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At least 55 records · Page 3

Erosion in radial inflow turbines. Volume 4: Erosion rates on internal surfaces

An analytic study of the rate at which material is removed by ingested dust impinging on the internal surfaces of a typical radial inflow turbine is presented. Results show that there are several regions which experience very severe erosion loss, and other regions that experience moderate levels of erosion loss: (1) the greatest amount of material loss occurs on the trailing edges of the nozzle blades where very high velocity, moderate angle impacts occur. The tip regions of ductile materials are also subjected to serious levels of erosion loss; (2) moderate amounts of erosion occur near the end of the scroll and on a few of the nozzle blades near this location. Results are presented in the form of surface contours that exist on the scroll and blade surfaces after continuous particulate ingestion with time.

Clevenger, W. B., Jr.↗

Metal (Cu,Al)/CNT Composite Wires for Energy Efficient Motors

This report summarizes the main results of research project on Metal/CNT nanocomposites conducted at University of Central Florida (UCF). It should be noted that the project was budgeted for three years, but the budget period 3 was unfortunately not funded and conducted in COVID19 pandemic years due to many reasons. The demonstration plan on the small motors was also removed according to the discussion with the DOE program manager. All research activities were focused on the (Cu,Al)/CNT material development and wire extrusion. Existing methods to fabricate Metal/CNTs were usually suffering from agglomeration of CNTs due to their density and stiffness differences. A new method is studied by the UCF research team, where CNTs are surface treated firstly, then coated with pure metals (i.e., Al, Cu, and Nickle). The metal encapsulation on CNT is expected to significantly improve the interfacial bonding between CNTs and the intimated metal matrices. The coated CNT powders were used to make sample materials through sintering, then a customized wire extrusion process was employed to fabricate wires. Measurement of material property improvements in mechanical strength, thermal conductivity, and electrical conductivity were conducted on both cylinder samples and extruded wires. In addition to the sintering process, casting on metal coated CNT powder was also investigated. The best results we achieved are summarized as follows. (1) The measured thermal conductivity of Al/CNT composite made with Ni-encapsulated CNTs and pure Al powders is about 85% better than that of pure aluminum fabricated. The measured electrical conductivity of fabricated Al/CNT is about 14-20% better than that of pure aluminum. (2) The measured electrical conductivity of Cu/CNT is about 14.5% better than that of pure copper fabricated. (3) The mechanical strengths of both Cu/CNT and Al/CNT (with about 1% wt. CNTs) are 70% better than pure metals although losing some material ductility. (4) Two-stage wire extrusion at high temperatures were designed and successfully conducted to fabricate wires of Metal/CNTs.

36 MATERIALS SCIENCE↗

Crack Turning and Arrest Mechanisms for Integral Structure

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Pettit, Richard↗

Microstructural Progression of Shear-Induced Mixing in a CuNi Alloy

Shear deformation has been highlighted in multiple research efforts for its ability to impart mechanical properties improvements and unique microstructures. When used to process and densify powdered material, these shear-based consolidation techniques are commonly referred to as friction consolidation (FC). In this paper, we have examined the microstructural evolution from compacted Cu and Ni powders to a consolidated Cu0.5Ni0.5 alloy. We have shown various stages of porosity reduction and preferential deformation being accommodated by the more ductile material early in the process, leading to formation of a tortuous microstructural zone. Porosity reduction was extensive, decreasing from ~65% in the unprocessed powder to ~1% in the fully consolidated alloy. The final consolidated alloy showed roughly a 2X hardness improvement over the unalloyed, compacted material. Unique aspects of this work include demonstration of the ability to use FC processing to produce a submicron and equiaxed grain size in samples within a 0.5 to 2 minute processing time.

Overman, Nicole R.↗

FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance

International technical experts in durability and damage tolerance of metallic airframe structures were assembled to present and discuss recent research findings and the development of advanced design and analysis methods, structural concepts, and advanced materials. The symposium focused on the dissemination of new knowledge and the peer-review of progress on the development of advanced methodologies. Papers were presented on: structural concepts for enhanced durability, damage tolerance, and maintainability; new metallic alloys and processing technology; fatigue crack initiation and small crack effects; fatigue crack growth models; fracture mechanics failure, criteria for ductile materials; structural mechanics methodology for residual strength and life prediction; development of flight load spectra for design and testing; and advanced approaches to resist corrosion and environmentally assisted fatigue.

