Internal Stress Field Research Articles

Numerical Investigation of the Role of Volumetric Transformation Strain on the Relaxation Stress and the Corresponding Hydrogen Interstitial Concentration in Niobium Matrix

The effects of relaxation stress on the hydrogen concentration in Niobium- (Nb-) H media were investigated by iterative numerical modeling approach. To calculate the transformation strain, relaxation stress, and corresponding relaxed hydrogen concentration around an edge dislocation, a new third-order polynomial formulation was utilized in the model. With the aid of this polynomial, hydrogen induced relaxation stress never exceeds the dislocation stress, which indicates that the total stress field never turns to compressive state and diverges the results. The current model calculates the hydrogen concentration not only in the vicinity of an edge dislocation but also far away from the dislocation. Furthermore, the effect of relaxation stress on the interaction energy was also captured in the model. Overall, the current findings shed light on the complicated hydrogen embrittlement mechanisms of metallic materials by demonstrating that hydrogen induced relaxation has a significant effect on the hydrogen atom concentration and the interaction energy between the existing internal stress field and the solute hydrogen atom.

Two-way shape memory effect in [001]B2-oriented Co-Ni-Al single crystals

In the present study, the necessary conditions for the two-way shape memory effect (TWSME) and its stress-free thermal cycling stability in the Co35Ni35Al30 single crystals, oriented along the [001]B2 direction, were investigated. The TWSME is attributed to the internal stress fields created through the generation of stable dislocation structures and retained martensite in two ways. First, the training involved 100 loading/unloading cycles at room temperature T=295 К with the maximum given strain of 6.0% in compression. Second, the ageing at T=423К for 1.0 h under a stress of 500 MPa was applied to the martensitic state along the [001]B2||[110]L10 direction. It was experimentally shown that the aged crystals demonstrated the best properties of the TWSME response when compared with the trained crystals: i.e., a higher operating temperature range (250-297K), the high cyclic stability of the reversible strain εTWSME=(3.1±0.3)% during thermal cycles and the low value of the temperature hysteresis (ΔT=24 К). In contrast, in the trained crystals the operating temperature range of the TWSME is shifted towards a low temperature region (220-275 K), after 100 thermal cycles the reversible strain εTWSME is significant decreased from 3.0 to 2.0% and the temperature hysteresis ΔT is increased from 33 to 50K.

A circular inhomogeneity incorporating surface/interface strain gradient elasticity

We derive a rigorous solution to the anti-plane shear problem of a circular elastic inhomogeneity with an imperfect interface described by surface strain gradient elasticity. The loadings considered include a uniform remote stress field and a screw dislocation applied either in the matrix or in the inhomogeneity. By using analytical continuation, the problem is reduced to a third-order differential equation for a single analytic function. The analysis indicates that in the absence of the screw dislocation, the internal stress field is uniform and is reliant on two size-dependent parameters arising from surface strain gradient elasticity. The size-dependent image force acting on the screw dislocation is derived. The conditions for the existence of equilibrium positions for the dislocation in the matrix or in the inhomogeneity are obtained. Several numerical examples are presented to illustrate the solution. As an application of the solution, the stabilities of a misfit screw dislocation dipole in the matrix and a screw dislocation pair in the inhomogeneity are also discussed.

In-process estimation of fracture surface morphology during wheel scribing of a glass sheet by high-speed photoelastic observation

