Shape Of Plastic Zone Research Articles

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.

Analytical solution of the stress field and plastic zone at the tip of a closed crack

The investigation of stress field and plastic zone distribution at the closed crack tip provides a fundamental basis for failure analysis and life prediction of geotechnical materials. Closed crack is a common crack in geotechnical materials. Studying the distribution of stress field and plastic zone at the tip of closed crack can provide theoretical basis for stability evaluation of geotechnical structures. In this study, we employ the superposition principle to obtain complex function solutions for the stress field and displacement field at the crack tip. Furthermore, we analyze the plastic zone distribution at the crack tip based on the Mohr Coulombs criterion. We investigate how factors such as crack angle, confining pressure, and material properties influence the stress field, displacement field, plastic zone size, and crack propagation direction. Our results demonstrate that this method effectively characterizes the distribution of stress field and displacement field at closed crack tips. Moreover, we elucidate that wing cracks are primarily formed due to tension-shear coupling effects. The solutions for the stress field and displacement field at the crack tip are obtained using the superposition principle. The distribution of the plastic zone at the crack tip is analyzed based on the M-C (Mohr-Coulomb) criterion. Subsequently, an analysis is conducted to investigate the influence of crack angle, confining pressure, and material properties on stress field, displacement field, plastic zone, and crack propagation direction. Lower crack angles and higher confining pressures effectively suppress slip between crack surfaces by reducing tension-shear coupling effects and inhibiting wing foil crack development. The results further indicate that the rock cohesion and internal friction angle exert negligible influence on the stress field, displacement field, plastic zone shape at the crack tip, as well as the growth direction of new cracks. The results demonstrate the effective representation of stress field and displacement field at the closed crack tip using this method. The stress distribution at the crack tip reveals that the tension-shear coupling effect primarily contributes to wing crack formation. Lower crack angles and higher confining pressures effectively suppress surface slip, reduce tension-shear coupling effects, and inhibit wing crack propagation. Furthermore, material properties do not influence the crack propagation angle, stress field, or displacement field.

Study of cyclic plastic zone ahead of the fatigue crack tip using Digital Image Correlation system

Structural components are susceptible to cyclic loadings during their operation. They are more prone to failure due to localized plastic deformation. The plastically deformed region ahead of the crack tip due to fatigue loading is the important factor responsible for fatigue crack propagation. The plastically deformed region is separated into monotonic and cyclic plastic zones. The cyclic plastic zone (CPZ) is approximately 1/3rd to 1/4th of the monotonic plastic zone (MPZ). The existing analytical expressions to calculate the size of the CPZ are based on elastic perfectly plastic analysis. In this paper, an experimental technique, namely 3D-Digital image correlation (DIC), is used to evaluate the size of the CPZ during the fatigue crack growth rate (FCGR) tests on CT specimens. The DIC system having two cameras is used to capture high-resolution images of crack region of CT specimen surface during the FCGR tests. The FCGR tests are carried out on nuclear piping material steel SA333Gr6 under constant load range and constant load ratio. The post-processing of DIC images revealed an asymmetric butterfly-type shape of the cyclic plastic zone. The DIC evaluated CPZ was compared with the CPZ obtained by a calibrated cyclic plasticity material model-based finite element (FE) analysis. It was observed that the average difference between DIC evaluated experimental CPZ and CPZ calculated by plane stress-based FE analysis is about 5%.

Research on the differentiated support technology for roadways based on the mechanical response of the plastic zone

AbstractWith the advancement of coal resources mining to the deep part, the control of the surrounding rock of the roadway has become one of the main problems in the field of mining. At the present stage, the bolt support technology of the roadway in China still faces problems such as unclear support mechanism and poor support effect. Based on the mechanism of bolt support, through theoretical analysis and experimental research, this study proposes the differentiated support technology for roadways based on the mechanical response of the plastic zone and applies this method in the Gada Coal Mine. The results of the study showed that the plastic zones with different shapes have different mechanical responses. compared with other plastic zone shapes, the control method of the roadway with a butterfly‐shaped plastic zone is more complex. Consequently, the support design of a bolt should not only consider the scope of the plastic zone of support construction but also grasp the development law of the plastic zone. Effective support measures should be taken as early as possible for roadways with butterfly‐shaped plastic zones to prevent aggressive development of the butterfly‐shaped plastic zone. Field tests show that this support method realizes the ideal supporting effect in practical applications.

