Plastic Zone Research Articles

Analytical solutions of combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay

AbstractThis paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first‐order differential equations by using the axisymmetric condition, equilibrium equations, and elastic‐plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress‐strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.

Research on the plastic radius of pile penetration in CPT clayey seabed

Offshore jackups are frequently employed for well workover or maintenance operations, necessitating repeated usage at the same location. Precisely defining the radius of the soil's plastic zone during pile penetration offers a theoretical foundation for establishing the minimum pile spacing required for subsequent well workover or maintenance activities. This study examines the radius of the plastic zone in the seabed of silty soil in the offshore region of the Yellow River Delta and the bearing capacity at various pile diameters following pile penetration, utilizing the Cone Penetration Test (CPT). The specific conclusions are as follows: (1) The disturbance radius of pile penetration into seabed silty soil ranges from approximately 2D to 3D; (2) Utilizing the pile bearing capacity calculation method proposed by Eslami and Fellenius, it is determined that the bearing capacity at a distance of 2.66D from the pile core is equivalent to the initial penetration bearing capacity; (3) According to the Mohr-Coulomb yield criterion theory, the plastic radius of pile penetration in seabed silty soil is calculated to be between 2.4D and 3.2D; (4) The disturbance radius derived from fitting the optimal bearing capacity curve aligns with the minimum pile spacing calculated according to the Mohr-Coulomb yield criterion theory, thereby confirming that the CPT test can accurately estimate the plastic radius of pile penetration.

Failure mechanism analysis and support strength determination of deep coal mine roadways – A case study

In order to solve the problems related to deformations, failures, and difficulties in support controls of deep coal mine roadways, the typical failure forms and characteristics of deep coal mine roadways were investigated and analyzed in this study. The distribution laws of plastic zones of circular roadways under different lateral pressure coefficients were expounded using a theoretical analysis method, and the influence of plastic zone scopes on the failure forms of roadways was explained. In addition, considering the distribution characteristics of plastic zones, a calculation method of the required support strength based on the plastic zone scopes was proposed. The primary and secondary factors affecting the support strength were then determined. A numerical simulation method was applied in order to analyze the distribution characteristics of the displacements and plastic zones of deep mine circular roadways under the conditions of no support scheme, an existing support scheme, and a support scheme determined by the proposed support strength calculation method (referred to in this study as the optimized support scheme), respectively. The simulation results showed that the support effects of the optimized support scheme were superior to those of the existing support scheme, and thereby more conducive to maintaining roadway stability. In addition, an on-site engineering test method was used to identify support schemes for bolting and shotcrete with wire mesh + concrete-filled steel tubular supports based on the plastic zone scopes and the support strength of roadways in order to determine the support parameters. As indicated by the field monitoring results, the proposed support strength calculation method and optimized support scheme had shown the ability to effectively control the large deformations of the tested roadway, and thereby guarantee its overall stability.

Short fatigue crack growth and retained austenite in steels processed via quenching and partitioning

Previous research has consistently found that introducing metastable retained austenite (RA) as a second phase retards the failure of steel under fatigue. However, the reasons for this benefit are not understood. Accordingly, the properties of RA most advantageous to resist fatigue are not known. Within this context, this paper examines the interaction between second-phase RA and short fatigue crack growth in a steel processed via quenching and partitioning, using quasi in situ electron backscatter diffraction experiments. Results show that most RA transforms into martensite under the plastic strain surrounding the crack. They also reveal various mechanisms whereby RA transformation delays short fatigue crack propagation; transformation-induced crack closure (TICC), crack deflection and branching, and roughness-induced crack closure (RICC). Crack deflection and branching are driven by a tendency of cracks to propagate towards transformed RA, which is against the previous assumptions in the literature. Furthermore, the impact of crack deflection/branching on retardation is more powerful than that of TICC acting alone. Microstructures including second-phase RA should avoid RA-lean areas and promote elongated RA grains, with relatively large size, and major axis normal to the preferential crack growth direction. Untransformed RA within the plastic zone (i.e. overstabilized) does not contribute to crack retardation.

