Complicated Stress Fields Research Articles

Re-orientation of principal stresses during tunnel excavation: Model development and support strategy

The safety and stability during the excavation and production of the tunnel is a key issue that must be addressed in tunneling engineering, which is pronounced under principal stress re-orientation. A mechanical model is therefore developed to determine the boundary curve of the failure zone of a supported circular tunnel under rotating the principal stress direction. Meanwhile, the effects of various environmental factors on the pattern of the failure zone are quantitatively analyzed. Subsequently, two critical morphological indexes are determined to elucidate the uniformity of the failure zone and the functional relationship between these two morphological indices and the environmental factors, respectively. Furthermore, technical approaches and control measures for maintaining the surrounding rock are put forward. In particular, the “long and short” coordinated hierarchical support technology has been recommended and is validated through a comparison of the designed schemes and several engineering cases. The results indicate that the proposed support technology resulted in a gradual reduction of the “butterfly wings” pattern and a more consistent failure zone in the surrounding rock. These findings are useful to ensure the overall stability and anti-interference performance of the surrounding rock of a tunnel under the complicated stress field, especially with regards to the deflection of principal stress.

Phase-Field Modeling of Fused Silica Cone-Crack Vickers Indentation.

In this paper, a 3D phase-field model for brittle fracture is applied for analyzing the complex fracture patterns appearing during the Vickers indentation of fused silica. Although recent phase-field models for the fracture caused by the indentation loading have been verified by some simpler academic axis-symmetric examples, a proper validation of such models is still missing. In addition, heavy computational costs, and a complicated compression stress field under the indenter, which demands different energy decompositions, have been identified as the most important impediments for the successful application of the phase-field method for such problems. An adaptive strategy is utilized for reducing the computational costs, and some modifications are introduced, which enable an accurate simulation of the Vickers indentation fracture. Here, the fracture initiation ring outside the contact zone is detected by using different energy decompositions, and the dominant cone-crack formation under the Vickers indenter is observed. Different contact conditions are investigated. The proposed model is validated by experimental measurements, and a quantitative and qualitative comparison between experimental and numerical results is conducted.

Flexural behavior and durability properties of recycled aggregate concrete (RAC) beams subjected to long-term loading and chloride attacks

Three beams subjected to long-term loading and chloride attacks, with various recycled coarse aggregate (RCA) replacement ratios of 0%, 50% and 100% respectively, were designed to investigate the effects of the RCA replacement ratio on the flexural behavior and durability properties. The results show that a higher RCA replacement ratio has a notable influence on the long-term performance of beams, leading to more chloride ion ingress, more severe steel corrosion and cracking damage, and lower flexural capacity. The maximum chloride content and steel corrosion are observed near the loading points because of the complicated stress fields induced by bending and shear in these regions.

Probabilistic fatigue assessment of notched components under size effect using critical distance theory

Notch features often raise critical influences on fatigue lives of engineering components, which deserve particular attentions for ensuring their structural integrity and reliability. The theory of critical distance provides a simple way to evaluate fatigue lives of notched components without extracting complicated stress fields within the notch vicinities. In this study, a probabilistic model for deducing fatigue life distribution of notched components is established by coupling the Weibull distribution with the theory of critical distance. In addition, the influence of size effect on critical distance values and predicting performance is characterized by two strategies, i.e. average approach and highly stressed volume-based approach. Experimental data of low carbon steel En3B and Al 2024-T351 were utilized for model validation and comparison. Predicted P–S–N curves indicate that the predicted scatter bands using highly stressed volume approach yield better correlations with experimental results than that by the average approach.

