Mixed Loading Research Articles

Extensive data of notch shape factors for V-notched Brazilian disc specimen under mixed mode loading

Abstract The linear elastic stress field was numerically analyzed around the V-notch tip in a recently developed disc-type test specimen, called the V-notched Brazilian disc (V-BD), under mixed mode in-plane loading. The notch stress intensity factors (NSIFs) which are very important parameters in brittle fracture assessment of V-notched components were calculated for V-BD specimen by using the finite element (FE) method for different notch geometries and wide range of mode mixities from pure mode I to pure mode II loading conditions. In order to simplify the obtained results to be used in practical applications, the NSIFs were converted to the dimensionless parameters called the notch shape factors (NSFs). These parameters are useful to compute more rapidly and conveniently the NSIFs in V-BD specimen for various notch angles and different notch tip radii. It is shown that the notch shape factors presented in this work combined with the appropriate failure criteria can be utilized to estimate the load-cell capacity of the test apparatus required for fracture test of V-BD specimens made of different brittle materials.

Micro-mechanical prediction of UD laminates behavior under combined compression up to failure: influence of matrix degradation

This article aims to model the behavior of carbon fiber-reinforced polymer laminates up to failure and predict the corresponding energy absorption, under mixed loadings involving compression. In Guimard JM, Allix O, Pechnik N and Thévenet P. [Statistical energy and failure analysis of CFRP compression behavior using a uniaxial microbuckling model. J Compos Mater 2007; 41: 2807–2828], a simplified 2D micro-model has been used in order to assess the influence of the fiber misalignment parameters on the micro-structural compression behavior, both in terms of critical stresses and dissipated energies. This article goes further by introducing the influence of a shear pre-stress and by considering an inelastic and damageable constitutive behavior for the matrix and not only an inelastic one as it is done in the literature. Together with fiber waviness, these three parameters are proven to be critical for the simulation of the kinking phenomenon. Particularly, the main effect of the damageable behavior of the matrix is to avoid unrealistically high hardening of the epoxy. This affects the results significantly and allows a better correlation of the model with experimental data. It is shown, by a statistical analysis, that failure stresses are sensitive to both shear pre-stresses and fiber waviness. Dissipated energies and kink-band size are found to be affected by a shear pre-stress as well but rather less sensitive to fiber waviness.

Evaluation of slant crack propagation under RCF in railway rail

Crack propagation due to rolling contact fatigue (RCF) could be a significant potential challenge to the integrity of railway rails because it may lead to a serious disaster. Fatigue cracks subjected to cyclic rolling contact force experience a complex non-proportional mixed loading and complicated boundary condition. In the present research, complex crack opening/closure/sliding/locked behaviors as the cyclic contact loading movement is analyzed considering liquid lubrication action on rail surfaces as well as crack faces. Based on a series of FE analyses, the calculations of the effective SIF ranges for RCF cracks under certain contact loading and boundary conditions are proposed in the form of polynomial functions which will be appropriately used to predict RCF crack growth rate.

Limited permeable crack moving along the interface of a piezoelectric bi-material

A plane problem for a crack moving with a subsonic speed along the interface of two piezoelectric semi-infinite spaces is considered. The crack is assumed to be free from mechanical loading. The limited permeable electric condition with an account of electric traction is adopted at its faces. A uniformly distributed mixed mode mechanical loading and an electric flux are prescribed at infinity. The problem is reduced to the Riemann–Hilbert problem by means of introducing a moving coordinate system and assuming that the electric flux is uniformly distributed along the crack region. An exact solution of this problem is proposed. It permits to find in closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region. The values of the electric flux are determined by solving the obtained equation. Thereafter, the stress and electric intensity factors as well as their asymptotic fields at the crack tip are also found. The particular case of a crack moving in a homogeneous piezoelectric material is considered. The values of the electric flux and the fracture parameters are found exactly in a simple form for this case. Also, a numerical analysis is performed for a crack propagating with a subsonic speed between PZT4 and PZT5 materials and for a crack moving in PZT4 material. The electric flux in the crack region, stress and electric intensity factors, crack opening and the energy release rate (ERR) are found as functions of the crack speed, loading and electric permeability of the crack medium. The influence of the electric traction on the crack faces upon the mentioned parameters is demonstrated.

