Modulus Gradient Research Articles

Thermal, High and Low Cycle Fatigue Life of 80 Micron Thick Graded Alumina PVD Coatings for Oxidation Resistance Application

In this study, to accommodate higher interfacial shear stress between alumina coating system and metallic substrate, coating modulus and compressive stresses are graded from interface to 80 µm thickness. . The modulus gradient is achieved by varying Al to O ratio by tuning the oxygen flow and compressive stresses are varied from 0.1GPa to 2.5GPa by changing bias voltage during the reactive sputtering process. Static thermal fatigue life of coated samples were evaluated using simple heating and cooling cycles, significant change in microstructures and mechanical properties were observed. Room temperature high fatigue cycle (HCF) was evaluated using vibration testing and the coating fatigue life was evaluated as 2.0X106 cycles. Low cycle fatigue was evaluated using axial compressive and tensile mode and the coatings were cracked beyond 10,000 cycles. The Micro tensile testing revelled that modulus and compressive stress graded coatings are failed at 1.1% tensile strain and which is higher tensile load bearing capacity than the monolithic stoichiometric alumina coating. Hardness and modulus of the 80 µm thickness is 34GPa and 240 GPa. At higher strain coating started cracking and post-microscopy analysis shows variation of crack width at different zones of the tensile specimen. .

A modulus gradient model for an axially loaded inhomogeneous elastic rod

A new gradient elasticity formulation is proposed for a one-dimensional linear elastic inhomogeneous rod. In the new formulation, similar to the differential relation between the local strain and the gradient enhanced strain in the classical models of gradient elasticity, a differential relation is proposed for the Young’s modulus. Analytical and finite element solutions of the proposed formulation are derived. Results of the proposed model are compared with a classical model of gradient elasticity for a model problem of carbon nanotube reinforced polymer composite.

Design and Fabrication of a Hierarchically Structured Scaffold for Tendon-to-Bone Repair.

A hierarchically structured scaffold is designed and fabricated for facilitating tendon-to-bone repair. The scaffold is composed of three regions with distinct functions: (i) an array of channels to guide the in-growth of cells and aligned deposition of collagen fibers, as well as integration of the scaffold with the tendon side, (ii) a region with a gradient in mineral composition to facilitate stress transfer between tendon and bone, and (iii) a mineralized inverse opal region to promote the integration of the scaffold with the underlying bone. Cell culture experiments confirm that adipose-derived stromal cells are able to infiltrate and proliferate through the entire thickness of the scaffold without compromised cell viability. The seeded stem cells exhibit directed differentiation into tenocytes and osteoblasts along the mineral gradient as a response to the gradient in Young's modulus. This novel scaffold holds great promise to promote the formation of a functional tendon-to-bone attachment by offering a structurally and compositionally appropriate microenvironment for healing.

Seamless modulus gradient structures for highly resilient, stretchable system integration

Hybrid system integration of rigid components into stretchable systems is often necessary when targeting for valuable functions in various scenarios. Among them, (Young's) modulus gradient structures for system integration demonstrate excellent mechanical performance when stretched. However, the mechanical reliability is still limited under large deformation due to the inherent interface between materials of different modulus. Here, a seamless transition between heterogeneous moduli parts made with polydimethylsiloxane (PDMS)-based elastomers is presented for stretchable system integration by simply tuning their modulus via introducing a small amount of an additive into some parts of the substrate. These gradient structures not only provide a high stretchability (∼250%) for the overall system, but also improve the resilience of the system (can be stretched up to 50,000 cycles from 0 to 150% global strain) at the same time. The seamless modulus gradient structures provide a simple and effective way of allowing highly resilient and stretchable system integration for various soft intelligent systems.

Dynamics of axially functionally graded cantilevered pipes conveying fluid

The linear dynamics of axially functionally graded (AFG) cantilevered pipes conveying fluid is studied, aiming at enhancing the dynamic stability of such fluid-interaction systems. Either the elastic modulus or the density of the AFG cantilevered pipe is assumed to be varied from the clamped to the free ends. The governing equation of the AFG pipe is derived first and then discretized by using the differential quadrature method (DQM). The effects of elastic modulus gradient and density gradient on the critical flow velocity for flutter instability are analyzed. It is found that, compared with uniform pipes, the decrease of density along the pipe length leads to a more stable system, while the opposite result may be obtained for the decrease of elastic modulus for small values of mass ratio. From the boundary curves of critical flow velocity versus density gradient and of critical flow velocity versus elastic modulus gradient, it is shown that the occurrence of Z-shape segments is possible when the mass ratio becomes large. Furthermore, the phenomenon of mode exchange has also been detected with increasing density gradient or elastic modulus gradient within a certain range of mass ratio.

