Plane-strain Modulus Research Articles

A coated hypotrochoidal compressible liquid inclusion neutral to a hydrostatic stress field after relaxation by interface slip and diffusion

We study the steady-state response of a three-phase composite composed of an internal hypotrochoidal compressible liquid inclusion, an intermediate isotropic elastic coating and an outer isotropic elastic matrix with simultaneous interface slip and diffusion occurring on the solid–solid interface when the matrix is subjected to a uniform hydrostatic stress field. We design a neutral coated hypotrochoidal liquid inclusion that does not disturb the prescribed uniform hydrostatic stress field in the surrounding matrix. The neutrality is achieved when the plane-strain bulk modulus or the compressibility of the elastic matrix is determined by solving a system of simultaneous linear algebraic equations for given geometric and material parameters of the coated liquid inclusion.

Elastic and inelastic behavior of boron nitride nanocones at finite strains

This research is carried out to characterize the mechanical behavior of boron nitride nanocones (BNNCs) via molecular dynamics (MD) simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The calculations of atomic interactions are performed based on the Tersoff-type potential function. The five elastic moduli are determined by applying four mechanical loadings i. e. uniaxial stretching, axial twist, plane-strain biaxial tension, and in-plane shear. It is found that all elastic constants depend on the apex angle of BNNCs, whereas wider ones have lower Young's and longitudinal shear moduli. In contrast, as the apex angle of the nanocones increases, their plane-strain bulk moduli and in-plane shear constants increase. In addition, Poisson's ratio decreases with an increase in the apex angle and length of the BNNCs. Moreover, the shorter and sharper BNNCs, the higher values of strain at which they fail under uniaxial tensile and axial twist loadings.

Elastic properties and pore structure characterization of selected shales in the sungai Perlis beds, Terengganu, Peninsular Malaysia

Studied drill core of the Sungai Perlis Beds in the Terengganu State, Peninsular Malaysia, consists of a diverse suite of organic rich shale lithofacies at various subsurface depths. Lithofacies were delineated on the basis bedding thickness, mineralogy, and organic richness carried out by X-ray diffraction and (XRD) total organic content (TOC) analysis. Field-emission scanning electron microscopy (FE-SEM) analysis was carried out to identify the pore structure, range of pore sizes and mineral arrangement within each lithofacies unit Elastic geomechanical properties (Young’s modulus and Poisson’s ratio) were measured on core samples from each lithofacies unit using static and dynamic approaches. The identified lithofacies include moderate TOC massive argillaceous shale (MTOCMAS), high TOC massive argillaceous shale (HTOCMAS) and high TOC massive siliceous shale (HTOCMSS). FE-SEM analysis shows that pores in all the lithofacies are mostly intergranular, associated with phyllosilicate minerals, and ranges from <1 micrometer to approximately 8 micrometer. Static and dynamic elastic properties measurement shows that shale lithofacies having a high content of phyllosilicate minerals has a lower Young’s modulus and a high Poisson’s ratio value while lithofacies rich in brittle minerals has a higher Young’s modulus and a low Poisson’s ratio value. A good correlation exists between mineralogical brittleness index of the lithofacies and their plane strain modulus. The plane strain modulus is found higher in lithofacies having abundance of brittle minerals in the matrix suggesting that the high TOC massive siliceous shale (HTOCMSS) would preferably allow formation of dense hydraulic fractures, as observed in the CT scan analysis of triaxially fractured specimen, compared to argillaceous shale lithofacies.

Unraveling the mechanical origin of stable solid electrolyte interphase

Summary The capability of a solid electrolyte interphase (SEI) in accommodating deformation is critical to the electrode integrity. However, the nanoscale thickness and environmental sensitivity of SEI make it challenging to characterize multiple mechanical parameters and identify an appropriate predictor for such capability. Here, we develop a feasible atomic force microscopy (AFM)-based nanoindentation test that circumvents the interference of the anode substrate and allows accurate probing of Young's modulus and elastic strain limit of SEI. The "maximum elastic deformation energy" (U) that an SEI can absorb is proposed to predict the stability of the SEI, as successfully demonstrated in Li/K metal anodes. We show that another asset of U is to provide a rapid and effective means to screen proper electrolytes for the stabilization of Sn and Sb microparticle anodes through building high-U SEIs. Overall, this new indicator, U, offers future directions toward rational design of robust SEIs for advanced anodes.

