Total Plastic Energy Research Articles

Damage analysis of a pseudoclassic reinforced concrete frame structure under the action of the Ms 6.8 Luding earthquake in China

Reinforced concrete (RC) moment-resistant frame structures are very commonly used worldwide. However, previous earthquakes have revealed the occurrence of strong beam–weak column (SBWC) failure, causing heavy human casualties and economic losses. This study analyzed the SBWC failure mechanism in RC frame structures with the pseudoclassic construction named "Que Ti" near the top of a slope topography, based on the author's recent investigation of the Ms 6.8 Luding earthquake in China. Eight refined finite element models (FEMs) were developed to simulate and analyze the influence of slope topography, pseudoclassic construction, and some structural characteristics on structural damage during an earthquake. Furthermore, discussions on using column-to-beam flexural strength ratios (CBFSRs) to mitigate SBWC failure are presented. The results demonstrated the proposed FEMs effectively simulated the performance of the pseudoclassic structure, especially the SBWC failure mode, as validated by their consistency with the observed structural damage during the earthquake. Moreover, it revealed that structures closer to the slope top experienced amplified ground motions during earthquakes, resulting in more severe damage. In addition, the Que Ti and infill walls increased the vulnerability to column damage and maximum requirement for the column shear force. Finally, to achieve the design objective of a strong column–weak beam (SCWB), the CBFSR should be at least increased to 1.8 for this pseudoclassic RC frame. This ensures a probability of the SBWC failure mode of less than 17% (meet less than 20% of recommendations) and proportion of the beam plastic energy dissipation exceeding 80% of the total plastic energy dissipation. The findings of this study are significant for enhancing seismic design and preventing earthquake disasters for the pseudoclassic structure.

Plastic buckling of oil storage tanks under blast loads

This paper deals with the dynamic behavior of cylindrical shells under blast loads, with special reference to plasticity and plastic buckling. Interest in this problem focuses on the response of steel vertical oil storage tanks with a flat roof under a nearby explosion. The problem is modeled using a finite element discretization of the structure, in which the loads are represented by an impulsive pressure which is variable around the circumference. The results for tanks show that, at low pressure levels, there is an elastic shell behavior, and first yield occurs as the peak blast pressure is increased. For subsequent increases of peak pressure, the dimple extends in the area affected by the pressures, so that vertical stripes with plastic material behavior are formed from top to bottom of the shell. For even higher pressures, a global mode develops with large amplitude displacements. The total plastic energy is investigated under increasing peak pressure levels. It is found that a change in slope occurs in total plastic energy versus peak pressure when plasticity spreads in the shell, and this is associated to the development of a plastic buckling mode. Parametric studies show that the main variable affecting the change in behavior of the shell as identified through the total plastic energy depends on the shell thickness and is only marginally affected by the shell height and diameter. These conclusions are valid for squat shells, such as those used in the oil industry, and may not be accurate for taller shells.

Hysteretic behavior of CFST column-steel beam bolted joints with external reinforcing diaphragm

In this study, three concrete-filled steel tubular (CFST) column-steel beam bolted joints with external reinforcing diaphragm were tested under cyclic loading using 1/2 scaled specimens, and the influence law of steel beam size and tie plate of high-strength bolts on the failure modes were discussed. The ABAQUS program was used to establish the three-dimensional solid finite element models of the joints, and the joint models were then verified by the test data. Taking the welded rigid joint with external reinforcing diaphragm as the benchmark, a connection detailing of bolted rigid joint and a method for classifying the joint were proposed. The stiffness, bearing capacity and plastic energy dissipation of the bolted joints with different structural detailing and reinforcing measures were compared and analyzed. The obtained results show that the bolted joints with external reinforcing diaphragm can be classified as semi-rigid joint. The stiffness and bearing capacity of the bolted joint can almost be equivalent with the welded rigid joint counterparts, when the external reinforcing diaphragm with stiffeners was connected to the steel beam using four rows of bolts and simultaneously setting web stiffeners at the beam ends. With the above configuration, the total plastic energy dissipation of the bolted joint is over 80% of that of the welded rigid joint counterpart, and the steel beam is found to be the main component contributing the plastic energy dissipation.

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.