A polynomial model for the adaptive computation of threshold of gradient modulus in 2D anisotropic diffusion filter

Anisotropic Diffusion (AD) filter is a non-linear spatial filter, widely used for denoising Magnetic Resonance (MR) images. But, the degree of smoothening and the quality of the morphological edges in the restored image are greatly influenced by the selection of the optimum value Threshold of Gradient Modulus (TGM), which is one of the important operational parameters of AD filter. The method for tuning TGM to its optimum value through trial and error is subjective, cumbersome and time consuming. As a solution to this, a polynomial model to compute the optimum value of TGM from the Standard Deviation (SD) of the noise is proposed in this article. The optimum values of TGM for MR images with completely different information content and noise statistics have been identified objectively with the help of a novel edge preservation metric termed as ‘Edge Content Ratio (ECR), with the support of subjective assessment of the quality of the restored images. The coefficient of prediction, r2 equal to 0.7431 is observed for the proposed polynomial model, formulated between the values of optimum TGM and SD of the noise, computed from the test MR images.

Microenvironmental Stiffness of 3D Polymeric Structures to Study Invasive Rates of Cancer Cells.

Cells are highly dynamic elements, continuously interacting with the extracellular environment. Mechanical forces sensed and applied by cells are responsible for cellular adhesion, motility, and deformation, and are heavily involved in determining cancer spreading and metastasis formation. Cell/extracellular matrix interactions are commonly analyzed with the use of hydrogels and 3D microfabricated scaffolds. However, currently available techniques have a limited control over the stiffness of microscaffolds and do not allow for separating environmental properties from biological processes in driving cell mechanical behavior, including nuclear deformability and cell invasiveness. Herein, a new approach is presented to study tumor cell invasiveness by exploiting an innovative class of polymeric scaffolds based on two-photon lithography to control the stiffness of deterministic microenvironments in 3D. This is obtained by fine-tuning of the laser power during the lithography, thus locally modifying both structural and mechanical properties in the same fabrication process. Cage-like structures and cylindric stent-like microscaffolds are fabricated with different Young's modulus and stiffness gradients, allowing obtaining new insights on the mechanical interplay between tumor cells and the surrounding environments. In particular, cell invasion is mostly driven by softer architectures, and the introduction of 3D stiffness "weak spots" is shown to boost the rate at which cancer cells invade the scaffolds. The possibility to modulate structural compliance also allowed estimating the force distribution exerted by a single cell on the scaffold, revealing that both pushing and pulling forces are involved in the cell-structure interaction. Overall, exploiting this method to obtain a wide range of 3D architectures with locally engineered stiffness can pave the way for unique applications to study tumor cell dynamics.

Flexoelectric response in soft polyurethane films and their use for large curvature sensing

The flexoelectric effect is simply defined as the coupling between the strain gradient and polarization in solid dielectrics. It may be seen as an alternative transduction mechanism to the piezoelectric effect to directly sense the curvature of bent flexible thin structures. In the case of large curvatures, flexible and compliant sensors are required and soft polar elastomers may be suitable for curvature sensing. In this study, we report the flexoelectric characterization of soft semi-crystalline polyurethane (PU) films with thicknesses ranging from 1.7 μm to 350 μm. Dynamic bending experiments have been performed on PU films deposited onto rigid steel substrates in the vicinity of the mechanical resonance frequency of the cantilever beams. Quasi-static flexoelectric coefficients of PU films could be obtained by using a classical oscillating model. A global large increase of μ12′ with the decreasing film thickness was found, especially for thicknesses lower than 25 μm. The variation of μ12′ is explained by the presence of a Young's Modulus gradient through the thickness of PU films. Besides, a concomitant uncommon dramatic decrease in the dielectric constant is observed. The combination of these two effects contributes to enhancing the flexocoupling “F” constant with the decreasing thickness. At last, the potential use of a 6.6 μm-thick soft PU film as a large curvature sensor has been experimentally demonstrated by subjecting a flexible Aluminum foil/Polyethylene terephthalate bilayered cantilever to large deflections. A curvature of about 80 m−1 (radius of curvature of ∼1.2 cm) could be sensed under low frequency (3 Hz) bending motion. These results may pave the way for the development of low cost and easy to implement soft flexoelectric elastomer-based large curvature sensors on highly flexible metallic structures.

