Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known −1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.     

Flexural and fatigue properties of a bone cement based upon polyethylmethacrylate and hydroxyapatite

Polymethylmethacrylate (PMMA) bone cement is commonly used in surgery to fix joint replacements into the bone. Although the operations are generally successful, loosening of the prosthesis does occur with fracture of the bone cement treated as the source of failure in some instances. Polyethylmethacrylate (PEMA) bone cement offers a promising alternative to PMMA due to its high ductility, low toxicity and low exotherm. In addition, hydroxyapatite (HA) particles can be added, while retaining the ductile properties of the material. In this study, the flexural and fatigue properties of this experimental cement, with and without HA reinforcement, have been examined. It was found that up to 40wt.% HA could be added with increases in both flexural strength and modulus. Specimens were subjected to tensiontension cyclic loading at a number of stress levels until catastrophic failure occurred. In comparison with a commercial PMMA cement, tested at relatively high stresses, the PEMA cement failed at lower cycles to failure. However, the data converged at the lower stresses employed which are closer to the physiological loading situation. With the addition of HA, although the cycles to failure were decreased, the deformation experienced by the PEMA-HA cement whilst being cycled was reduced.     

Fatigue of bone cement with simulated stem interface porosity

Cracks in bone cement have been observed in carefully examined post-mortem preparations of cemented stems. These cracks were probably caused by fatigue, and frequently appeared to initiate at pores. Ubiquitous porosity, occurring preferentially at, or near, the stem, is most likely caused by polymerization shrinkage. Preparation of air-free cement has only a marginal influence on the interface porosity, but pre-heating the stem in order to reverse the direction of polymerization can reduce or eliminate it. To estimate the impact of interface porosity on the fatigue strength of bone cement, test plates for this study were cast in a steel mold without release foils, and with one side of the mold warmer. Sample plates so prepared from chilled, partial vacuum-mixed PALACOS®R, have one face essentially pore-free and the other porous, the extent and morphology of the porosity being very similar to that observed on the stem–cement interface. Four-point bending fatigue strength, determined after 60 d conditioning in Ringer's solution at 37°C, was only 20 MPa (at 106 cycles, with the porous side under tension) compared to 30MPa for conventionally prepared, pore-free material. This corresponds to a 10–100 fold reduction in cycles to failure in the range of stresses predicted to occur in vivo. © 1998 Kluwer Academic Publishers     

Interfacial crack tip field in anisotropic/isotropic bimaterials

The co-cured joint is more efficient than the adhesively bonded joint for composite structures because of its several advantages. However, failure analysis of the co-cured joint has just a little been reported since the co-cured joining method was introduced. Observing based on the experimental results, failure starts at the interface corner of the co-cured joint. Therefore, it is important to consider stress intensities at the interface corner of the co-cured joint.

In this paper, the eigenvalue problem was used to determine asymptotic stress and displacement fields near the interface corner between composite and steel adherends. For obtaining stress intensities at the interface corner a path independent conservative line integral was used.     

Measurement of non-linear microcrack accumulation rates in polymethylmethacrylate bone cement under cyclic loading

Damage accumulation in the cement mantle used to fixate bone prosthesis is one failure scenario for joint reconstruction. It can be described as the phenomenon of numerous microcracks initiating and propagating within the material. Microcracks grow in the cement mantle causing it to gradually lose its mechanical integrity, leading to loosening of the prosthesis. In this study microcracking within acrylic bone cement was quantified over the course of a fatigue test. Identification of new cracks and the growth of pre-existing cracks was monitored at intervals during fatigue testing of five specimens at a mean cyclic stress of 7.5 MPa. Given these measurements, an average damage evolution curve was derived for acrylic bone cement. It was observed that the initiation sites for microcracks were the pore perimeters; therefore, the number of microcracks present in a sample is dependent on porosity. Variability was found within the results and the majority of the variability was accounted for by the difference in the porosity of each sample. Results have identified non-linear damage evolution. On a simplified level a power law equation can be used to describe the damage evolution process.     

Stress field near interface edge of elastic-creep bi-material

Stress fields on elastic-creep bi-material interfaces with different geometry of the interface edge are analyzed by finite element method. The results reveal that the stress highly concentrates near the interface edge at the loading instant and it gradually decreases as the creep-dominated zone expands from the small-scale creep to the large-scale creep. The stress singularity due to creep which resembles the HRR stress singularity appears near the interface edge in all cases. The stress intensity near the interface edge time-dependently decreases and becomes constant when the transition reaches the steady state. The magnitude is scarcely influenced by the edge shape of elastic material, though it depends on the edge shape of creep material. The stress intensity during the transition can be approximately predicted by the J-integral at the loading instant.     