Fatigue Crack Propagation Across the Multiple Length Scales of Technically Relevant Metallic Materials

The fundamentals of our understanding of fatigue crack propagation were formed more than 60 years ago by Paul C. Paris. Since then, the run toward new metallic materials and alloys with ever finer-grained microstructures has had a large impact on research. Along with enormous variation of the microstructural length scales (i.e., grain size), the essential parameters for the description of fatigue crack growth, such as the crack propagation rate and plastic zone size, also exhibit an immense change from the subnanometer to the micrometer regime. These enormous variations in the fatigue crack growth behavior's controlling parameters motivate this contribution. This article presents an overview of the effect of grain size, from the millimeter to the nanometer grain-size regime, on fatigue crack propagation of mainly ductile metals and alloys with an attempt to summarize the most important findings and underlying physical phenomena, including with respect to selected materials such as pure iron, nickel, and austenitic and pearlitic steel.

Investigation of fatigue crack growth behavior and crack tip plastic zone characteristics in welded structures based on local displacement fields

The fatigue crack growth behavior in welds is difficult to evaluate due to complex internal stresses and microstructural differences. This paper uses the CJP model based on displacement field variations to describe the fatigue crack growth behavior and the size of the crack tip plastic zone in welds. First, fatigue crack growth rate tests were conducted on base metal and as-welded specimens. The digital image correlation technique was used to capture the speckle pattern variations on the specimen surface during crack growth, obtaining the crack tip displacement field required by the CJP model. Based on this, by calculating the stress intensity factor ranges ΔK and ΔKCJP, two da/dN–ΔK(ΔKCJP) curves defined by the traditional and CJP models were obtained, proving the model’s applicability for describing fatigue crack growth behavior in welded joints. Finally, the CJP model was used to calculate and compare the crack tip plastic zones of base metal and as-welded specimens. It was found that the maximum error for the as-welded specimen was 37.84%, occurring at the initial stage of crack propagation and gradually decreasing with the fatigue process.

Mechanism and Prevention of Rock Burst in a Wide Coal Pillar under the Superposition of Dynamic and Static Loads

To address the frequent occurrence of rock burst disasters in areas with wide coal pillars during mining in the western mining area of China, the wide coal pillar area of the Tingnan coal mine in Shanxi Province was used as the research background. Theoretical analysis, numerical simulation, and field tests were used to establish the mechanical criterion and the energy criterion for the dynamic instability of wide coal pillars. The process and mechanism of wide coal pillar dynamic instability under dynamic and static load disturbances were revealed, and a wide coal pillar rock burst prevention and control scheme was proposed. The results indicated that when the load above a coal pillar reached the stress failure index and the energy failure index was met, the coal pillar reached the critical conditions for rock burst. With increasing static load, the stress, energy, and range of the plastic zone all showed increasing trends on both sides of the coal pillar. Under a given dynamic load, the stress and plastic zone range of the coal pillar significantly increased compared to those without a dynamic load. Under a given static load, the greater the dynamic load, the more likely the coal pillar was to undergo dynamic instability. The evolution of coal pillar dynamic instability was divided into three stages: energy accumulation, local instability, and dynamic instability. When the critical stress and energy conditions for coal pillar dynamic instability are exceeded, rock burst will occur. To reduce the static and dynamic loads of coal pillars, a rock burst prevention and control scheme of energy release and load reduction was proposed and applied onsite. The monitoring results showed that this control plan effectively reduced the stress of the coal pillar and the dynamic load generated by the fracture of the overlying rock layer, indicating safe mining in this area of wide coal pillars.

A Numerical Study of Reinforcement Structure in Shaft Construction Using Vertical Shaft Sinking Machine (VSM)

Using the Vertical Shaft Sinking Machine (VSM) for shaft construction is an emerging modern technology, which is also currently one of the most advanced techniques in the field of shaft sinking. Current research on VSM technology primarily focuses on mechanical and technical issues, neglecting the impact of the construction on the surrounding soil and the structure itself. This oversight leaves structural design lacking a reliable foundation. Additionally, there is insufficient information on the role of reinforcement design during construction in soft soils. These engineering challenges have hindered the widespread implementation of this new technology. Therefore, a series of numerical models were used to analyse the mechanical behaviour of shaft and soil during or after the sinking process, with the aim of addressing these gaps by investigating the influence of shafts constructed using VSM technology, and providing a scientific basis for reinforcement design in soft soil. The case study shows that increasing the soil-cement strength does not have a significant effect on the overall deformation of the soil surrounding the shaft, but leads to a notable reduction in the plastic zone volume, subsequently enhancing the overall stability of the neighbouring soil. The ring bottom beam design effectively reduces convergence deformation by about 50%, while also improving the horizontal internal force distribution near the cutting edge. However, this approach significantly escalates local vertical bending moments, necessitating thorough consideration in the design stage.

