Elastic-plastic Regime Research Articles

Elastic-plastic conductor damage evaluation at over 0.4% strain using a high-stress REBCO coil

Recent reports on screening current stress simulations of high-field REBCO magnets frequently present peak stresses over 1 GPa. However, this result is probably an unrealistic artifact of purely elastic calculations, considering the macroscopic yield and fracture stresses of approximately 900 MPa and less than 1.1 GPa for Hastelloy substrate-coated conductors. Here, we evaluate elastic-plastic conductor damage at over 0.4% strain using a high-stress REBCO coil exposed to a high field to explore this elastic-plastic regime. The coil was located off-center in a low-temperature superconductor magnet so as to induce a significant screening current in the enhanced radial field. Voltage taps, a Hall sensor, and two strain gauges were used for the instrumentation. We obtained strains exceeding 0.4% near the outward edge during the coil current charge from 350 A to 390 A, where the coil was exposed to external axial and radial magnetic fields of 13 T and 0.5 T. Post mortem results showed wavy plastic deformation, electrical damage, and REBCO defects. An elastic-plastic simulation reproduced the measured strains and predicted that ∼1 GPa stress is sufficient to induce ∼0.9% strain, thus validating our initial concerns with purely elastic models. This paper provides our experimental and simulation results.

Transition to plastic regime for Rayleigh-Taylor instability in soft solids.

Rayleigh-Taylor instability (RTI) is observed in soft materials that have significant resistance to yield. Estimating the instability threshold is critical to several engineering applications and has been the topic of several studies in past decades. However, limited attention has been given to the elastic-to-plastic (EP) transition threshold, where material properties vary significantly. This study explores the phase transition between the pure elastic and stable plastic regimes in RTI in a soft solid (mayonnaise) using a rotating wheel experimental setup with a time-varying acceleration profile. The material properties of the soft solid are characterized using rheological techniques. Different initial perturbation wavelength and amplitude combinations are used to analyze their role in the EP transition threshold and the subsequent maximum fully recoverable elastic strain. The effects of the initial perturbation dimensions, the steepness of the perturbation, and the mass of the perturbation on the stability of the samples, the EP transition thresholds, and the maximum fully recoverable elastic strains are analyzed. The samples with the largest full elastic recovery potentials and the parameters governing this phenomenon are identified, and the physics behind it is discussed. It is observed that increasing the initial perturbation wavelength decreases the required phase transition acceleration while increasing the maximum fully recoverable elastic strain. Finally, nondimensional parameters that involve the perturbation dimensions, as well as the mechanical properties of the material, are introduced to provide a generalized approach to the problem.

Fatigue Analysis of the Nickel-Based Superalloy Inconel 617 by Fatigue Experiments and EBSD Data-Based Finite Element Simulations in Correlation with E·m Theories

Nickel-based superalloys exhibit pronounced elastic anisotropy and, hence, the local grain orientation strongly affects the stress and strain distribution in the material under mechanical loadings. Therefore, the crack initiation and failure behaviour of components made from nickel-based superalloys are complex and hardly predictable. A better fundamental understanding of the phenomena that occur in nickel-based superalloys under a quasistatic and cyclic load is therefore desired. Previously, a continuum mechanics-based model has been successfully developed, considering the grain structure, the elastic anisotropy, and the Schmid factor, based on data from electron backscatter diffraction (EBSD). The E·m model was confirmed by the finite element method (FEM) simulations and experimental observations regarding the resulting average stresses and strains in the individual grains as well as the formation of slip bands under a quasistatic load with few restrictions. The behaviour under cyclic loadings has been investigated in this work to correlate the mechanical behaviour, simulated by the previously developed FE models, with the local stiffness and Schmid factors considering fatigue failure. For this purpose, the fatigue behaviour of Inconel 617 samples was characterised up to the high-cycle fatigue (HCF) regime, accompanied by EBSD measurements for stress amplitudes that resulted in strains close to the elastic–plastic regime. The EBSD data were used to create digital twins of the samples to simulate the mechanical reaction to a displacement similar to the associated strain of the fatigue tests. An analysis of the fractured samples by scanning electron microscopy was performed to retrace the location of the crack initiation supported by the EBSD measurements before and after fatigue testing. Two samples were investigated in detail that showed different fracture types. Sample 1 showed transcrystalline failure in a grain that showed a high Young’s modulus, Schmid factor, and resolved shear stress that indicates a failure due to the properties of the grain itself. In contrast, an intercrystalline failure was observed for sample 2 that showed large differences in the orientation and, hence, largely different mechanical properties in the area of failure as well. The observed failure types, the resulting stresses and strains calculated by the FE model, and the consideration of the E·m model showed an agreement of all the methods. Therefore, the findings of this work complement previous investigations of the mechanical behaviour of coarse-grained anisotropic nickel-based superalloys with a focus on the orientations of the grains towards the loading direction.

