Non-piezoactivity in piezoacoustics: basic properties and topological features

The existence conditions of zero electric fields E and zero electric displacements D are studied for bulk acoustic waves in piezoelectric crystals. General equations are derived for lines of zero electric fields, E(m)=0, and for specific points m ₀ of vanishing electric displacements, D(m ₀)=0, on the unit sphere of propagation directions m ²=1. The obtained equations are solved for a series of examples of particular crystal symmetry. It is shown that the vectors D _α (m) being generally orthogonal to the wave normal m are characterized by definite orientational singularities in the vicinity of m ₀ and can be described by the Poincaré indices n=0, ±1 or ±2. The algebraic expressions for the indices n are found both for unrestricted anisotropy and for a series of particular cases.     

Dislocation emission from nanovoid with the effect of neighboring nanovoids and surface stresses

In the light of the vital mechanism for nanovoid evolution depending strongly on the effect of neighboring nanovoids, a generalized self-consistent model is suggested to describe nanovoid growth by the dislocation emission from nanovoid surface accounting for the effect of neighboring nanovoids and surface stresses in ductile porous materials. The explicit solution of the critical stress for dislocation emission is derived by means of the complex variable method. Analysis shows the advanced model can be implemented as the effective means to address the strong dependence of the nanovoid growth by the dislocation emission upon the size and volume fraction of nanovoid, growth/shrinkage of the neighboring nanovoid, remote applied stress as well as the surface effect.     

Local stresses and strains in axially cracked cylindrical shells

A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where . The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging.     

Experimental means of analyzing stresses and strains in rocket propellant grains

This paper reviews several methods used by the author in the stress analysis of rocket propellantgrain models with different boundary conditions, subjected to different loading conditions. The objective of the analysis is to help the designer to develop a stress-wise better grain configuration. Some assumptions have to be introduced to attain this goal in a practical way since some propellants behave nonlinearly, nonelastically, and are heterogeneous and anisotropic. Several indices are presented to evaluate designs. The method used by the author to “optimize” designs is also presented.     

Determination of elastic-plastic stresses and strains from measured surface strain data

A rigorous approach founded in the fundamental principles of plasticity is used to develop an accurate numerical algorithm for the determination of stresses and elastic and plastic strains from total strain data measured on a structure surface. The approach used to develop the algorithm and its relationship to both the flow theory of plasticity and recent advances in tangent stiffness-based numerical solution procedures for elastic-plastic boundary value problems are presented. Verification of the method for plane stress problems is demonstrated. A discussion of how the method can be used with measured surface displacement data is proved.     

Evaluation of residual stresses and strains using the Eigenstrain Reconstruction Method

The study of residual stress has long been an important research field in science and engineering, due to the fact that uncontrolled residual stresses are detrimental to the performance of products. Numerous research contributions have been devoted to the quantification of residual stress states for the purpose of designing engineering components and predicting their lifetime and failure in service. For the purposes of the present study these can be broadly classified into two main approaches, namely, the interpretation of experimental measurements and process modelling. In this paper, a novel approach to residual stress analysis is developed, called here the Eigenstrain Reconstruction Method (ERM). This is a semi-empirical approach that combines experimental characterisation, specifically, residual elastic strain measurement by diffraction, with subsequent analysis and interpretation based on the eigenstrain theory. Three essential components of the ERM, i.e. the residual strain measurement, the solution of the inverse problem of eigenstrain theory, and the Simple Triangle (SIMTRI) method, are described. The ERM allows an approximate reconstruction of the complete residual strain and stress state in the entire engineering component. This is a significant improvement compared to the experimentally obtained limited knowledge of stress components at a selected number of measurement points, or to the simple interpolation between these points.     

Crack-tip stresses as computed from strains determined by stereoimaging

Measurements of the three in-plane elements of the strain tensor near a crack tip have been combined with the material constitutive behavior to compute the three inplane elements of the stress tensor and the mean stress. The method is illustrated with fatigue-crack plasticity results for 7075-T651 aluminum alloy.     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Bounds on stresses caused in structures by bounded anelastic strains

Summary Bounds are obtained on the stresses that can develop at an arbitrary section of a structure (such as a continuous beam, or a rigid frame) by anelastic strains of unknown distribution but bounded magnitudes. Examples of a continuous beam with two equal spans, and a portal frame are worked out in detail to illustrate the procedure.