Characterisation of a metallic foam–cement composite under selected loading conditions

An open-cell metallic foam was employed as an analogue material for human trabecular bone to interface with polymethyl methacrylate (PMMA) bone cement to produce composite foam–cement interface specimens. The stress-displacement curves of the specimens were obtained experimentally under tension, shear, mixed tension and shear (mixed-mode), and step-wise compression loadings. In addition, under step-wise compression, an image-guided failure assessment (IGFA) was used to monitor the evolution of micro-damage of the interface. Microcomputed tomography (µCT) images were used to build a subject-specific model, which was then used to perform finite element (FE) analysis under tension, shear and compression. For tension–shear loading conditions, the strengths of the interface specimens were found to increase with the increase of the loading angle reaching the maximum under shear loading condition, and the results compare reasonably well with those from bone–cement interface. Under compression, however, the mechanical strength measured from the foam–cement interface is much lower than that from bone–cement interface. Furthermore, load transfer between the foam and the cement appears to be poor under both tension and compression, hence the use of the foam should be discouraged as a bone analogue material for cement fixation studies in joint replacements.     

Investigation on the fatigue crack behavior of Zr702/TA2/Q345R composite plate with a crack normal to interface

In this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength.     

Failure prediction of a plate weakened by an elliptic hole under thermal or mechanical load

The failure initiation and crack trajectory are predicted for a plate weakened by an elliptic hole under thermal or mechanical load. The closed form solutions are obtained by using the complex variable theory and the fracture behavior is predicted by applying the strain energy density criterion. The results lead to a number of important conclusions. A general trend is that failure initiation always occurs at the site near the interface with material inhomogeneity while the fracture trajectory tends to spread away from the boundary of an elliptic hole whether thermal or mechanical loads are imposed in the given problem. Fracture initiation is most likely to take place at the site with relatively low temperature accompanied by the presence of tensile stress. Depending on material geometry, kinking phenomena are observed at the boundary layer adjacent to the interface. In general, the critical load in compression is larger than that in tension.     

形状记忆合金的力学及界面参数和体积分数对大块金属玻璃基复合材料增韧的影响

采用考虑塑性的超弹性材料模型和基于损伤塑性的准脆性材料模型,建立了三维单胞有限元模型,模拟了形状记忆合金颗粒增韧大块金属玻璃基复合材料的单调拉伸行为。讨论了形状记忆合金的力学参数、体积分数、界面厚度和界面材料参数对金属玻璃增韧效果的影响。结果表明:提高形状记忆合金的相变应变和马氏体塑性屈服应力将显著提高形状记忆合金颗粒增韧大块金属玻璃基复合材料的拉伸失效应变;形状记忆合金弹性模量超过50.0GPa、马氏体塑性屈服应力超过1.8GPa后,复合材料的拉伸失效应变变化不大。能同时兼顾失效应变和失效应力的形状记忆合金体积分数为15%左右。复合材料界面弹性模量和界面屈服应力的增加将提高复合材料的失效应力,但对失效应变影响不大;复合材料界面厚度的增加在提高失效应变的同时,也降低了复合材料的失效应力。     

In vitro study investigating the mechanical properties of acrylic bone cement containing calcium carbonate nanoparticles

A successful total hip replacement has an expected service life of 10-20 years with over 75% of failures due to aseptic loosening which is directly related to cement mantle failure. The aim of the present study was to investigate the addition of nanoparticles of calcium carbonate to acrylic bone cement. It was anticipated that an improvement in mechanical performance of the resultant nanocomposite bone cement would be achieved. A design of experiment approach was adopted to maximise the mechanical properties of the bone cement containing nanoparticles of calcium carbonate and to determine the constituents and preparation methods for which these occur. The selected conditions provided improvements of 21% in energy to maximum load, 10% in elastic modulus, 7% in bending strength and 8% in bending modulus when compared with bone cement without nanoparticles. Although cement containing nanoCaCO(3) coated in sodium citrate also enhanced the energy to maximum load by 28% and the elastic modulus by 14% when compared with control cement, it is not recommended as a factor in the production of nanocomposite bone cement due to reduction in the bending properties of the final bone cement.     

