Magnitude Of Plastic Strain Research Articles

Dislocation nucleation and evolution at the ferrite-cementite interface under cyclic loadings

Fatigue is of significant importance to the engineering applications of the structural materials. High-strength pearlite steel consisting of a ductile ferrite phase and a brittle cementite phase is a widely used structural metal for extreme load-bearing applications. However, the fatigue mechanisms of such important materials remain elusive, in particular, the atomic-scale dislocation behaviors at interface are poorly understood. We used molecular dynamics simulations to probe the mechanical response and deformation mechanism of the Bagaryatskii-oriented ferrite-cementite interface in pearlite. The interface was subjected to a hundred symmetric tension-compression deformation cycles. Three different loading schemes with strain magnitudes of 4.0%, 6.0%, and 9.0% are sophisticatedly designed to explore the cyclic plastic mechanisms under different conditions corresponding to pure elasticity, elasticity in tension but plasticity in compression, and plasticity in both tension and compression, respectively. During cyclic deformation, rapid dislocation accumulation occurs in the first 30 cycles, after which dislocation density decreases to a stable value in ferrite. It is found that the onset of plasticity is governed by dislocation nucleation from the ferrite-cementite interface. After slip into the ferrite phase, some dislocations annihilate at the interface. After a few tens of cycles, the dislocation nucleation and annihilation rates become equal, leading to a steady-state flow in cyclic deformation. Up to high cycles with large strain magnitude, the magnitude of plastic strain in pearlite is higher than critical values and slip crosses the interface from the ferrite phase to the brittle cementite phase. Dislocation slip in cementite will destroy the interface structure, which may be the plastic mechanism of final fatigue failure. Our simulations agree with experimental observations of dislocation evolution in the ratchetting of pearlitic steels and provide further atomic-scale mechanisms to explain the fatigue failure of these materials.

Acute angle ECAP die with modification for punchless back pressure provider

Abstract The channel angle (Φ) is the most critical parameter for an ECAP die and a variety of trials and variations were tried with ECAP with Φ values ranging from 90° to 135° by many researchers. Some finite element models suggest that reducing the Φ value further below (acute) increases the magnitude of plastic strain imparted to the work piece per pass, but the homogeneity of strain imparted reduces. Referring to some independent works, it can be understood that providing back pressure through a second punch in the exit channel and restricting the flow of material improves the dislocation density, adding to the strain imparted. With the advent of a new method of providing back pressure, by providing a back pressure notch on the roof of exit channel, eliminates the need for a back pressure punch and a dual axis Universal Testing Machine (UTM).

Bubble collapse induced cavitation erosion: Plastic strain and energy dissipation investigations

A meshless Smoothed Particle Hydrodynamics solver is used to simulate the collapse of a cavitation bubble near a solid material taking into account the complex fluid-structure interaction. A parametric study has been performed to study the effect of stand-off ratio, bubble size, driving pressure and strain rate on the material response. We focus on plastic strain magnitudes and plastic strain energy dissipation to compare different cases and their ability to cause material erosion. Findings indicate that, in the case of repeated collapses, cavities attached to the solid have an ability to initiate damage quicker but exhibit lower erosion rate compared to the cavities detached from the solid. The incubation time does not depend on the size of the bubbles, unlike the erosion rate which is strongly affected by the bubble size. It is also found that the amount of cumulated plasticity is overestimated by more than 150% when the strain-rate sensitivity is not taken into account in the material modelling which suggests that using an appropriate plasticity model that includes strain-rate sensitivity is mandatory while studying the phenomenon of cavitation erosion.

Modeling of an excavation-induced rock fracturing process from continuity to discontinuity

A convenient and efficient approach to simulate the excavation-induced rock fracturing process from continuity to discontinuity is proposed. The excavation boundary is considered to be an internal discontinuity, which is enriched by a Heaviside function. By using partition of unity concept and level set method, the cellular automaton updating rule for elasto-plastic fracturing induced by excavation is developed. The excavation induced rock mass strain localization is described by plasticity. A plastic strain-dependent criterion is proposed to link continuity and discontinuity, by which crack initiation and propagation of rock mass are described. By using the cellular automaton neighborhood information and level set method, the crack propagation path and excavation boundary can be tracked efficiently. The excavation and the induced crack initiation and propagation can be represented and simulated without explicit remeshing. This approach is implemented in a self-developed numerical model, i.e. a rock continuous-discontinuous cellular automaton (CDCA). The reliability and versatility of CDCA in the modeling of excavation-induced crack initiation, propagation, coalescence and block formation in rock mass are well demonstrated. The method helps estimate the onset of stable and unstable failure development, as well as the magnitude of plastic strain before cracking in rocks.

