Aspects of fracture mechanics in cryogenic model design. Part 1: Fundamentals of fracture mechanics
The use of fracture mechanics for predicting fracture and fatigue crack growth in metals is presented.
Hudson, C. M.↗
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Composite interlaminar fracture - Effect of matrix fracture energy
A major result of the use of the double cantilever beam test to provide a measure of the interlaminar fracture energy in composites subjected to simple Mode I-type loading is the observation that increasing the toughness of the matrix resin by as much as a factor of 20 produced a major (approximately four-fold) increase in interlaminar fracture energy. The data presently analyzed show that, with brittle polymers, resin toughness is fully transferred to the composite, while in the case of tougher polymers the resin toughness is only partially transferred due to the fibers' restriction of the crack tip deformation zone in the polymer, together with their changing of local stress field details. Factors which tend to increase interlaminar toughness are fiber nesting and bridging, as well as fiber breakage and pull-out during crack growth.
Hunston, D. L.↗
Probabilistic Risk Assessment for Bone Fracture - Bone Fracture Risk Module (BFxRM)
This presentation summarizes the concepts, development, and application of NASA's Bone Fracture Risk Module (BFxRM). The overview includes an assessmnet of strenghts and limitations of the BFxRM and proposes a numebr of discussion questions to the panel regarding future development avenues for this simulation system.
Monte Carlo Method↗
Probabilistic Fracture Mechanics and Optimum Fracture Control Analytical Procedures for a Reusable Solid Rocket Motor Case
A methodology for the reliability analysis of a reusable solid rocket motor case is discussed. The analysis is based on probabilistic fracture mechanics and probability distribution for initial flaw sizes. The developed reliability analysis is used to select the structural design variables of the solid rocket motor case on the basis of minimum expected cost and specified reliability bounds during the projected design life of the case. Effects of failure prevention plans such as nondestructive inspection and the material erosion between missions are also considered in the developed procedure for selection of design variables. The reliability-based procedure can be modified to consider other similar structures of reusable space vehicle systems with different failure prevention plans.
Hanagud, S.↗
Sharply notch cylindrical tension specimen for screening plane-strain fracture toughness. I - Influence of fundamental testing variables on notch strength. II Applications in aluminum alloy quality assurance of fracture toughness
A description is presented of studies which have been conducted to establish an improved technology base for a use of the sharply notched cylindrical specimen in quality assurance tests of aluminum alloy products. The results are presented of an investigation of fundamental variables associated with specimen preparation and testing, taking into account the influence of the notch root radius, the eccentricity of loading, the specimen diameter, and the notch depth on the sharp notch strength. Attention is given to the statistical procedures which are necessary to establish correlations between the sharp notch strength and the plane-strain fracture toughness for high-strength aluminum alloys.
Jones, M. H.↗
FRACTURE TESTING OF HIGH-STRENGTH SHEET MATERIALS. NASA-NRL COOPERATIVE PROGRAM ON SPECIMENS INTENDED FOR FRACTURE TOUGHNESS MEASUREMENTS THIRD REPORT OF A SPECIAL ASTM COMMITTEE
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Brown, W. F.↗
Fracture toughness characterization of several aluminum alloys in semi-brittle fracture
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Jones, D. L.↗
Characterizing Fractures Across the Astronaut Corps: Preliminary Findings from Population-Level Analysis
Despite evidence of bone loss during spaceflight and operational countermeasures to mitigate this loss, the subsequent risk of fracture among astronauts is not known. The physiologic process of diminished bone density and bone recovery during or following spaceflight is multifactorial. Such factors as age, sex, fracture history, and others may combine to increase fracture risk among astronauts. As part of the 2016 Bone Research and Clinical Advisory Panel (RCAP), the authors analyzed data collected on 338 NASA astronauts to describe the demographics, bone-relevant characteristics, and fracture history of the astronaut population. The majority of the population are male (n=286, 84.6%), have flown at least one mission (n=306, 90.5%), and were between the ages of 30 and 49 at first mission (n=296, 96.7% of those with at least one mission). Of the 338 astronauts, 241 (71.3%) experienced a fracture over the course of their lifetime. One hundred and five (43.5%) of these 241 astronauts only experienced a fracture prior to being selected into the Astronaut Corps, whereas 53 (22.0%) only experienced a fracture after selection as an astronaut. An additional 80 astronauts (33.2%) had both pre- and post-selection fractures. The remaining 3 astronauts had a fracture of unknown date, which could not be categorized as pre- or post-selection. Among the 133 astronauts with at least one post-selection fracture, males comprised 90.2% (n=120) compared to 84.5% of the entire Corps, and females accounted for 9.8% (n=13) compared to 15.4% of the Corps. Ninety-seven of the 133 astronauts with post-selection fractures (72.9%) had one fracture event, 22 (16.5%) had two fractures, and 14 (10.5%) had three or more fractures. Some astronauts with multiple fractures suffered these in a single event, such as an automobile accident. The 133 astronauts with a post-selection fracture accounted for a total of 188 fracture events. One hundred and four (78.2%) of astronauts with post-selection fractures experienced those fractures following their first mission (mean 12.7 +/- 11.1 years following first mission; range 14.0 days - 50.6 years). Additional analyses are ongoing and include examination of fracture history, skeletal site, mechanism, and type of fracture, age at time of fracture, time from spaceflight to fracture, as well as multivariable analysis comparing fracture events to non-events. The results of such analyses may reveal trends in risk factors for fracture among the astronaut corps that have yet to be systematically described through a corps-wide approach.
