Shear Stress Intensity Factor Research Articles

The interfacial behavior of an axisymmetric film bonded to a graded inhomogeneous substrate

With the development of high-tech applications such as thermal barrier coatings, stretchable and flexible electronics, etc, the key film/substrate systems are more commonly involving three-dimensional axisymmetric problems with graded inhomogeneous substrates. In these film/substrate systems, the effects of geometric and material factors of both the films and the substrates on the interfacial behavior are urgently needed to be uncovered. Herein, a novel theoretical axisymmetric model of an elastic film bonded to a graded substrate is proposed and solved by using Hankel integral transformation and orthotropic polynomials. The interfacial shear stress and the corresponding shear stress intensity factor as well as radial stresses and hoop stresses of both the film and the graded substrate are obtained. It is found that the present model works well to predict the interfacial behavior between an axisymmetric film and a graded substrate. Compared with cases with homogeneous substrates, choosing graded substrates can reduce the risk of edge fracture on the surface of the substrate. A film with a smaller elastic modulus and thickness is advantageous for the interface reliability of the film/substrate system under a thermal load. The results should be useful for not only understanding the load transfer mechanism of axisymmetric film/substrate system, but also providing a valuable guidance to optimize film/substrate structures in various practical and potential applications.

Microstructure size-dependent contact behavior of a thermoelectric film bonded to an elastic substrate with couple stress theory

Thermoelectric films linked to elastic substrates are typical engineering structures and have applications in heat recovery systems. This article uses the nonlocal heat conduction and couple stress theory to investigate the electric-thermal-elastic behavior of the thermoelectric film placed on the elastic half-plane. The internal characteristic lengths of both the thermoelectric film and the elastic substrate are introduced to reveal the scale effects. The coupling governing integro-differential equations in terms of the interface shear stress and tensile stress are derived for the thermoelectric film and the elastic substrate. The numerical results show how the distribution of the tensile and shear stress intensity factors is affected by the stiffness ratio of the substrate to the thermoelectric film, the internal characteristic lengths of the thermoelectric film and the elastic substrate, and the thickness to length ratio of the thermoelectric film. Compared with the classical model for a thicker thermoelectric film and stiffer elastic substrate, the present study demonstrates the necessity of taking into account the microstructure lengths of the thermoelectric film and the elastic substrate.

Failure Analysis on the Fracture Shaft of a Centrifugal Pump Used for Diesel Engine Cooling System

Shaft failures often occur, even in the shafts of centrifugal pumps. This study aims to determine the cause of shaft fracture through experimental and numerical study. The fracture surface was observed using Scanning Electron Microscopy (SEM) to identify the initial crack. The chemical composition test results show that the material used was in accordance with the AISI 420 standard, which is necessary to make Finite Element Analysis (FEA) modelling. Shear stress, strain and stress intensity factors were analysed around the fillet using FEA. The results show that the value of maximum stress intensity factor, KI, occurs in the multilevel shaft fillets that experienced initial cracks due to torsional loads. The shear stress value, obtained from the FEA, was higher than the shear stress value of the material. The KI value, also derived from the FEA, was higher than the KICvalue of the material.

Effect of Temperature on the Mechanical Properties of Carbon Composites

The purpose of this research is to investigate and analyze the effect of temperature on the mechanical properties of carbon composites, aluminum foam, and carbon nanotube reinforced aluminum foam. For this analysis, fatigue behavior of aluminum foam has been discussed, and interlaminar shear stress between single-walled carbon nanotube reinforced aluminum foam and multiwalled carbon nanotube reinforced aluminum foam has been compared. The comparison has shown that the interlaminar shear stress within the interface of single-walled carbon nanotube and aluminum foam is higher than that within the interface of multiwalled carbon nanotube and aluminum foam. Hence, the probability of stress concentration and crack initiation within the interface of single-walled carbon nanotube and aluminum foam is higher than that within the interface of multiwalled carbon nanotube and aluminum foam. Furthermore, thermal fatigue lives of different single-walled carbon nanotube reinforced matrix nanocomposites have been evaluated. Additionally, interaction between carbon and molten aluminum has been analyzed. Finally, a new relation for the thermal interlaminar shear stress intensity factor to predict the crack initiation sites on fiber/matrix interface has been introduced.

