Cumulative Probability Of Fracture Research Articles

FREM predicts 10-year incident fracture risk independent of FRAX® probability: a registry-based cohort study.

FREM was developed from Danish public health registers without DXA information to identify high imminent risk of major osteoporotic fracture (MOF) and hip fracture (HF), while FRAX® estimates 10-year fracture probability from clinical risk factors and femoral neck bone mineral density (BMD) from DXA. The FREM algorithm showed significant 1- and 2-year fracture risk stratification when applied to a clinical population from Manitoba, Canada. We examined whether FREM predicts 10-year fracture risk independent of 10-year FRAX probability computed with BMD. Using the Manitoba BMD Program registry, we identified women and men aged ≥ 45years undergoing baseline BMD assessment. We calculated FREM and FRAX scores, and identified incident fractures over 10years. Hazard ratios (HRs) for incident fracture were estimated according to FREM quintile, adjusted for FRAX probability. We compared predicted with observed 10-year cumulative fracture probability estimated with competing mortality. The study population comprised 74,446 women, mean age 65.2years; 7945 men, mean age 67.5years. There were 7957 and 646 incident MOF and 2554 and 294 incident HF in women and men, respectively. Higher FREM scores were associated with increased risk for MOF (highest vs middle quintile HRs 1.49 women, 2.06 men) and HF (highest vs middle quintile HRs 2.15 women, 2.20 men) even when adjusted for FRAX. Greater mortality with higher FREM scores attenuated its effect on 10-year fracture probability. In the highest FREM quintile, observed slightly exceeded predicted 10-year probability for MOF (ratios 1.05 in women, 1.49 in men) and HF (ratios 1.29 in women, 1.34 in men). Higher FREM scores identified women and men at increased fracture risk even when adjusted for FRAX probability that included BMD; hence, FREM provides additional predictive information to FRAX. FRAX slightly underestimated 10-year fracture probability in those falling within the highest FREM quintile.

Estimation of the Fracture Probability Parameters for Specimens Made by JIS SM490A Steel

This work established the fracture probability equation for JIS SM490A steel using the computational model supported by the local approach and the standard Crack Tip Opening Displacement (CTOD) fracture toughness experiments. As the experiments were conducted at a low temperature providing conditions for the brittle fracture, the specimen suffers a small plastic deformation until its failure. The computational model tries to represent the experiment results, estimating the scale and shape parameters of the Weibull distribution for the cumulative fracture probability equation. A procedure based on the local approach was executed to find the optimum values for the fracture probability equation. In addition, a plot was provided to show the distribution of likelihood values according to assumed values for the shape and scale parameters. In the end, a comparison between the experimental and predicted statistical distribution of critical CTOD was done successfully, indicating that material toughness can be predicted by the present model.

Osteoporosis-Related Fractures in HIV-Infected Patients Receiving Long-Term Tenofovir Disoproxil Fumarate: An Observational Cohort Study.

IntroductionPatients with HIV infection may have a higher prevalence of osteoporosis and osteopenia, as well as an increased risk of bone fracture compared with non-HIV-infected individuals. Antiretroviral therapy is thought to be one of factors associated to osteoporosis-related bone fractures.ObjectiveThe aim of this study was to assess the effects of long-term exposure to tenofovir disoproxil fumarate (TDF) on the cumulative risk of osteoporosis-related bone fractures in Japanese patients with HIV infection.DesignThis observational cohort study comprised a joint HIV-related drug survey of patients treated with TDF between April 2004 and March 2013.MethodsThirty-five healthcare facilities in Japan participated in the survey. The incidence of osteoporosis-related fractures was extracted from all adverse events (AEs) using standardized Medical Dictionary for Regulatory Activities queries, and used to calculate the fracture rate per 10,000 patient-years (PY). Kaplan–Meier analysis was used to estimate the cumulative probability of fracture during the study period.ResultsA total of 3251 patients who received TDF or TDF/emtricitabine between April 2004 and March 2013 were analyzed in this study; 93.5% of patients were male. The fracture rate was 13.5 per 10,000 PY in males and 42.2 per 10,000 PY in females. The mean age for male patients with osteoporosis-related fracture was 43.2 years, whereas it was 65.7 years in female patients. The cumulative probability of osteoporosis-related fracture increased after ≥ 5 years of TDF exposure. The rate of hip fracture (95% confidence interval) was 7.2 (3.1–14.2) per 10,000 PY.ConclusionsAmong HIV-infected patients in Japan, treatment with TDF for ≥ 5 years increases the risk of bone fractures in younger men, in addition to that seen in older post-menopausal women.