Rossi, Meredith M.↗
Formation and evolution of radial fracture systems on Venus
A survey of approximately 90 percent of the surface of Venus using Magellan data has been carried out to locate all radial fracture systems and to assess their association with other features such as volcanic edifices and coronae. Squyres et al. and Stofan et al. have discussed the association of radial fracture features in relation to coronae features, our approach was to assess the associations of all of the fracture systems. These fracture systems have two broad types of form - some fracture systems are associated with updomed topography, radiate from a point and have relatively uniform fracture lengths while others have a wider range of fracture lengths and radiate from the outer edge of a central caldera. Squyres et al. and Stofan et al. have interpreted both types of feature as reflecting tectonic fracturing resulting from uplift of the surface as a mantle plume impinges upon the crust. While it is true that a number of features are related to uplift and that such uplift will induce stresses consistent with radial fracturing, we explore the possibility that these fractures are not exclusively of tectonic origin. Purely tectonic fracturing will tend to generate a few main fractures/faults along which most of the stresses due to uplift will be accommodated leading to the triple-junction form common for terrestrial updoming. Though this type of feature is observed on Venus (e.g., feature located at 34S86), the majority of radial fracture systems display much more intensive fracturing than this through a full 360 degrees; this is difficult to explain by purely tectonic processes. The association of many of the fractures with radial lava flows leads us to interpret these fractures as reflecting dike emplacement: the form of the fractures being consistent with primarily vertical propagation from the head of a mantle plume. In the case of the second type of fracture system (those radiating from a central caldera), an even stronger case can be made that the fractures are not of tectonic origin. These features are not as commonly associated with updoming of the surface and where they are, the fractures extend out well beyond the edge of the topographic rise - an observation which is not consistent with the fractures being of tectonic uplift origin. Furthermore the fractures have a distribution of lengths (many short, fewer long) which is characteristic of dike swarms, and show direct associations with calderas and lava flows consistent with a volcanic origin. In addition, the longest fractures have a radial pattern only close to the center of the system but bend with distance to align themselves with the regional stress field - this behavior is very difficult to explain on purely tectonic grounds but is a pattern commonly seen for terrestrial dikes. For these reasons, we argue that many, if not the majority, of radial fracture systems found on Venus are the surface reflection of dike swarms, those associated with positive topography reflecting vertical emplacement and those radiating from calderas reflecting lateral propagation.
Parfitt, E. A.↗
Sensitivity Analysis of the Bone Fracture Risk Model
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.