The Change in the Shape Characteristics of the Plastic Zone in the Surrounding Rock of an Auxiliary Retracement Channel and a Reasonable Channel Spacing Determination Method

In underground coal mines, the stability of the retracement channel in the surrounding rock is crucial for the safe and efficient retracement of the equipment and to guarantee the continuity of the retracement work. To reveal the deformation and damage mechanism of the surrounding rock of an auxiliary retracement channel (ARC) and the determination method for the reasonable spacing of two retracement channels during the end of the mining period, the deviatoric stress field in front of the working face and the change in the shape characteristics of the plastic zone in the ARC are investigated in this paper. The formation of ultimate stress equilibrium, high deviatoric stress, decreasing deviatoric stress, and low deviatoric stress environments in front of the working face during the end of mining occur successively, and the different deviatoric stress environments are the main reasons for the different shape characteristics of the plastic zone in the surrounding rock. The changes in the shape characteristics of the plastic zone correspond to the changes in the shape characteristics in the zone with deviatoric stress and exhibit the following order: full plastic deformation zone, butterfly-shaped zone, elliptical zone, and circular plastic zone. A reasonable spacing determination method for the two retracement channels is proposed: the ARC is arranged in the decreasing deviatoric stress environment, where the surrounding rock plastic zone shape is elliptical, and the ARC is relatively stable. Based on this research result, the spacing of the double retracement channels at the Lijiahao 22-116 working face was determined to be 25 m, which achieved a positive application effect and allowed the safe and efficient retracement of the working face equipment.

Crack tip plastic zone shape for anisotropic material subjected to mode -I loading

This paper discusses the effect of anisotropy in terms of anisotropy ratio on ductile materials subjected to mode-I type of loading. Thin plate with plane stress condition is considered for this work. σ3 is taken as zero. For considering the effect of Poisson’s ratio, σ3 = ν (σ1 + σ2) is considered. Isotropic plane strain and anisotropic plane stress condition is considered to develop mathematical relations for stress triaxiality and plastic zone around the crack tip by using Hill – von Mises’s yield criterion. The effect of poisons ratio, anisotropy ratio and stress triaxiality is shown on the size of plastic zone around the crack tip. The results were generated and are compared in the form of polar plot for plane strain condition at different Poisson’s ratio. In addition to this, the effect of anisotropy ratio on stress triaxiality is also investigated. It was observed that increase in Poisson’s ratio causes significant reduction in the size of plastic zone around the crack tip. The increase in anisotropy ratio also shows the same trend, especially for its higher values. It is observed that anisotropy plane stress problem of fracture is almost equivalent to isotropic fracture in plane strain condition.

Investigation of Plasticity Effects on Growing Fatigue Cracks Using the CJP Model of Crack Tip Fields.

A growing fatigue crack gives rise to a plastic enclave that envelops the crack and can exert a shielding effect on the crack from the global elastic stress field driving fatigue propagation. This work presents the potential of the CJP model of crack tip fields to investigate the plasticity-induced shielding effects on growing fatigue cracks as well as its ability to characterise the size and shape of the plastic zone generated at the tip of a growing fatigue crack. The model was specifically developed to consider the influence of the plastic enclave generated around a fatigue crack on the surrounding elastic material. Different aspects related to fracture mechanics and its implications for fatigue crack growth have been investigated, namely plasticity-induced crack shielding, the retardation effect induced on fatigue crack growth due to the application of an overload and the estimate of the size and shape of the crack tip plastic zone. The model has been successfully applied by analysing displacement fields experimentally measured by DIC in different CT specimens made of 2024-T3 aluminium alloy and commercially pure titanium. Results presented in this work intend to contribute to a better understanding of the shielding effects during fatigue crack growth.