FRAX for fracture prediction shorter and longer than 10years: the Manitoba BMD registry.

FRAX® estimates 10-year probability of major osteoporotic fracture (MOF) and hip fracture. We examined FRAX predictions over intervals shorter and longer than 10years. Using a population-based clinical registry for Manitoba, Canada, we identified 62,275 women and 6455 men 40years and older with baseline dual-energy X-ray absorptiometry scans and FRAX scores. Incident MOF and hip fracture were assessed up to 15years from population-based data. We assessed agreement between estimated fracture probability from 1 to 15years using linearly rescaled FRAX scores and observed cumulative fracture probability. The gradient of risk for FRAX probability and incident fracture was examined overall and for 5-year intervals. FRAX predicted incident MOF and hip fracture for all time intervals. There was no attenuation in the gradient of risk for MOF even for years >10. Gradient of risk was slightly lower for hip fracture prediction in years >10 vs years <5, though HRs remained high. Linear agreement was seen in the relationships between observed vs predicted (rescaled) FRAX probabilities (R 2 0.95-1.00). Among women, there was near-perfect linearity in MOF predictions. Deviations from linearity, with a slightly higher observed than predicted MOF probability, were most evident in the first years following a fracture event and after 10years for hip fracture prediction in women using FRAX with BMD. Simulations showed that results were robust to large differences in fracture rates and moderate differences in mortality rates. FRAX predicts incident MOF and hip fracture up to 15years and could be adapted to predict fracture over time periods shorter and longer term than 10years in populations with fracture and mortality epidemiology similar to Canada.

A statistical approach to scaling size effect on strength of concrete incorporating spatial distribution of flaws

The spatial distribution of flaws in a solid has a direct impact on the cumulative probability of failure due to brittle fracture. Accordingly, two composite parameters incorporating the cumulative probability of failure and the volume of fracture process zone are identified and adopted to characterize the size effect on the strength of concrete. Instead of being pre-assumed a specific function, the cumulative distribution function of fracture strength, namely the cumulative probability of fracture, is inferred for either the Poisson or the uniform spatial distributions of flaws from the synchronized analysis of multiple strength data sets measured from different sized specimens of geometrical similarity under a same loading mode (proportional scaling). This approach is validated for the case of proportional scaling by evaluating three representative sets of published strength data of concrete from uniaxial tension, uniaxial and equibiaxial flexure tests. Depending on the specific specimen size, the spatial flaw distribution may follow either the Poisson postulates or the uniform law, while the strength distribution of concrete does not necessarily always follow the Weibull statistics.

Fracture Risk Score and Absolute Risk of Fracture

To report the 5- and 10-year absolute risk of fracture associated with the previously reported fracture risk (FRISK) score. All participants gave written, informed consent, and the Barwon Health Human Research Ethics Committee approved the study. An age-stratified population-based sample of women aged 60 years and older (n = 600) was recruited during 1994-1996. FRISK scores of 0-10 incorporating bone mineral density (BMD) at two sites (hip and spine), falls scores in the previous 12 months of 1-4, weight, and number of fractures as an adult were calculated. Fractures of the hip, spine, humerus, and wrist were ascertained during a median follow-up period of 9.6 years (interquartile range, 6.6-10.5). The cumulative probability of fracture at 5 and 10 years after baseline measurements was calculated by using actuarial methods. The utility of this model was compared with other FRISK algorithms, including the World Health Organization FRISK assessment tool FRAX designed for United Kingdom and that designed for the United States and the Garvan nomogram (Australia). This study supplies the 5- and 10-year absolute risk of fracture associated with all levels of the FRISK score. While there are modest differences in absolute risk of fracture seen for different numbers of prior fractures, the more marked differences occur across the different categories of falls scores and different categories of BMD. The receiver operating characteristic curves showed no significant difference in area under the curve for all four absolute risk of fracture algorithms. Absolute risk of fracture can be determined by using readily obtainable clinical information that may aid treatment decisions.

A study of prediction of static fracture strength of MEMS structure for strength design scheme

Aiming at development of evaluation scheme for strength design and reliability of MEMS structure, this paper proposes prediction method of static fracture strength of specimens patterned by Bosch process. Two types of specimens made of single crystal silicon with different stress distributions were prepared for measuring the fracture strength. Four-point bending test in different loading directions was carried out to consider distribution of the state of damage due to machining. Relationship between cumulative fracture probability and applied stress was investigated by applying Weibull statistics and performing finite element method (FEM) simulation. It demonstrated the possibility of quantitative prediction for the fracture strength of specimens with arbitrary shapes.

