Mismatch Of Elastic Properties Research Articles

Fracture behavior of brittle particulate composites consisting of a glass matrix and glass or ceramic particles with elastic property mismatch

The aim of this work is two-fold: i) elaborating dense and transparent inorganic glass composites with improved fracture properties, and ii) testing the theoretical analysis proposed in [1] and based on Poisson's ratio mismatch. Particulate composites, consisting of glass or ceramic particles embedded in a soda-lime-silica glass matrix, were synthesized and their fracture behavior was studied by means of the Single Edge Precraked Beam (SEPB) and Double Cantilever Drilled (DCDC) methods, using in situ experiments with X-ray tomography where possible. An important effect of the T-stress on the fracture toughness (KIc) was observed in the case of DCDC exdperiments. KIc is increased by about 40 % by incorporating 7 vol. % amorphous silica beads or SrAl2O4:Eu,Dy ceramic particles (SAED) with a 40 μm mean particle size. It is suggested that toughening results from the crack front trapping and pinning at particle sites and from the tortuous crack path in the case of a-SiO2 particles, and from the contribution of the intrinsic fracture surface energy of the ceramic particles, which are cleaved by the propagating crack, in the case of the SAED particles. The thermally induced stress field is believed to play a major role in the case of a-SiO2 particles. Two glass grades possessing Young's moduli similar to the one of the matrix but much larger Poisson's ratios were used to produce glass beads. However, the incorporation of these latter beads in the matrix was found to have a minor incidence on the fracture behavior.

Evaluation of mixed-mode stress intensity factors for anisotropic elastic solids with interface singularity

Abstract When a structure is composed of many different parts and each part is made of different materials, it is very possible that many interface corners appear in several local fields of the structure. Due to the mismatch of elastic properties, stress singularity may occur at the interface corners. The singular orders of stresses and their associated stress intensity factors (SIFs) are two important parameters for understanding failure initiation. Since the singular orders of general interface corners may be real or complex, distinct or repeated, several different definitions of SIFs have been proposed for different types of interfaces. In order to build a direct connection among all general interface corners (including cracks and interface cracks), a unified definition of SIFs was proposed in our previous studies. To calculate the uni-defined SIF accurately and efficiently, a special boundary element using the fundamental solution satisfying interface continuity conditions is established. The singular integrals involved in the associated boundary integral equations are solved by the setting of proper rigid body motions and the approximation through interpolation of nearby non-singular solutions. To avoid the unstable and inaccurate region near the corners, in this study we employ the path-independent H-integral, and derive the relations between H-integral and SIFs. Moreover, the auxiliary solutions of displacements and tractions required in the H-integral are provided for different integral paths. Several numerical examples, such as interface cracks, interface corners, single lap joints and delamination, are presented to demonstrate the methodology employed in this paper.

Mesoscopic Stacking Reconfigurations in Stacked van der Waals Film.

Mesoscopic-scale stacking reconfigurations are investigated when van der Waals (vdW)films are stacked. A method to visualize complicated stacking structures and mechanical distortions simultaneously in stacked atom-thick films using Raman spectroscopy is developed. In the rigid limit, it is found that the distortions originate from the transfer process, which can be understood through thin film mechanics with a large elastic property mismatch. In contrast, with atomic corrugations, the in-plane strain fields are more closely correlated with the stacking configuration, highlighting the impact of atomic reconstructions on the mesoscopic scale. It is discovered that the grain boundaries do not have a significant effect while the cracks are causing inhomogeneous strain in stacked polycrystalline films. This result contributes to understanding the local variation of emerging properties from moiré structures and advancing the reliability of stacked vdW material fabrication.

