Plastic Energy Dissipation Research Articles

Mechanical performance and fatigue life prediction of lattice structures: Parametric computational approach

Additive manufacturing (AM) highly complex lattice structures with exceptional engineering properties are of special interests for a wide range of engineering applications including biomedical (implant, scaffold), automotive (shock-absorbing, load sensors) and civil engineering (protective layers). This research focuses on developing a numerical framework to predict the mechanical and fatigue properties of lattice structures with various relative densities and architectures. The relationship between geometry parameters and relative density of four lattice structures is investigated. Finite Element Analysis (FEA) is employed to simulate uniaxial compression test so that the elastic modulus and yield strength of lattices are evaluated. Parametric studies on hundred designs for each lattice are conducted to obtain associated design maps. Among the lattice structures investigated, the Simple Cubic (SC) unit cell shows the highest elastic modulus and yield strength at any relative densities, while these properties of Body Centred Cubic (BCC) unit cell is the lowest. Numerical results also reveal the nonuniform distributions of strain & plastic dissipation energy between layers, when multilayer lattice structures are subjected to compression. The fatigue property of lattice structures is also predicted numerically showing the dependence on both relative density and unit cell topology. The normalised fatigue behaviour of SC and Simple Cubic Body Centred Cubic (SC-BCC) are independent of relative density, while Face Centred Cubic (FCC) and BCC are sensitive to its relative density.

Experimental and FEM analysis of mar behavior on amorphous polymers

Mar is a type of subtle surface damage caused by a sliding object barely visible to human eyes. This minor damage phenomenon has rarely been systematically studied. Significant research efforts for the fundamental understanding of mar behavior in polymers are still needed. In this study, the mar behavior of a series of model amorphous polymers, i.e., polymethylmethacrylate (PMMA), polycarbonate (PC), and polystyrene (PS), were investigated based on a modified ASTM/ISO scratch testing methodology and a corresponding finite element method (FEM) modeling. Furthermore, the mar-induced visibility and material parameter relationships were established through a systematic FEM parametric study. Experimental results show that PMMA has the highest mar visibility resistance, indicated by lower surface roughness variation and low contrast between marred region and the background. The numerical analysis showed that the maximum principal plastic strain (ε1p) and total dissipated plastic energy (Ep) can be considered for evaluating mar visibility resistance. Higher mar visibility resistance corresponds to lower ε1p and Ep values. Based on these two criteria, the parametric analysis shows that mar visibility resistance increases with lower modulus, higher yield stress, higher hardening slope, and lower softening slope. The usefulness of the present study for the preparation of mar resistant polymers is discussed.

Seismic Performance of Precast Concrete Columns with Improved U-type Reinforcement Ferrule Connections

This paper proposes a new kind of U-type reinforcement ferrule (URF) connection for the assembly of precast concrete (PC) components, which has a good fault-tolerance ability and low cost of construction with a simple post-grouting process. The modified connection features welded U ferrules, which can increase the bonding mechanism and internal stress transmission in the spliced region. A series of quasi-static cyclic tests were performed on URF-connected PC columns with different welding patterns. Comprehensive comparisons were performed on the load-bearing capacity, the plastic energy dissipation ability, the internal force transmission, the column ductility and the stiffness. The results indicated that PC columns with welded URF connections can ensure better lateral resistance than the cast-in-place concrete column. The weld type and length influence the connection performance, and the 15d-welded and full-length welded URF connections presented better connection performance and were suggested for the assembly of PC columns. Then, finite element analyses were performed to further reveal the working and failure mechanisms and the affecting mechanism of some working parameters. Parametric simulations indicated that the increase in the axial load ratio and the concrete strength in the postcast region had a slight but limited effect on improving the lateral resistance of the column connection.

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.