Assessment of mechanical properties by nano- and microindentation of alumina/zirconia composites

CCs (Ceramic Composites) are used as structural materials due to their exceptional combination of mechanical properties [56]. Therefore, the paper presents research results for common 3 mol% Y2O3 stabilised ZrO2 and pure Al2O3 ceramics as well as four Al2O3/ZrO2 composites. The above mentioned samples are different in composition ratio of: 20, 40, 60 and 80 wt% of Al2O3content. All of the samples were polished on one side. The tests were carried out at the Nanoindentation Tester (NHT3), Microindentation Tester (MHT3) and Hardness Tester. Four load levels were used: 0.002 N, 0.2 N, 20 N and 98.1 N. Berkovich tip was used for the smallest load and Vickers diamond tip for the other. The analysis of the results was carried out in the Indentation software, obtaining the force – depth indentation curves, plane strain modulus E* and Vickers hardness HV. This type of data is also necessary to properly build a numerical model.

Effect of nano-TiO2 on C–S–H phase distribution within Portland cement paste

We investigate the mechanisms by which titanium dioxide nanoparticles (nano-TiO2) interact with cement hydration products. To this end, we synthesize nanomodified cement samples with 1 wt% and 5 wt% of TiO2. We investigate the physical properties using depth-sensing-based methods such as statistical nanoindentation and microscopic scratch testing. Fourier transform infrared spectroscopy yields the chemistry, whereas micromechanics modeling provides insights into the nanostructure. The macroscopic plane strain modulus increases by 16% and 83%, respectively, and the macroscopic indentation hardness increases by 37% and 40%, respectively. The fracture toughness rises by 3% and 11%, respectively. Environmental scanning electron microscopy reveals a 30% reduction in crack width for TiO2 cement nanocomposites compared to plain cement. Meanwhile, Fourier transform infrared spectroscopy and statistical deconvolution show an increase in the fraction of high-density calcium silicate hydrates (by 22% and 12%, respectively), and in the fraction of calcium hydroxide (by 101% and 251%, respectively). Within the framework of the colloidal and granular models of C–S–H, the increase in stiffness and strength after nano-TiO2 modification of cement paste is due to the closely packed structure and the high atomic coordination number of high-density C–S–H. Similarly, due to the high dimensional stability of high-density C–S–H and calcium hydroxide, our results explain the reported improvements in drying shrinkage and creep properties following cement modification with nano-TiO2.

Planar hydraulic fracture growth perpendicular to the isotropy plane in a transversely isotropic material

The configuration of a hydraulic fracture (HF) propagating perpendicular to the isotropy plane of a transversely isotropic (TI) material is encountered in most sedimentary basins. We account for both elastic and fracture toughness anisotropy, and investigate fracture growth driven by the injection of a Newtonian fluid at a constant rate from a point source. In addition to the usual dimensionless parameters governing HF growth in isotropy, four dimensionless elastic parameters enter the problem for a TI material: the ratio β of elastic plane-strain modulus in the two orthogonal directions of the material frame, two Thomsen parameters ϵ, δ and the stiffness ratio C13/C11. Moreover, the ratio κ of fracture toughness in the two orthogonal directions as well as the details of the toughness anisotropy also plays a role on the development of the fracture geometry. We quantify HF growth numerically without any a-priori assumptions on the fracture shape. In doing so, we derive the exact expression for the near-tip elastic modulus as a function of propagation direction and extend to TI an implicit level set algorithm coupling a finite discretization with the near-tip solution for a steadily moving HF. A solution for a toughness dominated elliptical HF in a TI material is derived and used to verify our numerical solver. Importantly, the fracture shape is strictly elliptical only for a very peculiar form of toughness anisotropy. The evolution of the HF from the viscosity dominated regime (early time) to the toughness dominated regime (late time) results in an increase of the fracture elongation. The elongation of the fracture in the viscosity dominated regime scales as 0.76β−1/3 and increases as the propagation transition to the toughness dominated regime. We confirm the expressions for the transition time-scales in the two orthogonal directions of the material frame obtained from scaling considerations. The exact form of the toughness anisotropy plays a crucial role on the final fracture elongation in the toughness regime, which scales as β−2 for the case of an isotropic toughness, β−1 for an isotropic fracture energy and as (κ/β)2 for the peculiar case of an ‘elliptical’ fracture anisotropy. Our results also indicate that i) simplified approximations for the near-tip modulus previously derived are only valid for weak anisotropy (β < 1.2) and that ii) the other elastic parameters have a second order effect on HF growth (at most 10 percent).

