Plastic Energy Dissipation Research Articles

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.

Shear strengthening of RC short columns with ECC jacket: Cyclic behavior tests

This study aims at developing an easy-to-apply strengthening method for reinforced concrete (RC) short columns by using Engineered cementitious composite (ECC), which is a high-performance composite material with tensile strain-hardening behavior and multiple cracking mechanism in tension. Seven identical RC short columns were prepared, and five of them were strengthened with ECC jackets or ferrocement jacket. The main experimental parameters involve the jacketing schemes and the axial load. The failure modes, hysteresis response, deformation capacity, stiffness degradation and energy dissipation capacity of the specimens were studied by the lateral cyclic loading tests. The tests results show that the ECC jacketed columns failed in ductile modes, and exhibited significant improvement in plastic deformation ability and energy dissipation capacity compared with the control specimens. At the ultimate displacement point, the increase of the drift ratio and cumulative energy dissipation of the ECC jacketed columns were 19–111% and 102–549%, respectively, compared with the corresponding control specimens. Under higher axial loads, the ECC jacketing was still certified to be effectively in enhancing the seismic behavior of the original columns. The shear deformation and the shear strength of the original RC columns were effectively improved by the external ECC jacket, and a prediction method for the shear strength of the ECC jacketed columns was given based on the current Chinese codes.

The stress ratio effect on plastic dissipation during fatigue crack growth

Plastic energy dissipation is inevitable during fatigue crack growth. There have been previous attempts reported in literature to correlate the plastic dissipated energy (dW/dN) to fatigue crack growth rate (da/dN). However, at a given dW/dN, the da/dN changes with the ratio of minimum and maximum loads, known as the stress ratio. This paper describes an experimental study carried out on 2024-T3 central crack tension specimens to quantify the relation between dW/dN and da/dN. By selecting different stress ratios in the individual tests, the experiments reveal the influence of the stress ratio on this relationship. It is evident that dW/dN has no unique relationship with da/dN valid for the tested stress ratios. Instead, the relationship for each stress ratio is different. This is illustrated with the value of plastic dissipation per unit of fatigue crack growth (dW/da), representing the effective resistance to the crack increment. This value is not a constant, but changes with the stress ratios and da/dN values. Hence the plastic energy dissipation cannot be used directly for predicting crack growth.

Effect of soil in controlling the seismic response of three-dimensional PBPD high-rise concrete structures

In the last decades, valuable results have been reported regarding conventional passive, active, semi-active, and hybrid structural control systems on two-dimensional and a few three-dimensional shear buildings. In this research, using a three-dimensional finite element model of high-rise concrete structures, designed by performance based plastic design method, it was attempted to construct a relatively close to reality model of concrete structures equipped with Tuned Mass Damper (TMD) by considering the effect of soil-structure interaction (SSI), torsion effect, hysteresis behavior and cracking effect of concrete. In contrast to previous studies which have focused mainly on linearly designed structures, in this study, using performance-based plastic design (PBPD) design approach, nonlinear behavior of the structures was considered from the beginning of the design stage. Inelastic time history analysis on a detailed model of twenty-story concrete structure was performed under a far-field ground motion record set. The seismic responses of the structure by considering SSI effect are studied by eight main objective functions that are related to the performance of the structure, containing: lateral displacement, acceleration, inter-story drift, plastic energy dissipation, shear force, number of plastic hinges, local plastic energy and rotation of plastic hinges. The tuning problem of TMD based on tuned mass spectra is set by considering five of the eight previously described functions. Results reveal that the structural damage distribution range is retracted and inter-story drift distribution in height of the structure is more uniform. It is strongly suggested to consider the effect of SSI in structural design and analysis.