mathematical models↗
Increased Rates of Hip and Spine Fractures in Astronauts are Associated with Longer Spaceflight Durations
Given the accelerated declines in bone mineral density reported in US astronauts serving on the International Space Station, there is a possibility that a prolonged exposure to spaceflight could put astronauts at increased fracture risk during subsequent planetary explorations or after return to Earth. To date, there have been no fractures in astronauts during spaceflight. Recently-reported data from a flight study suggested that intake of the bisphosphonate alendronate combined with resistive exercise (on the Advanced Resistive Exercise Device – ARED) preserved more astronauts at their preflight skeletal status after a ~6-mos spaceflight than with ARED exercise alone. However, there is low acceptance of alendronate, or the recommended zoledronic acid, to suppress in-flight bone loss largely due to concern for unintended medication side effects and a perceived absence of astronaut fractures that can be directly attributable to spaceflight exposure. Hence, a recent survey of all astronaut fractures was analyzed to assess whether the rate of postflight fractures could be associated with extended spaceflight exposures. The fracture survey was of 262 astronauts across 8433.6 person-years (PY) and grouped according to previous exposure to a “Long Duration (LD)” spaceflight (3 mos or greater, but typically 6-mos). The number of fractures was modeled using count regression adjusting for i) the repeated measures within individuals across the groups, ii) the differing length of surveillance for each individual and iii) age at start of surveillance for each of the groups. Astronaut Group by Spaceflight Exposure #Individuals PY Covered No Exposure to Spaceflight 262 1882.7 No Exposure to LD spaceflight “Non-LD” 232 6121.3 Exposure to LD spaceflight 42 429.6 Analysis revealed an increased rate of hip and spine fractures for surveillance periods compared between LD Exposure and Non-LD Exposure: Hip – Relative Rate: 3.4 (95%CI: 1.0, 12.0); Spine– Relative Rate: 3.4 (95%CI: 1.0, 11.6). For all other skeletal sites, rates of fracture were similar for LD and Non-LD exposures. Data comparisons were conducted between groups of astronauts to preclude the interpretation of greater physical activity in astronauts as a contributing factor to fracture rates. This analysis of fracture data is the first report associating postflight hip and spine fractures in astronauts with exposure to extended duration spaceflights. Further analyses integrating co-morbidities for bone loss are planned.
skeleton↗
Probabilistic Risk Assessment for Astronaut Post Flight Bone Fracture
Introduction: Space flight potentially reduces the loading that bone can resist before fracture. This reduction in bone integrity may result from a combination of factors, the most common reported as reduction in astronaut BMD. Although evaluating the condition of bones continues to be a critical aspect of understanding space flight fracture risk, defining the loading regime, whether on earth, in microgravity, or in reduced gravity on a planetary surface, remains a significant component of estimating the fracture risks to astronauts. This presentation summarizes the concepts, development, and application of NASA's Bone Fracture Risk Module (BFxRM) to understanding pre-, post, and in mission astronaut bone fracture risk. The overview includes an assessment of contributing factors utilized in the BFxRM and illustrates how new information, such as biomechanics of space suit design or better understanding of post flight activities may influence astronaut fracture risk. Opportunities for the bone mineral research community to contribute to future model development are also discussed. Methods: To investigate the conditions in which spaceflight induced changes to bone plays a critical role in post-flight fracture probability, we implement a modified version of the NASA Bone Fracture Risk Model (BFxRM). Modifications included incorporation of variations in physiological characteristics, post-flight recovery rate, and variations in lateral fall conditions within the probabilistic simulation parameter space. The modeled fracture probability estimates for different loading scenarios at preflight and at 0 and 365 days post-flight time periods are compared. Results: For simple lateral side falls, mean post-flight fracture probability is elevated over mean preflight fracture probability due to spaceflight induced BMD loss and is not fully recovered at 365 days post-flight. In the case of more energetic falls, such as from elevated heights or with the addition of lateral movement, the contribution of space flight quality changes is much less clear, indicating more granular assessments, such as Finite Element modeling, may be needed to further assess the risks in these scenarios.
Risk Analysis↗
Fracture Control for Additively Manufactured Spacecraft Structures
This paper describes how the intent of current NASA fracture control requirements may be applied to “fracture critical” additively manufactured spacecraft hardware. Fracture control is a multi-discipline design and certification methodology that is applied in order to mitigate catastrophic failure of structures resulting from growth of an undetected crack-like defect. The methodology is defined in existing NASA standards and is required on all human-rated space structures. As legacy spacecraft structures have been built using primarily metallic and composite materials manufactured using well established methods, guidance for application of fracture control to parts composed of these material types has been established and is documented in several NASA requirements. Additive manufactured structures offer advantages in design flexibility and manufacturing efficiency and as a result are expected to continue to be used more and more in the future. Recently, relevant guidance has been published by NASA to define materials and processes requirements for certain additive manufactured hardware, but procedures for fracture control are not addressed yet in any requirements or guidance document. While use of additive manufactured parts in non-critical scenarios may be of relatively low concern in current structural certification processes, there is a need for new fracture control guidance in order to use and certify additively manufacture hardware that is “fracture critical” where failure of the part may result in loss of life or loss of vehicle. Assurance of damage tolerance, i.e., that as-built flaws in a given part either do not exist or will not grow to become catastrophic, is of particular interest to the fracture control community. This poses a challenge due to the fact that damage tolerance behavior is not well understood in additive manufactured parts compared to legacy material types and manufacturing techniques. The discussion contained herein is necessary at this time as new guidance in this area should be founded collaboratively by the technical community at large. Different hardware types (e.g., pressure vessel, structural member) are described to highlight specific challenges and solutions for each. The discussion concludes with considering specific disciplines within fracture control (non-destructive evaluation, materials & processes, fracture mechanics, and structural certification) in a proposed extension of existing fracture control requirements to additive manufactured parts.