Thermally induced delamination and buckling of a ceramic coating with temperature-dependent material properties from porous substrate at high temperatures

Ceramic coatings are ideal materials for thermal protection systems such as the thermal shield of the space shuttle. In a high-temperature environment, material properties of ceramics strongly depend on the temperature. The severe mismatch of material properties between the ceramic coating and the substrate can result in progressive mechanical failure of thermal protection system. This paper investigates delamination and buckling behaviors between a temperature-dependent ceramic coating and a porous substrate. The shear stress intensity factor at the tips of the delamination crack and buckling region are derived. Based on the stress intensity factor, the critical temperature of the coating buckling from the substrate is obtained. A fitting formula of the critical buckling temperature with respect to the length-to-thickness ratio of the coating, and the buckling region is obtained. It is found that the effect of the temperature dependence of material properties on delamination and buckling is more significant for higher temperatures than for lower temperatures. The critical temperatures of delamination and buckling are overestimated if the temperature dependence of material properties is neglected. The critical temperatures of delamination and buckling increase with the porosity of the substrate.

Criteria evaluation for the transition of cracking modes in a single-crystal nickel-base superalloy

Single-crystal nickel-base superalloys frequently experience two distinct fatigue crack growth modes. It has been observed that, under certain conditions, cracks transition from a path perpendicular to the loading direction to a crystallographic slip plane. As crystallographic cracking is associated with an increased fatigue crack growth rate, it is important to be able to predict when this transition occurs. In this work three different criteria for crystallographic cracking based on resolved anisotropic stress intensity factors are evaluated in a three-dimensional finite element context. The criteria were calibrated and evaluated using isothermal fatigue experiments on two different specimen geometries. It is suggested by the results, that a threshold value of a resolved shear stress intensity factor can act as a conservative criterion indicating cracking mode transition. Further, a trend hinting towards a loading frequency dependency could be observed.

Fracture and fatigue of the surface layer of layered media due to adhesive sliding contact

Layer cracking in a layered medium consisting of an elastic-perfectly plastic half-space (substrate) and a relatively stiff, elastic surface layer in adhesive sliding contact with a rigid asperity was analyzed with the finite element method using linear elastic fracture mechanics. The directions of tensile and shear mode fracture were determined from the maximum tensile and shear stress intensity factors (SIFs), respectively, whereas the directions of tensile and shear mode fatigue crack growth were determined from the maximum range of tensile and shear SIFs, respectively. The effects of asperity position, interfacial adhesion (Maugis parameter), crack depth, asperity interaction distance, layer thickness, and material properties of the elastic layer and the elastic-plastic substrate on fracture and fatigue crack growth in the layer are interpreted in the context of simulation results. It is shown that the propensity for fracture and fatigue in the layer is enhanced with increasing asperity interaction distance and Maugis parameter and decreasing crack depth and layer thickness. The numerical results of this study reveal that, for similar tensile and shear fracture toughness, layer fracture in adhesive sliding contact predominantly occurs by the out-of-plane tensile mode of fracture, whereas fatigue crack growth in the layer is a manifestation of the in-plane shear and out-of-plane tensile modes of fatigue crack growth.

A fracture mechanics analysis of asperity cracking due to sliding contact

Microfracture of surface protrusions residing on contacting surfaces, known as asperities, due to normal and shear surface traction occurs at various scales affecting the durability and performance of many mechanical components. In this study, microfracture of an asperity due to sliding against a rigid asperity was examined using a two-dimensional (plane strain) finite element model and linear elastic fracture mechanics. The effects of the asperity interference depth, sliding friction, crack position, and crack-face friction on the rate, direction, and dominant mode of crack growth were determined by the ranges of the maximum tensile and shear stress intensity factors. The asperity interference depth and sliding friction exhibited the most pronounced effects on the rate and direction of crack growth. A transition from shear to tensile dominant mode of crack growth was encountered with increasing asperity interference depth and/or sliding friction coefficient. Crack mechanism maps revealing the evolution of opening, slip, and stick between the crack faces are presented for a range of crack-face friction coefficient, asperity interference depth, and sliding friction coefficient. The simulation results provide insight into the underlying microfracture mechanics of asperities residing on sliding surfaces that exhibit different friction characteristics.

