Radial Tensile Stress Research Articles

Weibull Effective Area for Hertzian Ring Crack Initiation

Spherical or Hertzian indentation is used to characterize and guide the development of engineered ceramics under consideration for diverse applications involving contact, wear, rolling fatigue, and impact. Ring crack initiation can be one important damage mechanism of Hertzian indentation. It is caused by surface-located, radial tensile stresses in an annular ring located adjacent to and outside the Hertzian contact circle. While the maximum radial tensile stress is known to be dependent on the elastic properties of the sphere and target, diameter of the sphere, applied compressive force, and coefficient of friction, the Weibull effective area too will be affected by these parameters. However, estimations of a maximum radial tensile stress and Weibull effective area are difficult to obtain because the coefficient of friction during indentation is not known a priori. Circumventing this, the Weibull effective area expressions are derived here for the two extremes that bracket all coefficients of friction; namely (1) the classical, pure-slip frictionless case and (2) the case of an infinite coefficient of friction or pure stick.

Can traditional “cupping” treatment cause a stroke?

The case study of a patient who developed haemorrhagic stroke after ‘cupping’ to the cervical area is presented. We consider the various manners in which cupping might induce haemorrhagic or ischemic stroke with particular reference to the relevant pathologies of the major cervical arteries. The other possible causes due to the induced cupping stresses are also examined using a computer based simulation study. Cupping of the cervical area may cause a haemorrhagic stroke by an acute rise in blood pressure. The tensile radial stresses generated by cupping may potentially facilitate the development of a dissection in the presence of an intimal tear. Moreover, the possible presence of micro-inclusions can intensify the local stress concentration for a thin cap.

Preparation of graded multilayer materials and evaluation of residual stresses

It is generally difficult to join ceramics to alloys by conventional welding technologies to fabricate graded multilayer materials with various excellent engineering properties. In this study, MoSi 2 and 316L stainless steel are chosen a typical example and are joined together using the spark plasma sintering technique. To evaluate the joint quality, the interlayer system of the graded material is characterized using analysis of the residual stress by the finite element ANSYS code. The results show that dense uniformed joints can be achieved with such graded inter-layers because the coefficient of thermal expansion (CTE) of each interlayer closely matched over a wide temperature range. Such a compatibility between the graded inter-layers prevents MoSi 2 with low toughness from the occurrence of microcracks resulted from the residual stresses formed during cooling of the joint. Further theoretical analysis indicates that with the increase in the compositional distribution exponent ( P), maximum radial and axial residual tensile stress first increases and then decreases. In addition, with the increase in the number ( n) of graded layer, maximum radial and axial residual tensile stress decreases gradually.

Numerical study on the thermo-stress of ZrO2 thermal barrier coatings by high-intensity pulsed ion beam irradiation

This paper studies numerically the thermo-mechanical effects of ZrO2 thermal barrier coatings (TBCs) irradiated by a high-intensity pulsed ion beam in consideration of the surface structure. Taking the deposited energy of ion beams in TBCs as the source term in the thermal conduction equation, the distribution of temperature in TBCs was simulated. Then, based on the distribution, the evolution of thermal stress was calculated by the finite element method. The results show that tensile radial stress formed at the valley of TBC surfaces after irradiation by HIPIB. Therefore, if cracks happen, they must be at valleys instead of peaks. As for the stress waves, no matter whether through peak or valley position, tensile and compressive stresses are present alternately inside TBCs along the depth direction, and the strength of stress decreases with time.

Stresses around fiber ends at free and embedded ply edges

Using the finite element method, the stress state around fiber ends at a free surface in a unidirectional fiber composite was studied. The material is subjected to a thermal load consistent with a cryogenic application as well as ply level transverse tensile loading associated with thermal stresses in a laminate. At the free end the fiber–matrix interface sees tensile radial stresses as well as shear stresses. This makes the fiber end a likely site for interface debonding (crack initiation). These initial cracks can then link up and grow to become full through-thickness matrix cracks. The effect that an epoxy coating over the fiber ends has on the local stress distribution was also considered. These capped models simulate fiber ends embedded within a laminate. The epoxy cap has the effect of suppressing the interface stresses at the fiber end. The significance of these results in relation to cryogenic cycling tests using coupon specimens with free and embedded edges is discussed.