The influence of randomly oriented CNTs on the elastic properties of unidirectionally aligned composites

The modification of composites by CNTs is critically important to improve its strength and mechanical properties and widespread its practical applications in many areas of outdoor, construction buildings, engineering, and technology sectors. This paper examines the influence of CNTs on the elastic properties of unidirectionally aligned composites. The nano-inclusions, whose properties could be characterized by three parameters (length, diameter, Young's elastic modulus), are assumed to be ellipsoidal and randomly arranged. The unidirectionally aligned glass fibers were used as a macro-filler. The elastic properties of two systems: Matrix+CNT+Glass fibers and Matrix+Glass fibers were determined and compared using of Eshelby's and Mori-Tanaka's theories of inclusions. For the modified by CNTs composite of the four independent elastic constants, the transverse Young's modulus E22, in-plane shear modulus G12, out-plane shear modulus G23 and the plane-strain bulk modulus K23 appear to significantly increase with increasing CNT's concentration and length/diameter ratio while the longitudinal Young's modulus E11 increase insignificantly.

The effects of solid solution and oxide dispersion alloying on the viscoelastic behavior of Au alloy thin films

The effects of solid solution and oxide dispersion alloying on viscoelastic relaxation behavior of Au alloy films were investigated by using gas pressure bulge testing in the temperature range of 20–80 °C. Three sets of 500 nm thick films were fabricated for the study: nominally pure Au, Au-V solid solution alloys with V concentration ranging from 0.89 to 5.4 at% V, and a Au-V2O5 nanoparticle dispersion alloy with a V concentration of 5.4 at%. The residual stress, unrelaxed plane strain modulus, and normalized time-dependent effective modulus were determined as a function of alloy type and temperature. Both alloying approaches resulted in a refined grain size that was thermally stable. As expected, the fractional modulus decay measured after 3 h was greater at higher temperatures for all cases. Solid solution strengthening and dispersion strengthening were both effective at reducing the 3-h modulus decay, and the Au-V2O5 films showed the largest resistance to relaxation at all temperatures studied. Activation energy analysis reveals a value of approximately 0.11 eV, matching the Peierls barrier height, for pure Au and the two alloys. The results are consistent with a viscoelastic stress relaxation mechanism based on reversible dislocation bowing, weak solid solution hardening through elastic solute/dislocation interactions, and strong dislocation pinning associated with oxide nanoparticles.

In Situ Measurement of the Plane-Strain Modulus of the Solid Electrolyte Interphase on Lithium-Metal Anodes in Ionic Liquid Electrolytes

We present an experimental approach for in situ measurement of elastic modulus of the solid electrolyte interphase (SEI), which is formed from reactions between a lithium thin-film [on a polydimethylsiloxane (PDMS) substrate] and a room-temperature ionic liquid (RTIL) electrolyte. The SEI forms under a state of compressive stress, which causes buckling of the sample surface. In situ atomic force microscopy is used to measure the dominant wavelength of the wrinkled surface topography. A mechanics analysis of strain-induced elastic buckling instability of a stiff thin film on a soft substrate is used to determine the plane strain modulus of the SEI from the measured wavelength. The measurements are performed for three RTIL electrolytes: 1-butyl 1-methylpiperidinium bis(trifluoromethylsulfonyl)imide (P14 TFSI) without any lithium salt, 1.0 M lithium bis(trifluoromethylsulfonyl)imide (Li TFSI) in P14 TFSI, and 1.0 M lithium bis(fluorosulfonyl)imide (Li FSI) in P14 TFSI to investigate the influence of lithium salts on the plane strain modulus of the SEI. The measurements yield plane-strain moduli of approximately 1.3 GPa for no-salt P14 TFSI and approximately 1.6 GPa for 1.0 M Li TFSI in P14 TFSI and 1.0 M Li FSI in P14 TFSI. The experimental technique presented here eliminates some of the uncertainties associated with traditional SEI mechanical characterization approaches and offers a platform to engineer an SEI with desired mechanical properties by approaches that include altering the electrolyte composition.

An elliptical liquid inclusion in an infinite elastic plane

Beyond recent related literature, which focused on spherical incompressible liquid inclusions, the present work studies an elliptical compressible liquid inclusion in an infinite elastic plane under static remote mechanical loading. Here, it is assumed that the change of pressure inside the liquid inclusion is linearly related to the change of inclusion volume with the bulk modulus of the liquid as the proportionality coefficient. Also, the role of the liquid surface tension on the solid–liquid interface is examined especially when the size of the liquid inclusion is comparable to or smaller than the elastocapillary length. Our results show that both the surface tension and the change of liquid pressure have a significant effect on reducing the stress concentration factor at the endpoints of an elliptical liquid inclusion. In addition, the pressure change inside the liquid inclusion is studied when a uniaxial remote stress is applied perpendicular or parallel to the major axis of the elliptical liquid inclusion. In particular, the effective plane-strain Young's modulus of a solid–liquid composite containing circular liquid inclusions predicted by the present model is linearly related to the volume fraction of the liquid inclusions, in reasonable agreement with existing experimental data.

