Load Transfer Analysis at the Interface Between a Steel Post and Polyethylene Matrix Using Pull-Out Test: Experimental and Theoretical Parametric Study

In various kinds of orthopedic or dental prostheses, adequate fixation of prosthetic components to the host bone represents a great challenge. The short- and long-term fixation stabilities of the implants are often provided by the use of posts. In this work, a cylindrical steel post inserted in a predrilled High Density Polyethylene (HDPE) cylinder with an initial interference fit was used as a model to analyze the contribution of post fixation to the initial stability of Total Knee Arthroplasty (TKA) tibial component. To characterize the ability of the steel post/HDPE cylinder interface for transferring mechanical load, pull-out tests were carried out on the model post fixation for different initial interference fits and implantation lengths. Experimental ultimate pull-out force was found to increase in a quasi-linear fashion with increase in the interference fit or the implantation length. On the basis of Coulomb friction at the post/HDPE interface, an analytical model has been developed for the analysis of the experimental ultimate pull-out force results. For the ranges of initial interference fit and implantation length considered, the analytical model was fitted to the experimental results by adjusting the friction coefficient. The mean value of the friction coefficient obtained was 0.043. Finite element simulation was also carried out for the pull-out test using the ABAQUS program. It was found that the finite element simulation describes well the experimental ultimate pull-out forces than the analytical calculation.     

Pull-Out Response of a Steel Post Inserted in a Pre-Drilled HDPE Cylinder: Analytical and Finite Element Analyses Using Pressure-Dependent Friction

Abstract

For the aim of fixing and stabilizing the Total Knee Arthroplasty (TKA) tibial component, pull-out strength of the post is one of the most important factors to be considered. The material properties of bone, coupled with the principal dimensions of bone/post assembly such as diameter, interference fit and implantation length, may affect the pull-out strength of the post fixation. In this study, a cylindrical stainless steel post inserted in a pre-drilled High Density Polyethylene (HDPE) cylinder with an initial interference fit was taken as a model to assess the contribution of post fixation to the initial stability of TKA tibial component. Pull-out experiments were carried out for different initial interference fits and implantation lengths. Under pull-out loading, the micro-slip initiation and propagation at the post/cylinder interface was found to be progressive and was modeled using Coulomb friction at the interface. In order to examine the experimental ultimate pull-out force results, an analytical model was developed. The analytical model was fitted to the experimental results by adjusting the friction coefficient for the considered ranges of initial interference fit and implantation length. It was found that friction coefficient depends on initial interference fit (Δr) as well as on the initial contact pressure (σ0). For the considered interference fit values Δr = 01 mm, Δr = 02 mm and Δr = 03 mm (σ₀ = 1362 MPa, σ₀ = 2724 MPa and σ₀ = 4086 MPa), the values of adjusted friction coefficient are 0.091, 0.067 and 0.058, respectively. Finite Element simulation was also carried out for the pull-out test using the ABAQUS program. It was found that numerical, analytical and experimental results are all in good agreement.     

Finite element analysis of load transfer at a fibre–matrix interface during pull-out loading

Load transfer ability of the fibre–matrix interface is well known to mainly control the mechanical behaviour of fibre-reinforced materials. This load transfer phenomenon is of great importance in dentistry when a post is used for fixing a ceramic crown on the tooth. The pull-out test has been well accepted as the most important micromechanical test for evaluating the interaction properties between the fibre and matrix. In this study, a finite element model is developed to analyse the pull-out process of a steel fibre from an epoxy matrix. Based on the pull-out force–displacement curves, developed in our previous experimental work, specific load transfer laws at the fibre–matrix interface have been proposed for each stage of the pull-out process, i.e., before and after fibre–matrix debonding. Predicted initial extraction forces for different implantation lengths were fitted to experimental values and an initial interference fit of 4 μm was determined. An interfacial shear strength of 21 MPa was then determined by fitting the predicted debonding forces for different implantation lengths to the experimental values. According to the load transfer laws considered, analysis of the interfacial shear stress indicates that fibre–matrix debonding initiates simultaneously at both the lower and upper extremities of the interface.     