Ultrasonic elastography for nondestructive evaluation of dissimilar material joints

Dissimilar material joints or multilayered metals have become inevitable in the manufacturing industry due to the increasing demand for multifunctional materials with variable mechanical, thermal, or electrical characteristics in a single assembly. Lattice mismatch of materials at the interface of dissimilar materials leads to inferior mechanical characteristics. In particular, the mismatch in elastic properties indicated by a large initial elastic deformation is critical to determine the extent of variation in stress. However, nanoindentation, the most common and accepted technique to measure elastic modulus, is destructive, time-consuming, and can only examine mechanical properties within a limited area. A non-invasive elastographic mapping technique evaluates the mechanical properties using ultrasonic elastography to study incompressibility. The dissimilar joint between steel and copper was obtained via friction stir welding. The variation of the stress developed at the welded joint of the two different metals was evaluated from the dynamic bulk modulus map. A tensile test of the involved workpiece confirmed a good agreement with our analysis based on the dynamic bulk modulus elastographic mapping results. This study provides a rapid and non-invasive technique for the bulk metallurgic elastic modulus inspection to overcome the limitations of conventional methods.

Numerical prediction of interlaminar stresses in laminated composites

Laminated composite materials are extensively utilised in aerospace, aviation and automobile industries because of their high strength and low weight. When laminates are composed of layers with different orientations, classical lamination theory implies boundary tractions on free edges. Edge delamination in laminated composites has become significant in structural reliability. Due to more inter-laminar shear stresses nearer to the free edges of the laminates, more failure modes are developed in the laminates. Because of the complex fibre/matrix micro structure of laminated composite materials, an evaluation of these stresses becomes very important in composite materials design. Normally free edge inter-laminar stresses arise from the mismatch of elastic properties between two layers. Therefore it is necessary to predict the inter-laminar stresses of laminated composite plates. In this study, the free edge inter-laminar stresses of laminated composite materials are predicted numerically. Numerical prediction of inter-laminar stresses of non-hybrid and hybrid laminated composite plates are predicted. In hybrid category, carbon fibres and glass fibres are combined together and analysed. Numerical analysis of laminates is performed in ANSYS. The inter-laminar shear forces and stress distribution are plotted along thickness.

Asymptotic solution for interface crack between two materials governed by dipolar gradient elasticity

An asymptotic solution for interface crack between mismatched materials that obey a special form of linear isotropic strain gradient elasticity under conditions of plane strain is developed. It is shown that the asymptotic solution depends in a complicated manner both on a mismatch of elastic properties and a mismatch of the internal length scale parameter. Numerical analysis shows that the mismatch of elastic moduli and the gradient coefficient c respectively lift the degeneracy of the exponent p that is characteristic for a crack in homogeneous material. The total energy release rate Gint due to a crack extension along the interface is derived generalizing the classical virtual crack closure method. The reciprocal work contour integral method for the evaluation of amplitude factors in the asymptotic expansion is extended to interface crack in the linear isotropic strain gradient elasticity.

Analysis of stress concentrations in transversely loaded steel-fiber composites with nano-reinforced interphases

Continuous steel fiber polymer composites are susceptible to high stress concentrations under transverse loading. This is due to the high mismatch in elastic properties of steel fiber and polymeric matrix. In the present work, the effect of a nano-reinforced interphase on the stress concentrations is evaluated. Three types of nano-reinforcements are considered: 1) carbon nanotubes (CNTs) grown on fibers and 2) graphene nano-plates deposited on the fiber surface and 3) graphene nano-plates randomly distributed in the matrix. The study is carried out using finite element (FE) analysis with an intermediate homogenization step to obtain elastic properties of the nano-reinforced interphase. These properties are calculated using an inclusion based approach. Results indicate that the presence of the nano-reinforced interphase increases radial stress concentrations and those in the direction of the load. The suppression is only observed for shear stress concentrations in the case of the CNT interphase around the fibers.

