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All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

A Numerical and Experimental Study of Damage Growth in a Composite Laminate

The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.

McElroy, Mark↗
NASA NTRS2014

TPSAS-NF1676L-19616-DND

The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.

Mark McElroy↗
NASA NTRSDate not supplied

The Application of Artificial Intelligence Deep Learning to Visually Identify Micrometeoroid and Orbital Debris Impacts

Recent advances in Artificial Intelligence (AI) are changing the World. Novel approaches to training AI systems have led to dramatic reductions in the amount of time required. Training an AI system could take years and teams of people using traditional methods, but with the advancements of Deep Learning (DL) models this training can now be accomplished by an individual in a matter of minutes. The development of “fast AI” libraries has delivered AI to essentially everyone. Democratization of AI power has inspired many to revisit past problems that will benefit from DL approaches. For example, the application of AI has improved detection of breast cancer by 20% compared to traditional detection methods. Computer vision and machine learning are being used to identify soil deficiencies and provide planting recommendations to farmers. Success stories like these and many others have provided inspiration to see if AI can help improve one of our needed capabilities – that of visually identifying micrometeoroid and orbital debris (MMOD) impact damage to spacecraft from images of the spacecraft exterior. The need to visually locate and characterize spacecraft MMOD impact damage has been present since the early days of space travel. This is often done by either having a crew member take photographs of the spacecraft through a window using a hand-held camera or ground personnel directing externally-mounted cameras. The photographs are then transmitted back to Earth for visual analysis. This method of MMOD damage inspection works well and has been used on various spacecraft including the Space Shuttle and the International Space Station (ISS). One of the issues with the current method that we believe AI could improve is the speed and possibly the accuracy in identifying MMOD impacts. Note that detecting MMOD impacts in images can be very difficult. The visual appearance of an MMOD impact can change dramatically with lighting conditions, size of impact, depth of penetration, material types, surface waviness, fabric coverings, camera & lens, distance to surface, spacecraft orientation, analyst experience, and many other factors. Currently, this takes a team of highly-experienced specialists in both the fields of Image Analysis and MMOD impacts. This paper documents our initial research in training an AI DL model using the fast-AI library to identify actual and simulated MMOD impacts and perforations into exposed flat surfaces. While we recognize that this initial goal seems modest, it must be noted that what we have done would have taken teams of individuals and years of training just ten years ago. Our long-term goal is to add complexity and use-cases to the DL model being trained to expand the capabilities of this model so that it can be used to identify MMOD impacts on all types of spacecraft surfaces.

Cameron M Collins↗
DOE OSTI2025

Three-dimensional characterization of modifications in sapphire exposed to laser-induced damage using multimodal spectral microimaging

Sapphire (Al 2 O 3 ) is a commonly used dielectric material with many applications in lasers and optical systems. Owing to its high resistivity to laser induced damage, it is particularly suitable for use in high power laser systems. This work focuses on developing techniques to characterize material modifications in sapphire. These techniques were applied following localized laser induced ablation, commonly referred to as laser-damage, resulting from exposure to single 100-ps and 6-ns pulses. Measurements of fluorescence-based piezospectroscopy and confocal Raman microscopy were performed with spatial resolution on the order of 1 μ m. Raman microscopy reveals that the relaxation of material exposed to the rapid laser heating, elastic and viscoplastic deformation, melting, and solidification leads to the formation of a polycrystalline material phase. In addition, narrowband fluorescence lines, referred to as R 1 and R 2 , exhibit pressure-sensitive changes to their spectral profiles, allowing 3D internal stresses to be recorded with spatial resolution of the order of a few micrometers.

Laser-damage↗
NASA NTRS2024

Impact Response of Thermoplastic Composites – Experiments and Modeling

This study investigates the impact response of thermoplastic composite materials. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK reinforced with T700G (T700/LMPAEK ). Several High Energy Dynamic Impact (HEDI) tests were performed wherein an aluminum projectile impacted T700/LMPAEK panels at different velocities. In the impact experiment studied herein, the projectile impacted the T700/LMAPEK panel at 73.2 m/s and rebounded. The ensuing damage to the T700/LMPAEK panel was characterized via ultrasonic C-scans, visualizing damage modes including matrix cracking and delaminations. Since the projectile rebounded, the fiber breakage damage mode was not evident. The impact event was modeled using a combined continuum damage mechanics and cohesive zone analysis approach with the commercially available hydrocode LS-DYNA®. The dynamic deformation and damage of the continuum, i.e., the plies in the T700/LMPAEK laminate, was modeled using a Deformation Gradient Decomposition (DGD) material model, i.e., MAT299 available within LS-DYNA. The interlaminar regions were treated as zero-thickness cohesive zones, wherein the dynamic delamination mechanics was modeled using a traction-separation formulation. Mixed-mode delamination growth was captured using the Benzegaggh-Kenane (B-K) traction-separation interpolation law. Strain-rate sensitivity of interlaminar fracture toughness was included using approximations based on published literature. The outcomes of the modeling effort are discussed herein which demonstrate good correlations with test data regarding panel deflection, panel-projectile interactions, damage modes and damage extent.

