Stress Discontinuities Research Articles

Resistance of Heterogeneous Metal Compositions to Fracture under Dynamic and Cyclic Loads

This paper presents the results of experimental data analysis, which indicate an increased resistance of heterogeneous multilayer clad composites to dynamic loading destruction compared with homogeneous materials. The reason for this is the crack retardation caused by lamination at the boundary of the layers. The destruction of heterogeneous compact composite samples by cyclic off-center stretching also occurs with crack retardation, with the fractogram clearly demonstrating the transverse tightening of the sample section. We argue that crack nucleation plays a decisive role in the process of dynamic destruction of heterogeneous composites obtained by both multilayer cladding and explosion welding. This study presents generalized calculated data confirming the influence of the sign and magnitude of residual stresses (the appearance of a stress discontinuity) on the conditions of fatigue surface crack nucleation and propagation. Unlike homogeneous materials obtained by casting, forging (rolling), or cladding, which are characterized by a linear dependence of the crack propagation velocity on the dynamic stress intensity coefficient, for multilayer composites consisting of strong and viscous layers, a sharp crack deceleration is observed. This is due to the transition of the crack boundary between the strong and viscous layers. This paper presents studies of the corresponding properties of adjacent layers on the integral characteristics of the deposited composite.

Investigation of fracture toughness and microstructure of micro-scaled multilayer-DLC/silicon system via pillar splitting method

The fracture toughness of multilayer diamond like carbon (DLC) coated silicon microstructures was characterized using the pillar splitting method in this study. Two types of coating layers with different properties were alternately deposited by plasma-enhanced chemical vapor deposition at −200 V and −600 V, respectively, with the same total coating thickness (0.3 μm). The effects of different numbers of layers (2, 4, 8, and 12) of DLC coatings on the fracture behavior and fracture toughness enhancement of the coating/silicon system were investigated. Pillar splitting experiments showed that the fracture toughness of the coated samples was significantly increased by 24.6%–63.6% compared to bare silicon ones. With an increasing number of layers of DLC coatings, the protective effect of the coatings on the silicon substrate was continuously enhanced. The trends of finite element cohesive zone modeling simulations were highly consistent with experimental results. During the splitting process, a nonlinear deformation stage was observed for the first time in the load-displacement curve, which was attributed to stress discontinuity, increased interfacial dislocations, and energy absorption at the layer interfaces. The multilayer coating technology has broad prospects for improving the fracture toughness of materials and enhancing the stability and reliability of micro/nano devices.

On discontinuous stress and strain evolutions in machining of dissimilar laser cladded workpiece

During subsequent machining of laser cladded workpiece, the stress transferred in depth direction is different with conventional cast workpiece due to the geometrical discontinuity, resulting in the stress difference and strain discontinuity at the interface between the cladding layer and substrate. Elastic and plastic deformation will occur in the cladding layer and substrate, respectively, which ultimately reduces the service life of the cladded workpiece. In this study, the stress and strain evolution in subsequent machining of laser cladded workpiece was investigated using an orthogonal cutting model by finite element method. A dimensionless thickness ratio between uncut chip thickness and cladding layer thickness was set and the maximum thickness ratio without equivalent plastic strain (PEEQ) discontinuity at the interface was determined. In addition, the results indicated that the maximum thickness ratio first decreased and then increased with the increase of cutting speed, while increases with the increase of the yield strength of substrate. The synergetic effects of thickness ratio, cutting speed and yield strength of substrate on the strain discontinuity at the interface were also investigated based on Taguchi method. The optimal combination of parameters is determined based on the regression model and divided into areas with considering machining efficiency as well. The map of cutting configurations facilitates the selection of proper machining parameters in order to estimate the strain discontinuity in machining laser cladded workpiece, ensuring a better service life of the workpiece.

The Mechanical Properties and Fracture Characteristics of Shale Layered Samples from the Lucaogou Formation Considering Natural Crack and Mineral Distribution.

