Theory Of Stress Transfer Research Articles

Low modulus-yet-hard, deformable multicomponent fibrous B2-phase making a medium-entropy alloy ultra-strong and ductile

Introducing inclusions as the strength enhancer is an effective method to develop ultrastrong-yet-ductile metallic composites. However, the widely used high modulus hard-and-brittle inclusions in the low modulus matrix for strengthening often cause hetero-phase cracking and resultant reduced ductility of inclusion-reinforced composites. Here we present a novel strategy to design ultrastrong and ductile heterogeneous NiCoCr-based medium-entropy alloy uniting high modulus-yet-soft equiaxial-grained matrix combined with low modulus-yet-hard fibrous B2-inclusions. The image stress effect induced by the modulus mismatch can weaken the matrix/B2 interfacial resistance for dislocation transmission into the hard B2-phase, thus promoting their plasticity. Meanwhile, the strong matrix can effectively arrest cracks in B2-inclusions nucleated at their ideal strength to realize large ductility and great fracture resistance of composites. The fracture behavior of our designed alloys related to the fibrous B2-inclusions was rationalized in terms of the stress transfer theory. This work provides a novel pathway for designing high-performance multicomponent alloys even metallic composites utilizing the ideal strength of low modulus-yet-hard inclusions.

Layout of the First-Mining Working Face in the Protected Seam for Pressure Relief by Peak Stress Shift

An appropriate layout of the first-mining working face of protected seams is key to rockburst prevention in coal seams. By taking the first-mining working face in the 2-2# middle coal seam in Hulusu Coal Mine as the background, a mechanical model for the stress distribution after mining the upper protective seams was established through theoretical analysis and in situ measurement. The problem concerning the layout of the first-mining working face in the protected seam was transformed into one concerning the optimal horizontal distance L. Furthermore, based on the theory of stress transfer within a semi-infinite plane, the distribution of the vertical stress in the protected seam was deduced, for which numerical simulation was performed. Through calculation, it is best (in terms of roadway excavation) to set L to between 50 and 75 m; the mining-induced disturbance shows the least influence on the two roadways at L = 80 to 140 m and at L = 40 to 100 m, and the influence of the remaining coal pillar on mining of the working face is the least significant. Based on the analytic hierarchy process (AHP) evaluation method, the weights of three groups of contradictory criteria and the weighted values of the peak stress under different values of L were calculated. The results show that the global stress on the first-mining working face in the protected seams is lowest at L = 60 m. The results can provide a reference for the layout of the working faces in protected seams in adjacent coal mines.

Detecting All Possible Ionospheric Precursors by Kernel-Based Two-Dimensional Principal Component Analysis

Kernel-based two-dimensional principal component analysis (K2DPCA), a nonlinear method, was performed to examine ionospheric 2-D total electron content (TEC) variations obtained from the NASA Global Differential GPS (GDGPS) network, which consisted of low spatial resolution ionospheric TEC data, to detect TEC precursors prior to the China Ludian earthquake at 08:30:13 UT on 03 August 2014 ( $M = 6.1$ ). Simultaneously, two-dimensional principal component analysis (2DPCA), a linear method, was performed to examine data related to the same earthquake for comparison purposes. The results have shown that two TEC precursors were observed three days prior to this earthquake. The characteristics of all principal eigenvalues were considered to determine the TEC precursors of the earthquake in this paper. This paper aimed to differentiate the previous studies of Lin about 2DPCA using only the characteristic of the first principal eigenvalue to determine the TEC precursors of the earthquake. However, some other TEC precursors could be lost in processes that do not analyze the characteristics of other principal eigenvalues. Therefore, this research can be considered as a full analysis that examined the detailed surrounding TEC precursors of the earthquake and could be treated as a new study scope with 2DPCA and K2DPCA. The TEC precursor during 06:15 to 06:20 (UT) on 01 August 2014 localized near the epicenter was more intense compared with the characteristic of the first largest principal eigenvalue. However, another localized TEC precursor, which occurred from 06:15 to 06:20 (UT) on 01 August 2014 at a site west of the epicenter, was found to be more intense. The more plausible reason for the two TEC precursors could be the density variances caused by radon-gas release due to the fine crack stress transfer from the rocks according to Coulomb stress transfer theory as applied to a far TEC precursor. The durations of both TEC precursors were at least 5 min. This research could be treated as a full and detailed examination of surrounding TEC precursors. K2DPCA was better at identifying the TEC precursors.