McElroy, Mark↗
Fracture Control for Additive Manufactured Spacecraft Structures
This paper describes how the intent of current NASA fracture control requirements may be applied to “fracture critical” additively manufactured spacecraft hardware. Fracture control is a multi-discipline design and certification methodology that is applied in order to mitigate catastrophic failure of structures resulting from growth of an undetected crack-like defect. The methodology is defined in existing NASA standards and is required on all human-rated space structures. As legacy spacecraft structures have been built using primarily metallic and composite materials manufactured using well established methods, guidance for application of fracture control to parts composed of these material types has been established and is documented in several NASA requirements. Additive manufactured structures offer advantages in design flexibility and manufacturing efficiency and as a result are expected to continue to be used more and more in the future. Recently, relevant guidance has been published by NASA to define materials and processes requirements for certain additive manufactured hardware, but procedures for fracture control are not addressed yet in any requirements or guidance document. While use of additive manufactured parts in non-critical scenarios may be of relatively low concern in current structural certification processes, there is a need for new fracture control guidance in order to use and certify additively manufacture hardware that is “fracture critical” where failure of the part may result in loss of life or loss of vehicle. Assurance of damage tolerance, i.e., that as-built flaws in a given part either do not exist or will not grow to become catastrophic, is of particular interest to the fracture control community. This poses a challenge due to the fact that damage tolerance behavior is not well understood in additive manufactured parts compared to legacy material types and manufacturing techniques. The discussion contained herein is necessary at this time as new guidance in this area should be founded collaboratively by the technical community at large. Different hardware types (e.g., pressure vessel, structural member) are described to highlight specific challenges and solutions for each. The discussion concludes with considering specific disciplines within fracture control (non-destructive evaluation, materials & processes, fracture mechanics, and structural certification) in a proposed extension of existing fracture control requirements to additive manufactured parts.
McElroy, Mark↗
Risk of Bone Fracture due to Spaceflight-induced Changes to Bone
The Human Research Program (HRP) is taking a biomechanical approach to assessing subsequent fracture risk in active astronauts as a consequence of spaceflight exposure. Triennial testing of active and retired astronauts continues as Space Medicine monitors for a premature diagnosis of primary osteoporosis, which is associated with age-related bone loss and skeletal fragility. This updated 2023 Fracture Evidence Report has expanded the description of skeletal changes to capture the full effects of spaceflight on bone: • Recent analysis of fractures from health records of the full astronaut cohort, suggests an increased incidence rate of hip and spine fractures in astronauts following longer spaceflight duration flights compared to incident rates found in shorter duration flights. • Routine preflight-to-postflight surveillance by DXA (dual-energy x-ray absorptiometry) does not provide the full detection of loss and recovery in the long-duration (LD) astronaut nor the full recovery of hip trabecular bone. • The inclusion of hip quantitative computed tomography (QCT) in flight studies delineates effects of spaceflight, of countermeasures, and of post-flight recovery on cortical and trabecular bone parameters—some of which are verified predictors of hip fracture in the aged. • QCT detects and compares the distinct countermeasure effects of the pharmaceutical alendronate and of resistive exercise (on the Advanced Resistive Exercise Device, ARED) in specific cortical and trabecular bone sub-regions during spaceflight. • A published comparison of QCT-determined loss rates of hip trabecular bone in LD astronauts compared to terrestrial cohorts suggest that accelerated loss rates in trabecular volumetric BMD (vBMD) during spaceflight might be analogous to skeletal effects of accelerated loss rates in females due to menopause, potentially leading to disruptions in trabecular microarchitecture. • A dataset of finite element (FE) estimates of hip bone strength in aging terrestrial cohorts (spanning astronaut age-range) provides comparative context for changes in the FE of hip bone strength in LD astronauts, including comparison (force unit of newton) to percentiles (50th, 75th, and 100th) of sex-matched aged humans with hip fractures. • Risk of fracture, due to the mechanical overloading of bones, is being updated with IMPACT, the next-generation tool suite for probabilistic risk assessment (PRA) for exploration missions being created by the Exploration and Medical Capability Element (ExMC) at NASA. IMPACT is currently in development and will not be included in this 2024 update. The risk for fracture necessitates understanding the relationship between applied loads to bone and the biomechanical competence of bone. The Risk for Early Onset Osteoporosis focuses on the weakened condition of bone (including development of new technologies, measurements of novel skeletal attributes, translation of multiple measures to an index of bone fragility, and interpretations of data used to reflect a weakened bone), while the Risk for Fracture assesses factors that influence the probability an astronaut would encounter applied loads exceeding the biomechanical competence of bones, resulting in fracture. This Evidence Report combines the research gaps and tasks associated with both risks.