Roles of in-plane and out-of-plane T-stresses in crack tip plastic zones and fracture toughness under mixed mode I/II loading

Crack tip plasticity and fracture toughness are usually connected with T-stresses under mixed mode I/II loading conditions. By means of von Mises yield criterion, a new analytical solution of plastic zone size is proposed for mixed mode I/II cracks, and the theoretical relation is determined between plastic zone size and in-plane and out-of-plane T-stresses. Then three constraint parameters, i.e. rpmin1/2, rpmax1/2 and Apz1/4, are theoretically derived from plastic zone sizes and area. Subsequently, the influences of T-stresses and mode mixity on plastic zones are investigated. Based on the experimental data, the combined effects of in-plane and out-of-plane T-stresses on fracture toughness are analyzed in Al 7075-T651 and Al 7075-T6 alloys by using constraint parameters. The results show that, the size and shape of plastic zone are significantly affected by both in-plane and out-of-plane T-stresses, and also strongly influenced by mode mixity. For small scale yielding, the new analytical solution of plastic zone size is reasonable, and the constraint parameters rpmin1/2, rpmax1/2 and Apz1/4 are applicable for characterizing the in-plane and out-of-plane constraint effects comprehensively in mixed mode I/II cracks, then there are linear correlations between constraint parameters and fracture toughness.

Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation

The evolution of the plastic zone underneath the indenter is challenging to be described during nanoindentation, which is recently known to be crucial to establish a constitutive model that features the plastic properties of the substrate materials based on their indentation responses. Using molecular dynamics and axisymmetric finite element (FE) simulations in this study, we show that the plastic zone shape in the elastoplastic materials is hemispherical in a broad range of length scales under a three-sided pyramid-shaped Berkovich indenter. By considering the critical factors of the applied load–penetration depth (P–h) curve, dimensional analysis is performed to derive dimensionless functions regarding the radius of the hemispherical plastic zone. For the loading and unloading stages in extensive FE simulations, a set of polynomial functions are proposed by associating the instantaneous and residual plastic zone radii with constitutive parameters. In addition to Young's modulus and the hardening exponent, the ratio of the representative stress to the reduced modulus is found to be crucial for predicting the plastic deformation. Lastly, the proposed dimensionless function reveals that the plastic zone radii are drastically different for three representative materials with identical P–h curves as confirmed by three independent methods. This result suggests that the proposed plastic zone radius in the dimensionless analysis helps to overcome the challenging uniqueness issue for decades to determine the unique elastoplastic properties of materials based on nanoindentation responses.

Elastic Stress and Plastic Zone Distributions around a Deeply Buried Tunnel under the Nonhydrostatic Pressure

The elastic stress and the plastic zone are the important mechanical parameters to determine the tunnel support design. Based on Muskhelishvili’s complex variable function, the analytical solution for the elastic stress around a deeply buried noncircular tunnel under the nonhydrostatic pressure is firstly derived. The shape and size of the plastic zone of the surrounding rock mass are then determined by substituting the elastic stresses into the Drucker-Prager yield criterion. Finally, taking a horseshoe-shaped tunnel as an example, the analytical solutions of elastic stress distribution and plastic zone shape around the tunnel under different lateral pressure coefficients are in good agreement with ANSYS numerical solutions. The calculation results show that if the vertical in situ stress exceeds the critical value, with increasing lateral pressure coefficient, the hoop stress at the roof and floor of the tunnel increases significantly and the shape and size of the plastic zone change obviously.

The Research on Stability of Surrounding Rock in Gob-Side Entry Driving in Deep and Thick Seam

The gob-side entry driving is driving in low pressure area, which bears less support pressure and is easy to maintain, so it is widely used. Taking the gob-side entry driving in thick coal seam of Dongtan Coal Mine as an example, the reasonable size of pillar and the section of roadway are numerically simulated by combining numerical with measurement, and the roadway support is designed. According to the distribution of lateral stress in working face, eight pillars of different sizes are designed. By simulating and comparing the stress distribution of surrounding rock and the development range and shape of plastic zone in different positions, the pillar size of gob-side entry driving is optimized to be 4.5 m. According to the results of optimization of roadway section, the section of straight wall semi-circular arch roadway is adopted. According to the analysis, the roadway is supported by bolt + steel mesh + anchor cable. By observing the stability of roadway, it provides experience for the stability study of roadway the gob-side entry driving with small pillar in thick seam.