Forming mechanisms-related residual stress development in single point incremental forming

The mechanical properties of a component are significantly influenced by the prevailing residual stress state. A deliberate induction of compressive residual stresses or a reduction of tensile residual stresses can improve the component properties, such as fatigue strength. Single point incremental forming is a flexible manufacturing process to produce complex shaped parts by the computerized numerically controlled movement of a hemispherical forming tool. Because the process parameters can be locally adjusted it is possible to influence the residual stress state of the component. The influence of the forming mechanisms bending, shearing and membrane stretching, as well as the role of the hydrostatic compression on the residual stress state is widely unknown. This work aims to fill this gap. Therefore, linear grooves are formed into AA5083 sheets in a single-stage incremental forming process. The residual stress state of the unclamped sheet is measured on both sides of the groove center by means of X-ray diffraction. The relative intensity of the dominant forming mechanism is adjusted by adapting the relevant process parameters step-down increment Δz and tool radius RTool. The forming mechanisms are analyzed numerically by splitting the total plastic energy into the three forming mechanisms bending, shearing and membrane stretching. The numerical results for bending and membrane stretching could be validated by crystallographic analysis. A shift in the energy ratio of the forming mechanism from bending to shearing with increasing relative step-down increment Δz/RTool could be observed numerically. The maximum residual stress amplitudes are found for Δz/RTool < 1. The results indicate that a deliberate residual stress state can be induced by adjusting the dominant forming mechanism of the process.

Blast resistance and parametric study of sandwich structure consisting of honeycomb core filled with circular metallic tubes

Abstract Hierarchical sandwich structures have been popularly investigated due to its promotion in structural stress and stiffness. A composite Honeycomb structure Filled with Circular Tubes (short as HFCT) was proposed in the previous study. In this paper, the blast resistance performances of sandwich plate filled with HFCT core (short as SP-HFCT) are investigated numerically by considering plastic dissipation energy, deflection of back face-sheet and deformation modes. The comparisons of performance between the general honeycomb sandwich plate (short as GHP) and the SP-HFCT illustrate that the composited filling mode can effectively improve blast resistant capacity by reducing the maximum deflection of the back plate and improving the ratio of plastic energy dissipated by cellular core to the total plastic energy dissipated by sandwich plate. Parametric analyses are performed to evaluate the influence of matching effect between container and filler, filling mode and blast loading on the resistance performance of SP-HFCT. The results show that a stronger honeycomb container filled with weaker circular tubes is a more favorable configuration of HFCT core. Meanwhile, by filling circular tubes into a buckling area, a considerable mass efficiency improvement with respect to deflection resistance can be obtained. With the increasing of stand-off distance, the effectiveness of SP-HFCT against blast loads will be boosted.

Theoretical prediction for large deflection with local indentation of sandwich beam under quasi-static lateral loading

By taking local indention effect and foam core strength into account in the overall deflection process, a novel theoretical model is investigated to predict the large deflection with local indentation of sandwich beam under quasi-static lateral loading. The theoretical and numerical models of lateral crushing force and total plastic energy are proposed and the theoretical results agree well with numerical and experimental results of previous researches. The results conclude that local indention phase plays an important role in initial collapse deflection of sandwich beam when maximum deflection is greater than face sheets thickness. In addition, the theoretical results with and without local indention phase of total plastic energy are compared and it shows that total plastic energy of sandwich beam will be overestimated if local indention phase is neglected. The present analytical model can predict the large deflection behavior with local indention of sandwich beam reasonably.

Crush dynamics and transient deformations of elastic-plastic Miura-ori core sandwich plates

The response of elastic-plastic Miura-ori core sandwich plates to high-intensity dynamic loads is numerically studied using the commercial finite element software ABAQUS/ Explicit. Crushing simulations conducted on the Miura-ori core over a range of loading rates clearly illustrate the dynamic strengthening of the core by inertial effects, particularly at loading rates relevant to blast experiments. Exploratory design studies have been conducted to determine the influence of the unit cell parameters of the Miura-ori pattern on the energy dissipated by the core through plastic deformations, and to compare its performance with that of square honeycomb cores of equal areal density. Material strain rate effects, a material failure criterion and debonding between the core and the facesheets have not been considered. It is found that for low to moderate load intensities, the Miura-ori core consistently outperforms the corresponding honeycomb core in terms of plastic dissipation (by as much as 68%) and facesheet centroidal deflections, and offers a rich design space to tailor its mechanical performance. However, the plastic energy dissipated in the core as a fraction of the total plastic energy dissipated in the structure is nearly the same for the Miura-ori and the honeycomb core sandwich plates of equal core areal density.