Shale oil is one of the most promising alternative unconventional energies in the world, and recently the Lucaogou Formation showed significant exploration potential, becoming the primary target in northwestern China. This paper focuses on the mechanical properties and fracture characteristics of shale layered samples from the Lucaogou Formation, conducting uniaxial compressive tests with real-time micro-CT scanning, as well as mineral analysis after failure. It has been found that the mechanical and fracture features are both related to the composition, distribution, content and particle size of minerals, as well as natural fractures. The main crack tends to form in the weak mineral band, for example, calcite or clay band. Since the discontinuous stress usually forms at the interfaces of different minerals, the sample with several major minerals of close content is easier to break into a fractured zone, causing lower uniaxial compressive strength and elastic modulus, compared with the composition of only one dominant mineral. Also, the region will be more fractured after failure if the mineral particles there become smaller. Additionally, although natural cracks have a certain influence on the development of new fractures, not all of the natural ones will propagate into the final fracture network, some of them are just compacted and closed.

Stress field model for bond in reinforced concrete ties

The interaction of the reinforcing bars and the surrounding concrete plays an important role in structural concrete as it is decisive for the reinforcing bar anchorage and the load-deformation behaviour, including stiffness and deformation capacity. Therefore, understanding this interaction – commonly known as bond – is highly relevant to a safe and efficient structural concrete design. Bond depends on many parameters, which affect the local reinforcing bar-concrete interface as well as the global load transfer between the reinforcing bars and the surrounding concrete. The latter governs the formation of transverse and longitudinal cracks and the activation of transverse confinement, which are as decisive for bond as the local interface characteristics. Nonetheless, most bond models and code provisions focus on the local interface and merely account for the global configuration by means of empirically calibrated factors accounting, e.g. for good or bad bond conditions in confined or unconfined situations, respectively.This study investigates the potential of stress fields for modelling bond based on the lower-bound theorem of plasticity theory. Stress fields facilitate the investigation of the local interface and the global load transfer consistently in one model, providing valuable insight into the flow of forces. For simplicity, the fundamental case of a concrete tie reinforced with one deformed steel bar is studied in this paper, superimposing axisymmetric discontinuous stress fields originating at each reinforcing bar rib. Each stress field consists of a triaxial nodal zone adjacent to a rib and a conical compression field that spreads the bond force radially, and is equilibrated along its outer perimeter by axial tensile stresses and confining hoops. The model relies on geometric parameters and basic material properties. The validation against experiments on reinforced concrete ties shows a good correlation between the predicted and observed bond strength and the crack spacing. The predictions can be improved by assigning stiffnesses to the stress field components and requiring interface compatibility, i.e. ensuring contact between the concrete and the reinforcing bar at every rib. Even when assuming a simplified, linearly elastic constitutive behaviour for concrete, the consideration of interface compatibility allows for reproducing the steel strain dependency of the local and average bond stresses and the occurrence and impact of splitting cracks.

Multiple reinforcement measures of flysch landslide.

This work is mainly intended to investigate the flysch landslide reinforcement measures used in the Smokovac-Mateševo section of the North-South Expressway project in Montenegro. Bentley's Plaxis software is used for a numerical analysis of sliding surface parameters of flysch strata in the limit equilibrium state. This study analyzes the slope safety factor for rreinforcement measures such as rock bolts, retaining walls, anti-sliding piles, slope unloading and bolt anchoring and obtains an optimal combination of reinforcement application for the flysch landslide. The effects of seismic action on complex stress and the discontinuous stress boundary conditions arising from various reinforcement measures on landslide stability are also examined. The measures applied in this paper can be used as a reference for flysch landslide reinforcement or other similar slope engineering measures.

Numerical investigation on thermoelastic bending of sandwich plates with porous FGM layer

Porous Sandwich plates are finding increased use in many engineering applications including construction and shipbuilding industries. In recent decades, the laminated plates have much attractive because of the introduction of advanced composite materials such as functionally graded materials (FGMs). This material in which its characteristics are smoothly transient through certain dimensions can overcome many problems encountered in conventional laminated stacking composites, e.g., the inter-laminar stress discontinuity occurred by the mismatches in the characteristics of two distinct laminated layers. This study explores thermal elasto bending of FGM sandwich plates by using IGA (isogeometric analysis) method which be able to easily perform both the smoothness of higher-order distribution, the precise and cost-efficient in modelling of the geometries. A trigonometric higher shear deformable plate theory, which can take the thickness effects into account, is established with the zig-zag formulation to describe the continuity requirement based on the non-uniform rational B-spline (NURBS)-based IGA. Benchmark problems on the thermoelastic bending responses of FGM sandwich plates have been tested, and the results are validated to the reference problems reported in the open literature to evidence the analysis capability of the proposed IGA method. Additional parameter study highlight the impacts of the composition patterns, ingredient variation, plate geometric coefficient and thermal load type on the thermoelastic flexural behaviors.