A Finite Element Study of the Influence of Graphite Nodule Characteristics on a Subsurface Crack in a Ductile Cast Iron Matrix under a Contact Load

This paper describes a study of the effects of graphite nodule characteristics on a subsurface crack in austempered ductile iron (ADI). A representative specimen of ADI, subjected to sliding contact load, is modeled using finite elements aiming to obtain the shear stress intensity factor (KII). The parameters varied were (i) the nodule diameter (two different values were considered), (ii) the distance between the nodule and the tip of the crack and (iii) the position of the load relative to the tip of the crack. The results of the numerical simulations show that the smaller diameter nodule has a larger influence on KII, suggesting a higher contact fatigue crack propagation rate in the material with the smaller nodule. These results are the opposite of those observed in experimental studies and would appear to indicate that other factors should be also considered to ensure realistic estimates of the contact fatigue strength of ADI.

Numerical analysis of mixed-mode rupture propagation of faults in reservoir-caprock system in CO2 storage

Injection-induced seismicity and caprock integrity are among the most important concerns in CO2 storage operations. Understanding and minimizing fault/fracture reactivation in the first place, and rupture growth/propagation beyond its surface afterwards, are fundamental to achieve a successful deployment of geologic carbon storage projects. Rock fracture mechanics provides useful concepts to study the propagation of discontinuities such as pre-existing faults and fractures. In this paper, we aim at developing a methodology to investigate the rupture propagation likelihood of faults/fractures inside a reservoir and its surrounding (including the caprock) as a result of reservoir pressurization. In this methodology, mode I (tensile) and mode II (shear) stress intensity factors of a given fault/fracture are calculated based on Linear Elastic Fracture Mechanics. A fault/fracture can propagate either in mode I, mode II or a combination of both (also called mixed-mode) based on the comparison of the stress intensity factors and fracture toughness. The proposed methodology, which has been embedded into a hybrid Finite Element Method-Discrete Element Method in-house code called MDEM, has the capability to obtain the direction of mode I and mode II rupture in front of a fault/fracture tip. Two coefficients are defined as stress intensity paths (κ) for a fault/fracture, as the change of stress intensity factors for the two failure modes of a given discontinuity per unit pore pressure change of the reservoir after injection. Based on these stress intensity path coefficients, a relationship is given to calculate the threshold pressure buildup above which the two propagation modes may occur. We use the proposed methodology to investigate the rupture growth likelihood of faults in and around a closed reservoir due to its pressurization. Simulation results indicate that mode I failure is likely to occur inside the reservoir for faults with low dip angle in compressional stress regimes. However, the initiated mode I failure may not have the chance to grow upwards because the minimum principal is in the vertical direction and thus, the initiated rupture tends to rotate and grow horizontally. In contrast, mode I rupture is likely to occur in the caprock for faults with high dip angle in extensional stress regimes. The initiated rupture may grow upwards if the newly created fracture becomes hydraulically connected with the reservoir. We find that mode II rupture is not likely to occur in any of the investigated scenarios. Simulation results show that the coefficients of the stress intensity factors depend on the faults location, dipping angle, fault length, presence of other faults, reservoir aspect ratio and reservoir and caprock stiffness.

Axisymmetric thermo-elastic field in an infinite one-dimensional hexagonal quasi-crystal space containing a penny-shaped crack under anti-symmetric uniform heat fluxes

This paper is dedicated to investigating the problem of an infinite one-dimensional hexagonal quasi-crystal medium weakened by a penny-shaped crack and subjected to a pair of anti-symmetric and identical uniform heat fluxes. In view of the anti-symmetry with respect to the crack plane, this problem is formulated by a mixed boundary value problem of the half-space. Based on the general thermo-elastic solution, the mixed boundary value problem is solved by means of the generalized potential theory method. The thermo-elastic field variables in the entire three-dimensional space are explicitly expressed in terms of elementary functions. Some important physical quantities on the crack plane, e.g., temperature, crack slip displacement, shear stress and stress intensity factor, are also presented in closed-forms. Numerical calculations are carried out to validate the present analytical solution and to graphically show the distribution of the thermo-elastic coupling field around the crack. The present solution may be served as a benchmark for the experimental investigations by infrared-thermography technique.

Assessment of mixed mode crack propagation of crane runway girders subjected to cyclic loading

Crane runway girders are subjected to travelling wheel loads resulting in mixed mode crack tip loading. The paper addresses the assessment of crack propagation of crane runway girders being travelled over by wheel loads. Fractographic investigations of crack surfaces show shear mode crack growth and scabs due to friction between the crack flanks. Crack growth rates for steels subjected to tensile mode crack growth are evaluated. Stress intensity factors of crane runway girders under cyclic loading are obtained by numerical investigations. Numbers of cycles of crack growth are calculated by use of the shear stress intensity factor Kτ.