Defect-free glass separation techniques are in strong demand in glass processing industries. In this study, we intended to observe the internal stress field during/after wheel scribing of a glass sheet using the photoelastic method. First, we visualized the crack propagation behavior in a 0.7-mm-thick non-alkali glass sheet during mechanical scribing with a 2.0-mm-diameter serrated diamond wheel using high-speed imaging techniques. The observation results under various applied load conditions showed that the crack propagation behavior changed dramatically at a load of approximately 9–10N; the generated crack hardly propagated in the thickness direction under lower load conditions, in contrast to the rapid propagation under higher load conditions. The fracture surface morphology that was observed after cleavage also changed, from damaged to defect-free surfaces with increments in the applied load around the transition point (9–10N). This result indicated that the fracture surface morphology was determined by the crack propagation behavior. Second, the birefringence phase difference was measured from the upper side of the glass sheet to enable understanding of the stress fields induced by scribing wheel indentations. As a result, the phase differences that were distributed along the scribe line were shown to differ depending on the applied loads; the phase difference changed little under lower load conditions, but vanished immediately under higher load conditions. Therefore, these differences were dependent on whether or not rapid crack propagation occurred. The measured phase difference distribution thus included information about the crack propagation behavior, and this information could be used as a criterion for estimation of the fracture surface morphology. An in-process estimation method for the fracture surface morphology during mechanical wheel scribing was therefore developed based on high-speed polarization imaging techniques.

Nature of the structural degradation of rail surfaces during operation

Patterns in the transformation of the structural and phase states and the defect substructure of rail surface layers up to 10 mm thick during long-term operation (gross transit tonnages of 500 and 1000 mln t) are found via optical, scanning, and transmission electron microscopy. According to the nature of the fracture and the degree of defectiveness, three layers can be distinguished: a surface layer, a transition layer, and the base metal. It is shown that the operation of steel rails is accompanied by full fractures in surface layers up to 15 μm thick with lamellar pearlite grains and the formation of ferrite–carbide mixtures with nanosized particles. The deformation of steel increases the densities of scalar and excess dislocations, the curvature–torsion values of the crystal lattice, and the amplitudes of internal stress fields. Structural elements that can act as stress concentrators are identified.

Continuous Modeling of Dislocation Cores Using a Mechanical Theory of Dislocation Fields

A one-dimensional model of an elasto-plastic theory of dislocation fields is developed to model planar dislocation core structures. This theory is based on the evolution of polar dislocation densities. The motion of dislocations is accounted for by a dislocation density transport equation where dislocation velocities derive from Peach-Koehler type driving forces. Initial narrow dislocation cores are shown to spread out by transport under their own internal stress field and no relaxed configuration is found. A restoring stress of the lattice is necessary to stop this infinite relaxation and it is derived from periodic sinusoidal energy of the crystal. When using the Peierls sinusoidal potential, a compact equilibrium core configuration corresponding to the Peierls analytical solution is obtained. The model is then extended to use generalized planar stacking fault energies as an input and is applied to the determination of properties of planar dislocation cores in crystalline materials. Dissociations of edge and screw dislocation cores in basal and prismatic planes of Zirconium are shown.

Acoustic Properties of Isotropic Hypoelastic Materials with Residual Technological Stresses

A linearized statement was used to study the problem of propagation of small perturbations in isotropic uniformly stressed hypoelastic medium. The obtained results allow answering the question on how the initial stress field affects the parameters (velocity, shape, amplitude) of an acoustic impulse and how the impulse parameters depend on a propagation direction. The results show that there is evident similarity between “material anisotropy” initially inherent for instance in crystals and “field anisotropy” induced by a field of internal stresses in isotropic medium.

Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains

The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson’s ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape.

Inverse elastocaloric effect in a Ti-Ni alloy containing aligned coherent particles of Ti3Ni4

We have detected an inverse elastocaloric effect in a Ti-51Ni (at%) alloy which contains aligned coherent particles of Ti3Ni4 formed by aging under tensile stress. In this alloy, the temperature of the specimen decreases when stress is applied due to a stress-induced reverse martensitic transformation (from the R-phase to the B2-phase) The temperature decrease caused by this effect is about 1.1K at 300K. The internal stress field around the Ti3Ni4 precipitate is responsible for this effect. A further increase in the tensile stress causes a temperature rise due to a conventional elastocaloric effect.

