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Abstract This work presents a novel sensitivity approach that quantifies sensitivity to regimes of a model’s state variables rather than constitutive model parameters. This Physical Regime Sensitivity (PRS) determines which regimes of a model’s independent variables have the biggest influence on an experiment or application. PRS analysis is demonstrated on a strength model used in the simulation of a copper Taylor cylinder. In a series of simulations, the strength model was perturbed sequentially in local regimes of plastic strain, plastic strain rate, temperature and pressure, and then the prediction of cylinder shape was compared to unperturbed calculations. Results show, for example, that the deformed length of the cylinder was most sensitive to strength at a strain rate of 1.0 × 10 4 /sec., but the deformed footprint radius was most sensitive to strength at a strain rate of about 4.0 × 10 4 /sec. Compared to current histogram approaches, PRS can be used to design or interpret integrated experiments by identifying not just which regimes are accessed somewhere in the experiment but the causality question of which regimes actually affect the measured data. PRS should allow one to focus experimental and modeling efforts where they are most needed and to better interpret experiments.
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.
Plastic strain-induced phase transformations (PTs) and chemical reactions under high pressure are broadly spread in modern technologies, friction and wear, geophysics, and astrogeology. However, because of very heterogeneous fields of plastic strain $E$ p and stress σ tensors and volume fraction c of phases in a sample compressed in a diamond anvil cell (DAC) and impossibility of measurements of σ and $E$ p , there are no strict kinetic equations for them. Here, we develop a kinetic model, finite element method (FEM) approach, and combined FEM-experimental approaches to determine all fields in strongly plastically predeformed Zr compressed in DAC, and specific kinetic equation for α-ω PT consistent with experimental data for the entire sample. Since all fields in the sample are very heterogeneous, data are obtained for numerous complex 7D paths in the space of 3 components of the plastic strain tensor and 4 components of the stress tensor. Kinetic equation depends on accumulated plastic strain (instead of time) and pressure and is independent of plastic strain and deviatoric stress tensors, i.e., it can be applied for various above processes. Our results initiate kinetic studies of strain-induced PTs and provide efforts toward more comprehensive understanding of material behavior in extreme conditions.
Measurements of activation areas are used to investigate the effect of hydrogen on the kinetics of dislocation glide during cyclic deformation in cold-worked 316L stainless steel. Non-charged and hydrogen-precharged (H-precharged) specimens were tested in low cycle fatigue (LCF) under plastic strain control. A series of plastic strain rate changes was performed periodically at the peak true plastic strain from the first cycle to half-life, and at various plastic strain values around stable hysteresis loops near half-life to determine the operational activation area, Δ a ∗. Both material conditions demonstrate a rapid increase in Δ a ∗ during the initial rapid softening followed by a region of approximately constant values coinciding with a reduced rate of softening. Near half-life, hydrogen reduces Δ a ∗ at a given true stress due to its effect on the activation distance and obstacle spacing. The magnitudes of Δ a ∗ reveal that bypassing solutes, cutting forest dislocations, and initiating cross slip are important mechanisms of thermally activated dislocation glide at all amplitudes, except hydrogen suppresses cross slip at the lowest plastic strain amplitudes. These results are supported by electron microscopy characterization of deformed microstructures. A Haasen plot analysis indicates that forest dislocations control the kinetics of deformation in both material conditions. It also reveals the presence of athermal obstacles in both non-charged and H-precharged conditions, likely dense dislocation tangles and cell walls. Additionally, the effect of hydrogen on microstructure evolution (by reducing the propensity for cross slip) leads to a dependence of athermal stress on plastic strain amplitude.
Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.
Abstract Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J 2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J 2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J -integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.
