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Plasticity-mediated deformation instabilities in thin film-compliant substrate systems: direct three-dimensional simulations
Abstract Surface wrinkles driven by mechanical instability commonly form in thin-film structures attached to a compliant substrate. In this study, a recently developed computational approach is employed to simulate the formation and transformation of wrinkles involving plastic yielding of the thin film. The three-dimensional (3D) finite element models contain an embedded imperfection at the film-substrate interface, serving to trigger the bifurcation modes. Successful application of this technique to allow for film plasticity is demonstrated, including the evolution of 3D surface patterns and their correlation with the overall load–displacement response. The simulations reveal that plastic yielding transforms the surface instability patterns into more localized forms. Under uniaxial loading, the sinusoidal elastic wrinkles undergo the wrinkle-to-fold transition. With equi-biaxial loading, the initial square-checkerboard array turns into continuous tall ridges along the 45° directions. In both loading modes, the plasticity-induced instability patterns are only partially relieved upon unloading, leaving permanent features on the surface.
Experimental Validation of Exact Burst Pressure Solutions for Thick-Walled Cylindrical Pressure Vessels
Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels.
A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia
Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.
Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition
Abstract API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.
Evaluation of Maximum Allowable Working Pressure and Svensson Burst Pressure Recommended in API 579-1 2021 Edition
ABSTRACT API 579-1/ASME FFS-1 2021 Edition provides the minimum wall thickness, the maximum allowable working pressure (MAWP), and the membrane stress equations for thin and thick-walled cylindrical shells subject to internal pressure in Section 2C.3.3.1 of Appendix 2C – Thickness, MAWP, and Stress Equations for an FFS Assessment. The minimum wall thickness and MAWP are determined using the hoop stress and the Tresca yield criterion. Section 2C.7 – Estimation of Burst Pressure newly added the Svensson method for calculating burst pressure of cylindrical shells under internal pressure, where the plastic yielding is characterized by the von Mises yield criterion. For thin-walled cylinders, the von Mises flow solution of burst pressure in Equation (2C.179) was recommended. For thick-walled cylinders, an implicit burst pressure solution in an integral equation (2C.176) was recommended. But this integral equation is inconvenient to use in practice. It is well known that the classic plasticity theory includes the Tresca and von Mises yield criteria, with the Tresca criterion predicting a lower bound solution and the von Mises criteria predicting an upper bound solution. In addition, the present author developed an average shear stress yield criterion that can determine more accurate limit and burst pressures for thin and thick-walled cylinders. This work uses these three yield criteria to evaluate the minimum required wall thickness, MAWP and Svensson burst pressure recommended in the API 579 code.
An integrated EOS, pore‐crush, strength and damage model framework for near‐field ground‐shock
Abstract An integrated Equation of State (EOS) and strength/pore‐crush/damage model framework is provided for modeling near to source (near‐field) ground‐shock response, where large deformations and pressures necessitate coupling EOS with pressure‐dependent plastic yield and damage. Nonlinear pressure‐dependence of strength up to high‐pressures is combined with a Modified Cam‐Clay‐like cap‐plasticity model in a way to allow degradation of strength from pore‐crush damage, what we call the “Yp‐Cap” model. Nonlinear hardening under compaction allows modeling the crush‐out of pores in combination with a fully saturated EOS, that is, for modeling partially saturated ground‐shock response, where air‐filled voids crush. Attention is given to algorithmic clarity and efficiency of the provided model, and the model is employed in example numerical simulations, including finite element simulations of underground explosions to exemplify its robustness and utility.
A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states
Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. Here, a novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.
Environmental and Economic Implications of Emerging Plastic Recycling Technologies
Recycling will play a crucial role in mitigating plastic pollution and promoting a circular economy for polymers. Quantitative analysis can help guide the optimization and implementation of these plastic management strategies, enabling increased circularity while minimizing costs, energy use, greenhouse gas emissions, and other environmental impacts. This talk will outline the Bio-Optimized Technologies to keep Thermoplastics out of Landfills and the Environment (BOTTLE) Consortium's approach to analysis-guided plastic recycling research. Stringent process modelling, life cycle assessment, and techno-economic analysis are used to benchmark the technical feasibility, environmental impacts, and costs of chemical and biological recycling technologies in comparison to conventional fossil fuel-based plastic manufacturing. Across emerging recycling strategies, several key challenges become apparent - including plastic feedstock pretreatment requirements, high energy or chemical use, and recycled plastic yields and quality - highlighting opportunities for future innovation. Through this consistent and in-depth analysis approach, BOTTLE aims to provide the plastics community with key metrics and insights to drive plastic recycling innovation towards a more sustainable and circular economy.
