Total Plastic Work Research Articles

A constitutive model for the gravelly soil-structure interface considering particle breakage and fabric change

The isolated foundation with cushions is gaining popularity as a viable option for building bridges in active seismic zones due to its exceptional seismic isolation performance. However, the efficacy of this foundation relies heavily on the interactions within the cushion layer and between the caisson foundation and the cushion layer. The cushion layer, composed of 0.5 m thick crushed aggregate layer and 2.5 m thick pebble gravel, is susceptible to particle breakage and fabric change, which can significantly impact the overall behavior of the foundation. To better characterize the mechanical behavior of the cushion layer and the interface between aggregates and the structure, a new elastoplastic constitutive model is proposed in this study. The current model is built based on an existing constitutive model, Saberi’s model (Model-S). Two parameters are introduced, including a particle breakage coefficient, B10, calculated by total plastic work, and a fabric-dilatancy variable, z, to determine the interfacial dilatancy variation. The current model consists of 13 parameters in total. Comparison evident that the current interfacial constitutive model can better simulate the change of the physical state and asymmetrical response in the stress-displacement relationship due to symmetrical loading in different directions.

Adiabatic self-heating determination for Ti6Al4V at different temperatures

Nowadays, numerical models are one of the most widely used techniques to predict material performance subjected to different manufacturing processes. However, to obtain accurate predictions, these models require reliable input data from thermomechanical tests. Nevertheless, during the test performance the material is self-heated due to a phenomenon known as adiabatic self-heating. Despite the proven relevance of a proper characterization, adiabatic self-heating is not properly taken into account during thermomechanical tests. In addition, in the literature, two different definitions were found under the umbrella of adiabatic-self heating. On the one hand, it could be defined as the ratio between the heat spent to heat the sample to the plastic work, value commonly taken as 0.9. On the other hand, many authors define the adiabatic heating as the ratio between the heat experimentally measured to the total plastic work. This second approach, although seems easier, is neglecting heat losses. These two different approaches could lead to misunderstandings once this parameter is implemented in the models. This paper aims to clarify this issue. Moreover, the techniques found in literature aiming to measure this parameter are usually based on 2D approaches at low temperatures. In this paper, a 3D methodology to measure adiabatic self-heating is presented which considers all possible heat losses (conduction, convection, radiation and mass flux) through infrared measurements and Digital Image Correlation (DIC) technique. The adiabatic self-heating was measured for a widely used alloy (Ti6Al4V) obtaining promising results.

Effects of Microsphere Size on the Mechanical Properties of Photonic Crystals

Photonic crystal (PC) thin films that are self-assembled from different-sized silica microspheres were prepared for studying mechanical properties via nanoindentation at the submicron scale. We found that the silica photonic crystals (PCs) possessed a face-centered cubic (FCC) microstructure and their elastic modulus and hardness were in the range of ~1.81–4.92 GPa and 0.008–0.033 GPa, respectively. The calculated results proved that there were size-dependent properties in the silica PCs, in that the elastic modulus and hardness increased as the diameter decreased from 538 nm to 326 nm. After studying the total work and plastic work in the progressive deformation of silica PCs during the nanoindentation tests, we developed a two-stage deformation model to explain how the microsphere size affects the mechanical properties of PC thin films. The phenomenon of “smaller is stronger” is mainly due to the energy consumption, which combines the effects of microstructure collapse, microsphere slide, and reduced porosity during the whole loading and unloading process. In addition, the results of numerical simulation matched the experimental data and reflected the energy change rules of PCs during the indentation process. Furthermore, the study affords useful guidance for constructing high-performance films with proper design and potential application in next-generation PC materials.

Methods for determining the plastic work in bending and impact of selected factors on its value

The paper describes various methods which may be used in determining the deformation energy in the plastic region of bent wood. The present work focuses on various definitions of the plastic work of wood as well as the influence of various factors on its value. Approximated plastic work and total plastic work were determined for beech (Fagus Sylvatica L.) and aspen (Populus Tremula L.) wood. We took into consideration the following factors: wood species (WS) (Fagus Sylvatica L. and Populus Tremula L.), material thickness (MT) (4, 6, 10, and 18 mm), degree of densification (DOD) (10% and 20% of the original thickness), and the number of stressing cycles (NC) (0 versus 10,000). The study brings a new quantitative expression of an approximated plastic work “AW”, and total plastic work “BW” and the values of approximation error “ΔW”, which are made due the applied approximation.