Development and experimental verification of damage controllable energy dissipation beam to column connection

The present study develops and experimentally verifies a new type of precast concrete beam to column connection. The proposed damage controllable energy dissipation (DCED) beam to column connection places the replaceable steel connectors with low yield point in predetermined areas of beams to achieve the aim of controllable plastic development, energy dissipation and replaceability after the earthquake. Two 1/2 scale interior beam-column connections were designed, fabricated and tested under cyclic reversed loadings, including one monolithic specimen and one precast specimen. The hysteresis curves were recorded during the test, and the seismic indicators, such as strength, stiffness and energy dissipation capacity, were determined and analyzed. Test results demonstrate that the precast DCED connection has similar strength to the monolithic specimen, exhibits stable and plump hysteretic responses, and fails in a typical flexural mode, which is consistent with the criteria of strong column and weak beam. The plastic hinges in the steel connectors greatly reduces the damage in the DCED connection core and mitigates the deterioration in global stiffness of connection, meeting the requirements of damage controllable. Additionally, the DCED connection exhibits satisfactory energy dissipation capacity and has better seismic performance. It is a viable alternative to the seismic beam to column connections of precast concrete buildings in medium and high seismic intensity regions.

Fracture behavior and deformation mechanisms in nanolaminated crystalline/amorphous micro-cantilevers

In order to quantify the fracture toughness and reveal the failure mechanism of crystalline/amorphous nanolaminates (C/ANLs), in-situ micro-cantilever bending tests were performed on Ag/Cu–Zr and Mo/Cu–Zr C/ANLs in a scanning electron microscope over a wide range of cantilever widths from several microns to the submicron scale. The results demonstrate that the fracture behavior was strongly influenced by sample size and constituent phases, respectively. The Ag/Cu–Zr micro-cantilevers failed in a ductile manner, with fracture toughnesses higher than the Mo/Cu–Zr samples that exhibited brittle failure. Both materials also displayed different cantilever width-dependences of fracture toughness. The Ag/Cu–Zr beams showed a fracture toughness that increases with the cantilever width, mainly due to a size-dependent constraining effect on the deformation of the crystalline phase. For the Mo/Cu–Zr beams, the fracture toughness decreased gradually to a low plateau as the cantilever width exceeded ∼1500 nm, which can be rationalized by a transition in stress condition. The underlying fracture mechanism of the Ag/Cu–Zr micro-cantilevers was identified as the interconnection of microcracks initiated in the amorphous Cu–Zr layers, compared to a catastrophically penetrating crack propagation in the Mo/Cu–Zr samples. The discrepancy in size-dependent fracture behavior between the two material systems is discussed in terms of plastic energy dissipation of ductile phases, crack tip blunting, crack bridging and the effect of strain gradient in the plastic zone on crack propagation.

Low-cycle fatigue life prediction of a polycrystalline nickel-base superalloy using crystal plasticity modelling approach

A crystal plasticity model is developed to predict the cyclic plasticity during the low-cycle fatigue of GH4169 superalloy. Accumulated plastic slip and energy dissipation as fatigue indicator parameters (FIPs) are used to predict fatigue crack initiation and the fatigue life until failure. Results show that fatigue damage is most likely to initiate at triple points and grain boundaries where severe plastic slip and energy dissipation are present. The predicted fatigue life until failure is within the scatter band of factor 2 when compared with experimental data for the total strain amplitudes ranging from 0.8% to 2.4%. Microscopically, the adjacent grain arrangements and their interactions account for the stress concentration. In addition, different sets of grain orientations with the same total grain numbers of 150 were generated using the present model. Results show that different sets have significant influence on the distribution of stresses between each individual grain at the meso-scale, although little effect is found on the macroscopic length-scale.

Inverse bending and springback-control using magnetic pulse forming

In this study, electromagnetic-assisted stamping (EMAS) with magnetic-force reverse loading was introduced to control springback. Compared to conventional EMAS, this new method does not change the mold structure used in traditional stamping technology. Thus, this approach can greatly extend the operating lifetime of the mold and readily be adopted for commercial production. Results indicate that the equivalent plastic strain and the plastic dissipation energy increase, while the tangential stress and the elastic strain energy decrease considerably, with increasing in discharge-voltage. The simulation results accurately predict the sheet deformation for quasi-static stamping and dynamic magnetic pulse forming. Both simulations and experiments show that the angle after springback decreases with increasing in discharge-voltage.