Influence of amygdale on crack evolution and failure behavior of basalt

Amygdaloidal basalt is one of the two major types of surrounding rocks that are widely exposed in the super large-scale underground powerhouse caverns of Baihetan Hydropower Station, China. Excavation of the caverns induced a series of mechanical responses, including cracking and fracture relaxation. This study comprehensively explored the deformation and failure characteristics and the fracture evolution process of the amygdaloidal basalt using conventional MTS triaxial laboratory testing equipment and continuous–discontinuous modeling (FDEM) with the aim of clarifying its failure mechanism. The research results indicate that: (1) amygdales significantly changed the deformation and failure characteristics of basalt. Whereas the post-peak mechanical behavior of cryptocrystalline basalt was brittle, that of amygdaloidal basalt was brittle under low confining stresses and ductile under high confining stresses. Meanwhile, whereas the failure mode of cryptocrystalline basalt was fragmentation failure, that of amygdaloidal basalt was splitting failure at low confining stresses and shear failure at high confining stresses. (2) An FDEM model considering the heterogeneity of the rock mesostructure was established based on the statistical laws of the amygdales in real samples, and this confirmed the stress–strain curve characteristics, failure modes, and characteristic strengths measured in laboratory tests. (3) A complicated inhomogeneous stress field formed readily around amygdales and had a significant effect on the fracture path. (4) With an increase in confining stresses, the degree of tensile stress concentration at the upper and lower tips of amygdales decreased and the lateral displacement became restricted. Consequently, the total number of micro-cracks and the ratio of tensile cracks to shear cracks decreased, the crack initiation mode changed from tensional cracking to shear cracking at the tips of the amygdale, and the distribution of crack orientations transitioned from an approximately vertical direction to preferential concentration along fracture planes. The research results form a solid foundation for the accurate understanding of the mechanical response and fracture mechanism of the rock surrounding underground powerhouse caverns at Baihetan hydropower station, and also provide a reference for the prediction of the mechanical properties of rock with flaws and the stability control of engineering rockmasses.

Nonlinear bending and thermal post-buckling behavior of functionally graded piezoelectric nanosize beams using a refined model

We in this paper analyze the problem of the nonlinear bending, thermal buckling and post-buckling of functionally graded piezoelectric material nanobeams based on Eringen’s nonlocal elasticity theory. The beams with immovable clamped ends are exposed to the external electric voltages, a uniform transverse load as well as uniform temperature change. A refined beam model which can transform the Reddy beam model into the Timoshenko beam model is introduced into this study so that we can distinguish the role of transverse shear deformation in complicated stress field. The governing equations are induced by using the generalized variation principle, and then the approximate analytical solution of the FGP material nanobeams for nonlinear, thermal buckling, post-buckling are obtained by using a two-step perturbation method. Subsequently, detailed parametric studies are carried out to get an insight into the effects of different physical parameters, including the slenderness ratio, small scale parameter, volume fraction index and external electric voltages.

Use of analytical lateral-axial strain relation in FE analysis of axially loaded rectangular CFST columns

In a rectangular concrete-filled steel tube (CFST) column under axial compression, the concrete is under non-uniform and anisotropic confining stresses. To simulate such complicated triaxial stress field, finite element (FE) modelling is an effective tool. However, most previous FE models based on the plasticity theory augmented with associated or non-associated flow rules significantly underestimate the lateral and volumetric expansions of concrete at the inelastic stage and thus require solution dependent adjustments for compensation. Herein, an analytical lateral-axial strain relation of confined concrete derived from regression analysis of published experimental results is incorporated in a new FE model for the analysis of axial loaded rectangular CFST columns. This analytical lateral-axial strain relation allows direct evaluation of the lateral strains and should more accurately predict the lateral and volumetric expansions of confined concrete than the plasticity theory. The new FE model is applied to analyse tested specimens in the literature for verification and then used in a parametric study to evaluate the ductility of axially loaded rectangular CFST columns with different structural parameters.

Bi-material V-notched SIFs analysis by XFEM and conservative integral approach

In this paper, a new effective approach based on conservative integral approach associated with extended finite element method (XFEM) is developed for evaluating stress intensity factors (SIFs) of bi-material V-notched structures. The XFEM model for bi-material V-notches is established, which owns various features: (a) jump enrichment functions are taken for describing the intersection of notch-faces; (b) eight (real eigenvalue) or sixteen (complex eigenvalue) branch functions are employed for capturing nodes surrounding the notch-tip; and (c) interface enrichment function is used to model the material interface. These enrichments allow the representation of notch-faces and material interface independent of the finite element mesh. The conservative integral approach derived from the Betti reciprocal principle is used for the evaluation of SIFs. The conservative integral approach avoids the complicated stress fields around the notch-tip, so good accuracy of SIFs can be obtained. Also, the proposed XFEM model can easily be used to solve homogenous V-notched structures by setting the same material parameters of two materials. Numerical results of the SIFs calculated by the present method indicate the independence of integral paths. Several bi-material V-notched numerical examples for single and mixed modes fractures are analyzed to demonstrate the accuracy and effectiveness of the developed method.

Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc

Weight function method is a powerful tool for the determination of key parameters such as stress intensity factors and crack opening displacements for cracks in complicated stress fields. Accurate determination of the weight functions is of primary importance for successful applications of the method. This paper makes detailed accuracy evaluation of two kinds of widely used approximate (2D) weight function approaches, one being based on crack opening displacement for one reference stress, the other on two reference stresses coupled with a geometric condition. To eliminate possible sources of error, the edge-cracked circular disc with exactK-solutions is used for deriving the two kinds of weight functions and for benchmarking against the two weight function approaches. A highly accurate numerical weight function method using the complex Taylor series expansion and complex finite element computation is also used for assessing the related Green’s functions. Results from the evaluation will be instructive for accurate determination of weight functions for other finite edge-crack geometries.

Cymbiola nobilis shell: Toughening mechanisms in a crossed-lamellar structure

Natural structural materials with intricate hierarchical architectures over several length scales exhibit excellent combinations of strength and toughness. Here we report the mechanical response of a crossed-lamellar structure in Cymbiola nobilis shell via stepwise compression tests, focusing on toughening mechanisms. At the lower loads microcracking is developed in the stacked direction, and channel cracking along with uncracked-ligament bridging and aragonite fiber bridging occurs in the tiled direction. At the higher loads the main mechanisms involve cracking deflection in the bridging lamellae in the tiled direction alongside step-like cracking in the stacked direction. A distinctive crack deflection in the form of “convex” paths occurs in alternative lamellae with respect to the channel cracks in the tiled direction. Furthermore, a barb-like interlocking mechanism along with the uneven interfaces in the 1st-order aragonite lamellae is also observed. The unique arrangement of the crossed-lamellar structure provides multiple interfaces which result in a complicated stress field ahead of the crack tip, hence increasing the toughness of shell.

M- and $$\hbox {M}_{\text {int}}$$ M int -integrals for cracks normal to the interface of anisotropic bimaterials

A contour integral termed $$\hbox {M}_{\mathrm{int}}$$ is presented for describing the fracture behavior of cracks passing through or terminating normally at a bimaterial interface. The $$\hbox {M}_{\mathrm{int}}$$ -integral is defined by performing the conventional M-integral along a contour enclosing the cracks, with the coordinate system properly originated for measure of the integration points. The presented formulation is considered to be feasible for problems with generally anisotropic elastic materials. Physically, the energy parameter $$\hbox {M}_{\mathrm{int}}$$ is shown to be equivalent to twice the released potential energy required for creation of the cracks. Such relation is exactly valid when the crack length is small compared with the size of the specimen, and approximately satisfied for problems containing relatively large cracks. Also, due to path-independence, the $$\hbox {M}_{\mathrm{int}}$$ -integral can be performed along an arbitrary outer contour, which is chosen to be far from the crack tips. With this property, the complicated singular stress field in the near-tip areas can be avoided so that a complicated finite element model around the crack tips is not required in the calculation.