Non-contact embedded sensing by Magnetostrictive Carbon Fiber Reinforced Polymer (MagCFRP): A smart material for early inter-lamina localized damage detection

Although failure mechanics and plasticity of composite materials is a relatively new and volatile field, it has been long realized in the composite materials community that a composite’s true integrity lies in the constituents’ interfacial health. Composite materials allow scientists and engineers to design structural architectures with directional stress, strain, and thermal fields in mind while simultaneously reducing the system’s overall weight. While there are advantages to using composite materials like carbon fiber reinforced polymers (CFRPs), designing and implementing long-term sustainable aerospace structures out of CFRPs is bottlenecked by the brittle catastrophic failure mechanism high strength carbon composites exhibit. As the demand for these materials in critical loading regimes increases, it is paramount that scientists and engineers understand how CFRPs will behave in real-time and in predictive models for load profiles. This research’s motivation comes from the US Army’s future vertical lift vehicle initiative to transition from interval-based maintenance to condition-based maintenance (CDB). This paper explores a real-time, non-contact, and non-destructive evaluation (NDE) method for composite materials by performing localized magnetic flux scans (32 mm2 field of view) of CFRP embedded with Terfenol-D ([Formula: see text] microns in diameter), a magnetostrictive material. For Magnetostrictive Carbon Fiber Reinforced Polymer (MagCFRP) elastic regime testing, there was an observed localized magnetic flux gradient of more than 5 mT (4%) with a reversible flux of 100%. For MagCFRP elastic-plastic regime testing, a localized magnetic flux gradient of more than 3 mT (2%) with a reversible flux of only 25% was observed. Terfenol-D embedded CRFPs have shown promising results for detecting instantaneous stress and strain levels and detecting deviations in inter-lamina residual stress after critical loading. Acoustic emission (AE), Digital Image Correlation (DIC), and X-ray computed tomography (CT) scanning were used to validate the observed results.

The mechanical effect of soft pad on copper chemical mechanical polishing

Smaller transistor size challenges traditional chemical mechanical polishing (CMP) in semiconductor fabrication. Novel consumables and in-depth mechanism research can support defect mitigation and improve yield. This study focused on soft pad polishing of copper film from the perspective of mechanical effects. To reduce the defects, a soft pad is replacing the hard pad in the barrier layer polishing and over-polishing steps of copper CMP. When the contact behavior of pad asperity and wafer was in the elastic-plastic regime, the exponential influence factors of pressure, abrasive concentration, and sliding velocity on the material removal rate (MRR) were around 0.64, 0.22, and 0.64, respectively. Stick-slip friction with squeal noise scratched the copper film at the beginning and end of the CMP process. The pad conditioning removed polishing residues but deflected the pad asperity. Proper conditioning frequency is necessary to optimize the polishing process.

An Axisymmetric Problem of Suspension Filtering with Formation of Elastic–Plastic Cake Layer

The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy’s law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thickness are also established. The parameters of plasticity in terms of particle concentration and permeability mainly affect the corresponding indicators, i.e., on the particle concentration distribution and on the relative permeability of the cake. It is shown, that depending on the change in the model parameters characterizing the elastic–plastic properties of the cake, the filtration characteristics change significantly. This indicates a significant effect of the elastic–plastic deformation of the cake on the suspension filtration characteristics.