An inclined surface crack subject to biaxial loading

The elastic–plastic stress fields and mode mixity parameters for semi-elliptical surface cracks on biaxial loaded plates have been investigated using detailed three-dimensional finite element calculations. Different degrees of mode mixity are given by combinations of the far-field stress level, biaxial stress ratio and inclined crack angle. These analyses were performed for different surface flaw geometries to study the combined load biaxiality and mode mixity effects on the crack-front stress fields and the size and shape of the plastic zones. It is clear from considering the local stress distributions along the crack front that the elastic crack tip singularities have been derived for several particular cases of mixed mode biaxial loading. By theoretical analysis, the new formulae have been introduced for both the elastic and plastic mode-mixity parameters, accounting for ratios between the I/II, II/III and III/I modes. Particular attention was paid to the strong variations of the mode-mixity parameters along the semi-elliptical surface crack front. The mixed-mode behavior of the crack growth direction angle along the semi-elliptical crack front for different combinations of biaxial loading and inclination crack angles was also determined. It was done using methods based on the maximum tangential stress and the strain energy density criteria.

Surface crack growth simulation under mixed mode cyclic loading condition

Surface crack growth process by fatigue is simulated using S-version FEM. Complicated crack growth process in 3-dimensional field under mixed mode loading condition can be modelled easily by this method. Simulation results are compared with experimental ones, and it is pointed out that several factors should be taken into account for the accurate prediction of surface crack growth under mixed mode cyclic loading condition. One of them is plasticity induced crack closure effect, which becomes significant near free surface of the specimen and delays crack growth rate. Another factor is the effect of KIII at the deepest point of surface crack, which results factory roof on the fracture surface and affects crack growth rate, too. Effects of these 2 factors are studied by numerical simulation and they are considered in the crack growth analysis. It is shown that accurate and conservative predictions of surface crack growth processes are conducted well. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

ICONE19-44013 ROD EJECTION ACCIDENT BY THE COUPLED SYSTEM CODE ATHLET-QUABOX/CUBBOX

The paper considers a Rod Ejection Accident (REA) which has been calculated by the coupled-code system ATHLET-QUABOX/CUBBOX. For the present study, a MOX/UOX mixed core loading was developed on the basis of a generic PWR. The results are particularly focused on the fuel enthalpy rise which is the main safety criterion for such transient. A parametric REA study has been performed, showing the influence of some important thermal-hydraulic and neutron-physical parameters. Simulations have been performed using realistic or artificially decreased delayed neutron fractions for two different core states (HZP and 30% of the nominal power). Effective fuel rod temperature influence (i.e. Doppler coefficient) has been studied by using different correlations (0.5/0.5 weighting factors or the typical T_<Doppler> = 0.7 T_<Surface> + 0.3 T_<Center>) or by changing the fuel gap conductance. It is shown that the maximum enthalpy (and enthalpy increase) does not always appear in the affected fuel assembly but can also appear in the neighboring ones. This result is a direct consequence of the burn up dependence of the enthalpy. The paper also considers the case of local delayed neutron parameters and briefly describes the future REA studies foreseen at GRS such as an investigation of quantitative uncertainty propagation from the nuclear data to the transient behavior.

Optimal business decision system for multinationals: A multifactor analysis of selected manufacturing firms

Traditional MIS has been made more effective through the integration of organization, human and technology factors into a decision matrix. The study is motivated by the need to find an optimal mix of interactive factors that will optimize the result of decision to apply ICT to manufacturing processes. The study used Factor analysis model based on the sampled opinion of forty (40) operations/production managers and two thousand (2000) production line workers of three leading manufacturing firms: Uniliver Plc., PZ Plc, and Nigerian Breweries Plc operating in Aba Industrial Estate of Nigeria. The results shows that a progressive mixed factor loading matrix, based on the preferred ordered importance of resources factors in the formulation, implementation, monitoring, control and evaluation of ICT projects of the selected firms led to an average capability improvement of 0.764 in decision efficiency. This is considered strategic for achieving balanced corporate growth and development.

Partition of unity-based thermomechanical meshfree method for two-dimensional crack problems

We present a partition of unity-enriched element-free Galerkin method for thermoelastic two-dimensional crack problems. Therefore, the displacement field is enriched by the step enrichment. In the vicinity of the crack tip, the asymptotic branch enrichment functions commonly used in linear elastic fracture mechanics are employed. The same enrichment strategy is employed for the temperature field. Level set functions are used in order to model the crack surface. The accuracy of the method is demonstrated for three examples, one involves the crack propagation due to temperature and mixed traction-temperature loading conditions with complex curved crack paths.

