Study of load bearing capacity of an infinite sheet weakened by multiple collinear straight cracks with coalesced yield zones

This paper is concerned with the analytical solution of a multi-side damage problem. The objective is to investigate the load-bearing capacity of an infinite elastic-plastic plate weakened by three pairs of collinear straight cracks with coalesced yield zones. Stress intensity factors (SIFs) are obtained when yield zones are subjected to three different patterns of yield stress distribution, i. e., constant, linearly, and quadratically varying. Muskhelisvili's complex variable approach is applied for uncovering the solution to this problem. The problem is solved and analyzed rigorously based on Dugdale's hypothesis. The numerical results are deduced for the load-bearing capacity of the plate and yield zone lengths. These results are analyzed and demonstrated graphically for various mechanical loading conditions and different crack lengths.

Strip yield model for multiple straight cracks with coalesced yield zones: A theoretical study

The paper presents a complicated case of coalescence of yield zones between two internal cracks out of four collinear straight cracks weakened an infinite isotropic plate. Two solutions are presented for the case of opening and closing of multiple cracks under general yielding conditions. Using these two solutions and the principle of superposition, we found the analytical expressions for load-bearing capacity of the plate using complex variable method. A numerical study has been carried out to investigate the behavior of yield zone length concerning remotely applied stresses at the boundary of the plate and the impact of two outer cracks on the propagation of inner cracks due to coalesced yield zones. Results obtained are reported graphically.

Study on Web Pillar Stability in Open-Pit Highwall Mining

When highwall mining technology is applied to recover large amounts of residual coal left under the highwall of a big open-pit mine, reasonable coal pillar width is the premise for maintaining the stability of web pillars. By adopting the numerical simulation method, the characteristics of the abutment stress distributions in the web pillars under different slope angles and mining depths are studied, and the function of the stress distribution in the web pillar is established. The relationship between the abutment stress and the ultimate strength of the web pillar under different widths is also analyzed and used in combination with the failure characteristics of the pillar yield zone to explore the instability mechanism of the web pillar. The retaining widths of the web pillars are determined. Based on the modeling results, a mechanical bearing model of the web pillar is established, a cusp catastrophe model of pillar-overburden is constructed, and the formula for the web pillar instability criterion is obtained. By analyzing and calculating the ultimate strength of the web pillar, the formula for calculating the yield zone width at both sides of the pillar is achieved. Using the instability criterion of web pillars in highwall mining, a reasonable pillar width can be deduced theoretically, which provides significant guidance on the application of highwall mining technology.

Spreading Kinetics of Herschel-Bulkley Fluids Over Solid Substrates

The spreading kinetics of Herschel-Bulkley fluids on horizontal solid substrates were theoretically studied. The equations of film thickness were derived in both gravitational and capillary regimes. The dynamic contact angle for the capillary regime was also derived. Finally, a limiting result for the case of τ0 = 0 was obtained, which was compared with the known solution for validation. The results show that the yield behavior of the fluids had a significant impact on the spreading kinetics in both cases. Only when stress was larger than the yield stress, would substantial flow occur. The spreading zone was divided into two parts by the yield surface: sheared zone and yield zone, which was completely different from common Newtonian fluids or power-law fluids. The thickness of the yield zone mainly depended on yield stress and pressure gradient along the z-direction. According to the final evolution, both the film thickness and dynamic contact angle were affected not only by the power-law index but also by the yield behavior.

Application of Discontinuity Layout Optimization to Steel Parts and Steel Connections with a Single Bolt

Steel connections are designed with components such as bolts, plates, and welds. The proof of the plates loaded in-plane can be made by hand calculations or more realistic with a nonlinear FE-simulation. As an alternative method, a modified version of the discontinuity layout optimization (DLO) procedure is presented in this paper. The modification takes yield zone mechanisms into account. Furthermore, a compression-only contact was implemented to reproduce the bearing behaviour of bolted connections. The DLO procedure was tested on tensile specimens with and without bolts. The obtained collapse mechanisms and ultimate loads were compared to results from the Eurocode EN 1993-1-8, literature, and FE-simulations. Recommendations to the correct discretization of the tested specimens were given. Especially for the bearing behaviour, modification factors, based on a parameter study, were worked out. The DLO procedure reproduced the collapse loads and mechanisms of all considered cases correctly. The obtained bearing capacities are, in most cases, conservative compared to the Eurocode EN 1993-1-8. The presented research can be seen as the basis for future investigations on more complex problems in steel connections.

Research on the Layered Rock Mass Excavation Relaxation Stability of Underground Caverns

In order to compare the influence of rock mass parameters weakening on the deformation and stability of excavation caverns in layered rock mass, based on power generation system caverns of a hydropower station, the stability and deformation of the caverns is analyzed. The results show that the mechanical characteristics of the structure surface play a major role in controlling the stability of caverns. And the displacement and yield zone value of plan 3, which adopt elastic-plastic softening model, are significantly larger than other two. The method which consider the residual strength of structure surface is more suitable for the excavation calculation of layered rock mass cavern.

A Methodology to Assess Elbow Fittings With Localized Material Variations

Elbow fittings are manufactured using quenching and tempering heat treatment processes. Such fittings can occasionally exhibit localized regions with lower yield strength than the design target, potentially due to non-uniform heat treatment. This paper presents an analytical methodology to examine the influence of these localized lower yield zones on the load capacity of the affected pipe fitting. In parallel, full-scale testing has been performed to quantify the actual response of the elbows under a combination of different loading conditions. The experimental data is used to validate the analytical approach. Details of the analytical method include a two-fold criterion: a global failure based on elastic–plastic stress analysis and a local failure based on the tri-axial strain limit per ASME Boiler and Pressure Vessel Code Section VIII, Division 2. This paper presents the details of the finite element model development, assessment procedure, validation and parametric analysis of the size and location of the low yield zones in the elbow fittings. The fittings are analyzed for three possible operating scenarios: internal pressure, internal pressure with opening moment and internal pressure with closing moment. To characterize the influence of the low yield zone on the strength of the pipe, a parameter termed as “effective yield strength” is introduced. This approach is further demonstrated and found suitable for predicting burst pressures of components with lower yield zones of various diameters and thicknesses. This assessment method can be further extended to assess other pipeline components that exhibit similar behavior.

A Crack between Orthotropic Materials with a Shear Yield Zone at the Crack Tip

A plane problem for a crack between two anisotropic semi-infinite spaces under remote tensile-shear loading is considered. In the framework of the assumption that the crack faces are free of stresses an exact analytical solution of the problem is given on basis of the complex potentials approach. This solution possesses oscillating square root singularities in stresses and in the derivatives of the displacement jumps at the crack tips. To remove these singularities a new model founded on the introduction of the shear yield zones at the crack tips is suggested. This model is appropriate for the cases where interface adhesive layer is softer than the surrounding matrixes. Under this assumption the problem is reduced to the nonhomogeneous combined Dirichlet-Riemann boundary value problem with the conditions at infinity. An exact analytical solution of this problem is presented for the case of a single yield zone. The length of this zone is found from the finiteness of the shear stress at the end point of the zone. Due to such simulation the shear stress becomes finite at any point and the normal stress possesses only square root singularity at the crack tip. Therefore, the conventional stress intensity factor of the normal stress at the crack tip is used. The numerical illustration of the obtained solution is given.