Elastic Stress Field Research Articles

Stress relaxation aging of 7050 aluminum alloy under elastic and plastic loadings: A perspective from the geometrically necessary dislocations

Aerospace integral panels with large curvature often experience not only elastic loading but also plastic loading during creep age forming. However, the stress relaxation aging behaviors and mechanisms under loading stresses ranging from elastic to plastic regions, especially from the perspective of geometrically necessary dislocations (GNDs), have not been fully explored. The stress relaxation aging (SRA) behavior of 7050 aluminum alloy under elastic (200/250/300 MPa) and plastic loadings (350/400 MPa) are studied by uniaxial SRA, hardness and tensile tests, and corresponding mechanisms are clarified by Electron Back Scatter Diffraction (EBSD) tests and transmission electron microscopy (TEM) observations. Regardless of the loading stress, the stress relaxation of 7050 alloy shows a typical two-stage behavior (rapid stress reduction and stable stress relaxation rate). The second stage of stress relaxation under elastic loading shows an abnormal stress rebound, while the stress continuously decreases under plastic loading, and hardness and yield strength at 350 MPa are lower than that at 200 MPa during SRA. These results are attributed to strong dislocation pinning from small and dense precipitates at elastic loading and dislocations shearing large and sparse precipitates at plastic loading, respectively. Furthermore, both the stress reduction and its ratio increase with the increase of initial stress. GNDs contribute to the formation of low-angle grain boundaries (LAGBs) and accumulate at the LAGBs intersection to coordinate grain orientation for creep deformation. Compared to elastic loading, plastic loading promotes global growth of intragranular precipitates by elastic stress field and local heterogeneous nucleation and coarsening of precipitates at subgrain boundaries by more GNDs.

Using fractal voids to understand Mode I compressive fracture in brittle materials – A two-dimensional analysis

Unlike cases of direct or indirect tensile loading, analysis of Mode I fracture in cases of compressive loading must necessarily consider two-dimensional flaw geometries. The consequent analytical complications have resulted in little theoretical evolution towards understanding Mode I fracture in compressive loading. Researchers have recently observed that the linear elastic (LE) stress fields surrounding two-dimensional flaws in compression appear to have indicative value regarding Mode I fracture, but no rational framework has yet been proposed for their interpretation. Herein it is demonstrated that by idealizing void surfaces as fractal, and using what will be called the “small flaw assumption,” LE stress fields can be interpreted to obtain significant insight regarding brittle Mode I compressive fracture. Using fractal voids, a rational and consistent explanation for the satisfaction of the stress and energy criteria at the surface of two-dimensional flaws is presented. The discussion resolves many typical theoretical issues in the literature in a manner consistent with fundamental Griffith theory, and accounts for size and shape effects. The framework further enables the computationally efficient prediction of peak KI values associated with the propagation of line cracks from two-dimensional flaws from a brittle medium subject to macroscopic uniaxial compression via LE stress fields.

Superelasticity with narrow stress hysteresis and high cyclic stability in Co–V–Al polycrystalline alloy

Superelasticity of shape memory alloy associated with the martensitic transformation is extremely attractive for applications in sensors and biomedical. This application requires narrow stress hysteresis to reduce energy dissipation and a stable superelasticity cycle is an important factor in their practical applications. Co–V–Al alloys have inimitable advantages due to their narrow stress hysteresis, low-cost, and corrosion resistance, but the low number of superelasticity cycles restricts its development. Here, we report an intrinsic Co58V29Al13 polycrystalline alloy with a superelasticity stress hysteresis of 30 MPa at room temperature, the lowest among the alloys in this system, and a superelasticity strain of 3.6%. In addition, the sample shows no significant decay trend after 500 loading and unloading cycles. The high number of superelasticity cycles is mainly due to the elastic stress field generated around the dislocation during the cycle, which provides internal stress for martensite nucleation and reduces energy dissipation during martensitic transformation. This work provides essential guiding significance for the design of high-performance superelasticity alloys.