Considering large earthquake clustering in seismic risk analysis

Earthquakes cluster in space and time resulting in nonlinear damage effects. We compute earthquake interactions using the Coulomb stress transfer theory and dynamic vulnerability from the concept of ductility capacity reduction. We combine both processes in the generic multi-risk framework where risk scenarios are simulated using a variant of the Markov chain Monte Carlo method. We apply the proposed approach to the thrust fault system of northern Italy, considering earthquakes with characteristic magnitudes in the range ~[6, 6.5], different levels of tectonic loading dot{tau } = {10−4, 10−3, 10−2} bar/year and a generic stock of fictitious low-rise buildings with different ductility capacities μΔ = {2, 4, 6}. We describe the process’ stochasticity by non-stationary Poisson earthquake probabilities and by binomial damage state probabilities. We find that earthquake clustering yields a tail fattening of the seismic risk curve, the effect of which is amplified by damage-dependent fragility due to clustering. The impact of clustering alone is in average more important than dynamic vulnerability, the spatial extent of the former phenomenon being greater than of the latter one.

Stress transfer through fully bonded interface of layered materials

Plane strain elastic theory of stress transfer in multi-layered materials is formulated and is used to investigate the stress distribution of a coating system under a tensile load. When the substrate layer is subjected to a uniaxial load, the load is transferred to the coating through interfacial shearing stress. With the aid of a plane assumption, decoupled governing equations are obtained, and the general solution of the displacement field can be derived for both the coating and the substrate layers. Using the boundary conditions and the interfacial continuities, we obtain a closed-form solution for the elastic fields in both the overlay and the substrate layers, which takes the first-term of a series-form solution. Although the singularity effect of stress at the ends of the interface and loading points cannot be exactly illustrated due to the simplification and assumptions, the proposed formulation provides excellent agreement with the finite element results of the transferred stress in the thickness direction of the coating system. Comparisons with the existing models demonstrate the capability and limitation of the proposed formulation. This theory can serve as a baseline for future fracture analysis, inelastic analysis, and thermomechanical analysis of multi-layered materials.

Two-Dimensional Stress Analysis of Low-Temperature Cracking in Asphalt Overlay/Substrate Systems

Low-temperature cracking of an asphalt pavement is caused by the deformation mismatch between the asphalt overlay layer and the underlying pavement layer in cold climates or where rapid temperature change exists. When longitudinal tensile stress in the overlay reaches a certain level, transverse cracks will initiate at the surface to release the energy stored in the asphalt material. When crack spacing reduces to a certain value, crack density becomes saturated and no new cracks will form. The fracture behavior significantly changes with the properties of the underlying layer and the interface. A recently developed theory of stress transfer is used to obtain a closed-form solution for the elastic field in an asphalt overlay fully bonded to the underlying layer, based on the periodic boundary-value problem. Using the correspondence principle, the formulation is extended to consider the viscoelastic material behavior of asphalt materials, so that the time-dependent material behavior of asphalt pavements under climate change can be analyzed. The modeling results compare well with finite-element results. The analytical solution can be used in the simulation of low-temperature cracking of asphalt pavements under extreme temperature conditions.