Experimental characterization of materials subjected to combined loading conditions

In real life experience, machine and structure elements are subjected to complex loading history. Combined loading testes facilitate the understanding of materials behavior subjected to multiaxial stress state. In this paper are presented experimental investigations used to evaluate the influence of an initial type of loading on material properties which will be subsequently tested through another load type. Initial tests are tension tests, by different elongations, and subsequent tests are torsion tests, until break. Circular cross section specimens will be used in these tests. Tension tests have been performed on a universal testing machine. Subsequently torsion tests have been conducted through an attachable device. It was found that the energy associated with plastic deformation obtained by subsequent torsional tests has the dominant influence on the material total plastic energy, although initial test was tension.

Seismic analysis of a tall metal wind turbine support tower with realistic geometric imperfections

SummaryThe global growth in wind energy suggests that wind farms will increasingly be deployed in seismically active regions, with large arrays of similarly designed structures potentially at risk of simultaneous failure under a major earthquake. Wind turbine support towers are often constructed as thin‐walled metal shell structures, well known for their imperfection sensitivity, and are susceptible to sudden buckling failure under compressive axial loading.This study presents a comprehensive analysis of the seismic response of a 1.5‐MW wind turbine steel support tower modelled as a near‐cylindrical shell structure with realistic axisymmetric weld depression imperfections. A selection of 20 representative earthquake ground motion records, 10 ‘near‐fault’ and 10 ‘far‐field’, was applied and the aggregate seismic response explored using lateral drifts and total plastic energy dissipation during the earthquake as structural demand parameters.The tower was found to exhibit high stiffness, although global collapse may occur soon after the elastic limit is exceeded through the development of a highly unstable plastic hinge under seismic excitations. Realistic imperfections were found to have a significant effect on the intensities of ground accelerations at which damage initiates and on the failure location, but only a small effect on the vibration properties and the response prior to damage. Including vertical accelerations similarly had a limited effect on the elastic response, but potentially shifts the location of the plastic hinge to a more slender and, therefore, weaker part of the tower. The aggregate response was found to be significantly more damaging under near‐fault earthquakes with pulse‐like effects and large vertical accelerations than far‐field earthquakes without these aspects. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Development and application of a simplified model for the design of a super-tall mega-braced frame-core tube building

Resilience-based earthquake design for next-generation super-tall buildings has become an important trend in earthquake engineering. Due to the complex structural system in super-tall buildings and the extreme computational workload produced when using refined finite element (FE) models to design such buildings, it is rather difficult to efficiently perform a comparison of different design schemes of super-tall buildings and to investigate the advantages and disadvantages of different designs. Here, a simplified nonlinear model is developed and applied to compare two design schemes (i.e., the fully braced scheme and half-braced scheme) of a super-tall mega-braced frame-core tube building, which is an actual engineering project with a total height of approximately 540m. The accuracy of the simplified model is validated through a comparison of the results of modal analyses, static analyses and dynamic time history analyses using the refined FE models. Subsequently, the plastic energy dissipation of different components and the distribution of the total plastic energy dissipation over the height of the two design schemes are compared using the proposed simplified model. The analyses indicate that the fully braced scheme is superior because of its more uniform energy distribution along the building height and the large amount of energy dissipated in the replaceable coupling beams, which enables rapid repair and re-occupancy after an earthquake. In contrast, the potential damage in the half-braced scheme is more concentrated and more severe, and the damage in the core tubes is difficult to repair after an earthquake.

Influence of plastic deformation on single-fiber push-out tests of carbon fiber reinforced epoxy resin

In our study we present a procedure to measure and analyze single-fiber push-out force–displacement curves on carbon fiber reinforced polymers using a cyclic loading–unloading scheme. The measured cyclic force–displacement curves allow an energy-based evaluation of the interfacial failure, taking into account elastic, plastic and other dissipative energy contributions. Experimental and modeling results demonstrate that a deviation of the push-out curve from linear behavior does not correspond to crack opening but to a plastic deformation of the matrix. Evaluating the plastic energy yields a linear increase of the total plastic energy after a certain indenter displacement. This linear increase is attributed to stable crack propagation. Back-extrapolation of the linear part to zero total plastic energy using a linear regression yields the initiation of crack growth. It is concluded that for ductile matrix materials like polymers, a reliable interpretation of push-out data has to take into account plastic material deformation.