The rock fragmentation mechanism and plastic energy dissipation analysis of rock indentation

Based on theories of rock mechanics, rock fragmentation, mechanics of elasto-plasticity, and energy dissipation etc., a method is presented for evaluating the rock fragmentation efficiency by using plastic energy dissipation ratio as an index. Using the presented method, the fragmentation efficiency of rocks with different strengths (corresponding to soft, intermediately hard and hard ones) under indentation is analyzed and compared. The theoretical and numerical simulation analyses are then combined with experimental results to systematically reveal the fragmentation mechanism of rocks under indentation of indenter. The results indicate that the fragmentation efficiency of rocks is higher when the plastic energy dissipation ratio is lower, and hence the drilling efficiency is higher. For the rocks with higher hardness and brittleness, the plastic energy dissipation ratio of the rocks at crush is lower. For rocks with lower hardness and brittleness (such as sandstone), most of the work done by the indenter to the rocks is transferred to the elastic and plastic energy of the rocks. However, most of such work is transferred to the elastic energy when the hardness and the brittleness of the rocks are higher. The plastic deformation is small and little energy is dissipated for brittle crush, and the elastic energy is mainly transferred to the kinetic energy of the rock fragment. The plastic energy ratio is proved to produce more accurate assessment on the fragmentation efficiency of rocks, and the presented method can provide a theoretical basis for the optimization of drill bit and selection of well drilling as well as for the selection of the rock fragmentation ways.

Revisiting size effect due to work of new surface formation in mechanical micro-machining using FEM

Finite element simulations of chip formation have been carried out for uncut chip thickness of 4 µm to 24 µm by incorporating Johnson-Cook fracture model to study the energy spent in new surface formation in metal cutting. The plastic dissipation and the damage dissipation energy of the chip formation are analyzed for the orthogonal machining simulations carried out. From the analysis it has been shown that the damage dissipation energy in machining is negligible compared to the plastic dissipation energy and it increases with the enhancement in the ratio of uncut chip thickness to edge radius of the cutting tool.

Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential

The strength and deformation behaviour of granular soil is strongly dependent on its stress state and loading history. Due to the change of soil state, the plastic flow direction and loading direction are usually non-coaxial and a plastic potential different from the plastic loading function is generally mandatory for capturing correctly volumetric deformation. For that, some state variables have been involved phenomenologically in plastic equations, bringing about some complexity in model formulations and physically meaninglessness of certain parameters. This paper presents a new approach to describing the state-dependent stress-dilatancy behaviour of granular soil using fractional order derivations. Unlike integer-order derivative in the classical plasticity theory, the fractional order derivative is defined in an integral form. Originally, we relate the description of soil state to the definition of the integral lower and upper limits respectively as the current and critical stress states. By performing a fractional order derivative of the plastic yield function, a state-dependent stress-dilatancy equation is set up without additional state variables. As the integration range increases, the flow direction deviates gradually from the loading direction. However, they coincide with each other when critical state is reached where the lower and upper limits merge. For validation, an elastoplastic constitutive model is developed by incorporating the fractional equation into the modified Cam-clay model. A series of drained and undrained triaxial test results for different granular soils are simulated, and the issue of plastic energy dissipation in each simulation is also addressed.

Energy dissipation analysis of elastic–plastic materials

Presented is an energy dissipation analysis framework for granular material that is based on thermodynamics. Theoretical formulations are derived from the second law of thermodynamics, in conjunction with a few plausible assumptions on energy transformation and dissipation. The role of plastic free energy is emphasized by a conceptual experiment showing its physical nature. Theoretical formulation is adapted in order to be applied in elastic–plastic finite element method (FEM) simulations. Developed methodology is verified through comparison of input work, stored energy, and energy dissipation of the system. Separation of plastic work into plastic free energy and energy dissipation removes a common mistake, made in a number of publications, where energy dissipation can attain negative values (energy production) which is impossible.

A Fully Coupled Thermomechanical Model of Friction Stir Welding (FSW) and Numerical Studies on Process Parameters of Lightweight Aluminum Alloy Joints

This paper presents a new thermomechanical model of friction stir welding which is capable of simulating the three major steps of friction stir welding (FSW) process, i.e., plunge, dwell, and travel stages. A rate-dependent Johnson–Cook constitutive model is chosen to capture elasto-plastic work deformations during FSW. Two different weld schedules (i.e., plunge rate, rotational speed, and weld speed) are validated by comparing simulated temperature profiles with experimental results. Based on this model, the influences of various welding parameters on temperatures and energy generation during the welding process are investigated. Numerical results show that maximum temperature in FSW process increases with the decrease in plunge rate, and the frictional energy increases almost linearly with respect to time for different rotational speeds. Furthermore, low rotational speeds cause inadequate temperature distribution due to low frictional and plastic dissipation energy which eventually results in weld defects. When both the weld speed and rotational speed are increased, the contribution of plastic dissipation energy increases significantly and improved weld quality can be expected.

