Effect Of Stress Singularities Research Articles

Matching analysis and experimental study of mechanical properties of cement sheath interface

The cement sheath interface is an important component of the wellbore barrier system. A mismatch between the interfaces of the cement sheath may result in leakage. This paper presents a method for assessing cement sheath interface adaptability based on the Dundrus composite parameter method, and the corresponding test flow for evaluating cement sheath integrity is provided for verification. According to the calculation results, stress concentrations are more common at the first interface of the cement sheath. The second interface is relatively unaffected by stress concentration under the same working conditions as the first interface. Stress concentration at the interface can be effectively alleviated by increasing the elastic modulus of the cement sheath or decreasing the Poisson's ratio. However, if the elastic modulus of the cement sheath increases, the cement sheath will be more susceptible to plastic deformation, and the strength coefficient of the singular stress field at the interface will decrease by approximately 10%. As a result, reducing the Poisson's ratio of the cement sheath effectively reduces stress concentration at the interface end. Especially in sandstone formations, the strength coefficient of the singular stress field at the interface can be reduced by 63% at most, resulting in a good interface adaptability. As a result of the above calculations, three groups of cement slurries with different mechanical parameters were selected and tested. As expected, the test results confirmed the applicability of the method. In light of the above results, cement slurry engineers should factor in the stress singularity effect when designing cement slurry systems. To prevent plastic deformation, high-strength and low-elastic cement should be employed, and the Poisson's ratio should be appropriately reduced in order to prevent interface stress concentration, thereby ensuring the integrity of the cement sheath in an increasingly harsh downhole service environment.

Delamination-fretting wear failure evaluation at HAp-Ti-6Al–4V interface of uncemented artificial hip implant

Present research aims to develop a finite element computational model to examine delamination-fretting wear behaviour that can suitably mimic actual loading conditions at HAp-Ti-6Al–4V interface of uncemented hip implant femoral stem component. A simple finite element contact configuration model based on fretting fatigue experimental arrangement subjected to different mechanical and tribological properties consist of contact pad (bone), HAp coating and Ti–6Al–4V substrate are developed using adaptive wear modelling approach adopting modified Archard wear equation to be examined under static simulation. The developed finite element model is validated and verified with reported literatures. The findings revealed that significant delamination-fretting wear is recorded at contact edge (leading edge) as a result of substantial contact pressure and contact slip driven by stress singularity effect. The delamination-fretting wear behaviour is promoted under higher delamination length, lower normal loading with higher fatigue loading, increased porous (cancellous) and cortical bone elastic modulus with higher cycle number due to significant relative slip amplitude as the result of reduced interface rigidity. Tensile-compressive condition (R=−1) experiences most significant delamination-fretting wear behaviour (8 times higher) compared to stress ratio R=0.1 and R=10.

A novel semi-analytical method for notch stress and fatigue strength analysis of tube-flange welded joints

This paper presents a semi-analytic method to rapidly estimate the notch stress and fatigue strength for tube-flange welded joints. Considering the stress singularity effect at the weld toe, the parameters related to geometry and opening angle are simplified as singular intensity factors. The equivalent singular intensity factors can be fitted by the stress distribution rather than the peak stress at the corner. On this basis, the modified notch stress formulas for tube-flange welded joint (TFWJ) under pure bending or torsion load were fitted and verified. Meanwhile, the simple relationships between singular intensity factor, notch stress intensity factor, strain energy density and peak stress were further deduced, separately. The comparison results show that the fatigue assessment parameters calculated by the traditional approaches and the proposed method are in good agreement. Finally, four groups of fatigue data of TFWJs were summarized to verify the simplified assessment formulas.

A simplified method to predict the local stress field and N-SIF of V-shaped notch

The V-notch stress formula based on linear elastic theory shows that the notch stress at the corner tends to infinity due to stress singularity effect. In fact, infinite stress will not be obtained by the results of finite element analysis, and the stress results depend on the mesh size. Based on the concept of singular intensity value 'as', this paper presents a simple formula to evaluate the notch stress distribution and notch stress intensity factor (N-SIF). The simple notch stress evaluation formula has higher fitting precision and practicability. Meanwhile, in order to analyze the influence of mesh size on notch stress, a series of stress results of notched specimens with different opening angles and crack depths are systematically analyzed and compared. On this basis, the relationship equation between singular strength value 'as' and mesh size is derived, which provides a basis for accurately obtaining the N-SIF of V-notch under coarse mesh. After a series of verification, it is found that the result of fatigue strength evaluated by the simplified formula has a smaller scatter band.

