Strain Concentration Factors Research Articles

Strain concentration factor of heterogeneous materials and analytical influence functions based on Eshelby tensor

In this manuscript, Eshelby tensor is employed to assess the strain concentration that arises in the matrix phase at the interface, offering precise values and locations of maximum strain under specific loading conditions for both spherical and cylindrical inclusions. When compared to numerical simulation results, the analytical predictions grounded in the Eshelby tensor exhibit satisfactory accuracy. Then an analytical calculation method based on Eshelby tensor for the elastic strain influence functions of reduced-order homogenization (ROH) method is developed and adopted on particle-reinforced and fibrous composites, presenting its feasibility and advantage on off-line stage calculation of ROH method. The error analyses between analytical and numerical results are conducted. The numerical results also exhibit the necessity of finer interface partitioning to obtain the response on micro-scale with higher resolution.

Geometry and temperature effects on tensile properties and failure behaviors of open-hole and bolted-joint CF/PEKK composites

Temperature-dependent tensile properties of carbon-fiber-reinforced polyetherketoneketone (CF/PEKK) composites with varying width-to-diameter (W/D) ratios in open-hole (OH) and bolted joint (BJ) were investigated. CF/PEKK exhibited higher modulus and strength at lower temperature due to restricted polymer chain mobility, and lower values at elevated temperature due to increased polymer ductility. OH net tensile strength decreased with decreasing W/D, with strain retention dropping significantly at W/D ≤ 2. The approximate average strain concentration factor determined from digital image correlation slightly exceeded theoretical values due to semi-crystalline nature of PEKK. Distinct failure behaviors highlighting the complex interplay between temperature, W/D, and failure characteristics. Evaluating W/D and temperature effects on BJ CF/PEKK revealed changing failure modes. Bolted joint efficiency emphasizing the need to optimize W/D ratios above 2 to achieve high efficiency. These findings highlight the geometry and temperature interplay affects CF/PEKK composites, which are crucial for designing high-performance materials, especially for aerospace applications.

Tensile properties of GH4169 superalloy for smooth and notch specimens determined by tests and simulation

Tensile mechanical tests of GH4169 superalloy were performed for smooth and notch specimens at room temperature. Moreover, a finite element method (FEM) was employed by an Abaqus simulation software to provide the tensile test processes during elastic and plastic deformation. Comparing the experimental measurements with the simulation and analysis results, it was found that the [Formula: see text] value decreased with increasing [Formula: see text] value, and the [Formula: see text] value of smooth and notched specimens were close to the [Formula: see text] value of both elastic deformation and plastic deformation. Reasonable explanations were also provided for the stress concentration factor [Formula: see text] and strain concentration factor [Formula: see text].

Experimental and theoretical evaluation of influence of hole size on deformation and fracture of elastic perforated plate

As an ideal benchmark problem for the researches of solid mechanics and fracture mechanics, the influence of the hole size on the deformation and the fracture behaviors of perforated plates has been studied for more than sixty years. However, the seemingly simple problem has not been thoroughly answered yet. To gain more understanding of the hole-size dependence of the strain/stress concentration, the present study measured the stress and the strain concentration factors by using tensile tests together with the digital image correlation analysis. A noticeable hole-size dependence was observed for both concentration factors. The experimental observations can be reasonably explained in terms of a new formulation of strain energy density which considers the contributions of both the conventional strain and the high-order strain. It is shown that the strain energy density gets more uniformly distributed when the hole gets smaller. Accordingly, the maximum strain decreases as well. Due to the positive contribution of the higher-order strain energy, the material around the hole hardens and results in a concentration factor lower than three. Because of the influence of the length scale parameter, the stress cannot be scaled by a reference strain and this may lead to a discrepancy between the stress and the strain concentration factors.

