Extent Of Plastic Zone Research Articles

Research on the evolution law and control technology of deviatoric stress in the surrounding rock of gob-side entry retaining

Gob-side entry retaining (GER) play a crucial role in enhancing coal recovery, improving roadway stress conditions, and ensuring safe and efficient mining operations. This study focuses on investigating the stability characteristics of surrounding rock using flexible formwork concrete (FFC) along the headgate of 3405 panel. According to the fracture pattern of roof, a mechanical model of GER was developed. This study derived expressions for the support resistance of the filling body and determined its optimal bearing capacity. A FLAC3D numerical model was employed to simulate the GER process, segmented into early, middle, and late stages. Simulation results demonstrate a progression in peak deviatoric stress and extent of plastic zones in the surrounding rock. This evolution includes an initial minor increase (early stage), followed by rapid escalation (middle stage), and eventual stabilization (late stage). The middle stage emerges as critical, characterized by pronounced mining-induced stress effects on the roof. During this phase, significant changes are observed in deviatoric stress curves, with plastic zones rapidly migrating deeper into the rock mass. Practical implementation of the findings revealed a maximum deformation of the filling body of only 198 mm, affirming the feasibility of employing FFC in GER. This research provides valuable insights into managing stability concerns in GER thereby enhancing safety and operational efficiency in coal mining under similar conditions.

Factors Influencing Stope Hanging Wall Stability and Ore Dilution in Narrow-Vein Deposits: Part 1

Unplanned ore dilution negatively affects overall mine profitability by increasing operating costs (e.g., mucking, haulage, crushing, hoisting, milling, waste treatment, and low-grade ore upgrading). Eliminating ore dilution requires identifying and controlling the major causal factors, which are related to in-situ stress regimes, depth of stope undercut, ore dip/orientation, stope geometry, and quality of the host rock mass. In-situ stress regimes and depth of stope undercut were examined in a previous publication (see Part I). The results showed that the stability of the stope hanging wall significantly deteriorates when in situ stress regimes and depth of stope undercutting of the access drift increase. Conversely, the extent of plastic zones increases with such an increase. Also, the depth of stope undercutting has no impact on the deformation development of the rock mass. The objective of this paper is to assess stope hanging wall (HW) stability and ore dilution with respect to ore inclination and stope geometry in sublevel, open stoping, narrow-vein mines. A series of two-dimensional elasto-plastic numerical models was built to examine the effect of ore dip angle and stope geometry (height and width) on stope HW stability and ore dilution in a highly stressed environment (in-situ stress ratio = 2.5). The results are presented, discussed, and compared in terms of depth of relaxation zones, extent of plastic failure zones, and total displacement with respect to four stope dip angles (45°, 60°, 75°, and 85°), three stope widths (5, 7.5, and 10 m), and three stope heights (20, 30, and 40 m). Results show that stope HW stability improves when ore dip angle increases (i.e., steeply dipping ore deposits) because the depth of relaxation zones and extent of failure zones decreases. Dip angle had a negligible effect on HW deformation. Less dilution occurred at very steep (85°) inclination angles. At different ore dip angles, stope HW stability greatly deteriorated with increasing stope width and improved with decreasing stope height.

THE EFFECT OF CRITICAL TRACTION IN COHESIVE ZONE MODEL FOR FATIGUE CRACK GROWTH RETARDATIO

A cohesive zone model for simulation of fatigue crack growth is presented. The cohesive zone model is one of many alternative approaches used to simulate fatigue crack growth. The model incorporates a relationship between cohesive traction and separation in the zone ahead of a crack tip. The model introduces irreversibility into the constitutive relationships by means of damage accumulation with cyclic loading. The traction-separation relationship underpinning the cohesive zone model is not required to follow a predetermined path, but is dependent on irreversibility introduced by decreasing a critical cohesive traction parameter. The approach can simulate fatigue crack growth without the need for re-meshing and caters for single overloading. This study shows the retardation phenomenon occurring in elastic plastic-materials due to single overloading. Increasing the value of critical cohesive traction increases the extent of plastic zone at the crack tip which causes the fatigue crack growth to retard. Plastic materials can generate a significant plastic zone at the crack which is shown to be well captured by the cohesive zone model approach.