Flexural properties of functionally graded additively manufactured AlSi10Mg TPMS latticed-beams

Due to the recent boom in digital design for additive manufacturing and 3D printing, there has been a significantly growing interest in latticed structures for light design and improved mechanical properties. However, the focus in the literature has mostly been on compressive mechanical properties of uniformly latticed structures with little emphasis on flexural properties of latticed-beams that are functionally graded and hybridized with different lattice topologies. Therefore, this paper aims to explore the effect of lattice relative density gradation and hybridization on the specific flexural properties of prominent sheet-based triply periodic minimal surfaces (TPMS) cellular four-point loaded beams. First, the effective elastic properties of the cubic porous topologies are evaluated computationally to converge to certain sheet-based TPMS cellular structures capable of providing high flexural properties. Schwartz primitive (P) revealed high stiffness to shear loading, meanwhile, the F-Rhombic Dodecahedron (FRD) showed better resistance to uniaxial loading, and the Diamond (D) showed well-combined uniaxial and shear moduli. The selected four-point bend (4 PB) latticed-beams are functionally graded following a bilinear pattern and hybridized through the span of their length inspired by the shearing force and bending moment diagrams arising in the 4 PB beam, in view of the effective elastic properties of the TPMS topologies. The additively manufactured AlSi10Mg uniform, functionally-graded, and hybridized latticed-beams are tested in four-point bending and the results are compared with the finite element results. Both the experimental and numerical outcomes show good agreement within the elastic-plastic regime. From experimental results, it is found that functional grading and hybridization can considerably enhance the specific flexural modulus of sheet-based TPMS latticed-beams. Also, relative density gradation within the four-point bend specimens proved very essential in deflecting crack growth thereby retarding the final failure, meanwhile hybridization is conveyed to mitigate shear-band failure. Combination of functional gradation and hybridization on the latticed-beams resulted in a significant increase in the specific flexural stiffness. Therefore, this study provides guidelines on how to enhance the flexural properties of lightweight beams through lattice functional grading and hybridization.

Hydrogen embrittlement of pearlitic steel in the presence of cracks: A kinematic fracture criterion based on the crack tip strain rate

This paper offers a kinematic fracture criterion for hydrogen embrittlement (or hydrogen assisted cracking) of cracked samples of high strength pearlitic steel tested at very different loading/straining rates under cathodic electrochemical conditions promoting hydrogen entry and diffusion into the specimens. The local strain rate at the crack tip (crack tip strain rate CTSR) is shown to be the relevant variable governing the hydrogen embrittlement process. Calculation of the local strain rate is carried out on the basis of the elastic displacement distribution in the vicinity of a crack tip in conditions of plain strain. A local reference length is chosen next to the crack tip, at a distance estimated from the fractographic results of the tests that show a zone microscopically affected by hydrogen. The other relevant variable in hydrogen assisted cracking is the depth of the maximum hydrostatic stress point, which is obtained by using approximate stress distributions in the vicinity of the crack tip in the elastic-plastic regime, or calculated as the asymptotic depth (for quasi-static tests) of the hydrogen affected area.

Criterion for Critical Junctions in Elastic-Plastic Adhesive Wear.

We investigate elastic-plastic adhesive wear via a continuum variational phase-field approach. The model seamlessly captures the transition from perfectly brittle, over quasibrittle to elastic-plastic wear regimes, as the ductility of the contacting material increases. Simulation results highlight the existence of a critical condition that morphological features and material ductility need to satisfy for the adhesive junction to detach a wear debris. We propose a new criterion to discriminate between noncritical and critical asperity contacts, where the former produce negligible wear while the latter lead to significant debris formation.

Mechanical behavior of shape memory alloy fiber reinforced aluminum matrix composites

This study aims to investigate mechanical behavior of NiTi shape memory alloy (SMA) long-fiber reinforced aluminum (Al) matrix composites, experimentally and numerically. The composites with three different pre-memorized shapes of SMA fibers, which were straight-, wave- and rectangle-shaped fibers, were fabricated by powder metallurgical techniques. Three-point bending and tensile test results demonstrated that wave-shape SMA/Al composites showed the highest elastic modulus and strength, and wave-shape and rectangle-shape SMA/Al composites showed high Poisson’s ratio (lateral to longitudinal strain ratio in elastic-plastic regime). The experimental results were examined based on finite element analysis (FEA). It was concluded that internal stresses in the composites, which were introduced during the fabrication processes, highly affected their subsequent mechanical behavior of the composites.

