Modelling the mixed-mode failure of cement-bone interfaces

The main purpose of this study is the development of a failure model for the cement-bone interface in cemented hip prostheses. The model includes the mechanical behaviour of the cement-bone interface under mixed-mode loading, reproducing the initial linear behaviour up to a certain stress level, followed by an exponential strain-softening region. Four parameters for each stress mode (tension and shear) must be defined in order to fully characterize this mechanical behaviour: the interface strength t₀, the initial stiffness K₀, the interface displacement corresponding to full debonding of the interface δ_c and the failure energy G_c. To validate the potential of the associated numerical model, several tests were simulated, obtaining results close to the experimental ones. This formulation was also applied to simulate a more biomechanical although still academic problem: the debonding evolution of the bone-cement interface of the Exeter total hip arthroplasty system, including fatigue failure of the interface. We conclude that the mixed-mode failure interface model here proposed allows for more realistic simulations of the debonding process of cement-bone interfaces.     

Steady state crack growth in elastic-viscoplastic materials

A recent theory of Hart for the steady state propagation of a mode III crack in a ductile material is extended to modes I and II. When a crack is moving at non-zero velocity v, it is shown that for a broad class of materials the stress state at the crack tip is characterized by a r ^1/2 singularity and by a local stress intensity factor K. The local K is the sum of the apparent stress intensity factor K _A and a plastic contribution K _P. The value of K _A is calculated from the remote loading and the crack geometry under the assumption of linear elastic response alone. The quantity K _P characterizes stress relief of non-elastic flow. Numerical calculations are made to determine K as a function of K _A and v for elastic-viscoplastic materials. A dependence of v on K _A is obtained by imposing a kinetic law for v as a function of K. The plots of v vs. K _A show that below some critical values of K _A, steady state conditions cannot be sustained. Corresponding to the threshold value of K _A there is a definite value for the velocity.     

Double crack problem in nonlocal elasticity

The singular stress field around a sharp notch tip is expressed as a sum of two independent fields: a symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaigdaaeqaaaaaaaa!3CC3!\[1/r^{1 - \lambda _1 } \]and a skew-symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaikdaaeqaaaaaaaa!3CC4!\[1/r^{1 - \lambda _2 } \]. The intensities of the symmetric and skew-symmetric singular stress fields are defined in terms of constants K _I and K _II, respectively. In this study, a plane problem of a strip with single or double edge notches under tension or in-plane bending is considered. The bisector of the notch may be inclined to the edge, so that the two singular stress fields with different singularities may be created simultaneously at the notch tip. The body force method is used to calculate the stress intensity factors K _I and K _II. In numerical analysis, basic density functions of the body forces are introduced to characterize the stress singularity at the notch tip. The advantages of this technique are the high accuracy of results, due to the smoothness of the unknown weight functions, and the presence of the direct relation between the values of K _I and K _II and the values of unknown weight functions. The stress intensity factors are systematically calculated for the various geometrical conditions.     

Biochemical and histological evaluation of human synovial-like membrane around failed total hip replacement prostheses during in vitro mechanical loading

The biochemical role of the synovial-like membrane formed at the interface of eight aseptic failed total hip prosthesis has been investigated during in vitro mechanical loading. The study was carried out on four membranes from cemented prosthesis and four titanium alloy uncemented ones. Intermittent positive pressure leading to 20% deformation of the membrane (100 g/cm²)was applied to the membrane fragments in cycles (300 cycles/15 min) repeated three times at thirty minutes intervals in which interleukin-6 (IL6), prostaglandin-E2 (PGE2) and interleukin-1 (IL1) levels were quantified both in culture media and in tissue extracts. Histological, morphometrical and immunohistochemical studies were also carried out on the same membranes.Mechanical stress evidenced an increase in the release of the examined cytokines both in cemented and uncemented prosthesis tissues; particularly evident was IL6 trend of increase from cemented prosthesis and IL1 result from uncemented ones. Histomorphological and immunohistochemical data revealed no differences between membranes obtained from cemented and uncemented prosthesis as to cell proliferation, fibrosis, macrophages lymphocytes B and T population, vessels and nervous fibers. The results indicate that mechanical stress plays a fundamental role in increasing membrane production and release of cytokines known as bone-resorbing agents. Furthermore, the histologic finding of synovial-like membrane with the same histomorphological and immunohistochemical findings but with different biochemical response to mechanical stimulation, suggests that cells involved in the production and release of the considered mediators might have different strain behavior by different development conditions (previous contact with PMMA). © 2001 Kluwer Academic Publishers     

Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Fatigue thresholds and fatigue crack growth (FCG) rates in corner notched specimens of a forged Ti–6Al–4V aero-engine disk material were investigated at room temperature and 350 °C. The threshold stress intensity range, ΔK_th, was determined by a method involving a step change in stress ratio (the ‘jump in’ method). It was found that for three high stress ratios (R=0.7–0.9), where crack closure effects are widely accepted to be negligible, there were similar ΔK_th values at room temperature and 350 °C under the same R. For a given temperature, ΔK_th was observed to decrease from 3.1 to 2.1 MPam with R increasing from 0.7 to 0.9. The fatigue crack growth rate was influenced by increasing temperature. For high stress ratios, FCG rate at 350 °C was higher than that at room temperature under the same ΔK. For a low stress ratio (R=0.01), higher temperature led to higher FCG rates in the near-threshold regime, but showed almost no effect at higher ΔK. The influence of stress ratio and temperature on threshold and FCG rates was analysed in terms of a K_max effect and the implication of this effect, or related mechanisms, are discussed. In light of this, an equation incorporating the effects of the K_max and fatigue threshold, is proposed to describe FCG rates in the near-threshold and Paris regimes for both temperatures. The predictions compare favourably with experimental data.     

The fracture of boron fibre-reinforced 6061 aluminium alloy

The fracture of 6061 aluminium alloy reinforced with unidirectional and cross-plied 0/90°, 0/90/±45° boron fibres has been investigated. The results have been described in terms of a critical stress intensity,K _Q. Critical stress intensity factors were obtained by substituting the failure stress and the initial crack length into the appropriate expression forK _Q. Values were obtained that depended on the dimensions of the specimens. It was therefore concluded that, for the size of specimen tested, the values of the critical stress intensity,K _Q, did not reflect any basic materials property.     

Fracture toughness of selectively reinforced Al2124 alloy: precrack tip in the aluminium alloy side

Abstract

The fracture toughness of Al2124/Al2124+SiC bimaterials is affected by thermal residual stresses, elastic/plastic mismatch, precrack tip position, and failure mechanism. When the precrack tip is in the Al2124 side, final catastrophic failure occurs when ductile fracture of the Al2124 layer between the precrack tip and the composite side takes place, followed by fracture of the composite layer. For a precrack tip 2·0 mm from the interface, K _Q(5%) values are lower than the 'Al2124 only' value due to the near crack tip tensile residual stresses and higher stress triaxiality within the Al alloy ligament. At 0·5 mm from the interface, K _Q(5%) values increase and are usually as high as the 'Al2124 only' value due to the stronger shielding of the elastic/plastic mismatch. If the precrack tip is 2·0 mm from the interface, K _crit values of the bimaterial are higher than the 'Al2124 only' value and this is deduced to be due to the elastic/plastic mismatch shielding. At 0·5 mm from the interface, K _crit values are reduced because both the near tip tensile residual stress is higher and stress triaxiality levels of the ductile ligament are higher, although the elastic/plastic mismatch shielding is also higher at this position.     