Bifurcation and generalized mixed loading conditions in geomaterials

SUMMARYThe concept of bifurcation has been widely discussed, based, for example, on homogeneous tests in soil mechanics. Essentially two‐dimensional (axisymmetric) conditions have been considered. This paper aims at deriving a bifurcation criterion in geomechanics, independently of the problem's dimension. This criterion is related to the vanishing of the determinant of the symmetric part of the material's (or the discrete system's) constitutive (or stiffness) matrix. The derivation is essentially based on the notion of loading parameters (controlling the loading). Basically, a bifurcation occurs when the existence of a unique solution to the quasistatic problem, involving a given set of loading parameters, is lost. Interestingly, the criterion is shown to be independent of the choice of loading parameters. As a possible extension, the context of structure mechanics is considered, and the close connection between both soil and structure analysis is discussed. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Interpretation of the VENUS VIP-BWR program with APOLLO2.8 reference and optimized MOC schemes for 8 × 8 UO 2 and MOX BWR assemblies

The interpretation of the VIP-BWR program conducted in the CEN·SCK Mol VENUS critical facility (Belgium), has been performed with the new APOLLO2.8 product and its CEA2005V4.1 library based on the JEFF3.1.1 file. Both reference SHEM-MOC (281groups without equivalence) and Optimized BWR 26G (26 groups with equivalence) schemes are used for UO 2 and MOX BWR assembly calculations. The VIP-BWR program was aimed to provide an experimental database for BWR neutronics tools in mixed Gd poisoned configurations with 8 × 8 UO 2 and MOX assemblies. The experimental conditions are relatively representative of actual industrial BWR core characteristics, at least in terms of void fraction. Measured pin-by-pin power distributions enable to exact valuable information at various interfaces. For fresh (UO 2/UO 2–Gd) and recycled UO 2 (UO 2 only) cores loadings, the information is given through the “UO 2” core. In the case of partial MOX loadings (UO 2/MOX interface), the power distributions are available through the “T-MOX” core. All critical sizes are predicted within 1 with SHEM-MOC reference calculation scheme. For UO 2 core, the (C–E) on k eff are (95 ± 266) pcm and (203 ± 266) pcm for SHEM-MOC and Optimized scheme respectively. For MOX core, the results are (87 ± 214) pcm and (283 ± 214) pcm. The uncertainties take into account both measurement uncertainties and technological uncertainties such as enrichment, clad thicknesses, grid pitch or fuel densities. Average (C–E)/E on radial fission rate distributions are in excellent agreement in the UO 2 and UO 2–Gd assemblies. In mixed loading cores, the calculation shows an over prediction in the MOX fuel pin. This points out a systematic swing between UO 2 and MOX. For average fission rates in UO 2, the C/E results are within ± 0.2% with SHEM-MOC and Optimized BWR 26G. For average power in MOX, the C/E results are within ±0.5% with SHEM-MOC and ±0.9% with Optimized BWR 26G. The P MOX/P UO2 fission rate ratios are (+3.7 ± 1.8%) and (+2.5 ± 1.8%) for SHEM-MOC and Optimized BWR 26G respectively. The peak power in UO 2 and MOX cores are reproduced within ±0.8% for both schemes. These results confirm the capability of this product to correctly treat pin-by-pin power distributions in BWR UO 2 and island MOX bundles.

New mixed boundary, true triaxial loading device for testing three-dimensional stress–strain–strength behaviour of geomaterials

This paper presents a brief review of true triaxial apparatuses (TTAs) developed in the past and their advantages and limitations. Considering the limitations of previous designs, a new true triaxial loading device that provides mixed boundary conditions for a true triaxial apparatus (TTA) is introduced. This loading device consists of four sliding rigid plates and two flexible loading faces. The setup of the loading device together with the whole true triaxial system is described. Frictions between sliding plates and the soil membrane surfaces in the new loading device are examined. A three-dimensional finite element (FE) modelling study is carried out on the stress and strain distribution of a soil specimen subjected to loading from two different loading devices. It is found that stresses and strains of a soil specimen subjected to loading from the new sliding plates are far more uniform than those subjected to loading from nonsliding plates with preset gaps. Finally, the paper presents the applications of the present TTA with the new loading device for testing studies of a completely decomposed granite soil and a geofoam. Typical results are presented and discussed. It is found that the present mixed boundary loading device is very suitable for true triaxial testing on both soils and geofoam, especially under large strains or compression without corner contact problems.