Strength, deformation, and equation of state of tungsten carbide to 66 GPa
Here, strength, texture, and equation of state of hexagonal tungsten monocarbide (WC) have been determined under quasi-hydrostatic and non-hydrostatic compression to 66 GPa using angle-dispersive X-ray diffraction in the diamond anvil cell. Quasi-hydrostatic compression in a Ne pressure medium demonstrates that nanocrystalline WC is slightly less incompressible than bulk-scale WC, with respective bulk moduli of K 0 = 377 ± 7 and 397 ± 7 GPa and pressure derivatives K 0 ’ = 3.8 ± 0.3 and 3.7 ±0.3. This decrease in incompressibility with grain size is similar to behavior observed in other ceramics. Under nonhydrostatic compression, WC supports a mean differential stress of ~12-15 GPa at plastic yielding, which occurs at ~30 GPa. Strength in WC is anisotropic, with the (001) plane supporting 29-42% higher stress than stresses calculated from mean strain. Simulations using an Elasto-ViscoPlastic Self-Consistent model indicate that strength inferred from lattice strain theory may be overestimated due to effects of plastic deformation. Plastic deformation generates a texture maximum near $\langle\bar{2}110\rangle$ in the compression orientation, initially through prismatic slip on the {$10\bar{1}0$}$\langle\bar{1}2\bar{1}0\rangle$ and {$10\bar{1}0$}$\langle0001\rangle$ slip systems, followed by activation of pyramidal slip on {$10\bar{1}1$}$\langle\bar{2}113\rangle$ at ~40-50 GPa.
Competition between roughness and strength for scale-dependent surfaces
Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.
Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys
An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.
EXPERIMENTAL VALIDATION OF THEORETICAL BURST STRENGTH SOLUTION FOR DEFECT-FREE THICK-WALLED PIPES
The burst pressure of line pipes is an important strength property required in pipeline design and integrity management. Historically, the Barlow formula in conjunction with the ultimate tensile stress (UTS) of pipeline steels were utilized to estimate the burst strength of line pipes. However, the Barlow formula did not consider the plastic flow effect for ductile steels and is applicable only to thin-walled pipes. In 2006, the present author proposed a new multiaxial plastic yield theory and obtained a theoretical Zhu-Leis solution of burst strength for defect-free thin-walled pipes in term of UTS and strain hardening exponent n of pipeline steels. The Zhu-Leis solution has been validated by various burst test data for thin-walled pipelines for a wide range of steel grades from Grade B to X120. Recently, the present author extended the Zhu-Leis theory of plasticity to thick-walled pipes and obtained the Zhu-Leis solution of burst pressure for thick-walled pipes. The proposed burst pressure solution is applicable to both thin and thick-walled pipes. To experimentally validate the proposed theoretical burst pressure solution, this paper obtains a set of burst test data for three thick-walled pipes in Grade B carbon steel with a nominal diameter of 2.375 inches and three nominal wall thicknesses, resulting in D/t = 15.4, 10.9, 6.9. Through comparisons, these burst data validate the theoretical burst pressure solution for thick-walled pipes. Moreover, two additional burst test datasets collected from literature for thin and thick-walled pipes further validate the proposed burst pressure solution for both thin and thick-walled pipes.
An automated fast neutron computed tomography instrument with on-line focusing for non-destructive evaluation
A fast neutron tomography imaging instrument has been designed, built, and tested at The Ohio State University 500 kW Research Reactor on a fast neutron beamline with a peak neutron flux ≈5.4 × 107 n·cm−2·s−1 at 1.6 MeV median neutron energy. The instrument and beamline are also configurable for thermal neutron imaging. The imaging apparatus is composed of a lens coupled, water-cooled Electron Multiplying Charge Coupled Device camera, a front-surface mirror, and a high light yield plastic Polyvinyl toluene scintillator. The instrument sits on a mobile cart. A total of 5 motion-control stages are built into the system for XYZ and rotational degrees of freedom for sample positioning; the fifth stage fine tunes the focal distance between the camera and the scintillator to achieve on-line focusing. A Python code with a user-friendly graphical user interface controls the fully automated image acquisition, not requiring user interaction, yet facilitating tracking of the image acquisition. A complete fast neutron computed tomography dataset with 360 projections requires less than 3 h, with 30 s per projection. On-line focusing is accomplished with a commercial, off-the-shelf, dielectrically actuated liquid lens. Finally, tomographic reconstructions are visualized using the Livermore Tomography Tools software package. The effective pixel size (width and height) is ≈0.1058 mm, yielding a minimum voxel size of 0.1058 × 0.1058 × 0.1058 mm3, and produces a spatial resolution of 231 μm when calculated from knife-edge measurements.