Exploiting the adaptive neural fuzzy inference system for predicting the effect of notch depth on elastic new strain-concentration factor under combined loading

Exploiting the adaptive neural fuzzy inference system for predicting the effect of notch depth on elastic new strain-concentration factor under combined loading

Transformation field analysis as a background of clustering discretization methods in micromechanics of composites

A linear composite material (CM) consisting of a homogeneous matrix with either the periodic or random set of heterogeneities is considered. One of the first reduced-order models (ROMs), Transformation Field Analysis (TFA) by Dvorak for the pair strain-eigenstrain (or stress-eigenstress) is modified in terms of the “mixed” pair strain-eigenstress (or stress-eigenstrain) for implementation to clustering-based ROMs initiated by the self-consistent clustering analysis (SCA) by WK Liu. A set of consistency conditions are obtained for both the effective properties and modified eigenfield concentration factors. It is found that modified TFA represents a unified background of all three central clustering-based ROMs: the SCA, virtual clustering analysis (VCA), and finite element analysis–clustering analysis (FCA). One presents the scheme of estimation of inhomogeneous strain concentration factors in some prescribed clusters analyzed by the SCA (nonlinear problem). For statistically homogeneous CMs, a localized version of the modified TFA is proposed for clustering of the matrix (coating) in the vicinity of inclusions. VCA used for the analysis of a finite size inclusion can be modified for the implementation of a combination of both the modified TFA and functional gradient theory.

Experimental and numerical research on opening size effect of novel short fiber reinforced composite laminates

This study investigates the opening size effect of a novel short fiber reinforced quasi-isotropic composite laminate with unidirectionally arrayed chopped strands (UACS) under tensile load by approaches of simulations and experiments. The layup of [45/0/-45/90]s was used to fabricate novel carbon fiber laminates with various central hole diameter from 4 mm to 10 mm. Low notch sensitivity and strength reduction rate were observed in UACS open-hole laminates. It was found that when the width diameter ratio (d/w) of UACS laminate with open-hole is less than 20%, 80% of the original strength can be maintained, which can greatly reduce the design safety factor. Compared with continuous fiber laminates, high increase rate of strength reduction rate was induced by bi-angled slits with the increasing of open hole diameter. The strain distribution around the hole was affected significantly by bi-angled slits, which also inhibited the initiation and propagation of delamination effectively. The strain concentration factor of UACS laminates increases with the increasing open hole diameter. The damage progression of notched and unnotched UACS laminates were analyzed by simulation method, which are consistent well with experimental results.

Analysis of stress and strain concentration around a centralized elliptical hole in a monodomain liquid crystal elastomer sheet

Liquid crystal elastomers (LCEs) are a kind of soft materials which couple the high elastic deformability with the unique properties of liquid crystals. Such combination endows notched LCEs unusual stress and strain concentration behaviors, which is preliminary discussed by us in the case of a large sheet with a centralized circular hole. Here we extend our study from circular holes to more generalized, elliptical holes. We investigate the stress and strain fields around a centralized elliptical hole in a LCE sheet subjected to uniaxial stretches by finite element methods. The effects of the shape factor, defined as the ratio of the minor-to-major axis of the ellipse, are mainly concerned. Compared with common elastomers like neoHookean, LCEs get higher stress and strain concentration factors (SCFs), and the location of maximal strain deviates slightly from that of maximal stress. With the decrease of the shape factor (a sharper ellipse) the SCFs of LCEs rise much severer than those of neoHookean, and the deviation is diminishing. In addition, as the stretch increases, the region near the root is getting close to an approximately uniaxial stress state, and the high strain region will extend non-monotonously along the hole edge, which differs from a monotonous extension of the high stress region. All the unusual behaviors of LCEs above are attributed to the spontaneous strain induced by director rotation. Attempts to correlate stress and strain concentration behaviors to the spontaneous strain are made in this article.

Numerical study on the strain capacity of girth-welded X80 grade pipes

Strain capacity is an important performance indicator for designing and evaluating high-grade steel pipelines. Due to the inhomogeneity of material properties in welded structures, girth welds are one of the main factors that restrict the strain capacity of pipelines. In this paper, girth-welded pipes with cracks in the inner surface of the weld have been studied, and the ductile crack initiation and propagation behavior have been simulated using the Gurson model. The corresponding nominal strain at the onset of crack initiation was defined as the characteristic value of strain capacity. The influencing factors on the strain concentration area, strain concentration factor, and strain capacity of girth-welded pipes were quantitatively analyzed. A semiempirical calculation formula for the strain capacity of typical girth-welded X80 grade pipes has been proposed as a function of the crack size, mismatch coefficient of the weld, and softening degree of the heat affected zone (HAZ). This study can facilitate the defect assessment of girth-welded pipes.

