Calculation Of Stress Concentration Research Articles

A magnesium screw with optimized geometry exhibits improved corrosion resistance and favors bone fracture healing

Stress-induced corrosion impairs the mechanical integrity of magnesium (Mg) and its alloys as potential orthopedic implants. Although there has been extensive work reporting the effects of stress on Mg corrosion in vitro, the geometric design principles of the Mg-based orthopedic devices still remain largely unknown. In this work, a numerical simulation model mimicking fractured bone fixation and surgical animal models were applied to investigate the effects of the geometric design of Mg screws on the stress distribution and the stress-induced degradation behavior. Finite element (FE) analysis was used for calculation of stress concentrations around the Mg screws, with different thread type, thread pitch, and thread width. Afterward, the Mg screws of the pre-optimization and post-optimization groups exhibiting the highest and lowest stress concentrations, respectively, were implanted in the fractured distal femora and back subcutaneous tissue of rabbits. Encouragingly, there was a significant difference between the pre-optimization and the post-optimization groups in the degradation rate of the stressed screw parts located around the fracture line. Interestingly, there was no significant difference between the two groups in the degradation rate of the non-stressed screw parts. Consistently, the Mg screw post-optimization exhibited a significantly lower degradation rate than that pre-optimization in the back subcutaneous implantation model, which generated stress in the whole screw body. The alteration in geometric design did not affect the corrosion rate of the Mg screws in an immersion test without load applied. Importantly, an accelerated new bone formation with less fibrous encapsulation around the screws was observed in the Mg group post-optimization relative to the Mg group pre-optimization and the poly (lactic acid) group. Geometry optimization may be a promising strategy to reduce stress-induced corrosion in Mg-based orthopedic devices. Statement of significanceStress concentrations influence corrosion characteristics of magnesium (Mg)-based implants. The geometric design parameters, including thread type, thread pitch, and thread width of the Mg screws, were optimized through finite element analysis to reduce stress concentrations in a fractured model. The Mg screws with triangular thread type, 2.25 mm pitch, and 0.3 mm thread width, exhibiting the lowest maximum von Mises stress, showed a significant decrease in the volume loss relative to the Mg screws pre-optimization. Compared with the Mg screw pre-optimization and the poly(lactic acid) screw, the Mg screw post-optimization favored new bone formation while inhibiting fibrous encapsulation. Collectively, optimization in the geometric design is a promising approach to reduce stress-induced corrosion in Mg-based implants.

Crack Growth and Delamination Analysis in GFRP Composite Materials

The modeling of the structural behavior of composite materials is an interesting but complex task since the response of the material to loading structural may be difficult to predict, and the failure may be manifested in different forms. In cross-ply fiber-reinforced composites, the major failure mechanisms include: (i) the failure of the matrix material (transverse cracking), (ii) delamination and (iii) the breakage of the fibers. The process of the transverse cracking is a well studied damage mechanism and can be used in numerical simulations, in order to study the effects of various parameters on the crack density. In this paper, the finite element modeling of a cross-ply composite under uniaxial loading in tension is performed using ABAQUS software, considering all the potential damage mechanisms. The model takes into account shear-lag effect for the determination of the stress transfer and furthermore it adopts a homogenization procedure for the calculation of elastic and viscoelastic material properties. Stochasticity is introduced by assigning various interfacial strengths that follow a Gaussian distribution, so as to predict the cracking sequence up to saturation in the transverse to the 0∘ layers. The results are directly compared with available experimental measurements showing reasonable agreement. Finally, a cross-ply RVE model was created and loaded in uniaxial tension and crack propagation is modelled with the Extended Finite Element Method (XFEM). The stress concentration calculations around the crack tips are in agreement with the mesoscale model.

Analytical calculation of stress concentrations at welded flange necks

AbstractAnalytische Berechnung von Spannungskonzentrationen an Schweißnähten von RingflanschverbindungenRingflanschverbindungen für Rohrtürme, wie solche für Windenergieanlagen oder Schornsteine, sind einer erheblichen Ermüdungsbeanspruchung ausgesetzt. Neben den Schrauben muss auch die Schweißnaht, die den Flansch mit der Turmschale verbindet, gegen Ermüdungsversagen abgesichert werden. Aufgrund des Vorhandenseins des Flansches treten lokale Biegemomente in der Schale auf, die die nominelle Membranspannung erhöhen, d. h., es treten Spannungskonzentrationen auf. In dieser Arbeit wird ein analytisches Modell vorgestellt, um solche lokalen Biegemomente zu berechnen, sodass Spannungskonzentrationen bestimmt werden können. Das analytische Modell wird mit den Ergebnissen von 3D‐Finite‐Elemente‐Modellen verglichen, wobei eine gute Übereinstimmung festgestellt wird. Die Ergebnisse des vorgestellten Modells werden daher für Entwurfszwecke als angemessen erachtet.