Effect of damage modelling in numerical simulation of crash energy absorption behaviour of crush tubes and validation with experiments

Crush tubes are employed as frontal energy absorbing structures in road vehicles and they absorb crash energy by plastic deformation. Finite element analysis (FEA) is being used extensively in the early stages of crush tube design to study the method and magnitude of plastic deformation precisely ahead of prototyping and testing. Accurate definition of crush tube’s material including its post-yield and damage/failure behaviours forms a fundamental part of FEA for a realistic prediction of crush tube’s response to crash impact loads. Often, for the sake of simplicity or unavailability of data, it is a common practice in numerical simulations to ignore the damage criterion which leads to substantial differences between FEA predictions and experiments. Therefore, this article demonstrates the importance and effect of damage modelling in numerical simulation (FEA) of crash energy absorption behaviour of crush tubes. The results of numerical simulation of crush tubes with and without consideration of proper damage model are compared with carefully conducted axial crush experiments. The results show that the inclusion of damage model in numerical simulations improve the closeness of predictions compared to experiments irrespective of the magnitude of plastic strains in crush tubes. Crush tubes made of aluminium alloy H30 in WP condition and stainless steel SS304 grades are considered for this study.

Plastic strain gradients and transient fatigue crack growth: A computational study

Fatigue crack growth is analyzed for steady state and overload conditions. The model combines an elastic-plastic strain gradient hardening material and an irreversible cohesive zone model. Plastic strain gradients are found not to affect steady-state fatigue crack growth but play a key role in the overload response. Plastic strain gradient hardening lowers plastic strain magnitudes and alters the spatial distribution of plastic strain. This leads to reduced crack closure and higher crack growth rates during and after the overload. Using classical plasticity alone to describe fatigue crack growth following an overload is thus nonconservative.

Numerical Modeling of Nanostructured Tube Produced by ECAP

— tailoring material properties to specific application requirements is one of the major challenges in materials engineering. Grain size is a key factor affecting physical and mechanical properties of polycrystals materials. Grain size reduction in the metals and alloys can be achieved using Equal channel angular pressing (ECAP) method. In this work, Nanostructure thin walled copper tube specimens with 1 mm wall thickness and 23mm diameter have been produced successfully with ECAP method using flexible polyurethane rubber pad to prevent the tube walls from collapsing. Furthermore, this paper details the development of a numerical simulation to analyse the fabrication of thin walled tube through ECAP process. A copper tube was pushed through a channel with a series of 90° bends. During each successive bend, the magnitude of plastic strains accumulate in the copper tube. A three dimensional numerical simulation was used to model the process and determine the extent of plastic deformation that takes place during each bend process. The numerical simulation was developed using the finite element (FE) code, ABAQUS V6.13, and analysed using the explicit solver.

Cracking Problems in the Segments of Tabriz Metro Tunnel: A 3D Computational Study

This paper presents numerical models of tunnel segments with respect to the steel rebars using a finite element method under TBM thrust jack referring to the Tabriz metro line 2. The analyses have been carried out in five different steps. Numerical modellings have been done from the lowest ratio of reinforcement (the weakest case) to the highest ratio of it (the strongest case), which means that the curved longitudinal rebars were only placed within the concrete in the first step of the analysis, then other types of rebars are added gradually. The results indicated that stress contours in the z-direction (S33) of the model was approximately equal in all the steps. While distributed stress indicated more different behavior than the S33, which the maximum compressive and tensile distributed stresses are just applied on the reinforcement. The higher the reinforcement ratio, distributed stresses are increased step by step. So, it may be noticed that the reinforcement ratio was so crucial to the stresses which are needed to bear. A cracking form of the segment has been analyzed using different types of strains. The curved longitudinal rebars have a remarkable impact on cracking form in the z-direction in step 1, so that the magnitude of plastic strain in the z-direction (PE33) was remarkably decreased when they were placed within the concrete. Although adding the other main rebars has a negligible impact on the cracking form in z-direction whereas they can decline the plastic strain in the x-direction (PE11). The rebars which were added to the model in step 3, decrease the cracks around the shoulders of the segment. Nonetheless, all the rebars have not affected the segment behavior. Finally, in step 5, the cracking mechanism between the loading surfaces has completely changed. Also, displacement contours showed that the magnitude is decreased when the rebars are added to the reinforcement in every step.