Estimation of Stress Corrosion Cracking Growth Behavior Under Weld Residual Stress in the Bottom of a Reactor Pressure Vessel by Finite Element Analysis

A method for evaluating crack growth by repeatedly modeling and analyzing the transitional crack shapes is developed for a general computing environment in which a commercial finite element preprocessor and analysis code are used. The proposed method calculates stress intensity factors (SIFs) by finite element analysis (FEA) by directly distributing estimated weld residual stress obtained from noncracked components on the crack surface on the basis of the superposition principle. In present case, to specify a nonuniform residual stress distribution, a subroutine for a commercial FEA code (ABAQUS) was developed. Arbitrary crack shapes during the crack propagation were expressed by applying the submodeling technique which allowed arbitrary crack shapes to be meshed. The sequence of steps in the proposed method was designed to make it possible to consider complicated stress distributions, such as weld residual stress, and to express arbitrary crack shapes. The applicability of the proposed FEA based method was verified by comparing the result of a stress corrosion cracking (SCC) growth analysis results of a flat plate obtained with the proposed method and with the ASME code procedure. As an application example, the SCC growth behavior of a crack at the bottom of a nuclear reactor pressure vessel (RPV) involving a dissimilar metal weld and a unique geometry was evaluated by the proposed method. The evaluation results were compared with results obtained using a conventional method, i.e., the influence function method (IFM). Since both sets of results were in reasonable agreement, it was concluded that IFM can be applied to this case. Previously, it was difficult to assess the applicability of conventional methods, such as the code procedure and IFM, to a complicated problem because of the existence of complicated residual stress fields, dissimilar metals, and the complicated crack shapes involved. The proposed method using FEA allows the applicability of conventional methods to complicated crack growth evaluations to be assessed.

The microstructure and ferroelectricity of BiScO3–PbTiO3 nanoceramics at morphotropic phase boundaries

Dense (1 - x)BiScO3–xPbTiO3 nanoceramics with morphotropic phase boundaries and an average grain size of 11 nm were prepared. Synchrotron X-ray diffraction studies revealed that tetragonal and monoclinic phases coexist, and the grain boundary regions could be modeled as a paraelectric cubic phase. The grain boundary regions possessed complicated stress and electric fields. The polarization switching became more difficult under electric field due to the restriction and screening effect of grain boundary regions. The nanoceramics retained ferroelectricity with d33* = 292.9 ± 29.8 pm V-1 and d33 = 19.8 pC N-1.

Modelling Crack Growth within Graphite Bricks due to Irradiation and Radiolytic Oxidation

During operation, nuclear graphite structures are exposed to gradients of neutron radiation and temperature. They are also prone to radiolytic oxidation, subsequent porosity changes and weight loss. These processes cause significant changes in the material properties of graphite and create complicated stress fields within graphite bricks. Significant efforts have been made to analyse these stresses over recent years. In this paper, the influence of stresses within a typical graphite brick, during operation, on crack growth is studied. A finite element (FE) mechanical constitutive model is implemented in ABAQUS as a user-subroutine (UMAT) in conjunction with a damage model to simulate crack growth within the graphite brick. The damage model is a linear traction separation model and it is applied with XFEM enrichment to model crack initiation and growth. The results indicate that the cracks initiate in the vicinity of the keyway roots where the maximum principal stress is at its peak. Complete failure was not observed from the simulation of the graphite brick under 30 years of irradiation conditions with a maximum brick temperature of 500°C. Computed stresses and crack lengths were found to be largely dependent on the FE mesh refinement and the results of mesh sensitivity studies are also presented in this paper.

Influence of indenter shape on nanoindentation: an atomistic study

The influence of indenter geometry on nanoindentation was studied using a static molecular dynamics simulation. Dislocation nucleation, dislocation locks, and dislocation movements during nanoindentation into Al (001) were studied. Spherical, rectangular, and Berkovich indenters were modeled to study the material behaviors and dislocation activities induced by their different shapes. We found that the elastic responses for the three cases agreed well with those predicted from elastic contact theory. Complicated stress fields were generated by the rectangular and Berkovich indenters, leading to a few uncommon nucleation and dislocation processes. The calculated mean critical resolved shear stresses for the Berkovich and rectangular indenters were lower than the theoretical strength. In the Berkovich indenter case, an amorphous region was observed directly below the indenter tip. In the rectangular indenter case, we observed that some dislocation loops nucleated on the plane. Furthermore, a prismatic loop originating from inside the material glided upward to create a mesa on the indenting surface. We observed an unusual softening phenomenon in the rectangular indenter case and proposed that heterogeneously nucleating dislocations are responsible for this.