Fracture response of 1422-mm diameter pipe with double-V groove weld joints and circumferential crack in fusion line

A circumferential crack in the fusion line is a major threat to the structural integrity of the pipeline girth weld because it may possibly lead to fracture failure when subjected to large plastic deformations. For the newly constructed X80 pipeline with an outside diameter (OD) of 1422 mm in China, the complicated configuration of welded joints and the outer diameter are outside the range of the general fracture assessment standards, such as BS 7910. Furthermore, during the pipe manufacture process, pipeline designers merely specify the minimum yield strength limit according to the pipe steel grade. This results in a wide variation range in the choice of yield strength values of the base metal. This also leads to a serious problem in the fracture assessment of pipe girth weld because the weld strength is commonly considered to be either evenly matched or overmatched. The foregoing factors make it difficult to perform an accurate fracture assessment using conventional standards. This study therefore aims to investigate the fracture behavior of 1422-mm OD pipelines with a double-V groove weld and circumferential crack in the fusion line. The specific effect of material mismatch and the realistic operational parameters that influence the fracture capacity of the pipe are examined via a series of numerical investigations. First, a rigorous three-dimensional finite element model to simulate the pipe girth weld is established by utilizing the ABAQUS finite element code package. The weld, which has a canoe-shaped surface crack in the fusion line between the heat-affected zone and root welding metal, is subjected to biaxial loading conditions. The keyhole method is adopted to simulate the crack front as well as the crack tip to eliminate the stress singularity effect during deformation. A refined mesh strategy is introduced to ensure the accurate simulation of the stress and strain fields in the vicinity of the crack tip. Based on the numerical model, the J-integral fracture parameter, which is clearly defined based on a strict mechanical theory, is chosen to characterize the effect of strength matching ratio, internal pressure, and yield to tensile strength ratio on the crack driving force. A new strain-based J-integral prediction formula is proposed based on numerical results.

Effective notch stress method for fatigue assessment of sheet alloy material and bi-material welded joints

Abstract As notch stress can effectively reflect the influence of welding geometry on local stress concentration, it can be used for fatigue strength evaluation of complex welded joints. In order to avoid stress singularity effect caused by the corner, virtual radius is introduced into fatigue evaluation of welded structures. However, the virtual radius recommended by the current specifications is only for steel and aluminum alloy materials, and is not applicable for thin-plate structures, especially for welded structures of special alloy materials and dissimilar materials. Considering the influence of alloy materials and size effect on hypothetical virtual notch stress, based on effective notch stress theory and finite element method, the optimal virtual radius values suitable for thin-plate alloy welded structures are proposed and verified respectively. After optimizing the virtual radius, the scatter band index of the notch stress S–N curve is significantly lower than the result of nominal stress.

A combined FEM and three-dimensional asymptotic solution based analysis on stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in stretched plates

C0-type triangular “layered” plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST) are employed to investigate the weakening effects of localized elliptical (circular being a special case) cylindrical surface flaws in isotropic plates. Numerical results indicate severe transverse shear deformation in the vicinity of a surface flaw boundary. In addition, a recently developed asymptotic solution to the problem pertaining to the stress fields in the neighborhood of the circumferential corner line or line of intersection of a circular cylindrical external part-through open hole and an interior surface of an isotropic plate, subjected to far-field extension (mode I), in-plane shear (mode II) loadings, is presented. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening plates, are numerically assessed, because of their role in crack initiation.

Stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in cross-ply plates and validity of St. Venant’s principle in the presence of interacting singularities

Effects of localized elliptical (circular being a special case) cylindrical surface flaws in laminated composite plates are investigated by using C°-type triangular composite plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST). Numerical results for a cross-ply laminate compromised by the presence of an external part-through elliptical/circular cylindrical slot indicate the existence of severe cross-sectional warping in the vicinity of the surface flaw and plate boundaries. Furthermore, three-dimensional nature of the stress concentration factor in the neighborhood of the elliptical or circular cylinder shaped surface flaw boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the surface flaw. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening laminated composite plates, are numerically assessed, because of their role in crack initiation. Finally, the interaction of this singularity with free edge stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of St. Venant’s principle) in regards to testing of laminated composite specimens are thoroughly investigated.

Evaluation of Fatigue Damage in Adhesive Bonding: Part 2: Single Lap Joint

The damage parameters for crack initiation in a single lap joint (SLJ) are determined by combining continuous damage mechanics, finite element analysis (FEA) and experimental fatigue data. Even though a SLJ has a simple configuration, the stresses in the adhesive region are quite complex and exhibit multi-axial states. Such a condition leads to the need to introduce a general value for the triaxiality function in the damage evolution law rather than using a triaxiality function which equals unity, as in the case of a uni-axial stress state, e.g., the bulk adhesive test specimen presented in Part 1 of this paper. The effect of stress singularity, due to the presence of corners at edges, also contributes to the complex state of stress and to the variability of the triaxiality function along the adhesive layer in a SLJ. The damage parameters A and β determined in Part 1 for bulk adhesive are now extended to take into account the multi-axial stress state in the adhesive layer, as calculated from FEA.