Evaluation of fracture behavior of polyethylene/CaCO3 nanocomposite using essential work of fracture (EWF) approach

The fracture behavior of two series of polyethylene (PE) films, both the unreinforced and reinforced with different amounts of nanoscale calcium carbonate (CaCO3) particles was investigated in this research work by means of the essential work of fracture (EWF) approach under the loading condition of mode I. For this purpose, EWF test was conducted on deeply double edge notched tension (DDENT) specimens; and the essential and non-essential components of fracture work, were estimated using the plots representing the variation of the specific total work of fracture (wf) versus the ligament length of the specimen. The results showed that the crack resistance for the PE/CaCO3 nanocomposites was lower than that of the unreinforced PE, and for the case of nanocomposite samples, the total plastic energy absorbed during fracture increased with increasing CaCO3 content up to 2·5 wt-% and then decreased for nanocomposite samples containing 5 wt-%CaCO3. The plastic zone size decreased with increasing CaCO3 content, whereas the specific plastic work per unit volume increased with increasing weight percent CaCO3. The observed trends were rationalized using the fracture and deformation mechanisms of nanocomposites.

Development of a simplified model and seismic energy dissipation in a super-tall building

The seismic design of super-tall buildings has become an important research topic in earthquake engineering. Limited research has been conducted on the distribution of plastic energy dissipation among the different components of super-tall buildings when subjected to strong earthquakes. A simplified two-dimensional (2D) nonlinear model is developed based on the analysis of Shanghai Tower, an actual super-tall building with a total height of 632m. The accuracy of the simplified model is validated by comparing the results from modal analyses, and static and dynamic time-history analyses of the refined finite element model. Then, the proposed simplified model is used to determine the plastic energy dissipation of different components and the distribution of the total plastic energy dissipation over the height of the Shanghai Tower under different seismic intensities. The analysis indicates that the total plastic energy is mainly concentrated in the upper four Zones of the building and that the outrigger is the major plastic energy dissipation component in the Shanghai Tower.

FEM Evaluation of the Dissipated Energy in Front of a Crack Tip under 2D Mixed Mode Loading Condition

Numerical and experimental studies of fatigue crack growth under both pure mode I and combined mode I and II were performed. A CT-like specimen with an additional hole for mixed-mode loading made from an Al-alloy D16CT1 was used. A 2D elastic-plastic FEM simulation of a growing fatigue crack allowed us to determine the value of the total plastic energy dissipation per cycle throughout the cyclic (reversed) plastic zone directly from the elastic-plastic stress and strain fields in the vicinity of a crack tip. According to the Klingbeil's theory, the total plastic energy dissipated ahead of a crack tip is related to the fatigue crack growth rate. To review this theory, experimentally observed fatigue crack growth rates were correlated to the computed energies for both straight and slant crack growth. Moreover, a comparison according to the conventional concept of an equivalent stress intensity factor is presented.

Dynamic lateral crushing of empty and sandwich tubes

The dynamic lateral crushing behaviour of short empty and sandwich circular tubes is examined in this paper. Unlike the conventional impact method, the specimens were placed on the bottom platen of an Instron machine with a constant upwards velocity and then the tube collided with the fixed upper rigid platen. Load-deflection curves of empty tubes were first obtained and analysed. From the viewpoint of deformation modes and plastic strain energy absorbed by the tube quadrants around the proximal surface and distal surface, a critical velocity of impact is determined which corresponds to a mode change. A relationship is found to exist between the critical velocity and thickness-to-diameter ratio as well as the yield stress and density of the material. To understand the dynamic crushing behaviour of short aluminium foam-filled sandwich tubes by two rigid platens, further tests and corresponding finite element analysis were performed, respectively. Similar to the observations in the quasi-static tests, the mode of dynamic collapse is bending, with the formation of plastic bending zones accompanied with core crushing. Corresponding FE models for ABAQUS/Explicit were developed and validated against the experimental observations. Detailed deformation features and energy absorption characteristics during the crushing process were identified. It was found that increasing the compression velocity leads to an increase in the total internal plastic energy dissipation for both empty and sandwich tube. The propagation of plastic bending in the form of double-moving-hinges is the main mechanism of energy dissipation, as opposed to the low velocity impact which involves stationary plastic deformation zones.