A New Approach Towards Life Prediction of Case Hardened Bearing Steels Subjected to Rolling Contact Fatigue

Abstract The failure of a bearing-raceway assembly is governed by the spatial distribution of subsurface stresses at the vicinity of a bearing-raceway contact and the evolution of these stresses during rolling contact fatigue (RCF) loading. In this paper, we propose an experimental methodology that allows one to accurately measure the location and magnitude of the cyclically evolving elastoplastic von Mises stresses in terms of microhardness numbers. An M50NiL steel rod is subjected to RCF by three silicon nitride (Si3N4) balls for over several hundred million cycles at 5.5 GPa contact stress level. Microindentation hardness measurements within the subsurface RCF-affected regions of the rod revealed significant material hardening. A mechanistic methodology to construct a stress-life (S-N) diagram for RCF loading is proposed. S-N diagrams are constructed based on maximum von Mises stress amplitude and volume average von Mises stress amplitude. The effects of elastic modulus and yield strength gradient on stress fields are also considered in this analysis. Comparison of S-N diagrams based on both stress amplitudes indicates that the maximum von Mises stress amplitude overpredicts the fatigue strength of material in S-N diagrams. The experimental results obtained by following this methodology can help construct material hardening models for RCF, which may lead to an improved estimate of bearing fatigue life.

The effects of the interface on microstructure and rheo-mechanical properties of polyamide 6/cellulose nanocrystal nanocomposites prepared by in-situ ring-opening polymerization and subsequent melt extrusion

Polyamide 6 (PA6) nanocomposites containing cellulose nanocrystals (CNCs) were prepared via a multi-step process consisting of in-situ anionic ring-opening polymerization and subsequent melt extrusion. The effect of surface modification of the CNCs with aminopropyl triethoxysilane (APS) was studied in detail using microscopic, mechanical and rheological techniques and compared with that of the neat CNC nanocomposites. Solid-state 29Si NMR analysis was used to confirm the interfacial bond formation between the PA6 matrix and surface modified CNCs. SEM images showed that upon surface modification, the morphology of CNCs within the matrix transformed from a fibrillar structure towards more individually dispersed nanocrystals with enhanced dispersion and higher interfacial area. The matrix-particle interphase was further investigated using quantitative nanomechanical mapping (QNM) to study the role of interfacial modification on thickness of interphase and development of a broader modulus gradient across the interface. The quality of dispersion and development of the rigid interfacial layer in the modified system resulted in significant improvement in solid-state mechanical properties of the nanocomposites. In addition, melt rheological studies showed significant improvements of melt elasticity and strength in shear and elongational flow in the nanocomposites systems.

Improving stress shielding following total hip arthroplasty by using a femoral stem made of β type Ti-33.6Nb-4Sn with a Young's modulus gradation.

Stress shielding-related bone loss occurs after total hip arthroplasty because the stiffness of metallic implants differs from that of the host femur. Although reducing stem stiffness can ameliorate the bone resorption, it increases stress at the bone-implant interface and can inhibit fixation. To overcome this complication, a novel cementless stem with a gradient in Young's modulus was developed using Ti-33.6Nb-4Sn (TNS) alloy. Local heat treatment applied at the neck region for increasing its strength resulted in a gradual decrease in Young's modulus from the proximal to the distal end, from 82.1 to 51.0GPa as calculated by a heat transfer simulation. The Young's modulus gradient did not induce the excessive interface stress which may cause the surface debonding. The main purpose of this study was to evaluate bone remodeling with the TNS stem using a strain-adaptive bone remodeling simulation based on finite element analysis. Our predictions showed that, for the TNS stem, bone reduction in the calcar region (Gruen zone 7) would be 13.6% at 2years, 29.0% at 5years, and 45.8% at 10years postoperatively. At 10 years, the bone mineral density for the TNS stem would be 42.6% higher than that for the similar Ti-6Al-4V alloy stem. The stress-strength ratio would be lower for the TNS stem than for the Ti-6Al-4V stem. These results suggest that although proximal bone loss cannot be eliminated completely, the TNS stem with a Young's modulus gradient may have bone-preserving effects and sufficient stem strength, without the excessive interface stress.

