The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 2. Experimental Results

Background

This paper is Part 2 of a study on the scope of the ultrasonic Surface Reflection Method (SRM). Part 1 deals with the theoretical conditions for a satisfactory usage of this method.

Objective

This second part validates the practical feasibility and reliability of the SRM method by comparison with the conventional Transmission Method (TM) in cases where the latter is applicable.

Methods

Two experimental devices (one for SRM and one for TM) are developed and measurements of shear and bulk moduli are carried out at ultrasonic frequency (610 kHz) and at room temperature.

Results

The experimental conditions in terms of sample geometry, pulse characteristics and interfacial transmission required to obtain a given accuracy on the measurement are stated. The SRM is then validated against other experimental methods and is used to determine the shear modulus of a carbon black filled neoprene at ambient temperature (T?=?21 °C) and ultrasonic frequency.

Conclusions

The benefit brought by this method is well demonstrated: a unique measurement allows the determination of all the moduli of a highly damping isotropic material (carbon black filled neoprene) not achievable by other methods.

     

Real-Time Multibody System Dynamic Simulation: Part II. A Parallel Algorithm and Numerical Results

ABSTRACT

This paper presents a computational algorithm that exploits inherent parallelism in the modified recursive formulation presented in Part I of the paper. Computational data flows to implement the algorithm are defined. By combining the topological analysis method presented in Part 1 of the paper, an efficient general purpose dynamic simulation algorithm is developed. Examples using the code developed show that real-time simulation can be achieved for moderately complex mechanical systems using a shared memory multiprocessor.     

Dynamic Subsurface Deformation and Strain of Soft Hydrogel Interfaces Using an Embedded Speckle Pattern With 2D Digital Image Correlation

Background

Subsurface mechanisms can greatly affect the mechanical behavior of biological materials, but observation of these mechanisms has remained elusive primarily due to unfavorable optical characteristics. Researchers attempt to overcome these limitations by performing experiments in biological mimics like hydrogels, but measurements are generally restricted due to the spatio-temporal limitations of current methods.

Objective

Utilization of contemporary 3D printing techniques into soft, transparent, aqueous yield-stress materials have opened new avenues of approach to overcoming these roadblocks. By incorporating digital image correlation with such 3D printing techniques, a method is shown here that can acquire full-field deformation of a hydrogel subsurface in real-time.

Methods

Briefly, the method replaces the solvent of a transparent and low polymer concentration yield-stress material with an aqueous hydrogel precursor solution, then a DIC speckle plane is 3D printed into it. This complex is then polymerized using photoinitiation thereby locking the speckle plane in place.

Results

Full-field deformation measurements are made in real-time as the embedded speckle plane (ESP) responds with the bulk to the applied load. Example results of deformation and strain fields associated with indentation, relaxation, and sliding contact experiments are shown.

Conclusions

This method has successfully observed the subsurface mechanical response in the bulk of a hydrogel and has the potential to answer fundamental questions regarding biological material mechanical behaviors.

     

Analytical Model and Experimental Verification of the Interfacial Peeling Strength of Electrodes

Background

The interfacial peeling strength of lithium-ion battery electrodes is a very important mechanical property that significantly affects the electrochemical performance of battery cells.

Objective

To characterize the interfacial peeling strength of an electrode, an analytical model based on the energy balance principle is established by considering the state of charge (SOC), the energy release rate, the tensile stiffness, and the peeling angle.

Methods

Uniaxial tensile tests and 180-degree peeling tests are conducted to determine the Young’s modulus and the interfacial peeling strengths of electrodes at different SOCs, respectively. The experimental data serve as a validation of the accuracy of the analytical model.

Results

The interfacial peeling strength of the electrode shows a strong reliance on many factors. Specifically, the interfacial peeling strength increases with the SOC and the energy release, and decreases with the peeling angle. When the tensile stiffness of the active layer equals that of the current collector, the interfacial peeling strength has a maximum value.

Conclusions

By comparing with experimental data of the 180-degree peeling test, the model prediction shows excellent agreement at different SOCs, and the analytical model established in this paper can be used to guide and assess the interfacial properties of electrodes for industry.

