Strain Concentration Factors Research Articles

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.

応力集中部に存在するき裂のCTOD簡易推定方法に関する研究

In this study, new evaluation method of local strain for the fracture assessment of the crack in the strain concentration was proposed. This method based on the relationship between the definition of local strain applied to the assessment method for brittle fracture of steel-frame structure WES2808-03 and liner fracture mechanics.2-dimensional FE-analyses of the cross weld joint models with weld toe crack were conducted. Local strains at the stress concentration were calculated by the proposed method and CTODs were measured. And the relationships between local strains and CTODs were discussed. These results were compared with the CTOD design curve employed in WES2805-97 and the Level 2 FAD employed in BS7910-99, and the accuracy of assessment curves was investigated. The results demonstrate that the CTOD design curve gives slightly conservative estimation but FAD gives unsafe estimation in the case of Lr > 1.The relationship among stress concentration factor and crack size and K-value was also investigated, and the suitability of estimation equation of strain concentration factor employed in WES2805 was discussed. The equation gives smaller strain concentration factor, but the influence of the results on the CTOD estimation by CTOD design curve is not serious.

A Study on the Structural Stress Analysis of the Steel and the GFRP Laminated Composite Cylindrical Shell with a Stiffened Circular Cutout

The strain distribution around the unstiffened and stiffened circular cutout of the isotropic stainless steel (ANSI type 304) and the GFRP laminated composite cylindrical shells subjected to axial compression are studied. The experimental results are obtained and compared with numerical analysis. In experiment, the strain is measured around the circular cutout by strain measuring system under the axial uniform compression loading. The numerical analysis is performed by the commercial finite element code ANSYS. The strain concentration factor (SCF) is defined to investigate the strain concentration around the circular cutout. The SCF of the stainless steel cylindrical shell with a stiffened cutout is decreased 39% in experiment and 50 % in numerical analysis. The SCF of GFRP laminated composite cylindrical shell is decreased 22% in experiment and 31 % in numerical analysis.

Stress and strain concentration factors of completely overlapped tubular joints under lap brace IPB load

This paper presents parametric equations to predict the stress concentration factor (SCF) of completely overlapped tubular joints under lap brace in-plane bending (IPB) load. A completely overlapped tubular joint specimen is first tested for the verification and calibration of finite element (FE) models. The experimental results showed that the strain distribution near the weld toe is fairly linear. The maximum strain concentration factor (SNCF) of the joint occurs at the lap brace crown heel under IPB load. For the FE analysis, both 8-node thick shell and 20-node solid elements are suitable for modelling the joint. A set of parametric equations is proposed for predicting the SCF of completely overlapped tubular joints based on 5184 FE models. The parametric equations are verified against the acceptance criteria of Fatigue Guidance Review Panel. The assessment of the proposed equations is based on the database of FE analysis and test results. The comparison of SCF between the proposed parametric equations and the existing T / Y -joint parametric equations showed that the results do not agree reasonably well under IPB load.

Stress and strain concentrations of completely overlapped tubular joints under lap brace OPB load

The stress and strain concentrations of a completely overlapped tubular joint specimen are experimentally investigated under lap brace out-of-plane bending (OPB) load. The experimental results showed that the strain distribution near the weld toe is fairly linear. The maximum strain concentration factor of the joint occurs at the through brace saddle near the lap brace. For the finite element (FE) analysis, both 8-node thick shell and 20-node solid elements are suitable for modelling the joint specimen. A set of parametric equations is proposed for predicting the stress concentration factor (SCF) of completely overlapped tubular joints based on 5184 FE models. The parametric equations are verified against the acceptance criteria of Fatigue Guidance Review Panel. The assessment of the proposed equations is based on the database of FE analysis and test results. The comparison of SCF showed that the existing T/Y-joint parametric equations for predicting the SCF of completely overlapped tubular joints are inappropriate under OPB load.