Accuracy of the Fatigue Lifetime of Polysilicon Predicted from its Strength Distribution

AbstractThis paper discusses the accuracy of the distribution of the fatigue lifetime of polysilicon thin films predicted from their strength distribution. On the basis of the authors' previous studies, where the fatigue process determining the lifetime was formulated using the well-known fatigue crack extension Paris' law, prediction error ranges for polysilicon specimens with different levels of strength are determined. The errors of the predicted fatigue lifetime in the logarithmic scale, defined as △logN= |log10Nexp-log10Npred| whereNexpandNpredwere the experimental and predicted number of cycle, were found to be less than 1 in the range of the cumulative fracture probability F between 0.1 and 0.9. Therefore, based on the measured Paris' law parameters of polysilicon, the fatigue lifetimes of different polysilicon thin film structures can be predicted from their strength distributions with errors of roughly 10% in the logarithmic scale, which was average of percentages of △logNto log10Nof experimental data.

2841 シリコン薄膜の疲労特性とその評価(S08-3 微小機械設計・開発のための実験力学の新展開(3),S08 微小機械設計・開発のための実験力学の新展開)

Static strength tests and dynamic fatigue tests were conducted on polycrystalline silicon thin films patterned under two different etching process conditions. Statistical analysis was performed to integrate all the test results on the basis of equivalent initial crack length. The cumulative fracture probability was formulated as a function of the applied stress and the number of fatigue cycles. It was found that the extension behavior of initial cracks was the same, regardless of the distributions of initial cracks which depended on the etching conditions.

Microscale modelling of cleavage fracture at low temperatures: influence of heterogeneities at the granular scale

ABSTRACTA methodology is proposed in this paper to compute local probability of fracture of a representative volume element from microstructural and fractographic information. A microscale approach is reported for cleavage fracture modelling of bainitic reactor pressure vessel steel. A fine metallographic and micro‐mechanical characterization has been performed. Morphological information has been used to generate realistic three‐dimensional (3D) aggregates and a suitable calibration process has been set up to identify an accurate crystal plasticity model for A508 bainitic steel. Simulation results have been successfully compared with macroscopic stress–strain curve. Taking benefits of a fine mechanical description of local stress and strain fields in aggregates, a post‐processing has been implemented to compute stress to failure values, for several realizations of an experimental carbides sizes distribution. A cumulative probability of fracture is proposed for this steel.

Probability of cleavage fracture for a crack propagating by fatigue

Standard fracture toughness tests use fatigue pre-cracked specimens loaded monotonically from zero to failure. Scatter in toughness (cleavage) occurs because steel is metallurgically inhomogeneous, and because each specimen has its crack tip in a different local microstructure. A probability of fracture toughness distribution can be obtained by conducting multiple repeat tests on the same steel. This is often used to make probabilistic structural fracture predictions for combinations of crack length and applied load. However, it is likely the true structural situation involves gradual extension of a fatigue crack under a cyclic load. The question then arises as to how often the probability of fracture for the structure needs to be re-calculated. It could be argued that each fatigue load cycle moves the crack tip to a new position and gives a different instantaneous probability of fracture. But if this were the case, the predicted cumulative probability of fracture would quickly tend to unity. This paper describes cold temperature, wide plate fatigue tests designed to investigate this apparent contradiction. The steel is 15 mm thick, grade A, ship plate and the tests involve propagation of a fatigue crack from 300 mm to 650 mm length under a constant amplitude fatigue cycle of 10–100 MPa at −50 °C. The cold temperature fatigue tests do not show an obviously increased probability of fracture compared with the standard monotonic load tests. Nevertheless, in view of uncertainties surrounding the issue, a cumulative probability of fracture determined at 5 mm intervals through the steel is recommended for safe structural predictions.

Temperature dependence of Weibull stress parameters: Studies using the Euro-material

This work demonstrates the temperature invariance of the Weibull stress modulus, m, for a 22Ni–MoCr37 pressure vessel steel through calibrations at two extreme temperatures of the ductile-to-brittle transition. This temperature invariance reflects the characterization of microcrack size distribution in the material described by the modulus. The calibrations performed here also demonstrate the clear dependence of the Weibull scale parameter, σ u, on temperature. The increase of σ u with temperature reflects the increase in microscale toughness of ferritic steels. The calibration procedure employs a three-parameter Weibull stress model which includes the effects of a minimum (threshold) toughness, K min. The calibrations suggest that K min increases gradually with temperature. Finally, an engineering procedure is presented to enable practical applications of the Weibull stress model for defect assessments. This procedure combines the demonstrated temperature invariance of m, a recently developed method for predicting the variation of σ u with temperature using the Master Curve, and calibration of the Weibull stress parameters at one temperature. The (calibrated) temperature invariant m and the estimated σ u as a function of temperature are used to predict the cumulative probability of fracture for several large datasets without direct calibration.