General point load weight function for semi-elliptical crack in finite thickness plates

General point load weight function for semi-elliptical crack in finite thickness plates is derived. It is used to calculate stress intensity factors for any point along the crack front with the crack faces under two dimensional stress distributions. The comparison between the results obtained from the derived weight function and those available in literature is presented, indicating a good accuracy. In order to determine the pattern of crack growth, and to estimate fatigue life, this weight function can be easily used in plates as applied in industry under complicated stress fields such as residual stress field due to welding.

Magnetically actuated peel test for thin films

Delamination along thin film interfaces is a prevalent failure mechanism in microelectronic, photonic, microelectromechanical systems, and other engineering applications. Current interfacial fracture test techniques specific to thin films are limited by either sophisticated mechanical fixturing, physical contact near the crack tip, or complicated stress fields. Moreover, these techniques are generally not suitable for investigating fatigue crack propagation under cyclical loading. Thus, a fixtureless and noncontact experimental test technique with potential for fatigue loading is proposed and implemented to study interfacial fracture toughness for thin film systems. The proposed test incorporates permanent magnets surface mounted onto micro-fabricated released thin film structures. An applied external magnetic field induces noncontact loading to initiate delamination along the interface between the thin film and underlying substrate. Characterization of the critical peel force and peel angle is accomplished through in situ deflection measurements, from which the fracture toughness can be inferred. The test method was used to obtain interfacial fracture strength of 0.8-1.9J/m2 for 1.5-1.7μm electroplated copper on natively oxidized silicon substrates.

Assessing the effect of residual stresses on the fatigue behavior of integrally stiffened structures

Residual stresses emerge quite often in real structures due to the various manufacturing processes such as, welding, forming, cutting, milling, etc. In such cases, development of cracks at regions influenced by manufacturing operations demand additional attention. In the present work a numerical methodology has been developed, based on three-dimensional Finite Element Analysis, for the calculation of Stress Intensity Factors at cracks in welded components. The residual stress fields, which are used in SIF calculations, have been computed by the numerical simulation of the thermo-mechanical process. A numerical algorithm based on interpolation principles is developed, in order to introduce the three-dimensional field in the computational model of the cracked structure. The SIF calculation methodology is initially validated for the case of a welded plate by comparison of numerical results with existing analytical solutions. A cracked stiffened panel is analysed afterwards and the calculated fatigue crack propagation results are compared to experimentally measured data. Finally, the numerical procedure is applied to study the effect of more complicated residual stress fields on SIF values developing at cracks located in stiffened panels.

Stress intensity factor for an embedded elliptical crack under arbitrary normal loading

In this paper we introduce the boundary value problem of three-dimensional classical elasticity for an infinite body containing an elliptical crack. Using the method of simultaneous dual integral equations, the problem is transformed to the system of linear algebraic equations. Stress intensity factor is obtained in the form of the Fourier series expansion. Several solutions for specific cases of applied polynomial stress fields are derived and compared with existing results. Eligibility of the method for more complicated stress fields is demonstrated on the example of partially loaded elliptical crack.

Seismic anisotropy of the crust in Yunnan, China: Polarizations of fast shear-waves

Using seismic data recorded by Yunnan Telemetry Seismic Network from January 1, 2000 to December 31, 2003, the dominant polarization directions of fast shear-waves are obtained at 10 digital seismic stations by SAM technique, a systematic analysis method on shear-wave splitting, in this study. The results show that dominant directions of polarizations of fast shear-waves at most stations are mainly at nearly N-S or NNW direction in Yunnan. The dominant polarization directions of fast shear-waves at stations located on the active faults are consistent with the strike of active faults, directions of regional principal compressive strains measured from GPS data, and basically consistent with regional principal compressive stress. Only a few of stations show complicated polarization pattern of fast shear-waves, or are not consistent with the strike of active faults and the directions of principal GPS compressive strains, which are always located at junction of several faults. The result reflects complicated fault distribution and stress field. The dominant polarization direction of fast shear-wave indicates the direction of the in-situ maximum principal compressive stress is controlled by multiple tectonic aspects such as the regional stress field and faults.