Surface reliability of annealed and tempered solar protective glasses: Indentation and scratch behavior

Solar glass is exposed to mechanical contact cleaning and sand particle impact during operation in outdoor environments resulting in optical efficiency loss as well as decrease in mechanical integrity, durability and reliability. The current study investigates the mechanical behavior of two different solar surface glasses through a series of low and high load indentation and scratch experiments. Nanoindentation experiments are performed on the glass substrate in order to measure the hardness and elasticity moduli at different depths below the surface. Scratch experiments are also preformed to find the critical load for the extent of plastic zone or the onset of micro-cracking. The influence of heat treatment for photovoltaic glasses on mechanical properties such as elastic modulus and hardness, and surface properties such as friction coefficient and elastic recovery is examined in this study in which heat treatment is found to affect both mechanical and surface properties. Also, different resistance behavior is observed in low and high load experiments as well as in indentation vs. scratch experiments.

Study of nanoindentation mechanical response of nanocrystalline structures using molecular dynamics simulations

Molecular dynamics (MD) simulations are performed to study the nanoindentation onto three different crystal structures including the single crystalline, polycrystalline, and nanotwinned polycrystalline copper. To reveal the effects of crystal structure and twin-lamellae-thickness on the response of nanoindentation, we evaluate the evolution of crystalline structure, dislocation, strain, indentation force, temperature, hardness, and elastic recovery coefficient in the deformation zone. The results of MD simulations show that the hardness, elastic recovery ratio and temperature of those three nanocrystalline copper strongly depend on crystal structure and twin-lamellae-thickness. It is also revealed that as nanoindenter goes deeper, the extent of plastic zone becomes substantially larger. Initial dislocation always nucleates at the beneath of indenter, and the discrete drops of indentation force observed at certain indentation depths, indicates dislocation bursts during the indentation process. In particular, the twining and detwining are dominant over the dislocation nucleation in driving plasticity in nanotwinned polycrystalline during nanoindentation, which are in good agreement with the previous work. Furthermore, we find that plastic deformation has a strong dependence on crystal structure. The plastic deformation of the single crystalline copper relies on the generation, propagation and reaction of dislocations, that of the polycrystalline copper depends on the dislocation–grain boundary (GB) interactions, and that of the nanotwinned polycrystalline copper relies upon the dislocation–twin boundary (TB) interactions as well as twining/detwining. This work not only provides insights into the effects of crystal structure and two-lamellae-thickness on the mechanical properties of copper under nanoindentation, but also shed lights onto the guideline of understanding other FCC nanocrystalline materials.

Analysis and Construction Techniques for a Water Seal for Underground Mines Subjected to Water Inrush

A case history is presented for a reinforced concrete water seal constructed to resist high-pressure water inflows in a deep coal mine in China. A 3-D numerical model of the structure, developed using FLAC3D, provided a better understanding of the distribution of stresses and displacements and the extent of plastic zones in the rock surrounding the water seal structure. The modeling showed that about 80 % of the total stress caused by the water pressure acted on the water side of the first tapered plug and that the magnitude of the total stress caused by the water pressure gradually decreases along the axial direction of the chamber behind the seal. Based on the modeling, a full-face curtain grouting scheme was proposed to improve the effectiveness of the reinforced concrete water seal. To assess the proposed grouting scheme, an area behind the seal was filled with water and the stability of the surrounding rock was monitored. The conclusions regarding the effectiveness of the grouting and water seal construction techniques may provide valuable guidance for the construction of other water seals.