3953 多結晶シリコン薄膜の強度と疲労特性(S21-3 強度物性と信頼性,S21 ナノ・マイクロ構造体の強度物性と信頼性)

Static strength tests and dynamic fatigue tests were conducted on a polycrystalline silicon material, which is one of the most common materials to compose micro electromechanical systems. Scatter of static strength was explained in terms of the distributed length of equivalent cracks, which in tern was analyzed with the fatigue crack propagation law to estimate the distribution of fatigue lifetime. By fitting the experimental data to the theory, the cumulative probability of fracture was plotted in a three dimensional manner as a function of both the amount of applied stress and the number of fatigue cycles. This plot quantitatively characterizes the reliability of the polycrystalline silicon material examined in this study.

An in vitro comparison of the shear bond strength of a resin-reinforced glass ionomer cement and a composite adhesive for bonding orthodontic brackets

The shear bond strength (SBS) of a light-cured, resin-reinforced glass ionomer and a composite adhesive in combination with a self-etching primer was compared after different setting times to evaluate when orthodontic wires could be placed. Additionally, the fracture site after debonding was assessed using the Adhesive Remnant Index (ARI). Eighty freshly extracted human premolars were used. Twenty teeth were randomly assigned to each of four groups: (1) brackets bonded with Transbond XT with a Transbond Plus etching primer and debonded within 5 minutes; (2) brackets bonded with Fuji Ortho LC and debonded within 5 minutes; (3) brackets bonded as for group 1 and debonded within 15 minutes; (4) brackets bonded as for group 2 and debonded within 15 minutes. The SBS of each sample was determined with an Instron machine. The mean SBS were, respectively: (1) 8.8 +/- 2 MPa; (2) 6.6 +/- 2.5 MPa; (3) 11 +/- 1.6 MPa and (4) 9.6 +/- 1.6 MPa. Interpolating the cumulative fracture probability by means of a Weibull analysis, the 10 per cent probabilities of fracture for the groups were found to be attained for shear stresses of 6.1, 3.1, 8.3 and 7.1 MPa, respectively. Chi-square testing of the ARI scores revealed that the nature of the remnant did not vary significantly with time, but the type of bonding material could generally be distinguished in leaving more or less than 10 per cent of bonding material on the tooth. After debonding, the Transbond system was likely to leave adhesive on at least 10 per cent of the bonded area of the tooth. The present findings indicate that brackets bonded with either Transbond XT in combination with Transbond Plus etching primer and Fuji Ortho LC had adequate bond strength at 5 minutes and were even stronger 15 minutes after initial bonding.

The effect of reinforcement with woven E-glass fibers on the impact strength of complete dentures fabricated with high-impact acrylic resin

Statement of problem The fracture of acrylic maxillary complete dentures occurs frequently during service through heavy occlusal force or accidental damage. Purpose The purposes of this study were to measure the impact strength of maxillary complete dentures fabricated with high-impact acrylic resin and to evaluate the effect of woven E-glass fiber-reinforcement on the impact strength of the complete dentures. Material and methods Preimpregnated woven E-glass fibers (Stick Net) were used to reinforce 10 complete denture bases fabricated with a heat-polymerized high-impact acrylic resin (Lucitone 199). Ten unreinforced complete dentures served as a control group. All specimens were stored in water at 37°C for 2 months before testing. The impact strengths (J) of the dentures were measured with a falling-weight impact test. The impact strengths of both groups were compared by a repeated measures analysis of variance (α = .05). The Weibull distribution was also applied to calculate the cumulative fracture probability as a function of impact strength. Results The mean impact strength of the control dentures was 90.0±38.1 J at crack initiation, and 95.9±37.7 J at complete fracture, whereas the impact strength of reinforced dentures was 201.7±77.9 J and 277.9±102.5 J, respectively. Statistical analysis showed that impact strength of the high-impact acrylic complete denture was significantly increased by the addition of woven E-glass fiber ( P<.0001). Conclusion The impact strengths of maxillary complete dentures fabricated with high-impact acrylic resin increased by a factor greater than 2 when reinforced with woven E-glass fiber.