Tensile radial stress in the spinal cord related to arachnoiditis or tethering: a numerical model

Spinal arachnoiditis comprises fibrous scarring of the subarachnoid space, following spinal trauma or inflammation, and is often associated with syringomyelia. We hypothesised that cord-to-dura attachments could cause transient tensile cord radial stress, as pressure waves propagate. This was tested in a fluid-structure interaction model, simulating three types of cord tethering, with 'arachnoiditis' confined to a short mid-section of the cord. The annular system was excited abdominally with a short transient, and the resulting Young and Lamb waves and reflections were analysed. Radial mid-section tethering was less significant than axial tethering, which gave rise to tensile radial stress locally when the cord was not fixed cranially. Simulated as inextensible string connections to the dura, arachnoiditis caused both localised tensile radial stress and localised low pressure in the cord as the transient passed. The extent of these effects was sensitive to the relative stiffness of the dura and cord. Tensile radial stress may create a syrinx in previously normal cord tissue, and transiently lowered pressure may draw in interstitial fluid, causing the syrinx to enlarge if fluid exit is inhibited. The suggested mechanism could also explain the juxtaposition of syrinxes to regions of arachnoiditis.

Mechanical testing of titanium/aluminium–silicon interfaces by push-out

Mechanical properties of Ti/Al–7Si assemblies produced by insert moulding were studied with a classical push-out test and a variant that is the circular-bending test. Special care has been taken for controlling both the reactivity at the Ti/Al–7Si interface and the metallurgical health of the Al–7Si matrix. Mechanical tests until complete debonding have been completed with interrupted tests, metallographic characterizations and FEM analysis of elastic stress state. A mean shear strength of the interface of about 120 MPa was obtained. When the Ti insert is solely fretted in the matrix, without chemical interaction between Ti and the Al–7Si alloy, the mean shear strength is significantly lower (48 MPa). This result clearly shows that chemical interaction at the interface (formation of a thin TiSi layer at the Ti side and a thick Al3Ti(Si) layer at the Al–7Si alloy side) improves the mechanical properties of the assembly. It is also shown that the failure sequence is characterized both by crack propagation from bottom to top and matrix yielding from top to bottom. Actually, interface damaging begins by crack initiation at the specimen bottom face (not at the top face and under the indenter) in a nearly pure mode I solicitation at a radial tensile stress of about 100 MPa.

Design and Spin Test of a Hybrid Composite Flywheel Rotor with a Split Type Hub

A study is conducted on lowering the radial tensile stresses and increasing the performance of the fiber wound composite flywheel rotor by applying pressure on the inner surface of the rotor using a split type hub that spreads in the radial direction due to the centrifugal force. A conventional solid or ring type hub in most cases produces tensile stresses within the rotor, possibly causing delamination and eventually lowering the maximum speed of the rotor. The relationship between the stresses of the rotor and the thickness of the hub is derived and applied to the single and hybrid rotors. A hybrid composite rotor of 180 mm inner diameter and 340 mm outer diameter is designed and fabricated, which reaches only the strength ratio of 0.58 at the maximum rotating speed of 40,000 rpm. A spin test was conducted to show the improved performance of the rotor with the split type hub by measuring the mechanical strains from the rotor. The radial and circumferential strains at four different locations are measured up to 30,000 rpm using a wireless telemetry system, and they are in good agreement with the analytical calculations. The rotor has survived a spin test of up to 40,000 rpm, which corresponds to the usable energy of at least 500 W h with the safety factor of 1.7.

NUMERICAL INVESTIGATION ON CERAMIC COATINGS UNDER SPHERICAL INDENTATION WITH METALLIC INTERLAYER- PART I: UNCRACKED COATINGS

Radial stress distribution and plastic damage zones evolution in ceramic coating/metallic interlayer/ductile substrate systems under spherical indentation were investigated numerically by axisymmetric finite element analysis (FEA) for a typical ceramic coating deposited on carbon steel with various indenter radius-coating thickness ratios and interlayer thickness-coating thickness ratios. The results showed that the suitable metallic interlayer could improve resistance of ceramic coating systems through reducing the peak tensile radial stress on the surface and interface of ceramic coatings and plastic damage zone size in the substrate under spherical indentation.

Stress analysis of ceramic coatings under spherical indentation: Influence of a metallic interlayer

Spherical indentation problems of ceramic coatings/metallic interlayer/ductile substrate were investigated numerically by axisymmetric FEA for two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel. Various indenter radius-coating thickness ratios and interlayer thickness-coating thickness ratios were used in the modeling. Radial stress distributions were discussed in connection with model parameters. The results showed that the suitable metallic interlayer could improve resistance of ceramic coating systems through reducing the peak tensile radial stress on the surface and interface of ceramic coatings.