Fabrication and Modeling of Nitride Thin-Film Encapsulation Based on Anti-Adhesion-Assisted Transfer Technique and Nitride/BCB Bilayer Wrinkling

This paper presents buckled nitride thin-film encapsulation using anti-adhesion layer-assisted transfer technique and benzocyclobutene (BCB)/nitride bilayer wrinkling due to elastic property mismatch between the two attached materials. A 900-nm silicon nitride film is deposited on a Si carrier wafer coated with hydrophobic monolayer, and then nonpatterned nitride film is directly bonded to BCB sealing rings prepared on a target wafer at 250 °C. As bonding and subsequent cooling proceed, shearing force generated by BCB shrinking is applied to the thin nitride film. After bonding, the Si carrier wafer is mechanically separated, leaving only nitride membrane inside BCB ring. Thus, self-patterning and self-alignment have been achieved. Interestingly, most different-size nitride membranes are successfully transferred even though large-size ones have partially collapsed or highly deformed. Also, finite-element method modelings have been carried out to comprehend the formation of the wrinkling of thin elastic film on compliant substrate as well as the debonding of the transfer process of the thin film. It is found that Young's modulus of compliant substrate is significant to the wavelength of the wrinkle and maximum deflection of the buckled film. The debonding may apply substantial force to the elastic film, and thus the nitride membrane needs stabilization time as its shape changes after the debonding.

Cohesive-zone modelling of crack nucleation and propagation in particulate composites

A cohesive-zone approach is used to study the interaction between an approaching crack and a particle embedded in a matrix material as a function of the mismatch in elastic and fracture properties. Crack-particle interaction is a crucial issue governing fracture behavior of particle-dispersed materials. Special attention is given in the present work to the effect of the mismatch in fracture properties, namely fracture strength and energy, which has not been fully-explored in the literature. Based on extensive finite element simulations using cohesive elements, the basic fracture mechanisms governing the crack-particle interaction are identified, namely particle fracture, crack deflection and interface debonding. The details of the cracking sequences are elucidated and the role of secondary cracks is highlighted. The effect of pre-existing flaws on the fracture behavior is analyzed both for flaws inside the particle as well as flaws on the particle/matrix interface. Several flaw configurations in terms of size, orientation and location are considered. In addition, the effect of the mismatch between the matrix and the interface fracture properties is also considered for a wide range of adhesive characteristics. The results of the simulations are summarized in the form of several fracture maps for different configurations, whereby the main fracture mechanisms are identified in regions inside a two-dimensional space of strength and toughness mismatch between the particle and the matrix. It is observed that the mismatch in the fracture properties usually plays a more dominant role on the crack trajectory than the mismatch in elastic properties in a particle-dispersed system. Pre-existing flaws/defects in the particle and the interface are found to be one of the principal controlling factors that alter the crack propagation characteristics. These results can be used as a guideline for designing particulate composite system with a preferred fracture mechanism, namely matrix cracking, interface debonding or particle fracture.

Stress analysis of a crack in a fiber-reinforced layered composite

Brittle matrix composites such as fiber-reinforced cements and ceramics are often bonded to dissimilar materials such as metals or other ceramics. The mismatch in elastic properties can affect the growth of matrix cracks located near the bonded interface. In this paper, a bonded system comprising of an elastic layer sandwiched between two identical elastic half-spaces is considered. A mathematical model is developed based on the distributed dislocation technique, for the analysis of a bridged straight crack embedded in the elastic layer. The bridging tractions are considered to be dependent on the crack opening displacement. The stress field is assumed to be plane stress or plane strain and all three-dimensional effects are disregarded.The numerical results include the critical stress required to initiate failure of the matrix and the failure of fibers bridging the crack. The dependencies of these critical values upon the thickness of the composite layer as well as the mismatch in elastic properties are presented in dimensionless form. The results can be used to estimate the residual strength of bonded composites with a flaw near the material interface.

Characterization of free edge effects: influence of mechanical properties, microstructure and structure effects

The elastic property mismatch between plies with different orientations induces stress concentrations near free edges. This free edge effect can cause early delamination of composite structures. Laminates with 15° and –15° plies are studied experimentally to highlight the free-edge effect and the induced micromechanism damage. Full field measurements under tensile loading are performed at macroscopic and mesoscopic scales on edges of the sample. Results show displacement gradients and strain concentrations near interlaminar interfaces. Residual displacement gradients are measured after unloading, which highlights local damage at interlaminar interfaces. Observations at the microscopic scale show that cracks appear at fibre/matrix interfaces and propagate between adjacent fibres along interlaminar interfaces. A comparison of the results obtained on different composites highlights the influence of mechanical properties and material microstructure on edge effects. The study of samples with dropped plies highlights the influence of the combination of both geometric and material singularities on edge effects.