The United States High Performance Research Reactor Program’s objective is to reduce the amount of highly enriched uranium currently implemented in research reactors. The conversion of these research reactors requires designing a monolithic U10Mo plate fuel, with the fuel plate geometry being dependent on each research reactor. The process of forming the plates includes a hot isostatic pressing (HIP) to manufacture a prototypic plate. In the case of the Missouri University Research Reactor (MURR) design demonstration element (DDE) plate manufacture, plates that have been through HIP are then curved using dies and a hydraulic press to impart the desired curvature. Both fabrication processes impart residual stresses into each fuel plate region, with the curvature of the plates taking some regions of the fuel plate up to their material yield stresses, accompanied by plastic strain. The amount of plastic strain and stress imparted onto each MURR DDE plate is determined by the radius of curvature, thickness of each region, and overall width of the fuel plates. Furthermore, this work aims to predict the yield stresses and strain using ABAQUS to simulate the proposed fabrication process of the MURR DDE plates, accompanied by discussion over the stresses and strains as to their relation to nuclear fuel performance and the impact they will have during early irradiation.
Stress relaxation cracking (SRC) is considered one of the major failure mechanisms for 347H stainless steel welds at elevated service temperatures or during post weld heat treatment (PWHT), especially within the heat-affected zone (HAZ). This work focuses on the characterization of SRC susceptibility within 347H physically simulated arc welded HAZ at elevated temperatures. A four-step SRC thermomechanical test in combination with finite element modeling (FEM) of the welding and testing processes is developed to establish a susceptibility map for HAZ. The test first runs a thermal cycle with three different peak temperatures (1335, 1275, and 1150 °C) to duplicate representative HAZ subzone microstructures, followed by time-to-failure examination under a variety of pre-stress (260–600 MPa) and pre-strain conditions (0.03–0.19) as a function of reheat temperatures between 750 and 1050 °C. With the aid of FEM, SRC susceptibility maps are generated to identify the threshold stress, plastic strain, and creep strain as a function of test temperature. It was found out that HAZ subzone with a lower peak temperature (1150 °C) appears to be slightly less susceptible to SRC than the other two subzones that experienced higher peak temperatures. Generally, time-to-fracture reduces with increasing initially applied stress and strain for all test temperatures. The pre-stress thresholds decrease from about 500 to 330 MPa as the testing temperature increases from 800 to 1050 °C, while the corresponding initial plastic strain thresholds reduces from 0.15 to 0.06. The SRC susceptibility was also evaluated through the Larson–Miller Parameter (LMP) analysis as a function of plastic strain, initial stress and starting stress upon reaching the testing temperature, respectively. The 1050 °C test with a high pre-applied strain (0.1) exhibits an extremely short time to failure (t = 3 s) that lies outside the general trend in LMP analysis. Additionally, it was identified that a plastic strain above 0.07 is identified to significantly reduce the bulk creep strain tolerance to fracture and therefore increases SRC susceptibility. Hardness measurement and fractography analysis indicated that the strain aging of niobium carbonitrides and other potential phases in conjunction with intergranular precipitates contributes to an increase in microhardness and increased intergranular cracking susceptibility.
Crack growth in ductile single crystals (DuSCs) is orientation dependent due to the anisotropies of crystal plasticity and elastic tensor. This study develops a phase-field model incorporating both crystal plasticity and crack growth and proposes a general method to decompose the elastic energy into compressive and tensile parts to prevent crack growth under compression in the phase-field description. The phase-field model, in combination with three Euler angles, is employed to simulate orientation-dependent crack growth in DuSCs. The contributions from crystal plasticity and anisotropic elasticity are compared, and the former is found to dominate in the anisotropy of crack growth in copper single crystals. Furthermore, the simulation results demonstrate that crystal orientation strongly affects the heterogeneous distribution of plastic strain and the interaction between plastic strain and crack growth. High-throughput phase-field simulations are performed with exhaustive crystal orientations, and the results are explained based on the anisotropy of the Taylor factor.
Wallace’s theory for overdriven shocks in solids provides a theoretical framework for the strength of materials in the strong shock regime at strain rates unobtainable by current experimental means. Using irreversible thermodynamics, this theory incorporates heat and plastic flow as dissipative mechanisms under shock conditions allowing for the calculation of properties such as deviatoric stresses, plastic strains, and plastic strain rates. Though the theory is over four decades old, it has been used to calculate the strength behavior of only a small handful of metals. In this work, we have recaptured the ability to conduct this analysis, and two crucial aspects of the overdriven theory will be discussed: 1) the modeling assumptions that comprise this theoretical approach and 2) what information is needed to calculate the strength behavior for new materials.
