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Numerical methodology for treating static and dynamic dislocation problems near a free surface

Abstract Simulation of dislocation dynamics enables researchers and scientists to explore the plastic behavior of crystalline materials under loading. Analytic solutions for the stress field due to a linear dislocation segment near a free surface are case-specific, e.g. dealing with either a horizontal segment or a vertical segment, and therefore hard to implement in time-dependent dislocation dynamics simulations as different dislocation segments could be differently oriented. This article presents a generalized numerical framework to find the stress field beneath a free surface due to the presence of a dislocation segment. The framework can be expanded to non-flat surfaces. Also, three-dimensional discrete dislocation dynamics simulations are performed here, which clearly show the effect of free surfaces on the flow stress of a material.

Siddique, Abu Bakar↗

Androgynous { 10 1 ¯ 2 } twin in zinc

Under ambient conditions, Zn is a hexagonal metal with a large c / a ratio of 1.856. Plastic deformation is predominantly accommodated by basal 〈 a 〉 slip and compression twins on the { 10 1 ¯ 2 } planes. Increasing hydrostatic pressure drastically reduces the c / a ratio of Zn and, when a critical threshold of c / a = 3 at about 10 GPa is crossed, the { 10 1 ¯ 2 } twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when c / a = 3 , remains unknown. Here, we strain-cycle a textured polycrystalline sample of pure Zn at uniform hydrostatic pressures ranging between 2 and 17 GPa, over which the c / a ratio crosses the c / a = 3 compressive-tensile transition for { 10 1 ¯ 2 } twins. During deformation, the state of the sample is monitored through x-ray diffraction to extract texture and internal strain evolution. By comparing the experimental results with the predictions of an elastoviscoplastic polycrystal simulation, we confirm the androgynous nature of { 10 1 ¯ 2 } twin response at low and high pressures. When c / a = 3 , polycrystalline Zn does not display any evidence of twinning and its plastic behavior is controlled by mostly basal and pyramidal 〈 c + a 〉 slip activity, with a very small contribution of prismatic 〈 a 〉 slip. Evidence for the activity of other { 10 1 ¯ n } twinning modes, which have been suggested for Zn under high pressure, are not observed. Published by the American Physical Society 2024

Merkel, Sébastien (ORCID:000000032767581X)↗

Verification Testing For Solid-Element Material Models 11-19 in DYNA3D/ParaDyn

This technical report documents the creation and implementation of verification tests for solid-element material models 11 through 19 available in DYNA3D/ParaDyn. The verification tests covered all aspects of each material model, except for the Weibull distribution functionality in material models 15 and 19. General test cases were created to verify the elastic and plastic behavior of the material models. Other additional tests were developed to examine the intricacies of each material model. Each test involved the use a kinematic load case and specification of material parameters necessary to activate corresponding features of the material model. The load cases prescribed the full time history of the kinematic motion for the solid elements, and these loads are independent of the material model or element formulation. When possible, closed form solutions were then derived for each verification test in a continuum setting. The DYNA3D simulations for each test were carried out over a unit time interval, t ϵ [0, 1], and the as implemented DYNA3D response was compared to the closed form solutions evaluated at discrete points in time. A relative error measure was determined for each test to justify the proper implementation of the material model. The relative errors comparing the DYNA3D solution to the analytical solution were, in general, on the order of machine precision except where noted. This signifies the proper implementation of solid-element material models 11-19. In the development of these verification tests, six bugs were found and fixed in the source code. Additionally, this work generated eighteen DYNA3D input decks and answer extraction scripts in the DYNA3D/ParaDyn Software Quality Assurance test suite, which are comprised of a total of 285 solid-element tests. Testing for each material model utilizes two input decks and answer extraction scripts, where one focuses on the linear elastic response and the other examines the inelastic and remaining functionalities of the material model. In total, this work added 285 individual verification test problems in the DYNA3D/ParaDyn test suite.