Small scale fracture and strength of high-entropy carbide grains during microcantilever bending experiments

The fracture behaviour of (Hf-Ta-Zr-Nb)C high-entropy carbide grains was investigated by microcantilever bending experiments, and fracture related properties (e.g. strength, toughness) were determined using linear beam theory. Microcantilevers were FIB-milled from large grains with {001} and {101} orientations and were subjected to micro-bending experiments. SEM based fractographic analysis of the broken cantilevers revealed that approximately half of them fractured at the fixing position at FIB-induced surface cracks, while the rest of the beams failed at small cracks located at submicron size pores or inclusions. In all cases, fracture occurred on the {001} cleavage plane. The fracture strength of beams fractured at the fixing position was 11.8 ± 0.2 GPa, while the strength of the beams that failed at submicron defects was in the range of 3.8-8.9 GPa. The calculation of stress concentration in the vicinity of pores revealed that local stress field exceeded the value that induced cracking in ‘defect free’ beams.

Bending analysis of a symmetric laminated composite plate containing a polygonal shaped cut-out

The presence of cut-out in a structure may result in to strength degradation due to alteration of load lines around it. In application such as ship decks and aircrafts structures where the composites are majorly used, the calculation of stress concentration around such cot-outs is essential to avoid major failures. The performance of laminated composites containing these cut-outs largely depends upon the fiber arrangement, number of layers, shape and corner radius of hole and type of loading. The present study investigates the effect of these parameters on the stress concentration around polygonal shaped cut-out in symmetric laminated plate subjected to bending loading. Additionally, the effect of number of ply groups on stress concentration is also addressed. The stress concentration is evaluated by using a close form solution given by Muskhelishvili's complex variable formulation. The numerical results are obtained for graphite/epoxy plate weakened by triangular, pentagonal and hexagonal shaped hole considering in-plane equi-biaxial, cylindrical and twisting bending loading at infinity. The present results can be useful to the designer who needs to reduce the stress concentration around polygonal shaped hole in composite laminate.

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

A variational numerical-analytical method (called the RVR method) is suggested for calculating the strength and stiffness of statically loaded non-thin orthotropic shell structures weakened by holes (stress concentrators) of arbitrary shapes and sizes. The theoretically substantiated new method is based on the Reissner variational principle and the method of I. N. Vekua (the method of decomposing the desired functions into the Fourier series of the orthogonal Legendre polynomials with respect to the coordinate along the constant shell thickness). In this case, the use in the proposed RVR method of the general equations of three-dimensional problems of the linear theory of elasticity makes it possible to determine the total stress-strained state of an elastic shell (in particular, a plate) with holes. At the same time, using the R-functions, at the analytical level, the geometric information of boundary-value problems for multiply connected domains is taken into account and solutions structures are constructed that exactly satisfy different variants of boundary conditions. The use of a software-implemented algorithm for the two-sided integral assessment of the accuracy of approximate solutions in the study of mixed variational problems helps automate the search for such a number of approximations in which the process of convergence of solutions becomes stable. For orthotropic and isotropic materials, the possibilities of the RVR method are shown in numerical examples of solving the corresponding boundary value problems of calculating the stress concentration in a cylindrical shell with an elliptical or rectangular hole under axial load. The results of the performed tests are discussed, and the features characteristic of the new method prove that it can be effectively used in the design of critical lamellar and shell elements of structures in various fields of modern technology.

Numerical calculation of stress concentration of various subsurface and undercutting pit types

Abstract In this study, the stress concentration effect of single subsurface (D type) pit types and undercutting (E type) pit types with various pit depth and diameter has been investigated with respect to uniaxial loading by conducting a series of 3D stress analyses systematically. Finite element analyses have been conducted in order to determine the stress concentration factor of pits. Pit aspect ratio q/a and a/2c are the main parameters affecting the value of the stress concentration factor for subsurface types of pits. e/a and e/2c are also pit aspect ratios affecting the value of the stress concentration factor for undercutting types of pits. Some equations have been made to estimate the stress concentration factor depending on the geometrical parameters from the results of stress analyses. The stress concentration factor can be calculated using an equation obtained with a correlation coefficient (R2) of 0.993 for D types (subsurface) pits. The stress concentration factor can also be calculated using an equation obtained with a correlation coefficient (R2) of 0.995 for E types (subsurface) pits.

Optimization of finite plates with polygonal cutout under in-plane loading by gray wolf optimizer

This article investigates the optimum design of isotropic finite plates with different polygonal cutouts under in-plane loading (uniaxial tensile, biaxial, and pure shear load). This purpose is pursued by a gray wolf optimization algorithm. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. The objective function used for this algorithm seeks to minimize the value of stress concentration factor around different cutouts. The method used for the calculation of stress concentration is based on analytical solution of Muskhelishvili complex variable and conformal mapping with plane stress assumption. The plate is assumed to be isotropic, linear elastic, and finite (the ratio of cutout side to plate’s longest side in the square and triangular cutouts and the ratio of diameter of circle circumscribing other n-gonals to the plate’s longest side are greater than 0.2). Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the polygonal cutout leading to an increase in load-bearing capacity of the structure.