     

Quantitative Study of Residual Strain and Geometrically Necessary Dislocation Density Using HR-EBSD Method

Background

Optical metrology is widely used to measure materials’ deformation and mechanical properties but current fundamental research requires more precise measurement of microstructure and deformation in internal materials. Electron backscattered diffraction (EBSD) technique measures crystal orientation in individual grain and high resolution EBSD (HR-EBSD) method provides information about residual strain and GND density.

Objective

Deformation of two stainless steels Nitronic 60 and Tristelle 5183 with different proportions of ferrite and carbides are characterised.

Methods

Push-release bend testing was used to provide progressive increasing bending stress in two iron-based material samples. HR-EBSD and high resolution digital image correlation (HR-DIC) methods characterised residual strain, GND density and plastic strain distributions in each sample.

Results

Nitronic 60 and Tristelle 5183 were deformed and obtained 3.8% and 0.9% plastic strain ?xx. High GND densities distributed neighbouring grain boundaries in Nitronic 60 while high GND densities distributed around carbides, especially intragranular carbides in Tristelle 5183.

Conclusions

HR-EBSD and HR-DIC quantitative characterised deformation in two iron-based alloys, grain/twin boundaries and carbides resulted in GND density increase, promoted work hardening and accumulated high residual elastic strain. Heterogeneous grain/carbide size distribution leaded to stress concentration and cause carbide decohesion and brittle fracture of sample.

     

Real-Time Multibody System Dynamic Simulation: Part I. A Modified Recursive Formulation and Topological Analysis

ABSTRACT

ABSTRACT With the advent of parallel computers and recursive dynamics formulations, multibody mechanical systems such as ground vehicles can be simulated in real time. This permits the engineer to rapidly modify design parameters, evaluate dynamic performance, and improve designs, prior to fabrication and testing. Perhaps more important, real-time simulation can be used for simulation with the operator-in-the-loop, permitting system design to be optimized for the capability of the human operator. To achieve the goal of real-time simulation, a modified recursive dynamics formulation and a topological analysis method for the formulation are presented in Part I. A parallel computational algorithm that exploits inherent parallelism in the modified recursive formulation and numerical results will be presented in Part II. By combining the topological analysis method and the parallel algorithm, an efficient general-purpose dynamic simulation method is developed for real-time simulation on shared memory parallel processors.     

Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations

Abstract

Functionally graded porous materials (FGPMs) have a wide range of applications as hollow members in biomedical and aeronautical engineering. In the FGPMs, the porosity is varied over the material volume because of the density change of pores. In the present work, an analytical treatment on the size-dependent nonlinear secondary resonance of FGPM micro/nano-beams subjected to periodic hard excitations is proposed in the simultaneous presence of the nonlocality and strain gradient size dependencies. Based upon the closed-cell Gaussian-random field scheme, the mechanical properties of the FGPM micro/nano-beams are extracted corresponding to the uniform and three different functionally graded patterns of the porosity dispersion. The nonlocal strain gradient theory of elasticity is applied to the classical beam theory to formulate a newly combined size-dependent beam model. Thereafter, an analytical solving methodology based on the multiple time-scales together with the Galerkin technique is adopted to achieve the nonlocal strain gradient frequency–response and amplitude–response curves associated with the subharmonic and superharmonic external excitations. For the subharmonic excitation, it is observed that the nonlocality causes to shift the junction point of the stable and unstable branches to the higher value of the detuning parameter. However, the strain gradient size dependency plays an opposite role. For the superharmonic one, it is illustrated that the nonlocal size effect makes an increment in the height of jump phenomenon and shifts the peak to higher value of the detuning parameter. However, the strain gradient small scale effect leads to decrease the height of the jump phenomenon and shifts the peak to lower value of the detuning parameter.     

Design Sensitivity Analysis in Structural Mechanics. I. Static Response Variations

ABSTRACT

The dependence of the solution of boundary-value problems of structural mechanics on design variables that specify material properties and distribution is characterized. Prototype problems treated include beams, plates, and plane elastic solids. Symmetry and positive definiteness properties of the elliptic differential operators that govern system response are used to show that their inverses, hence the displacement fields, are Frechet differentiable with respect to design variables. Formulas for the derivatives are given and used to obtain computable formulas for design sensitivity coefficients (first variation) of integrals that arise in optimal design formulations. The results establish an extension of the concept of “well-posed” problems of structural mechanics to include continuity (in fact, differentiability” of static structural response with respect to distributed design variables and design parameters     

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

Background

Experimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.

Objective

The main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.

Methods

X-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.

Results

The results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.

Conclusions

In-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

     

Investigation of the Effects of Environmental Fatigue on the Mechanical Properties of GFRP Composite Constituents Using Nanoindentation

Background

Fatigue failure criteria for fibre reinforced polymer composites used in the design of marine structures are based on the micromechanical behaviour (e.g. stiffness properties) of their constituents. In the literature, there is a lack of information regarding the stiffness degradation of fibres, polymer matrix and fibre/matrix interface regions affected by environmental fatigue.

Objective

The aim of present study is to characterize the stiffness properties of composite constituents using the nanoindentation technique when fatigue failure of composites is due to the combined effect of sea water exposure and cyclic mechanical loads.

Methods

In the present study, the nanoindentation technique was used to characterize the stiffness properties of composite constituents where the effects of neighbouring phases, material pile up and viscoplasticity properties of the polymer matrix are corrected by finite element simulation.

Results

The use of finite element simulation in conjunction with nanoindentation test data, results in more accurate estimation of projected indented area which is required for measuring the properties of composite constituents. In addition, finite element simulation provides a greater understanding of the stress transfer between composite constituents during the nanoindentation process.

Conclusions

Results of nanoindentation testing on the composite microstructure of environmentally fatigue failed composite test coupons establish a strong link to the stiffness degradation of the fiber/matrix interface regions, verifying the degradation of composite constituents identified by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) analysis.

     

A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems

ABSTRACT

ABSTRACT A recursive formulation of the equations of motion of constrained mechanical systems with closed loops is derived, using tools of variational and vector calculus. Kinematic couplings between pairs of contiguous bodies presented in Part 1 of this paper are generalized. Lagrange multipliers are introduced to account for the effects of joints that are cut to define a tree structure. Constraint Jacobian terms are added to the reduced variational equations derived in Part I. Cut-joint constraint acceleration equations are derived, to complete the reduced equations of motion. Lagrange multipliers associated with each cut-joint are eliminated at the first junction body encountered that permits closing the loop that constraints in cut joint. The inductive algorithm developed in Part I is used to calculate accelerations for the system. A multi-loop compressor is analyzed to illustrate use of the method.     

A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.

     

Alumina as a Computed Tomography Soft Material and Tissue Fiducial Marker

Background

The use of 3D imaging is becoming increasingly common, so too is the use of fiducial markers to identify/track regions of interest and assess material deformation. While many different materials have been used as fiducials, they are often used in isolation, with little comparison to one another.

Objective

In the current study, we aim to directly compare different Computed Tomography (CT and μCT) fiducial materials, both metallic and nonmetallic.

Methods

μCT imaging was performed on a soft-tissue structure, in this case heart valve tissue, with markers from eight different materials attached. Additionally, we evaluated the same markers with DiceCT stained tissue in a fluid medium.

Results

All of the metallic markers generated significant artifacts, and were found unsuitable for soft-tissue μCT imaging, whereas alumina markers were found to perform the best, with excellent contrast and consistency.

Conclusions

These findings support the further use of alumina as fiducial markers for soft material and tissue studies that utilize CT and μCT imaging.

     

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis,simulations and inverse method

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling

Micromechanical analyses of unidirectional continuous-fibre reinforced composite materials were performed to study the mechanisms of deformation and fracture of the constituents, and their influence on the mechanical properties of the composite. Special focus was given to the matrix material behaviour as well as to the interface between constituents. The matrix was modelled using a pressure dependent, elasto-plastic thermodynamically consistent damage model. Cohesive elements were used to model the interface between matrix and fibres. Part I of this paper details the continuum model developed for a typical epoxy matrix. Part II will focus on micromechanical analyses of composite materials and the estimation of its elastic and strength properties.     