A numerical analysis of flexure induced cylindrical cracks during indentation of thin hard films on soft substrates

In this paper, the fracture behavior of a thin hard film, perfectly bonded to a soft substrate, containing circumferential (cylindrical) cracks subjected to spherical indentation is studied using the finite element method. These cracks emanate upwards from the film–substrate interface and are driven by the flexure of the film over the soft substrate under indentation. The film is taken to be linear elastic while the substrate obeys an elastic–plastic constitutive model with linear strain hardening. Three values for the substrate yield strength are considered in the analysis. The variation of energy release rate and mode mixity are examined as functions of crack length and load, for cracks located near and away from the indentation axis. The results show that, when the crack length is small, predominantly mode I conditions prevail due to tensile radial stresses near the interface. As the crack length increases, the mode mixity gradually changes from mode I to II. For cracks located near the axis, the crack growth process is stable over a range of crack lengths up to about a third of the film thickness and thereafter becomes unstable. The role of the substrate yield strength on the above issues is investigated.

C-Shape Specimen for Tensile Radial Strength of Thick, Filament-wound Rings

The objective of this investigation is to evaluate a new method of testing thick, C-shaped rings for determining the radial tensile strength of thick, filament-wound composite structures such as flywheel rotors. The proposed method of loading C-rings with a hydraulic jack is simpler than previously used loading methods and is shown to be quite tolerant of eccentricity of the jack. It is shown by sectioning a C-ring that residual stresses in the specimen are negligible. Based on a detailed stress analysis and post-failure inspections of appropriately dimensioned specimens, it is concluded that failure is caused by radial tensile stress at a single critical location in the specimen. The radial tensile strengths of four candidate flywheel rotor materials measured with C-rings were generally less than strengths measured with flexure specimens. The simplicity of specimen preparation and testing by the proposed method, in conjunction with promising early results, suggests that the C-ring test method is suitable for widespread use and possible standardization.

画像相関法による伝統的蟻継手のひずみ分布解析

In Japan, the shapes of traditional wooden joints are based upon carpenters′ experiences. However, in terms of strength, it is not revealed whether these shapes are optimum or not. For dovetail joints (ari-tsugi in Japanese), which have been frequently used in traditional timber constructions, an inclination of 1/6 is empirically and often used. In this paper, we conducted the tension tests with dovetail joint specimens of various inclinations and base widths, and examined whether empirical shape is optimum or not. Then strain distributions were calculated by digital image correlation (DIC). The results were as follows : (1) Joints with the inclination of 1/3 were 25∼35% stronger than that of 1/6, therefore empirical shape was not optimum. In comparison with the inclination, the effect of the base width to tensile strength was not significant. (2) Radial tensile strain concentrated on the corner of notches in the mortise side (female part of joint), where more than 2% of tensile strain was observed just before the fracture occurred. However, there was little difference between radial strain distributions whether inclination and base width were large or small. On the bottom of the mortise, approximately 0.7% of tensile strain observed in early wood just before the fracture occurred, but there was little strain in late wood. (3) On shear strain, concentration on the notch was remarkable with inclination increase. Consequently, the fracture of dovetail joints was caused due to the complex stress state, though the main factor of it can be radial tensile stress or strain.

Analysis of stresses during the freezing of solid spherical foods

An analytical model is presented to calculate thermal stresses and strains during the freezing of a spherical food, taking into account both the expansion during phase change and subsequent thermal contraction due to temperature decrease. The Young modulus and Poisson ratio are assumed to undergo a step change at the freezing point. The expansion due to phase change cause a uniform and virtually constant isotropic tensile stress in the unfrozen core. In the frozen shell, this expansion gives rise to tensile radial stress and compressive tangential stress. The thermal contraction subsequent to phase change causes reverse effects, i.e. uniform compressive stress in the unfrozen core and compressive radial stress in the frozen shell, while tangential stress is tensile on the outside and compressive on the inside of the frozen shell. The effect of thermal contraction is noticeable only at cryogenic temperatures.