Identifying the Best High‐Biomass Sorghum Hybrids Based on Biomass Yield Potential and Feedstock Quality Affected by Nitrogen Fertility Management Under Various Environments
The growing interest in high-biomass sorghum ( Sorghum bicolor L. Moench), hereafter referred to as sorghum, as a bioenergy feedstock in the United States requires an understanding of geographical adaptation to identify the most suitable hybrids for the Midwest. In this study, 13 sorghum hybrids (H1–H13) were evaluated for biomass yield potential in central and southern IL over two growing seasons (2022 and 2023). In addition to biomass yield, the effects of nitrogen (N) fertilization on yield, nutrient removal (N, P, and K), and feedstock composition (cellulose, hemicellulose, lignin, and soluble fractions) were determined to identify the best-performing sorghum hybrid across environmental gradients. The experimental design was a split-plot arrangement within a randomized complete block design with four replications at each of two locations: N rates (0 and 112 kg-N ha −1 ) as a whole plot factor and 13 sorghum hybrids as a subplot factor. As a result, complex genotypes (13 hybrids) by environment (2 sites and 2 years) and management (2 N rates) interactions were observed in biomass yield. The best hybrids at both sites were H1 (ATx2932/F10702_PSL) and H13 (TX08001), which were very photoperiod sensitive (PS). These hybrids produced superior biomass yield, and they also exhibited less nutrient removal and high energy-rich feedstock compositions (cellulose, hemicellulose, and lignin). Biomass yield potential was associated with morphological and phenological traits according to environmental conditions. Low-yielding hybrids were short-stature (H5 and H6) with pollinators (F10801_PSL-3dw and F10805_PSL-3dw) that are recessive at the Dw3 locus. Moderate PS hybrids (H7, H8, H11, and H12) that produced grain panicles at harvest showed high biomass yield plasticity and excessive nutrient removal as they accumulated high K concentrations in biomass tissues and high N and P in grain panicles.
Understanding the transient large amplitude oscillatory shear behavior of yield stress fluids
A full understanding of the sequence of processes exhibited by yield stress fluids under large amplitude oscillatory shearing is developed using multiple experimental and analytical approaches. A novel component rate Lissajous curve, where the rates at which strain is acquired unrecoverably and recoverably are plotted against each other, is introduced and its utility is demonstrated by application to the analytical responses of four simple viscoelastic models. Using the component rate space, yielding and unyielding are identified by changes in the way strain is acquired, from recoverably to unrecoverably and back again. The behaviors are investigated by comparing the experimental results with predictions from the elastic Bingham model that is constructed using the Oldroyd–Prager formalism and the recently proposed continuous model by Kamani, Donley, and Rogers in which yielding is enhanced by rapid acquisition of elastic strain. The physical interpretation gained from the transient large amplitude oscillatory shear (LAOS) data is compared to the results from the analytical sequence of physical processes framework and a novel time-resolved Pipkin space. The component rate figures, therefore, provide an independent test of the interpretations of the sequence of physical processes analysis that can also be applied to other LAOS analysis frameworks. Each of these methods, the component rates, the sequence of physical processes analysis, and the time-resolved Pipkin diagrams, unambigiously identifies the same material physics, showing that yield stress fluids go through a sequence of physical processes that includes elastic deformation, gradual yielding, plastic flow, and gradual unyielding.
The mechanical response of micron-sized molecular crystals
Abstract Microstructures and corresponding properties of compacted powders ultimately depend on the mechanical response of individual particles. In principle, computational simulations can predict the results of powder compaction processes, but the selection of appropriate models for both particle–particle interactions and particle deformations across all relevant length scales remain nontrivial tasks, especially in material systems lacking detailed mechanical property information. The work presented here addresses these issues by conducting uniaxial compressions in situ inside of a scanning electron microscope to characterize the mechanical response of individual micron-sized particles of a molecular crystal, hexanitrohexaazaisowurtzitane (CL-20). This experimental approach enabled the collection of quantitative force and displacement data alongside simultaneous imaging to capture morphology changes. The results reveal information about elastic deformation, yield, plastic deformation, creep, and fracture phenomena. Accordingly, this work demonstrates a generalizable approach for assessing the mechanical response of individual micron-sized molecular crystal particles and utilizing those responses in particle-level models. Graphic abstract