Impact modeling↗
NASA NTRS1977

Fatigue damage in notched composite laminates

This communication describes the results of an experimental investigation of the fatigue characteristics of a boron-epoxy laminate containing an unloaded circular hole. The study focuses upon characterization of the fatigue damage incurred and its influence upon axial tensile residual strength. Two apparent anomalies in the fatigue behavior for this laminate were observed. First, the fatigue damage was observed to propagate tangentially to the edge of the notch (parallel to the direction of the load), in contrast to propagation in contemporary metallic materials which is perpendicular to the load direction. Second, the residual strength characteristics for the laminate have revealed a significant increase in residual strength subsequent to a fatigue loading of 500,000 cycles at R = 0.1 and S = 0.8 and 0.67 (S = maximum stress/static ultimate). Failure analyses of the fatigue damage are conducted utilizing ultrasonic 'C' scan techniques.

Pipes, R. B.↗
NASA NTRS2005

Assessment of Microbiologically Influenced Corrosion Potential in the International Space Station Internal Active Thermal Control System Heat Exchanger Materials: A 6-Momths Study

The fluid in the Internal Active Thermal Control System (IATCS) of the International Space Station (ISS) is water based. The fluid in the ISS Laboratory Module and Node 1 initially contained a mix of water, phosphate (corrosion control), borate (pH buffer), and silver sulfate (Ag2SO4) (microbial control) at a pH of 9.5+/-0.5. Over time, the chemistry of the fluid changed. Fluid changes included a pH drop from 9.5 to 8.3 due to diffusion of carbon dioxide (CO2) through Teflon(reistered Trademark) (DuPont) hoses, increases in dissolved nickel (Ni) levels, deposition of silver (Ag) to metal surfaces, and precipitation of the phosphate (PO4) as nickel phosphate (NiPO4). The drop in pH and unavailability of a antimicrobial has provided an environment conducive to microbial growth. Microbial levels in the fluid have increased from >10 colony-forming units (CFUs)/100 ml to 10(exp 6) CFUs/100 ml. The heat exchangers in the IATCS loops are considered the weakest point in the loop because of the material thickness (=7 mil). It is made of a Ni-based braze filler/CRES 347. Results of a preliminary test performed at Hamilton Sundstrand indicated the possibility of pitting on this material at locations where Ag deposits were found. Later, tests have confirmed that chemical corrosion of the materials is a concern for this system. Accumulation of micro-organisms on surfaces (biofilm) can also result in material degradation and can amplify the damage caused by the chemical corrosion, known as microbiologically influenced corrosion (MIC). This paper will discuss the results of a 6-mo test performed to characterize and quantify the damage from microbial accumulation on the surface of the ISS/ATCS heat exchanger materials. The test was designed to quantify the damage to the materials under worst-case conditions with and without micro-organisms present at pH 8.3 and 9.5.

Roman, Monsi C.↗
NASA NTRS1987

Space station integrated wall damage and penetration damage control. Task 5: Space debris measurement, mapping and characterization system

The procedures and results of a study of a conceptual system for measuring the debris environment on the space station is discussed. The study was conducted in two phases: the first consisted of experiments aimed at evaluating location of impact through panel response data collected from acoustic emission sensors; the second analyzed the available statistical description of the environment to determine the probability of the measurement system producing useful data, and analyzed the results of the previous tests to evaluate the accuracy of location and the feasibility of extracting impactor characteristics from the panel response. The conclusions were that for one panel the system would not be exposed to any event, but that the entire Logistics Module would provide a modest amount of data. The use of sensors with higher sensitivity than those used in the tests could be advantageous. The impact location could be found with sufficient accuracy from panel response data. The waveforms of the response were shown to contain information on the impact characteristics, but the data set did not span a sufficient range of the variables necessary to evaluate the feasibility of extracting the information.

