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At least 19 records

Plastic work constrained elastoplastic topology optimization

An elastoplastic topology optimization framework for limiting plastic work generation while maximizing stiffness is presented. The kinematics and constitutive model are based on finite strain linear isotropic hardening plasticity, and the balance laws are solved using a total Lagrangian finite element formulation. Aggregation of the specific plastic work combined with an adaptive normalization scheme efficiently constrains the maximum specific plastic work. The optimization problem is regularized using an augmented partial differential equation filter, and is solved by the method of moving asymptotes where path-dependent sensitivities are derived using the adjoint method. The numerical examples show a clear dependence on the optimized maximum stiffness structures for different levels of constrained specific plastic work. It is also shown that due to the history dependency of the plasticity, the load path significantly influences the structural performance and optimized topology.

42 ENGINEERING↗

Modification of Ni-20Cr corrosion dealloying behavior in molten fluorides via cold work induced plastic deformation

The corrosion dealloying behavior of cold-worked (CW) Ni20Cr alloy (wt%) was studied in molten LiF-NaF-KF (or FLiNaK) salts at 600 °C, equal to a homologous temperature (TH) of 0.52. Alloys were cold-rolled to achieve reductions of thickness of 10%, 30%, and 50% introducing plastic deformation and a high density of dislocations. Potentiostatic holds (Eapplied) were applied in two different electrode potential regimes. At 1.75VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, Cr dealloying to Cr(II) and Cr(III) is predominant, while at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, both Ni and Cr are oxidized in molten FLiNaK at 600 °C. In these potential regimes, dealloyed Ni20Cr displayed bicontinuous porosity within the grain interior and at grain boundaries, driven by the high driving force for Cr dissolution and sustained by defect mediated outward solid state diffusion of Cr in parallel with surface diffusion of Ni. The bicontinuous porous structure developed was observed to undergo further coarsening and densification of the Ni-rich ligaments at a higher electrode potential. The main effect of CW observed is the introduction of plastic deformation and dislocation substructures that serve as short-circuit paths for Cr solid state diffusion to surfaces exposed to FLiNaK. This modified the evolution of the bicontinuous porous structure which increased with CW substantially. Kinetic analysis reveals that the Cr dealloying at +1.75 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ and 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ is initially charge transfer controlled, except for the 50% CW condition at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, where the process becomes limited by slow Cr defect mediated bulk diffusion. The rate determining factors are explored and compared to experimental results.

Chan, Ho Lun↗

Thermomechanical Modeling of Copper

The plastic deformation of metals is a dissipative process. Some fraction of the plastic work is converted to heat which, given the temperature dependent response of metals, produces a thermal-mechanical coupling. In various cases, for instance when the loading is dynamic, this interaction can impact the resulting response of a material and/or system. Thus, appropriately capturing the heat generation from plastic work is necessary for various solid mechanics analysis. Determination of the fraction of work converted to heat has been long studied. Recent developments have demonstrated that the fraction is not constant but depends on various state variables. Resolving these features requires combined modeling and experimental studies. To this end, 304L stainless steel – a poor thermal conductor – was recently subjected to such an investigation. Advanced modeling capabilities were deployed to assess novel thermomechanically coupled experiments. As a complement to that study, in the current work a similar investigation is performed on copper – a good thermal conductor – to assess performance on the opposite end of the spectrum. The current document discusses these modeling efforts.

36 MATERIALS SCIENCE↗

Thermal-Mechanical Elastic-Plastic and Ductile Failure Model Calibrations for 6061-T651 Aluminum Alloy from Plate

Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The matters of interest here are the elastic-plastic response and ductile failure behavior of 6061-T651 aluminum alloy under the conditions described above. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of a modular $J_2$ plasticity model with isotropic hardening as well as a ductile failure model. Both included modules that accounted for temperature and strain rate dependence. The models were coupled with an adiabatic heating module to calculate the temperature rise due to the conversion of plastic work to heat. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10 –4 and 10 3 1/s as well as four geometries of notched tension specimens and two tests on specimens with shear-dominated deformations. The test data collected allowed the calibration of both the plasticity and the ductile failure models. Most test specimens were extracted from a single piece of plate to maintain consistency. Notched tension tests came from a possibly different plate, but from the same lot. When using the model in structural finite element calculations, element formulations and sizes different from those used to model the test specimens in the calibration are likely to be used. A brief investigation demonstrated that the failure model can be particularly sensitive to the element selection and provided an initial guide to compensate in a specific example.