The Influence Factors Analysis of Initial Excess Pore Water Pressure Caused by Construction of Shield Tunnels

Excess pore water pressure caused by construction dissipated, resulting in consolidation settlement. The formula of initial excess pore water pressure around tunnel lining was deduced by stress relief theory, and its formula within the region of its distribution at any point was subsequently deduced by stress transfer theory. By comparing the measured data, shows that the calculated closed to the measured, and with the distance increased the initial excess pore water pressure decreased in a concave curve shape. When the depth of tunnel increased or the diameter decreased, would made initial excess pore water pressure between the tunnel bottom and tunnel center horizon around tunnel lining more different. At a certain depth, the mast initial excess pore water pressure above tunnel axis, away from the axis reduced; showing a similar PECK shape.

Reinforcement efficiency of multi-walled carbon nanotube/epoxy nano composites

Mechanical reinforcement of polymer matrices loaded by carbon nanotubes is expected to benefit by both the high aspect ratio and the very high modulus of such nanofillers and, consequently, it depends not only by their content within the hosting system but also by the state of dispersion. This work analyses the effect on the bending modulus of dispersed multi-walled carbon nanotube (MWCNT) into an epoxy system. Results indicate that reinforcement efficiency is characterised by two limiting behaviours whose transition region coincides with the development of a percolative network of nanotubes. Well below the percolation threshold, the carbon nanotubes, contribute to the composite modulus with their exceptional modulus (in this case a value of 1.780 TPa was found), whereas it dramatically decreases above this limit due to the reduction of the effective aspect ratio and the micron sized cluster formation. An estimate of the maximum reinforcement induced by carbon nanotubes has been proposed based on percolation and stress transfer theory for large aspect ratio fillers.

Explanation for fracture spacing in layered materials

The spacing of opening-mode fractures in layered materials--such as certain sedimentary rocks and laminated engineering materials--is often proportional to the thickness of the fractured layer. Experimental studies of this phenomenon show that the spacing initially decreases as extensional strain increases in the direction perpendicular to the fractures. But at a certain ratio of spacing to layer thickness, no new fractures form and the additional strain is accommodated by further opening of existing fractures: the spacing then simply scales with layer thickness, which is called fracture saturation. This is in marked contrast to existing theories of fracture, such as the stress-transfer theory, which predict that spacing should decrease with increasing strain ad infinitum. Recently, two of us (T.B. and D.D.P.) have used a combination of numerical simulations and laboratory experiments to show that, with increasing applied stress, the normal stress acting between such fractures undergoes a transition from tensile to compressive, suggesting a cause for fracture saturation. Here we investigate the full stress distribution between such fractures, from which we derive an intuitive physical model of the process of fracture saturation. Such a model should find wide applicability, from geosciences to engineering.

Theory of stress transfer in a 0°—90°—0° cross-ply laminate containing a parallel array of transverse cracks

Two new analytical methods have been developed that can predict the stress transfer between the 0 and 90° plies in a 0°—90°—0° cross-ply laminate containing transverse cracks. Account is taken of thermal residual stresses arising from a mismatch in thermal expansion coefficients of the 0 and 90° plies. The first method is based on a 2-D model which assumes that generalised plane strain conditions prevail. The theoretical approach retains all relevant stress and displacement components, and satisfies exactly the equilibrium equations, the interface conditions, and other boundary conditions involving stresses. The stress—strain—temperature relations are satisfied either exactly or in an average sense. The 2-D representation can be used to predict the stress and displacement fields for a laminate containing parallel transverse cracks. In this paper the solutions are used to estimate the dependence of the longitudinal values of Young's modulus, Poisson's ratio, and thermal expansion coefficient on the density of transverse cracks. The second analytical method extends the 2-D model so that it can apply to 3-D problems which arise, for example, when edge effects or orthogonal cracking are to be taken into account. For the special case of very large laminate widths the 2- and 3-D models predict results which are very close to each other for both glass fibre/epoxy and carbon fibre/epoxy laminates. It is shown how the 3-D model can be used to predict the transverse Young's modulus and thermal expansion coefficient. Theoretical predictions of the dependence of Poisson's ratio on transverse crack density indicate that experimental measurements can be sensitive to the strain measurement technique used, and to specimen width when using a transverse extensometer. Theoretical predictions, for glass fibre/epoxy and carbon fibre/epoxy laminates, of the dependence of Young's modulus and Poisson's ratio on the crack density are compared with some experimental results.