A new model for time-efficient analysis of nonlinear composites with arbitrary orientation distribution of fibres

This study aims to develop a time-efficient and accurate method for estimating the effective nonlinear behaviour of composites reinforced with misaligned short fibres. The ground-breaking aspect of the proposed approach is combining the two-stage hybrid homogenization method with the novel formulation of the pseudo-grain discretization method. The numerical solution of the equivalent inclusion problem is conducted in the first homogenization stage for the finite number of pseudo-grains. The obtained solution can be generalized for arbitrary orientation distribution and volume fraction of fibres during the time-efficient second homogenization stage. The proposed method's accuracy has been verified both in linear elastic and elastic–plastic regimes by comparing the obtained results with reference solutions achieved by using well-established analytical and numerical methods.

Design and Optimization of a Curved-Crease-Folding Process Applied to a Light Metallic Structure

Presently, the realization of complex, unconventional designs using efficient modalities is possible due to an increasing interest in interdisciplinary approaches: materials science, mathematics, IT, architecture, etc. Computerized techniques, among which the algorithmic/generative design is the most advanced one, that are associated with the individualized production methods are used for finding solutions for modern spatial forms with an unconventional spatial geometric shape, which are generically called “free-forms”. This work presents the design, realization and testing of a thin-walled metallic structure proposed as a light structural unit. An integrated research approach was proposed that utilized an algorithmic/digital design applied to the curved-crease-folding method with the study (at different length scales) of the metallic material behaviour after folding. An original method was proposed for the digital design and simulations. The specific mechanical behaviour of the metallic material in the elastic–plastic regime was used in this case to improve the structural performances; mechanical and structural tests were realized to analyse the behaviour of the entire structure. The results are useful for enhancing the accuracy of the digital design, the structural simulation programs and the fabrication methods.

A theoretical model for elastic-perfectly plastic flat cylindrical punch indentation

Instrumented indentation is widely used to evaluate the hardness and other mechanical properties of materials. This requires a theoretical model for the indentation curve (load vs. penetration) based on the Young's modulus, Poisson's coefficient, yield stress, hardening exponent, friction, and shape of the indenter. Several papers have been devoted to modeling spherical, conical, or pyramidal indentation in cases of both elastic and plastic deformation; in contrast, there are relatively few theoretical studies on flat cylindrical punch in the elastic–plastic regime. Indeed the singularity in the stress field at the edge of the contact is difficult to solve even if the aim is only to obtain an approximate solution. In this paper, after reviewing the theoretical basis of flat cylindrical indentation for elastic and rigid-plastic materials three different steps have been used to describe the entire progress of penetration: pseudo-elastic, elastic–plastic and full plastic. This final condition begins when the entire contact area undergoes plastic deformation. Using this classification as the starting point, a new simplified equation represents the stiffness of the specimen under flat cylindrical indentation, taking into account the elastic–perfectly plastic behavior. Integrating this equation gives the curve of indentation for an elastic–perfectly plastic material. As the characteristic parameters of this equation are unknown, in this paper the results of an extended numerical investigation using finite-element models of many different materials facilitates their calculation and validates the model. Using this new model, the direct and the inverse problems of flat indentation can be solved with good accuracy as shown through several FEM analyses. Finally, considering that the new model does not take the hardening effect into account, experimental data from the literature facilitate the verification of the relevance of this approximation. This final check successfully assesses the accuracy and the usefulness of the new method.