36 MATERIALS SCIENCE↗

DROP DURABILITY ASSESSMENT OF ELECTRONIC ASSEMBLIES UNDER OFF-AXIS LOADING WITH SKEWED FIXTURES

This thesis studies drop durability of electronic assemblies when the acceleration vector is oriented at 45° to the out-of-plane direction of the circuit card. The off-axis drop tests are accomplished with a skewed fixture and are conducted as a proxy for multiaxial drop testing. Advanced shock testing and vibration test methods have been developed over the last few decades to better represent real-world field environments during ground-based laboratory testing. However, many of these test methods require expensive and specialized equipment not available in most laboratories. An alternative approach for approximating simultaneous loading along multiple axes on conventional equipment utilizes skewed fixtures which have seen use in off-axis random vibration and drop impact testing. These methods generally rely on the conversion of a uniaxial input load from the test equipment (using a uniaxial drop tower or shaker) into a multiaxial load when resolved in the reference frame of the test article (mounted on a skewed fixture). Skewed fixture design is presented and recommendations for conducting skewed angle drop testing are introduced based on local measurements along the skewed face of the fixture to accurately monitor the impact event. Characterization tests were performed with a skewed fixture, at simultaneous acceleration loads from 500 to 3,000 g in two (in-plane and out-of-plane) directions, while meeting standard time domain tolerances. Upon experimental characterization, drop shock durability tests were conducted on a printed circuit assembly (PCA). Mean drops-to-failure were measured and quantified with Weibull statistics. Dominant solder joint failure modes were identified via failure analysis. Prior work on inclined angle impact testing is limited, and the majority of solder joint interconnect level fatigue studies are conducted considering perpendicular loading normal the circuit card. Low-cycle fatigue curves are generated based on plastic strain and plastic work density within the solder joint. A multiscale nonlinear finite element model is used to relate board-level flexure to solder joint interconnect level plastic strain. A high strain rate solder constitutive model allows for accurate modeling of solder plasticity resulting from high-impact drop shock. Fatigue parameters are computed from the Coffin-Manson relation and Palmgren-Miner damage accumulation. This work serves to apply established low-cycle fatigue methods for conventional drop shock loading (impact normal to circuit card) to non-perpendicular loading with a skewed fixture.

Hower, Jonathan [Kansas City National Security Cam↗

Thermal-Mechanical Elastic-Plastic and Ductile Failure Model Calibrations for 304L Stainless Steel Alloy

Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The material of interest here is 304L stainless steel, and the objective of this work is to calibrate thermal-mechanical models: one for the constitutive behavior and another for failure. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of the models. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10 –4 and 10 3 1/s. It also included notched tension and shear-dominated compression hat tests specifically designed to calibrate the failure model. All test specimens were extracted from a single piece of plate to maintain consistency. The constitutive model adopted was a modular $J_2$ plasticity model with isotropic hardening that included rate and temperature dependence. A criterion for failure initiation based on a critical value of equivalent plastic strain fitted the failure data appropriately and was adopted. Possible ranges of the values of the parameters of the models were determined partially on historical data from calibrations of the same alloy from other lots and are given here. The calibration of the parameters of the models were based on finite element simulations of the various material tests using relatively ne meshes and hexahedral elements. When using the model in structural finite element calculations, however, element formulations and sizes different from those in the calibration are likely to be used. A brief investigation demonstrated that the failure initiation predictions can be particularly sensitive to the element selection and provided an initial guide to compensate for the effect of element size in a specific example.

36 MATERIALS SCIENCE↗

Attaining regularization length insensitivity in phase-field models of ductile failure

In this work, a cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.