Seismic behavior of lightweight aggregate concrete frame

A one-fifth scale, two-story, two-bay reinforced lightweight aggregate concrete (LWAC) frame subjected to quasi-static cyclical loading was analyzed to investigate the seismic behavior of this innovative system, primarily focusing on the failure modes, plastic hinge mechanism, load-deformation response, skeleton curves, stiffness degradation and energy dissipation capability. Overall, the test demonstrates that the LWAC frame meets the requirement of a “strong-column and weak-beam, strong-joint and weak-member” design criteria, exhibiting a mixed failure mechanisms consisting of both the beam hinge mechanism and column hinge mechanism. The former was the predominant failure mechanism and was fully developed after reaching the peak load point, while the latter was the inevitable result in the final failure of the LWAC frame. The fatter hysteretic loop and the displacement ductility factor Δu/Δy of 3.49 observed from LWAC frame indicate excellent energy dissipation and reliable displacement ductility capability, which are comparable to those of NWC frames. The test data observed in this study can provide theoretical guidance for the application of LWAC frames in seismic regions.

A micro-scale cutting model for UD CFRP composites with thermo-mechanical coupling

Cutting a unidirectional carbon fiber-reinforced polymer (UD CFRP) structure is the basic unit for CFRP machining, which is a complex thermal-mechanically coupled process. To reveal the deformation mechanism and predict cutting force in UD CFRP micro cutting, a micro-scale fracture model for UD CFRP cutting with thermal-mechanical coupling is demonstrated in this paper, which captures the failure modes for fibers, matrix and the interface based on a micro-level RVE using a relatively simple damage-based fracture method. The thermal-mechanical coupling model at the micro scale is developed on the basis of the plastic energy dissipation and frictional heating during cutting. Failure models for the fiber, matrix and interface region are applied depending on the material properties of each of these three phases. Numerical simulations based on the above model with different fiber orientations were performed to predict the deformation and forces of different components in UD CFRP. Cutting experiments with the same fiber orientations as considered in the simulations were carried out to validate the force and deformation results. The predicted force and deformation patterns match well with evidence from our experiments. In general, the cutting force is larger than the thrust force regardless of fiber orientation. The cutting force reaches a maximum as the fiber orientation approaches 90°, but thrust forces do not vary substantially across cases. When the fiber orientation is acute, the deformation of fibers is much smaller than when the cutting angle is obtuse. Surface roughness follows the same trend with cutting angle as fiber deformation.

Dependence of hardening and saturation stress in persistent slip bands on strain amplitude during cyclic fatigue loading

Cyclic loading of FCC single crystals leads to the formation of persistent slip bands (PSBs) over a wide range of applied strain amplitudes. The hardening and saturation stress associated with cyclic loading of Cu single crystals are reproduced with 3-D discrete dislocation dynamics simulations. Evolution of the dislocation microstructure in PSB channels and walls during cyclic loading is shown to explain key features of plastic deformation. Screw dislocation segments are found to deposit edge components near PSB channel walls resulting in the nucleation of half-loops that expand into neighbouring channels. The saturation stress is found to be 34 MPa at an applied strain amplitude, , within the range of experimental observations. It is shown that once PSBs are formed, subsequent cycling at lower strain amplitudes does not lead to their elimination, but the cyclic stress–strain behaviour is modified. At lower values of of previously formed PSBs, the saturation stress is found to decrease to 24 MPa at . Plastic energy dissipation in hysteresis loops is also significantly reduced but not removed. However, some reverse plasticity is shown to take place upon unloading at low values of , and is a direct result of strain recovery of loops that expand into neighbouring channels during the loading phase.

THE MODIFIED MOHR – COULOMB AND DRUCKER – PRAGER MODELS. INFLUENCE OF ECCENTRICITY ON HYSTERESIS LOOP AND ENERGY LOSS

The eccentricity parameters appearing in the modified Mohr-Coulomb and Drucker-Prager models are studied. The influence of the eccentricity on shape and size of the hysteretic loop and plastic dissipation energy are analyzed. Both kinematic and force loadings are considered.