Interaction between dynamic recrystallization and phase transformation of Ti-43Al-4Nb-1Mo-0.2B alloy during hot deformation

The β solidified γ-TiAl alloy holds important application value in the aerospace industry, while its complex phase compositions and geometric structures pose challenges to its microstructure control during the thermal-mechanical process. The microstructure evolution of Ti-43Al-4Nb-1Mo-0.2B alloy at 1200 °C/0.01 s−1 was investigated to clarify the coupling role of dynamic recrystallization (DRX) and phase transformation. The results revealed that the rate of DRX in α2+γ lamellar colonies was comparatively slower than that in βo+γ mixed structure, instead being accompanied by intense lamellar kinking and rotation. The initiation and development rates of DRX in α2, βo, and γ phases decreased sequentially. The asynchronous DRX of the various geometric structures and phase compositions resulted in the uneven deformed microstructure, and the dynamic softening induced by lamellar kinking and rotation was replaced by strengthened DRX as strain increased. Additionally, the blocky α2 phase and the terminals of α2 lamellae were the preferential DRX sites owing to the abundant activated slip systems. The α2→βo transformation within lamellar colonies facilitated DRX and fragment of α2 lamellae, while the α2→γ transformation promoted the decomposition of α2 lamellae and DRX of γ lamellae. Moreover, the varied βo+γ mixed structures underwent complicated evolution: (1) The γ→βo transformation occurred at boundaries of lamellar colonies, followed by simultaneous DRX of γ lamellar terminals and neighboring βo phase; (2) DRX occurred earlier within the band-like βo phase, with the delayed DRX in enclosed γ phase; (3) DRX within the βo synapses and neighboring γ phase was accelerated owing to generation of elastic stress field; (4) Dispersed βo particles triggered particle stimulated nucleation (PSN) of γ phase. Eventually, atomic diffusion along crystal defects in βo and γ phases caused fracture of band-like βo phase and formation of massive βo particles, impeding grain boundary migration and hindering DRXed grain growth of γ phase.

ELECTRON IRRADIATED PI2610 POLYIMIDE FILMS ON MONOCRYSTALLINE SILICON

The optical and strength properties of electron-irradiated films of a polyimide composition (polyimide PI2610) deposited on the surface of single-crystalline silicon wafers of the KDB-10 grade by centrifugation were studied. Irradiation with electrons with an energy of 5 MeV was carried out on a linear accelerator U-003 in the dose range 1·1014 – 2·1015 cm–2. It has been experimentally established that at an irradiation dose of Ф = 1∙1014 cm–2, relaxation of elastic stress fields in the polyimide film is observed, which is expressed in modification of the shape of bands with maxima at 1349 and 1700 cm–1, caused by vibrations of the C–N–Cst bond and the C=O double bond imide ring. Polyimide PI-2610 films on silicon are quite stable when irradiated with electrons. A noticeable transformation of the ATR spectrum at a dose of 2∙1015 cm–2 was observed only in the region of stretching vibrations of C–H and O–H bonds, which is due to radiation-induced processes on by-products of polyimide synthesis and residual solvents. No noticeable decrease in the intensity of absorption bands caused by vibrations of the skeleton of the aromatic ring, imide ring, single and double C–C and C–O bonds, and imide C=O bonds was observed.

Influence of mechanical properties on material deformation behavior of different ceramics in scratching

To understand the differences in material removal behavior during grinding for different ceramics, scratching of Al2O3, AlN, Si3N4 and ZrO2 (3Y-TZP) ceramics by a cube-corner diamond indenter was investigated in this paper. Scratching characteristics, including material deformation, scratching force, coefficient of friction (COF) and scratching damage of different ceramics were compared and analyzed. Elastic recovery rate model and stress field model were built to analyze the mechanism of material deformation and scratching damage during scratching on different ceramics. The results demonstrated that material deformation behaviors vary significantly, and depend on mechanical properties of the ceramics. Ceramics with higher hardness exhibit shallower penetration depth of scratching, while higher fracture toughness results in shorter maximum surface damage distance. Elastic recovery rate model can predict the extent of material deformation. The ceramic with the highest elastic recovery rate is Al2O3, followed by Si3N4, ZrO2, and finally AlN. Elastic recovery rate decreases with increase in force. In stress field model, AlN exhibits the highest maximum principal stress, followed by Al2O3 and Si3N4, with ZrO2 displaying the lowest stress. These distribution patterns are consistent with the results of scratching damage pattern.