Effect of crosslinking agents on poly(ethylmethacrylate) bone cements

Asceptic loosening of cemented joint prostheses in many cases is related to the mechanical failure of the acrylic bone cement. Poly(methylmethacrylate) bone cements are widely used in orthopaedic surgery although there are well-known disadvantages. A lower modulus bone cement based on poly(ethylmethacrylate)–n-butylmethacrylate with a lower polymerization exotherm, and a low monomer extractibility, is a promising alternative. The effect of incorporating crosslinking agents in order to improve the mechanical performance of the PEMA bone cement is reported. Three different bifunctional dimethacrylate crosslinking agents with different chain lengths and degrees of flexibility were incorporated in the monomer phase, and cements formulated. The setting time was found to decrease in the presence of the cross-linking agents and the polymerization exotherm decreased in the presence of triethylene glycol dimethacrylate and polyethylene glycol dimethacrylate, n=400. Incorporation of triethylene glycol dimethacrylate showed an increase in the tensile strength and modulus with a decrease in the strain at maximum stress. However, polyethylene glycol dimethacrylate, n=400, did not improve the mechanical properties appreciably which may be attributed to the low crosslinking density and higher flexibility of the spacer group in the crosslinking agent.     

Static and fatigue mechanical characterizations of variable diameter fibers reinforced bone cement

Fibers can be used to improve the mechanical properties of bone cement for the long-term stability of hip prostheses. However, debonding of the fibers from the matrix due to the poor fiber/matrix interface is a major failure mechanism for such fiber reinforced bone cements. In this study, a novel fiber (variable diameter fibers or VDFs) technology for reinforced bone cement was studied to overcome the interface problem of short-fiber composites. These fibers change their diameters along their length to improve the fiber/matrix interfacial bond by the mechanical interlock between the VDFs and the matrix. A novel composite made from novel ceramic VDFs incorporated in PMMA matrix was developed. Both static and fatigue tests were carried out on the composites. Conventional straight fiber (CSF) reinforced bone cement was also tested for comparison purposes. Results demonstrated that both the stiffness and the fatigue life of VDF reinforced bone cement are significantly improved (P < 0.05) compared with the unreinforced bone cement. VDF contents of 10% by volume increased the fatigue life over unreinforced bone cement by up to 100-fold. Also, the fatigue life and modulus of toughness of VDF reinforced cement were significantly greater than those of CSF reinforced cement (P < 0.05 and P < 0.001, respectively). Scanning electron microscopy (SEM) micrographs revealed that VDFs can bridge the matrix cracks effectively and pullout of VDFs results in much more extensive matrix damage than pullout of CSFs increasing the resistance to fatigue. Therefore, VDF reinforced cement was significantly tougher, having a greater energy dissipation capacity than CSF reinforced cement. VDFs added to bone cement could potentially avoid implant loosening due to the mantle fracture of bone cement and delay the need for revision surgery.     

Stress Reduction of 3D Printed Compliance‐Tailored Multilayers

Multilayered multi‐material interfaces are encountered in an array of fields. Here, enhanced mechanical performance of such multi‐material interfaces is demonstrated, focusing on strength and stiffness, by employing bondlayers with spatially‐tuned elastic properties realized via 3D printing. Compliance of the bondlayer is varied along the bondlength with increased compliance at the ends to relieve stress concentrations. Experimental testing to failure of a tri‐layered assembly in a single‐lap joint configuration, including optical strain mapping, reveals that the stress and strain redistribution of the compliance‐tailored bondlayer increases strength by 100% and toughness by 60%, compared to a constant modulus bondlayer, while maintaining the stiffness of the joint with the homogeneous stiff bondlayer. Analyses show that the stress concentrations for both peel and shear stress in the bondlayer have a global minimum when the compliant bond at the lap end comprises ≈10% of the bondlength, and further that increased multilayer performance also holds for long (relative to critical shear transfer length) bondlengths. Damage and failure resistance of multi‐material interfaces can be improved substantially via the compliance‐tailoring demonstrated here, with immediate relevance in additive manufacturing joining applications, and shows promise for generalized joining applications including adhesive bonding.     

Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.     