The shear fracture toughness, KIIc, of graphite

The critical shear stress intensity factor, KIIc, here-in referred to as the shear fracture toughness, KIIc (MPa√m), of two grades of graphite are reported. The range of specimen volumes was selected to elucidate any specimen size effect, but smaller volume specimen tests were largely unsuccessful, shear failure did not occur between the notches as expected. This was probably due to the specimen geometry causing the shear fracture stress to exceed the compressive failure stress. In subsequent testing the specimen geometry was altered to reduce the compressive footprint and the notches (slits) made deeper to reduce the specimen's ligament length. Additionally, we added the collection of Acoustic Emission (AE) during testing to assist with the identification of the shear fracture load. The means of KIIc from large specimens for PCEA and NBG-18 are 2.26 MPa√m with an SD of 0.37 MPa√m and 2.20 MPa√m with an SD of 0.53 MPa√m, respectively. The value of KIIc for both graphite grades was similar, although the scatter was large. In this work we found the ratio of KIIc/KIc≈1.6.

Rate-dependent fracture modes in human femoral cortical bone

An accurate understanding of fracture in human bone under complex loading scenarios is critical to predicting fracture risk. Cortical bone, or dense compact bone, is subject to complex loading due to the inherent multi-axial loading conditions, which are also influenced by the anisotropy of the microstructure. When determining critical fracture parameters, bone is traditionally idealized as isotropic. This paper presents a method to examine rate-dependent mode mixity associated with cortical bone crack initiation. Four-point bend experiments have been conducted on cortical femoral bone samples from three human donors at quasi-static (slow), intermediate, and dynamic loading rates. Digital image correlation was used to obtain full-field displacement maps at the crack tip during the experiments. An over-deterministic least squares method is presented and used to evaluate Mode I (opening) and Mode II (shear) stress intensity factors (SIF) for fracture initiation at slow (10 $$^{-2}$$ MPa-m $$^{1/2}$$ s $$^{-1}$$ ), intermediate (15 MPa-m $$^{1/2}$$ s $$^{-1}$$ ), and high ( $$4.5^{4}\,\hbox {MPa-m}^{1/2}\,\hbox {s}^{-1}$$ ) stress intensity factor rates. Results show that under dynamic loading, the critical SIF in Mode I assuming material anisotropy is approximately 50 % lower than fracture toughness assuming isotropy. Additionally, critical Mode I and II SIFs had the lowest values at the highest rate of loading examined, decreasing to one third of the values under quasi-static loading. Crack growth in the low and intermediate SIF rates appears to be Mode II dominant, and shows a transition to completely mixed-mode at the high rate of loading. These results suggest that the conventional assumption of isotropy is a conservative estimate at low and intermediate rates, but overestimates fracture strength at dynamic rates.

Opening and contact zones of an interface crack in a piezoelectric bimaterial under combined compressive-shear loading

A plane problem for a tunnel electrically permeable interface crack between two semi-infinite piezoelectric spaces is studied. A remote mechanical and electrical loading is applied. Elastic displacements and potential jumps as well as stresses and electrical displacement along the interface are presented using a sectionally holomorphic vector function. It is assumed that the interface crack includes zones of crack opening and frictionless contact. The problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved analytically. From the obtained solution, simple analytical expressions are derived for all mechanical and electrical characteristics at the interface. A quite simple transcendental equation, which determines the point of separation of open and close sections of the crack, is found. For the analysis of the obtained results, the main attention is devoted to the case of compressive-shear loading. The analytical analysis and numerical results show that, even if the applied normal stress is compressive, a certain crack opening zone exists for all considered loading values provided the shear field is present. It is found that the shear stress intensity factor at the closed crack tip and the energy release rates at the both crack tips depend very slightly on the magnitude of compressive loading.

Numerical Solution for an Epicycloid Crack

A flat crack,Ω, is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values forΩsuch that the problem of finding the resulting force can be written in the form of hypersingular integral equation. Employing conformal mapping, the integral equation is transformed to a similar equation over a circular region,D. By making a suitable representation of hypersingular integral equation, the problem is reduced to solve a system of linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.