The effects of stress ultrasonic rolling on the surface integrity and fatigue properties of TiB2/7050 Al composite

In the present work, a new surface mechanical strengthening (SMS) technique named stress ultrasonic rolling (SUR), which is ultrasonic rolling (UR) assisted with a uniaxial tensile elastic stress field, was reported and successfully conducted on 5 % wt TiB2/7050Al composite. Based on the experimental analysis and numerical simulation, the effects of SUR on surface integrity and fatigue performance of the composite were comprehensively investigated. Compared with ordinary UR, SUR further enhanced the fatigue strength at 106 cycles of the composite by 5 % and prolonged the fatigue life of the composite under the stress level of 532.8 MPa by 1.8 to 3.3 times, which are attributed to the comprehensive effect of excellent surface finish, larger and deeper compressive residual stress (RSc) layer, dispersed TiB2 particles distribution in the surface, and superficial nanocrystalline structures. Besides, the assistance of uniaxial tensile elastic stress field did not increase the amount of surface plastic deformation, which indicates the RSc generated by SUR should have similar mechanical and thermal stability to that produced by ordinary UR treatment.

3D elasticity solutions for stress field around square hole in functionally graded plate

Since the square holes are widely used in many structures and machines, the purpose of this work is to obtain analytical solutions for the three-dimensional (3D) elastic stress field of transversely isotropic functionally graded (FG) infinite plates containing a single square hole with small round corners subjected to far-field loads or on the edges of the holes. Based on the generalized England-Spencer plate theory, material parameters can vary continuously and arbitrarily along the thickness direction of the plate, the solutions are obtained by using the conformal mapping technology combined with the Cauchy integral method. Concentration factors of internal forces Kij around the square hole are explicitly expressed. The obtained explicit expressions of solutions can be validated against the classical two-dimensional (2D) solutions when the material degenerates into an isotropic and homogeneous material. The detailed numerical examples are given to further investigate the influence of several parameters such as the material gradient factor and load conditions on the stress field around the hole. The present 3D analytical solutions can not only provide an in-depth understanding of the 3D stress field of FG plates with holes, but also be utilized as a benchmark to verify the numerical solutions of the same problems.

Prediction of Subsurface Microcrack Damage Depth Based on Surface Roughness in Diamond Wire Sawing of Monocrystalline Silicon.

In diamond wire saw cutting monocrystalline silicon (mono-Si), the material brittleness removal can cause microcrack damage in the subsurface of the as-sawn silicon wafer, which has a significant impact on the mechanical properties and subsequent processing steps of the wafers. In order to quickly and non-destructively obtain the subsurface microcrack damage depth (SSD) of as-sawn silicon wafers, this paper conducted research on the SSD prediction model for diamond wire saw cutting of mono-Si, and established the relationship between the SSD and the as-sawn surface roughness value (SR) by comprehensively considering the effect of tangential force and the influence of the elastic stress field and residual stress field below the abrasive on the propagation of median cracks. Furthermore, the theoretical relationship model between SR and SSD has been improved by adding a coefficient considering the influence of material ductile regime removal on SR values based on experiments sawing mono-Si along the (111) crystal plane, making the theoretical prediction value of SSD more accurate. The research results indicate that a decrease in wire speed and an increase in feed speed result in an increase in SR and SSD in silicon wafers. There is a non-linear increasing relationship between silicon wafer SSD and SR, with SSD = 21.179 Ra4/3. The larger the SR, the deeper the SSD, and the smaller the relative error of SSD between the theoretical predicted and experimental measurements. The research results provide a theoretical and experimental basis for predicting silicon wafer SSD in diamond wire sawing and optimizing the process.

Evaluation of disclination Frank vector in ridge kink microstructure

ABSTRACT This study conducts dislocation-based modelling and numerical analysis to clarify the presence of disclinations within kinked deformation microstructures using the framework of differential geometry. Although the existence of disclinations has long been postulated, a mathematical foundation for this phenomenon still needs to be provided. In this study, we develop kink deformation models using planar arrays of edge dislocations. The dislocation density is represented using a level-set function, and the governing equations are solved numerically through the finite element method. We then introduce the holonomy method to demonstrate the presence of disclinations by quantitatively measuring the Frank vector. At first, we validate the accuracy of the method by comparing it with the theoretical predictions provided by the grain boundary theory. Subsequently, we performed qualitative validation of the model by comparing the macroscopic deformation observed in experiments. Finally, we evaluate the Frank vector within the ridge kink model, providing quantitative evidence for the presence of disclinations in the kinked deformation microstructure. We also illustrate the distribution of elastic stress fields generated by disclinations at the termination point of the kink interface.

