Extending the stress-analysis range of brittle coatings

In this paper, an attempt is made to extend in both directions the range of the stresses that can be determined using brittle coatings: (1) by sensitizing the coating to determine small stresses, and (2) by the use of a new calibration device that allows the application of very large strains. The increase in sensitivity is obtained by bathing the coating with cold water under load. The coating used in this manner is shown to have a strain sensitivity as low as 100 μin./in., well below the 400 μin./in. limit imposed by crazing of the coating as it is normally used. The fixture to apply large strains is described and the method applied to several brittle coatings to calibrate them up to 10,000 μin./in. (1 percent) strain sensitivity. In conjunction with the above studies, a short test was conducted on the effects of repetitive loading on a brittle coating. Load history was shown to affect strain sensitivity in some cases.     

Surface pressure field mapping using luminescent coatings

In recent experiments we demonstrated the feasibility of using the oxygen dependence of luminescent molecules for surface pressure measurement in aerodynamic testing. This technique is based on the observation that for many luminescent molecules the light emitted increases as the oxygen partial pressure, and thus the air pressure, the molecules see decreases. In practice the surface to be observed is coated with an oxygen permeable polymer containing a luminescent molecule and illuminated with ultraviolet radiation. The airflow induced surface pressure field is seen as a luminescence intensity distribution which can be measured using quantitative video techniques. Computer processing converts the video data into a map of the surface pressure field. The experiments consisted of evaluating a trial luminescent coating in measuring the static surface pressure field over a two-dimensional NACA-0012 section model airfoil for Mach numbers ranging from 0.3 and 0.66. Comparison of the luminescent coating derived pressures were made to those obtained from conventional pressure taps. The method along with the experiment and its results will be described.     

Measurements of thermally induced stress waves in a thin rod using birefringent coatings

When an elastic body is heated rapidly, significant inertial stresses are developed if the imposed heating rates cause a substantial temperature change in times which are short relative to the mechanical response time of the body. This work describes a method for inducing and measuring the thermally induced elastic stress waves in an unrestrained thin rod. Rapid heating was accomplished electrically by discharging a low-inductance capacitor bank (0.1 μH, 2800 J) through the rod. Utilizing the frozen-stress technique, an initial fringe pattern was introduced into thin strips of a birefringent material securely bonded to each side of the rod. The longitudinal strain oscillations were measured by direct observation of the movement of the fringe patterns with a high-speed framing camera. Interpretation of these measurements required a dynamic calibration and application of a dynamic correction factor for the reinforcing effect of the coating. Oscillations with periods from 35 to 250 μsec and stress amplitudes up to 900 psi were measured and compared with the uncoupled thermoelastic theory. Good agreement was obtained, and it was concluded that this technique is suitable for transient measurements in the presence of large magnetic fields which normally restrict the use of electronic methods.     

Lueders' lines detection by means of brittle coatings

The objective of this paper is to compare some of the techniques used to detect Lueders' lines and present the results of a more extensive study using the brittle-coating method. A hot-rolled steel tensile specimen was yielded plastically under successively higher amounts of load and the resulting Lueders' lines were recored using oblique-incident light, etching, photoelastic coatings and brittle coatings. When the results from the various methods were compared, the authors found some advantages in the use of brittle coatings. This method was then used to record the Lueder's lines in beams under pure bending and simple bending, and in plates with notches and holes.     

Crack stabilization in a brittle body using stiffeners

The behavior of a crack under uniaxial tension in the presence of reinforcement is studied. The reinforcing members (riveted stiffeners) are modeled by point loads. Only four members nearest to the crack are taken into account. It is shown that stiffeners allow one to arrest a crack and prevent its catastrophic growth. Relations between the geometrical and force characteristics for which the crack is stabilized are obtained. The stabilization mechanism is discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 137–143, November–December, 2006.     

Continuum interpolation of stress fields in brittle fracture

The locally nonlinear behavior of crack stresses is first represented by adjustable boundary conditions near the crack tip. The actual boundary conditions are then determined by continuity conditions imposed on a general parameterized solution. The thus modified formulation yields finite crack tip stresses consistent with atomistic and other hybrid models of brittle fracture.     

On the stress tensor in nematic liquid crystals

Summary This paper presents an analysis on the stress tensor in non-heat conducting nematic liquid crystals. Essentially it is shown that the Lee-Eringen theory possesses two inconsistent versions for the stress tensor. The first version appears to be incapable of describing the flow problems of nematic liquid crystals and the second version is shown to be similar to the stress tensor as proposed in the Ericksen-Leslie theory.

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Zusammenfassung Diese Arbeit beinhaltet eine Untersuchung des Spannungstensors in nicht-wärmeleitenden nematischen flüssigen Kristallen. Es wird vor allem gezeigt, daß die Theorie vonLee undEringen zwei nicht miteinander verträgliche Darstellungen des Spannungstensors enthält. Die erste scheint nicht imstande zu sein, die Strömungsverhältnisse bei nematischen flüssigen Kristallen richtig zu beschreiben. Von der zweiten wird dagegen gezeigt, daß sie einen ähnlichen Ausdruck für den Spannungstensor liefert wie die Theorie vonEricksen undLeslie.