Lempriere, B. M.↗
NASA NTRS1992

Damage tolerance of a composite sandwich with interleaved foam core

A composite sandwich panel consisting of carbon fiber-reinforced plastic (CFRP) skins and a syntactic foam core was selected as an appropriate structural concept for the design of wind tunnel compressor blades. Interleaving of the core with tough interlayers was done to prevent core cracking and to improve damage tolerance of the sandwich. Simply supported sandwich beam specimens were subjected to low-velocity drop-weight impacts as well as high velocity ballistic impacts. The performance of the interleaved core sandwich panels was characterized by localized skin damage and minor cracking of the core. Residual compressive strength (RCS) of the skin, which was derived from flexural test, shows the expected trend of decreasing with increasing size of the damage, impact energy, and velocity. In the case of skin damage, RCS values of around 50 percent of the virgin interleaved reference were obtained at the upper impact energy range. Based on the similarity between low-velocity and ballistic-impact effects, it was concluded that impact energy is the main variable controlling damage and residual strength, where as velocity plays a minor role.

Ishai, Ori↗
NASA NTRS2026

Development, Characterization, and Validation of Elevated-Temperature Constitutive Models: Deformation and Damage

This report provides a brief review of experimentally observed hereditary and nonhereditary material behavior along with background information on standard as well as advanced internal state variable constitutive modeling at elevated temperature. A description of exploratory, characterization, and validation testing is presented along with a detailed outline of what constitutes “sufficient” data content (i.e., quality and quantity) for developing or enhancing, characterizing, and validating a particular sophisticated nonlinear time- and history-dependent (hereditary) class of constitutive models known as GVIPS (generalized viscoplasticity with potential structure). The tests described are necessary to reveal a material’s behavior in the reversible (or viscoelastic) and irreversible (or viscoplastic) regimes, for the identification of both deformation and damage model parameters. Results presented are primarily for metallic materials. In all cases, both uniaxial and multiaxial tests are described, and the linkage between the specific tests and the parameters within the model that can be characterized from the results of these tests are also discussed. Discussion is also provided relative to the role information management must play relative to material data collection, analysis, maintenance, and dissemination. The need for such an information system is particularly important as both analyst and designer move toward utilizations of sophisticated, nonlinear time- and history dependent (hereditary) constitutive models. Lastly, the concept of state space and its utility in understanding and establishing constitutive models is addressed throughout. The intent behind this document is to help both the modeler and experimentalist understand each other’s specific points of view and provide guidance for both model development and characterization. Emphasis has been placed on providing the mechanician with information regarding how tests are performed and what issues to be aware of when interpreting results. It is hoped that experimentalists will take away a new perspective on the types of information that modelers and analysts are looking for from them.

Constitutive Modeling↗
NASA NTRS2023

Progressive Damage and Failure Analysis of Thermoplastic Composites in Low Velocity Impact Using MAT299

As part of the NASA Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project, state-of-the-art progressive damage and failure analysis (PDFA) tools developed for use with thermosets are being evaluated for use in modeling alternative material systems, like thermoplastics. Experimental low-velocity impact data of a thermoplastic material system, AS4D/PEKK-FC, is presented and includes characterization of the impact damage mechanisms as well as associated load and displacement data. Following the presentation of experimental results, two simulation approaches using the PDFA tool MAT299 in the commercial off-the-shelf finite element software LS-DYNA are employed to predict damage area and force-displacement responses of thermoplastic panels subjected to various impact energies. The first modeling method uses solid elements with a high-density mesh and a ply-by-ply modeling approach similar to previously published work for thermosets. This method has the capability of capturing individual crack development, progression, and delamination on a per ply basis. The second modeling method uses TSHELL elements that have in-plane dimensions that are an order of magnitude larger than the elements used in the solid element approach and reduces the number of elements through the thickness of the laminate. The second method produces a lower-fidelity model with reduced run times that is incapable of monitoring every delamination plane and damage within each ply. Results from both simulation methods are compared to experiment, and limitations of the methods are discussed.

Composite material↗
NASA NTRS2023

Progressive Damage and Failure Analysis of Thermoplastic Composites in Low Velocity Impact Using MAT299

As part of the NASA Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project, state-of-the-art progressive damage and failure analysis (PDFA) tools developed for use with thermosets are being evaluated for use in modeling alternative material systems, like thermoplastics. Experimental low-velocity impact data of a thermoplastic material system, AS4D/PEKK-FC, is presented and includes characterization of the impact damage mechanisms as well as associated load and displacement data. Following the presentation of experimental results, two simulation approaches using the PDFA tool MAT299 in the commercial off-the-shelf finite element software LS-DYNA are employed to predict damage area and force-displacement responses of thermoplastic panels subjected to various impact energies. The first modeling method uses solid elements with a high-density mesh and a ply-by-ply modeling approach similar to previously published work for thermosets. This method has the capability of capturing individual crack development, progression, and delamination on a per ply basis. The second modeling method uses TSHELL elements that have in-plane dimensions that are an order of magnitude larger than the elements used in the solid element approach and reduces the number of elements through the thickness of the laminate. The second method produces a lower-fidelity model with reduced run times that is incapable of monitoring every delamination plane and damage within each ply. Results from both simulation methods are compared to experiment, and limitations of the methods are discussed.