Effect of Stress Singularity on Stress Distribution and Initial Debonding of Interface End

Interfacial stress distribution of bonded quarter planes subjected a concentrated force was re-investigated based on Bogy’s solution [1]. It’s found that the characteristic length of the singularity of interface end (δ), varies with the index of stress singularity at interface end from millimeter to nanometer. This is a unique characteristic of stress singularity at interface end. How the characteristic length of the singularity of interface end (δ) influences the initial de-bonding of the interface end is a new question worth to pay attention. It’s found in the photoelasticity experiments that usually the debonding initiated at the interface end with singularity, but as the index of stress singularity, as well as the characteristic length of singularity of interface end, decrease to some extent, the initial debonding moves to an inner point near the interface end. This phenomenon clearly shows the index of stress singularity has obvious influence on the debonding of interface end.

The Effects of Stress Singularity on Welded Gusset Plates Loaded in Tension

In spite of the extensive study of gusset plates under monotonic tension loading over the years, the stress singularity (unbounded stress) effect caused by the boundary condition at the corners of the fixed edges of the plates has seldom been considered by researchers and structural design engineers. Since the development of the tensioned stress concentration resulting in fracturing of gusset plates can be expedited by the stress singularity effect, the effects of stress singularity on steel gusset plates should not be neglected. The stress concentration of welded gusset plates caused by the stress singularity effect is investigated using the finite element method in this study. Numerical investigations of the interaction between the stress singularity effect on the gusset plates and the Whitmore effective section of the gusset plates are also conducted. Based on the investigation results, optimal configurations and modified Whitmore effective widths for gusset plates loaded in tension are presented and discussed. Later in this paper a practical design example is given which considers both the optimal configuration and the modified Whitmore effective section of the gusset plate.

Stress Singularity Effect on Beam Flanges in Moment Connections

The ductility capacity of the directly welded flange connection was found to be insufficient after the 1994 Northridge earthquake. The Enlarged End Section (EES) connection which considers the stress singularity effect on beam flanges can be utilized as a means to improve the performance of welded moment connections. The corner of a steel plate contains stress singularities (unbounded stresses) when the corner is bounded by free-free edges and when the angle of the corner is larger than 180°. Also, the corner of a steel plate contains stress singularities when the corner is bounded by fixed-free edges and when the angle of the corner is larger than 61.3°. Nonlinear static finite element analyses of two types of beam-to-column moment connections were conducted. These two types of connections are (1) the constant-beam-section connection, and (2) the Enlarged End Section connection. The result of the finite element analyses shows that the Enlarged End Section connection exhibits much higher strength and ductility capacities.

Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement

Peak stress levels predicted in finite element analysis (FEA) usually depend on mesh density, due to singular points in the model. In an earlier study, an FEA algorithm was developed to simulate the damage accumulation process in the cement mantle around total hip replacement (THR) implants. It allows cement crack formation to be predicted, as a function of the local cement stress levels. As the simulation is driven by mesh-dependent peak stresses, predicted crack formation rates are also likely to be mesh dependent. The aim of this study was to evaluate the mesh dependence of the predicted crack formation process, and to present a method to reduce the mesh dependence. Crack-propagation experiments were simulated. Experimental specimens, representing transverse slices of cemented THR reconstructions, were subjected to cyclic torsional loading. Crack development around the corners of the stem was monitored. The experiments were simulated using three meshes with increasing levels of mesh refinement. Crack locations and orientations were accurately predicted, and were virtually independent of the level of mesh refinement. However, the experimental crack propagation rates were overestimated considerably, increasing with mesh refinement. To eliminate the effect of stress singularities around the corners of the stem, a stress averaging algorithm was applied in the simulation. This algorithm redistributed the stresses by weighted spatial averaging. When damage accumulation was computed based on averaged stresses, the crack propagation rates predicted were independent of the level of mesh refinement. The critical distance, a parameter governing the effect of the averaging algorithm, was optimized such that the predicted crack propagation rates accurately corresponded to the experimental ones. These results are important for the validity and standardization of pre-clinical testing methods for orthopaedic implants.

Failure Transition in Fatigue Crack Propagation of Epoxy Adhesives under Mode I Loading. Effect of Stress Singularity at the Interfacial Edges of DCB Specimens on Failure Transition.