Flexural effects of sandwich beam with a plate insert under in-plane bending

The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study. An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stress.The shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces. The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure. The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads. The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert.

Fracture of metal coated elastomers

Polydimethylsiloxane (PDMS) substrates were coated with thin layers of gold varying in thickness between 40 nm and 160 nm. Arrays of parallel cracks formed when a tensile strain was applied to the coated system, with the spacing between the cracks being approximately inversely proportional to the strain. When the crack profiles were examined, it was noted that the cracks extended deep into the substrate—to depths up to two orders of magnitude greater than the film thickness. This extension of the cracks into the substrate is the result of the large mismatch in elastic properties between the metal and soft substrate, and plays a role in the development of the cracking pattern. Despite the relatively large strains that can be applied through the elastomeric substrate, there was no evidence of macroscopic plasticity in the metal films, and numerical analyses showed that the crack profiles were consistent with elastic deformation of the metal. A quantitative comparison of the crack depth and spacing with the predictions of a companion mechanics analysis indicated that the observed spacing and depth were consistent with the metal film being much tougher than the elastomeric substrate. However, for this level of toughness to be exhibited in a metal film would require plastic deformation over a scale much larger than would be expected in such a geometry. This inconsistency may be resolved by recognizing that rupture of a thin metal film can be associated with shear localization that results in a mode-II failure, rather than by classical mode-I crack propagation. This results in a failure mechanism for a metal film that is a high-strain, but low-energy process, with substrate cracking absorbing the excess elastic energy available upon rupture of the film. Such a failure mechanism is consistent with earlier observations for the failure of thin metal films, and this work suggests that failure of an elastomeric substrate may contribute to an additional loss of constraint enhancing this localization.

Extracting thin film hardness of extremely compliant films on stiff substrates

A previously reported method for extracting the thin film hardness from nanoindentation into a film on an elastically mismatched substrate was applied to four different cases of extreme mismatch in elastic properties: Parmax, Ultem, Polysulfone and Perfluorocyclobutyl polymer thin films on Si substrates. All of these cases represent extremely compliant films on a stiff substrate, where the ratio of film shear modulus to substrate shear modulus ranged from 0.008 to 0.036. Analyzing the nanoindentation data into these film/substrate systems poses a significant limitation when using the Oliver and Pharr method as the hardness increases rapidly with indentation depth. Therefore, a method involving the measured contact stiffnesses to more accurately determine the correct contact areas was used to extract the true hardness of the polymer thin films. The results indicate that our method is able to remove the substrate effects as well as the complications arising from pile-up and surface roughness to yield a wide plateau in hardness despite the extreme elastic mismatch conditions.

Effect of Indenter Elastic Modulus on Hertzian Ring Crack Initiation in Silicon Carbide

Hertzian ring cracking in two SiCs was studied as a function of elastic property mismatch between indenter and target. Ring crack initiation forces (RCIF) were measured using ZrO2, steel, Si3N4, Al2O3, and WC balls. The SiCs were similar; however, ∼20% of the grains in one were larger than the largest grains in the other. Decreasing indenter stiffness resulted in lower RCIFs and initiation occurred at lower forces in the SiC containing larger grains. Using a spherical indenter with similar elastic properties as the target provides a simpler interpretation and useful and confident estimates of ring crack initiation stresses.

Interfaces Between two Dissimilar Elastic Materials

Due to the mismatch of elastic properties, stress singularity usually occurs near the tips of interface corners/cracks between two dissimilar materials, which may initiate failure of materials and structures. The singular order of stresses near the interface corners/cracks is a good index for the understanding of failure initiation. However, in engineering applications one usually feels only the knowledge of singular orders is not enough for the prediction of failure initiation since it only reflects the local combination and is nothing to do with the far-field environment and the external loading condition. These global influential factors are reflected through another important parameter – stress intensity factor. Therefore, for interface problems it is important to know the singular orders as well as their associated stress intensity factors. However, due to the complexity of stresses near the tip of interface corners/cracks, most of the existing calculation methods will encounter the problems of accuracy and convergency. With this understanding, recently several works regarding the interfaces between two dissimilar elastic materials are studied in our research group. One is devoted in the improvement of boundary element method by including the fundamental solution of bimaterials, and the other is the improvement of the computational method for stress intensity factors by establishing a path independent H-integral for general interface problems.