Experimental Investigation of Large Deformation Fracture for Rubber Materials

With the increasing investigation on reliability and stability of engineering structures, it becomes important for reseach on mechanical properties of materials under fracutre conditions. Concerning to fracture problems of large deformation materials, deformation characteristics of the crack tip field is necessarily needed. This paper presents an experimental analysis on a double-cracked rubber disk under the I-II mixed-mode fracture condition. Deformation properties around the crack tip are described through analyzing displacement information acquired by digital moiré method of circular and radial gratings. Also the existence of sector division mode under mixed loading condition is verified, and it is also found experimentally that the shear component makes the sectors shift.

Molecular-dynamics-based cohesive zone law for brittle interfacial fracture under mixed loading conditions: Effects of elastic constant mismatch

One approach for performing a finite-element simulation of interfacial fracture is to use a cohesive zone model. The cohesive zone model defines the interfacial traction–separation relation. Experimental determination of such a relation has been difficult. Most previous work has been confined to tensile loading, and much less has been devoted to mixed-mode loading conditions. Even so, specific laws are often assumed rather than predicted. Our recent work has used molecular dynamics (MD) simulation methods to derive a general cohesive zone law for the fracture between two brittle materials under any mixed-mode loading conditions. Here we extend our method and use it to explore the effect of elastic constant mismatch between adjacent materials. In particular, we construct two bilayer structures where the cohesive energies and lattice constants of the constituent materials are kept the same, but the elastic constant mismatch of the two materials in one structure differs from that in the other. We then use MD simulations to study the fracture and to derive the cohesive zone laws for both structures. The effect of elastic constant mismatch on fracture will then be discussed.

Electric polarization induced by mechanical loading of Solnhofen limestone

Electromagnetic radiation was detected while loading a sample of Solnhofen limestone, which is not a piezoelectric material. The sample was subjected to mixed tensile and shear loading. The signals observed are associated with a fall-off in electric polarization induced by the loading, and represent the second time derivative of the polarization. The polarization is ascribed to the complicated type of loading, leading to the existence of a chosen direction, which makes polarization possible.

Simultaneous bilateral Achilles tendon ruptures associated with statin medication despite regular rock climbing exercise

Introduction Ruptures of the Achilles tendon are common however simultaneous ruptures occur less frequently. Eccentric loading exercise programmes have been used to successfully treat Achilles tendinopathy. Case report We report a case of simultaneous bilateral Achilles tendon rupture in a patient predisposed to rupture due to longstanding raised serum lipoprotein and recently introduced therapeutic statin medication. The patient was also a keen rock climber and had regularly undertaken loading exercise. Conclusion This case illustrates that the therapeutic effect of mixed loading exercises for the Achilles tendon may not be adequate to overcome the predisposition to rupture caused by hyperlipidaemia and statin medication.

Analysis of stress intensity factors for three-dimensional interface crack problems in electronic packages using the virtual crack closure technique

In this study the fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles, along the curvilinear front of a three-dimensional bimaterial interface crack in electronic packages are considered by using finite element method with the virtual crack closure technique (VCCT). In the numerical procedure normalized complex stress intensity factors and the corresponding phase angles (Rice, J Appl Mech 55:98–103, 1988) are calculated from the crack closure integrals for an opening interface crack tip. Alternative procedures are also described for the cases of crack under inner pressure and crack faces under large-scale contact. Validation for the procedure is performed by comparing numerical results to analytical solutions for the problems of interface crack subjected to either remote tension or mixed loading. The numerical approach is then applied to study interface crack problems in electronic packages. Solutions for semi-circular surface crack and quarter-circular corner crack on the interface of epoxy molding compound and silicon die under uniform temperature excursion are presented. In addition, embedded corner delaminations on the interface of silicon die and underfill in flip-chip package under thermomechanical load are investigated. Based on the distribution of the fracture mechanics parameters along the interface crack front, qualitative predictions on the propensity of interface crack propagation under thermomechanical loads are given.