Influence of Temperature-Dependent Properties of Aluminum Alloy on Evolution of Plastic Strain and Residual Stress during Quenching Process

To lessen quenching residual stresses in aluminum alloy components, theory analysis, quenching experiments, and numerical simulation were applied to investigate the influence of temperature-dependent material properties on the evolution of plastic strain and stress in the forged 2A14 aluminum alloy components during quenching process. The results show that the thermal expansion coefficients, yield strengths, and elastic moduli played key roles in determining the magnitude of plastic strains. To produce a certain plastic strain, the temperature difference increased with decreasing temperature. It means that the cooling rates at high temperatures play an important role in determining residual stresses. Only reducing the cooling rate at low temperatures does not reduce residual stresses. An optimized quenching process can minimize the residual stresses and guarantee superior mechanical properties. In the quenching process, the cooling rates were low at temperatures above 450 °C and were high at temperatures below 400 °C.

Experimental Analysis of Elastic-Plastic Free Vibrations of Beam Models Caused by Impact

An experimental analysis was performed to model transverse impact of free-free and free supported square duralumin beams loaded at different locations along their length. The applied impact load was obtained from tests carried out on a single Hopkinson pressure bar equipped with a high speed camera. The experimental set-up consisted of an Hopkinson measuring bar that is brought in contact with the beam. In this one-point impact experiment, a cylindrical striker, fired by the air gun, impacts the Hopkinson bar and generates stress waves that travel along the bar and impinge upon the aluminum beam. The stress waves are recorded by strain gages mounted on the Hopkinson measuring bar. These are used to calculate the applied load on the beam. Dynamical displacements of the impact zone of tested beam were recorded by the high speed camera. The dynamic experiments show that the plastic deformation, adjacent to the impact location, is due to combined dominant bending and stretching modes. Most of the plastic deformation is confined to the impact zone of tested beams. The plastic strain magnitude and distribution near the impact zone is similar for all tested impact locations, but higher for the more symmetrical impacts. The conversion of impact energy into kinetic, elastic strain energy and plastic dissipation work is characterized for various impact locations along the specimen of beam.

Accurate springback prediction in deep drawing using pre-strain based multiple cyclic stress–strain curves in finite element simulation

The focus of this work is the accurate prediction of springback in deep drawing for DP600 material. A novel method is used for the characterization of material which leads to simultaneous generation of multiple cyclic stress–strain curves with different magnitude of plastic strains in a single experiment. An enhanced finite element simulation model is also presented which is capable of application of these multiple pre-strain based cyclic stress–strain curves in a single simulation. After each increment, the elements are grouped based on their pre-strain levels independent of the element location and assigned the relevant stress–strain curve. Simulations are performed with the Yoshida Uemori (YU) model, Chaboche–Roussilier (CR) model and an isotropic hardening model for the prediction of springback for hat geometry and tunnel geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat and tunnel geometry for model with multiple cyclic stress–strain curves is 0.8mm and 1.6mm respectively in contrast to the deviation of 1.8mm and 4.2mm for the simulation model with single cyclic stress–strain curve respectively. It is shown that the simulation model with multiple cyclic stress–strain curves predicts the springback more accurately than the other models with single stress–strain curve.

