Longitudinal Tensile Loading Research Articles

A finite element stress analysis of aircraft bolted joints loaded in tension

AbstractAccurate stress and strain analysis in bolted joints is of considerable interest in order to design more efficient and safer aerospace structural elements. In this paper, a finite element modelling of aluminium alloy 7075-T6 bolted plates, which are extensively used in aircraft structures, is discussed. The ANSYS Finite Element (FE) package was used for modelling the joint and estimating the stresses and strains created in the joint due to initial clamping forces and subsequent longitudinal tensile loadings. A double-lap bolted joint with a single bolt and nut was considered in the study. A three-dimensional (3D) finite element model of the joint was generated, and then subjected to three different simulated clamping forces followed by different levels of longitudinal tensile load. 3D surface-to-surface contact elements were employed to model the contact between the various components of the bolted joint. Friction effects were considered in the numerical analysis; and moreover, the clearance between the bolt and the plates was simulated in the model. FE results revealed beneficial compressive stresses near the hole edge as a result of applying the clamping. It was found that a higher clamping force can significantly decrease the magnitude of the resultant tensile stress at the hole edge and also bearing stress in the joint when subjected to the longitudinal tensile load.

인장하중을 받을 때 PZT 웨이퍼의 크립 거동: 실험과 모델링

두께방향으로 분극처리되어 있는 상업용 PZT 웨이퍼가 폐쇄회로와 개방회로의 두 가지 전기적 경계조건에서 길이 방향으로 일정한 크기의 인장하중을 받는다. 하중과정 동안 두께 방향으로의 전기밀도와 평면내 변형률의 시간에 따른 변화를 측정한다. 두 가지 전기적 경계조건에서의 서로 다른 거동 특성을 시편 내부에서 발생하는 전기장과 분극역전 현상으로 설명한다. 마지막으로 관측된 크립 거동을 예측하기 위한 정규분포 형식을 가지는 자유에너지 함수를 도입하고 모델의 예측과 실험결과를 비교한다.

A Numerical Simulation of Time-Dependent Interface Failure Under Shear and Compressive Loads in Single-Fiber Composites

We performed a numerical simulation of a time-dependent interfacial failure accompanied by a fiber failure, and examined their evolution under shear and compressive loads in single-fiber composites. The compressive load on the interface consists of Poisson’s contraction for matrix resin subjected to longitudinal tensile load. As time progresses, compressive stress at the interface in the fiber radial direction relaxes under the constant longitudinal tensile strain condition for the specimen, directly causing the relaxation of the interface frictional stress. This relaxation facilitates the failure of the interface. In this analysis, a specific criterion for interface failure is applied; apparent interfacial shear strength is enhanced by compressive stress, which is referred as quasi-parabolic criterion in the present study. The results of the stress recovery profile around the fiber failure and the interfacial debonding length as a function of time simulated by the finite element analysis employing the criterion are very similar to experimental results obtained using micro-Raman spectroscopy.

Effect of fiber distribution and realignment on the nonlinear and inhomogeneous mechanical properties of human supraspinatus tendon under longitudinal tensile loading

Tendon exhibits nonlinear stress-strain behavior that may be partly due to movement of collagen fibers through the extracellular matrix. While a few techniques have been developed to evaluate the fiber architecture of other soft tissues, the organizational behavior of tendon under load has not been determined. The supraspinatus tendon (SST) of the rotator cuff is of particular interest for investigation due to its complex mechanical environment and corresponding inhomogeneity. In addition, SST injury occurs frequently with limited success in treatment strategies, illustrating the need for a better understanding of SST properties. Therefore, the objective of this study was to quantitatively evaluate the inhomogeneous tensile mechanical properties, fiber organization, and fiber realignment under load of human SST utilizing a novel polarized light technique. Fiber distributions were found to become more aligned under load, particularly during the low stiffness toe-region, suggesting that fiber realignment may be partly responsible for observed nonlinear behavior. Fiber alignment was found to correlate significantly with mechanical parameters, providing evidence for strong structure-function relationships in tendon. Human SST exhibits complex, inhomogeneous mechanical properties and fiber distributions, perhaps due to its complex loading environment. Surprisingly, histological grade of degeneration did not correlate with mechanical properties.

