic procedures and interesting mechanobiology. Therefore, the objective of this study was to measure anatomic variation in the elastic anisotropy and inhomogeneity of human cortical bone tissue along the entire length (15%–85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants) of the femoral diaphysis, using ultrasonic wave propagation in the three orthogonal specimen axes. The elastic symmetry of tissue in the distal and extreme proximal portions of the diaphysis (15%–45% and 75%–85% of the total femur length, respectively) was, at most, orthotropic. In contrast, the elastic symmetry of tissue near the mid- and proximal mid-diaphysis (50%–70% of the total femur length) was reasonably approximated as transversely isotropic. The magnitudes of elastic constants generally reached maxima near the mid- and proximal mid-diaphysis in the lateral and medial quadrants, and decreased toward the epiphyses, as well as the posterior and anterior quadrants. The elastic anisotropy ratio in the longitudinal and radial anatomic axes showed the opposite trends. These variations were significantly correlated with the apparent tissue density, as expected. In summary, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology.