The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 1. A Theoretical Analysis

Background

This paper deals with the possible field of application of ultrasonic Surface Reflection Method (SRM) to achieve the mechanical characteristics of isotropic materials. This method is based on the measurement of the amplitude of the reflected wave at the interface between reference material and the material to be characterised. Objective: The purpose of Part 1 of this paper is to establish the theoretical conditions for the applicability of SRM.

Methods

First, the theoretical formulas necessary to obtain the mechanical properties of the material to be tested will be established. Then, on the basis of these analytical formulas, the validity of the results for the material to be studied will be discussed according to the choice of the mechanical properties of the reference material through uncertainty calculations. The measurand error of SRM is then compared to that of traditional methods (transmission, transmission in water bath, pulse-echo).

Results

The analytical solution to the inverse problem (the mechanical characteristics of the tested medium based on those of the reference medium and the waves’ amplitude) will be given. From this analytical solution, an analysis of the measurand error will be performed and a method for choosing the reference material will be proposed.

Conclusions

It appears that SRM is better suited than traditional methods in two specific cases: measurement of small deviations of mechanical properties from a reference material or characterisation of high damping materials. In Part 2 of this paper, the practical conditions of applicability of the method are described and then applied to different kinds of materials.

     

Impact of reinforcing filler on the dynamic moduli of elastomer compounds under shear deformation in relation to wet sliding friction

In pursuit of a better understanding of the relationship between wet sliding friction and bulk viscoelastic properties of elastomer compounds, especially the contribution from different reinforcing fillers, the linear thermorheological behavior, the nonlinear dynamic moduli under shear deformation (for strain up to about 140%), and the wet sliding friction have been characterized in detail for crosslinked compounds of low-cis polybutadiene filled with different reinforcing fillers including carbon black, graphitized carbon black, and precipitated silica. We examine the scenario of possible extra energy dissipation via higher harmonic excitation in rubber compounds coupled with dynamic deformation consisting of components at many frequencies during sliding of rubber on a rough surface. While no straightforward explanation is identified relating the observed difference in wet sliding friction arising from different fillers to the bulk viscoelastic properties, some unexpected viscoelastic features arising from the compounds are observed.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part II: applications and validation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. In Part I the governing equations of the aforementioned problem have been derived, leading to the formulation of five boundary value problems with respect to the transverse displacements, to the axial displacement and to two stress functions. These problems are numerically solved using the Analog Equation Method, a BEM based method. In this Part II, numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. Thus, the results obtained from the proposed method are presented as compared with those from both analytical and numerical research efforts from the literature. More specifically, the shear deformation effect in nonlinear free vibration analysis, the influence of geometric nonlinearities in forced vibration analysis, the shear deformation effect in nonlinear forced vibration analysis, the nonlinear dynamic analysis of Timoshenko beams subjected to arbitrary axial and transverse in both directions loading, the free vibration analysis of Timoshenko beams with very flexible boundary conditions and the stability under axial loading (Mathieu problem) are presented and discussed through examples of practical interest.

     

Obtaining a Wide-Strain-Range True Stress–Strain Curve Using the Measurement-In-Neck-Section Method

Background

Measuring true stress–strain curve over a large-strain-range is essential to understand mechanical behavior and simulate non-linear plastic deformation. The digital image correlation (DIC) technique, a non-contact full-field optical measurement technique, is a promising candidate to obtain a long-range true stress–strain curve experimentally.

Objective

This paper proposes a method for measuring true stress–strain curves over a large-strain-range during tensile testing using DIC.

Methods

The wide-strain-range true stress–strain curves of dual-phase and low carbon steels were extracted on the transverse direction in the neck region. The axial strain on the neck section was estimated by averaging the inhomogeneous deformation on the cross-section of the tensile specimen. The true stress was calculated from the engineering stress and the cross-sectional area of the neck.

Results

The validity of the proposed method was assessed by comparing the experimental load–displacement responses during tensile testing with the finite element method (FEM) simulation results. The stress and strain on the neck section estimated using the FEM and DIC, respectively, were proven to satisfy the uniaxial condition and successfully obtained.

Conclusions

The experimental results agree well with the FEM results. The proposed concept can be applied to various deformation modes for accurately measuring long-range true stress–strain curves.

     

Determination of in-plane and out-of-plane shear moduli of composite materials

A general closed-form relationship was derived between torque and angle of twist for a prismatic composite specimen in terms of the geometric parameters and shear properties of the laminae. In the case of unidirectional laminates, relations are expressed in terms of three principal shear moduli, G₁₂, G₂₃ and G₁₃. An experimental method was developed for determining these moduli by measuring surface and edge strains with strain gages. Unidirectional coupons of graphite/epoxy and silicon carbide/glass ceramic were tested in torsion and the three shear moduli were determined in each case.     

Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant

The mechanical behaviour of isotropic and incompressible vulcanized natural rubbers (NR's) and that of quasi-incompressible carbon black filled vulcanized natural rubbers (NR 70) are considered both theoretically and experimentally. We start by generalising the neo-Hookean model to derive an original form of the strain energy density function (W). W satisfies the hypothesis of the Valanis–Landel function, which allows reducing the number of needed experimental tests to identify the parameters of the model. In the present study, in the order to identity the analytical form of W, we undertake only simple tension tests. The two-dimensional field of in-plane homogeneous displacements is determined here using a home-developed image analysis cross-correlation technique. Our model is also identified using results taken from the literature in the case of (NR's) for different types of solicitations, including simple tension, equibiaxial tension and pure shear deformation. Comparison of numerical results with the experimental data indicates that the present model can characterise the hyperelastic behaviour of NR's and that of NR 70 for all the tested modes of deformation. Moreover, it seems to be valid over a wide range of deformation intervals.     

Rheology of carbon black suspensions. V. Heat-induced gelation and its reversibility

Linear viscoelastic properties of carbon black (CB) suspensions in a mixture of a rosin-modified phenol resin-type varnish (Varnish-1)/an alkyd resin-type varnish (Varnish-2), which exhibited a sol?Cgel transition on an increase in CB concentration, were investigated from 30°C to 80°C. The viscoelastic properties were reversible from 30°C to 60°C. In contrast, at temperatures above 60°C, the storage (G??) and loss (G??) moduli were irreversible and increased significantly with increasing temperature. This increase in the moduli is due to a change of the dispersion state to agglomerated state by heating. The agglomerated state was held, when the suspensions were lowered at 30°C. However, the G?? and G?? recovered to the original values upon shearing. This heat-induced gelation should be a universal feature for suspensions of weakly attractive particles. The temperature and shearing histories of the suspensions were discussed in relation to adsorption of polymeric component in the varnish on the CB particles.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton–Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.

     

On Anisotropic Elastic Materials for which Young''s Modulus E ( n ) is Independent of n or the Shear Modulus G ( n , m ) is Independent of n and m

It is shown that, among anisotropic elastic materials, only certain orthotropic and hexagonal materials can have Young modulus E(n) independent of the direction n or the shear modulus G(n,m) independent of n and m. Thus the direction surface for E(n) can be a sphere for certain orthotropic and hexagonal materials. The structure of the elastic compliance for these materials is presented, and condition for identifying if the material is orthotropic or hexagonal is given. We also study the case in which n of E(n) and n, m of G(n,m) are restricted to a plane. When E(n) is a constant on a plane so are G(n,m) and Poisson's ratio ν(n,m). The converse, however, does not necessarily hold. A plane on which E(n) is a constant can exist for all anisotropic elastic materials. In particular, existence of such a plane is assured for trigonal, hexagonal and cubic materials. In fact there are four such planes for a cubic material. For these materials, not only E(n) is a constant, two other Young's moduli, the three shear moduli and the six Poisson's ratio on the plane are also constant.     

The nonlinear viscoelastic response of carbon black-filled natural rubbers

Three series of tensile relaxation tests are performed on natural rubber filled with various amounts of carbon black. The elongation ratio varies in the range from λ=2.0 to 3.5. Constitutive equations are derived for the nonlinear viscoelastic behavior of filled elastomers. Applying a homogenization method, we model a particle-reinforced rubber as a transient network of macromolecules bridged by junctions (physical and chemical cross-links, entanglements and filler clusters). The network is assumed to be strongly heterogeneous at the meso-level: it consists of passive regions, where rearrangement of chains is prevented by surrounding macromolecules and filler particles, and active domains, where active chains separate from temporary nodes and dangling chains merge with the network as they are thermally agitated. The rate of rearrangement obeys the Eyring equation, where different active meso-domains are characterized by different activation energies. Stress–strain relations for a particle-reinforced elastomer are derived by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data. It is demonstrated that the filler content strongly affects the rearrangement process: the attempt rate for separation of strands from temporary nodes increases with elongation ratio at low fractions of carbon black (below the percolation threshold) and decreases with λ at high concentrations of filler.     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model

A phenomenological uniaxial model is derived for implementation in the time domain, which captures the amplitude and frequency dependency of filled elastomers. Motivated by the experimental observation that the frequency dependency is stronger for smaller strain amplitudes than for large ones, a novel material model is presented. It utilizes a split of deformation between a generalized Maxwell chain in series with a bounding surface plasticity model with a vanishing elastic region. Many attempts to capture the behaviour of filled elastomers are found in the literature, which often utilize an additive split between an elastic and a history dependent element, in parallel. Even though some models capture the storage and loss modulus during sinusoidal excitations, they often fail to do so for more complex load histories. Simulations with the derived model are compared to measurements in simple shear on a compound of carbon black filled natural rubber used in driveline isolators in the heavy truck industry. The storage and loss modulus from simulations agree very well with measurements, using only 7 material parameters to capture 2 decades of strain (0.5–50% shear strain) and frequency (0.2–20 Hz). More importantly, with material parameters extracted from the measured storage and loss modulus, measurements of a dual sine excitation are well replicated. This enables realistic operating conditions to be simulated early in the development process, before an actual prototype is available for testing, since the loads in real life operating conditions frequently are a combination of many harmonics.     

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions

Abstract

The nonplanar, nonlinear, resonant forced oscillations of a fixed-free beam are analyzed by a perturbation technique with the objective of determining quantitative and qualitative information about the response. The analysis is based on the differential equations of motion developed in Part I of this paper which retain not only the nonlinear inertia but also nonlinear curvature effects. It is shown that the latter play a significant role in the nonlinear flexural response of the beam.     

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.     

Arterial Wall Stiffening in Caveolin-1 Deficiency-Induced Pulmonary Artery Hypertension in Mice

Background

Pulmonary artery hypertension (PAH) is a complex disorder that can lead to right heart failure. The generation of caveolin-1 deficient mice (CAV-1^?/?) has provided an alternative genetic model to study the mechanisms of pulmonary hypertension. However, the vascular adaptations in these mice have not been characterized.

Objective

To determine the histological and functional changes in the pulmonary and carotid arteries in CAV-1^?/? induced PAH.

Methods

Pulmonary and carotid arteries of young (4–6 months old) and mature (9–12 months old) CAV-1^?/? mice were tested and compared to normal wild type mice.

Results

Artery stiffness increases in CAV-1^?/? mice, especially the circumferential stiffness of the pulmonary arteries. Increases in stiffness were quantified by a decrease in circumferential stretch and transition strain, increases in elastic moduli, and an increase in total strain energy at physiologic strains. Changes in mechanical properties for the pulmonary artery correlated with increased collagen content while changes in the carotid artery correlated with decreased elastin content.

Conclusions

We demonstrated that an increase in artery stiffness is associated with CAV-1 deficiency-induced pulmonary hypertension. These results improve our understanding of arterial remodeling in PAH.

     

Nanoindentation of Calcified and Non-calcified Components of Atherosclerotic Tissues

Background

Biomechanical models predicting plaque rupture and device-tissue interactions rely on accurate material properties to produce reliable simulation results. However, there is a wide variation in the reported stiffness properties for advanced atherosclerotic lesions.

Objective

The purpose of this study was to characterise isolated calcified and non-calcified portions of ex vivo carotid atherosclerotic tissues using nanomechanical techniques and compare the results against those from previous studies.

Methods

Eleven carotid plaque samples were acquired from patients undergoing endarterectomy. Calcification was characterised using traditional instrumented indentation (TII) (n?=?06). Micro-Computed Tomography was used to identify areas of calcification. Ferrule-top cantilever nanoindentation (FTC) was conducted on non-calcified tissue regions (n?=?05). Adjacent tissue slices were stained with Alizarin Red to select regions of non-calcified tissue for testing. Scanning electron microscopy was employed to qualitatively assess the calcified and non-calcified samples’ surface roughness.

Results

The results from this study demonstrate over 6 orders of magnitude difference in stiffness between the elastic moduli of calcified (22.40 [17.70–27.55] GPa) and non-calcified (8.16 [3.85–14.78] kPa) carotid atherosclerotic tissues. Microscopy analysis indicates a larger variation in surface roughness produced with non-calcified tissue cryosectioning than with calcified tissue metallographic preparation, which may account for the increased amount of indent failures with FTC (32%) than with TII (11%).

Conclusions

Performing high-resolution imaging and nanomechanical approaches in parallel produce results that clarify the wide range in reported properties for advanced atherosclerotic lesions. Future studies should examine the viscoelastic nature of diseased human arterial tissues.

     

Effective elastic properties of porous materials: Homogenization schemes vs experimental data

In this paper, we focus on the prediction of elastic moduli of isotropic porous materials made of a solid matrix having a Poisson's ratio vm of 0.2. We derive simple analytical formulae for these effective moduli based on well-known Mean-Field Eshelby-based Homogenization schemes. For each scheme, we find that the normalized bulk, shear and Young's moduli are given by the same form depending only on the porosity p. The various predictions are then confronted with experimental results for the Young's modulus of expanded polystyrene (EPS) concrete. The latter can be seen as an idealized porous material since it is made of a bulk cement matrix, with Poisson's ratio 0.2, containing spherical mono dispersed EPS beads. The Differential method predictions are found to give a very good agreement with experimental results. Thus, we conclude that when vm=0.2, the normalized effective bulk, shear and Young's modulus of isotropic porous materials can be well predicted by the simple form (1 − p)² for a large range of porosity p ranging between 0 and 0.56.