Harris, Charles E.↗

FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance, part 2

The international technical experts in the areas of durability and damage tolerance of metallic airframe structures were assembled to present and discuss recent research findings and the development of advanced design and analysis methods, structural concepts, and advanced materials. The principal focus of the symposium was on the dissemination of new knowledge and the peer-review of progress on the development of advanced methodologies. Papers were presented on the following topics: structural concepts for enhanced durability, damage tolerance, and maintainability; new metallic alloys and processing technology; fatigue crack initiation and small crack effects; fatigue crack growth models; fracture mechanics failure criteria for ductile materials; structural mechanics methodology for residual strength and life prediction; development of flight load spectra for design and testing; and corrosion resistance.

Harris, Charles E.↗

Plasticity and Damage Modeling of Stress Asymmetry and Dynamic Behavior of AFS Additive Manufactured Aluminum Alloy 2219

The Solid State Additive Manufacturing (AM) process referred as MELD that fabricated the samples in this study, provides a new path for repairing, coating, joining and additive manufacturing metals and metal matrix composites. This research will be the first application of a physics-based microstructure dependent internal state variable (ISV) plasticity and damage material model to capture the mechanical response of an AM Aluminum Alloy (AA) 2219 via the MELD process. In this research, a microstructure-based internal state variable (ISV) plasticity-damage model was used to capture the mechanical behavior of AFS 2219 aluminum alloy. Aeroprobe Corporation, creator and patent holder for the MELD process, fabricated the material by pushing a solid filler rod of AA2219-T861 material through a hollow rotating tool onto an AA2219 T851 plate substrate. As feedstock, solid or powder precursor metals are pushed through a nonconsumable rotating cylindrical tool. Herein, added layers are deposited and metallurgically bonded to substrate material or previously deposited layers by the heat generated from the rotating tool through plastic deformation of the filler material. Once a layer has been added, the tool height increases, and starts the deposition of the next layer. This process results in beneficial properties such as grain refinement, homogenization and reduced porosity (fully dense). This process will experience temperatures similar to those in the weld nugget zone (WNZ) in friction stir welding (FSW), ranging from 0.6-0.9 Tm, with Tm being the melting point of the material. MELD is highly scalable with AA deposition rates reaching over 1000 cm3/hr, which allows for MELD being used for repairs, coatings, and building components. A motivating factor driving the research for physics-based history dependent material modeling of MELD components is the ability to accurately capture the stress-state and strain rate dependence in the material caused by variations in material microstructure from the MELD processing of new or repaired components. The ISV model incorporates microstructural content and is consistent with continuum level kinematics, kinetics, and thermodynamics. These features allow the ISV model to capture large deformations at the structural scale using the kinematic and isotropic hardening, while microscale damage is obtained from the microstructural features. The benefits of the ISV model arise from the inclusion of structure-property relationships identified from microstructural characterization and experimentation. The Bauschinger effect (BE) is an important concept, vital in the accurate prediction of cyclic stress-strain response of ductile materials such as metals. The ISV model has been successfully used to capture the behavior and damage, and the BE of different aluminum alloys and steels. The ISV model uses kinematic and isotropic hardening to help capture deformations of the material at the macro scale. To understand this hardening relationship, calculating the kinematic and isotropic hardening relationship in the material is warranted for a high-fidelity model. Electron Backscattered Diffraction (EBSD) was used to characterize the as-fabricated microstructure, where a fully-dense equiaxed grain morphology with average grain size of 2.5 μm was observed. Microhardness mapping of the as-built structures, monotonic tension and compression experiments at both quasi-static (0.001/s) strain rates, tension-followed-by-compression and compression-followed-by-tension experiments were performed to obtain the set of plasticity and damage constants necessary to capture strain rate and stress state behavior of this additive material. To calibrate the plasticity-damage model, a single set of constants were determined to capture the different stress states the MELD AA2219. One set of the constants was determined from experimental true stress-strain curves for the tension and compression data. Additionally, microstructural information and data from the open literature were used as the other model constants. This research is a first of its kind for AFS AA2219, includes correlating the ISV model to the monotonic experimental results that capture the isotropic and kinematic plasticity mechanical response.