Analysis of a pull-out test with real specimen geometry. Part II: the effect of meniscus

This paper continues our study on the platelet model of the pull-out specimen, in which the matrix droplet shape is approximated by a set of thin parallel disks with the diameters varying along the embedded fiber. Using this model, the fiber tensile stress and the interfacial shear stress profiles were calculated for real-shaped matrix droplets, including menisci (wetting cones) on the fibers, taking into account residual thermal stresses and interfacial friction. Then, these profiles were used to numerically simulate the processes of crack initiation and propagation in the pull-out test and to obtain theoretical force-displacement curves for specimens with different embedded lengths and wetting cone angles. Our simulations showed that the interfacial crack in real-shaped droplets initiated at very small (practically zero) force applied to the fiber, in contrast to the popular ‘equivalent cylinder’ approximation. As a result, the equivalent cylinder approach underestimated the interfacial shear strength (IFSS) value determined from the pull-out test and at the same time overestimated the interfacial frictional stress; the smaller was the wetting cone angle, the greater the difference. We also investigated the effects of the embedded fiber length and interfacial frictional stress in debonded areas on the calculated IFSS. The simulated force–displacement curves for the real-shaped droplets showed better agreement with experimental curves than those plotted using the equivalent cylinder approach.     

Indirect estimation of fiber/polymer bond strength and interfacial friction from maximum load values recorded in the microbond and pull-out tests. Part I: local bond strength

The techniques aimed at adhesion strength measurement between reinforcing fibers and polymer matrices (the pull-out and microbond tests) involve the measurement of the force, F _max, required to pull out a fiber whose end is embedded in the matrix. Then, this maximum force value is used to calculate such interfacial parameters as the apparent bond strength, τ_app, and the local interfacial shear strength (IFSS), τ_d. However, it has been demonstrated that the F _max value is influenced by interfacial friction in already debonded regions, and, therefore, these parameters are not purely 'adhesional' but depend, in an intricate way, on interfacial adhesion and friction. In the last few years, several techniques for separate determination of adhesion and friction in micromechanical tests have been developed, but their experimental realization is rather complicated, because they require an accurate value of the external load at the moment of crack initiation. We have developed a new technique which uses the relationship between the maximum force and the embedded length ('scale factor') to separately measure fiber-matrix interfacial adhesion and friction. Using the equation for the current crack length as a function of the applied load, based on a stress criterion of interfacial debonding, we modeled the pull-out and microbond experiments and obtained the maximum force value versus the embedded length. By varying τ_d and interfacial friction, τ_f, to fit experimental plots, both interfacial parameters were estimated. The micromechanical tests were modeled for three types of specimen geometries (cylindrical specimens, spherical droplets, and matrix hemispheres in the pull-out test) with different levels of residual thermal stresses and interfacial friction. The effect of all these factors on the experimental results is discussed, and the importance of specimen geometry is demonstrated. One of the most interesting results is that the 'ultimate' IFSS (the limiting τ_app as the embedded length tends to zero) is not always equal to the 'local' bond strength.     

Indirect estimation of fiber/polymer bond strength and interfacial friction from maximum load values recorded in the microbond and pull-out tests. Part II: Critical energy release rate

A new approach to experimental data treatment in the pull-out and microbond tests has been developed. It uses the relationship between the maximum force recorded in these tests and the embedded length ('scale factor') to separately determine adhesional interfacial parameters (critical energy release rate, local bond strength) and interfacial friction in debonded regions. The new method does not require the measurement of the debond force, which corresponds to interfacial crack initiation, and is, therefore, much more convenient and simpler than 'direct' techniques involving continuous monitoring of crack growth. Using the equation for the current crack length as a function of the load applied to the fiber, based on a fracture mechanics analysis of interfacial debonding, we modeled the pull-out and microbond experiments and obtained the maximum force versus the embedded length. By varying the critical energy release rate and interfacial frictional stress to fit experimental plots, both interfacial parameters were determined for several fiber-polymer pairs. Effects of specimen geometry, residual thermal stresses, and interfacial friction on the measured values are discussed. The results are compared with those obtained with our similar stress-based approach. The energy criterion works when the embedded length is not very short, and in this range of embedded length it is better than the stress criterion. Both criteria can be complementarily used for interface characterization.     