Combined approach for fatigue crack characterisation in metals

In this work a comprehensive characterisation of the fatigue crack growth of an Al 2024 alloy is presented. A powerful Christopher-James-Patterson (CJP) model is used for multi-parameter characterisation of the crack state at a few different locations through the fatigue crack growth. The CJP model of crack tip displacements and stress fields was proposed in order to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic-plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been verified. Thus, the model can predict the driving force component of the crack and additional components that account for different shielding mechanisms. CJP model is combined with full-field non-contact Digital Image Correlation (DIC) so that the model can be fed at any moment with real experimental information. The results are then correlated with Paris law data for Al 2024 alloy through Scanning Electron Microscopy (SEM) observations of the fracture surface. In this work the effect of crack length and load level are thoroughly studied and validated with fatigue crack growth rate measurements.

Plastic zone analysis of SS316L and Ti6Al4V materials under mixed mode loading conditions

In present work, plastic zone size and shapes are investigated to predict failure of hip implant materials Ti6Al4V and SS316L (titanium and stainless steel, respectively). Generally, they fracture due to crack propagation in presence of wear which initiates the crack. Plastic zone analysis of SS316L and Ti6Al4V are carried out under standard fracture modes of failure that are first and mixed mode (tensile and shear loading). Crack inclination angle is one of the important parameters to simulate mixed-mode loading conditions. Analytical formulations of plastic zone analysis validated by finite element modeling based on von-Mises criteria. Further, isolines are plotted which explains the variation of plastic zone and geometry near the crack tip. Results obtained under plane strain and plane stress conditions through analytical formulations are in close relevance with FEM. Finally, it is observed that SS316L has large plastic zone which results in slower crack propagation and better life as compared to Ti6Al4V.

Stress resultant plasticity for plate bending in the context of roll forming of sheet metal

AbstractModeling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach toward constructing the governing equations of bending of an elastic‐plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for a material surface, namely resultant bending moments and dissipative work. This function is then identified by comparison of the exact solutions for a uni‐axial or isotropic bending experiment within the structural model and with the continuum model of a through‐the‐thickness element. We validate the approach against both the fully three‐dimensional simulations as well as the results of the traditional elastic‐plastic plate analysis, the latter one featuring the continuum laws of plasticity treated in the integration points along the thickness direction. We considered benchmark problems from the literature as well as a prototype for the roll forming problem. Besides good agreement regarding the shape of plastic zones and force‐deflection characteristics, experiments also demonstrate higher computational efficiency of the new stress resultant model.

New algorithm for optimised fitting of DIC data to crack tip plastic zone using the CJP model

The work presented in this paper provides guidance in optimally determining the appropriate fitting region used in digital image correlation (DIC) when fitting a crack tip field model to DIC data. In this work, the technique is applied to the CJP crack tip field model and uses the Levenberg-Marguardt (L-M) iterative method to solve for the crack tip position. This is combined with an error analysis of the main term of the Williams series expansion for crack tip stresses and the extrapolation of Saint-Venant’s principle to determine the optimum fitting region for use in DIC fit with the multi-parameter solution for the CJP crack tip field model. A comparison is then made between the size and shape of the crack tip plastic zone obtained using the Williams and the CJP models. This demonstrated that as the plastic zone size increased, there was a deterioration in accuracy of the description of the crack tip plastic zone using the Williams series expansion, while the CJP description remains more accurate. In addition, KF, the stress-intensity factor that drives crack growth in the CJP model has a strong linear relationship with the plastic zone area, which indicates that KF is a direct driving force for crack growth and there is a clear relationship between ΔKCJP and ΔKI.

Research on the Deformation Mechanism of Mining Roadway Stratiform Surrounding Rock with Nonuniform Stress Field

Aiming at the failure problems of mining roadway stratiform surrounding rock influenced by asymmetrical high stress, firstly, the rock instability conditions of different structural plane angles were summarized based on the mechanical model of rock joints and instability criterion. Secondly, stresses, plastic zone, and displacement of surrounding rock with different structural plane angles were calculated and analyzed with the theoretical calculation method or numerical simulation method, respectively. The distribution characteristics of plastic zone of surrounding rock under different influence factors are further studied, and the results show that the lateral pressure coefficient can change the size and shape of plastic zone at the same time. The damage mechanism was analyzed through the above study. Research studies show that the shear and tension failure area of plastic zone were directly determined by the maximum shear stress and the minimum principal stress. The effect of structure planes on stress has two sides, one to destroy the continuity and the other to strengthen discreteness and laddering nature. When the angle between maximum shear stress and structure plane increases, the extended mode and distribution pattern of plastic zone change substantially as well. The #15 haulage roadway is taken as engineering background, and the above research’s results are verified by the comprehensive analysis. The research results can enrich the butterfly plastic zone theory and provide the basis for roadway supporting design.