Rivera, O. G.↗

Results of FY 2023 Alloy 617 and Alloy 709 High-Temperature Crack-Growth Testing

This report summarizes the work performed at Idaho National Laboratory under the “Creep, fatigue and creep-fatigue crack growth tests” task of the “Long-Term VHTR Material Qualification – INL” work package. Work was performed this year to validate the crack growth monitoring setup used with the test frames against both continuous crack length monitoring using an optical camera, as well as post-mortem analysis of marker bands on the fracture surface. Delays prevented the use of a gauge to measure load-line displacement for early tests, and so the creep-fatigue crack growth setup was evaluated using the actuator displacement for a load-line displacement setup. While not ideal, this allowed examination of the shortcomings with the current software setup that was originally designed for performing stress corrosion crack growth rate studies. The method for data collection was modified to link the crack growth monitoring software with Instron’s Wave Matrix software. Once the load-line displacement gauge arrived, the crack growth equipment was successfully modified to permit continuous monitoring of both load-line displacement and crack length. This is critical for creep-fatigue and creep crack growth rate studies for ductile material, as it permits the C* and Ct analyses. Test results are shown for Alloy 617 fatigue and creep-fatigue (without the gauge for load-line displacement measurements), as well as creep-fatigue of Alloy 709, which was performed with the completed test setup, allowing for crack length and load-line displacement monitoring.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Final report on assessment of molten salt corrosion testing of unirradiated and ion irradiated advanced manufactured high entropy alloys

Generation IV reactors and future fusion reactor designs have led to more demanding materials performance requirements due to their increased operating temperatures, corrosive coolants, and increased radiation doses compared to the current light-water reactor fleet. Among the innovative nuclear technologies under development, molten salt reactors stand out for their potential to offer superior fuel utilization, intrinsic safety characteristics, and economic viability. Of the proposed Generation IV designs, the gas fast reactor operates at 450 to 850°C and the molten salt reactor operates at 565 to 850°C, with the molten salt reactor design needing molten salt corrosion resistant materials [1, 2]. These increased temperatures and more extreme corrosion environments necessitate higher material performance, such as creep strength, radiation-tolerant microstructures, corrosion resistance, and high-temperature tensile properties. Hastelloy-N, a nickel-based alloy with additions of molybdenum and chromium, has been successfully employed to contain molten fluoride salt at temperatures up to 705°C. However, Hastelloy-N becomes embrittled upon neutron irradiation, primarily due to the accumulation of helium produced by (n,a) transmutation reactions. Furthermore, the corrosive nature of molten fluoride and chloride salts presents a formidable challenge, as these salts can react with and dissolve alloying elements such as Cr, Mo, and Fe, leading to selective leaching, loss of protective oxide layers, and accelerated degradation. High entropy alloys (HEAs) and refractory high entropy alloys (RHEAs) have emerged as a prominent area of interest, due to their ability to achieve tailored chemical compositions for specific applications. Unlike conventional alloys, HEAs are characterized by having multiple principal elements in equimolar or near equimolar ratios, leading to an unconventional alloying strategy [3]. This alloying strategy is believed to promote unique properties, such as single-phase stabilization of chemically compatible elements, lattice distortion effects due to atomic radius differences, and proposed sluggish diffusion effects. For extreme-environment applications, RHEAs have garnered much research interest because of the possibility of creating relatively ductile materials that can operate in extremely high-temperature environments, beyond the operating temperatures where other Ni-based superalloys begin to lose strength [4-6]. Idaho National Laboratory (INL) initiated a joint international effort with the Czech Republic to explore the feasibility of manufacturing HEAs for high-temperature nuclear applications using advanced manufacturing. This effort was funded at INL by the United States Department of Energy's Office of Nuclear Energy under the Advanced Reactor Technologies and Advanced Materials and Manufacturing Technologies (AMMT) Program. The HEAs were specifically designed for the corrosive and irradiation environments experienced in gas-cooled fast reactors, molten salt reactors, and fusion power. These alloys have been manufactured by multiple processes to determine the impact of manufacturing processes on the performance of the alloys in corrosive and irradiation environments. Preliminary molten salt corrosion testing showed that equimolar MoNbTiV and MoNbTi alloys exhibit exceptional performance, with arc-melted variants demonstrating only minimal degradation after 1000 hours of exposure to molten chloride salt at 700°C. Conversely, Nb2TiVZr2 showed significant molten salt corrosion susceptibility and microstructural instability during high-temperature molten salt exposures, and was, therefore deemed unfit for molten salt reactor applications. The MoNbTiV, MoNbTi, and Nb2TiVZr2 alloys were further evaluated through ion irradiation experiments conducted at the Michigan Ion Beam Laboratory at the University of Michigan. The microstructural stability and the evolution of irradiation-induced defects were characterized to assess the irradiation resistance of each of these alloys.