The effect of grain size on viscoelastic relaxation behavior of Au thin films

The effect of grain size on viscoelastic relaxation behavior of Au thin films was investigated by using gas pressure bulge testing to measure the changing normalized plane-strain modulus as a function of time. We observed more rapid and extensive relaxation with increasing grain sizes. The normalized modulus of the Au films is shown to be linearly dependent on the square of the in-plane grain size. Transmission electron microscopy suggests that an increase in grain size allows a higher fraction of mobile dislocation segments to bow under an applied stress, resulting in a proportional increase of the relaxation of coarser-grained films.

Mechanism of Three-Dimensional Surface Wrinkle Manipulation on a Compliant Substrate

In this work, the surface wrinkle modulation mechanism of the three-dimensional (3D) film/substrate system caused by biaxial eigenstrains in the films is studied. A theoretical model based on the energy minimization of the 3D wrinkled film/substrate system is proposed which shows that the change of the surface wrinkle amplitude is determined by four dimensionless parameters, i.e., the eigenstrain in the film, plane strain modulus ratio between the film and substrate, film thickness to wrinkle wavelength ratio, and initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude decreases (even almost flat) upon contraction eigenstrain in the film, while increases for that of expansion eigenstrain. Parallel finite element method (FEM) simulations are carried out which have good agreements with the theoretical predictions, and experimental verifications are also presented to verify the findings. Besides, different patterns of 3D surface wrinkles are studied and the similar surface wrinkle modulation is also observed. The findings presented herein may shed useful insights for the design of complex stretchable electronics, cosmetic products, soft devices and the fabrication of 3D complex structures.

Matrix coatings based on anodic alumina with carbon nanostructures in the pores

The nanoporous anodic alumina matrixes thickness of 1.5mm and pore sizes of 45, 90 and 145nm were formed on Si substrates. The tubular carbon nanostructures were synthesized into the matrixes pores by pyrolysis of fluid hydrocarbon xylene with 1% ferrocene. The structure and composition of the matrix coatings were examined by scanning electron microscopy, Auger analysis and Raman spectroscopy. The carbon nanostructures completely filled the pores of templates and uniformly covered the tops. The structure of carbon nanostructures corresponded to the structure of multiwall carbon nanotubes. Investigations of mechanical and tribological properties of nanostructured oxide-carbon composite performed by scratching and nanoindentation showed nonlinear dependencies of the frictional force, penetration depth of the cantilever, hardness and plane strain modulus on the load. It was found that the microhardness of the samples increases with reduced of alumina pore diameter, and the penetration depth of the cantilever into the film grows with carbon nanostructures size. The results showed the high mechanical strength of nanostructured oxide-carbon composite.

Mechanism of Surface Wrinkle Modulation for a Stiff Film on Compliant Substrate

In this work, the surface wrinkle modulation of the film/substrate system caused by eigenstrain in the film is studied. A theoretical model is proposed which shows the change of the wrinkle amplitude is completely determined by four dimensionless parameters, i.e., the eigenstrain in the film, the plane strain modulus ratio between the film and the substrate, the film thickness to wrinkle wavelength ratio, and the initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude becomes smaller (even almost flat) for the contraction eigenstrain in the film, while for the expansion eigenstrain it becomes larger. If the expansion eigenstrain exceeds a critical value, secondary wrinkling on top of the existing one is observed for some cases. In general, the deformation diagram of the wrinkled film/substrate system can be divided into three regions, i.e., the change of surface wrinkle amplitude, the irregular wrinkling, and the secondary wrinkling, governed by the four parameters above. Parallel finite element method (FEM) simulations are carried out which have good agreement with the theoretical predictions. The findings may be useful to guide the design and performance of stretchable electronics, cosmetic products, biomedical engineering, soft materials, and devices.

Dynamic pile impedances for laterally–loaded piles using improved Tajimi and Winkler formulations

Lateral dynamic soil–pile interaction is investigated through an improved Tajimi type solution. The soil is treated as a continuum with hysteretic material damping as previously proposed by the authors, and the pile is modelled as beam using traditional strength-of-materials solutions. Following the pioneering work of Novak and Nogami, a more accurate analytical model for the static and harmonic response of a pile in a soil layer overlying rock is proposed, and closed form expressions for pile head stiffness are derived. Results are validated through comparisons against rigorous solutions from literature. Hereafter, the Winkler model was considered as a simple alternative for predicting pile head stiffness and damping. An extensive review of available Winkler moduli demonstrated that the Winkler model performance strongly depends on the selection of the respective moduli but found to be satisfactory in static conditions. Most existing expressions for dynamic Winkler moduli were found to render the model incapable of capturing resonant effects. Consequently, a new expression for a dynamic Winkler modulus is derived based on a modification of the classic dynamic plane strain modulus of Baranov–Novak. Implemented in the Winkler model this expression is capable of accurately computing dynamic stiffness attenuation and damping increase for frequencies up to the first resonance over a wide range of pile slenderness ratios.