The Development of a New Shock Absorbing Uniaxial Graded Auxetic Damper (UGAD).

Auxetic structures are efficient cellular materials that can absorb blast/impact energy through plastic deformation, thus protecting the structure. They are developing sacrificial solutions with light weight, high specific strength, high specific toughness and excellent energy dissipating properties, due to its negative Poison’s ratio nature. The use of auxetic and non-auxetic panels in blast resistant structures had been relatively perceived by researchers. Nonetheless, implementation of those energy dissipaters, explicitly as a uni-axial passive damper is restrained to limited studies, which highlight the potential need for further explorations. The aim of this paper is the design of a new uniaxial graded auxetic damper (UGAD) that can be used as a blast/impact/shock absorber in different scales for different structural applications. First, the geometry, material, numerical model and loading are introduced. Then, a detailed parametric study is conducted to achieve the most efficient graded auxetic system. Moreover, the designed auxetic damper is numerically tested and its static and dynamic constitutive relations are derived and validated analytically. The selection of optimum parameters was based on the ratio of the reaction force to the applied load (RFd/P) and plastic dissipation energy (PDE). The final designed UGAD contains three auxetic cores that have the same geometry, material grade (6063-T4), size and number of layers equal to eight. The cell-wall thickness t of the three auxetic cores is 1.4 mm, 1.8 mm and 2.2 mm, respectively; composing a graded auxetic system. The performance of the three auxetic cores together have led to a wide plateau region (80% of total crushing strain) and variant strength range (1–10 MPa), which in return, can justify the superior performance of the UGAD under different blast levels. Finally, the 3D printed prototype of the UGAD is presented and the possible applications are covered.

Structure design of reinforced honeycomb paperboard core and characterization of its out‐of‐plane bearing strength

Honeycomb paperboard's out‐of‐plane bearing performance is one of the important properties in packaging field application. Further improvement of its bearing performance has important value in engineering practice. In this paper, a honeycomb core structure was designed, and the bonding dimension and manufacturing process were designed. The mechanism of out‐of‐plane quasi‐static compression deformation of reinforced honeycomb paperboard was analyzed by experiments. The theoretical model of out‐of‐plane platform stress was constructed by applying the plastic deformation, plastic energy dissipation and energy conservation theory. The results show that the improved structure can be mechanically bonded in a flat state with less technological changes. Under the same honeycomb core material and core size parameters, the bearing strength of the improved structure increases by an average of 3.9 times to conventional structure. In order to meet the same compressive strength requirement, the improved structure can reduce the performance requirements of honeycomb core material or increase the core size compared with the conventional structure. When the honeycomb core cell is larger, the tension on the core layer required for the production process is reduced. The theoretical and experimental data are in good agreement with each other, and the relative errors are all less than 13%.

Bi-material topology optimization for energy dissipation with inertia and material rate effects under finite deformations

In this study, a bi-material topology optimization framework is developed for maximizing plastic energy dissipation under a combination of material rate effects, inertia effects, and large deformations. In the developed framework, rate effects are considered by employing a finite deformation viscoplastic model and finite element analysis is carried out using F-bar elements for spatial discretization and the Hilber-Hughes-Taylor algorithm for time integration. A bi-material interpolation strategy is proposed within the density-based design parameterization and used to combine material phases with different phenomenological behavior. Consistent design sensitivities are obtained using a time-dependent adjoint method. Design examples reveal that a much higher percentage of the total energy can be dissipated as plastic work when a soft energy dissipating elasto-viscoplastic phase is combined in an optimized way with a stiffness providing hyperelastic phase than when the energy dissipating phase is considered alone. Moreover, isolating the influence of material rate effects from inertia effects provides insight into how optimized designs can exploit these phenomena.