Assessment of Hydro-Mechanical Behavior of a Granite Rock Mass for a Pilot Underground Crude Oil Storage Facility in China

The hydro-mechanical behavior of a pilot underground crude oil storage facility in a granite host rock in China was analyzed using the finite element method (FEM). Characterization of hydro-mechanical behavior of the rock mass was performed using laboratory test, field monitoring, back analysis of field measurements and permeability tests. FEM numerical analyses were used to assess the hydro-mechanical behavior of the granite to study several design and construction issues. The containment properties of the storage facility were investigated without and with the water curtain system. Results showed that the stored oil would leak into rock mass if a water curtain system is not provided, whereas the containment property of the facility will be maintained when a water curtain system is in place. On the influence of cavern excavation sequence, it was indicated that the excavation of the caverns from left to right is a better choice than right to left for the containment property of the facility. On the influence of permeable condition, it was found that the extent of plastic zones, horizontal convergence and crown settlement under permeable condition are lower than those under impermeable condition due to the different stress paths in the rock mass experienced during excavation.

Impact response of elasto-plastic granular and continuum media: A comparative study

A comparative study of the impact response of three-dimensional ordered granular sphere packings and continuum half-spaces made of elastic-perfectly plastic materials is conducted. Energy dissipation and plastic zone volume are characterized, and scaling laws with respect to material properties, size and loading variables are derived for both continuum and discrete (granular) systems. Due to stress concentration at contacts, energy dissipation in granular systems occurs at much smaller impact loads than in continuum systems. At higher impact loads, the fraction of energy dissipated and the extent of plastic zone are much larger in the discrete system than in the continuum case. Though the size of plastic zone is much larger in discrete systems, the volume of material involved in dissipating a fraction of impact energy is comparable for continuum and granular systems.

Elastic–plastic analysis of interaction between an interface and crack in bi-materials

The objective of the present work is to investigate the interaction between interfaces and cracks in metal/alumina bi-materials. The behaviour is analyzed by the determination of the J integral and the plastic zone at the crack tip using the finite-element methods. Different orientations of the crack according to the bi-materials interface were examined such as cracks parallel and perpendicular to the interface and inclined cracks. The effects of the mechanical properties of the joint materials, the crack length and the metal thickness on the extent of plastic zone and the J integral at the crack tip were also highlighted. The obtained results allow us to deduce mathematical relations giving the variation of the J integral and the plastic zone according to the crack position.

A closed-form solution for a spherical cavity in the elastic–brittle–plastic medium

A theoretically consistent closed-form solution for a spherical cavity in a brittle–plastic infinite medium subject to a hydrostatic stress field was derived. Both linear Mohr–Coulomb (M–C) and nonlinear Hoek–Brown (H–B) yield criteria are considered, and a non-associated flow rule is employed in the solution. Plastic radius, stresses and displacements are explicitly expressed as the functions of radial coordinates, internal pressure and strength parameters. In elastic-perfectly plastic analysis, results for displacements and stresses are in good agreement with those published. Comparison of brittle–plastic solutions with the elasto-plastic ones indicates that brittle–plastic behavior of rock mass increase the extent of plastic zone and the displacements around the cavity significantly. Ground response curves (GRC) are constructed for both M–C and H–B criteria and the potential applications are discussed.

Effect of Poisson’s ratio on crack tip fields and fracture behavior of metallic glasses

A study of the effect of Poisson’s ratio on the stationary mode I crack tip fields in amorphous alloys is conducted. Finite element simulations under plane strain, small scale yielding conditions are performed with a Mohr–Coulomb based constitutive model that accounts for pressure sensitivity of plastic flow as well as the localization of plastic strain into discrete shear bands. Simulations are also performed with von Mises and Drucker–Prager constitutive models. While the Poisson’s ratio does not alter the crack tip fields significantly when the material obeys these two models, it has a marked influence in the Mohr–Coulomb case with softening. A higher Poisson’s ratio reduces the extent of plastic zone and plastic strain levels in front of the notch tip as well as that within the simulated shear bands around the notch root at a given level of stress intensity factor. The implications of these observations on toughness of metallic glasses are discussed.