Strain and stress concentration of completely overlapped tubular CHS joints under basic loadings

A completely overlapped tubular circular hollow section (CHS) joint specimen is tested under lap brace axial loading (AX), in-plane (IPB) and out-of-plane bending (OPB) to determine the strain concentration factor (SNCF) at the intersection of members for the verification of a finite element (FE) model. The experimental results showed that the strain distribution on the outer surface of members near the weld toe of the joint is fairly linear. The maximum SNCF of the joint occurs at the through brace saddle near the lap brace under AX and OPB and at the lap brace crown heel under IPB. The SNCF at the intersection of the chord and through brace for the joint under IPB and OPB is negligible. For the FE analysis, the comparison of SNCF between the test specimen and the 8-node thick shell FE model under AX, IPB and OPB load cases shows reasonably good agreement with average differences of 7.9%, 10.6% and 5.8% respectively. The comparison of stress concentration factor (SCF) revealed that the existing T/Y-joint equations are not suitable for predicting the SCF of completely overlapped tubular CHS joints. The SCF of completely overlapped tubular CHS joints can effectively be reduced by proper control of its geometrical properties.

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.

Load combination effects on stress and strain concentration of completely overlapped tubular K(N)-joints

The stress and strain concentration of a completely overlapped tubular K(N) joint specimen under lap brace axial (AX), in-plane (IPB) and out-of-plane bending (OPB) is experimentally investigated. The combination effect of these loadings on the stress concentration of the joint is also studied. The test results showed that the maximum strain concentration factor of the joint under AX and OPB occurs at the saddle of through brace near the lap brace. For the joint under IPB, it occurs at the crown heel of lap brace. The peak hot spot stress (HSS) of the joint under combined loading is found occurred at a position between the crown and the saddle of members. A comparison of HSS showed that the equation proposed by Gulati et al. agrees reasonably well but the design recommendation, API RP2A, over predicts the test data. In the numerical analysis, the finite element model with 8-node thick shell element simulates very well the joint specimen. It is concluded that the existing equation for simple joints based on a superposition of stresses of basic load cases is suitable for predicting the stress concentration of completely overlapped tubular K(N)-joints under combined loading.

Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending

The FEM is employed to study the effect of notch depth on a new strain-concentration factor (SNCF) for rectangular bars with a single-edge notch under pure bending. The new SNCF K ε new is defined under the triaxial stress state at the net section. The elastic SNCF increases as the net-to-gross thickness ratio h 0/ H 0 increases and reaches a maximum at h 0/ H 0 = 0.8. Beyond this value of h 0/ H 0 it rapidly decreases to the unity with h 0/ H 0. Three notch depths were selected to discuss the effect of notch depth on the elastic–plastic SNCF; they are the extremely deep notch ( h 0/ H 0 = 0.20), the deep notch ( h 0/ H 0 = 0.60) and the shallow notch ( h 0/ H 0 = 0.95). The new SNCF increases from its elastic value to the maximum as plastic deformation develops from the notch root. The maximum K ε new of the shallow notch is considerably greater than that of the deep notch. The elastic K ε new of the shallow notch is however less than that of the deep notch. Plastic deformation therefore has a strong effect on the increase in K ε new of the shallow notch. The variation in K ε new with M/ M Y, the ratio of bending moment to that at yielding at the notch root, is slightly dependent up to the maximum K ε new for the shallow notch. This dependence is remarkable beyond the maximum K ε new . On the other hand, the variation in K ε new with M/ M Y is independent of the stress–strain curve for the deep and extremely deep notches.

Effect of notch depth on strain-concentration factor of notched cylindrical bars under static tension

Abstract The effect of the notch depth on the strain-concentration factor (SNCF) is studied for circumferentially notched cylindrical bars under static tension. The employed new SNCF is defined under the triaxial stress state at the net section. The elastic SNCF increases as the net-to-gross diameter ratio d 0 / D 0 increases and reaches a maximum at the depth of d 0 / D 0 ≈ 0.7 . Beyond this value of d 0 / D 0 it rapidly decreases to the unity with d 0 / D 0 . The elastic SNCF of the extremely deep notch of d 0 / D 0 = 0.2 is almost equal to that of the shallow notch of d 0 / D 0 = 0.95 . Nevertheless, the SNCF of the shallow notch sharply increases with plastic deformation at the notch root, while the SNCF of d 0 / D 0 = 0.2 increases only slightly. The SNCF of the deep notch of d 0 / D 0 = 0.6 also increases with plastic deformation and reaches a peak value. This peak value is nearly equal to or slightly lower than that of the shallow notch and hence the plastic SNCF of shallow notches cannot be neglected. The variations of the SNCF with P / P Y , the ratio of tensile load to that at yielding at the notch root, depends only on the notch geometry up to general yielding.