Plastic deformation behavior during unloading in compressive cyclic test of nanocrystalline copper

Deformed coarse-grained polycrystalline metals always unload elastically where permanent dislocation network well-developed in the loading regime hinders the movement of dislocations and allows only the elastic relaxation of stress. Such elastic unloading behavior is, however, unexpected in nanocrystalline metals because the dislocation network cannot effectively form inside nanometer-scale grains. In this work, we report the experimental finding of significant plastic deformation that emerges in the unloading regime in the compressive cyclic test at room temperature of nanocrystalline Cu. The magnitude of plastic strain produced during unloading depends strongly on loading and unloading rates. This plastic unloading behavior arises from the rapid absorption of dislocations accumulated during loading, which was quantitatively interpreted by performing the incremental unloading test and developing a relationship between the dislocation density and the loading and unloading rates based on the models of the statistical absorption of dislocations by grain boundaries and the dislocation emission from grain boundary ledges. Concurrently, the evolution of deformation structures during the cyclic deformation was also analyzed in terms of the interactions of gliding dislocation–twin boundaries.

Joining aluminium alloys with reduced ductility by mechanical clinching

The joinability of aluminium alloy sheets with reduced ductility produced by mechanical clinching is analyzed. A modified tool set geometry was developed to reduce the localization and magnitude of plastic strain. Sheets preheating was adopted to increase the material formability. Optical microscopy and scanning electron microscopy were utilized to observe possible presence of cracks in clinched connections and to perform dimensional analysis. Mechanical characterization tests comprising micro-hardness test and single lap shear tests were conducted to evaluate the influence of the processing conditions on joints strength.

Effect of Localized Microstructure Evolution on Higher Harmonic Generation of Guided Waves

The use of nonlinear ultrasonics to characterize microstructural evolution is investigated with the aim of enabling earlier remaining useful life prediction and thereby greatly improving condition based maintenance. Higher harmonic generation is sensitive to microstructural features, whose evolution is indicative of ongoing damage processes. Localized plastic deformation is controlled in an aluminum sample by varying the notch length, which dictates the extent of the plastic zone. The essentials of higher harmonic generation analysis for ultrasonic guided waves are highlighted to provide a means to select a primary mode that generates a strong higher harmonic. Experimental methods to use magnetostrictive transducers for third harmonic generation measurements are described. Experimental results on aluminum plates indicate that plastic deformation increases the third harmonic by up to a factor of five and that the harmonic amplitude ratio $$A_{3}$$ / $$A_{1}^{3}$$ is sensitive to the plastic strain magnitude. These initial results show that when the plastic strain is localized, the $$A_{3}$$ / $$A_{1}^{3 }$$ ratio appears to be proportional to the plastic zone-to-propagation distance ratio.

Numerical evaluation of the material response of a railway wheel under thermomechanical braking conditions

The material response of a railway wheel subjected to thermomechanical rolling contact is evaluated. Thermal and mechanical loads are combined in a three-dimensional sequentially coupled analysis where nodal temperatures from a transient thermal analysis are applied as predefined fields in a structural analysis featuring an elastic–plastic material model. The mechanical contact load is prescribed as a moving Hertzian contact stress distribution with a surface shear stress distribution corresponding to full or partial slip conditions. Modelling aspects studied in detail are the feasible model resolution at the contact patch, the influence of sequences of thermal and mechanical loads, and the influence of wheel–rail interfacial shear distributions. The study identifies feasible mesh sizes and load application strategies to obtain a good accuracy at reasonable computational efforts. Further, differences in predicted material response under full slip and partial slip conditions are assessed. It is found that for a given total tangential force, partial slip conditions result in larger plastic strain magnitudes in a thin layer near the contact surface.

Advanced Numerical Analysis of Jack-Up Spudcan Penetration in Layered Sandy Soil

Quasi-static numerical model of jack-up spudcan penetration in layered sandy soil was presented in this paper, based on explicit procedure. Three different methods, such as Lagrangian analysis, Lagrangian analysis with distortion control and Lagrangian-Eulerian analysis, were used to control soil negative element volumes or other excessive distortion. The results showed that, reasonable and stable numerical results could be solved by Lagrangian-Eulerian analysis. The magnitude of plastic strain, however, decreases at first and then increases to the maximum.