Pressure-induced phase transformations (PTs) in Si, the most important electronic material, have been broadly studied, whereas strain-induced PTs have never been studied in situ. Here, we reveal in situ various important plastic strain-induced PT phenomena. A correlation between the direct and inverse Hall-Petch effect of particle size on yield strength and pressure for strain-induced PT is predicted theoretically and confirmed experimentally for Si-I→Si-II PT. For 100 nm particles, the strain-induced PT Si-I→Si-II initiates at 0.3 GPa under both compression and shear while it starts at 16.2 GPa under hydrostatic conditions. The Si-I→Si-III PT starts at 0.6 GPa but does not occur under hydrostatic pressure. Pressure in small Si-II and Si-III regions of micron and 100 nm particles is ~5–7 GPa higher than in Si-I. For 100 nm Si, a sequence of Si-I → I + II → I + II + III PT is observed, and the coexistence of four phases, Si-I, II, III, and XI, is found under torsion. Retaining Si-II and single-phase Si-III at ambient pressure and obtaining reverse Si-II→Si-I PT demonstrates the possibilities of manipulating different synthetic paths. The obtained results corroborate the elaborated dislocation pileup-based mechanism and have numerous applications for developing economic defect-induced synthesis of nanostructured materials, surface treatment (polishing, turning, etc.), and friction.
In situ tensile testing in a scanning electron microscope (SEM) in conjunction with high-resolution electron backscatter diffraction (HR-EBSD) under load was used to characterize the evolution of geometrically necessary dislocation (GND) densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg—4Al alloy. The increase in GND density was investigated at plastic strains of 0 %, 0.6 %, 2.2 %, 3.3 % from the area including 76 grains and correlated with (i) geometric compatibility between slip systems across grain boundaries, and (ii) plastic incompatibility. We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility, from which uniaxial tensile stress-strain response of polycrystalline Mg—4Al are computed and compared with experimental measurement. The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.
A formulation for a dimensionless coefficient c b is derived that represents a scale of microstructural softening for alloys which follow Kocks-Mecking (K-M) work hardening behavior. The variation of the true plastic strain ε p between the proportional limit σ y and the strength σ u at the instability is determined using the Considère criterion. Parameterization of the model is limited to variables expressly measured within tensile experiments. Further development is now made for the softening factor c bi through the individual and sequential stages 3 and 4 of plastic deformation during K-M work hardening Q behavior. Application is shown for tensile test results of Ti-6Al-4V made by different additively manufactured (AM) processes. It is found that the variation in plastic strain as a function of c bi produces a continuous curve representative of the alloy system. The results of data analysis indicate that Θ o3 and c b3 increase, while Θ o4 and c b4 decrease, as the total plastic strain ε p increases. Furthermore, formulations derived for K-M stages 3 and 4 enable the evaluation of other material parameters such as the activation volume ν* for the onset of plastic deformation. This activation volume is found to be near constant, at a ν*-value of 0.353±0.036 nm 3 as computed using a strain-rate sensitivity of strength exponent m of 0.014, irrespective of the AM method used to produce the Ti-6Al-4V alloy.
PFE Auxiliary Systems conducted drop testing on SAVY-4000 containers to evaluate structural response under 12-foot drop conditions. In support of that effort, a finite-element modeling capability was developed to simulate drop response across multiple container sizes and impact orientations. The purpose of this work was to provide a consistent analysis framework that could support interpretation of testing, compare response trends across multiple configurations, and generate quantities of interest for later comparison with experimental data. More broadly, the analysis and testing were intended to assess whether the containers continued to perform their primary function after a 12-foot drop, namely maintaining structural integrity and containment of the contents. The modeling approach combined an implicit preload analysis with an explicit drop simulation so that each drop event began from a mechanically realistic assembled condition, including compression of the silicone O-ring. Separate models were developed for 2-quart, 5-quart, 12-quart, and 10-gallon containers. The results were evaluated in terms of strain-gauge response, collar-lid gap behavior, and accumulated plastic strain. In addition, parametric studies were performed on the 2-quart container to assess sensitivity to O-ring stiffness, friction, canister thickness, geometry tolerance, and mesh density. The simulations showed that predicted drop responses depended strongly on both container size and drop orientation. Gap metrics identified cases in which the predicted collar-lid opening exceeded the nominal O-ring cross-section threshold, while plastic strain metrics identified localized regions of elevated permanent deformation. Parametric studies showed that the predicted response was especially sensitive to the assumed O-ring stiffness and contact friction, while the geometry tolerance study produced smaller changes in the cases examined. The main value of this work was that it established a repeatable modeling and simulation workflow to support drop-test implementation, evaluate effects of future configuration changes, and understand modeling assumptions that most influenced predicted response. At the current stage, the results were viewed as preliminary model predictions rather than validated predictions. The next step would be to compare drop-test data to the model so that predictive values of the workflow could be refined and used with greater confidence to assess whether the containers maintained structural integrity and containment of the contents after a 12-foot drop.