Reduction in clamping force due to applied longitudinal load to aerospace structural bolted plates

The main purpose of the present work is to experimentally and numerically study why and how the magnitude of the bolt clamping force reduces in the aerospace structural bolted plates when they are subjected to a longitudinal tensile load. In the experimental method, a holed plate of aluminium alloy 7075-T6 was clamped using a single bolt fastener, and then tested under an increasing static longitudinal tensile load. The bolt clamping magnitude was determined by using the measured axial compressive strains of a steel bush placed between the nut and plate. Two clamped specimens with different initial clamping forces were studied. In each specimen the actual clamping forces were determined during the longitudinal loading on the plate. In the numerical method, a three-dimensional (3D) finite element model was generated in order to simulate and quantify the bolt clamping force in the plate model loaded in tension. Both experimental and numerical results showed that the clamping force reduces considerably in the aluminium bolted plates under the longitudinal tensile loading. This is because of the transverse contraction of the plate material that causes the clamped material to release from the initial compression, and as a result, the clamping force to relax.

Effects of inter-fibre spacing on damage evolution in unidirectional (UD) fibre-reinforced composites

A three dimensional (3D) micromechanical study has been performed in order to investigate local damage in UD composite materials under transverse and longitudinal tensile loading. In particular, the influence of non-uniform distribution of fibres in RVEs (representative volume element) with a hexagonal packing array and the effects of thermal residual stresses has been investigated. To examine the effect of inter-fibre spacing and residual stress on failure, a study based on the Maximum Principal Stress failure criterion and a stiffness degradation technique has been used for damage analysis of the unit cell subjected to mechanical loading. Results indicate a strong dependence of damage onset and its evolution from the fibres position within the RVE. Predicted mechanical properties, damage initiation and evolution are also clearly influenced by the presence of residual stress.

Recent Development of Planar Cruciform Experiment on Biaxial Tensile Deformation and Failure of Unidirectional Glass/Epoxy Composite

Inadequate experimental characterization of strength and deformation behavior of unidirectional fiber composites under planar biaxial stresses has hindered the development of complete material models. Here the recent development of a cruciform specimen with unidirectional gage section is presented, suitable to test glass/epoxy under combined high transverse and longitudinal tensile loads. The experimental program developed comprises of six different biaxial tensile load ratios. The results show significant influence of longitudinal stress on transverse nonlinearity of a glass/epoxy. Failure loci and failure modes in biaxial tensile strain and stress domains are presented, indicating a reduction of transverse strength by high longitudinal loads.

Pre-stressed adhesive strap joints for thick composite sandwich structures

A simple but effective design to improve the strength of thick adhesive composite strap joints is validated with experiment and finite element method. The strap joint under investigation, with a particular application to naval ship structures, consists of two thick woven E-glass/vinyl ester laminates joined together with two steel doublers. Longitudinal tensile loads are applied to the joints, resulting in large concentrated shear and peel stresses near the free edges of bondlines. The new design intends to reduce the adhesive peel stress by application of through-the-thickness compressive pre-stress along the bondline and thus leads to an increase of joint strength. Experiment results show that all the joint failures are delamination of the top layer of the laminated adherends. The test further confirms that joint strength increases significantly by applying the transverse pre-stress. Finite element analysis reveals that the pre-stress can effectively reduce the magnitude even reverse the sign of the peel stress in the adhesive layer and the adherends. Recessing the adhesive leading edge could magnify the pre-stress effect and reduce the adhesive peel stress, but would increase the shear stress. For those composite joints with low transverse interlaminar strength and susceptible to delamination, this simple design/technique can considerably improve their joint strength.

Experimental investigation of the transverse mechanical properties of a single Kevlar ® KM2 fiber

A new experimental setup is developed to investigate the transverse mechanical properties of Kevlar ® KM2 fibers, which has been widely used in ballistic impact applications. Experimental results for large deformation reveal that the Kevlar ® KM2 fibers possess nonlinear, pseudo-elastic transverse mechanical properties. A phenomenon similar to the Mullins effect (stress softening) in rubbers exists for the Kevlar ® KM2 fibers. Large transverse deformation does not significantly reduce the longitudinal tensile load-bearing capacity of the fibers. In addition, longitudinal tensile loads stiffen the fibers' transverse nominal stress–strain behaviors at large transverse deformation. Loading rates have insignificant effects on their transverse mechanical properties even in the finite deformation range. An analytical relationship between transverse compressive force and displacement is derived at infinitesimal strain level. This relation is used to estimate the transverse elastic modulus of the Kevlar ® KM2 fibers, which is 1.34 ± 0.35 GPa.

Bonded butt joints in pultruded GRP panels—an experimental study

The strength of bonded butt joints in pultruded material is investigated experimentally. The joints are bonded with commercially available two-part, cold curing, epoxy and acrylic adhesives. The aim of this work is to investigate the comparative strength of the butt joints when adhesives of differing stiffness are used to join a variety of pultruded materials. The effect of joint configuration, including a novel finger joint configuration, and mechanical surface preparation are also explored. The bonded specimens were tested to failure under static longitudinal tensile loading at room temperature. The results indicate that the quality and content of the pultruded material is an important factor in joint efficiency. The novel finger-joint configuration provides some interesting results when compared to the standard double butt-strap joints.