Toward revealing full atomic picture of nanoindentation deformation mechanisms in Li2O-2SiO2 glass-ceramics

Obtaining full understanding of deformation mechanisms in Li2O-2SiO2 glass-ceramics subjected to sharp contact loading is a pressing need for many industrial applications. We herein conduct systematic molecular dynamics simulations to reveal atomic details that are otherwise extremely challenging to probe experimentally. Our study shows that glass-ceramics exhibit a dramatically different plastic deformation map compared to glass, where the nanocrystalline phase dictates the plastic zone shape. Shear flow preferentially nucleates and travels along the interfaces before moving to the surrounding glass and nanocrystals. Dislocations, amorphization zones around the indenter, and shear flow at glass and crystal interfaces help to dissipate contact energy and deconcentrate the deformation, thereby increasing fracture toughness and discouraging the development of catastrophic cracks. Additionally, extensive discussions on the effect of LS2 nanocrystal aspect ratio, location and orientation with respect to indenter in shaping the plastic zone also help to establish a solid knowledge in understanding surface damage behaviors of glass-ceramics as observed in many real applications.

Surrounding Rock Failure Characteristics and Water Inrush Mechanism of Roadway above the Aquifer in Nonuniform Stress Field

The expansion of the roadway surrounding rock failure zone may connect the floor aquifer and cause the roadway water inrush. In order to reveal the mechanism of the roadway water inrush above confined water, we established the force model of the roadway surrounding rock above confined water in nonuniform stress field and studied the shape characteristics and expansion law of the roadway surrounding rock plastic zone. The results show that the roadway surrounding rock will form three kinds of plastic zone under different lateral pressure coefficients: circular, elliptical, and butterfly; when the shape of plastic zone is circular or elliptic, the maximum radius increases linearly with the increase of regional stress; when the shape is butterfly, the maximum radius increases exponentially with the increase of stress. Under the condition of a larger bidirectional stress ratio, the surrounding rock of the roadway will show butterfly-shaped failure, and small stress change will cause malignant expansion of the plastic zone; when the plastic zone is connected with the underlying aquifer, confined water of floor will enter the rock mass from the water diversion point and eventually flood into the roadway, causing floor water inrush.

A quantitative evaluation method on the stability of roadway surrounding rock in partial confining stress based on plastic zone shapes

The reliability of reinforced concrete structures is frequently compromised by the deterioration caused by reinforcement corrosion. Evaluating the effect caused by reinforcement corrosion on structural behaviour of corrosion damaged concrete structures is essential for effective and reliable infrastructure management. In lifecycle management of corrosion affected reinforced concrete structures, it is difficult to correctly assess the lifecycle performance due to the uncertainties associated with structural resistance deterioration. This paper presents a stochastic deterioration modelling approach to evaluate the performance deterioration of corroded concrete structures during their service life. The flexural strength deterioration is analytically predicted on the basis of bond strength evolution caused by reinforcement corrosion, which is examined by the experimental and field data available. An assessment criterion is defined to evaluate the flexural strength deterioration for the time-dependent reliability analysis. The results from the worked examples show that the proposed approach is capable of evaluating the structural reliability of corrosion damaged concrete structures.

Fracture mechanisms and micromechanical deformation processes of polyethylene/calcium carbonate nanocomposite films

AbstractThe fracture behavior of medium density polyethylene/calcium carbonate (MDPE/CaCO3) nanocomposites was evaluated using the essential work of fracture (EWF) test. Fracture surfaces and the deformation zone in front of the precrack were studied using different microscopy techniques. Microscopic observations proved that extensive shear deformation of matrix due to debonding of nanoparticles plays the most important role on deformation mechanism of polyethylene nanocomposite. Large quantities of energy can be absorbed by plastic deformation of matrix polymer. This is why the specific plastic work (wp) of nanocomposites is higher than that of polyethylene. The presence of voids formed due to debonding of nanoparticles, reduces the load carrying capacity of the matrix and consequently leads to the reduction of the specific EWF (we). Besides, it causes easily crack propagation that may restricts the area where plastic deformation takes place and results in the reduction of plastic zone shape factor (β).