Influence of notch radius and R-curve behaviour on the fracture toughness evaluation of WC-Co cemented carbides

In this work the apparent fracture toughness of different grades of WC-Co cemented carbides has been evaluated by means of the single edge V-notched beam (SEVNB) method. The results are analysed, as a function of both the binder mean free path and the maximum steady-state crack shielding value, following a theoretical approach which assumes the existence of a small crack at the notch tip. The experimental findings indicate that larger defects at the notch tip and/or existence of R-curve behaviour imply higher (i.e. less restricted) values of the minimum notch radius required in SEVNB specimens for a reliable assessment of the fracture toughness of cemented carbides.     

Comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane

A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the μ/(1−ν) in the single material is substituted by the harmonic mean of μ/(1− ν) in the bimaterial where μ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of Fx versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of Fx for m=0 is larger than that for m=−1. This revised version was published online in August 2006 with corrections to the Cover Date.     

Computational modeling of debonding behavior at the bone/cement interface with experimental validation

Both clinical examinations and in vitro physical experiments have shown that the fixation interfaces of cemented components are actually critical sites affecting the long-term stability and survival of prosthetic implants after implantation. This study aims to investigate the interfacial debonding behavior of bone/cement composite structures and attempts to establish an analysis model for clinical applications involving cemented prosthetic components. The mechanical properties of the bonded interface were characterized by interfacial strength, interfacial stiffness, and fracture toughness; the measured values of tensile strength, shear strength, and fracture toughness were 4.94 MPa, 5.94 MPa, and 0.34 MN/m^3/2, respectively. The measured strengths of the different configurations from this study are in good agreement with the experimental results available in the literature. In addition, we generated a finite element model with the same geometry as that of the experimental specimen used in the fracture test. The extent of interfacial debonding was further determined by means of the surface damage criteria and the fracture characteristics of the interface crack. The finite element model with an elastic interface predicted that the stress intensity factor (SIF) at the bone/cement interface crack varies nonlinearly with the applied load, which shows that the interface disintegrates at the load level, as was measured in the fracture experiments. It was possible to verify that the proposed simulation model was capable of describing the interfacial mechanical behavior of cemented components.     

Parallel crack near the interface of magnetoelectroelastic bimaterials

A parallel crack near the interface of magnetoelectroelastic bimaterials is considered. The crack is modelled by using the continuously distributed edge dislocations, which are described by the density functions defined on the crack line. With the aid of the fundamental solution for the edge dislocation, the present problem is reduced to a system of singular integral equations, which can be numerically solved by using the Chebyshev numerical integration technique. Then, the stress intensity factor (SIF), the magnetic induction intensity factor (MIIF) and the electric displacement intensity factor (EDIF) at the crack tips are evaluated. Using these fracture criteria, the cracking behaviour of magnetoelectroelastic bimaterials is investigated. Numerical examples demonstrate that the interface, mechanical load, magnetic load and material mismatch condition are all important factors affecting the fracture toughness of the magnetoelectroelastic bimaterials.     

Internal–external circumferential crack behaviour in the cement layer of total hip replacement

This study aimed to investigate crack behaviour at the internal and external surfaces of the cement layer in total hip replacement. A three‐dimensional model of the femur with the cemented prosthesis was developed and analysed. Cracks were placed on the internal, external and both internal and external surfaces of the cement layer. Stress intensity factors were measured during gait. Results revealed that the stress intensity factors modes I and III were the most dominant in the crack propagation in the cement layer. The domain of mode I was the medial and lateral sides of the cement layer. Meanwhile, the domain of mode III was the anterior and posterior sides of the cement layer. The stress intensity factor and distance from the distal end indicated an inverse relationship. The internal and external cracks had no significant interaction. Moreover, stress intensity factors at the external surface of the cement layer were higher than those on the internal surface.     

Reinforcement of hydrated portland cement with high molecular mass water-soluble polymers

A small amount of polymer in water solution form (polyvinylpyrolidone or polyvinylalcohol) was added to a mix high silicate cement + amorphous silica, with reduced water to cement ratio. It was shown that as the molecular mass of the polymer is increased, the fracture stress and the stored energy at fracture of the specimens improved. The polymer induces an increase of the critical stress intensity factor (K _Ic ) (crack initiation). The fracture behaviour of the polymer modified cement paste beyond the elastic domain is also affected by PVA or PVP additions. The dissipated energy measured using the crack opening displacement CMOD was increased by a factor of two with 4wt% of PVP and by a factor of three with 3wt% of PVA, as a consequence of operative toughening mechanisms. The increase of mechanical properties is explained in case of PVP by crack interactions due to CSH microstructure modifications, and with PVA by crack bridging mechanisms as a consequence of dispersed polymer rich nodules in the hydrates phase.     