Passive Control Systems for the Blast Enhancement of Glazing Curtain Walls Under Explosive Loads

Glass curtain walls are used in modern buildings as envelopes for wide surfaces due to a multitude of aspects. In glass curtain walls, tensile brittle panels are connected - through mechanical or adhesive joints - with steel frameworks or aluminum bracing systems, and due to the interaction of several structural components, the behaviour of the so assembled system is complex to predict, especially under exceptional loading conditions such as explosive events. In the paper, glazing curtain walls are investigated by means of Finite-Element (FE) numerical simulations, under the effect of air blast pressures of variable intensity. Their typical dynamic behaviour and criticalities under high-strain impact loads are first analyzed. By means of extended nonlinear dynamic FE parametric studies, innovative devices are applied to traditional curtain walls, at their support points, in order to improve their expected dynamic response. Two possible solutions, namely consisting of viscoelastic (VE) or elasto-plastic (PL) dampers, are proposed as passive control systems for the mitigation of maximum effects in the façade components deriving from the incoming blast pressures. As shown, although characterized by specific intrinsic mechanical behaviours, either VE or PL dampers can offer beneficial structural effects. In the first case, major advantages for the façade components derive from the additional flexibility and damping capacities of VE devices. In the latter case, PL dampers introduce additional plastic energy dissipation in the traditional curtain wall assembly, hence allowing preventing severe damage in the glazing components. It is thus expected that the current outcomes could represent a valid background for further experimental validation as well as detailed assessment and optimization of the proposed design concept.

Determination of earthquake safety of RC frame structures using an energy-based approach

An energy-based approach for determining earthquake safety of reinforced concrete frame structures is presented. The developed approach is based on comparison of plastic energy capacities of the structures with plastic energy demands obtained for selected earthquake records. Plastic energy capacities of the selected reinforced concrete frames are determined graphically by analyzing plastic hinge regions with the developed equations. Seven earthquake records are chosen to perform the nonlinear time history analyses. Earthquake plastic energy demands are determined from nonlinear time history analyses and hysteretic behavior of earthquakes is converted to monotonic behavior by using nonlinear moment-rotation relations of plastic hinges and plastic axial deformations in columns. Earthquake safety of selected reinforced concrete frames is assessed by using plastic energy capacity graphs and earthquake plastic energy demands. The plastic energy dissipation capacities of the frame structures are examined whether these capacities can withstand the plastic energy demands for selected earthquakes or not. The displacements correspond to the mean plastic energy demands are obtained quite close to the displacements determined by using the procedures given in different seismic design codes.

A pseudo-coupled analytic fluid-structure interaction method for underwater implosion of cylindrical shells

Underwater implosion, the rapid collapse of a structure caused by hydrostatic pressure, is a fully coupled, highly dynamic and nonlinear fluid-structure interaction (FSI) problem. The primary motivation behind studying implosion is the short-duration, high-pressure pulse generated in the surrounding water. This paper presents a simplified analytic method to estimate the energy in the pressure pulse, based on potential flow theory. The method accounts for the varying fluid pressure and accompanying FSI. The focus is on long, thin, unstiffened metallic cylindrical shells that collapse in mode 2. The implosion pulse energy is shown to be equal to the maximum system kinetic energy developed during collapse. The kinetic energy is calculated using an energy balance approach and analytic solutions for plastic energy dissipation and energy required to compress the internal air. The time-varying fluid pressure, and subsequently the work done by the fluid on the cylinder, is found using a novel explicit time-stepping methodology. The result is a pseudo-coupled analytic solution for the fluid pressure time history and implosion pulse energy. Solutions for pulse energy agree with RANS numerical simulations within 5%.

Electrical resistivity and creep behavior of hypoeutectic Sn–0.5Cu based solders for flip chip technology