On the anisotropic fracture behaviour of AA2050-T84 thick plate

Anisotropy in the fracture behaviour of AA2050-T84 was investigated using 2D digital image correlation (DIC)-assisted 3-point bending fracture toughness test on specimens with crack propagation direction oriented along the normal direction (ND) and rolling direction (RD). The tensile properties along the RD indicated slightly higher yield strength (482 ± 8 MPa) than ND sample (469 ± 9 MPa), while the fracture toughness in terms of energy release rate was higher when the notch was oriented along the ND (35.3 ± 1 kJ/m2) compared to the RD (18.5 ± 0.9 kJ/m2). Fractography of the fractured surfaces and detailed electron backscatter diffraction (EBSD) analysis of the microstructure along crack paths unveiled higher crack tortuosity with extensive secondary cracking in the TD-ND specimen than in the TD-RD. DIC measurements clearly showed a larger deformation zone for the TD-ND specimen also as which corroborated the plastic zone size determined using linear elastic fracture mechanics (LEFM). Additionally, the crystallographic model of tilt and twist angle differences between the neighbouring grains was employed to explain the increase in crack path tortuosity and higher dissipation of plastic work contributing to superior fracture toughness for the TD-ND sample.

Investigation into the stress‒strain compatibility and fracture behaviour of a TC18 titanium alloy with a multistage lamellar microstructure

Understanding the fracture mechanism is essential for optimizing the mechanical properties of titanium alloys. The relationship between fracture behaviour and the multistage lamellar microstructure of the TC18 (Ti–5Al–5Mo–5V–1Cr–1Fe) alloy was investigated via in situ tensile and three-point bending tests. The results indicate that the TC18 alloy, featuring a multistage lamellar microstructure (including a β matrix, primary lamellar α phase, bundles, and secondary lamellar α phase), exhibits an excellent combination of strength and ductility. The precipitation of the secondary lamellar α phase significantly enhances the alloy's strength but weakens the stress‒strain compatibility of the microstructure. This results in a smaller crack-tip plastic zone (CTPZ) and causes dislocations to concentrate more at the grain boundaries and, to a lesser extent, at the phase interfaces. Consequently, in the later stages of crack propagation, microvoids and microcracks tend to form at dislocation pile-ups. With increasing stress, these microvoids and microcracks rapidly coalesce, leading to a greater proportion of intergranular fracture and thus reducing the fracture toughness of the alloy.

Elastoplastic mechanical behavior analysis of surface-coated Zircaloy-4 cladding under multi-field coupling

The elastoplastic mechanical behavior of Zircaloy-4 (Zr-4) cladding, coated with chromium (Cr) or FeCrAl on its surface, is explored under the coupled effects of multi-field coupling. Utilizing the Finite Element Software ABAQUS, simulations are conducted to calculate the evolution of stress and strain over two complete fuel cycles. Comparisons are drawn between the coated and uncoated Zircaloy-4 cladding materials. The results indicate that the application of surface coatings significantly mitigates stress levels in the cladding during the first fuel cycle. During the second fuel cycle, all three types of cladding exhibit relatively minor plastic strain, which is attributed to the unloading and reloading process between cycles. Notably, the plastic zone propagates from the interior to the exterior of the cladding. When compared to traditional Zircaloy-4 cladding, the coated cladding exhibits improved elastoplastic mechanical behavior. The operational mechanism of the coating for different stresses in cylindrical coordinates and its response to unloading and reloading cycles are also investigated. Specifically, the coated claddings exhibit an evident delay in reaching full plasticity compared to uncoated claddings. Furthermore, FeCrAl coating material initially shows good performance, and it needs to be verified in more aspects in the future. Results and Conclusions in this paper can provide reference and guidance for future experiments.

Isothermal and thermomechanical fatigue crack growth behavior and modelling of 316LN stainless steel with the superposition of HCF loading

This work comparatively investigates the effect of superposition of high-cycle fatigue (HCF) loading on the crack growth behavior of 316LN stainless steel in isothermal fatigue (IF) and thermomechanical fatigue (TMF) tests. Results show that a deflection of the crack growth rate is observed in the tests without HCF loading. The superposition of HCF loading leads to a marked increase of crack growth rate in IF and out-of-phase TMF tests while a minimal variation in in-phase TMF test. Moreover, the crack growth rate in in-phase TMF test is smaller than the IF and out-of-phase TMF tests due to the different shape and evolution behavior of plastic zone at crack tip. Finally, the model based on the cumulative damage rule of time-dependent and cycle-dependent components is proposed, which considers the characteristics of plastic zone size and grain size and leads to a satisfactory prediction result.