Prediction of creep rupture in unidirectional composite: Creep rupture model with interfacial debonding and its propagation

This paper describes a creep rupture model that takes into account the interfacial debonding and its propagation around broken fibers in unidirectional fiber-reinforced polymers. The interfacial debonding is accompanied by fiber breaks under a longitudinal tensile load, and the interfacial debonding length depends on both the fiber stress at the moment of the fiber breaks and the properties of the interfacial adhesion. In this paper, the interfacial debonding length, its propagation as a function of time, the probability of fiber breaks and an interfacial shear stress are investigated by fragmentation tests with a single glass fiber embedded in each vinylester resin specimen. Subsequently, it was found that a relationship between the fiber strength and the fiber effective length, the length of the debonding length and stress recovery length subtracted from one fiber length, was log linear, and that the larger the fiber stress, the longer was the interfacial debonding length. Next, creep tests were performed to investigate the creep constants of the vinylester resin, and interfacial debonding propagation tests were also performed to identify the interfacial debonding-propagation behavior as a function of time using single fiber composites subjected to constant strains. We modified the creep rupture model by taking into account the interfacial debonding length, which has a time-dependent characteristic, into a conventional Curtin–McLean creep rupture model. It was found that the predicted creep rupture time of the modified model was shorter than that of the conventional model and that there was no threshold creep stress in the modified model unlike in the conventional model because the interfacial debonding propagation makes the prediction creep rupture time lower as time progresses.

Mechanical Properties of Nylon6 Cord-Rubber Composite Subjected to Biaxial Tensile Loads

Effects of perpendicular tensile loads on the mechanical behavior and biaxial tensile load ratios on stress-strain behaviors of single ply of nylon cord-rubber composite are studied respectively under biaxial tensile conditions employing a cruciform specimen. Experimental results indicate that transverse mechanical properties of nylon cord-rubber composite with longitudinal constant tensile loads are distinct from its uniaxial transverse tensile mechanical properties. This can be attributed to the action of longitudinal tension that makes the material rigidify in the direction perpendicular to the fiber. The mode of failure is representative of matrix-dominated failure. However, effects of transverse constant tensile load on longitudinal tensile mechanical properties are indistinctive compared with corresponding uniaxial longitudinal tensile mechanical properties. This could be due to a larger difference between longitudinal and transverse mechanical properties. Its dominating failure mode is typical fiber-dominated mode. Effects on biaxial tensile load ratios on its transverse stress-strain behaviors are obvious; whereas, longitudinal stress-strain behaviors under different biaxial tensile load ratios are almost identical. Large differences between longitudinal and transverse tensile properties can be direct reasons resulting in dissimilarities between longitudinal and transverse tensile mechanical behaviors of cord-rubber composite under biaxial tensile loading.

A synergistic damage-mechanics analysis of transverse cracking in [± θ/90 4] s laminates

The deformational response of [± θ/90 4] s laminates under longitudinal tensile loading is treated by a synergistic approach that combines continuum damage mechanics (CDM) and micromechanics. The constraint of θ° plies on transverse cracks in 90° plies is represented by a crack-opening displacement (COD) parameter in the CDM model and is expressed in terms of the ply properties and ply thickness ratios on the basis of a finite-element calculation. A methodology is proposed for predicting the laminate stiffness variations with crack density and applied strain (or stress) for various values of ply orientation θ and is found to give good results.

Evaluation of oxide dispersion strengthened (ODS) molybdenum and molybdenum–rhenium alloys

Oxide dispersion strengthened (ODS) molybdenum alloys being developed for high temperature applications possess excellent high temperature strength and creep resistance. In addition they exhibit a ductile-to-brittle transition temperature (DBTT) in the worked and stress-relieved condition under longitudinal tensile load well below room temperature. However, in the recrystallized condition, the DBTT may be near or above room temperature, depending on the volume fraction of oxide dispersion and the amount of prior work. Dilute rhenium additions (7 and 14 wt%) to ODS molybdenum were evaluated to determine their effect on low temperature ductility. The addition of 7 wt% rhenium to the ODS molybdenum did not significantly enhance the mechanical properties. However, the addition of 14 wt% rhenium to the ODS molybdenum resulted in a DBTT well below room temperature in both the stress-relieved and recrystallized condition. Additionally, the tensile strength of ODS Mo-14 Re is greater than the base ODS molybdenum at 1000–1250°C.