純曲げを受ける片側切欠材のひずみ集中係数

The strain-concentration factor was calculated using finite element method for plane-strain rectangular bars with a single-edge U-notch under pure bending. The strain-concentration factor employed is newly defined under the triaxial stress state at the net section. This new strain-concentration factor increases from its elastic value to the maximum as plastic deformation develops from the notch root. The maximum strain-concentration factor of a shallow notch is considerably greater than that of a deep notch, although the elastic strain-concentration factor is reversed. Plastic deformation around the notch root has a stronger effect on the strain-concentration factor of shallow notches. This is because plastic deformation develops mainly in the vicinity of the notch root for shallow notches. The strain-concentration factor employed here corresponds well to the distribution of the longitudinal strain at the net section. The variation of the strain-concentration factor with M/MY, the ratio of bending moment to that at yielding at the notch root, is dependent on the stress-strain curve for shallow notches, especially beyond the deformation level at which the maximum strain-concentration factor occurs. The integral of the longitudinal strain at the net section is negative in elastic deformation for single-edge notches. It varies from negative to positive value with plastic deformation around the notch root.

Parametric equations for stress concentration factors in completely overlapped tubular K(N)-joints

This paper presents parametric equations to predict the stress concentration factors (SCF) of completely overlapped tubular K(N)-joints under lap brace axial compression. 192 finite element (FE) models of the joint have been created for the parametric study using a commercial FE package, MARC. In the analysis, both 8-node thick shell and 20-node solid elements are found suitable for modelling the joint. The comparison of strain concentration factors (SNCF) between the FE models and the tested specimen shows that the difference is less than 0.42. However, in view of the computational effort, the FE model with 8-node thick shell element is used for the parametric analysis. The study reveals that the effect of through brace to chord wall thickness ratio on SCF of the joint is most crucial. The maximum SCF occurs on the through brace saddle near the lap brace. The gap size on the through brace surface between the outer surfaces of the chord and the lap brace significantly affects the SCF. Based on the FE data, a set of parametric equations is derived to predict the SCF of the joint. The reliability of the equations has been verified against the requirement of the Fatigue Guidance Review Panel.

The application of a homogenized overall and local anisotropic damage constitutive model to unidirectional and cross-ply CFCC with oblique loading directions

A homogenized anisotropic damage constitutive model is proposed to describe the mechanical behavior of continuous fiber-reinforced ceramic matrix composites (CFCC) for different loadings direction and laminate stacking sequences. An overall fourth-order damage effect tensor is introduced to account for the overall damage of the composites. In addition, two local (matrix and fiber) fourth-order damage effect tensors are introduced to analyze the local effects of damage experienced in both matrix and fibers. The overall and local damage tensors are correlated through a homogenization procedure. New expressions are derived for the stress and strain concentration factors of the damaged composite. The model is simulated by macro-microscopic finite element method (FEM). As applications of the model, unidirectional and cross-ply CFCC laminates with oblique loading directions are analysed to discuss the effects of fiber arrangement and orientation on the macroscopic mechanical behavior.

Numerical determination of representative volumes for granular materials

A numerical approach has been proposed to quantify the size of representative volume elements (RVEs) for materials that consist of particles in a matrix material. Various series of random particle distributions with different densities have been generated, which are used as input for nonlinear finite element simulations. A statistical procedure has been used to determine averages and standard deviations for each test series. Several criteria have been taken to quantify the size of the RVE, including peak load, dissipated energy and strain concentration factor. The various criteria lead to different RVE sizes. Furthermore, the sensitivity of these three properties to the particle size distribution is assessed. An investigation is made in which smaller particles in an RVE were replaced by larger ones while the aggregate density distribution was kept constant. Finally, the interaction is studied between the size of the RVE and the internal length scale of the underlying level of observation.