A High-Accuracy Empirical Formula for the Strain Concentration Factor in Countersunk Holes

This paper presents a modified high-accuracy empirical formula for the strain concentration factor in a centrally-placed countersunk holes in isotropic plate under uniaxial tension. Finite Element Method (FEM) was used to investigate the effect of the problem geometric parameters including, plate width and thickness, as well as the hole radius, countersinking depth and angle on the strain concentration factor. The important influence of Poisson’s ratio was also thoroughly discussed. Based on the FEM-generated data and nonlinear regression, a general and high-precision equation for the strain concentration factor was developed. The formulation process was based on producing a general formula for computing the strain concentration factor with unknown coefficients. Such coefficients are determined by minimizing the relative error between the fitted equation and the FE data using nonlinear least squares method. The results of this newly-developed equation were validated with FEA. The comparison showed high accuracy of the present equation in evaluating strain concentration factor in countersunk holes with a relative approximate error of less than 7%. Besides, this equation was efficiently employed to test the various geometric and material parameters on the strain concentration value of countersunk holes. The results of the present equation were compared to the results of older equation available in literature. The comparison proved much higher accuracy of the present equation in evaluating strain concentration factor especially for deeper and larger countersunk holes than the previously published formula.

Strain and stress concentration of ductile composites in full-range deformation by digital image correlation

This study investigates the variation in open-hole strain/stress concentrations within the full deformation range of a ductile self-reinforced poly (ethylene terephthalate) (srPET) composite using the digital image correlation (DIC). Subsequently, DIC was applied to brittle open-hole polymethyl methacrylate (PMMA) for comparison. This demonstrated the influence of the ductility of srPET. The strain concentration factor (Kɛ) of PMMA was constant with a full deformation range and agreed with theoretical concentration factor (Kt). By contrast, the Kɛ of srPETs was divided into five stages based on the propagation of yield extent (beginning from the hole edge) of the specimen, starting from Kt and then increasing to the peak, followed by the lowest value.

Experimental study on the progressive failure of double‐flawed granite samples subjected to impact loads

AbstractIn this paper, the split Hopkinson pressure bar device and high‐speed camera system are applied to carry out the impact tests of fine‐grained granite samples with two parallel preexisting flaws, whose angles are 0°, 15°, 30°, 45°, 60°, 75°, and 90°. The dynamic compressive strength of the double‐flawed granite samples is affected by the flaw angle. By analyzing the experimental results, the peak strengths of the double‐flawed granite samples are in low level when the flaw angles are varying from 45° to 75°, while the peak strengths of the double‐flawed granite samples are in high level when the flaw angles are in the ranges of 0°–30° and 75°–90°. The strain concentration factor is investigated based on the digital image correlation technology. Moreover, the mechanical properties, energy absorption, cracking behaviors, failure modes, and the progressive failure mechanism of the double‐flawed granite samples under impact loads are revealed.

Investigation of the tensile strain response of the girth weld of high-strength steel pipeline

The in-depth analysis of the tensile strain response of the girth weld is very important for the safety assessment of the pipeline. This study is carried out through a combination of experiment and numerical simulation. The microstructure and hardness distribution of the girth weld are obtained. Based on the digital image correlation (DIC) technique, the tensile strain response of the girth weld during the whole tensile process is obtained by using the full wall thickness specimens. The results show that the strain concentration first occurs near the outer surface of heat-affected zone (HAZ). Then, a significant strain concentration area connecting from the outer surface of HAZ to the inner surface of weld metal (WM) is gradually formed. Eventually, the crack initiates on the outer surface of the girth weld and extends to the inner surface. Considering the material constraint effect of the girth weld, a constitutive relationship determination method combing DIC technique and finite element analysis is proposed. Based on the method, the detailed constitutive parameters of the girth weld are obtained. The accuracy of the parameters is verified. The full-scale pipeline girth weld is analyzed by finite element method. The results show that the area near the interface between the root weld layer and the filler weld layer of WM is the most significant strain concentration area under different internal pressures. The change characteristics of the strain concentration factor of the girth weld are also obtained. The increase of internal pressure can reduce the strain capacity of the pipeline.