Application of Natural Frequencies for Prediction of Apple Texture Based on Partial Least Squares Regression

Abstract Experimental modal analysis was performed to identify natural frequencies to predict the texture of inhomogeneous tissues of apple (Malus domestina cv. ‘Golden Delicious’). Partial least squares calibration models based on natural frequencies with or without weight and density were created for predicting apple texture representing by yield gradient and initial modulus. The prediction models shown good prediction ability for texture of skin but impossible for flesh (all determination coefficients for skin models were more than 0.5 while for flesh models less than 0.5). A nondestructive and rapid method was provided to evaluate the fruit texture.

Mapping porous microstructures to yield desired mechanical properties for application in 3D printed bone scaffolds and orthopaedic implants

Porous design of orthopaedic implants affords the advantages of minimizing stress shielding and improving the osseointegration and long-term stability. However, the marked error in the manufactured porous structure relative to the designed model yields limited application of the porous design. This study aimed to develop a methodology to derive the relationship between the porosity, the structural characteristic parameters and the mechanical properties of a typical structural unit, to lay the foundation of a porous structural design for 3D-printed implants with gradient modulus. Mathematical expressions related to porosity were determined based on various parametrical characteristics of porous units; the effective modulus of such a porous structure was studied under variable axial loading by using finite element analysis to gain insight into the anisotropic properties of the porous structure, and to evaluate the effects of parametrical variation on the aforementioned properties. For validation purposes, samples were manufactured via selective laser melting (SLM) 3D printing technology and mechanically tested. Results indicated that porous design can reduce the effective modulus of implants by 75–80%. A general methodology was developed for evaluating BCC structural units to determine design parameter correlations, the porosity and the effective modulus of the structure.

Effect of Cyclic Loading on Surface Instability of Silicone Rubber under Compression.

This work combines experiments and finite element simulations to study the effect of pre-imposed cyclic loading on surface instability of silicon rubber under compression. We first fabricate cuboid blocks of silicon rubber and pinch them cyclicly a few times. Then, an in-house apparatus is set to apply uniaxial compression on the silicon rubber under exact plane strain conditions. Surprisingly, we find multiple creases on the surface of silicone rubber, significantly different from what have been observed on the samples without the cyclic pinching. To reveal the underlying physics for these experimentally observed multiple creases, we perform detailed nanoindentation experiments to measure the material properties at different locations of the silicon rubber. The modulus is found to be nonuniform and varies along the thickness direction after the cyclic pinching. According to these experimental results, three-layer and multilayer finite element models are built with different materials properties informed by experiments. The three-layer finite element model can excellently explain the nucleation and pattern of multiple surface creases on the surface of compressed silicone rubber, in good agreement with experiments. Counterintuitively, the multilayer model with gradient modulus cannot be used to explain the multiple creases observed in our experiments. According to these simulations, the experimentally observed multiple creases should be attributed to a thin and stiff layer formed on the surface of silicon rubber after the pre-imposed cyclic loading.

Wrinkle surface instability of an inhomogeneous elastic block with graded stiffness

Surface instabilities have been studied extensively for both homogeneous materials and film/substrate structures but relatively less for materials with continuously varying properties. This paper studies wrinkle surface instability of a graded neo-Hookean block with exponentially varying modulus under plane strain by using the linear bifurcation analysis. We derive the first variation condition for minimizing the potential energy functional and solve the linearized equations of equilibrium to find the necessary conditions for surface instability. It is found that for a homogeneous block or an inhomogeneous block with increasing modulus from the surface, the critical stretch for surface instability is 0.544 (0.456 strain), which is independent of the geometry and the elastic modulus on the surface of the block. This critical stretch coincides with that reported by Biot (1963 Appl. Sci. Res. 12 , 168–182. ( doi:10.1007/BF03184638 )) 53 years ago for the onset of wrinkle instabilities in a half-space of homogeneous neo-Hookean materials. On the other hand, for an inhomogeneous block with decreasing modulus from the surface, the critical stretch for surface instability ranges from 0.544 to 1 (0–0.456 strain), depending on the modulus gradient, and the length and height of the block. This sheds light on the effects of the material inhomogeneity and structural geometry on surface instability.