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Übersicht Es werden Grenzen für die Spannungen ausgerechnet, die in beliebigen Querschnitten eines Tragwerkes (z. B. in einem durchlaufenden Balken oder in einem Fachwerk) entstehen können, wenn nichtelastische Dehnungen begrenzter Größe aber unbekannter Verteilung auftreten. Als Beispiele werden ein durchlaufender Balken mit zwei Feldern sowie ein Fundamentrahmen durchgerechnet, um die Einzelheiten des Berechnungsganges zu zeigen.

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This research was supported by the Advanced Research Projects Agency (Project DEFENDER) and was monitored by the U.S.Army Research Office-Durham under Contract DA.31-124-ARO-D.257.     

An experimental determination of the fields of strains and stresses in the elastoplastic range

In order to determine the fields of strains and stresses in the elastic and plastic ranges, for the plane-stress problem, a so-called chromorheological (CHR) model has been utilized. On one side of the model the development of plastic deformations, including the elastoplastic boundaries at any stage of loading, can be either visually observed or recorded on film. On the other side of the model, a birefringent coating is adhered from which regular experimental data can be obtained. These data, together with the yield condition, render the possibility of finding the state of stresses at all the points of the known elastoplastic boundaries. The problem of stress in the plastic range is statically determinate. The experiment provides all the data on the boundaries, and thereby the field of stresses in the plastic range can be calculated. The field of strains in the elastic and plastic zones can be obtained by the well-known method of photoelasticity. In this way, the relationship between stresses and strains in the plastic zones can be worked out. The effectiveness of the approach on a strip with a central hole has been proven by experimental research.     

Direct Strain Oscillation: a new oscillatory method enabling measurements at very small shear stresses and strains

As shown previously, a rotational rheometer equipped with an electronically commutated motor (EC-motor) allows one to conduct stress and strain experiments with the same rheometer in rotational mode. A new method has now been developed to improve further strain controlled oscillatory measurements by adjusting the strain directly within a single oscillation cycle. Generally, a strain controlled oscillatory test in a stress controlled rheometer consists of the following steps: applying one full oscillation cycle with an arbitrary stress amplitude, measuring the strain amplitude, adjusting the stress in the next oscillation cycle, and repeating this routine until the desired strain amplitude is reached. The newly developed direct strain oscillation mode employs a different approach. It does not require a full oscillation cycle but uses a real-time position control and adjusts to the desired strain directly on the sine wave. Therefore, the actual movement of the measuring system follows directly the required change in strain during each individual oscillation cycle. This new oscillatory mode has several major advantages: (1) the possibility of conducting real strain controlled tests in oscillation, (2) the exact strain setting right from the first oscillation cycle, i.e., no or only very slight overshoot in strain, (3) faster data acquisition even within an oscillation cycle, (4) it allows the measurement at extremely low angular resolution and low torques. Due to the absence of strain overshoots and the ability of testing at small deflection angles and low torques this new method is especially helpful for measurements on samples with low viscosities and weak structures such as gels, emulsions, suspensions, colloids, and foams.     

A crystal plasticity model that incorporates stresses and strains due to slip gradients

This work is concerned with incorporating the kinematic and stress effects of excess dislocations in a constitutive model for the elastoplastic behavior of crystalline materials. The foundation of the model is a three term multiplicative decomposition of the deformation gradient in which the two classical terms of plastic and elastic deformation are included along with an additional term for long range strain due to the collective effects of excess dislocations. The long range strain is obtained from an assumed density of Volterra edge dislocations and is directly related to gradients in slip. A new material parameter emerges which is the size the region about a continuum point that contributes to long range strains.Using Hookean elasticity, the stress at a point is linearly related to the sum of the elastic plus the long range strain fields. However, the driving force for slip is postulated to be due only to the elastic stress so that the long range stress is a back stress in the constitutive relationship for plastic deformation. A consistent balance of the total deformation rate with the three proposed mechanisms of deformation leads to a set of differential equations that can be solved for the elastic stress, rotation and pressure which then implicitly defines the material state and equilibrium stress. Results from the simulation of a tapered tensile specimen demonstrate that the constitutive model exhibits isotropic and kinematic type hardening effects as well as changes in the pattern of plastic deformation and necking when compared to a material without slip gradient effects.