Measurement of the Adhesion of a Viscoelastic Sphere to a Flat Non-Compliant Substrate

The adhesion between a single polystyrene bead (radius, 27 μm) and a flat silica surface has been measured with an atomic force microscope as a function of two variables: (a) The maximum applied load and, (b) the loading time at a constant maximum applied load. Analysis of the results indicates significant plastic deformation of the bead under the action of the load forces. There is also evidence for time-dependent viscoelastic effects as a load is exerted on the bead. The contact zone of the polystyrene bead used for these experiments was examined using Scanning Electron Microscopy. The microscope images revealed a surface covered in small polymer beads with a radius of only 115 nm. In the contact zone these beads had undergone substantial and permanent deformation as a function of the applied load. Basic geometric analysis reveals that the large sphere is not contacting the flat surface under any load. The results presented here indicate the value of being able to measure adhesion using an atomic force microscope. The importance of being able to characterise the contact zone accurately is also highlighted.     

Measurement of the Adhesion of a Viscoelastic Sphere to a Flat Non-Compliant Substrate

The adhesion between a single polystyrene bead (radius, 27 μm) and a flat silica surface has been measured with an atomic force microscope as a function of two variables: (a) The maximum applied load and, (b) the loading time at a constant maximum applied load. Analysis of the results indicates significant plastic deformation of the bead under the action of the load forces. There is also evidence for time-dependent viscoelastic effects as a load is exerted on the bead. The contact zone of the polystyrene bead used for these experiments was examined using Scanning Electron Microscopy. The microscope images revealed a surface covered in small polymer beads with a radius of only 115 nm. In the contact zone these beads had undergone substantial and permanent deformation as a function of the applied load. Basic geometric analysis reveals that the large sphere is not contacting the flat surface under any load. The results presented here indicate the value of being able to measure adhesion using an atomic force microscope. The importance of being able to characterise the contact zone accurately is also highlighted.     

Development of an elastomer with a high static or breakaway friction coefficient

This paper reviews the literature concerning the measurement of friction coefficients (μ) for elastomers and summarizes our data measured under static or breakaway conditions against epoxy painted steel using ～ 176 psi contact pressure. Although largely related to missile launch system applications, the μ values presented are specific for interface pairs, normal loading force, and speed. Therefore, this article should serve as a starting point for those requiring specific friction data for selected elastomers.     

A study of the mechanisms involved in initial friction process of continuous drive friction welding

The effects of the welding conditions on the initial friction process of continuous drive friction welding are investigated using 20-Mild steel. The results show that the friction interface will sequentially experience three typical friction behaviours of abrasion, slide and stick before the initial peak torque. The torque in slide stage shows a platform feature, which transforms to stick stage with a rapidly increasing feature of the torque. As the friction pressure increases from 15 to over 60 MPa, the initial joining location (i.e. corona bond) shifts from one-fourth of the specimen radius (1/4R) towards 1/2R. The maximum surface temperatures show initial slow rising, platform and rapid rising features before the highest temperature appears, which is corresponding to the interface friction status of abrasion, slide or stick. The initial joining location virtually coincides with the location where the maximum temperature is attained.     