Structural modifications induced by compressive plastic deformation in single-step and sequentially irradiated UHMWPE for hip joint components

Structural modifications were studied at the molecular scale in two highly crosslinked UHMWPE materials for hip-joint acetabular components, as induced upon application of (uniaxial) compressive strain to the as-manufactured microstructures. The two materials, quite different in their starting resins and belonging to different manufacturing generations, were a single-step irradiated and a sequentially irradiated polyethylene. The latter material represents the most recently launched gamma-ray-irradiated polyethylene material in the global hip implant market. Confocal/polarized Raman spectroscopy was systematically applied to characterize the initial microstructures and the microstructural response of the materials to plastic deformation. Crystallinity fractions and preferential orientation of molecular chains have been followed up during in vitro deformation tests on unused cups and correlated to plastic strain magnitude and to the recovery capacity of the material. Moreover, analyses of the in vivo deformation behavior of two short-term retrieved hip cups are also presented. Trends of preferential orientation of molecular chains as a function of residual strain were similar for both materials, but distinctly different in their extents. The sequentially irradiated material was more resistant to plastic deformation and, for the same magnitude of residual plastic strain, possessed a higher capacity of recovery as compared to the single-step irradiated one.

The Effects of Concurrent Power and Vibration Loads on the Reliability of Board-Level Interconnections in Power Electronic Assemblies

The effect of concurrent vibration and electrical power loads on the solder interconnections of a surface-mount power transistor package has been investigated in this work. Both cyclic and constant power loadings were separately combined with vibration over a wide amplitude range. Single load vibration and power cycling tests were conducted for comparison. In addition to lifetime analysis, the failure modes occurring under each test case were carefully studied from cross-sectional samples, and the failure mechanisms were rationalized with the help of finite-element calculations and microstructural analysis. A substantial reduction in interconnection lifetimes was observed in the combined load tests as compared with the lifetime under single load tests. Three different failure modes were found within all the different test cases: 1) ductile crack propagation through bulk solder, 2) recrystallization assisted crack propagation, and 3) mixed mode propagation with both mechanisms. The failure mode changes were dependent mainly on the magnitude of plastic strain induced by the mechanical vibration. The results of this study provide insight in designing more comprehensive reliability tests as well as achieving higher levels of test acceleration without compromising the validity of results.

Slip transfer and plastic strain accumulation across grain boundaries in Hastelloy X

In this study, high resolution ex situ digital image correlation (DIC) was used to measure plastic strain accumulation with sub-grain level spatial resolution in uniaxial tension of a nickel-based superalloy, Hastelloy X. In addition, the underlying microstructure was characterized with similar spatial resolution using electron backscatter diffraction (EBSD). With this combination of crystallographic orientation data and plastic strain measurements, the resolved shear strains on individual slip systems were spatially calculated across a substantial region of interest, i.e., we determined the local slip system activity in an aggregate of ∼600 grains and annealing twins. The full-field DIC measurements show a high level of heterogeneity in the plastic response with large variations in strain magnitudes within grains and across grain boundaries (GBs). We used the experimental results to study these variations in strain, focusing in particular on the role of slip transmission across GBs in the development of strain heterogeneities. For every GB in the polycrystalline aggregate, we have established the most likely dislocation reaction and used that information to calculate the residual Burgers vector and plastic strain magnitudes due to slip transmission across each interface. We have also used molecular dynamics simulations (MD) to establish the energy barriers to slip transmission for selected cases yielding different magnitudes of the residual Burgers vector. From our analysis, we show an inverse relation between the magnitudes of the residual Burgers vector and the plastic strains across GBs. Also, the MD simulations reveal a higher energy barrier for slip transmission at high magnitudes of the residual Burgers vector. We therefore emphasize the importance of considering the magnitude of the residual Burgers vector to obtain a better description of the GB resistance to slip transmission, which in turn influences the local plastic strains in the vicinity of grain boundaries.

The Role of Slip Transmission on Plastic Strain accumulationacross Grain Boundaries

In the present study our aim is to develop a deeper understanding of strain accumulation in the vicinity of grain boundaries (GBs) within a polycrystalline aggregate. We focus on the role of slip transmission in the uniaxial plastic deformation of a nickel-based superalloy,Hastelloy-X. Utilizing high resolution ex-situ digital image correlation (DIC) and electron backscatter diffraction (EBSD), we establish the most likely dislocation reactions due to slip transmission and use this information to calculate the residual Burgers vector and plastic strain magnitudes across each interface. From our analysis, we quantitatively show an influence of the magnitude of the residual Burgers vector on plastic strains across GBs.