Variation of internal stresses as a function of deformation and distance from sources in Cu–Al polycrystalline alloys

Internal stress fields in deformed Cu–Al polycrystalline alloys are studied via TEM. The sources of such stresses are determined. Internal stress fields are measured as a function of distance from different sources. The effect grain size has on the formation of internal stresses is determined.

Rail strengthening in prolonged operation

In rail operation (with traffic corresponding to passed tonnage of gross loads of 500 and 1000 million t), the surface layer of the steel is significantly strengthened. Electron-microscope data permit quantitative analysis of the contribution of different mechanisms to rail strengthening in prolonged operation, at different distances from the contact surface. The strengthening is multifactorial: it involves substructural strengthening associated with nanofragment formation; dispersional strengthening by carbide particles; the formation of atmospheres at dislocations; and polar stress due to interphase and intraphase boundaries. The significant increase in the surface strength of rail steel after prolonged operation (passed tonnage of gross loads of 1000 million t) is due to the presence of long-range internal stress fields and to the fragmentation of material with the formation of nanostructure.

Time-dependent interfacial sliding in nano-fibrous composites under longitudinal shear

We use complex variable methods to analyze time-dependent deformations of an isolated elastic nano-fiber embedded in an infinite elastic matrix under longitudinal shear subjected to uniform stress at infinity. In order to incorporate nanoscale size-effects into our continuum-based model, the nano-fiber and the matrix are each endowed with separate and distinct surface elasticities described by the Gurtin–Murdoch model. The fiber/matrix interface is allowed to slide via a diffusion-controlled mechanism. We show that the characteristic relaxation time and time-dependent stress distribution in the composite can be described completely by three size-dependent parameters and a size-independent mismatch parameter. Further, we note that the internal stress field is spatially uniform yet size- and time-dependent. Finally, we obtain the effective anelastic and size-dependent shear modulus of the fibrous composite using the mean-field method of Mori–Tanaka.

Spatial evolution and fractal characteristics of natural fractures in marbles under uniaxial compression loading based on the source location technology of acoustic emission

Natural fractures are widely distributed in rocks. Generally, there are four types of natural fractures, i.e., single, parallel, intersected and mixed. Uniaxial compression tests on naturally fractured marble samples, taken from the transportation tunnels of Jinpin II hydropower station in southwestern China, are conducted with a MTS815 rock mechanics testing system. The acoustic emission (AE) events are monitored by PCI-II AE system. The spatial evolutions of different natural fractures have been successfully located and tracked according to the AE ringing number. Experimental results indicate that the failure process of fractured marble is locally progressive. The AE event accumulation is strongly related to the loading process and stress redistribution in rock. For the former two types, i.e., single and parallel natural fractures, the spatial AE event distributions in marbles are relatively simpler than those of the other two. The corresponding strong AE event numbers (with ringing number greater than 20) increase with the compressive stress along the naturally fractured surfaces when the stress is low. When the compressive stress is close to the failure strength of the rock, AE events first appear around the natural fracture tip, then spread along the final rupture direction. For the marble containing intersected natural fractures, strong AE events are approximately uniformly distributed at the initial stage of the compression test. Later, the AE events increase when the compressive stress gets higher continuously, and then concentrate around the intersection points of fractures. The case with mixed natural fractures has the most complex AE event distribution than those of the others. However, it is still not difficult to determine the internal weakness parts and stress field based on the spatial AE event distribution. The fractal dimension of the spatial AE event distribution, capable of describing the mechanical behavior and structural damage of rock materials, is estimated by a newly developed analysis method. The parameters of AE events for different types of natural fractures, such as AE accumulative value, amplitude and absolute energy, are statistically analyzed. The present testing scheme can be an initial step toward further development of in situ microseismic monitoring techniques for complex fractures. Moreover, the obtained experimental and analytical results can facilitate the investigation on rock mass failure and instability mechanism.