High-resolution measurement of contact stresses and friction in indentation and machining by full-field photoelasticity

An experimental study has been made of the sliding plastic contact in wedge indentation and machining of ductile metals. The use of full-field photoelasticity has allowed direct determination of interface pressure and shear stress distribution along the tool (indenter) and workpiece sliding contact at micron-scale resolution. Sapphire, a transparent photoelastic material that possesses sufficiently high hardness to indent and machine metals, is used as the tool material. It is shown that the Coulomb friction model applies only at the edges of the contact where the interface pressure falls below a certain value associated with the material's flow stress. Within the plastic contact zone, the mode of friction as well as the relationship between interface pressure and shear stress are very complex. In both cases, it is shown that shear stress neither remains constant nor varies in proportion to the pressure. It is proposed that the complex nature of friction and stress field at the sliding contact can be understood through simultaneous observations of the metal plastic flow at and near the interface. Using in situ measurements of the velocity field near the interface and local stress distribution at the contact from photoelasticity, friction contribution to the overall work is calculated and shown to be substantial (greater than one-third) in the case of machining.

Research on Stability of Mining Roadway of "Three Soft" Coal Seam based on FLAC3D

In order to reduce the serious roadway deformation during mining, the support scheme is optimized. Based on the actual geological data of mining roadway 11070, the plastic zone morphology, stress field and displacement distribution of roadway under different support schemes are analyzed by numerical simulation. The results show that scheme 1 has better supporting effect and higher roadway stability, which provides a reference for the same type of roadway support.

Effects of drilling parameters on stress relief performance during mining

Abstract This study investigated the effects of borehole diameter and borehole interval on the stress relief performance of coal seams during mining. A discrete element numerical model was established based on the Voronoi and block models, and the stress relief performance was investigated in terms of axial stress, vertical displacement, and plastic zone development using the control variates method. The results showed that a decrease in the distance from the workface was accompanied by an increase in the effects of mining, the stress concentration, and the vertical displacement of the roof. Coal mining had positive effects on fracture propagation in front of the workface. As the borehole interval increased, the density of boreholes in the coal seams decreased, reducing the stress concentration and fracture propagation in front of the workface. The stress relief performance of the boreholes in the coal seams was improved at an borehole interval of 8 m. However, as the borehole diameter increased, the stress concentration near the boreholes decreased, reducing the effects of the workface mining on stress relief through the boreholes. Meanwhile, increasing the borehole diameter decreased the vertical displacement of the roof but exacerbated fracture propagation in front of the workface, which improved the stress relief performance of the boreholes in the coal seams. This study provides a reference for arranging boreholes in coal seams during mining.

Seismic Performance of Precast Concrete Exterior Beam-Column Joint with Disc Spring Devices

ABSTRACT To improve the seismic performance of precast concrete reinforced frame structures which are widely used worldwide, and enable a certain repairable function for the precast structure after an earthquake, this paper proposes a new type of precast concrete frame joint using a full grouting sleeve connection with a disc spring device. The disc spring device was connected in series to the longitudinal reinforcement located in the plastic hinge zone at the beam end to provide a restoring force and protect the concrete. Six exterior beam-column joints consisting of one cast-in-situ beam-column joint and five precast concrete frame joints, using a fully grouted sleeve connection equipped with or without a disc spring device, were designed and fabricated. The failure process, hysteretic characteristics, and energy dissipation capacity of the joint specimens were analyzed based on reversed cyclic loading test. The results showed that the energy dissipation and seismic performance of the newly precast concrete joints equipped with the disc spring device were better than those of the precast concrete frame joints connected by ordinary grouting sleeves without a disc spring device. The disc spring device proposed in this study plays a similar role as a damper in the precast joint during loading and has the characteristics of concentrated damage as it transfers part of the damage in the joint core area to the built-in disc spring area at the beam end. Additionally, the deformation of the precast joints under a lateral seismic load was theoretically calculated, the calculated results were in good agreement with the experimental results.