Effect of bolt clamping force on the fracture strength of mixed mode fracture in an edge crack with different sizes: Experimental and numerical investigations

To investigate the effect of bolt clamping force, resulting from torque tightening, on the mixed mode fracture (I and II) strength and effective geometry/loading factor of an edge crack with different lengths, experimental and numerical studies have been carried out. In the experimental part fracture tests were conducted on three batches of simple edge crack and bolt torque tightened with 3.5 and 7 N m edge crack at three different crack sizes of Poly methyl-methacrylate (PMMA) rectangular plate. The specimens’ fracture strength was obtained using a tensile test machine at different loading angles by employing a modified Arcan fixture. In numerical part, finite element simulations were employed to model the three test specimen batches at the three crack lengths to obtain their stress intensity geometry/loading factors. The results show that the bolt tightening torque significantly reduces the effective geometry/loading factor, and thus increases the joint fracture strength compared to bolt-less simple edge crack specimens. However, the bolt clamping effect on increasing the fracture strength was almost the same for different crack lengths.     

The effect of gentamicin sulphate on the fracture properties of a manually mixed bone cement

This work investigates the effect of adding gentamicin, an antibiotic, on the fracture properties of bone cement. Endurance limit, fatigue crack propagation and fracture toughness were determined for a polymethylmethacrylate‐based cement, containing 10% w/w of barium sulphate as radiopacifying agent, and the same formulation modified by the addition of 4.22% w/w of gentamicin sulphate. The antibiotic does not affect the endurance limit nor the fracture toughness of the material. There are significant differences in the parameters of the Paris' law fitting the crack growth data: once the main crack is nucleated, it initially propagates at a lower rate but thereafter accelerates faster in gentamicin loaded bone cement. Despite this difference, the growth rate for the same stress intensity factor remains of the same order of magnitude in both formulations. The addition of 4.22% w/w of gentamicin sulphate to radiopaque bone cement has a negligible total effect on the fracture properties of the material.     

Fracture measurements on cement paste

This paper describes an investigation into the fracture behaviour of hardened cement paste. Notched specimens of the material were tested to failure in flexure and tension. In the initial flexural tests on beams of fixed overall depth, the stress intensity factor at failure as calculated from linear-elastic fracture mechanics appeared to be a material constant. However, further investigation showed that this factor varied with specimen size, and suggested that linear-elastic fracture mechanics and the concept of fracture toughness are not readily applicable to hardened cement paste, which would appear to be a relatively notch insensitive material whose strength is not greatly reduced by the presence of flaws. A “tied crack” model explains semi-quantiatively the observed behaviour.     

裂纹止裂技术及裂纹动态扩展规律研究

为了对动态荷载作用下水泥粉煤灰砂浆的裂缝动态扩展行为进行研究,提出了一种大尺寸带V型底边的半圆边裂纹(SECVB)试件,其V形底部具有止裂功能。SECVB试件的V形底部设计为180°,150°和120°三个角度。采用落锤冲击装置进行了冲击试验,并使用裂纹扩展计(CPG)用于测量裂纹扩展的相关参数。利用有限差分程序AUTODYN对裂纹扩展行为进行了数值模拟,并用有限元程序ABAQUS计算了裂纹的动态应力强度因子(DSIF);根据CPG测量的裂纹萌生时间和扩展时间来确定临界应力强度因子。试验和数值模拟结果表明,SECVB试件适合于研究动态荷载作用下水泥粉煤灰砂浆的裂纹扩展行为和止裂行为。在裂纹扩展过程中,裂纹可能在一段时间内止裂,并且裂纹在起始时刻的断裂韧度高于裂纹扩展时的断裂韧度。     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Mechanical and thermal behaviour of an acrylic bone cement modified with a triblock copolymer

The basic formulation of an acrylic bone cement has been modified by the addition of a block copolymer, Nanostrength^® (NS), in order to augment the mechanical properties and particularly the fracture toughness of the bone cement. Two grades of NS at different levels of loading, between 1 and 10 wt.%, have been used. Mechanical tests were conducted to study the behaviour of the modified cements; specific tests measured the bend, compression and fracture toughness properties. The failure mode of the fracture test specimens was analysed using scanning electron microscopy (SEM). The effect of NS addition on the thermal properties was also determined, and the polymerisation reaction using differential scanning calorimetry. It was observed that the addition of NS produced an improvement in the fracture toughness and ductility of the cement, which could have a positive contribution by reducing the premature fracture of the cement mantle. The residual monomer content was reduced when the NS was added. However this also produced an increase in the maximum temperature and the heat delivered during the polymerisation of the cement.     

Examination of the failure behaviour of wood with a short crack in the tangential-radial system by single-edge-notched bending test

Single-edge-notched tests of a tangential-radial system were conducted on agathis specimens to analyze the failure behaviour of wood with a short crack. The nominal bending strength and mode I critical stress intensity factors of the specimens with various crack lengths were measured, and the influence of the crack length on these properties was examined. The nominal bending strength of the cracked specimens was significantly lower than that of a crack-free specimen, even when the crack was extremely short. This finding suggests that the fracture mechanics theory is essential for analyzing the failure behaviour of wood with a very short crack. However, the mode I critical stress intensity factor still depended on the crack length. When considering the fracture process zone developing at the crack tip, the critical intensity factor could be predicted effectively.     