Cavitation resistance of epoxy-based multilayer coatings: Surface damage and crack growth kinetics during the incubation stage

Four epoxy-based multilayer coating systems, with thicknesses of 380±20μm, 650±10μm, 720±30μm and 920±20μm, were applied manually onto stainless steel samples and subjected to vibratory cavitation tests according to ASTM G32-09 standard. In order to correlate the cavitation resistance of the coating systems with some of their mechanical properties, instrumented micro indentation tests were performed to determine hardness, resilience, total plastic work, among others, as a function of the thickness of the coatings. Examination of the surfaces by Scanning Electron Microscopy (SEM) revealed that the surface damage in all the coatings was caused by incubation and growth of cracks. Statistical analysis of crack growth data allowed determining a behavior law characteristic for each coating system, which was adjusted with proper parameters related to the mechanical properties measured by micro indentation. In particular, a good correlation was obtained among cavitation resistance, coating thickness and hardness-to-Young modulus ratio H/E.

Coupled hydro-mechanical fault reactivation analysis incorporating evidence theory for uncertainty quantification

The injection of water (or CO2) at high pressure is a common practice to enhance oil production. A crucial component of this activity is the estimation of the maximum pressure at which the fluids can be injected without inducing the reactivation of pre-existing faults that may exist in the formation. The damage zones typically formed around the geological faults are highly heterogeneous. The materials involved in the damage zones are characterized by the huge variation of their properties and high uncertainties associated with them. To estimate the maximum allowable injection pressure this paper presents a novel approach based on: a coupled hydro-mechanical formulation (for the numerical analyses); a criterion based on the total plastic work (for the fault reactivation); and the evidence theory (for uncertainty quantification). A case study based on information gathered from an actual field is presented to illustrate the capabilities of the proposed framework.

Effect of Moisture Content on the Viscoelastic Properties of Individual Wheat Kernels Evaluated by the Uniaxial Compression Test Under Small Strain

ABSTRACTWheat product quality is related to its physicochemical properties and to the viscoelastic properties of the kernel. The aim of this work was to evaluate the viscoelastic properties of individual wheat kernels using the uniaxial compression test under small strain (3%) to create experimental conditions that allow the use of the elasticity theory to explain the wheat kernel viscoelasticity and its relationships to physicochemical characteristics, such as weight tests, size, and ash and protein contents. The following viscoelastic properties of the kernels of hard and soft wheat cultivars at two different moisture contents (original and tempered at 15%) were evaluated: total work (Wt), elastic work (We), plastic work (Wp), and modulus of elasticity (E). There was a significant decrease in Wt as the moisture content increased. In the soft wheat Saturno, Wt decreased 80% (from 0.217 to 0.044 N·mm) as the moisture content increased. Individual wheat kernels at their original moisture content showed higher We than under the tempered condition. Wp increased as the moisture content increased. E decreased as the moisture content increased. The soft wheat Saturno showed the highest decline (54.9%) in E (from 14.18 to 6.39 MPa) as the moisture content increased. There were significant negative relationships between the viscoelastic properties and the 1,000‐kernel weight and kernel thickness. The uniaxial compression test under small strain can be applied to evaluate the viscoelastic properties of individual wheat kernels from different classes and cultivars.

Ductility of 304 stainless steel under pulsed uniaxial loading

The enhanced ductility that 304 stainless steel is exhibiting under pulsed loading (Zhang and Yuan, 2009) is investigated here using a combination of experiments and analysis. The simplest loading case, i.e., uniaxial tension, was selected to avoid the complicating effects of multiaxial stress states and/or contact and friction with a rigid die. Three types of tensile tests were performed: monotonic, pulsed and hold. For a range of strain rates, the pulsed and the hold tests exhibited different elongation-to-fracture from the monotonic tests. Digital image correlation and infrared thermography were employed to further probe this behavior. It was discovered that since the pulsed tests lasted longer than the corresponding monotonic ones (i.e., those with the same loading speed) but the total plastic work expended was comparable, milder deformation-induced heating developed in the pulsed tests. Since the resulting temperature gradients act as imperfections that trigger the localization of deformation, the enhanced elongation-to-fracture in the pulsed tests was attributed to the milder gradients that developed. Subsequently, a special isothermal tension test was used to de-couple the mechanical from the thermal behavior of the material and was repeated at various strain rates and temperatures. The material properties determined from this test were used as input to coupled, thermomechanical finite element simulations of the experiments. Despite numerous simplifications, such as constant thermal properties with temperature, the simulations captured the essential physics of the problem and yielded very close predictions of the elongation-to-fracture observed in the experiments.

Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity

The bulk metal forming processes were simulated by using a one-step finite element (FE) approach based on deformation theory of plasticity, which enables rapid prediction of final workpiece configurations and stress/strain distributions. This approach was implemented to minimize the approximated plastic potential energy derived from the total plastic work and the equivalent external work in static equilibrium, for incompressibly rigid-plastic materials, by FE calculation based on the extremum work principle. The one-step forward simulations of compression and rolling processes were presented as examples, and the results were compared with those obtained by classical incremental FE simulation to verify the feasibility and validity of the proposed method.

Simulation of wheel impact test using finite element method

In order to achieve better quality, the wheel design and manufacturing use a number of wheel tests to ensure that the wheel meets the safety requirements. The impact performance of wheel is a major concern of new design wheel. The wheel impact test is intended to evaluate the impact performance of wheel, that the striker is dropped from a specified height above the tire–wheel assembly. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test. The wheel modeled as an elastic–plastic body is mounted at an incline of 13° to horizontal, and the striker is prescribed an initial velocity to simulate a drop height. The total plastic work concept of ductile fracture mechanics is used to predict the impact failure of wheel. Three-dimensional finite element method is employed to obtain the strain energy density of wheel at impact, and the critical strain energy density is based on the total plastic work of wheel material. Compared with actual tests, the finite element results show the total plastic work approach can be used to predict the wheel fracture during the impact test.

Finite element modeling of elasto-plastic contact between rough surfaces

This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an elasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elasto-plastic response of the material is described by a J 2 isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress σ y decreases, scaling as a power of σ y over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses.

On the relationship between stress–dilatancy, anisotropy, and plastic dissipation for granular materials

Techniques of modern thermomechanics are used to analyse the stress–dilatancy relation for shear deformations of frictional, granular materials. Central to this approach is the recognition that in general, deformations of granular materials can involve stored plastic work. It is recognised that in shear deformations, where the shape of the grains induces the dilatancy, the confining pressure is a constraint and dissipates no energy. Nevertheless it is shown that, in such a shear deformation, the total plastic work rate is equal to the rate of energy dissipation, and that this is given by Thurairajah's classical observations. It is further shown that anisotropy is necessarily induced, and that the stress–dilatancy relation is given by Taylor's well-known formula. It is also demonstrated that the extant procedure for deducing yield conditions and flow rules from specified dissipation functions is invalid.

Simulation of the orientation dependence of stored energy during rolling deformation of low carbon steels

In order to furnish some input data to Monte Carlo codes developed for the simulation of static recrystallization in low carbon steels, two polycrystalline models are used in conjunction with four different hardening laws to estimate numerically the stored energy within individual grains, which is due to the increase in dislocation density during rolling. Three quantities are calculated as a function of final orientation, which are believed to be good estimates of this energy: these are the average dislocation density (linked to the square of an average reference shear stress), the total plastic work and the final plastic work rate. It is thus found that the three selected parameters present the same variation trends for a given model, whatever the hardening law. However, the Taylor and VPSC models lead to opposite conclusions: at the end of the simulated rolling process, the (respectively ) orientations are the hardest (respectively softest) with the Taylor model and the softest (respectively hardest) with the VPSC one; thus, the present data cannot be used in the present state to perform recrystallization simulations but may be used to validate the different polycrystalline models, since they are more sensitive to the interaction law than the texture evolution or macroscopic response.

Cyclic Viscoplastic Constitutive Equations, Part II: Stored Energy—Comparison Between Models and Experiments

The cyclic constitutive equations developed at ONERA have been incorporated into a general thermodynamic framework (Part I). In the present part, systematic comparisons are given between the model predictions and experimental data for both the mechanical response and the energy stored in the material. The models are specified in their rate—independent-form and closed-form solutions are obtained for tension-compression monotonic and cyclic conditions. By superposing one or two nonlinear kinematic rules and one isotropic hardening equation, the available experimental data are fairly well reproduced. In particular it is possible to describe the low values of stored energy, the decrease of the ratio of stored energy to total plastic work as a function of strain, and the partial release of stored energy at every half cycle of a cyclic loading.

Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation

Cyclic viscoplastic constitutive equations are increasingly used for the inelastic analysis of structures under severe thermomechanical conditions. The purpose of the paper is to show how the classical models can be modified in order to follow the general principles of thermodynamics with internal variables. Using the restrictive framework of standard generalized materials, the state variables associated to various kinds of kinematic and isotropic hardening are selected. The evolution equations for these internal variables are then formulated in a slightly less restrictive form. For each hardening process, the separation of the total plastic work into energy dissipated as heat and energy stored in the material is discussed in detail.

Active Earth Pressure Founded on Displacement Field

This paper develops a numerical procedure for calculating the active earth pressure against a retaining wall, which allows consideration of the movements of retaining wall and backfill soil. The limit equilibrium analysis, which has been the principal concept for designing geotechnical structures, has the deficiency that the analysis cannot necessarily consider soil-structure displacements at failure. The design technique for overcoming this deficiency may have to provide a definite collapse mode like a potential slip surface, because the stability analysis subjected to a final collapse mode will keep on playing a major role in engineering practice. The proposed procedure assumes 1) Mohr-Coulomb and Coulomb yield criteria respective for backfill soil and friction interface, 2) fundamental non-associated flow rules related to the yield criteria, and 3) elastic-perfectly plastic stress-strain relationship. The procedure uses the initial stress method in FEM, and a set of yield stresses in each finite element is determined so as to minimize the total plastic work, because the procedure tries to solve the active earth pressure problem without considering the loading history. By use of these assumptions, the procedure enables to produce a definite failure region like a collapse mode supposed in the limit equilibrium analysis. The problem formulation based on these assumptions discloses an important property of Coulomb friction interface that the stresses on the interface are rather insensitive to varying some factors when keeping the initial stresses constant. The validity of the proposed procedure is verified by applying the procedure to several hypothetical case studies, where comparisons are made with Coulomb method, and where many important aspects in the earth pressure problem are clarified.

A failure criterion for beams under impulsive loading

An energy criterion is suggested in this paper for predicting the inelastic failure modes of beams subjected to large dynamic loadings. The experimental results of Menkes and Opat on the failure of impulsively loaded beams may be interpreted to show that the length of a plastic hinge varies with the ratio of the plastic shear work to the total plastic work dissipated at a hard point or other region of intense localized plastic strain. The variation of this parameter is obtained from a theoretical analysis for the impulsive loading of a rigid, perfectly plastic clamped beam with plastic yielding governed by an interaction yield surface which combines the influences of bending, shear and membrane tension. The Cowper-Symonds dynamic constitutive relation is used to study the influence of material strain rate sensitivity.

Fatigue crack speed of materials with linear hardening

This investigation deals with the steady propagation of a fatigue crack in a thin plate, subjected to cyclic tensile remote loading. The problem is analyzed according to a Dugdale model of the fracture process zone. Material stretches periodically in the fracture process zone prior to its failure. The effect of crack closure is considered in the analysis. Unlike previous work, our study is based on a constitutive relation of the linear work-hardening for material in the fracture process zone. The criterion of total accumulative plastic work is adopted for determination of the growth rate of the fatigue crack. Theoretical results thus obtained are compared with experimental data.

Dual potentials and extremum work principles in single crystal plasticity

T his paper is concerned with modelling the rigid plastic deformation of a rate insensitive single crystal by crystallographic slip when subjected to mixed boundary conditions. By introducing a flow polyhedron as the dual surface of the classical yield polyhedron, new extremum work principles are derived, which enable the unknown stress and strain rate components to be evaluated. In particular, it is shown that by using a suitable mixture of the yield and flow polyhedra as a function of the boundary conditions, the total internal plastic work rate per unit volume is a minimum for the actual solution. Alternatively the total external plastic work is maximal.

Steady fatigue crack growth under tensile load

Fatigue crack speed is analysed based on the criterion of total accumulative plastic work. Closure of crack surface during unloading is included in the study. Fatigue crack speed per cycle of loading is found to be dependent on two parameters k m = K max/K f and R = K min/K max where K f is the fatigue Fracture toughness defined by the condition that dl/dN approaches infinity as k m approaches unity. Our theoretical fatigue crack speeds are compared with experimental data.