Composite material↗
DOE OSTI2025

Ion implantation of magnesium guests into type II silicon clathrate films: an alternate approach to doping a cage-like silicon allotrope

Type II silicon clathrates, with their unique cage-like structure, offer exciting potential for applications in thermoelectrics, photovoltaics, and quantum materials due to their tunable electronic and thermal properties. This study investigates the use of ion implantation to introduce targeted guest atoms, which act as dopants, into type II Si clathrate films. The focus is on Mg as a test case for implantation, a dopant previously unreported in type II Si clathrates. The effects of ion implantation on the metastable Si clathrate structure were examined through systematic investigation of implant parameters. Time-of-flight secondary ion mass spectrometry depth profiling confirmed the successful implantation of Mg, while X-ray diffraction and confocal Raman spectroscopy demonstrated minimal structural damage at lower fluences, with the clathrate framework retaining its integrity without converting to other phases. At the higher end of the fluence range implantation caused localized transitions from clathrate to amorphous silicon. Implant activation using rapid thermal annealing was examined with the clathrate structure stable up to 500 °C and being converted to diamond silicon above this temperature. Post-implantation and activation structural characterization showed evidence of damage reversal. Electron paramagnetic resonance studies provided indirect evidence of dopant incorporation. These findings establish a foundation for introducing alternative guests/dopants into the Si clathrate cages through ion implantation, advancing their tunability for next-generation quantum and optoelectronic devices.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Thermomechanical Fatigue Damage/Failure Mechanisms in SCS-6/Timetal 21S [0/90](Sub S) Composite

The thermomechanical fatigue (TMF) deformation, damage, and life behaviors of SCS6/Timetal 21S (0/90)s were investigated under zero-tension conditions. In-phase (IP) and out-of-phase (OP) loadings were investigated with a temperature cycle from 150 to 650 deg C. An advanced TMF test technique was used to quantify mechanically damage progression. The technique incorporated explicit measurements of the macroscopic (1) isothermal static moduli at the temperature extremes of the TMF cycle and (2) coefficient of thermal expansion (CTE) as functions of the TMF cycles. The importance of thermal property degradation and its relevance to accurate post-test data analysis and interpretation is briefly addressed. Extensive fractography and metallography were conducted on specimens from failed and interrupted tests to characterize the extent of damage at the microstructure level. Fatigue life results indicated trends analogous to those established for similar unidirectional(0) reinforced titanium matrix composite systems. High stress IP and mid to low stress OP loading conditions were life-limiting in comparison to maximum temperature isothermal conditions. Dominant damage mechanisms changed with cycle type. Damage resulting from IP TMF conditions produced measurable decreases in static moduli but only minimal changes in the CTE. Metallography on interrupted and failed specimens revealed extensive (0) fiber cracking with sparse matrix damage. No surface initiated matrix cracks were present. Comparable OP TMF conditions initiated environment enhanced surface cracking and matrix cracking initiated at (90) fiber/matrix (F/M) interfaces. Notable static moduli and CTE degradations were measured. Fractography and metallography revealed that the transverse cracks originating from the surface and (90) F/M interfaces tended to converge and coalesce at the (0) fibers.

Castelli, Michael G.↗
NASA NTRS2023

Modeling of Response of Thermoplastic Composites Under High Energy Impact

This work investigates the response of a thermoplastic panel under high energy ballistic impact. The composite material system is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK3). Several high energy dynamic impact tests were performed where an aluminum projectile impacted various panels at different impact velocities. For this work, the test performed at an impact velocity of 73.2 m/s was investigated. The projectile rebounded upon impact, and the damage to the panel was characterized through ultrasonic and CT-scanning. Response of the panel under impact and the associated damage is discussed. Numerical simulation of the impact process was performed using the LS-DYNA® computer code [1] with a new material model MAT_COMPOSITE_DAMAGE_DGD (MAT 299), a modification over MAT 261 material model in terms of an improved representation of damage coupling and additional capability for strain rate effects. Delaminations were modeled using cohesive zone contact formulation in LS-DYNA®, wherein the mixed-mode fracture is captured via the Benzegaggh-Kenane (B-K) mode-dependent fracture energy interpolation law. Simulation of this impact test demonstrates a good match of results in terms of panel deflection and panel-projectile interactions. The overall extent of delaminations was under-predicted by the simulation. This work forms the basis to model tests performed at higher velocities, involving projectile penetration of panel.