Plastic dissipation energy at a bimaterial crack tip under cyclic loading

A theory has been introduced that relates the fatigue crack growth rate to the total plastic energy dissipated ahead of a crack tip under cyclic loading. Due to advances in computational efficiency, the reversed plastic zone can now be resolved adequately using the finite element method. The authors have previously published results for the plastic dissipation energy for cracks in homogeneous materials under mixed mode I and II loading. The purpose of the current research is to expand that set of results to include interface cracks in a general layered material. Applications of crack growth along a bimaterial interface include soldering, layered manufacturing, thermal spray coating, welding, brazing, or any other process that deposits a material onto a substrate where often it is more energetically favorable for a crack to grow along the interface than to propagate into either of the contiguous materials. Results of the plastic dissipation energy are obtained using 2-D elastic–plastic plane strain finite element analysis of a sharp crack along a bimaterial interface. Results show the plastic dissipation energy is proportional to the square of the strain energy release rate. By normalizing the results for the plastic dissipation with respect to the loads and material properties, it can be seen that the plastic dissipation energy has the greatest dependence on the mode mix ratio, followed by elastic and plastic property mismatches, respectively. Furthermore, a definition of the mode mix ratio based on dissipated energy is presented, which provides physical motivation for the characteristic length parameter needed to quantify the mode mix along a bimaterial interface.

A Dissipated Energy Approach to Fatigue Crack Growth in Ductile Solids and Layered Materials

This paper summarizes recent work on a new theory of fatigue crack growth in ductile solids based on the total plastic energy dissipation per cycle ahead of the crack. The fundamental hypothesis of the theory proposes a unified criterion for crack extension under monotonic and fatigue loading, so that the fatigue crack growth rate is given explicitly in terms of the total plastic dissipation per cycle and the monotonic fracture properties of the material. The total plastic dissipation per cycle is obtained by 2-D elastic-plastic finite element analysis of a stationary crack under constant amplitude loading, for both mode I (C(T)) and general mixed-mode I/II specimen geometries. Both elastic-perfectly plastic and bi-linear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over a wide range of relevant mechanical properties and mixed-mode loading conditions. Results are further extended to include fatigue delamination of layered material systems, where either discrete mismatches or a continuous grading of mechanical properties can exist across the interface.

굽힘이력을 고려한 딥드로잉공정의 유한요소역해석

This paper introduces a new approach to take account of bending history in finite element inverse analysis during sheet metal forming process. A modified membrane element was adopted for finite element inverse analysis so that bending-unbending energy was additionally imposed in the total plastic energy, predicting bending-unbending regions using the geometry of the final shape and tools. An algorithm was applied to a cylindrical cup deep drawing process. The blank shape and the distribution of the thickness strain were compared with those obtained from the incremental finite element analysis in order to evaluate the effect of the bending history. The algorithm reduced the difference between the results of the inverse analysis from those of the incremental analysis due to bending history. The analysis was also carried out with the variation of the thickness of the initial blank to investigate the effect of bending deformation. The results showed that the difference was remarkably reduced as the thickness of the initial blank increased. This indicates that the finite element inverse analysis cooperated with the suggested scheme is useful to obtain more accurate results, especially when bending effects are significant.

Mechanical properties and fracture behavior of injection and compression molded polypropylene/coal gangue powder composites with and without a polymeric coupling agent

Abstract Coal gangue powder filled polypropylene composites modified with maleic anhydride grafted polypropylene (PP-g-MA) were prepared. The mechanical properties and fracture behavior of the injection and compression molded composites were investigated, respectively. It was found that the yield strength measured on injection-molded dumbbell specimens and melt flow rate (MFR) varied slightly while the impact toughness measured on injection-molded rectangular specimens decreased with increasing particles loading. With proper amount of PP-g-MA incorporated, both the yield and impact strength of the composites were improved. The essential work of fracture (EWF) results measured on compression-molded thin sheets showed that the fracture toughness decreased considerably at low content of coal gangue (5 wt% in the composites) and then increased markedly with increasing fillers loading, back to appreciably lower than that of pure PP, while the total plastic energy showed gradual decrease due to the reduction of both shape factor and specific plastic work. For the modified composites containing about 5 wt% PP-g-MA, the fracture toughness was higher than that of the base PP/coal gangue (80/20) composites. It was attributed to the remarkable improvement of crack-resistance in necking and subsequent fracture stage. Though the total plastic energy values of the modified composites only showed slight fluctuation, the specific plastic work of fracture was improved markedly with respect to the composites only coal gangue filled into.