Fracture↗
Fracture modes of high modulus graphite/epoxy angleplied laminates subjected to off-axis tensile loads
Angleplied laminates of high modulus graphite fiber/epoxy were examined in several ply configurations at various tensile loading angles to the zero ply direction to determine the effects of ply orientations on tensile properties, fracture modes, and fracture surface characteristics of the various plies. Experimental results consist of stress-strain data, selected plots, fracture stresses and strains, and scanning electron microscope (SEM) photographs of fracture surfaces. It was found that the stress-strain curves were linear to fracture, and that although fracture surface characteristics for a given fracture mode are similar to those for the same fracture mode in uniaxial specimens, no simple load angle range can be associated with a given fracture mode. It was also concluded that SEM results must be supplemented with ply stress calculations in order to identify ranges of fracture modes occurring as a function of ply orientation with respect to the load direction.
Sinclair, J. H.↗
Mechanics of fracture - Fundamentals and some recent developments
An overview is presented of the fundamental aspects of and recent developments in fracture mechanics. Reference is made to linear elastic fracture mechanics including the state of stresses and displacements in the vicinity of cracks, effects of crack geometry and orientation on stress intensity factors, energy balance of Griffith, Irwin's stress intensity concept, and linear elastic fracture mechanics testing for fracture toughness. Other aspects of this paper include the non-linear behavior of materials and their influence on fracture mechanics parameters, consideration of viscoelasticity and plasticity, non-linear fracture toughness parameters as C.O.D., R-curve and J-integral, and a non-linear energy method, proposed by Liebowitz. Finite element methods applied to fracture mechanics problems are indicated. Also, consideration has been given to slow crack growth, dynamic effects on K(IC), Sih's criterion for fracture, Lee and Liebowitz's criterion relating crack growth with plastic energy, and applications of fracture mechanics to aircraft design. Suggestions are offered for future research efforts to be undertaken in fracture mechanics.
Liebowitz, H.↗
Deformation and fracture of thin sheet aluminum-lithium alloys: The effect of cryogenic temperatures
The objective is to characterize the fracture behavior and to define the fracture mechanisms for new Al-Li-Cu alloys, with emphasis on the role of indium additions and cryogenic temperatures. Three alloys were investigated in rolled product form: 2090 baseline and 2090 + indium produced by Reynolds Metals, and commercial AA 2090-T81 produced by Alcoa. The experimental 2090 + In alloy exhibited increases in hardness and ultimate strength, but no change in tensile yield strength, compared to the baseline 2090 composition in the unstretched T6 condition. The reason for this behavior is not understood. Based on hardness and preliminary Kahn Tear fracture experiments, a nominally peak-aged condition was employed for detailed fracture studies. Crack initiation and growth fracture toughness were examined as a function of stress state and microstructure using J(delta a) methods applied to precracked compact tension specimens in the LT orientation. To date, J(delta a) experiments have been limited to 23 C. Alcoa 2090-T81 exhibited the highest toughness regardless of stress state. Fracture was accompanied by extensive delamination associated with high angle grain boundaries normal to the fatigue precrack surface and progressed microscopically by a transgranular shear mechanism. In contrast the two peak-aged Reynolds alloys had lower toughness and fracture was intersubgranular without substantial delamination. The influences of cryogenic temperature, microstructure, boundary precipitate structure, and deformation mode in governing the competing fracture mechanisms will be determined in future experiments. Results contribute to the development of predictive micromechanical models for fracture modes in Al-Li alloys, and to fracture resistant materials.
Wagner, John A.↗