Seismic Control Strategy of a Multi-Story Subway Station Based on Probability Density Evolution Method

The method to protect the whole station structure by installing flexible devices at the column end has been proved to be effective in typical station structures. However, the damping effects and application of this method to multi-story subway station structures still need further study. In this paper, a stochastic analysis method, probability density evolution method (PDEM), is adopted to estimate the damping effect of a four-story subway station structure with lead rubber bearings (LRBs) installed in the central column. Stochastic analysis results show that the internal forces and plastic energy dissipation of columns installed LRBs are greatly reduced and the reliability is improved. Internal forces and plastic energy dissipation of columns without the installation of LRBs increase and the reliability decrease. There is little difference in structural deformation and plastic energy dissipation of structural components when LRB is installed in the middle of the column or at the column ends. When LRBs are installed only in some of the stories, the overall reliability of the structure is lower than that of the structure without LRB. When LRBs are installed in the columns of all stories, the structural reliability is higher than that of the structure without LRB. Based on the above results, to obtain better seismic control effect by installing LRBs, the multi-story subway station structure should be installed with LRBs in the columns of all stories, and LRBs can be installed at the upper, middle and lower end of the columns.

Correlation of localized residual stresses with ductile fracture toughness using in situ neutron diffraction and finite element modelling

Localized residual stresses were correlated to ductile fracture toughness quantitatively in steel and aluminium alloys using in situ neutron diffraction method coupled with elastic-plastic finite element modelling. Local out-of-plane compression (LOPC) method generated compressive and tensile residual stresses in the vicinity of the fatigue pre-crack front in two compact tension (CT) specimens, respectively, and the evolution of the stress fields was simultaneously measured using in situ neutron diffraction technique under mode-I fracture loading. The results clearly showed that the localized tensile residual stress apparently accelerated stress transfer at the mid-thickness of the CT specimen compared to the specimen having compressive residual stress. The coupled quasi-static ductile fracture simulations and neutron diffraction results revealed a clear correspondence of fracture initiation toughness with localized residual stresses in both steel and aluminium alloys. In the aluminium case, tensile residual stress of 208 MPa was obviously detrimental to the fracture toughness resulting in a 43% reduction while compression of −220 MPa increases by up to 14%. On the other hand, localized residual stress in steel hardly affected fracture initiation toughness due to high plastic dissipation energy. This experiment-simulation coupled study quantitatively elucidates the distinctive role of plastic deformation and stress triaxiality in ductile fracture initiation between steel and aluminium alloy.

Molecular dynamics simulation of plastic deformation and interfacial delamination of NiTi/Ag bilayer by cyclic-nanoindentation: Effects of crystallographic orientation of substrate

This paper presents a comparative study of plasticity and fracture behavior of the NiTi/Ag bilayer for the different crystallographic orientations of the substrate. Molecular dynamic (MD) simulation was used to determine the deformation mechanism, dislocation density, plastic energy dissipation and delamination of the NiTi/Ag bilayers near the interface, when NiTi aligned at (1 0 0), (1 1 1), (1 1 0), (3 2 1), (2 1 0) and (2 1 1) faces during the cyclic-nanoindentation test. The Griffith energy balance model was used to estimate the energy release associated with the delamination. The results of the simulation are suggested the dependence of deformation mechanism, energy release rate (Gin), interfacial toughness (Kin) and average plastic energy dissipation per unit cycle (Eplastic) of NiTi/Ag bilayer on the crystallographic orientation of the NiTi substrate. Prismatic dislocation loop and the nest-like organization of the twins were responsible for the plastic deformation of the NiTi/Ag bilayers when NiTi aligned at (211,010,111) and (100,210,321) faces, respectively. The values of Gin and Kin of the bilayers were in the range of 64.27–147.71 J/m2 and 77–192 J/m2, respectively. The values of Eplastic is increased in the following order: NiTi (2 1 1) < NiTi (3 2 1) < NiTi (1 0 0) < NiTi (2 1 0) < NiTi (1 1 1) < NiTi (0 1 0). The average dislocation densities produced for the indenter radius of 30 Å were in the range of 1.23 × 1019–1.84 × 1019 m−2. The results show that the NiTi (0 1 0)/Ag case has the larger dislocation density than other bilayers. Both of hardness and the interfacial toughness of the NiTi/Ag at different crystallographic orientations were consistent with the free energy data obtained from Jarzynski’s equality for nanoindentation results, which were in the range of 3.35 × 10−4−7.81 × 10−4 eV/atom. Due to high interfacial toughness and hardness plus lower plastic energy dissipation, the NiTi (2 1 1)/Ag bilayer may show the better results for engineering and medical applications.