42 ENGINEERING↗

Localized Strain Analysis of Ce- and Mg-Treated Cast Iron under Uniaxial Compression

Cast iron exhibits a wide range of mechanical properties, depending on its microstructural features. The microstructure of cast iron consists of several microconstituents with different elastic-plastic behavior, making the strain non-uniform across the bulk material. To understand the individual effects of these microconstituents on the overall mechanical behavior, local strain analysis using digital image correlation analysis was carried out. Samples with two different compositions (varying cerium, magnesium and silicon) were processed at different solidification velocities in a Bridgman furnace. Sections of the directionally solidified samples were loaded under uniaxial compression to measure global and local strain behavior. Despite the variability of the microstructure, the stress–strain curves obtained by digital image correlation (DIC) were found to react in a well-controlled way to changes in solidification velocity. It was observed that high-strain failure (greater than 15%) was accompanied by local straining of the softer ferritic phase, but during low-strain failure, local straining was not prominent. Higher nodularities, due to higher solidification velocities, raised the compressive strength without affecting the toughness significantly. Higher percentages of carbides led to higher compressive strengths with corresponding losses in ductility. The continuity of the matrix was also found to play an important role in the behavior during compression.

ductile failure↗

Physical property measurements of doped cesium iodide crystals

Mechanical and thermal property values are reported for crystalline cesium iodide doped with sodium and thallium. Young's modulus, bulk modulus, shear modulus, and Poisson's ratio were obtained from ultrasonic measurements. Young's modulus and the samples' elastic and plastic behavior were also measured under tension and compression. Thermal expansion and thermal conductivity were the temperature dependent measurements that were made.

Synder, R. S.↗

On the relation of J sub I to work done per unit uncracked area - Total, or component 'due to crack'

The J sub I relation, introduced by Rice (1968), expresses the work done on a quasiplanar specimen of specified width (or depth) for a fixed uniform crack length when the displacement of the load is increased from zero to some given value. The relation remains the same if the work done and its logarithmic derivative are calculated in terms of the component of the displacement that is 'due to the crack' rather than the total displacement. J sub I is studied as a function of displacement for a precracked, three-point-loaded bend specimen and also in the extremes of linear-elastic, and rigid/perfectly plastic behavior.

Srawley, J. E.↗

Design and fabrication of realistic adhesively bonded joints

Eighteen bonded joint test specimens representing three different designs of a composite wing chordwise bonded splice were designed and fabricated using current aircraft industry practices. Three types of joints (full wing laminate penetration, two side stepped; midthickness penetration, one side stepped; and partial penetration, scarfed) were analyzed using state of the art elastic joint analysis modified for plastic behavior of the adhesive. The static tensile fail load at room temperature was predicted to be: (1) 1026 kN/m (5860 1b/in) for the two side stepped joint; (2) 925 kN/m (5287 1b/in) for the one side stepped joint; and (3) 1330 kN/m (7600 1b/in) for the scarfed joint. All joints were designed to fail in the adhesive.

Shyprykevich, P.↗

Effect of swaging on the 1000 C compressive slow plastic flow characteristics of the directionally solidified eutectic alloy gamma/gamma prime-alpha

Swaging between 750 and 1050 C has been investigated as a means to introduce work into the directionally solidified eutectic alloy gamma/gamma prime-alpha (Ni-32.3 wt percent Mo-6.3 wt percent Al) and increase the elevated temperature creep strength. The 1000 C slow plastic compressive flow stress-strain rate properties in air of as-grown, annealed, and worked nominally 10 and 25 percent materials have been determined. Swaging did not improve the slow plastic behavior. In fact large reductions tended to degrade the strength and produced a change in the deformation mechanism from uniform flow to one involving intense slip band formation. Comparison of 1000 C tensile and compressive strength-strain rate data reveals that deformation is independent of the stress state.

Whittenberger, J. D.↗

The role of material properties in adhesion

When two solid surfaces are brought into contact strong adhesive bond forces can develop between the materials. The magnitude of the forces will depend upon the state of the surfaces, cleanliness and the fundamental properties of the two solids, both surface and bulk. Adhesion between solids is addressed from a theoretical consideration of the electronic nature of the surfaces and experimentally relating bond forces to the nature of the interface resulting from solid state contact. Surface properties correlated with adhesion include, atomic or molecular orientation, reconstruction and segregation as well as the chemistry of the surface specie. Where dissimilar solids are in contact the contribution of each is considered as is the role of their interactive chemistry on bond strength. Bulk properties examined include elastic and plastic behavior in the surficial regions, cohesive binding energies, crystal structure, crystallographic orientation and state. Materials examined with respect to interfacial adhesive interactions include metals, alloys, ceramics, polymers and diamond. They are reviewed both in single and polycrystalline form. The surfaces of the contacting solids are studied both in the atomic or molecularly clean state and in the presence of selected surface contaminants.