Fatigue and fracture properties of thin metallic foils

Metallic thin foils are essential structural parts in microsystems ,which may be subjected to fatigue loading caused by thermal fluctuations and mechanical vibrations influencing their reliability in numerous engi- neering applications. It is well known that the fatigue properties of bulk material cannot be adopted for small scaled structures. For a better understanding of the 'size-effect' in the present investigation fatigue crack growth near threshold in the high cycle fatigue regime and associated fracture processes were studied. Free- standing rolled and electrodeposited Cu-, Mo- and Al foils of thickness from 20m to 250m in different conditions have been tested in a special experimental set up operating at RD 1 and a testing frequency of 20 kHz. At a given constant strain value the fatigue crack growth behaviour has been recorded accompanied by intermittent observation of the change of the dislocation structure in the vicinity of the growing crack by use of the electron channeling contrast imaging (ECCI)-technique in a scanning electron microscope (SEM). In a load shedding technique fatigue threshold stress intensity factor values have been derived and compared with data of bulk material. Typical crack growth features were detected depending on thickness and grain sizes of the foils. Various criteria (compliance , extent of plastic zones and plastic strain gradients) were selected for the explanation of this anomalous behaviour. Additionally fractomicrographs of uniaxial strained and fatigued foils have been studied to obtain further insight of the effect of dimensional constraint.

Elasto‐plastic finite element analysis with fuzzy parameters

AbstractIn this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker–Prager yield criterion and the elasto‐plastic matrix are fuzzified for the non‐linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non‐probabilistic entropy is also proposed.

A METHOD FOR THE EVALUATION OF PLASTIC ZONE AROUND UNDERGROUND OPENINGS BASED ON MEASURED DISPLACEMENTS

In this paper a method is proposed for evaluating the extent of plastic zones appearing around underground openings by using displacements measured during excavations, The elasto-plastic boundary is determined by comparing the maximum shear strain occuring around the openings with the critical shear strain of materials. Both the maximum and critical shear strains can be determined by a back analysis for measured displacements.Computer simulations using the finite element method are carried out in order to prove this proposed method. The method does not require any elasto-plastic analysis, but an only ordinary elastic analysis is sufficient.

Incremental analysis of elastic-plastic frames at finite spread of yielding zones

In elastic-perfectly plastic frames finite zones of yielding develop under monotonically increasing loads. The classical deformation analysis assumes that the elastic rigidity reduces locally to zero at the generalized yield hinges only. Such an approach underestimates the deformations during the loading history and at collapse. A method is proposed in order to evaluate the displacements of elastic-plastic frames when the actual spread of plastic zones is included in the analysis. In comparison with the classical method the developed technique accounts for the axial and flexural stiffness variation along each beam member due to the partial yielding of cross-sections. The actual extent of plastic zones depends on the stress resultant distribution in the structure. The proposed method is based on an incremental analysis procedure formulated by means of the independent elastic-plastic kinematical compatibility equations, and casts a computeroriented technique for evaluating the influence of the finite extension of plastic zones, accounting for the interaction between axial force and bending moment, and for variable crosssections and loads along structural members. The evaluation of the stiffness reduction in the partially plastic elements is specified for Ishape cross-section and is performed according to two different concepts: (a) through an analytical evaluation of the elastic core size, by means of appropriate formulae developed for the cross-section shape under investigation; (b) through a step-wise linear rigidity variation, which requires a preliminary generation of interaction domains of equal stiffness in the space of the active stress resultants for standard profiles. The essential features of the method and those of the program application are illustrated in simple examples, showing the order of magnitude of the actual displacements in comparison with the results of the classical deformation analysis of elastic-plastic frames.

Deflection of elastic-plastic frames at finite spread of yielding zones

Abstract In elastic-perfectly plastic beams and frames finite zones of yielding develop under the collapse load. The classical deflection analysis assumes that the elastic rigidity reduces locally to zero at the yield hinges only. Such an approach underestimates the deflections at collapse. A method is proposed in order to evaluate the displacements of elastic-plastic frames when the actual spread of plastic zones is included in the analysis. In comparison with the classical method the developed technique accounts for the flexural stiffness variation between the hinges and due to the partial yielding of cross-sections. The actual extent of plastic zones depends on the bending moment distribution in the structure. The method contains both the algorithms and program for the deflection evaluation, specified for I-shape cross-sections. The elastic-plastic moment-curvature relations are derived and integrated to obtain additional rotations due to the flexural stiffness variation when the structure transforms in a mechanism. A linear programming program developed earlier is modified to account for the supplementary rotations. The essential features of the method and those of the program application are illustrated purposely in simple examples, showing the order of magnitude of the actual displacements in comparison with the results of the classical deflection analysis of elastic-plastic beams and frames.