Fatigue behaviour of borosilicate glass-ceramic matrix,nicalon (silicon carbide) fibre composites

Uniaxial fatigue damage analyses were performed on borosilicate glass-ceramic matrix, Nicalon (silicon carbide) fibre reinforced unidirectional composites. The fibre volume fraction varied from about 0.25 to 0.60. Load-controlled tension-tension fatigue tests (R ratio = 0.1) were conducted at room temperature and 540°C (1000°F). The fatigue life was found to decrease with increasing cyclic stress level and a power-law relationship of the form _app = _uts(2N _f)^b was established where _app is the applied maximum stress, _uts the monotonic tensile strength, N _f is the number of cycles to failure and b is the fatigue strength exponent. The fatigue damage evolution manifested itself as a decrease in stiffness of the composite with fatigue cycles. This stiffness drop was associated with matrix cracking followed by fibre-matrix debonding and fibre sliding breakage/pull-out, and final failure, respectively at 540°C. The damage evolution at room temperature was associated with degradation of the matrix followed by steady breakage of fibres with no debonding/pull-out, leading to eventual failure of the net section of the composite. In general, quantitative microscopic observations of debonded and pulled-out fibres showed a good correlation with the observed reduction in stiffness. A predictive model to interpret the drop in stiffness is presented and validated using experimental results from the current study.     

A TECHNICAL NOTE. INFLUENCE OF MEAN STRESS ON FATIGUE IN SEVERAL ALUMINIUM ALLOYS UTILIZING Kcmax THRESHOLD PROCEDURES

Recent interest in the constant K_max (K^c_max) threshold testing procedure has resulted in a more in-depth study of the influence of K_max level on fatigue response and ΔK_th in aluminium alloys. Under R^c= 0.1 conditions, which cause large amounts of closure, ΔK^th levels were typically 2 to 4 Mpam. However, under K^c_max test procedures, associated with no measurable closure at threshold, ΔK_th was typically 1 Mpam. A slight K^c_max level effect on ΔK_th was observed at high K_max values for some of the alloys, and was deemed to be a pure mean stress effect, separate from closure arguments.     

The effect of mixed mode I/III on crack evolution in brittle solids

A modification of Sommer's classical experiment [4] has been used to fracture rods of a brittle epoxy resin in mixed mode I/III stress conditions. The nucleation and growth of cracks in an increasing K _III/K _I stress field have been investigated, particularly in relation to the formation of river lines and the evolution of multiple cracks between river lines to form smooth helicoid surfaces. The fractographic features associated with the progressive development of river line patterns involving crack bowing at river line steps, interaction between arrays of cracks and the coalescence of river lines are described. As K _III/K _I increases the scale of the river line patterns increases but the patterns remain self similar. Using principles from differential geometry it is shown that helicoid surfaces can be generated entirely by crack evolution involving tilting without twiting.Emeritus Goldsmiths' Professor of Metallurgy, University of Cambridge, U.K.     

Very high cycle fatigue properties of high‐strength spring steel 60SiCrV7

The very high cycle fatigue properties of spring steel 60SiCrV7 for automotive suspension system with different hydrogen contents were studied by using ultrasonic fatigue testing and fatigue crack growth testing. The results show that the S–N curves exhibit continuous drop of fatigue lives and no obvious horizontal line exists. Similar fracture surface features were observed for all the specimens that failed mainly from internal inclusions with surrounding granular bright facet (GBF). Fatigue strength decreases remarkably with increasing hydrogen content. The applied stress intensity factor range at the periphery of GBF ΔK_GBF is approximately proportional to 1/3 power of the square of GBF area. The average values of ΔK_GBF for uncharged specimens are close to crack growth threshold ΔK_th, which indicates that ΔK_GBF could be regarded as the threshold value governing the beginning of stable fatigue crack propagation. The increase of hydrogen content tends to reduce ΔK_GBF.     

Analysis of three-dimensional interface cracks using enriched finite elements

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K _I, K _II, and K _III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.     

Fibre reinforcement and fracture response in geopolymeric mortars

The inorganic polymeric cement called geopolymer or PSS, has been studied in recent years as a binder for mortar and concrete. The present work reports the fracture toughness studies in mortars made of PSS cement matrix reinforced by wollastonite microfibers (Ca(SiO₃)). K_I‐curves for PSS cement composites were determined according to the superposition asymptotic assumption and compared with reference Portland cement (PC) composites. The maximum toughness gain occurs in both composite systems with V_f = 2%. For higher fibre volumes (3 and 5%), K_I values decrease, due to an increase in porosity. Microstructural analyses showed that toughening mechanisms, as debonding and pullout of the fibers, are more common in PSS cement composites than in the reference PC composites. The difference of toughness between PSS and PC cement (0% of fibers) is about 80%. This demonstrates the high performance of these geopolymeric materials.     