Buckley, D. H.↗

Ceramic microstructure and adhesion

When a ceramic is brought into contact with a ceramic, a polymer, or a metal, strong bond forces can develop between the materials. The bonding forces will depend upon the state of the surfaces, cleanliness and the fundamental properties of the two solids, both surface and bulk. Adhesion between a ceramic and another solid are discussed from a theoretical consideration of the nature of the surfaces and experimentally by relating bond forces to interface resulting from solid state contact. Surface properties of ceramics correlated with adhesion include, orientation, reconstruction and diffusion as well as the chemistry of the surface specie. Where a ceramic is in contact with a metal their interactive chemistry and bond strength is considered. Bulk properties examined include elastic and plastic behavior in the surficial regions, cohesive binding energies, crystal structures and crystallographic orientation. Materials examined with respect to interfacial adhesive interactions include silicon carbide, nickel zinc ferrite, manganese zinc ferrite, and aluminum oxide. The surfaces of the contacting solids are studied both in the atomic or molecularly clean state and in the presence of selected surface contaminants.

Buckley, D. H.↗

Ceramic microstructure and adhesion

When a ceramic is brought into contact with a ceramic, a polymer, or a metal, strong bond forces can develop between the materials. The bonding forces will depend upon the state of the surfaces, cleanliness and the fundamental properties of the two solids, both surface and bulk. Adhesion between a ceramic and another solid are discussed from a theoretical consideration of the nature of the surfaces and experimentally by relating bond forces to interface resulting from solid state contact. Surface properties of ceramics correlated with adhesion include, orientation, reconstruction and diffusion as well as the chemistry of the surface specie. Where a ceramic is in contact with a metal their interactive chemistry and bond strength is considered. Bulk properties examined include elastic and plastic behavior in the surficial regions, cohesive binding energies, crystal structures and crystallographic orientation. Materials examined with respect to interfacial adhesive interactions include silicon carbide, nickel zinc ferrite, manganese zinc ferrite, and aluminum oxide. The surfaces of the contacting solids are studied both in the atomic or molecularly clean state and in the presence of selected surface contaminants.

Buckley, D. H.↗

Measuring Hole Elongation in Bolted Joints

Measurement does not affect joint parameters. Verification of analytical and strength-prediction methods for bolted composite joints based generally on data obtained experimentally from double-lap-joint specimens. In mechanically fastened joints, stresses maximal at fastener holes. Ability to measure accurately hole elongations without affecting joint parameters provides better understanding of elastic and plastic behavior of joint material leading to failure mechanisms in mechanically fastened joints required for design of more-efficient, lightweight composite joints.

Wichorek, G. R.↗

North America-Pacific plate boundary, an elastic-plastic megashear - Evidence from very long baseline interferometry

Data obtained by Mark III VLBI measurements of radio signals from permanent and mobile VLBI sites for 5.5 years of observations, starting in October 1982, were used to derive a picture of the earth crust deformation near the North America-Pacific plate boundary. The data, which included the vector positions of the VLBI sites and their rate of change, were used for comparison with a number of lithospheric deformation models based upon the concept that the motions of points near the North America-Pacific plate boundary are a linear combination of North America and Pacific velocities. The best of these models were found to fit 95 percent of the variance in 139 VLBI length and transverse velocity observations. Instantaneous shear deformation associated with plate tectonics is apparently developing in a zone 450 km wide paralleling the San Andreas Fault; some of this deformation will be recovered through elastic rebound, while the rest will be permanently set through plastic processes. Because the VLBI data have not been collected for a significant fraction of the earthquake cycle, they cannot discriminate between elastic and plastic behaviors.

Ward, Steven N.↗

A numerical model for the thermo-elasto-plastic behaviour of a material

This paper presents a numerical model for the thermo-elasto-plastic behavior of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non-isothermal cases. The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.

Ray, Sujit K.↗

Plasticity analysis of fibrous composite laminates under thermomechanical loads

Elastic-plastic behavior of fibrous composite laminates is analyzed for coupled in-plane mechanical loads and uniform thermal changes. Constitutive equations of the individual fibrous layers are derived from a vanishing fiber diameter model that represents the essential axial constraint between the phases. This permits derivation of closed form equations for the overall yield condition, stress concentration factors, and instantaneous compliance. Thermoelastic properties of the phases and yield stress of the matrix phase are functions of temperature. The effect of the model assumptions on the predicted behavior of composite laminates is examined by comparing the calculated response under cyclic thermal changes to available theoretical results and experimental measurements.

Bahei-El-din, Yehia A.↗

Applicability of Similarity Principles to Structural Models

A systematic account is given in part I of the use of dimensional analysis in constructing similarity conditions for models and structures. The analysis covers large deflections, buckling, plastic behavior, and materials with nonlinear stress-strain characteristics, as well as the simpler structural problems. (author)

Goodier, J N↗