On the features of inhomogeneous residual stress identification using the digital speckle interferometry and the hole-drilling method

A phenomenological approach to the actual problem of determining the inhomogeneous residual stress-strain state in the components of high-tech engineering systems at the stages of their design and operation is presented. The approach is based on physical and mechanical methods of measuring displacements. Current physical models describe the physical regularities of the residual states attributed to changes in the structure by the interaction of defects and dislocations in the field of micro- and meso-stresses. At the same time, there are the problems of the transition to the macrolevel, the construction of multilevel models, and the conversion of these models in engineering practice. In the framework of phenomenological approaches, in the general case, the solution of this problem requires the solution of three-dimensional inverse problems of thermoelasticity. A well-known mechanical method for determining a uniform field of residual elastic stresses recommended by ASTM E837 is described. The method proposed earlier by one of the authors for determining an inhomogeneous (in the plane) field of residual elastic stresses is discussed. A method of the three-dimensional inhomogeneous residual elastic stress-strain state determination based on the experimental determination of the displacement vector components by the method of step-by-step point hole-drilling and data of digital speckle interferometry and digital image correlation is developed. The constitutive relations for the components of the displacement vector are written in the form of Volterra integral operators. The basic operator functions are the functions of four variables, i.e., the coordinates of the cylindrical system (r, θ, z) associated with the hole, and the hole depth h. A method for verification of the basic functions is presented. The problem is reduced to the determination of three displacement functions of three variables: hole radius r, h, and z. Numerical simulation of basic functions is carried out. The obtained results are consistent with the known experimental data and calculated values of the deformation on the surface depending on the depth of the hole according to the ASTM E837 Standard.

The Porothermoelastic Stress Evolution of Inhomogeneous Solid due to Near-Surface Reservoir

Anisotropic and heterogeneous solids, comprising a minimum of two or more elements with different properties, appear pervasively in rock materials including the pore structure and mineral composition of quartz and granite and usually have extensive applications in construction aggregates, dimension stone, geotechnical engineering, and petrology/geology. The elastic stress fields of inhomogeneous materials or composites inevitably change due to the presence of heterogeneous microstructure under applied external conditions, and hence the total mechanical and physical properties are affected by the temperature and pore pressure fluctuations beneath the surface. In this paper, the thermoporoelastic (TPE) approach on the basis of eigenstrain concept is introduced to predict the stress fields in fluid-saturated porous geologic materials like hydrocarbon reservoirs or aquifers by accounting for the coupling between thermal, poroelastic, and mechanical effects. It is an extension of the micromechanical theory that also incorporates thermal effects like pore pressure changes and temperature alternations. In addition, the TPE approach provides an important multiphysical modeling tool for understanding subsurface fluid-rock interactions and stress states in applications like unconventional oil/gas and geothermal energy.

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

Cylindrically bent diamond single-crystal plates have a great potential for creating energy dispersive spectrometers and focusing crystal monochromators. When they are designed, it is necessary to take into account the significant stresses that appear on bending the plates. The strain tensor and the elastic stress fields in a cylindrically bent single-crystal (110) diamond plate are calculated. The calculations are based on experimental data obtained by local Laue diffraction. The calculation results can be used to design new X-ray optical devices with the ability to control their parameters.

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

Scratch-induced surface formation mechanism in C/SiC composites

Due to the extremely complex composition of C/SiC composites, their material removal mechanisms are significantly different from those of conventional single-phase ceramic materials. Therefore, the grinding removal mechanism of C/SiC composites must be investigated so that the components based on these composites can be machined efficiently and with low damage. In this paper, nano-scratch experiments with various cutting depths are carried out along different fiber orientations to simulate the material removal process in grinding and theoretically clarify the damage failure mechanism based on different cutting thicknesses. According to the assessment of surface and subsurface morphology of the various constituents in the scratch grooves regarding different fiber orientations, the multiple brittle breakage modes and surface integrity of carbon fiber are revealed. Green’s function is applied to establish a half-space anisotropic analytic elastic stress field considering the microstructural characteristics of material, and the crack nucleation and propagation principles during micro brittle fracture regime for nano-scratch experiment are elucidated based on the fracture mechanics and the maximum principal stress criterion. The formation mechanism of machined surface morphology in macro brittle removal process is investigated under the crack deflection effect at the weak interface and based on the elastic foundation beam theory. The related findings can provide a reasonable reference framework for optimizing the grinding technology, material and tool design regarding C/SiC composites.