Fracture Behavior of Brittle Coating Layer on Metal Substrate

The compressive fracture and spalling of multiply-cracked brittle coating layer on metal substrate under tensile stress was studied for the anodic-oxidized aluminum wire with the Al2O3 coating layer and galvannealed IF steel plate with the intermetallic compound coating layer consisting of ζ, δ1 and Γ1 and Γ phases. The thin Al2O3 coating layer on Al wire was fractured by buckling in the circumferential direction by the compressive hoop stress, but thick layer was debonded by the tensile radial stress at interface. The thickness of the coating layer at the transition from the compressive fracture to interfacial debonding was around 30 µm. In the galvannealed steel plate sample, the (ζ+δ1) phases were fractured by buckling in the width direction, resulting spalling of the (ζ+δ1) phases in the first stage, and the remained (δ1+Γ1+ Γ) phases or (Γ1+Γ) phase was again fractured by buckling, followed by the spalling of the remained phase.

Fracture and debonding behavior of coated brittle alumina layer on ductile aluminum substrate wire

The fracture and debonding behavior of the Al2O3 layer coated on a ductile aluminum substrate wire was studied experimentally and analytically. When tensile strain was applied, the brittle Al2O3 coating layer showed multiple cracking perpendicular to the tensile axis. After the multiple cracking, compressive fracture of the Al2O3 layer arose in the circumferential direction when the layer was thinner than around 30 μm, while interfacial debonding between the Al2O3 layer and aluminum substrate arose when it was thicker. Such a difference in behavior between thin and thick layers could be accounted for by the difference in the layer thickness-dependence of the tensile radial stress at the interface and the compressive hoop stress of the Al2O3 layer calculated by the finite element method; the former stress increases while the latter one decreases with increasing layer thickness.

A Boussinesq wedge analysis of the tensile stress region in a rail head beneath compressive and traction point loads

Investigations into the causes of damage to rail heads and on rolling contact fatigue, date back a considerable time and are described in a large number of expertise literature on the many different aspects of this complex problem. The present paper is prompted by the naïve observation that fatigue crack propagation is more likely to occur in a tensile stress environment than in a highly compressive one and it therefore seeks to locate a region of radial or longitudinal tensile stresses on a rail head during the rectilinear motion of the train, providing favourable conditions for mode I or mixed-mode crack propagation.

Some Aspects of Designing Multirim Composite Flywheels

Approximate solutions are given for stresses in a flexible cylindrical interlayer connecting concentric, rigid, cylindrical rims subjected to three loading cases: (i) rotation about the axis of symmetry; (ii) in-plane translation of the rims relative to each other; (iii) out-of-plane rotation of the rims relative to each other. The solutions are important for the multiple filament-wound composite rims used in energy storage flywheels, where the elastomeric interlayer idea has been proposed as a means of preventing high radial tensile stresses, which would otherwise break down the rims at less than optimal speeds. The compliances associated with the second and third loading cases are also given, establishing a simple means of analysis of the critical vibration frequencies of multirim flywheel rotors.

Modelling poroelastic hollow cylinder experiments with realistic boundary conditions

AbstractA general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time‐domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and Cleary, Rev. Geophys. Space Phys. 1976; 14:227; Schmitt, Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30:1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127:391).The new solution is used to model laboratory tests on thick‐walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3–5 1/s.It is found that solutions with idealized step‐function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for α and ν than are measured at long time.The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open‐hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts. Copyright © 2004 John Wiley & Sons, Ltd.

Analysis of residual stresses in a single fibre–matrix composite

Thermal stresses are induced in fibre/matrix composites due to the difference in coefficients of thermal expansion of the constituent materials. The present theoretical method is developed for the analysis of thermal stresses in fibres of finite length embedded in a matrix. Based on the complementary energy approach and minimization of the total complementary energy, the method yields closed-form solutions for the thermal residual stresses, which satisfy the requirements of a free surface around the fibre/matrix composite. The analysis shows that a radial-tensile stress concentration appears at both ends of the composite, subjecting the interface in the vicinity to tension. The interfacial shear stress peaks at some distance into the interface from the fibre ends. A parametric study further shows that thermal stresses are dependent upon the material and geometric properties of the constituents. Stress concentrations shift nearer to the ends of the composite with increase in fibre length while reduction in matrix radius will further accentuate the stress concentrations. A softer matrix tends to reduce the peak interfacial shear and radial-tensile stresses. A small mismatch in the coefficient of thermal expansion between fibre and matrix induces very low thermal stresses in the constituents. The stress concentrations, existing very close to the fibre ends tend to augment the fibre debonding stresses due to mechanical loading and will influence the analysis of interfacial properties in fibre pull- and push-out tests.