Continuous Tow Steering Around an Elliptical Cutout in a Composite Panel

Cutouts are widely used to accommodate windows, openings for access purposes, or fasteners in the primary structural parts of airplanes. The presence of cutouts in composite panels results in stress or strain concentrations, leading to potentially reduced load-carrying capacity. Steering tows around cutouts using emerging techniques in three-dimensional (3-D) printing and advanced fiber placement can potentially alleviate such problems. Continuous tow steering around cutouts also eliminates fiber cutting, thereby precluding ply-level 3-D stress concentration, which could otherwise lead to delamination-induced damage. This work examines stress and strain concentrations, using continuous tow steering, around a representative wingbox access hole. Buckling response under compression loading together with stress and strain concentrations under both tensile and compression loads are examined. A steered configuration shows a 26% improvement in buckling performance in comparison with the equivalent straight-fiber configuration. Under tensile loading, the maximum stress and strain concentration factors around the cutout are 29 and 32% larger, respectively, for straight-fiber orientations than those with steered tows around the cutout. For the compression loading condition, the direct strain of the panel with straight-fiber orientations was found to be three times that of steered-fiber trajectories in the vicinity of the cutout.

Unusual stress and strain concentration behaviors at the circular hole of a large monodomain liquid crystal elastomer sheet

Liquid crystal elastomers combine the hyperelasticity of elastomers with the multi-functionality of liquid crystals and have emerged as an important class of soft active materials. Monodomain liquid crystal elastomers under loading exhibit the soft elastic behavior due to the stress induced director rotation and the resulting spontaneous strain. Here, we numerically study their stress and strain concentration behavior by considering the classical example, a large sheet with a small circular hole in the middle under uniaxial loading. The concentration behavior is found to be very different from regular elastomers. Firstly, the concentration factors are much bigger at both small and large strains. Secondly, the locations of the strain concentration may not coincide with that of the stress concentration. Detailed analysis of the director rotation and the resulting spontaneous strain around the free edge of the hole are shown to be the main causes for the unusual concentration behavior. Moreover, under a given strain, the stress level of the LCE sample, and therefore the free energy, is slightly lower than that of the neo-Hookean material, while the local free energy density on the hole edge is much bigger due to the severer concentrations. By considering material parameters obtained from various samples of polysiloxane and polyacrylate side-chain nematic elastomers, we find that their stress and strain concentration behaviors are qualitatively similar but quantitatively quite different. As a result, at a prescribed strain, the samples with a larger maximal spontaneous strain has severer stress and strain concentrations. The stress concentration factor difference scaled by a coupling constant that combines the effect of the two material parameters, r and a, increases as the semi-soft coefficient a decreases. Similar results are found for the scaled maximal spontaneous strains and the scaled strain concentration factor difference at small strains.

A High-Temperature Digital Image Correlation Method and its Application on Strain Measurement of Film Cooling Holes

In this paper, a digital image correlation (DIC) method is developed and applied on film cooling holes in the submillimeter scale in high temperature. Compared with the traditional DIC method, the speckle patterning method and the optical system are improved. In detail, a kind of high temperature-resistant black paint is selected as the basecoat, and the white ZrO2 particles are evenly distributed on the specimen using high-pressure splashing method. Besides, to eliminate the radiation effect of the high-temperature specimen, the blue light source is used to illuminate the specimen, and the optical bandpass filter is placed in front of the camera to allow the blue light passing. In order to verify the DIC method, the strain measurement on a specimen with single skew hole is performed. The relative error in high temperature of the maximum strain between the measurement results and the numerical simulation results given by the finite element method (FEM) is 12%. The strain concentration factor of the single skew hole is measured as 1.83. Finally, the developed method is applied to the strain measurement of the structure with multiple film cooling holes in 870°C. The X-shape strain distribution can be observed at the hole with maximum stress, which suggests that the strain field of multiple holes has coupling effect. In addition, the strain concentration factor of multiple film cooling holes increases to 2.34.