36 - MATERIALS SCIENCE↗

Unveiling the Fatigue Behavior of 2D Hybrid Organic–Inorganic Perovskites: Insights for Long-Term Durability

2D hybrid organic–inorganic perovskites (HOIPs) are commonly found under subcritical cyclic stresses and suffer from fatigue issues during device operation. However, their fatigue properties remain unknown. Here, the fatigue behavior of (C 4 H 9 -NH 3 ) 2 (CH 3 NH 3 ) 2 Pb 3 I 10 , the archetype 2D HOIP, is systematically investigated by atomic force microscopy (AFM). It is found that 2D HOIPs are much more fatigue resilient than polymers and can survive over 1 billion cycles. 2D HOIPs tend to exhibit brittle failure at high mean stress levels, but behave as ductile materials at low mean stress levels. These results suggest the presence of a plastic deformation mechanism in these ionic 2D HOIPs at low mean stress levels, which may contribute to the long fatigue lifetime, but is inhibited at higher mean stresses. The stiffness and strength of 2D HOIPs are gradually weakened under subcritical loading, potentially as a result of stress-induced defect nucleation and accumulation. The cyclic loading component can further accelerate this process. The fatigue lifetime of 2D HOIPs can be extended by reducing the mean stress, stress amplitude, or increasing the thickness. These results can provide indispensable insights into designing and engineering 2D HOIPs and other hybrid organic–inorganic materials for long-term mechanical durability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tuning the Mechanical Properties of Crosslinked Copolymers via Sequence and Solvent‐Selective Swelling for Vat Photopolymerization

Block copolymers (BCPs) offer distinct advantages for vat photopolymerization by enabling mechanically programmable network structures through microphase-separated morphologies that can be kinetically trapped during curing, yielding properties unattainable in homogeneous resins. However, the respective roles of repeat-unit sequence and solvent environment, together with their interplay in directing network formation and mechanical performance, remain unclear. Here, we synthesize a series of CO 2 -based polycarbonate copolymers comprising a crosslinkable glassy poly(vinyl cyclohexene carbonate) (PVCHC, A block) and a non-crosslinkable soft poly(propylene carbonate) (PPC, B block). The polymer sequence is systematically varied (ABA, BAB, and statistical), and solvent choice controls block-selective swelling to jointly control gelation behavior, microphase morphology, and mechanical response through changes in the accessibility and local environment of photocrosslinkable vinyl groups during network formation, as revealed by photorheology and small angle x-ray scattering. By tuning polymer sequence and curing solvent, we transform nominally identical formulations from brittle to highly ductile materials, achieving a three-orders-of-magnitude range in toughness (0.003 to 9.1 MJ m −3 ). These results establish clear structure–processing–property relationships and identify polymer sequence and selective solvation as powerful strategies for programming both printability and performance of block copolymer resins for additive manufacturing.

additive manufacturing↗

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

Simulation and analysis of the 3D double shock-induced recompression of spall using a hybrid PAGOSA with FLIP+MPM

In this work, an innovative hybrid algorithm PAGOSA with FLIP + MPM is first presented by coupling PAGOSA with the particle FLIP + MPM, and applied to systematically exploring the 3D recompression of spall induced by double-shock waves in ductile materials as the few existing studies are currently limited to the pure longitudinal recompression of spall, and ignore the 3D effects. This algorithm solves the difficulties the grid-based methods encounter when applied to capturing the fracture in material. We first validate the capabilities of PAGOSA with FLIP + MPM to predict different fracture/fragmentation cases by solving two benchmark problems and comparing with the analytical solutions or the experiment results. The convergences and the infinity-norm errors are also investigated. Subsequently, the 3D effects are demonstrated by simulating the spallation in material using PAGOSA with FLIP + MPM and comparing with those in the longitudinal cases. Additionally, some factors that affect the spallation with 3D effects are also discussed. Finally, the recompressions of spall in material with/without 3D effects are systematically simulated and analyzed. The recompression of spall driven by a high explosive is also simulated to show the ability of PAGOSA with FLIP + MPM to handle this kind of problem. The conditions that can lead to a recompression of spall are explored. Also, numerical results show that PAGOSA with FLIP + MPM can accurately predict different fracture cases, that the 3D effects play an important role in fracture/fragmentation, and the recompression of spall is very sensitive to the occurrence conditions, shows great differences when considering 3D effects in real applications. Moreover, the present hybrid method can be easily extended to other grid-based techniques employed for fracture in materials.