A multi-scale stiffness fractal model of joint interfaces

Stiffness characterization of mechanical interfaces is quite crucial for the analysis of several tribological behaviors. The stiffness of different machine tools varies greatly, particularly for computer numerical control machine. Therefore, this research aims at providing an assessment of influence factors for stiffness of joint interfaces theoretically. Based on fractal roughness parameters independent of scale and contact mechanics theory, the contact area of joint interface is studied, and the multi-scale normal contact stiffness model and multi-scale tangential contact stiffness model are proposed. Meanwhile, the problem of the deformation of any contact asperity is considered as three separate regimes. The laws of area-displacement and force-displacement under elastic-plastic regime are established. The transition which is in the deformation mechanism of asperity from elastic to plastic is consistent with classical contact mechanics. The analysis of numerical calculation results indicates the approximate linear relation among dimensionless normal load and key parameters. Moreover, these key parameters have been divided into two main categories for the multiscale model of joint interfaces, one is fractal parameters such as fractal dimension D and fractal roughness parameter G, and the other is interfacial parameters. In addition, tangential load and friction factor are two important factors to the tangential stiffness.

Calculating molten-salt central-receiver lifetime under creep-fatigue damage

One of the major uncertainties in the design of molten-salt solar receivers is the estimation of the lifetime because solar receivers have to withstand high temperature, thermal stress and corrosive-media in addition to daily star-up and shutdown. The first step to estimate the receiver damage and therefore, to monitor and manage the receiver life cycle, is to obtain properly the tube stresses under daily operating conditions. Whit this aim, we propose a straightforward low-computational cost procedure to determine the stresses under elastic-plastic regime. In addition, the stress relaxation due to visco-elastic behavior of the material, is also calculated. The analytical thermo-elastic, elastic-plastic and relaxation stress models for the high-nickel alloy Haynes 230 were verified against finite element simulations showing a good accuracy with a low-computational cost.For exemplification purposes, a reference operation day of a molten-salt solar receiver like Gemasolar is investigated. A receiver creep-fatigue damage assessment was developed for a flat aiming strategy. The results showed that the fatigue damage is 0.03% of the total damage. The average-field-receiver efficiency was 42.18% with a predicted lifetime higher than the expected. On the contrary, the receiver lifetime increases unnecessarily and the field-receiver efficiency drops to 26.25% when the receiver is operated limiting the stress as one third of the ultimate tensile strength (UTS/3). This limit results in a loss of revenues of around 250,000€ per month. Hence, the excessive level of conservatism produced by stress limit methods are not suitable for solar receivers due to the resulting economic penalties.

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic-Plastic Regime under Cyclic Loading.

In exact analyses of bodies in the elastic–plastic regime, the behavior of the material above critical stress values plays a key role. In addition, under cyclic stress, important phenomena to be taken into account are the various types of hardening and the design of the material or structure. In this process, it is important to define several groups of characteristics. These include, for instance, the initial area of plasticity or load which defines the interface between elastic and plastic deformation area. The characteristics also include the relevant law of plastic deformation which specifies the velocity direction of plastic deformation during plastic deformation. In the hardening condition, it is also important to determine the position, size and shape of the subsequent loading area. The elasto-plastic theory was used for the analysis of special compliant mechanisms that are applied for positioning of extremely precise members of the Compact Linear Collider (CLIC), e.g., cryomagnets, laser equipment, etc. Different types of deformation hardening were used to simulate the behavior of particular structural elements in the elastic–plastic regime. Obtained values of stresses and deformations may be used in further practical applications or as default values in other strain hardening model simulations.

Identification of fatigue damage mechanism in PA38-T6 aluminum alloy under multiaxial loadings – initial research

This paper presents results of the initial research which originated from previous work, which was aimed to study the effect of asynchronous loadings in elastic-plastic strain range. Among the others, a study of fatigue cracks on the fatigued specimens’ surfaces, was performed.The aim of the present work is to identify the mechanisms of initiation and propagation of small fatigue cracks in selected materials under multiaxial loadings, including asynchronous cases. To study the evolution of small cracks and main crack formation, the cellulose acetate thin foil replication technique was utilized. Fatigue tests were performed on thin-walled tubular specimens, which were mirror-polished after CNC machining, to avoid the influence of unwanted factors.This paper presents the first part of fatigue tests, performed on specimens manufactured from PA38-T6 (AW 6060-T6) aluminum alloy. Fully reversed axial, torsional and 90º out-of-phase loadings were applied in elastic-plastic strain regime, with strain control. For these loading cases a shear damage mechanism was identified, based on the observation of small cracks. The small cracks initiated ate grew on maximum shear strain planes. The main crack formed at the very end of fatigue life by coalescence of small cracks of high density, regardless the applied loading case and level. An interesting difference in cracking behavior was observed in case of out-of-phase loading, on the low loading level. Small cracks propagated, and the main crack formed by linking of a few propagating cracks.The research is in progress and will be extended to the lower levels of strain as well as other cases of loadings, including asynchronous loadings. It is planned to conduct the research using other materials, for example non-alloy steel and austenitic stainless steel.