Assessment of Elasticity, Plasticity and Resistance to Machining-induced Damage of Porous Pre-sintered Zirconia Using Nanoindentation Techniques

Porous pre-sintered zirconia is subject to white machining during which its elasticity, plasticity and resistance to machining-induced damage determine its machinability and final quality. This study used nanoindentation techniques and the Sakai's series elastic and plastic deformation model to extract the resistance to plastic deformation from the plane strain modulus and the contact hardness for pre-sintered zirconia. The modulus and the resistance to plasticity were used to calculate the relative amount of elasticity and plasticity. The fracture energy and the normalized indentation absorbed energy were used to deconvolute the resistance to machining-induced cracking based on the Sakai–Nowak model. All properties were extracted at a 10 mN peak load and loading rates of 0.1–2 mN/s to determine the loading rate effects on these properties. We found that the resistance to plasticity and the resistance to machining-induced cracking were independent of the loading rate (ANOVA, p > 0.05). The elastic and plastic displacements depended on the loading rate through power laws. This loading rate-dependent deformation behaviour was explained by the maximum shear stress generated underneath the indenter and the indentation energy. The plastic deformation components and the indentation absorbed energy at all loading rates were higher than the elastic deformation components and the elastic strain energy, respectively. Finally, we established the linkage among the pore structure, indentation behaviour and machinability of pre-sintered zirconia.

On the rocking and walking flat punch: Effect of elastic dissimilarity

With an appropriate combination of constant and varying loads, a punch may “walk” or “ratchet”, if rigid body motion is allowed. Here, a full numerical analysis is conducted to study the effect of material dissimilarity on a simple configuration. It is found that walking starts from much lower loads than in the case of similar materials, and higher shift per cycle is predicted with the same load and rocking motion, even accounting for the change of the plane strain modulus. Both elastic shakedown or cyclic dissipation are found, and convergence in these cases is relatively slow, whereas it occurs after 2 cycles of oscillations, in the walking case.

Accuracy analysis of plane-strain bulge test for determining mechanical properties of thin films

The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite element analysis, and then the accuracy of the plane-strain bulge test in determining the mechanical properties of thin films in terms of our finite element results was analyzed. The results indicate that although the determination of the plane-strain modulus in the light of the plane-strain bulge equation is fairly accurate, the calculation of the residual stress is not satisfied as expected, especially for low residual stress. Finally, an approach is proposed for analyzing bulge test data, which will improve the accuracy and reliability of this bulge test technique.

Dimensionless Compliance With Effective Modulus in Crack Length Evaluation for B × B Single Edge Bend Specimens

In ASTM standard E1820, the crack size, a, may be evaluated during J-integral or crack-tip opening displacement (CTOD) resistance testing using the measured crack-mouth opening displacement (CMOD) elastic unloading compliance C (UC). The equation given to relate a to dimensionless compliance BCE (the product of thickness B, the compliance C and the modulus of elasticity E) in E1820 incorporates Young's modulus E rather than the plane-strain modulus E/(1 − υ2) where υ is Poisson's ratio. However, the three-dimensional (3-D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither plane-stress nor plane-strain condition, especially for B×B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of plain- and side-grooved B×B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using plane-stress and plane-strain assumptions with the CMOD compliance calculated from FEA for the 3-D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using plane-strain or plane-stress assumptions can be as high as 5–10%, respectively, especially for shallow-cracked specimens. In the present study, an effective modulus with value between plane-stress and plane-strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plain-sided and side-grooved specimens, respectively, using this effective modulus. The effect of material removal to accommodate integral knife edges on the CMOD compliance was studied and taken into account in the crack length evaluations in the present study. Elastic unloading tests were conducted to measure the compliance of SE(B) specimens with two widths W and notch depths a/W from 0.1 to 0.5. Notch depths of the specimens evaluated by using the measured compliance and assumptions of plane stress, plane strain, and effective moduli were compared with the notch depths of the specimens used in the tests. It was found that best agreement of notch depth was achieved using the effective modulus.