Small-scale bicrystal creep experiments were performed on contacts formed via in situ high-temperature diffusion bonding of metal-oxide interfaces including Ag-ZrO 2 , Pd-ZrO 2 , Pt-ZrO 2 , and Ag-high entropy oxide. This work characterizes deformation and failure at metal-oxide interfaces during mechanical loading. Interfacial sliding can be activated easily, while tensile interfacial creep was not observed at any condition of stress or temperature measured. Plastic strain, instead, localizes within the metal under tensile loading. A variety of mechanisms for plastic strain occur in the metal including lattice dislocation-mediated plasticity, twinning, low-angle grain boundary formation, and low-angle grain boundary creep. Surface and low-angle grain boundary diffusion occur under conditions where no metal-oxide tensile creep is observed, highlighting the significant differences in their interfacial mechanical response. High-temperature interfacial failure occurs when the mean curvature at the contact neck is approximately zero and the applied stresses comparable to brittle fracture stresses. The brittle fracture stresses were measured to be σ ƒ = 180 ± 90 MPa at the Ag-ZrO 2 interface at 225 °C, σ ƒ = 460 ± 160 MPa at the Pd-ZrO 2 interface at 680 °C, and σ ƒ = 640 ± 440 MPa at the Pt-ZrO 2 interface at 1010 °C.
Second phases play a significant role in the development of high-performance magnesium alloys with rare earth elements. Here, in situ tensile tests combined with synchrotron radiation were carried out to investigate the deformation behavior of β phases in a WE (Mg–Y–Gd–Nd) alloy. By lattice strain analysis, it was found that micro load continuously transferred from the soft α-Mg matrix to the hard β phases during the whole plastic deformation, while this behavior was much more obvious at the beginning of deformation. Based on diffraction peak broadening, Williamson–Hall (W–H) plotting was used to study the microstrain of β phases. The results showed that the microstrain of β phases increased rapidly within 4% plastic strain and reached the maximum at plastic strain of ~6.5%. Since the β phases acted as hard phases, the microstrain was considered as a sign of the stress concentration near phase interfaces. It was also suggested that the effective release of local stress concentration at the β/α-Mg interface benefited the ductility of the WE alloy by the plastic deformation of β phases and phase interface sliding.
Abstract Magma ascent and eruption are driven by a set of internally and externally generated stresses that act upon the magma. We present microstructural maps around melt inclusions in quartz crystals from six large rhyolitic eruptions using synchrotron Laue X-ray microdiffraction to quantify elastic residual strain and stress. We measure plastic strain using average diffraction peak width and lattice misorientation, highlighting dislocations and subgrain boundaries. Quartz crystals across studied magma systems preserve similar and relatively small magnitudes of elastic residual stress (mean 53–135 MPa, median 46–116 MPa) in comparison to the strength of quartz (~ 10 GPa). However, the distribution of strain in the lattice around inclusions varies between samples. We hypothesize that dislocation and twin systems may be established during compaction of crystal-rich magma, which affects the magnitude and distribution of preserved elastic strains. Given the lack of stress-free haloes around faceted inclusions, we conclude that most residual strain and stress was imparted after inclusion faceting. Fragmentation may be one of the final strain events that superimposes stresses of ~ 100 MPa across all studied crystals. Overall, volcanic quartz crystals preserve complex, overprinted deformation textures indicating that quartz crystals have prolonged deformation histories throughout storage, fragmentation, and eruption.