Analysis of fatigue crack initiation in cyclic microplasticity regime

The present work provides description of fatigue crack initiation in metals subjected to cyclic loading within the nominal elastic or initial elastic-plastic regimes next passing to elastic response during cyclic deformation and shake down process. It is assumed that damage growth proceeds due to action of local stress, specified as the sum of mean stress and its fluctuations induced by material inhomogeneities such as grain boundaries, inclusions, cavities, boundary asperities, also due to design notches or holes introduced into the element. The damage growth model is proposed, based on the critical plane concept. The macrocrack initiation then corresponds to a critical value of accumulated damage. The modelling of damage growth is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using the coherent laser light. The damage growth effect is analysed by microindentation tests. The fatigue tests are performed for high strength steel specimens with central hole.

Deep learning based predictive modeling for structure-property linkages

Crystal plasticity finite element method (CPFEM) based simulations have been traditionally used for analyses of deformation in metals. However, CPFEM simulations are computationally expensive, especially for problems like fatigue where analyses are based on deformation cycles. Moreover, correlations of structure-property linkages based on homogenization and localization are not easily conceived.In this work deep learning based models have been proposed that are able to predict macroscopic properties based on features extracted from the microstructure with minimal human bias. The model is able to predict property against a given structure within dual phase, isotropic elastic-plastic regime. A systematic approach for finding optimal depth and width of neural network has been identified that reduces the overall development effort. It is observed that in the absence of a large training dataset, performance of a convolutional neural network (CNN) model degrades if too many layers and/or too many neurons are used. The CNN model is able to identify soft and hard regions of microstructures and is able to correlate structure-property relation in forward sense i.e. for homogenization. In this work, it has been demonstrated that human intervention is not needed for feature extraction and selection leading to minimization of researcher’s bias. The drawback of CNN model interpretability is overcome by using Respond-CAM feature visualization.

New CMOD based η-factor equations considering R-O strain hardening for circumferential through-wall cracked pipe under bending moment

The fracture study of circumferential through-wall cracked (CTWC) pipe under bending load is of interest for integrity assessment of conventional piping system and especially important for Leak-Before-Break (LBB) analysis of primary heat transport piping system of nuclear power plants (NPP). The fracture study in the elastic-plastic regime needs to obtain material J-resistance curve where J-integral is usually calculated from test data using the η-factor methodology. The evaluation of J-R curve for CTWC pipe is also important for study of transferability of material fracture resistance data from small specimen to full scale components. Further, η-factor to evaluate J-integral may be based on either load-lone-displacement (LLD) or crack mouth opening displacement (CMOD). The conventionalη-factor equations for CTWC pipe are LLD based and derived based on the assumption that the material is elastic perfectly plastic. However, use of LLD based η-factor needs to subtract no-crack displacement which poses additional difficulty and real materials always show some form of strain hardening. Therefore, an effort has been made in this paper to obtain the CMOD based η-factor for CTWC pipe considering material strain hardening as per the Ramberg-Osgood (R-O) relation. In the present study, plastic η-factor (ηpl) has been evaluated by elastic-plastic finite element analyses (FEA) over a wide range of crack angles (2θ = 30°–150°) and R-O strain hardening exponent (n = 2–7) for three R/t ratios (5, 10 and 20). To capture the ovalization of pipe cross section during deformation, geometric non-linearity is also considered in FEA. Based on these FEA, new ηpl equations are proposed by 2-D surface curve fitting for different R/t ratios. For validation of FE model, a separate set of geometrically linear FEA was also carried out for comparison of FE J-integral with EPRI Handbook solutions. Further, semi-analytical η-factor derived from EPRI relations of J-integral and CMOD were also compared with the present (geometric-linear) finite element results. In both the cases, the matching was very good.