For flip-chip applications, there is a need to develop lead-free solders with low cost and suitable soldering characteristics, as a replacement for the traditional Sn–Pb solder. In this work, we investigate the effect of adding small amount of Zn and Bi elements into hypoeutectic Sn–0.5Cu Pb-free solders, which allows modification of their microstructure and improves their physical properties. Tensile creep testing was performed and a Garofalo hyperbolic-sine power-law relationship was created from experimental data to predict creep deformation mechanism as a function of stress and temperature. Results show that the favorable creep resistance of Sn–2.0Zn–0.5Cu solders was reduced considerably with Zn addition, having ten times higher creep rate at room temperature than Sn–0.5Cu. Of particular note is the observation of plastic energy dissipation ability of Zn-containing solder joints at room temperature. In contrast, with Bi addition, the number of fine Bi particles increased and the coarse Cu6Sn5 intermetallic compounds (IMCs) are emerged, which enhanced significantly the creep resistance and fracture time of Sn–2.0Bi–0.5Cu solder. The resistivity values of Sn–0.5Cu, Sn–2.0Zn–0.5Cu and Sn–2.0Bi–0.5Cu solders were on the order of 28–48% lower than that of Sn–40Pb solder (17.0 μΩ cm).

Experimental research of replaceable Q345GJ steel shear links considering cyclic buckling and plastic overstrength

Coupon tests confirmed that Q345GJ steel had good ductility and rarely cyclic hardening. Therefore, 12 shear links using such steel were designed and tested. The explored parameters included web aspect ratio, flange width-thickness ratio, the equivalent link length coefficient eVp/Mp, stiffener spacing and thickness, hysteretic loadcase, and welding details. Discussions and analysis on the failure mode, the hysteretic behavior of shear load and displacement angle, the strain distribution, the bearing capacity and stiffness, the plastic overstrength, the deformation and energy dissipation capacity, were also conducted. The shear links had satisfactory energy dissipation capacity under multiple hysteretic loading with almost no cyclic hardening. Web aspect ratio and stiffener spacing had determinate influence on cyclic web buckling, as well as the ultimate deformation capacity. Yet, more intensive stiffener spacing was prone to result in more serious stress concentration in the web, and caused web fracture. Also, smaller coefficient eVp/Mp was harmful to the ultimate deformation capacity. The ultimate plastic overstrength Vu/Vp of the shear links was about 1.35 to 1.5, influenced by web aspect ratio, the coefficient eVp/Mp, and stiffener spacing. To avoid cyclic flange fracture, the coefficient eVp/Mp was also suggested be within 1.7.

Effect of using linear multiple tuned mass dampers on concrete structures with hysteresis behavior

In this research, performance multiple tuned mass dampers (MTMDs) with consideration of the hysteresis behavior and cracking effect of concrete structures under near field earthquake records with high intensity are carefully investigated. Inelastic analysis was performed by employing Takeda hysteresis model, on mathematical model in a state-space form using a program written in Matlab. In the first step, optimum parameter of TMD for single story frame equipped by spectrum TMD is obtained. In the second step, the best place of MTMDs for ten-story frame from two aspects, plastic energy dissipation and maximum lateral displacement, has been studied. And in the last step, the effect of building height in performance of MTMDs is investigated by analysis of a twenty-story resistance frame. Results show that entering the structure into the field of nonlinear behavior and increasing structure height, TMD does not affect the linear behavior of structure. On the other hand, by using the TMD better energy distribution is formed in structure and maximum energy of plastic hinges is reduced. To achieve the best place TMD should multiple target criteria parameters and all potential placement of MTMD simultaneously applied.

Study on the deformation behavior of β phase in Ti–10V–2Fe–3Al alloy by micro-indentation

The Ti–10V–2Fe–3Al alloy composed of β phases was varied by the β-solution treatment. In order to characterize the indentation deformation behavior of β phase, the micro-indentation tests were conducted in the indenter load ranging from 50 mN to 450 mN and the loading rates range from 4.84 mN/s to 19.36 mN/s at ambient temperature. The influences of β-solution treatment temperature, loading rate and indenter load on the micromechanics properties were investigated. The results showed that both the micro-hardness and Young's modulus of β phase declined drastically with the increase of indenter load, while remained the same level when the indenter load was above 300 mN. It was observed that the specimen under β-solution treatment of 820 °C and the loading rate of 19.36 mN/s possessed a higher micro-hardness and Young's modulus than that of others. The plastic energy dissipation, which was significantly influenced by the β-solution treatment temperature and loading rate, increased with the growth of indenter load exerted on the specimens and can be expressed in a power-law function of indenter load for β phase. In addition, the average plastic energy dissipation density in the micro-indentation was a linear function of the micro-hardness and its decrease with indenter load is attributed to the decline of geometrically necessary dislocations (GNDs).