Seismic performance of steel beam-to-column moment connections with different structural forms

A novel scheme of steel moment connections shared by flange cover-plate strengthening and web opening weakening is proposed in this study. Four steel beam-to-column moment connections with different structural forms (standard connection, cover-plate reinforced connection, web-opening weakened connection, and equal strong (ES) connection) were tested under cyclic loading. The effects of the local structural forms at the beam end on the failure modes, bearing capacity, strength and stiffness degradation, and ductility and energy dissipation capacity of the connection were analyzed and discussed. The test results indicate that the connections with local structural forms achieve satisfactory ductile behavior by the plastic hinge moving outside. The strength and stiffness degrade gradually owing to a large plastic strain accumulation, and the plastic deformation capacity and energy dissipation capacity improve significantly. Specifically, compared to the standard connection, the displacement ductility coefficient and cumulative energy dissipation of the ES connection increased by 20.0% and 27.9%, respectively, under the premise that maximum strength and initial stiffness remain unchanged, indicating superior seismic performance. Moreover, finite element analysis considering a stress triaxiality dependent fracture criterion was performed, and demonstrated good agreement with the experimental results. Based on the experiment and numerical simulation, the feasibility of the ES connection was verified to provide practical design applications.

A unified phase field damage model for modeling the brittle-ductile dynamic failure mode transition in metals

Dynamic brittle fracture and shear banding are typical failure modes in metals under high strain rate loading. In this paper, a unified phase field damage model is developed to capture the above two failure modes’ transition naturally by allowing the critical energy release rate to vary with the stress triaxiality to distinguish the material failure properties of tensile fracture and shear banding. Besides this, compared with the existing elastic-plastic phase field fracture models, the plastic dissipation energy before the damage evolution is excluded in the failure energy to model ductile failure more physically, and the degradation function of the yield stress is introduced which not only provides a damage softening mechanism for the ductile failure but also ensures a proper simulation of the brittle fracture. The unified phase field damage model is applied to study the brittle-ductile failure mode transition in Kalthoff test. The results show that stress wave propagation plays an important role in the brittle-ductile failure mode transition. The shear banding requires more energy for initiation and will be activated straightly as the plastic wave passes the notch tip for high impact velocity. While for low impact velocity, the energy will be released by selecting the brittle fracture mode which requires less energy when the reflected tensile wave superimposes at the notch tip. For our simulation, the damage softening contributes considerably more to the shear banding than the thermal softening. This model can be used to simulate the complex dynamic failure of metal under impact loading.

Dynamic Crushing Analysis of a Three-Dimensional Re-Entrant Auxetic Cellular Structure.

Dynamic behaviors of the three-dimensional re-entrant auxetic cellular structure have been investigated by performing beam-based crushing simulation. Detailed deformation process subjected to various crushing velocities has been described, where three specific crushing modes have been identified with respect to the crushing velocity and the relative density. The crushing strength of the 3D re-entrant auxetic structure reveals to increase with increasing crushing velocity and relative density. Moreover, an analytical formula of dynamic plateau stress has been deduced, which has been validated to present theoretical predictions agreeing well with simulation results. By establishing an analytical model, the role of relative density on the energy absorption capacity of the 3D re-entrant auxetic structure has been further studied. The results indicate that the specific plastic energy dissipation is increased by increasing the relative density, while the normalized plastic energy dissipation has an opposite sensitivity to the relative density when the crushing velocity exceeds the critical transition velocity. The study in this work can provide insights into the dynamic property of the 3D re-entrant auxetic structure and provides an extensive reference for the crushing resistance design of the auxetic structure.