Modification of epoxy resin by polysulfone to improve the interfacial and mechanical properties in glass fibre composites. II. Adhesion of the epoxy-polysulfone matrices to glass fibres

Adhesion of epoxy-polysulfone (PSF) matrices to glass fibres of 12–30 μm in diameter was studied under both quasi-static and cyclic loadings. A pull-out technique was used for adhesion measurement. It was shown that incorporation of PSF into epoxy resin changed its adhesion to fibres. A maximum was observed in the adhesion strength vs. PSF content dependence at 10 wt% thermoplastic concentration. The results obtained were compared with the data on the epoxy-PSF matrices adhesion to thick steel wire (d = 150 μm) and Nylon-6 fibres (d = 250 μm). Similar values of the adhesion strength increase (22–25%) confirmed that all the changes at the interface were connected primarily with the matrix. A new preferably non-destructive cyclic loading technique was used to test the systems under cyclic loading at varying force amplitudes, frequencies and displacement amplitudes. In this technique the interphase behaviour is characterised by two variables: by the phase angle between the deformation applied to the matrix and the force transferred by the matrix to the fibre, and also by the amplitude of this force. Minimal force amplitudes were observed for the joints with 10 wt% polysulfone. Moreover, phase-angle values for epoxy-10% polysulfone joints were minimal among all the systems investigated. Increase in the number of loading cycles caused much more damage to unmodified epoxy matrix than that to epoxy-polysulfone matrices. Thus, modification of epoxy resin by polysulfone enhanced its adhesion to fibres under both quasistatic and cyclic loadings, especially for epoxy-10% polysulfone matrix. The possible mechanism of the phenomenon observed is discussed.     

不同龄期钢纤维增强水泥砂浆纤维拉拔试验与模拟研究

钢纤维增强水泥基复合材料作为一种多相复合材料,其增强增韧效果的发挥依赖于钢纤维与基体之间的界面粘结性能。通过开展不同龄期的钢纤维增强水泥基复合材料单根纤维拉拔试验及数值模拟研究,分析了龄期对钢纤维增强水泥砂浆界面粘结性能的影响,建立了不同龄期的单根纤维拉拔细观模型,通过将模拟结果与试验结果进行对比验证模型的有效性。根据所建立的细观模型分别对不同龄期钢纤维增强水泥砂浆纤维-基体间的界面粘结作用机理及纤维-基体间粘结表面在纤维拔出过程中的应力变化进行了分析。结果表明:所建立细观模型模拟得到的纤维最大拉拔力及荷载-滑移曲线与试验结果吻合较好,钢纤维的最大拉拔力及钢纤维-水泥砂浆基体的界面粘结强度均随着龄期的增加而增加;在7 d龄期内界面粘结强度的增长速度较快,7 d龄期后增长速度放缓;随着龄期的增加,不同龄期段的界面粘结强度的增长率逐渐减小并趋于稳定。采用拟合得到的粘结表面材料参数能够有效模拟各龄期下单根钢纤维从水泥砂浆中的拔出过程。     

Fatigue debonding in fibrous composites

The increased use of fibrous composites in various applications has drawn attention to the behaviour of such materials under fatigue loading. One possible collapse mechanism under this type of loading is progressive de-bonding between the fibre and the matrix. In order to investigate this mechanism, a basic model (or unit cell) was selected and the crack growth rate was measured when a time varying load was applied. The model consisted of an epoxy cylinder (transparent) with a steel bar in its centre. It was assumed that the length of the debonded region (the crack length) at a certain moment depended in some way on the potential energy release rate, in analogy with Paris' crack growth law. To investigate this relationship the energy release rate had to be calculated, and methods for so doing are discussed. Plane bimaterial specimens were also tested to investigate the conditions under which a crack in the interface between two elastic bodies begins to grow.     

