Strain Field Development of a Rectangular Dislocation Loop in a Semi-Infinite Medium with Verification

The strain and stress fields of a rectangular dislocation loop in an isotropic solid that is a semi-infinite medium (half medium) are developed here for a Volterra-type dislocation. Specifically, the loop is parallel to the free surface of the solid. The elastic fields of the dislocation loop are developed by integrating the displacement equation of infinitesimals dislocation loops over a finite rectangular loop area below the free surface. The strains and stress then follow from the small strain tensor and Hooke’s law for isotropic materials, respectively. In this paper, analytical verification and numerical verification for the elastic fields are both demonstrated. Equilibrium equations and strain compatibility equations are applied in the verification. Also, a comparison with a newly-developed numerical method for dislocations near a free surface is performed as well. The developed solution is a function of the loop depth beneath the surface and can be used as a fundamental solution to solve elasticity, plasticity or dislocation problems.

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

Instability of interstitial clusters under ion and electron irradiations in ceramic materials

Dynamic crack growth along elastic bimaterial interfaces have been studied extensively in the past decade by many researchers. In contrast, studies of dynamic interfacial fracture under elastic-plastic conditions are still very limited. In this presentation, the results of an analytic investigation of the asymptotic stress and deformation fields at the tip of a dynamically growing interface crack between a ductile material and a rigid substrate under plane stress conditions will be reported. The ductile material is taken to be ideally plastic and obey the J2 flow theory of plasticity. Under steady-state conditions, the asymptotic structure of the crack-tip stress, velocity and strain fields has been obtained. The study reveals that two types of crack-tip sectors exist, namely uniform and nonuniform plastic sectors and that the stress, strain and velocity fields are bounded in all sectors. In a uniform sector, the rectangular Cartesian components of the stress, strain and velocity fields are constant, and there is no plastic strain accumulation. In a nonuniform sector, the stress, strain and velocity components at a point depend on the angular position of the point in the crack-tip polar coordinate system and are governed by a system of simultaneous ordinary differential equations. This is a sector where plastic strains can accumulate. A general crack-tip sector assembly has been obtained for a practical range of crack growth speeds. Several nontrivial families of admissible solutions of the crack-tip fields based on this general assembly of uniform and nonuniform crack-tip sectors will be presented and discussed. Finally, comparisons with corresponding plane strain solutions (Deng, 1993 a) will be made.

Reinforced concrete buildings require special consideration under dynamic excitations due to their anisotropic material properties. Strain compatibility equations are used in concrete analysis and design with assumptions about the stress and strain field across member section and member length. However, these assumptions fall short of describing real life behavior when concrete elements deteriorate, age or undergo cyclic loading. This paper addresses the structural health of reinforced concrete buildings and proposes an analytical model to account for concrete damage through loss of bond. The proposed model relates steel loading that causes bond distress to design parameters such as development length and bar properties, and therefore could be complemented by field measurement. The paper proposes a diagnosis method and discusses the sustainability of the structure by assisting in a simplistic decision rule as to whether to perform minor fixes, major rehabilitation, or disposal. Emphasis is placed on the difference between reversible and irreversible effects of cyclic loading on structural behaviour, and draws a distinction between damage to the girder and damage to the column in the overall structural system. The model is compared to empirical results to address field challenges faced when the structure is subjected to severe conditions in its ambient environment, or to unusual loading. Deterioration in concrete causes alteration in its composite behavior with the reinforcing steel. This affects the fundamental period of the structure, and its response to seismic loading.

Evaluating stress and strain fields in anatomical structures is a way to test hypotheses that relate specific features of facial and skeletal morphology to mechanical loading. Engineering techniques such as finite element analysis are now commonly used to calculate stress and strain fields, but if we are to fully accept these methods we must be confident that the applied loading regimens are reasonable. Multibody dynamics analysis (MDA) is a relatively new three dimensional computer modeling technique that can be used to apply varying muscle forces to predict joint and bite forces during static and dynamic motions. The method ensures that equilibrium of the structure is maintained at all times, even for complex statically indeterminate problems, eliminating nonphysiological constraint conditions often seen with other approaches. This study describes the novel use of MDA to investigate the influence of different muscle representations on a macaque skull model (Macaca fascicularis), where muscle groups were represented by either a single, multiple, or wrapped muscle fibers. The impact of varying muscle representation on stress fields was assessed through additional finite element simulations. The MDA models highlighted that muscle forces varied with gape and that forces within individual muscle groups also varied; for example, the anterior strands of the superficial masseter were loaded to a greater extent than the posterior strands. The direction of the muscle force was altered when temporalis muscle wrapping was modeled, and was coupled with compressive contact forces applied to the frontal, parietal and temporal bones of the cranium during biting.