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Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations, the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1] to characterize discontinuous cracks in brittle materials. This method can well describe the crack initiation and propagation without assuming the shape, size and orientation of the initial crack in advance. In this paper, a phase field method based on Miehe's approach [Miehe et al., Comp. Meth. App.Mech. Eng.(2010)] is applied to simulate different crack propagation problems in twodimensional(2 D), isotropic and linear elastic materials. The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM). The validity, accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature. Several numerical examples are presented to show the effects of the loading type(tension and shear), boundary conditions, and initial crack location and orientation on the crack propagation path and force-displacement curve. Furthermore, for a single edge-cracked bi-material specimen, the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed. It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials, and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.     

Blind-hole residual stress determination using optical interferometry

The in-plane method and the out-of-plane method are used to analyze blind-hole residual stress as measured by optical interferometry. The in-plane method, which constructs a relation between the in-plane displacement field and the residual stress released from blind-hole drilling, is applicable when the sensitivity vector of the interferometer used in the measuring system is parallel to the object surface. Three in-plane displacements obtained from one interference pattern are sufficient to determine the residual stress. The out-of-plane method, which establishes a new relation between the out-of-plane displacement field and the released residual stress, is suggested when the sensitivity vector is perpendicular to the object surface. Two relative out-of-plane displacements extracted from one interference pattern are sufficient to determine the residual stress. With the adoption of these two methods, interpolating calculation is not needed to determine the fringe order of each data point, since the selections of the required data points are flexible using these two methods. Two experiments, one for the in-plane method and the other for the out-of-plane method, were carried out to illustrate the applicability and usefulness of these two methods.     

Phase field modeling of fracture in anisotropic brittle solids

A phase field model of fracture that accounts for anisotropic material behavior at small and large deformations is outlined within this work. Most existing fracture phase field models assume crack evolution within isotropic solids, which is not a meaningful assumption for many natural as well as engineered materials that exhibit orientation-dependent behavior. The incorporation of anisotropy into fracture phase field models is for example necessary to properly describe the typical sawtooth crack patterns in strongly anisotropic materials. In the present contribution, anisotropy is incorporated in fracture phase field models in several ways: (i) Within a pure geometrical approach, the crack surface density function is adopted by a rigorous application of the theory of tensor invariants leading to the definition of structural tensors of second and fourth order. In this work we employ structural tensors to describe transverse isotropy, orthotropy and cubic anisotropy. Latter makes the incorporation of second gradients of the crack phase field necessary, which is treated within the finite element context by a nonconforming Morley triangle. Practically, such a geometric approach manifests itself in the definition of anisotropic effective fracture length scales. (ii) By use of structural tensors, energetic and stress-like failure criteria are modified to account for inherent anisotropies. These failure criteria influence the crack driving force, which enters the crack phase field evolution equation and allows to set up a modular structure. We demonstrate the performance of the proposed anisotropic fracture phase field model by means of representative numerical examples at small and large deformations.     

The determination of elastic parameters of a half-space using a monochromatic vibration field at the surface

The paper presents a method to determine Lamé parameters λ, μ and density ϱ in a layered half-space, using monochromatic vibrations of its surface, excited by a harmonic source which is assumed to be known. The equations governing the vibrations are reduced to the Sturm-Liouville problem in scalar form for Love-type displacements, and in matrix form for the Rayleigh type. The scalar and matrix potentials of the Sturm-Liouville equations can be recovered from the corresponding impedance. Explicit formulas are given to construct the potentials by amplitudes and wavenumbers of normal (progressive) modes and attenuated standing waves. The potentials then are used to determine the elastic parameters and the density. The method can also be used for the acoustic equation.     

On the definition of the stress tensor in granular media

This paper investigates the definition of the stress tensor within a granular assembly, when inertial effects are likely to occur. It is shown that the stress tensor can be expressed as a sum of two terms. A first term corresponds to the standard definition of the stress, according to the Love–Weber formula; this term is related to the contact forces existing within adjoining particles. A second term accounts for dynamic effects related to rotation velocities and accelerations of the particles. These results are checked from discrete numerical simulations in order to examine in which context the contribution of inertial effects should not be omitted. With this aim, the simulation of a granular specimen collapse and then a silo discharge is considered.     

Force flux and the peridynamic stress tensor

The peridynamic model is a framework for continuum mechanics based on the idea that pairs of particles exert forces on each other across a finite distance. The equation of motion in the peridynamic model is an integro-differential equation. In this paper, a notion of a peridynamic stress tensor derived from nonlocal interactions is defined. At any point in the body, this stress tensor is obtained from the forces within peridynamic bonds that geometrically go through the point. The peridynamic equation of motion can be expressed in terms of this stress tensor, and the result is formally identical to the Cauchy equation of motion in the classical model, even though the classical model is a local theory. We also establish that this stress tensor field is unique in a certain function space compatible with finite element approximations.     

A prediction of the pressure field in a plane turbulent jet using an algebraic stress model

A numerical prediction is obtained for the mean pressure field in the similarity region of a plane turbulent jet. An algebraic stress model, which introduces non-isotropic relations for the Reynolds stress components, is used to close the mean momentum equation. The full two-dimensional form of the transport equations is retained and the resultant equation set solved elliptically. The numerical prediction simulates many of the characteristics of the pressure field measured by experimental studies. However, the overall level of the predicted field is lower than the experimental values. The level obtained for the mean pressure field depends strongly on the prediction for the transverse normal Reynolds stress component 〈u₂u₂〉. The pressure field is shown to represent a small negative contribution to the net strearnwise momentum balance.     

Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called ‘fracture-mode map’, whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.