A stress-transfer model for the development of extension fracture boudinage

The term boudinage is used to describe a wide variety of extensional structures in deformed rocks. This paper is mainly concerned with boudinage resulting from through-layer extension fractures followed by separation of the layer segments, thus forming boudins with more or less rectangular cross-sections. In principle, this process is similar to the break up of fibres in fibre-reinforced composite materials extended parallel to the fibre direction. Both processes are controlled by the transfer of stress from the matrix to the fibre (or layer) and a mathematical model for fibre-matrix stress transfer (the ‘fibre-loading’ model) is well established. We have used this as a basis for developing a stress transfer model for boudinage. The only difference in the basic mathematical formulation results from geometric differences between the two systems; the geometric expressions in the fibre-loading model have, therefore, been rederived for the layer-matrix case. Stress-transfer theory predicts that the tensile stress in a layer segment rises from a minimum at the end of a segment to a maximum at the centre. This behaviour, which is clearly shown by finite-element models of boudinage structure, suggests that extension fracture boudinage develops by successive ‘mid-point’ fracturing. According to stress-transfer theory, the process will continue until a layer is reduced to segments (boudins) all of which are shorter than some critical length (for which the tensile fracture strength of the layer is equal to the tensile stress at the mid-point). In practice, successive fracturing will be influenced by two other factors: (1) in nature the controlling material properties (tensile fracture strength, elastic moduli) will not be single-valued but will have a distribution reflecting local variations in lithology and microstructure and (2) major pre-deformation flaws may be present in a layer which will control the ‘starting length’ of layer segments. These factors are incorporated with the stress-transfer theory into a statistical (Monte Carlo) model for extension fracture boudinage which results in a prediction of boudin aspect ratios. The predicted distribution compares very closely with the observed distribution of 91 quartzite boudins within Lower Carboniferous slates at Tintagel, Cornwall. The stress-transfer model implies that boudin-defining fractures occur sequentially so that inter-boudin gap lengths will be unequal. Strain estimates based on boudinage structure will vary according to which part and how much of a layer is sampled. A much improved strain estimate is possible based on sequentially closing the inter-boudin gaps. The stress-transfer theory also leads to the possibility of estimating palaeostress from boudinage structure and is the only model available which predicts an aspect ratio distribution of boudins formed by extension fracture. Other than our own, we know of no published data on boudin aspect ratio distributions. Hence, further elaboration of the model is not possible until more field data is available. We hope that our work will encourage the systematic measurement of boudinage as well as the development of alternative models.

Integrated circuits for the industrial world : L. Maul, Solid State Technology, September (1970), p. 43

Plane strain elastic theory of stress transfer in multi-layered materials is formulated and is used to investigate the stress distribution of a coating system under a tensile load. When the substrate layer is subjected to a uniaxial load, the load is transferred to the coating through interfacial shearing stress. With the aid of a plane assumption, decoupled governing equations are obtained, and the general solution of the displacement field can be derived for both the coating and the substrate layers. Using the boundary conditions and the interfacial continuities, we obtain a closed-form solution for the elastic fields in both the overlay and the substrate layers, which takes the first-term of a series-form solution. Although the singularity effect of stress at the ends of the interface and loading points cannot be exactly illustrated due to the simplification and assumptions, the proposed formulation provides excellent agreement with the finite element results of the transferred stress in the thickness direction of the coating system. Comparisons with the existing models demonstrate the capability and limitation of the proposed formulation. This theory can serve as a baseline for future fracture analysis, inelastic analysis, and thermomechanical analysis of multi-layered materials.