42 ENGINEERING↗

Equation of state and strength of diamond in high-pressure ramp loading

Diamond is used extensively as a component in high-energy-density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first-principles theoretical models of equilibrium multiphase EOS, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to ~10 TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Grüneisen EOS. We also performed DFT calculations of the elastic moduli, and calibrated an algebraic elasticity model for use in simulations. We then estimated the flow stress of diamond by comparison with the stress-density relation measured experimentally in ramp-loading experiments. Furthermore, the resulting constitutive model allows us to place a constraint on the Taylor-Quinney factor (the fraction of plastic work converted to heat) from the observation that diamond does not melt on ramp compression.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints

We report a recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

42 ENGINEERING↗

High pressure phase transition and strength estimate in polycrystalline alumina during laser-driven shock compression

Alumina (Al 2 O 3 ) is an important ceramic material notable for its compressive strength and hardness. It represents one of the major oxide components of the Earth's mantle. Static compression experiments have reported evidence for phase transformations from the trigonal α-corundum phase to the orthorhombic Rh 2 O 3 (II)-type structure at ~90 GPa, and then to the post-perovskite structure at ~130 GPa, but these phases have yet to be directly observed under shock compression. In this work, we describe laser-driven shock compression experiments on polycrystalline alumina conducted at the Matter in Extreme Conditions endstation of the Linac Coherent Light Source. Ultrafast x-ray pulses (50 fs, 10 12 photons/pulse) were used to probe the atomic-level response at different times during shock propagation and subsequent pressure release. At 107 ± 8 GPa on the Hugoniot, we observe diffraction peaks that match the orthorhombic Rh 2 O 3 (II) phase with a density of 5.16 ± 0.03 g cm –3 . Upon unloading, the material transforms back to the α-corundum structure. Upon release to ambient pressure, densities are lower than predicted assuming isentropic release, indicating additional lattice expansion due to plastic work heating. Furthermore, using temperature values calculated from density measurements, we provide an estimate of alumina's strength on release from shock compression.

33 ADVANCED PROPULSION SYSTEMS↗

Phase transitions in high-purity zirconium under dynamic compression

In this work, we present results from ramp compression experiments on high-purity Zr that show the α → ω, ω → β, as well as reverse β → ω phase transitions. Simulations with a multi-phase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic α ! ! transition occurs ~ 9 GPa above the equilibrium phase boundary, the ω → β transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ω – β line at P = 29:2 GPa, and T = 490 K. The thermodynamic path in the interior of the sample lies ~ 100 K above the isentrope at the point of the ω → β transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the non-equilibrium α → ω transition. The inferred rate of the α → ω transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress s ji has the same effect on the nucleation rate as a pressure increase δP = cϵ ij s ji /(ΔV/V); where c is a geometric constant ~ 1 and, ϵ ij are the transformation shear strains. The small fractional volume change ΔV/V ≈ 0:1 at the α → ω transition amplifies the effect of shear stress, and we estimate that for this case δP is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Microstructural and nanomechanical studies of PVD Cr coatings on SiC for LWR fuel cladding applications

The microstructure and nanomechanical properties of pure Cr coatings deposited on SiC with various physical vapor deposition (PVD) methods have been investigated for the mitigation of hydrothermal corrosion of SiC-SiC f (SiC fiber-reinforced SiC matrix) composite fuel cladding in light water reactors (LWR). Cr coatings (4–7 μm thick) were deposited on unbiased SiC substrates using six variants of magnetron sputtering processes: (i) standard (S-DCMS), (ii) pulsed (P-DCMS), (iii) ion-assisted (I-DCMS), and (iv) pulsed ion-assisted direct current magnetron sputtering (PI-DCMS), (v) high-power impulse magnetron sputtering (HiPIMS), and (vi) bipolar HiPIMS (B-HiPIMS). Microstructural characterization and nanoindentation testing were used to evaluate effects of deposition technique on coating microstructure and nanomechanical properties. The application of positive reverse pulses to the sputter target induced coarsening of the columnar grain structure, while ion bombardment of substrates during deposition promoted densification of the coating microstructure. Both effects are exemplified in B-HiPIMS deposition, resulting in a high-density microstructure with compressive residual stress. Material pile-up around nano-indents and plastic work during nanoindentation were analyzed to understand deformation behavior of the coatings. Finally, the results suggest the B-HiPIMS process to be among the promising methods for the deposition of Cr coatings on SiC-SiC f for LWR cladding application.