Fatigue crack initiation and propagation behaviors in DCB specimens were investigated using a rubber modified epoxy as adhesive. Glass substrates were used to observe the failure transition (cohesive→interfaicial) in fatigue crack growth. In order to know the effect of stress singularity at the interface edges on the failure transition, tapered and chamfered DCB specimens. (S55C substrates) having nominaly zero/greatly reduced stress singularities were also used. The experimental results revealed that a cohesive fatigue crack in the adhesive layer once stopped with decreasing a strain energy release rate range. Simultaneously a new interfacial crack initiated and propagated near the arrested crack tip. Tapering and chamfering the edges of DCB adherends delayed the interfacial crack initiation. It was found that the interfacial crack initiation due to stress singularity at the interfacial edges was the major driving force for failure transiton.

Finite Element Analysis of Stress Singularities in Attached Flip Chip Packages

Cracking and delamination at the interfaces of different materials in plastic IC packages is a well-known failure mechanism. The investigation of local stress behavior, including characterization of stress singularities, is an important problem in predicting and preventing crack initiation and propagation. In this study, a three-dimensional finite element procedure is used to compute the strength of stress singularities at various three-dimensional corners in a typical Flip-Chip assembled Chip-on-Board (FCOB) package. It is found that the stress singularities at the three-dimensional corners are always more severe than those at the corresponding two-dimensional edges, which suggests that they are more likely to be the potential delamination sites. Furthermore, it is demonstrated that the stress singularity at the upper silicon die/epoxy fillet edge can be completely eliminated by an appropriate choice in geometry. A weak stress singularity at the FR4 board/epoxy edge is shown to exist, with a stronger singularity located at the internal die/epoxy corner. The influence of the epoxy contact angle and the FR4 glass fiber orientation on stress state is also investigated. A general result is that the strength of the stress singularity increases with increased epoxy contact angle. In addition, it is shown that the stress singularity effect can be minimized by choosing an appropriate orientation between the glass fiber in the FR4 board and the silicon die. Based on these results, several guidelines for minimizing edge stresses in IC packages are presented. [S1043-7398(00)00904-X]

Computational methods for creep fracture analysis by damage mechanics

Some mechanical problems of the computational method of creep fracture analysis based on continuum damage mechanics are discussed. After brief review of the local approach to creep crack growth analysis by means of finite element analysis and continuum damage mechanics, intrinsic feature of the fracture analysis in the framework of continuum theory and the causes of mesh-dependence of the numerical results are discussed. Then, a series of numerical analyses are performed for a plate specimen with a central crack to show the characteristics of the mesh-dependence. In view of these results, the effects of stress-singularity at the crack tip as an essential cause of the mesh-dependence are discussed by analyzing the magnitude of stress in the finite element at the crack-tip. As another major cause of the mesh-dependence of the numerical results, ill-natured stress-sensitivity of the constitutive and the evolution equation of the conventional Kachanov–Rabotnov creep damage theory is elucidated by performing sensitivity analysis of the relevant equations. In order to suppress this singular stress sensitivity at the critical stage of damage, a new creep damage model is developed. Finally, the effects of the preceding damage field on stress singularity of the asymptotic stress field at mode I creep crack are analyzed to furnish a criterion to overcome the mesh-dependence in computational method for creep fracture analysis.

On cracks emanating from wedges in expanded PVC foam

An experimental and analytical study was made on the effect of stress singularities on the strength of expanded PVC foam materials of different densities. Experiments were performed on specimens with different wedge geometries ranging from sharp cracks, with the ordinary inverted square root stress singularity, to shallow reentrant corners with weak singularities. A brittle fracture criterion based on a generalized stress intensity factor, called Q, at the wedge tip was fitted to experimental data. The critical stress intensity factor, Q cr for crack initiation depends on the wedge geometry. This dependence was estimated from simple point-stress criteria and a criterion due to Seweryn [Brittle fracture criterion for structures with sharp notches. Engng Fracture Mech. 47, 673–681 (1994)] and good agreement with experimental data was obtained. When the point-stress criterion was applied to Mode II sharp cracks, poor agreement with published data was found. A critical study of the Mode II crack specimen was therefore initiated, leading to the conclusion that the commonly used specimen gives erroneous values of K IIc and the reason seems to be due to crack surface friction. A new Mode II crack specimen which eliminates crack surface friction was proposed and tested, and good agreement with the point-stress criterion was obtained. A criterion for homogeneous materials proved to be adequate also for the porous PVC foams.

Investigation into Subdivided FEM Model of DIssimilar materials Effect of Stress Singularity on Subdivided FEM Model.

In this work, a proper subdivided finite-element method (FEM) model was investigated to analyze the residual stress on dissimilar materials. Stress singularity is one of the most important factors in the evaluation of the residual stress distributions. As the results of FEM analysis for residual stress are affected by the subdivided model, calculated stress singularity is compared with Bogy's theory to discuss the reliability of the applied model. With TiB2-Ni bonding material, the index of stress singularity was analyzed using some subdivided FEM models. It was found that a proper subdivided FEM model existed in which the calculation converged.