Plastic Energy Dissipation in Lumbar Spine Implants: A Contact Mechanics Point of View

In this study, an elastoplastic contact model is developed for L1–L5 lumbar spine implants. Roughness effect is included to estimate energy loss which is an indication of wear and subsequently the issue of metal debris in body. A Gaussian function is assumed for the distribution of asperities. The contact surfaces of the implants are assumed to be spherical caps. Subsequently, a least-square approach is applied to obtain an approximate expression for the contact force using the data from integration over contact zone. The energy loss is calculated, next, which is due to plastic deformations of asperities. The numerical results indicate that for a given loading–unloading condition, the amount of energy dissipation increases in L1–L4 lumbar spine implants, while it decreases from L4 to L5 implants. The implants geometrical specifications are chosen to cover a wide range of patients' age. Finally, a closed-form expression is obtained for the plastic energy dissipation per cycle in terms of plasticity index for the lumbar spine L4, as the worst-case scenario. Such a function can serve as a very useful tool for implant designers and manufacturers.

Experimental and numerical studies on hysteretic behaviour of stainless steel welded box-section columns

Eight specimens were tested under cyclic loading to investigate hysteretic behaviour of stainless steel welded box-section columns. Failure modes, plastic development capacity, energy dissipation and ductility of the specimens were studied, and the influence of the width-to-thickness ratio as well as the axial load ratio on the hysteretic behaviour were analyzed. The test results obtained herein were used to validate finite element (FE) models, which were subsequently employed for parametric investigations to generate further data about the hysteretic behaviour of such columns over a wide range of parameters including the width-to-thickness ratio, the axial load ratio and the slenderness ratio. The FE results were utilised to assess whether codified classification limits of cross-section in 1993‐1‐4+A1 (2015) are also applicable for stainless steel columns subjected to combined constant axial force and cyclic loading. The test results indicate that with larger width-to-thickness ratio the hysteresis curve becomes less plump, the ductility coefficient and the plastic development capacity are smaller; whilst effects of the slenderness ratio are not significant; the influence of the axial load ratio on the plastic development capacity is related to the width-to-thickness ratio. In addition, it is found that EN 1993‐1‐4 could be conservative for the classification of the stainless steel welded box-section columns class 3 and class 4 cross-sections，whereas it could be unsafe for the classification of the stainless steel welded box-section columns class 1 cross-section.

Retracted] Multidimensional Fragility Analysis for a NEES Frame Structure by Integrating a New Energy Damage Index: Cumulative Plastic Strain

Cumulative plastic strain (CPS) damage index is proposed in this study for seismic fragility analysis by integrating the force analogy method into the energy balance equation, and CPS can be defined as the ratio of the demand of plastic dissipation energy to its capacity. The cumulative plastic strain can indicate the structural damage cumulative effect under earthquakes, which makes it especially suitable to be selected as the damage index for the structural component. Threshold values of cumulative plastic strain for different performance limit state (PLS) levels are obtained through the degree of consistency of interstory drift‐based fragility curves and CPS‐based fragility curves. Regarding the multidimensional fragility evaluation, CPS and the floor acceleration will be selected as the quantification indices for performance limit state of the structural component and nonstructural component, respectively. The probabilistic seismic demand model (PSDM) following multivariate logarithmic normal distribution will be developed, and taking PLS uncertainty and correlation into consideration, multidimensional PLS function is constructed to identify the structural failure domain. A full‐scale 2‐bay 2‐story frame structure for the Network for Earthquake Engineering Simulation (NEES) project is employed as the case study structure to demonstrate the proposed theory. Nonlinear dynamic time‐history analysis is carried out for the structure to obtain its maximum responses under earthquakes. Consequently, the multidimensional fragility curves can be derived on the basis of CPS. Besides, the influence of PLS threshold value, engineering demand parameter (EDP) correlation, and PLS correlation on the multidimensional fragility is investigated. Results show that (1) CPS damage index can fully consider the cumulative effect of damage under earthquakes, which makes up for the deficiency of the interstory drift damage index in this aspect, (2) the multidimensional fragility framework can deal with the PLS correlation and EDP correlation simultaneously, which will generate a more precise seismic damage assessment result, and (3) multidimensional fragility is sensitive to PLS threshold values and PLS correlation parameters.