On the methodologies of stress analysis of composite structures: Part 2: New experimental approaches

The rapidly increasing technological importance of composite materials and composite structures is leading to the development of new, more advanced models of their actual response to mechanical and thermal loads. This in turn results in the development of new experimental and analytical methods for determination of the mechanical and thermal responses of such structures and materials to various loads. In this respect the reliability and the predictive power of various methods and techniques of stress analysis become very important since all the analytical, experimental and numerical methods used for the determination, prediction and optimization of the actual mechanical responses of composite structures and materials are based on the concepts of strain and stress. Because of the inherently three-dimensional stress and strain states in composite materials and structures and the wide use of viscoelastic polymers as the matrix and some reinforcing fiber materials, a more rigorous type of modelling than had been common in the past is needed of all the involved physical phenomena which influence the strain and stress states at the local and global levels. Also, a more rigorous analysis of practical consequences of the physical and mathematical simplifications is required to assure reliability and accuracy of various methods of stress analysis. The influence of the above-mentioned factors on the reliability and applicability of analytical and experimental procedures is illustrated by examples of actual material responses.Part 2 of this paper presents theories and techniques of three new methods of strain/stress analysis which have been developed on the basis of comprehensive physical models of involved phenomena: the isodyne, strain gradient and thermoelastic effect methods. Presented examples illustrate the efficacy of these methods.     

Dextrous Workspaces of Manipulators,Part III: Calculation of Continuation Curves at Bifurcation Points

ABSTRACT

An efficient numerical method is presented to obtain all tangent vectors at bifurcation points of continuation curves that define the boundary of manipulator workspaces. The method developed is based on analytical criteria presented in Part I of this paper [1] and computational methods presented in Part II [2]. As observed in the latter paper, difficulties in mapping boundaries of accessible output sets include (1) systematically finding an initial point on the boundary and (2) efficiently calculating tangent vectors at multiple bifurcation points. The first difficulty has been solved by Haug, Luh, Adkins, and Wang [3]. The second difficulty is resolved in this paper.     

New evaluations for multiaxial-stress properties of ceramic materials

This paper suggests some new evaluations for multiaxial-stress properties of ceramic materials. These evaluations include some that have been used for other kinds of materials, as well as others which have not been previously employed. In some cases, these methods represent modifications of existing evaluations. The paper is confined to macroscopic behavior based upon bulk laboratory specimens. The influences of volume, stress gradients and localized behavior are not considered here since considerable attention has recently been devoted to these questions. The important problem of fracture strength will not be considered since this property appears to be considerably influenced by localized microscopic behavior. However, new evaluations of remaining mechanical properties for states of combined stresses will be presented. These include elastic and plastic strength, stiffness, ductility, resilience and toughness. Emphasis on combined-stress properties was selected since recent critical reviews indicate the need for for such an evaluation. Part A of this paper outlines new experiments that are needed to evaluate the mechanical properties and to confirm theories proposed in Part B. In Part B of this paper, new macroscopic engineering-type theories for combined-stress behavior are presented for the first time. These theories attempt to predict combined-stress behavior from uniaxial tension and compression (or pure bending and compression) behavior. These theories provide for materials such as ceramics with different properties in tension and compression. A final section of this presentation is devoted to improvements in the evaluations of other mechanical properties of materials as related to high-temperature creep and fatigue properties.     

On the methodologies of stress analysis of composite structures: Part 1: State of the art—phenomenological and physical methodologies

The rapidly increasing technological importance of composite materials and composite structures is leading to the development of new, more advanced models of their actual response to mechanical and thermal loads. This in turn results in the development of new experimental and analytical methods for determination of the mechanical and thermal responses of such structures and materials to various loads. In this respect the reliability and the predictive power of various methods and techniques of stress analysis become very important since all the analytical, experimental and numerical methods used for the determination, prediction and optimization of the actual mechanical responses of composite structures and materials are based on the concepts of strain and stress. Because of the inherently three-dimensional stress and strain states in composite materials and structures and the wide use of viscoelastic polymers as the matrix and some reinforcing fiber materials, a more rigorous type of modelling than had been common in the past is needed of all the involved physical phenomena which influence the strain and stress states at the local and global levels. Also, a more rigorous analysis of practical consequences of the physical and mathematical simplifications is required to assure reliability and accuracy of various methods of stress analysis. The influence of the above-mentioned factors on the reliability and applicability of analytical and experimental procedures is illustrated by examples of actual material responses.Part 2 of this paper presents theories and techniques of three new methods of strain/stress analysis which have been developed on the basis of comprehensive physical models of involved phenomena: the isodyne, strain gradient and thermoelastic effect methods. Presented examples illustrate the efficacy of these methods.