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heating on a “nanoscale” plate is considered. The focus is on the anomalous heat transfer mechanisms that result from anomalous diffusion of hot electrons and are characterized by retarded thermal conduction, accelerated thermal conduction, or transition from super-thermal conductivity in the short-time response to sub-thermal conductivity in the long-time response and described by the fractional Jeffreys equation with three fractional parameters. The recent double-strip problem, Awad et al., Eur. Phy. J. Plus 2022, allowing the overlap between two propagating thermal waves, is generalized from the semi-infinite heat conductor case to thermoelastic case in the finite domain. The elastic response in the material is not simultaneous (i.e., not Hookean), rather it is assumed to be of the Kelvin–Voigt type, i.e., σ=Eε+τεε˙, where σ refers to the stress, ε is the strain, E is the Young modulus, and τε refers to the strain relaxation time. The delayed strain response of the Kelvin–Voigt model eliminates the discontinuity of stresses, a hallmark of the Hookean solid. The immobilization of thermal conduction described by the ordinary Jeffreys equation of heat conduction is salient in metals when the heat flux precedence is considered. The absence of the finite speed thermal waves in the Kelvin–Voigt model results in a smooth stress surface during the heating process. The temperature contours and the displacement vector chart show that the anomalous heat transfer characterized by retardation or crossover from super- to sub-thermal conduction may disrupt the ultrafast laser heating of metals.

Thermal Stress Formation in a Functionally Graded Al2O3-Adhesive Single Lap Joint Subjected to a Uniform Temperature Field

This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al2O3-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated.

Analysis of discontinuity stress at shell and elliptical head juncture using theory of beam on elastic foundation

A thin-walled pressure vessels under internal pressure generates higher amount of stresses at shell-head juncture compared to membrane stress. These localized stresses are generated due to change in the shape of the meridian. The change in shape of the meridian is seen at the head and shell junction. The discontinuity in shape changes the direction of resultant stress. To predict the accurate stresses around the discontinuity region, bending of beam on an elastic foundation is used as part of the analytical analysis. Charts have been plotted of various stresses generated near juncture. The method is applied to pressure vessel with cylindrical shell and elliptical head. The theoretical results are then compared to the analytical results obtained from finite element analysis (FEA). In the present work, the discontinuity stresses have been evaluated analytically and the same is also compared with the finite element analysis results. It is found that the results of FE analysis closely agrees with the analytical results maximum percentage variation of 1.19.

Stresses at grain boundaries: The maximum incompatibility stress in an infinitely extended elastic bicrystal under uniaxial loading

In a material under stress, grain boundaries may give rise to stress discontinuities. Stress localization is crucial to materials' behavior such as segregation, precipitation, and void nucleation. Here, the stress state at a grain boundary perpendicular to a uniaxial external stress is studied systematically. The grain boundary with the most extreme stress discontinuity is determined for cubic materials within the elastic limit for a bicrystal model. Additionally, grain boundaries with negligible stress discontinuity are identified. The influence of the elastic tensor components, C11, C12, and C44, and grain orientation is studied quantitatively.

Numerical analysis of bonded and unbonded prestressed RC beams using cohesive and non-compatible rod elements

This research presents a numerical approach to simulate prestressed RC beams. It combines state-of-the-art finite element models to simulate the concrete (including fracture), tendons, passive reinforcements, and the rebar–concrete interaction. This provides more realistic simulations and rich details on deformability, crack patterns, and axial and contact stress distributions in passive reinforcements and tendons. Concrete fracture is simulated using cohesive elements with a constitutive model based on the plasticity theory and fracture mechanics, enabling crack development and propagation prediction. Reinforcements are simulated using rod elements with incompatible nodes. Special contact elements link rod to bulk elements and are placed along the reinforcements and at tips. These contact elements also predict relative displacements between rebars and concrete. Prestressing is simulated by setting initial stresses in tendons and applying forces to its nodes simultaneously. The approach also includes two numerical techniques to improve the convergence of the highly nonlinear problem. Five experimental beams are simulated. In all cases, the numerical load–deflection curves agree with the experiments. Fracture patterns also match rupture modes. Finally, contact stress discontinuities in tendons due to crack development are examined in more detail.