基础内预埋锚杆抗拔试验研究

通过对建筑基础筏板内预埋锚杆进行抗拔试验检测其抗拔承载性能,对锚杆周围混凝土受抗拔力破坏形式进行研究。研究表明：在埋入锚杆最底端加拧1个螺母,起扩大头作用,增大锚杆侧阻力,较好地固定锚杆,抗拔试验破坏时,断裂部位发生在千斤顶施加荷载作用点附近,而并非将锚杆整体拔出;加载至锚杆材料屈服破坏点对应荷载739 kN附近,荷载-位移曲线呈线性变化,加载量大于该值后,锚杆塑性变形逐渐发展,抗拔过程主要是锚杆杆体自身形变的过程,前半阶段主要为弹性变形,后半阶段主要为塑性变形,直至锚杆被拉断;从筏板内锚杆取芯样来看,抗拔对锚杆周边混凝土产生一定拉裂,裂缝不大,主要在上部300 mm处。     

Study on the friction interface evolution during rotary friction welding of tube

In this study, evolution characteristics of the friction interface during rotary friction welding of tube were investigated. The friction interface that obtained at different welding stage were observed by confocal laser scanning microscopy. The results show that the friction interface transforms from sliding friction state to visco-plastic deformation state when the welding torque reaches the peak value. In addition, based on the thermodynamic framework extracted from the maximum entropy production principle, an analytical model for transition criterion from sliding friction to visco-plastic deformation was established. The model was verified by the corresponding experimental results of eight alloys, which indicated that the accuracy and generality of the model is satisfactory.     

全钢载重子午线轮胎侧偏特性有限元分析

以275/70R22.5 RT606全钢载重子午线轮胎为研究对象,运用有限元分析软件TYABAS和Abaqus建立轮胎侧偏特性分析有限元模型,并研究不同负荷的稳态滚动条件下,侧向力和回正力矩随侧偏角的变化规律。结果表明:在单一垂直负荷下,随着侧偏角的增大,侧向力的绝对值逐渐增大,当侧偏角为-5°和5°时,回正力矩分别达到极小值和极大值;在同一侧偏角下,随着负荷的增大,侧向力的绝对值逐渐增大。侧偏刚度仿真结果与试验结果一致,验证了仿真分析方法的有效性。     

涤纶熔体增压泵过载保护失效分析

对涤纶熔体纺丝的增压泵易发生故障损坏,泵轴折断,扭矩限制器连接轴折断,摩擦副打滑等过载保护失效的原因进行分析,经过理论计算,得出扭矩限制器的预紧力矩值。结果表明,扭矩限制器的预紧力矩的确定参照其理论计算值,可有效地保证熔体增压泵安全,保证摩擦副在正常负载下打滑时而正常运转。     

子午线轮胎稳态滚动的有限元分析

以子午线轮胎11.00R20为例,考虑轮胎变形的几何非线性,以及轮胎与地面、轮胎与轮辋的大变形非线性接触等,建立子午线轮胎稳态滚动的有限元分析模型。对轮胎进行了静负荷工况以及稳态滚动工况下的受力分析、接地特性分析等。并提取了轮胎的滚动半径。研究结果有利于了解轮胎的力学特性,以便进一步优化轮胎结构,提高轮胎性能。     

Adherence and Rolling Kinetics of a Rigid Cylinder in Contact with a Natural Rubber Surface

Equilibrium conditions of a rigid cylinder in contact with the flat and smooth surface of a natural rubber sample are studied using concepts of fracture mechanics, such as the strain energy release rate or the stress intensity factor. It is shown that an equilibrium contact area exists if the applied force per unit axial length is greater than a negative critical value, closely related to the cylinder radius and mechanical and superficial properties of the elastic solid. Due to the intervention of molecular attraction forces, of van der Waals type, a light cylinder rolls under an inclined rubber surface and it is displayed that the rolling speed is the same when the cylinder rolls upon the same inclined surface. It has been verified that if a flat rubber substrate, with an adequate length, is rotated at constant angular velocity, a steel cylinder rolls alternately upon and under the surface, unceasingly without falling down.     

全钢载重子午线轮胎胎圈损坏引出的钢丝帘线抽出力探讨

研究钢丝帘线的直径、材质和结构对钢丝帘线抽出力的影响。试验结果表明,钢丝帘线的直径和强度增大、结构紧密,钢丝帘线的抽出力反而减小;在采用高强度、紧密型钢丝帘线提高轮胎性能时应关注抽出力降低的影响。