Image restoration method based on fractional variable order differential

In this paper, we study image restoration problem by using fractional variable order differential technique. Our idea is to make use of fractional order differential diffusion equation of evolution procedure into the image restoration problem. An image often exists different low-frequency and high-frequency components, such as flat, texture and edge, etc. Because fractional order differential can enhance the high-frequency components of a signal, meanwhile, nonlinearly preserve the low-frequency components of the signal, we can adapt suitable fractional differential orders to restore their components. In particular, different differential orders can be used in an image at the same time. In order to obtain the restored image automatically, we choose the fractional differential orders by the value of gradient modulus of the image and use the discrete Fourier transform to implement the numerical algorithm. We also provide an iterative scheme in the frequency domain. Experimental results are reported to demonstrate that the visual effects, the combined image similarity index and the peak signal to noise ratio of restored images by using the proposed method are very good, and are competitive with the other testing methods.

Development of quantitative Local Electrochemical Impedance Mapping: an efficient tool for the evaluation of delamination kinetics

Local Electrochemical Impedance Mapping (LEIM) methodology was adopted to quantify the propagation of electrochemically active regions with a micrometric precision. The method consisted in the use of the gradient modulus of the admittance map as a parameter for the spatial quantification. Numerical simulations were used to optimize the experimental conditions, namely the AC frequency, the distance between the local bi-probe and the working electrode, and the distances between the probes for the local bi-probe used for the local current mapping. This analysis was reinforced by experimental verifications on coated electrodes. The quantitative LEIM methodology was successfully applied to follow the delamination kinetics on Zn coated with the polyvinyl butyral polymer in NaCl solutions. At 1 kHz, the LEIM response only reflected the position of the anodic front beneath the polymer because oxygen reduction reaction was diffusion limited and hence, independent of the applied potential. This novel LEIM methodology completes the set of usual tools used to investigate the delamination mechanisms on metal substrates.

A new method of edge detection based on the total horizontal derivative and the modulus of full tensor gravity gradient

With the rapid development of gravity gradient measurement, the full tensor gravity gradient data has been used more and more frequently in the edge detection. This article focuses on the problem that the effect of edge detection of deep geological body is not clear and false edges among positive and negative anomalies using the common edge detection method. We present a new edge detection method which is based on the total horizontal derivative and the modulus of full tensor gravity gradient. Comparing with the model experiments, it is proved that this method is clearer and more accurate in detecting the edges of geological body especially for the deep model with almost no false edge interference. Finally, the method is applied to the processing of the actual data in St. Georges Bay, Canada, and the edge results are satisfying.

An inverse approach to determine complex modulus gradient of field-aged asphalt mixtures

This study develops a new mechanical-based method to determine the complex modulus and modulus gradient of field-aged asphalt mixtures using the direct tension test. Due to the non-uniform aging nature of the field cores, the mechanical responses must be measured at different depths. Meanwhile, the monotonic load is not applied at the neutral axis of the field core specimen due to the modulus gradient, the tensile part of the strain is used and should be separated from the measurement because of the eccentric loading. The modulus gradient parameters, the location of the neutral axis, and the stress distribution are first obtained using the elastic formulas for a series of loading times. Then the complex modulus is determined using the Laplace transform and the elastic–viscoelastic correspondence principle. An inverse approach and iteration are then proposed by using the pseudo strain to accurately calculate the modulus gradient parameters after the relaxation modulus and reference modulus are determined.

An improved fingerprint orientation field extraction method based on quality grading scheme

Orientation pattern is an important feature for characterizing fingerprint and plays a very important role in the automatic fingerprint identification system (AFIS). Conventional gradient based methods are popular but very sensitive to noise. In this paper, we present an improved fingerprint orientation field (FOF) extraction method based on quality grading scheme. In order to effectively remove the noise, the point orientations are fitted by using 2D discrete orthogonal polynomial. The role of the gradient modulus is taken into full account, and the weights of the point orientations are obtained by computing the similarity of the fitted point orientations. The block qualities are assessed by the coherence of point orientations and the block orientations are estimated based on quality grading scheme. In the proposed method, it does not need any prior knowledge of singular points. To validate the performance, the proposed method has been applied to fingerprint singularity detection and fingerprint recognition. We compared the proposed method with other state-of-the-art fingerprint orientation estimation algorithms. Our statistical experiments show that the proposed method can significantly improve in both singular point detection and matching rates, and it is more robust against noise.