RESEARCH ON THE EFFECT OF LOADING CONDITIONS ON THE STRENGTH AND DEFORMATION BEHAVIORS OF ROCKS

The paper aims at a numerical study of strength and deformation behaviors of rocks under different loading conditions in uniaxial compression with an elasto-plastic cellular automaton (EPCA2D) code. Two loading conditions, i.e. with and without considering frictions between loading platens and rock specimen's ends, are used in the failure processes of heterogeneous rocks. Rock specimens are assumed to be the same heterogeneity, i.e. the specimens with different sizes have the same probability of containing flaws. Under this condition, it is concluded that the strength and deformation behaviors of rocks are influenced by the heterogeneity a little. The mismatch of elastic properties of the platen and the rock in influencing the stress distribution at the ends of the specimen is the dominant cause for the so-called strength and deformation size effects, which in turn affects the final failure patterns of rocks.

Earthquake slip between dissimilar poroelastic materials

A mismatch of elastic properties across a fault induces normal stress changes during spatially nonuniform in‐plane slip. Recently, Rudnicki and Rice showed that similar effects follow from a mismatch of poroelastic properties (e.g., permeability) within fluid‐saturated fringes of damaged material along the fault walls; in this case, it is pore pressure on the slip plane and hence effective normal stress that is altered during slip. The sign of both changes can be either positive or negative, and they need not agree. Both signs reverse when rupture propagates in the opposite direction. When both elastic and poroelastic properties are discontinuous across the fault, steady sliding at a constant friction coefficient, f, is unstable for arbitrarily small f if the elastic mismatch permits the existence of a generalized Rayleigh wave. Spontaneous earthquake rupture simulations on regularized slip‐weakening faults confirm that the two effects have comparable magnitudes and that the sign of the effective normal stress change cannot always be predicted solely from the contrast in elastic properties across the fault. For opposing effects, the sign of effective normal stress change reverses from that predicted by the poroelastic mismatch to that predicted by the elastic mismatch as the rupture accelerates, provided that the wave speed contrast exceeds about 5–10% (the precise value depends on the poroelastic contrast and Skempton's coefficient). For faults separating more elastically similar materials, there exists a minimum poroelastic contrast above which the poroelastic effect always determines the sign of the effective normal stress change, no matter the rupture speed.

The deformation of the front of a 3D interface crack propagating quasistatically in a medium with random fracture properties

One studies the evolution in time of the deformation of the front of a semi-infinite 3D interface crack propagating quasistatically in an infinite heterogeneous elastic body. The fracture properties are assumed to be lower on the interface than in the materials so that crack propagation is channelled along the interface, and to vary randomly within the crack plane. The work is based on earlier formulae which provide the first-order change of the stress intensity factors along the front of a semi-infinite interface crack arising from some small but otherwise arbitrary in-plane perturbation of this front. The main object of study is the long-time behavior of various statistical measures of the deformation of the crack front. Special attention is paid to the influences of the mismatch of elastic properties, the type of propagation law (fatigue or brittle fracture) and the stable or unstable character of 2D crack propagation (depending on the loading) upon the development of this deformation.

Surface Strengthening of Zirconia Toughened Alumina (ZTA) Using Glass Infiltration Technique

Molten Soda lime glass (SLG) was penetrated into the surface of ZTA at 1500°C for the holding time of 1 to 10 h. The depth of the glass penetration increased with increasing holding time. The thermal expansion mismatch and elastic property mismatch between the penetrated glass and ZTA produced residual compression in the surface region during cooling. This residual compression enhanced the flexural strength and fracture toughness remarkably.