Stress concentration factors of brace in-plane loaded bird-beak SHS gap K-joints

Experimental and numerical investigations have been performed to study the stress concentration factors (SCFs) of brace in-plane loaded bird-beak gap K-joints. Four bird-beak SHS gap K-joint specimens were tested. Hot spot strain distributions along the weld toes at crown and saddle area were determined, from which the strain concentration factors (SNCFs) can be extrapolated. Parametric study was then implemented through numerical analyses to explore the influences of the three key non-dimensional parameters (i.e. β, 2γ, τ) on the SCFs, and the SCF design formulae were established correspondingly. Besides, the comparisons between the SCFs of bird-beak gap K-joints and conventional ones were also carried out. The results revealed that the brace crown area possessed the greatest SNCFs within entire bird-beak joint. The diamond bird-beak gap K-joints generally possess less stress concentrations than the square bird-beak counterparts with the same member geometries. Moreover, it is shown that the SCFs of conventional gap K-joints are much greater than those of the bird-beak counterparts investigated in this study.

Strain Localizations in Notches for a Coarse-Grained Ni-Based Superalloy: Simulations and Experiments.

Alloys used for turbine blades have to safely sustain severe thermomechanical loadings during service such as, for example, centrifugal loadings, creep and high temperature gradients. For these applications, cast Ni-based superalloys characterized by a coarse-grained microstructure are widely adopted. This microstructure dictates a strong anisotropic mechanical behaviour and, concurrently, a large scatter in the fatigue properties is observed. In this work, Crystal Plasticity Finite Element (CPFE) simulations and strain measurements performed by means of Digital Image Correlations (DIC) were adopted to study the variability introduced by the coarse-grained microstructure. In particular, the CPFE simulations were calibrated and used to simulate the effect of the grain cluster orientations in proximity to notches, which reproduce the cooling air ducts of the turbine blades. The numerical simulations were experimentally validated by the DIC measurements. This study aims to predict the statistical variability of the strain concentration factors and support component design.

A fatigue life prediction method distinguishing fracture modes for Ni-based single crystal superalloys considering porosity defect

Microporosity is one of the most common defects in nickel base single crystal (N-SC) superalloys, which is a great threat to fatigue performance. In this paper, nine porosity-related fatigue damage parameters for N-SC superalloys were selected by referring to those parameters originally proposed for casting and 3D printing metal materials as well as the critical plane damage parameters commonly used in N-SC superalloys. According to the plastic constitutive model of single crystals, a crystal plastic finite element (CPFE) model was established to evaluate these different fatigue damage parameters, and the parameters of CPFE were calibrated by the low cycle fatigue (LCF) hysteresis loop obtained from the fatigue test. The evaluation results showed that the geometric mean of stress–strain concentration factor (GCF) kg was a satisfactory parameter to quantify the effect of porosity defects on fatigue. Inspired by the discovery and considering the slip systems characteristics of N-SC superalloys, the geometric mean of resolved stress–strain concentration factor (GRCF) krg on slip systems was proposed, and it was found that the max(krg,kg) could be used to predict the fracture modes of N-SC superalloys. Based on the max(krg,kg), a porosity-related fatigue life prediction method which can distinguish the fracture modes was put forward. The prediction results showed that the fracture mode prediction results were consistent with the test results, and the life prediction results were also improved compared with the GCF parameter.

Analysis and optimization of the strain concentration factor in countersunk rivet holes via finite element and response surface methods

PurposeThe purpose of this paper is to investigate the strain concentration factor in a central countersunk hole riveted in rectangular plates under uniaxial tension using finite element and response surface methods.Design/methodology/approachIn this work, ANSYS software was elected to create the finite element model of the present structure, execute the analysis and generate strain concentration factor (,) data. Response surface method was implemented to formulate a second order equation to precisely compute (,) based on the geometric and material parameters of the present problem.FindingsThe computations of this formula are accurate and in a great agreement with finite element analysis (FEA) data. This equation was further used for obtaining optimum hole and plate designs.Originality/valueAn optimum design of the countersunk hole and the plate that minimizes the (,) value was achieved and hence validated with FEA findings.