Effect of SH-type waves and shear stress discontinuity on a moving loaded composite structure

Effect of SH-type waves and shear stress discontinuity on a moving loaded composite structure

A refined spectral element model for wave propagation in multiscale hybrid epoxy/carbon fiber/graphene platelet composite shells

The propagation of elastic waves in heterogeneous media is of interest for impact dynamics and non-destructive detection. This work presents a refined spectral element model (RSEM) to study the wave propagation in multiscale hybrid composite (MHC) shells subjected to impulsive loadings. The doubly-curved MHC shell consists of epoxy, carbon fibers, and graphene platelets (GPLs). The GPLs are functionally distributed along the thickness of the shell. For the three-phase MHC, the Halpin-Tsai micromechanical model in conjunction with the Mori-Tanaka approach is exploited to determine the effective material properties. In the framework of four-variable shear deformation theory, the governing equations along with the natural boundary conditions are derived using Hamilton's principle. A two-node spectral shell element is developed according to the closed-from solutions. The accuracy of the RSEM is verified by comparison with published results in aspects of the natural frequency and transient responses. The wave dispersion characteristics, including the wave number, phase velocity, and group velocity are examined. In the context of high frequency and short wavelength, the proposed RSEM achieves high computational efficiency benefiting from its independence of mesh structure. The time domain responses clearly indicate the wave-boundary interactions, e.g., wave reflection, dispersion, and interference. It is revealed that the present model can well capture the fundamental wave modes of the MHC shell. Moreover, the inclusion of GPLs plays a significant role in improving transverse moduli and mitigating the discontinuities of inter-laminar shear stress.

Thermal-elastic analysis of laminated plates based on the incompatible generalized partial mixed method

Based on the generalized Hellinger-Reissner (H-R) mixed variational principle, the incompatible generalized partial mixed finite element method (IGPMFEM) is proposed in this paper for the thermomechanical stress analysis of laminated composites and sandwich plates. This method inherits the advantages of the generalized mixed element method, allowing for the simultaneous introduction of displacement and stress boundary conditions, and satisfies the discontinuity of the in-plane stresses at the material interface. Introduction of incompatible displacement mode adds higher-order terms in the polynomial expansion of the exact displacements, effectively improving the bending performance and the element accuracy. Although adding stress components would normally increase the computational effort, we address this issue by the elimination method, considering only the out-of-plane stress variables to reduce the matrix dimensions. The accuracy and effectiveness of the proposed method are evaluated by comparing the numerical results of this method with existing elasticity solutions, while the effect of stress boundary conditions is also investigated.

Graphical modeling of discontinuous stress field for RC deep beams under uniform load

AbstractThe fanning compression stress pattern in RC deep beams under uniform load presents a challenge to formulating the configuration of strut‐and‐tie model (STM). To this end, this paper proposes an alternative method for creating a graphical discontinuous stress field model (DSFM) to fill up the whole beam continuum. It comprises a certain number of trapezoidal stress‐bands with varying bandwidths, and their stress values can be calculated based on force equilibrium conditions. Several stress subfields are defined through a certain stress combination from several directions. The DSFM is implementable for both service limit state (SLS) and ultimate limit state (ULS) in that its configuration is primarily oriented by elastic stress field and only a limited plastic redistribution is allowed for plastic failure. The graphical procedure of DSFM is demonstrated and examined by a test deep beam example, which shows that the predictions are fairly in good agreement with the test results.

Recovery strategies, a posteriori error estimation, and local error indication for second‐order G/XFEM and FEM

AbstractThis article presents a computationally efficient and straightforward to implement a posteriori error estimator for second‐order G/XFEM and FEM approximations. The formulation is based on the recently proposed block‐diagonal Zienkiewicz–Zhu (ZZ‐BD) a posteriori error estimator. The focus is on linear elastic fracture mechanics (LEFM) problems but the proposed error estimator formulation is general and can be adapted to other types of problems such as those involving material interfaces. The proposed ZZ‐BD error estimator is based on a new strategy to recover stress fields from second‐order G/XFEM and FEM approximations. This recovery procedure involves locally weighted projections of raw stresses on an approximation space for discontinuous and singular stress fields. The basis functions for these stress approximations are defined using a low‐order partition of unity together with polynomial, discontinuous, and singular recovery enrichment functions. These singular enrichments are provided by the gradient of G/XFEM enrichments for LEFM problems and are, thus, available in most G/XFEM implementations. They also lead to a more computationally efficient stress recovery procedure than the one in the original ZZ‐BD error estimator. The adopted G/XFEM are optimally convergent with the error in the energy norm of . Numerical experiments show that the error of the recovered stress field converges at the same rate as the discretization error. They also show that the effectivity index of the error estimator is close to the unity and that it provides good local error indicators for mesh adaptivity algorithms. Second‐order FEM for elasticity problems is a special case of the G/XFEM adopted here. This is exploited to define a block‐diagonal ZZ error estimator for the FEM as a special case of the proposed estimator for the G/XFEM. This brings the computational efficiency, simplicity, and accuracy of the ZZ‐BD error estimator, originally developed for the G/XFEM, to second‐order standard FEM.