A Study of Shear Stress Intensity Factor of PP and HDPE by a Modified Experimental Method together with FEM

Shear testing is one of the most complex testing areas where available methods and specimen geometries are different from each other. Therefore, a modified shear test specimen (MSTS) combining the simple uniaxial test with a zone of interest (ZOI) is tested which gives almost the pure shear. In this study, material parameters of polypropylene (PP) and high density polyethylene (HDPE) are first measured by tensile tests with a dogbone shaped specimen. These parameters are then used as an input for the finite element analysis. Secondly, a specially designed specimen (MSTS) is used to perform the shear stress tests in a tensile testing machine to get the results in terms of forces and extension, crack initiation etc. Scanning Electron Microscopy (SEM) is also performed on the shear fracture surface to find material behavior. These experiments are then simulated by finite element method and compared with the experimental results in order to confirm the simulation model. Shear stress state is inspected to find the usability of the proposed shear specimen. Finally, a geometry correction factor can be established for these two materials in this specific loading and geometry with notch using Linear Elastic Fracture Mechanics (LEFM). By these results, strain energy of shear failure and stress intensity factor (SIF) of shear of these two polymers are discussed in the special application of the screw cap opening of the medical or food packages with a temper evidence safety solution.

Fracture mechanics analysis of asperity cracking due to adhesive normal contact

A two-dimensional linear-elastic fracture mechanics analysis of asperity cracking induced by adhesive normal contact was performed with the finite element method. Normal contact between two elastic asperities was analyzed with the equivalent contact system of an elastic asperity with equivalent radius of curvature and effective elastic modulus compressed by a rigid plane. Surface adhesion was modeled by nonlinear springs obeying a constitutive force-distance law derived from the Lennard–Jones potential. The maximum ranges of the tensile and shear stress intensity factors were used to determine the crack-growth direction and the dominant mode of asperity fracture in terms of the Maugis parameter (a function of the equivalent radius of curvature, work of adhesion, effective elastic modulus, and intermolecular equilibrium distance), friction coefficient at the crack interface, maximum surface interference, and crack position. Finite element simulation results indicate that the direction and the rate of crack growth are mostly affected by the Maugis parameter and the maximum surface interference. A transition from shear to tensile dominant mode of crack growth is encountered with the increase of the Maugis parameter and/or the decrease of the maximum surface interference. Opening, slip, and stick between the crack faces during loading and unloading are discussed in the context of crack mechanism maps.

Size effect on crack kinking in a piezoelectric strip under impact loading

An impermeable crack in a piezoelectric strip under in-plane mechanical and electric impact loading is considered. The crack is located at an arbitrary position and parallel to the surfaces of the piezoelectric strip. Fourier and Laplace transforms are applied to reduce the mixed-mode crack problem (modes I and II) to a system of singular integral equations. Full singular fields around the crack tip are obtained asymptotically in an explicit form and the hoop and shear stress intensity factors are determined. Laplace inversion is applied to get the mechanical and electrical fields in the time domain. The crack kinking phenomenon is investigated by applying the criterion of maximum hoop stress intensity factor. Numerical results show that the geometry of the cracked strip and the electric loading significantly influence the singular field distributions around the crack tip. Mixed-mode crack may tend to kink out of the original crack plane, and the crack kinking angle depends on the distribution of the hoop stress around the crack tip and the maximum value of the hoop stress intensity factors (HSIFs).

산-염기 표면처리된 MWNTs의 첨가가 탄소섬유 강화 복합재료의 기계적 계면특성에 미치는 영향

In this work, the effect of chemical treatments of multi-walled carbon nanotubes (MWNTs) on the mechanical interfacial properties of carbon fiber fabric-reinforced composites was investigated. The surface properties of the MWNTs were determined by acid and base values, Fourier transform infrared spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS) analyses. The mechanical interfacial properties of the composites were assessed by interlaminar shear stress (ILSS) and critical stress intensity factor (). The chemical treatments based on acid and base reactions led to a significant change of surface characteristics of the MWNTs, especially A-MWNTs/carbon fibers/epoxy composites had higher mechanical properties than those of B-MWNTs and non-treated MWNTs/carbon fibers/epoxy composites. These results were probably due to the improvement of interfacial bonding strength, resulting from the acid-base interaction and hydrogen bonding between the epoxy resins and the MWNT fillers.