Brittle fracture evaluation of a fine grain cement mortar in combined tensile-shear deformation

Different laboratory experiments are usually conducted to characterize the fracture behaviour and integrity properties of newly developed structural materials. However, the reported fracture tests data for an improved high strength cement mortar (HSCM) under combined tension-shear loading are not in agreement with theoretical predictions obtained from well-known fracture criteria. It is shown in this paper that the significant difference existing between the experimental and theoretical results is due to ignoring the effect of  T -stress on the processes of crack growth in the HSCM test specimens. A modified fracture model is then used to show that the theoretical predictions can be corroborated by the experimental results when the effect of  T -stress is taken into account.     

Fracture behaviour of thermosetting polymers for ophthalmic lenses

In the worldwide market we found strongly positioned two thermosetting materials for ophthalmic lenses: CR-39 and Superfin. In this work, the fracture behaviour of both materials is studied through the application of Linear Elastic Fracture Mechanics (LEFM) using two geometries: double torsion and three point bending. The fracture toughness has been determined by the double torsion technique. CR-39 showed a continuous and stable crack propagation, whereas Superfin exhibited a stick-slip behaviour whose instability decreased when the strain rate increased. The values at crack initiation agreed with the fracture toughness results of single edge notched tests in bending geometry.     

Automatic 3-D crack propagation calculations: a pure hexahedral element approach versus a combined element approach

This article presents an evaluation of two different crack prediction approaches based on a comparison of the stress intensity factor distribution for three example problems. A single edge notch specimen and a quarter circular corner crack specimen subjected to shear displacements and a three point bend specimen with a crack inclined to the mid-plane are examined. The stress intensity factors are determined from the singular stress field close to the crack front. Two different fracture criteria are adopted for the calculation of an equivalent stress intensity factor and crack deflection angle. The stress intensity factor distributions for both numerical methods agree well to available reference solutions. Deviations are recorded at crack front locations near the free surface probably due to global contraction effects and the twisting behaviour of the crack front. Crack propagation calculations for the three point bending specimen give results that satisfy intuitive expectations. The outcome of the study encourages further pursuit of a crack propagation tool based on a combination of elements.     

Effect of residual stress on delamination from interface edge between nano-films

The focus in this study is on the effect of residual stress on the delamination crack initiation from the interface edge between thin films, Cu/TiN, where the stress is intensified by the free edge effect. The delamination tests, where the mechanical stress is applied on the interface, show that the specimen with the thinner Cu film has an apparently higher strength at the interface edge. The residual stress in the films is then evaluated by curvature measurement of film/substrate coupon and the influence on the delamination is analyzed. The residual stress increases with the increase of film thickness and remarkably intensifies the stress near the edge. By superimposing the contributions of the applied load and the residual stress, a good agreement is obtained in the normal stress intensity near the interface edge at the delamination independent of the Cu thickness. This signifies that the combination of intensified stresses due to the applied load and the residual stress governs the crack initiation at the interface edge, and the toughness at the interface edge is evaluated by the stress intensity factor on the basis of the fracture mechanics concept.     

Element-wise algorithm for modeling ductile fracture with the Rousselier yield function

Within the theme of ductile fracture in metals, we propose an algorithm for FEM-based computational fracture based on edge rotations and smoothing of complementarity conditions. Rotation axes are the crack front nodes in surface discretizations and each rotated edge affects the position of only one or two nodes. Modified edge positions correspond to the predicted crack path. To represent softening, porous plasticity in the form of the Rousselier yield function is used. The finite strain integration algorithm makes use of a consistent updated Lagrangian formulation which makes use of polar decomposition between each increment. Constitutive updating is based on the implicit integration of a regularized non-smooth problem. The proposed alternative is advantageous when compared with enriched elements that can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, fracture examples making use of the Rousselier yield function are presented. The Ma-Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/displacement accuracy.     

Crack propagation in ceramics under cyclic loads

Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.     

CTOD for the through-the-thickness crack in a plate of arbitrary thickness

The sectional thickness of plate-like components has a significant influence on the fatigue and fracture properties. This effect is primarily due to the differences in the through-the-thickness stresses prevailing at the tip of a crack in a finite-thickness plate or shell. Characterization of this effect to date has remained largely empirical. The current paper presents new analytical results for CTOD for the through-the-thickness crack in infinite plates with various thicknesses. These results are based on a recently developed solution for an edge dislocation in infinite plate of arbitrary thickness. The analytical predictions of the CTOD and the constraint factor are compared with the three-dimensional FE results. It is shown that the analytical and the numerical results are in good agreement when the numerical calculations are not affected by the size of the FE mesh and by the boundaries of the FE model.