Single-fibre polymer composites

We have used Raman spectroscopy to measure the axial stress distribution along a fibre during a quasi-static single fibre pull-out test. The stress distribution at the debonding front during the progress of debonding gives the maximum interfacial shear strength _s directly. In addition, the stress distribution along the fibre after debonding can be used to evaluate the interfacial normal stress and the frictional coefficient. For the plasma treated high modulus polyethylene (PE) fibres used here, _s is found to be 28 MPa by this method, while the apparent mean interfacial shear strength _a obtained from the regular single fibre pull-out test varies from 3 to 15 MPa with the fibre embedded length I _e. Stress distributions derived from the shear-lag theory fit the experimental data for fully bonded fibres well, giving values for the shear-lag constant K and the stress transfer length 1/ [1]. According to the shear-lag theory, _s = l _eacoth(l _e). If can be found for a given system from Raman spectroscopy, _s can be evaluated from the pull-out test using this equation.The regular pull-out tests, corrected for residual stress and interfacial friction, give the same _s but not the same or pull-out load as the slower Raman test. The shear-lag constant K can be expressed as a function of the matrix shear modulus and geometric terms. One of these terms is the effective interfacial radius, r _e, the radius at which the strain in the matrix equals the average matrix strain. Raman measurements indicate that r _e is small, only four times the fibre radius. This result is supported by polarizing optical microscopy. The model of Greszczuk [2], which assumes a uniform shear within an effective interaction thickness b _i, gives a similar result. We find that b _i = 20 m, about twice the fibre radius. Using the pull-out test data, as for other fibre composites, b _i and r _e predicted by shear-lag theories do not agree with the results of microscopy to this extent. In these cases _s is much larger than the yield strength of the matrix and as neither treatment considers plastic deformation of the matrix agreement should not be expected.     

Fracture behaviour of glass-fibre mat-reinforced structural nylon RIM composites studied by microscopic and acoustic emission techniques

The fracture and failure behaviour of continuous glass-fibre mat-reinforced nylon block copolymer were studied at monotonic increased loading at different temperatures (T=–40 to 80 °C and deformation rates (v=1 and 1000 mm min^–1). The fracture toughness,K _c, was determined on compact tension specimens of different size in order to elucidate size effects.K _c increased with increasing glass-fibre mat content and with deformation rate, whereas increasing temperature resulted in lowerK _c values.K _c was unaffected by the free ligament width of the compact tension specimens used. The failure manner was studied by acoustic emission and microscopic techniques (transmitted light and scanning electron microscopy). Simultaneous monitoring of the failure mode by acoustic emission and transmitted light microscopy allowed the failure sequence to be deduced and led to a reliable discrimination between the observed failure events based on their acoustic emission signal characteristics (e.g. amplitude, energy). For this composite with a very ductile thermoplastic matrix the following failure steps were concluded: (a) fibre debonding due to crack-tip blunting, (b) network-type deformation of the glass-fibre mat with concomitant fibre debonding and voiding of the matrix, (c) formation of kinked strands with crack opening due to matrix yielding, (d) fracture of the bent filaments within the strands followed by pull-out processes (fibre-fibre, fibre-matrix). The development of the damage zone was also assessed by acoustic emission via localization of the related events. It was established that the damage zone reaches its maximum dimension at the maximum load and only its shape changes along the crack-growth direction upon further loading.     