36 MATERIALS SCIENCE↗

Evidence of non-isentropic release from high residual temperatures in shocked metals measured with ultrafast x-ray diffraction

Shock experiments are widely used to understand the mechanical and electronic properties of matter under extreme conditions. However, after shock loading to a Hugoniot state, a clear description of the post-shock thermal state and its impacts on materials is still lacking. We used diffraction patterns from 100-fs x-ray pulses to investigate the temperature evolution of laser-shocked Al–Zr metal film composites at time delays ranging from 5 to 75 ns driven by a 120-ps short-pulse laser. We found significant heating of both Al and Zr after shock release, which can be attributed to heat generated by inelastic deformation. A conventional hydrodynamic model that employs (i) typical descriptions of Al and Zr mechanical strength and (ii) elevated strength responses (which might be attributed to an unknown strain rate dependence) did not fully account for the measured temperature increase, which suggests that other strength-related mechanisms (such as fine-scale void growth) could play an important role in thermal responses under shock wave loading/unloading cycles. Our results suggest that a significant portion of the total shock energy delivered by lasers becomes heat due to defect-facilitated plastic work, leaving less converted to kinetic energy. This heating effect may be common in laser-shocked experiments but has not been well acknowledged. High post-shock temperatures may induce phase transformation of materials during shock release. Another implication for the study is the preservability of magnetic records from planetary surfaces that have a shock history from frequent impact events.

42 ENGINEERING↗

Thermomechanical Microstructural Predictions of Fracture Nucleation of Zircaloy-4 Alloys With δ and ε Hydride Distributions

Abstract A crystalline dislocation-density formulation that was incorporated with a nonlinear finite-element (FE) method was utilized to understand and to predict the thermomechanical behavior of an hexagonal closest packed (h.c.p.) zircaloy system with hydrides with either face-centered cubic (f.c.c.) or body-centered cubic (b.c.c.) hydrides. This formulation was then used with a recently developed fracture methodology that is adapted for finite inelastic strains and multiphase crystalline systems to understand how different microstructurally based fracture modes nucleate and propagate. The interrelated microstructural characteristics of the different crystalline hydride and matrix phases with the necessary orientation relationships (ORs) have been represented, such that a detailed physical understanding of fracture nucleation and propagation can be predicted for the simultaneous thermomechanical failure modes of hydride populations and the matrix. The effects of volume fraction, morphology, crystalline structure, and orientation and distribution of the hydrides on simultaneous and multiple fracture modes were investigated for radial, circumferential, and mixed distributions. Another key aspect was accounting for temperatures changes due to the effects of thermal conduction and dissipated plastic work and their collective effects on fracture. For hydrided aggregates subjected to high temperatures, thermal softening resulted in higher ductility due to increased dislocation-density activity, which led to higher shear strain accumulation and inhibited crack nucleation and growth. The predictions provide validated insights into why circumferential hydrides are more fracture-resistant than radial hydrides for different volume fractions and thermomechanical loading conditions.

Engineering↗

Modeling inter- and intra-granular dislocation transport using crystal plasticity

Here, this work presents the development of a crystal plasticity material model that incorporates both dislocation transport within grains and dislocation transfer across grain boundaries. This model has been implemented in the open-source finite element code MOOSE. In addition, a novel geometry-based criterion is developed to determine the direction of dislocation transfer across grain boundaries. The transfer criterion incorporates the geometric features of the grain boundary, such as the grain boundary plane normal, and its misorientation, which is accounted for through the orientation of the incoming and outgoing slip systems. The model is tested with several cases, including a copper single crystal, bi-crystal, and polycrystal. The development of the transfer criterion, implementation of the model, and its application to these test cases are discussed in detail.

36 MATERIALS SCIENCE↗