Numerical implementation of a crystal plasticity model with dislocation transport for high strain rate applications

This paper details a numerical implementation of a single crystal plasticity model with dislocation transport for high strain rate applications. Our primary motivation for developing the model is to study the influence of dislocation transport and conservation on the mesoscale response of metallic crystals under extreme thermo-mechanical loading conditions (e.g. shocks). To this end we have developed a single crystal plasticity theory (Luscher et al (2015)) that incorporates finite deformation kinematics, internal stress fields caused by the presence of geometrically necessary dislocation gradients, advection equations to model dislocation density transport and conservation, and constitutive equations appropriate for shock loading (equation of state, drag-limited dislocation velocity, etc). In the following, we outline a coupled finite element–finite volume framework for implementing the model physics, and demonstrate its capabilities in simulating the response of a [1 0 0] copper single crystal during a plate impact test. Additionally, we explore the effect of varying certain model parameters (e.g. mesh density, finite volume update scheme) on the simulation results. Our results demonstrate that the model performs as intended and establishes a baseline of understanding that can be leveraged as we extend the model to incorporate additional and/or refined physics and move toward a multi-dimensional implementation.

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the extended defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.

Formation of internal stress fields in rails during long-term operation

The structure and the internal stress fields in R65 rails withdrawn from operation because of side wear after long-term operation are studied and estimated. A high scalar dislocation density (higher by a factor of 1.5–2), the fragmentation of cementite lamellae, and the precipitation of carbide particles are detected in the layers adjacent to the roll surface. The stresses at the boundaries of the particles with the ferrite matrix can exceed the ultimate strength of the steel.

State of Ni–Cr–B–Si–Fe/WC coatings after plasma powder surfacing with nanopowder modifier

The structure and phase state and internal stress fields of plasma powder Ni–Cr–B–Si–Fe/WC surface coatings are compared in the presence and absence of a modifier: Al2O3 nanoparticles. PS-12NVK-01 powder alloy applied to a steel 20 substrate is studied by transmission diffraction electron microscopy of thin films, scanning electron microscopy, and X-ray structural and local X-ray spectral analysis. The phase composition of the alloy is determined; its defect structure and internal stress are studied. The structure of the material is analyzed before and after the introduction of Al2O3 nanopowder in the melt. Introducing the modifier reduces the grain size of the material; leads to the formation of tungsten carbide W2C and the boride Fe3Ni3B in the carbide subsystem; and reduces the internal stress and scalar dislocation density.

Inference of Internal Stress in a Cell Monolayer

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply Bayesian inversion stress microscopy to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi one-dimensional geometry.

Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation

Using complex variable methods and conformal mapping techniques, we demonstrate rigorously that two inhomogeneities of irregular shape interacting with a screw dislocation can indeed maintain uniform internal stress distributions. Our analysis indicates that while the internal uniform stresses are independent of the existence of the screw dislocation, the shapes of the two inhomogeneities required to achieve this uniformity depend on the Burgers vector, the location of the screw dislocation, and the size of the inhomogeneities. In addition, we find that this uniformity of the internal stress field is achievable also when the two inhomogeneities interact with an arbitrary number of discrete screw dislocations in the matrix.

Numerical simulation of stress distribution in heterogeneous solids during high pressure processing

It is generally assumed that the internal stress distribution in foods under high pressure processing (HPP) is uniform, which may not be true for solid foods with hard inclusions, like meats with bones or for particulate foods. Our objective was to simulate the internal stress distribution during HPP of a model heterogeneous solid food made with a gel and a wood inclusion and determine how mechanical properties affect the internal stress distribution. It was determined that hydrostatic pressure decreased and shear stress was generated at the interface between the soft solid and the hard inclusion. The differences in pressure and shear stresses increased as the shear modulus of the soft solid increased. Our studies suggest that a better understanding of the mechanical properties that affect the development of the internal stress field is needed, since they could affect the achieved microbial inactivation levels at different locations in HPP solid foods.