Asymptotic techniques in elastic-plastic analysis of structures

Elastic-plastic structures can nowadays be analyzed with the powerful numerical procedures of the finite element method. Nevertheless, in many engineering applications, analytical expressions capable of predicting with sufficient accuracy the stress distributions, the extent of the plastic zones and the load displacement behavior could be of great practical value. For simple structures and loading stages not too far from the elastic limit, such analytical expressions may be obtained by using perturbation methods and asymptotic expansions. A small dimensionless parameter ϵ is defined as the ratio of a length characterizing the extent of the narrow plastic zone, to a conveniently chosen typical dimension of the structure. Stresses and displacements are formally expanded as asymptotic series in terms of powers of ϵ. For each order of magnitude, the exact basic relations lead to a separate set of simplified differential equations which can be integrated analytically or numerically by using standard procedures. The method is very general and can be applied to several classes of plastic behaviour and of structural problems. Three examples of very simple structures are chosen in particular to illustrate the applicability of the perturbation method to engineering problems: (1) For a simply supported beam under a concentrated load, ϵ is chosen as the ratio of the largest axial extension of the plastic zone to twice the beam length. (2) The case of a long thin cylindrical shell subject to a gradually increasing radial ring of load is algebraically more involved but can be treated similarly. (3) For a simply supported circular plate under a ring of load, ϵ is defined as the thickness ratio of the central plastic zone which is assumed to be sufficiently thin in the first stage of loading beyond the elastic limit. Both Tresca's and von Mises' yield criteria with the associated flow rule (rate theory) can be used. The method can also be applied to more involved geometries (in conjunction with linear FE-procedures) and more complex material behaviour.

On the plastic zone and residual stresses within a strip and a half plane under a moving load

A quasi-steady solution has been obtained for the determination of the extent of plastic zones and the amplitude of the residual stresses in (1) an elasto-plastic strip lying on a rigid frictionless base and (2) a half-plane, under the first passage of a moving load. The load is assumed to be applied with a semi-elliptic pressure distribution which is of sufficient magnitude to cause plastic yielding in the body. A work-hardening material obeying von-Mises' yield criterion is considered. A numerical solution procedure, based on discretizing the plastic strain field in the coordinate system moving with the load into uniformly strained rectangular or semi-infinite elements has been developed. Numerical results are obtained for a strip with linear work-hardening material properties. The effect on the distribution of residual stresses created by the ratio of load half-width to strip thickness is also discussed.

An Improved Upper Bound to Maximum Deflections of Elastic-Plastic Structures at Shakedown

ABSTRACT A method is presented providing an upper bound to the maximum shakedown deflections for elastic-perfectly plastic structures. The influence of plastic zones is taken into account. Residual stresses required by the Melan theorem can be expressed in terms of stresses due to ideal plastic hinges and of stresses due to the finite extent of plastic zones. Making use of this fact a bound on the total energy dissipated in a shakedown process as well as a bound to the permanent displacement have been derived. This bound permits an estimate of the deflections at shakedown. Application of the method is illustrated by means of two examples.

The Effect of Plasticity and Crack Blunting on the Stress Distribution in Orthotropic Composite Materials

A detailed study of the plasticity and crack-tip blunting effects on toughening materials with rectilinear anisotropy is presented. The most important results are the prediction of the extent of plastic zone and the nature of stress distribution produced by the blunting effect in the tensile mode. The analysis was confirmed experimentally and numerically (finite-element method) on a unidirectional fiber-reinforced composite.