A non-axisymmetric cylinder with an oblique flange has broad application prospects. Spinning is the main production process for this kind of workpiece. Finite element modeling is a necessary method to study some key problems that are difficult to be solved merely through experiments, such as the strain and stress fields in the development of this spinning technology. In this study, the spinning process of a non-axisymmetric oblique flange cylindrical part was established and simulated using ABAQUS/explicit software. The credibility of the simulation result was validated through an experiment. The influence of the axial roller feed along the cylinder wall on the distribution of wall thickness and stress and strain during the forming process was analyzed. The change in stress field and strain field with time was analyzed, and the quantitative relationship between forming conditions and forming results was described. Furthermore, the forming principle of the flange was analyzed. It would be beneficial for flange forming to reduce the increasing distance of the cylinder wall in the 180° direction (parameter c) and the vertical distance from the closest point to the spindle as the roller returns back in the 180° direction (parameter d), to a certain extent. Hence, a workpiece with an ideal appearance was obtained. By comparing the wall thickness distribution, the design and optimization of the roller path were once again verified to be reasonable.

Screw dislocation equations in a thin film and surface effects

Strain fields at contacts between small particles

This study determines the influence law of the maximum eccentric uncoupling coefficient on the pressure field distribution at the hole wall through theoretical analysis to investigate the time-varying effect of the maximum eccentric uncoupling coefficient on the stress field of an eccentric charge structure. The findings from the theoretical analysis indicate that when the maximum eccentric uncoupling coefficient (K) is 1, the pressure at the ring hole wall exhibits a circular distribution. As K increases, the pressure distribution at the ring hole wall becomes elliptical, with the elliptical eccentricity increasing progressively. This research employs an ultra-high-speed digital imaging system to assess the impact of the maximum eccentric uncoupling coefficient on the attenuation pattern of the stress field within the elastic vibration region. The results demonstrate that the eccentric charge structure’s effect on the strain field is predominantly observed in its time and strength effects. This is evident in the strain field’s time delay on the non-eccentric side and the fact that the strain field’s strength on this side is weaker than on the eccentric side. In the elastic vibration region, the primary type of radial stress is compressive, whereas the circumferential stress is chiefly tensile. As the measurement point’s distance increases, the peak values of both radial compressive and circumferential tensile stresses diminish exponentially. Interestingly, the attenuation index of the radial stress is notably lower than that of the circumferential stress. The change in the K value has a minimal impact on the attenuation indices of both radial and circumferential stresses. At equal distances from the eccentric side, the peak values of both radial and circumferential stresses display a consistent pattern with K and a linear pattern at distances from the eccentric side and in symmetry. The stress field’s intensity and attenuation pattern on the eccentric side remain largely unaffected by variations in K. Conversely, the stress field attenuation on the non-eccentric side is significantly influenced by K value changes, as is the symmetric side.

A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.© (1987) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Stress fields and energies of interface curved dislocations

Critical thickness during three-dimensional epitaxial growth—A self-consistent approach

When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.

The pursuit of high-performance energy storage has led to significant research on the fundamental processes in lithium-ion batteries (LIBs), where lithium transport within active materials is crucial for their rate performance, capacity, and longevity. Traditionally, lithium diffusion in solid-solution materials has been assumed to follow Fick’s law, aiming to minimize concentration gradients, similar to behavior in liquids or gases. This led to the widespread belief that lithium diffusion creates a uniform lithium distribution within solid-solution particles. However, diffusion is not solely driven by concentration gradients but by chemical potential gradients, which consider thermodynamic factors such as strain/stress, mixing free energy, and interfacial energy.Active battery materials undergo anisotropic lattice volume changes during lithium insertion and extraction, generating strain and stress fields that affect diffusion. This suggests that lithium concentration gradients may not always align with chemical potential gradients, causing deviations from the expected diffusion direction, especially in single-crystalline solid-solution materials. If diffusion were only driven by concentration gradients, predictable patterns, such as core-shell or uniform distributions, would emerge during cycling based on the limiting regime.1 However, direct evidence showing dynamic lithium diffusion pathways deviating from conventional patterns or concentration gradients is still lacking, highlighting the need for deeper investigation into these processes.Using operando scanning transmission soft X-ray microscopy with high spatial resolution and chemical sensitivity to track nanoscale intraparticle lithium transport,2 and post-cycling Bragg coherent diffraction X-ray imaging to directly reveal three-dimensional intraparticle strain fields, we uncovered strain-associated lithium transport dynamics within single-crystalline LiNi1/3Mn1/3Co1/3O2 (scNMC) particles during cycling. Contrary to the expected thermodynamic solid-solution behavior of scNMC, our observations reveal near-uniform but fluctuating regions of lithium-dense and lithium-dilute areas during cycling. These fluctuations suggest that nanoscale lithium diffusion can proceed counter to concentration gradients, driven by local strain fields. Additionally, we demonstrate that an increased presence of lithium-dilute regions near the surface enhances lithium surface insertion kinetics, emphasizing the importance of controlling surface lithium distribution to improve rate performance. Our study provides novel insights into nanoscale solid-state ion transport, with potential applications in batteries, solid-state fuel cells, and memristors.References Xu et al. Joule 6, 2535-2546 (2022).Lim et al. Science 353, 566-572 (2016). Figure 1