The use of interlayers in modeling interface crack propagation

Delaminations are a common mode of failure at interfaces between two material layers which have dissimilar elastic constants. There is a well-known oscillatory nature to the singularity in the stress fields at the crack tips in these bimaterial delaminations, which creates a lack of convergence in the modewise energy release rates. This makes constructing fracture criteria somewhat difficult. An approach used to overcome this is to artificially insert a thin, homogeneous, isotropic layer (the interlayer) at the interface. The crack is positioned in the middle of this homogeneous interlayer, thus modifying the original ‘bare’ interface crack problem into a companion ‘interlayer’ crack problem. Individual modes I and II energy release rates are convergent and calculable for the companion problem and can be used in the construction of a fracture criterion or locus. However, the choices of interlayer elastic and geometric properties are not obvious. Moreover, a sound, consistent, and comprehensive methodology does not exist for utilizing interlayers in the construction and application of mixed-mode fracture criteria in interface fracture mechanics. These issues are addressed here. The role of interlayer elastic modulus and thickness is examined in the context of a standard interface fracture test specimen. With the help of a previously published analytical relation that relates the bare interface crack stress intensity factor to the corresponding interlayer crack stress intensity factor, a suitable thickness and elastic modulus are identified for the interlayer in a bimaterial four-point bend test specimen geometry. Interlayer properties are chosen to make the interlayer fracture problem equivalent to the bare interface fracture problem. A suitable mixed-mode phase angle and a form for the fracture criterion for interlayer-based interface fracture are defined. A scheme is outlined for the use of interlayers for predicting interface fracture in bimaterial systems such as laminated composites. Finally, a simple procedure is presented for converting existing bare interface crack fracture loci/criteria into corresponding interlayer crack fracture loci.     

Three-dimensional analysis of interface cracks in rubber materials

Three-dimensional and plane stress finite element analyses were carried out to investigate the stress fields and fracture parameters of interface cracks in rubber materials. The tearing energy computations for any arbitrarily shaped 3D crack front in dissimilar materials were obtained using the virtual crack extension method. The finite element results obtained are validated against existing alternate solutions and experimental data for cracks in homogeneous as well as bimaterial cases. The effects of different rubber material models, tearing energy distributions, crack extension angles, and three-dimensional regions at the crack tip for interface cracks are presented and discussed. It is shown that nonlinear materials have larger three-dimensional effects near the interface crack front, and that this effect increases as the material mismatch increases.     

Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings

The main objective of this work is to obtain analytical solutions for thick-walled cylinders subjected to internal and external pressure in which the entire wall is made of functionally graded material or of only a thin functionally graded coating present on the internal homogeneous wall. We assume that the materials are isotropic with constant Poisson’s ratio; as far as the Young modulus is concerned, we consider a power and an exponential. The proposed analytical solutions show the effects of the different profiles describing the graded properties of the materials on the stress and displacement fields; in addition, comparisons between graded coating and conventional homogeneous coating highlight the advantage of the graded material on the interface stress reduction. Furthermore, we show how even a thin graded coating can be useful to satisfy the requirements of a specific application without having to make an entire wall with graded properties. This investigation permits us to optimize the elastic response of cylinders under pressure by tailoring the thickness variation of the elastic properties and to reduce manufacturing costs given by the technological limitations that occur to produce entire functionally graded walls.     

Effect of interfacial thickness and stiffness on the stress distributions in fibre reinforced cementitious composites

The different microstructure of the fibre–cement interface might result in different failure mechanisms. It is expected that improvement of strength and toughness in fibre-reinforced cementitious composites will depend on their interfacial thickness and stiffness. A three-phase model, subject to a transversely uniform tensile stress, was utilized to investigate the effect of interfacial thickness and stiffness on the stress distributions near the fibre–cement interface and the corresponding failure mechanism. The results suggest that optimum interfacial microstructure of fibre-reinforced cementitious composites can be tailored to obtain a higher strength and toughness. Optimum interfacial thickness and stiffness was evaluated for various reinforcements, including steel, carbon, glass and polypropylene fibres. This revised version was published online in November 2006 with corrections to the Cover Date.     

Material selection in the design of the tibia tray component of cemented artificial knee using finite element method

Aseptic loosening of the tibial component; which may be caused by mechanical stress shielding in the bone and may require revision surgery; is the primary concern of total knee replacement (TKR). The stiffness of the implant material had a marked influence on the stresses developed in the constituents and surrounding bones of the artificial knee and then will affect the bone stress shielding. Therefore, the functionally graded materials had been developed as a potential tibia tray material of TKR due to its improved capability of stress distribution. In the current investigation two dimensional finite element models have been developed to study bone and interface stresses for six different tibial prothesises (titanium, CoCrMo and four functional graded materials “FGM” models). The utilization of FGM tibia tray with elastic modulus changing gradually in vertical direction downwardly showed a favorable stress distribution outcome. Furthermore, the results has revealed that the FGM tibia tray will reduce the stress shielding in the surrounding bones of the artificial knee which will increase the life of the total knee prosthesis.