Cortical bone trajectory for lumbar pedicle screws

Background context Achieving solid implant fixation to osteoporotic bone presents a clinical challenge. New techniques and devices are being designed to increase screw–bone purchase of pedicle screws in the lumbar spine via a novel cortical bone trajectory that may improve holding screw strength and minimize loosening. Preliminary clinical evidence suggests that this new trajectory provides screw interference that is equivalent to the more traditionally directed trajectory for lumbar pedicle screws. However, a biomechanical study has not been performed to substantiate the early clinical results. Purpose Evaluate the mechanical competence of lumbar pedicle screws using a more medial-to-lateral path (ie, “cortical bone trajectory”) than the traditionally used path. Study design Human cadaveric biomechanical study. Methods Each vertebral level (L1–L5) was dual-energy X-ray absorptiometry (DXA) scanned and had two pedicle screws inserted. On one side, the traditional medially directed trajectory was drilled and tapped. On the contralateral side, the newly proposed cortical bone trajectory was drilled and tapped. After qCT scanning, screws were inserted into their respective trajectories and pullout and toggle testing ensued. In uniaxial pullout, the pedicle screw was withdrawn vertically from the constrained bone until failure occurred. The contralateral side was tested in the same manner. In screw toggle testing, the vertebral body was rigidly constrained and a longitudinal rod was attached to each screw head. The rod was grasped using a hydraulic grip and a quasi-static, upward displacement was implemented until construct failure. The contralateral pedicle screw was tested in the same manner. Yield pullout (N) and stiffness (N/mm) as well as failure moment (N-m) were compared and bone mineral content and bone density data were correlated with the yield pullout force. Results New cortical trajectory screws demonstrated a 30% increase in uniaxial yield pullout load relative to the traditional pedicle screws (p=0.080), although mixed loading demonstrated equivalency between the two trajectories. No significant difference in construct stiffness was noted between the two screw trajectories in either biomechanical test or were differences in failure moments (p=0.354). Pedicle screw fixation did not appear to depend on bone quality (DXA) yet positive correlations were demonstrated between trajectory and bone density scans (qCT) and pullout force for both pedicle screws. Conclusions The current study demonstrated that the new cortical trajectory and screw design have equivalent pullout and toggle characteristics compared with the traditional trajectory pedicle screw, thus confirming preliminary clinical evidence. The 30% increase in failure load of the cortical trajectory screw in uniaxial pullout and its juxtaposition to higher quality bone justify its use in patients with poor trabecular bone quality.

Degradation, fatigue, and failure of resin dental composite materials.

The intent of this article is to review the numerous factors that affect the mechanical properties of particle- or fiber-filler-containing indirect dental resin composite materials. The focus will be on the effects of degradation due to aging in different media, mainly water and water and ethanol, cyclic loading, and mixed-mode loading on flexure strength and fracture toughness. Several selected papers will be examined in detail with respect to mixed and cyclic loading, and 3D tomography with multi-axial compression specimens. The main cause of failure, for most dental resin composites, is the breakdown of the resin matrix and/or the interface between the filler and the resin matrix. In clinical studies, it appears that failure in the first 5 years is a restoration issue (technique or material selection); after that time period, failure most often results from secondary decay.

Fractographic Analysis of K3 Nickel-Titanium Rotary Instruments Submitted to Different Modes of Mechanical Loading

The aim of the present study was to analyze the fracture surface of nickel-titanium K3 rotary files submitted to different modes of mechanical loading. Torsional and flexural fatigue tests were realized separately in 2 groups of files. Additional 2 groups of files were tested in mixed loading modes, torsional test after incomplete flexural fatigue test and flexural fatigue test after incomplete torsional test. Scanning electronic microscopy observation was used to make a fractographic analysis of the files under test. The files fractured during torsional resistance tests showed fractographies with a central area containing dimples, which are oval-shaped depressions in the microstructure in places of high local plastic deformation. The peripheral area of these files' fractographies presented a flattened aspect without dimples. The fractographies of the files fractured by flexural fatigue presented one area with radial striations and another area containing dimples. The fractographic patterns observed when mixed loading modes were imposed correspond to the pattern defined by the second stage test. The patterns established for the fractured files provide consistent bases to explain the fracture process in clinical conditions by fractographic analysis.