3D effects↗

Temperature and time effects of post-weld heat treatments on tensile properties and microstructure of Zircaloy-4

Opportunities exist to expand the application of Zircaloy-4 (Zry-4) into lower-temperature (<100°C) applications. Welded areas within these structures are potential failure points and post-weld heat treatments (PWHTs) are not yet standardized for application in this temperature range. Zry-4 tungsten inert gas (TIG) welds were given PWHTs from 450-900°C with hold times from 0.5-48 hours to investigate changes to tensile properties and microstructure. Treatment of 800°C for 1 hour was found to produce the most ductile material, measured by total elongation of the tensile bar (16.5%). Furthermore, both PWHT time and temperature were observed to increase total elongation, except in extreme (>800°C or >18hours) cases, but the effect of temperature was stronger. The second order cumulative annealing parameter shows a trend with tensile properties. Average grain sizes in the fusion zone and heat affected zone did not change under any of the PWHTs until the development of an undesirable blocky-alpha phase, which was only observed to form in the heat affected zones for hold times greater than 18hr at 800°C.

36 MATERIALS SCIENCE↗

Data-driven electron-diffraction approach reveals local short-range ordering in CrCoNi with ordering effects

Abstract The exceptional mechanical strength of medium/high-entropy alloys has been attributed to hardening in random solid solutions. Here, we evidence non-random chemical mixing in a CrCoNi alloy, resulting from short-range ordering. A data-mining approach of electron nanodiffraction enabled the study, which is assisted by neutron scattering, atom probe tomography, and diffraction simulation using first-principles theory models. Two samples, one homogenized and one heat-treated, are observed. In both samples, results reveal two types of short-range-order inside nanoclusters that minimize the Cr–Cr nearest neighbors (L1 2 ) or segregate Cr on alternating close-packed planes (L1 1 ). The L1 1 is predominant in the homogenized sample, while the L1 2 formation is promoted by heat-treatment, with the latter being accompanied by a dramatic change in dislocation-slip behavior. These findings uncover short-range order and the resulted chemical heterogeneities behind the mechanical strength in CrCoNi, providing general opportunities for atomistic-structure study in concentrated alloys for the design of strong and ductile materials.

36 MATERIALS SCIENCE↗

Apparatus for measuring strength in biaxial compression

We report most measurements of compressive strength of ductile materials have involved Hopkinson–Kolsky bars or Taylor anvils placing samples in uniaxial compression. In these geometries, strain is limited by the tendency of the sample to petal, in analogy to necking in uniaxial tension. Estimation of strength for any other form of the stress tensor requires assuming a shape of the yield surface; because data exist only for uniaxial compression, these assumptions are untested. In an imploding spherical shell, compression is biaxial, the plastic strain may not be small, and the material behavior may be nonlinear as a result of work hardening and heating by plastic work. We outline a method of measuring the strengths of materials in biaxial compression, both quasistatically and dynamically, using the compression of thin spherical shells. We suggest surrounding the shell with an annulus filled with a mixture of H 2 and Cl 2 gases whose homogeneous ignition is initiated by a flash of blue and near-ultraviolet light. Less promising approaches are described in Appendixes A–C .

47 OTHER INSTRUMENTATION↗

LEAD - LEArning Damage

LEAD is a suite of scripts to enable rapid estimation of model parameters for damage models for ductile materials using machine learning. In its current version, the only supported damage model is TEPLA, though others are planned. The data we train on are comprised of free surface velocity data as well as porosity data. Some details about our method can be found in the preprint LA-UR-23-20468 (arxiv.org/abs/2301.07790)

Blaschke, Daniel↗

Finite deformation implementation of a mixed-mode single-integral type cohesive zone with reorienting surfaces of separation

To model material ductile failure and crack propagation, cohesive zone elements can be embedded along potential fracture paths in a finite element simulation. When damage criteria are met, elements in the mesh decohere, simulating the formation and propagation of a crack. In this paper, we present a novel computational algorithm based on finite deformation theory, essential to modeling crack initiation and growth in solids undergoing large deformations. This new algorithm was formulated within a Lagrangian frame of reference to extend previous cohesive zone algorithms to include modeling crack growth in finite deformation contexts. The local coordinate system, necessary for defining an embedded cohesive zone, is constructed based upon the current configuration and is updated within the nonlinear iteration process, thereby resulting in the convergence of the solution for a growing crack in a large deformation quasi-static setting. The model’s accuracy was demonstrated by comparing finite element model simulation results with the analytic case of a constant surface separation, as shown in the verification examples. The power and efficacy of the algorithm to capture large deformations during crack growth were then demonstrated with a double cantilever beam example case. It indicates that the model can be applied to a variety of physical circumstances for predicting crack initiation and growth with delamination and fracture.

42 ENGINEERING↗