Discontinuous low temperature stress and plant growth regulators during the germination period promote roots growth in alfalfa (Medicago sativa L.)

In high-cold regions, alfalfa is susceptible to cold damage during the seed germination. The effects of discontinuous low temperature stress and plant growth regulators (PGRs) on alfalfa were studied in response to the high day/night temperature differentials in the area. The experiments included seed germination, seedling cold tolerance and plant recovery. Variable temperatures (VT) of 0 °C/15 °C, 5 °C/20 °C and 10 °C/25 °C were set and seeds were soaked with alginate oligosaccharides (AOS), brassinolide (BR) and diethyl aminoethyl hexanoate (DA-6) during the germination period. Parameters such as seed germination and mean germination time (MGT), phenylalanine ammonia-lyase (PAL) activity and oligomeric proanthocyanidins (OPC) content of early seedlings, dry matter accumulation and root crown of the restored plants were analysed. The results showed that low variable-temperature (LVT) stress prolonged the MGT but had little inhibitory effect on germination percentage. Early seedlings adapted to LVT stress by regulating their own water and OPC content, PAL activity and other parameters. LVT induced early alfalfa seedlings to increase their underground biomass by shortening root length and increasing root diameter, and those that had accumulated more underground biomass had faster growth rates and higher total biomass when the ambient temperature rose. AOS also promoted an increase in root crown diameter and root dry weight. This research proved that LVT stress and AOS during the germination process can lead to better growth of alfalfa in high cold regions.

Bearing capacity of concentric anchorage zones in post-tensioned members: A stress field solution

The post-tensioned anchorage zones are generally subdivided into local and general zones, which are treated with semi-empirical approaches and strut-and-tie models separately in many design codes. Even with their functions that look different, the two adjacent zones are intrinsically related in terms of the compression dispersion mechanism. Holding this view, this paper intends to present a mechanical model to integrate their combined actions. Firstly, two confinement effects in anchorage zones are studied: the local confinement under the bearing plate and the passive confinement by bursting reinforcement. Then, a discontinuous stress field model for concentric anchorage zones is proposed, which allows for a triaxial state of compression stresses in the local zone and the contribution of bursting reinforcement in the general zone simultaneously. After that, an explicit bearing capacity formula for anchorage zones is derived, in which the ultimate failure can be attributed to either the yielding of the distributed tension subfield or the crushing of fan subfields. The prediction of bearing capacity is in fairly good agreement with the collected test results.

A Method for Computing Slip-Line Fields with Stress Discontinuity in Cohesionless Backfills

A method for computing slip-line fields in the case of cohesionless backfills with stress discontinuity was proposed. The potential failure zone is divided into the Rankine zone and the transition zone, and the Rankine zone is rigorously determined using the theory of plastic mechanics. The potential failure zone and the Rankine zone are then further divided into a series of triangular slices. On the basis of the force and moment equilibrium conditions of a typical triangular slice, the recurrence equation of the lateral force is established. Furthermore, the relationship between the failure surface inclination angle and the interslice force inclination angle is established by satisfying the Mohr–Coulomb criterion. An iterative procedure for calculating the lateral force of the triangular slices by changing the failure surface inclination in the transition zone is performed until the interslice force satisfies the stress condition of the transition zone boundary, resulting in a stress discontinuity line if the Rankine zone and the transition zone intersect and the intersection line satisfies the stress characteristics of stress discontinuity. Example studies are performed to verify the present method, which shows that the soil–wall interface friction has the most significant effect on stress discontinuity, and the location of the stress discontinuity line gradually approaches the backfill surface with an increase in retaining wall inclination.