Effect of the shape and size of interfacial micro-cavities on the adhesion of elastic solids

Microstructuring surfaces may strongly affect the adhesive behaviour at the contact interface, resulting in enhanced or weakened adhesion depending on the geometry of the surface structures and material properties. In this study we investigate the effects of size, shape and geometrical distribution of micro-cavities on the adhesion between an elastic solid and a rigid substrate. We show that reducing the lattice size by keeping constant the cavity size, may significantly weak the adhesion strength of the interface as a consequence of the interaction of the elastic stress and deformation fields generated by each single microcavity.

Second Harmonic Generation Studies of Interfacial Strain Engineering in BaZr0.2Ti0.8O3

AbstractFilm ferroelectrics demonstrate large breakdown strength, high energy density, and many unique phenomena not found in bulk materials. In this investigation, a rhombohedral BaZr0.2Ti0.8O3 (BZT) solid solution and various film‐substrate misfit strains are utilized to optimize the energy storage performance of ferroelectric thick films. Optical second harmonic generation is applied in both reflection and transmission geometries to reveal the renovation of entangled rhombohedral and tetragonal phases in the BZT films under compressive misfit strains. It is shown that the interfacial strain between the BZT film and substrate introduces the tetragonal domains. The competition between the tetragonal and rhombohedral phases creates the self‐assembled, anisotropically strained morphotropic structures to effectively accommodate the elastic and electrical stress fields through inside the thick BZT film. The BZT films demonstrate exceptional energy storage performance because of the adaptable nano‐domain structure within the bulk of the BZT films and may be engineered to optimize the superior performance of BZT films in energy storage.

An analytical approach for evaluation of linear elastic stress fields around sharp V-shaped notches in plates

In the context of the theory of elasticity, the stress state at a sharp notch is singular, and the degree of stress singularity depends on the notch opening angle. Most existing analytical approaches for evaluating asymptotic linear elastic stress fields ahead of V-notches rely on notch stress intensity factors (N-SIFs). This paper presents an alternative analytical approach for evaluating notch stress fields by taking advantage of traction-based structural stress and Williams’ eigenfunction methods. To better represent notch stress fields, the first order and higher order terms of eigenfunction are included in the present study. The analytical solutions are then compared to the stress fields resulting from finite element analysis for validation purposes. The stress contours evaluated by the analytical approach are nearly identical to the numerical results corresponding to three distinguishing notch opening angles under pure Mode I loading, which signifies the effectiveness and robustness of the analytical solution methodology developed in the present study. Subsequently, the approach is extended to accommodate Mode II loading by introducing a skew-symmetric term in the stress function. The generalized method is then applied on a welded cruciform joint, which precisely captures the notch fields compared to FEA results.

Theoretical model for the effect of porosity on correlations of point load tests of rocks

Point load test (PLT) is one of the most adopted indirect ways to estimate uniaxial compressive strength of rocks. Yet, the estimation can be interfered by rock porosity that has rarely been considered in model development. In this study, a theoretical model for the interpretation of results of PLTs considering the effect of porosity is proposed. The model was developed using the elastic stress field inside diametrically loaded sphere within the framework of linear elastic fracture mechanics and requires only basic physical parameters including porosity and Poisson's ratio. Apart from the point load index (PLI), an extra parameter, subtended angle, is included in the interpretation, which accounts partly for the wide range of the ratio between PLI and uniaxial compressive strength observed in experiments. The predictions of the proposed model compare reasonably well with data for a variety of rocks, which demonstrates the validity of the model.

Investigation of Plasticity Effects on Growing Fatigue Cracks Using the CJP Model of Crack Tip Fields.

A growing fatigue crack gives rise to a plastic enclave that envelops the crack and can exert a shielding effect on the crack from the global elastic stress field driving fatigue propagation. This work presents the potential of the CJP model of crack tip fields to investigate the plasticity-induced shielding effects on growing fatigue cracks as well as its ability to characterise the size and shape of the plastic zone generated at the tip of a growing fatigue crack. The model was specifically developed to consider the influence of the plastic enclave generated around a fatigue crack on the surrounding elastic material. Different aspects related to fracture mechanics and its implications for fatigue crack growth have been investigated, namely plasticity-induced crack shielding, the retardation effect induced on fatigue crack growth due to the application of an overload and the estimate of the size and shape of the crack tip plastic zone. The model has been successfully applied by analysing displacement fields experimentally measured by DIC in different CT specimens made of 2024-T3 aluminium alloy and commercially pure titanium. Results presented in this work intend to contribute to a better understanding of the shielding effects during fatigue crack growth.