Stress and Failure Analysis of Brittle Matrix Composites. Part II: Failure Analysis

A linear elastic fracture mechanics analysis of a cylindrical element of matrix with a single fiber and two matrix annular cracks perpendicular to the fiber direction under longitudinal tensile load was undertaken. The order of singularity and the angular dependence of the stress field in the neighborhood of the crack periphery were determined by using the stress function approach proposed by Zak and Williams. The stress intensity factor was evaluated by combining the results of the local stress solution with a finite element analysis. The case of fiber debonding originating from the periphery of the annular cracks was also studied. For that problem both opening-mode and sliding-mode stress intensity factors and the strain energy release rate were determined. These results help to understand the various failure mechanisms including matrix cracking, debonding along interfaces and kinking of interface cracks into fibers in brittle matrix composites.

Longitudinal splitting in unidirectional fibre-reinforced composites with an open hole

Splitting of unidirectional aramid, glass and carbon fibre-reinforced composites near a circular hole has been studied. Under longitudinal tensile loading four splits growing in the fibre direction were observed near the hole. The splits grew with an increase in the applied load. R curves were determined, and an increase in fracture toughness, GIIc, with an increase in split length was observed. The increase in fracture toughness was explained by the presence of fibres bridging opposite sides of splits. GIIc values at a split length of 50mm were 4 to 10kJ m−2, roughly 10-times higher than for mode I loading. At a fixed split length an increase in GIIc with an increase in the hole diameter was observed.

Finite element modelling of damage development during longitudinal tensile loading of coated fibre composites

Abstract In this paper, results of finite element calculations of the stress state near a broken coated fibre in unidirectional carbon fibre–epoxy matrix composites are presented. For this aim, a simplified two-dimensional axisymmetric model has been developed. A part of the model contains an equivalent composite medium and, to this end, elastic constants of a coated fibre composite were separately calculated and used as input data in this analysis. The influences of coating thickness, coating stiffness and assumed crack pattern on the stresses in the broken fibre and in adjacent, unbroken fibres are evaluated, and their possible impact on composite longitudinal tensile strength is discussed

Acoustic emission study of failure mechanisms in ceramic matrix composite under longitudinal tensile loading : 59955 Luo, J-J.; Wooh, S-C.; Daniel, I.M. Journal of Composite Materials, Vol. 29, No. 15, pp. 1946–1961 (1995)

Acoustic emission study of failure mechanisms in ceramic matrix composite under longitudinal tensile loading : 59955 Luo, J-J.; Wooh, S-C.; Daniel, I.M. Journal of Composite Materials, Vol. 29, No. 15, pp. 1946–1961 (1995)

Acoustic emission study of failure mechanisms in ceramic matrix composite under longitudinal tensile loading : 57052 Luo, J.J.; Wooh, S.C.; Daniel, I.M. Review of Progress in Quantitative Nondestruction Evaluation, Brunswick, Maine (United States), 1–6 Aug. 1993. Vol. 13A, pp. 469–476. Edited by D.O. Thompson and D.E. Chimenti, Plenum Press (1994) ISBN 0-306-44731-2

Acoustic emission study of failure mechanisms in ceramic matrix composite under longitudinal tensile loading : 57052 Luo, J.J.; Wooh, S.C.; Daniel, I.M. Review of Progress in Quantitative Nondestruction Evaluation, Brunswick, Maine (United States), 1–6 Aug. 1993. Vol. 13A, pp. 469–476. Edited by D.O. Thompson and D.E. Chimenti, Plenum Press (1994) ISBN 0-306-44731-2

Effects of Compaction on the Stiffness and Strength of Plain Weave Fabric RTM Composites

Changes in fiber architecture which result from the compaction of fabric plies can be a major cause for scatter and inconsistencies in measured mechanical properties. The need to quantify and provide insight into the influence of compaction on both the stiffness and strength of plain weave fabric composites, has led to the development of a model. The proposed model extends an existing modelling technique, a point-wise lamination approach using Classical Laminate Theory, to analyse the compaction problem. The analysis, which is valid for crimp angles less than 20°, is applied in both the warp and weft directions, with ply nesting being ignored at this point in time. In this paper, the formulation of the proposed model is presented. Numerical results generated from the model are compared with experimental data and other analytical methods, in order to validate the model. A discussion on the findings from the analysis are also given, with particular focus on the initial failure mode and stress/strain distributions predicted by the model for a longitudinal tensile load case at various levels of compaction. The model was found to easily model fabrics of varying fiber architecture, making it a useful tool in providing insight and quantification on the effects on stiffness and strength caused by fiber architecture changes resulting from compaction.