Probabilistic modeling of weld fracture in steel frame connections Part II: seismic loading

This work develops and applies a probabilistic model to study the dynamic, nonlinear fracture behavior in the beam lower-flange to column welds found in moment resistant steel frames. The effort focuses on connection designs used prior to the 1994 Northridge earthquake (A36 beams, A572 columns and E70T-4 welds with access holes, shear tabs and continuity plates). The study applies the same probabilistic model to examine and compare fracture behavior in the simpler pull-plate specimen developed after the Northridge event to simulate conditions at the lower-flange connection. 3-D finite element analyses, coupled with an advanced micro-mechanical fracture model based on the Weibull stress, are used to assess the relative significance of loading rate, residual stresses, plasticity, access hole geometry, beam yield strengths, and various weld (backup bar) modifications. The present work considers only the initiation of brittle fracture triggered by a transgranular cleavage mechanism typical of that exhibited by ferritic steels (and welds) operating in the ductile-to-brittle transition region. Key computational results express the cumulative probability of fracture in terms of the beam moment at the face of the column and an equivalent beam moment for the pull-plate specimen. Part I of this study examines these same issues for connections and for pull-plate specimens under static loading as used in recent laboratory studies.

Bone mass measurement: Prediction of risk

Accurate assessment of individual fracture risk requires measurement of bone mass (density). Another strong risk factor for identifying women or men who will develop fractures in the near future is the presence of previous (spine and nonspine) fractures. However, the occurrence of a low-trauma fracture almost anywhere in the skeleton is indicative of a more advanced stage of disease and is associated with a substantial, further increase in fracture risk, independent of bone mass. Thus, prevention of the first fracture should received priority. In a clinical setting, initial assessment of bone mass can be combined with other, known risk factors and projected over the patient's remaining life expectancy, to estimate future, cumulative fracture probability. Estimates such as “remaining lifetime fracture probability” can also approximate the impact and cost-effectiveness of treatment, allowing for more objective and rational therapeutic planning for individual patients.

Principles and the Uncertainty Principles of the Probabilistic Strength of Materials and Their Applications to Seismology

The principles of Fracture-Statistics Mechanics are presented using two functional equations, namely one for the cumulative probability of fracture, and another for the local probability of fracture. These two functional equations are independent and they become compatible only when the volume considered is very small. The determination of the specific-risk function can be made by means of integral equations, without having to specify the analytical expression for this function. This two principles give two principles of uncertainty. Some applications to seismology are given where it is shown that the possibilities of predicting the instant of occurrence and the magnitude of an earthquake are null. Only the probability of occurrence of an earthquake of a given magnitude in a given place can be known. The instant of occurrence, the magnitude and the location are aleatory.

Interface and internal compatibility in a copper fibre cement composite

This paper presents the mechanical behaviour of a compacted composite formed by short ductile copper fibres randomly distributed in portland cement matrix. The samples, a half with fibres and the other without them, were subjected to compression fatigue. So, 1 hertz and the value of stress corresponding to the 1% of the probability of fracture by gradual load were used. Diagrams of cumulative probability of fracture against cycles are obtained for both types of samples. Scanning electron microscopy shows that the mechanisms of fracture are different in each case. Samples of compacted neat-cement paste finish their life with a catastrophic fracture whereas samples of composite behave like a pseudoductile material devoid of catastrophic failure. The results are discussed and compared with the ones obtained by thermal shock and by the interface brittleness theory, as well as with the statistical theory of time-dependent fracture for cementitious materials subjected to cyclic loading. So, in the thermal shock microcracks are generated in the interface matrix-fibre which simultaneously act as emmitings and sumps of cracks whereas this does not occur in mechanical fatigue.

Application of probabilistic thermomechanical models to large and/or complex structures

Abstract An affine probabilistic model is used to show how the cumulative and local probabilities of fracture of yielding can be determined in complex and/or large structures. The theory of probabilistic strength of materials supplies an expression allowing the cumulative probability of fracture, or yielding of a large and/or complex structure to be computed, taking into account the knowledge of the said probabilities in a material similarly manufactured but smaller, using an affine transformation. The result is independent of the stress field and of the analytical form of Weibull's specific risk function. The system must be loaded gradually, and if there is some thermal shock then the time in which the thermal perturbation is dissipated into the structure must be greater than the time occupied by the elastic wave in going through the structure, such that the assumption of gradual loading still holds. Costs in terms of time and money are reduced by using smaller models and by considering a time-transformation that allows the testing of structures subjected to thermal stresses to be speeded up.