Assessment of failure modes of a rising stem type gate valve according to ASME BPVC Section-VIII, Division-2 criteria

Assessing the structural integrity of valves is crucial during the development process. Design by analysis involves evaluating unconventional geometries and loads by researching and classifying stresses, then comparing them to allowable values. Although ASME BPVC Section-VIII, Division-2 does not specifically cover valves, key valve design standards reference this code. Hence, this numerical study aims to develop and apply specialized stress analysis models for evaluating plastic collapse and local failure in a rising stem-type gate valve. The methodology is developed to assess the elastic behavior of the valve under stress to evaluate plastic collapse. It is also designed to assess plastic collapse and local failure by considering the material’s behavior beyond the elastic range and into the plastic deformation zone. A numerical model using the ANSYS–MECHANICAL tool was developed based on the finite element technique. The main failure modes of a rising stem-type gate valve according to ASME BPVC Section-VIII, Division-2 criteria were considered. The main contribution to valve development is providing specialized stress analysis models and numerical simulations, mainly focusing on the rising stem-type gate valve and aligning it with relevant ASME standards. The results showed that the maximum von Mises stress in the valve body was 200.6 MPa, staying below the yield limit, while the screws surpassed the yield limit with 725.72 MPa, entering the plastic deformation zone.

Development of Plastic Zone Near Tip of Interfacial Crack with Contacting Faces

Development of Plastic Zone Near Tip of Interfacial Crack with Contacting Faces

Fatigue fracture of 316L steel manufactured by selective laser melting method

The kinetics of short cracks in 316L steel samples made by selective laser melting was studied. The structural sensitivity of such cracks, which form on technological defects at the early stage of fatigue is noted. The cracks develop predominantly along the fusion boundaries and slow down their growth at the boundaries of the melt pools. An increase in the crack opening of arrested cracks lead to the formation of a plastic zone at their tips, localization of deformation, a decrease in opening and continued growth with an increase in the number of cycles. The alternation of the processes of propagation and deceleration of short cracks during loading is reflected in the kinetic diagram of fatigue failure which has rate growth thresholds with spacing between them being close to the scanning step during steel manufacturing. The diagram is described by the Paris equation with the same exponent at the growth stage of both short and long cracks. The plotted fatigue curve was compared with fatigue curves for the same material produced by traditional and additive methods. It was shown that the plotted fatigue curve, as well as the fatigue curves for similar materials taken from literary sources, lie much lower than the fatigue curve for the same steel obtained by the traditional method. However, the use of optimal manufacturing modes, as well as subsequent heat treatment, leads to the fatigue characteristics of «additive» steel being similar to those of steels produced by the traditional method. The macro- and microrelief of the fracture surfaces of the samples was studied, the stages of stable and accelerated crack growth were identified, the crack lengths at fracture surfaces corresponding to these stages were evaluated and the predominate fracture mechanisms at each stage were described. It is shown that the observed knee point in the fatigue curve is accompanied by an increase in the damage of the lateral surface of the samples with an increase in the stress amplitude and transition to a more ductile fracture relief, which is explained by the switch from the plane-strain state to a plane-stressed state of the sample material realizing at the tip of the macrocrack.

Research on crack distribution characteristics and control technology of surrounding rock in soft rock roadway under different lateral pressure coefficients

AbstractTo solve the problem of controlling large deformation of surrounding rock in deep soft rock roadway, the distribution characteristics and deformation mechanism of surrounding rock cracks in soft rock roadway under different lateral pressure coefficients are studied using numerical simulation, theoretical analysis, and field measurement. The results show that under different lateral pressure coefficients, the range of surrounding rock cracks shows three forms: round, oval, and butterfly. No matter what lateral pressure coefficient the roadway is in, the surrounding rock cracks always appear in the plastic zone, and there is a high correlation between the surrounding rock crack range and the plastic zone. The stress characteristics of the surrounding rock in the plastic zone include two main aspects. One is that the direction of the principal stress of the surrounding rock is deflected, which is manifested as an annular distribution of the direction of the maximum principal stress around the roadway. The direction of the minimum principal stress in the upper part of the roadway points to the center of the roadway, and the direction of the minimum principal stress in the lower part of the roadway deviates from the center of the roadway. Second, the ratio of the maximum to minimum principal stress in the surrounding rock is large. Under this stress characteristic, the surrounding rock in the plastic zone has strong shear dilation. The shear dilation makes the crack of the surrounding rock open so that the surrounding rock is squeezed into the roadway space, and then the roadway produces large deformation. Due to the large range of cracks in the butterfly‐shaped plastic zone, the shear dilation deformation produced by the butterfly‐shaped plastic zone is far more than that of the round/oval plastic zone. According to the crack range of roadway surrounding rock under different lateral pressure coefficients, the corresponding support scheme is put forward. Field experiments show that the support scheme can effectively control the deformation of surrounding rock and meet the requirements of roadway use.