A Homogenization Procedure for the Numerical Simulation of Mechanical Behavior of CFCC by Considering the Overall and Local Anisotropic Damage

An anisotropic damage constitutive model was presented to characterize mechanical behavior of continuous fiber-reinforced ceramic matrix composites (CFCC) with two-scale damage. An overall fourth-rank damage effect tensor was introduced to account for the overall damage of the composite system. In addition, two local (matrix and fiber) fourth-rank damage effect tensors were introduced to account for the local effects of damage experienced by both the matrix and fibers. The overall and local damage tensors were correlated together using homogenization procedure. In terms of the homogenization methods, the effective elastic properties were obtained, and the stress and strain concentration factors were derived for damaged composites. The model was applied in detail to the unidirectional laminate that was subjected to uni-axial tension. The results were compared well with experimental data. The effects of important parameters such as the fiber volume fraction and the damage material parameters on the nonlinear behavior of the composites were investigated. The model provided a useful tool for understanding the overall dependence of stress-strain behavior on all the underlying constituent material properties.

浅い環状切欠のひずみ集中係数(材料力学)

浅い環状切欠のひずみ集中係数(材料力学)

606 純曲げを受ける片側切欠材のひずみ集中係数(材料力学)

606 純曲げを受ける片側切欠材のひずみ集中係数(材料力学)

CEA and JNC approaches for creep–fatigue evaluation of weldments and inter-comparison through benchmark analyses

Creep–fatigue is an important failure mode in elevated temperature components especially for weldments. To establish rational design-by-analysis methods for weldments, the CEA and JNC have developed creep–fatigue evaluation methods. Both organizations have compared data and ideas through two kinds of benchmark analyses. The CEA benchmark is fatigue and creep–fatigue evaluation of welded plates under reverse bending at 550 °C. The JNC benchmark is creep–fatigue evaluation of a welded vessel under cyclic thermal transients. The main differences in the methods are the strain concentration factors for base metal fatigue strength reduction factors of weldments. To evaluate inferior performance of weldments to base metal, the CEA pays attention to material strength reduction in the weld metal, while the JNC examines strain redistribution between the base and weld metals. Both the CEA and JNC calculations gave good results for welded plates. Both methods obtained conservative results for a welded vessel because evaluation methods for base metal are conservative.

Compressive behavior of pultruded composite plates with circular holes

Compressive behavior of E-glass fiber/isophthalic polyester resin matrix pultruded composite sheet material is reported for two thicknesses. The effect of circular holes on compressive strength and failure strain was also investigated. In the first series of tests, compression tests were performed with plate specimens without any hole. These specimens were instrumented with several pairs of back-to-back axial strain gages at different locations on the surface of the specimen to capture global buckling (if any) during compression. In the second series of tests, plate specimens with circular holes were prepared. A wide range of diameter to width ratio of D/ W=0.075–0.75 was chosen. The open-hole specimens were also instrumented with several strain gages (combination of single and strip gages) in and around the surface of the hole to determine the strain distribution, strain concentration factor, transverse and through-the-thickness normal strain, etc. A relationship between the compressive strength and hole-diameter was established, and compared with the base line material properties. Finally, an attempt was made to determine the compressive failure initiation mechanisms and failure progression mechanisms in the presence of holes through sectioning and examining under a stereo microscope.

A statistical micromechanics-based multi-scale framework for effective thermomechanical behaviours of particle reinforced composites

Particle-reinforced composite materials have been widely used as they can exhibit nearly isotropic material properties and are often easy to process. Some silicon carbide particle reinforced aluminium composites with high volume concentration of reinforcement exhibit excellent thermophysical properties and can be used in advanced electronic packaging. In this paper, a statistical micromechanics-based multi-scale material modelling framework is introduced to describe the macroscopic effective thermomechanical properties of the particle-reinforced composite. The formulation differs from most of the existing methods in that the interaction effects among the reinforcing particles are directly accounted for by considering pair-wise interaction and statistical information on particle distribution is included. The strain and stress concentration factor tensors that relate the local average strain and stress fields, respectively, to the corresponding global average fields are derived according to the theory of average fields. The effective coefficient of thermal expansion for the particle-reinforced composite material is derived. Comparisons of the prediction from the proposed framework to the results from other existing methods are presented. The results are expressed in analytical closed-form in terms of the thermal and mechanical properties of the two constituent phases and the volume fraction of particles. No parameter estimation or data fitting is required.