Quantitative Evaluation for Influence of Complex Surface Texture on Fatigue Reliability from Meso-characteristics (3rd Report, Approximated Calculation of Stress Concentration of 2-Dimensional Complex Surface)

In this paper, the practical method to estimate the stress concentration factor (SCF) of two dimensional surface complex roughness is proposed. In the present method, the surface roughness is approximated with an infinite row of colinear notches which consists on “the local configuration” and “the average configuration”. The SCF values of the notches are calculated independently, and the SCF of the surface roughness is obtained by the superposition of each SCF values. The application limit of the present method is examined with the exact or Finite Element Method (FEM) solution. Moreover, the problem of colinear row of arbitrary notches which are satisfied with the application limit is solved by the present method and FEM. Comparing the present solution with FEM solution, the validity of the present method is examined.

Calculation of stress concentration caused by a coated particle in polymer matrix to determine adhesion strength at the interface

The mechanical problem of a coated particle embedded within a cylindrical rod under tensile load is considered. The motivation for the calculations is to determine the maximum radial stress at the particle surface as a function of applied load. Assuming that normal stresses at the interface are responsible for debonding, the adhesion strength can be determined from critical loads at debonding initiation. Analytical and finite element solutions of the stress field around a particle under uniaxial load are derived as functions of the mechanical properties of the particle, the matrix and the interphase. A non-linear relation between the true stress and logarithmic strain is considered for the interphase and the matrix. The effect of the interphase on the stress concentration strongly depends on the ratio between the elastic modulus of the matrix and the interphase and on the Poisson's ratio of the interphase. The consideration of an interphase leads to a non-uniform stress distribution within the particle. The ratio between the particle diameter and the cross section of the sample has a decisive influence on the shape of the non-linear relation between applied load and maximum radial stress.

The fundamental matrix for a certain random walk

Consider the random walk {Sn} whose summands have the distribution P(X=0) = 1-(2/π), and P(X = ± n) = 2/[π(4n2−1)], for n ≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean time xk for the random walk starting from S0 = k to exit the interval. The explicit formula yields the limiting behavior of xk as N → ∞ with k fixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By letting N → ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting from k = 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

The fundamental matrix for a certain random walk

Consider the random walk {Sn} whose summands have the distributionP(X=0) = 1-(2/π), andP(X= ±n) = 2/[π(4n2−1)], forn≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean timexkfor the random walk starting fromS0=kto exit the interval. The explicit formula yields the limiting behavior ofxkasN→ ∞ withkfixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By lettingN→ ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting fromk= 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.

Calculation of Stress Concentration at the Edge of Island Layer: Demonstration for GaAs/Si

An improved shear lag analysis was proposed to precisely calculate longitudinal stress distribution in hetero- structures with island layers. It is assumed that each layer consists of many imaginary thin layers in order to calculate internal stress distributions over the entire heterostructure. This method is applied to the calculation of stress in a GaAs/Si heterostructure whose GaAs layer is separated or selectively grown similarly to the island layer, in order to determine the effect of island layer on the concentration of stress at the island edge and on the reduction of stress in the GaAs layer. In the stress distribution in the Si layer close to the heterointerface, a sharp and high peak of tensile stress appears at the edge of the GaAs island layer with misfit dislocations. This stress distribution agrees with the experimental one measured by Raman scattering. The tensile stress in the GaAs layer with misfit dislocations can be clearly reduced by decreasing the length of the GaAs island layer.

Calculation of stress concentration in the manipulator element using a combined finite and boundary element method

Elastic stress concentration in a manipulator element is calculated within the framework of the two-dimensional stressed state model. The purpose here is to make recommendations for selecting the radius of joining of the beam parts of the element based on analysis of maximum stresses in the stress concentration zone. Combination of the finite element and boundary element methods is proposed for solving the problem. A coarse finite element subdivision is used for the initial calculation for the entire element. Then, the solution is refined by using boundary elements in the identified zone. Comparison of calculation results with solutions obtained by the finite element and boundary element methods points to the effectiveness of the proposed algorithm for stress concentration calculations.

Some Equations of Stress Intensity Factor K Value for Structural Members in Hulls

Verification for the cargo tank of the liquefied gas carrier that it is of safe life, type B design which presupposes a limited fracture calls for analysis of fracture mechanism of the tank structure.There is a move, as well, towards performing the similar analysis for ships other than the liquefied gas carrier to assure their structural safety.When analyzing the fracture mechanism, in what manner to calculate the stress intensity factor K is one of important consideration. This problem has been explored by No. 3 Standardization Research Committeel) and No. 169 Research Committee of the Shipbuilding Research Association of Japan, etc., but these researches contain not all members of hulls.The author carried out fatigue tests on some types of tank structural members, to obtain data on the initiation and propagation of fatigue cracks. Propagation of the fatigue crack can be defined by the Paris' law which employs K as parameter. Based on these data, as well as using the ordinary methods of K and stress concentration calculations by finite element method, etc., the author devised an approximation formula to obtain K for each of the following four types of tank structural members.1) Crack at the bracket end jointed in “T”, “L”, or overlapped form to the longitudinal.2) Crack at the end of stiffener reinforcing the bracket.3) Crack at the end of web stiffener in corner R of girder joints.4) Crack at the snipped end of the built up type of the girder.