Composite Materials↗
NASA NTRS1997

The Merging of Fatigue and Fracture Mechanics Concepts: A Historical Perspective

The seventh Jerry L. Swedlow Memorial Lecture presents a review of some of the technical developments, that have occurred during the past 40 years, which have led to the merger of fatigue and fracture mechanics concepts. This review is made from the viewpoint of 'crack propagation.' As methods to observe the 'fatigue' process have improved, the formation of fatigue micro-cracks have been observed earlier in life and the measured crack sizes have become smaller. These observations suggest that fatigue damage can now be characterized by 'crack size.' In parallel, the crack-growth analysis methods, using stress-intensity factors, have also improved. But the effects of material inhomogeneities, crack-fracture mechanisms, and nonlinear behavior must now be included in these analyses. The discovery of crack-closure mechanisms, such as plasticity, roughness, and oxide/corrosion/fretting product debris, and the use of the effective stress-intensity factor range, has provided an engineering tool to predict small- and large-crack-growth rate behavior under service loading, conditions. These mechanisms have also provided a rationale for developing, new, damage-tolerant materials. This review suggests that small-crack growth behavior should be viewed as typical behavior, whereas large-crack threshold behavior should be viewed as the anomaly. Small-crack theory has unified 'fatigue' and 'fracture mechanics' concepts; and has bridged the cap between safe-life and durability/damage-tolerance design concepts.

Newman, James C., Jr.↗
NASA NTRS2016

Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates

The Finite Element Analysis-Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to characterize and predict the progressive damage response of silicon-carbide-fiber-reinforced reaction-bonded silicon nitride matrix (SiC/RBSN) composite laminate tensile specimens. Studied were unidirectional laminates [0] (sub 8), [10] (sub 8), [45] (sub 8), and [90] (sub 8); cross-ply laminates [0 (sub 2) divided by 90 (sub 2),]s; angled-ply laminates [plus 45 (sub 2) divided by -45 (sub 2), ]s; doubled-edge-notched [0] (sub 8), laminates; and central-hole laminates. Results correlated well with the experimental data. This work was performed as a validation and benchmarking exercise of the FEAMAC/CARES program. FEAMAC/CARES simulates stochastic-based discrete-event progressive damage of ceramic matrix composite and polymer matrix composite material structures. It couples three software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life), and (3) the Abaqus finite element analysis program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating-unit-cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC, and Abaqus is used to model the overall composite structure. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events that incrementally progress until ultimate structural failure.

composite structures↗
NASA NTRS2004

Distribution of Inclusion-Initiated Fatigue Cracking in Powder Metallurgy Udimet 720 Characterized

In the absence of extrinsic surface damage, the fatigue life of metals is often dictated by the distribution of intrinsic defects. In powder metallurgy (PM) alloys, relatively large defects occur rarely enough that a typical characterization with a limited number of small volume fatigue test specimens will not adequately sample inclusion-initiated damage. Counterintuitively, inclusion-initiated failure has a greater impact on the distribution in PM alloy fatigue lives because they tend to have fewer defects than their cast and wrought counterparts. Although the relative paucity of defects in PM alloys leads to higher mean fatigue lives, the distribution in observed lives tends to be broader. In order to study this important failure initiation mechanism without expending an inordinate number of specimens, a study was undertaken at the NASA Glenn Research Center where known populations of artificial inclusions (seeds) were introduced to production powder. Fatigue specimens were machined from forgings produced from the seeded powder. Considerable effort has been expended in characterizing the crack growth rate from inclusion-initiated cracks in seeded PM alloys. A rotating and translating positioning system, with associated software, was devised to map the surface inclusions in low-cycle fatigue (LCF) test bars and to monitor the crack growth from these inclusions. The preceding graph illustrates the measured extension in fatigue cracks from inclusions on a seeded LCF test bar subjected to cyclic loading at a strain range of 0.8 percent and a strain ratio (max/min) of zero. Notice that the observed inclusions fall into three categories: some do not propagate at all (arrest), some propagate with a decreasing crack growth rate, and a few propagate at increasing rates that can be modeled by fracture mechanics. The following graph shows the measured inclusion-initiated crack growth rates from 10 interrupted LCF tests plotted against stress intensities calculated for semi-elliptical cracks with the observed surface lengths. The expected scatter in the crack growth rates for stress intensity ranges near threshold is observed. These data will be used to help determine the distribution in growth rates of cracks emanating from inclusions as well as the proportion of cracks that arrest under various loading conditions.

Bonacuse, Peter J.↗