Antiplane strain problem of diamond inclusion

In this paper, the singular stress fields created by an antiplane deformation at an inclusion corner are studied. It is shown that these singular stress fields can be separated into two independent types: a symmetric type with the stress singularity of 1/ ^1–1 and a skew-symmetric type with the stress singularity of 1/ ^1–2. These two types of the singular stress field can not occur simultaneously at the corner. If G ₂<G ₁, there exists only the singularity of the skew-symmetric type, and if G ₂>G ₁, there exists only the singularity of the symmetric type. A general expression of stress fields in the vicinity of the corner is presented. In the expression the singular stress fields for the symmetric type and the skew-symmetric type are defined in terms of the constants K _III, ₁ and K _III, ₂, respectively. K _III, ₂ and K _III, ₂ have to be determined from the complete boundary conditions of the given problem. For the problem of an infinite plate containing a diamond inclusion and subjected to a uniform longitudinal shear stress at infinity, the values of K _III, ₁ and K _III, ₂ are obtained by body force method. In the body force method, the investigated stresses are simulated by the superposition of the fundamental stress fields due to point forces. In order to obtain accurate solutions, the basic density functions of the distributed point forces are used, so that the stress singularities at the corner tip can be simulated by the point forces.     

Stress intensity factors for a semiinfinite crack with branches

The stressed state of an elastic plane weakened by a semiinfinite branching crack whose branches are either shear cracks or cracks of a mixed type is determined by the method of singular integral equations for the case where the stressed state at the tip of the semiinfinite crack without branches is characterized by stress intensity factorsK ₁ ⁰ andK _II ⁰ . The values of these factors are obtained for the cases of one, two, and three branches and different values of geometric parameters. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 1, pp. 45–50, January–February, 1997.     

Micromechanics of solvent crazes in polystyrene

Double exposure holographic interferometry (DEHI) is used to determine the strain energy release rate, craze opening displacement profile, and craze stress profile ofn-heptane and methanol crazes growing from cracks in polystyrene.n-heptane crazes have strain energy release rates (SERRs) close to those of cracks and their stress profile is almost crack-like in that the tensile stress across the craze falls almost to zero. On the other hand, the SERRs of methanol crazes are only 30 to 55% the SERR of a crack depending on stress intensity factorK _I of the precrack from which they are grown. The stress profile of the methanol craze shows it to be strongly load-bearing away from the craze tip, apparently as a result of the strain hardening of the craze fibrils. The stress concentration in front of the methanol craze tip is only 40% of that in front of then-heptane craze tip. The opening displacements of the methanol craze are almost as large as those of a crack very near its tip but are much less than those of a crack at large distances behind the tip. The Dugdale model of a strip yielding zone provides a poor representation of the craze opening displacements of the growing methanol craze. Dry (static) methanol crazes have larger opening displacements in response to an incremental tensile strain at moderate prestrains than at either low or high prestrains, suggesting that the craze fibrils undergo a yielding/strain-hardening process as the strain is increased similar to that observed in polycarbonate crazes by Kopp and Kambour. Dryn-heptane crazes do not show this response but rather open linearly with increasing prestrain. The opening displacement for long (dry)n-heptane crazes is almost crack-like whereas the largest opening of a dry methanol craze is only 20% of that of a crack. Dry methanol crazes break at aK _IC that is 40% of theK _IC of precracked but uncrazed specimens. The strongest (shortest) dryn-heptane crazes fail at only 7% ofK _IC of uncrazed specimens and theK _IC of the dryn-heptane crazes decreases markedly with increasing craze length.     

On scattering of measured values of fracture toughness parameters

The values of fracture toughness K _1C of C-Mn steels and weld metal were calculated from values of COD measured in standard specimens tested at low temperatures. The analysis of scattering of 42 values of K _1C measured in normalized C-Mn steel showed that the highest value of K _1C could be as large as 360 percent of the lowest. The factors affecting the scattering were investigated in detail and it was found that the scattering was mainly caused by the variation of locations of cleavage initiation. The local fracture stress σ was found to be the most stable parameter and combined with the minimum cleavage distance min which is determined by the triaxiality of stress reaching a critical value, it could be used to characterize the lower boundary of fracture toughness of steels. This revised version was published online in July 2006 with corrections to the Cover Date.