Elastic-perfectly Plastic Material Research Articles

A model for oblique impacts on material surfaces

Many practical situations of material damage, wear, and erosion involve collisions between small particles and surfaces at inclined angles. While there are many well-validated models of normal incidence impact situations, elastic-plastic models for oblique incidence impact events are lacking. Here the finite element method is used to predict the normal and tangential coefficient of restitution in oblique impacts for hard, elastic spheres impacting an elastic-perfectly plastic material surface. The proposed model covers various impact angles ranging from 0° to 45°, within a limiting impact velocity below which the effects of heating are negligible. The normal coefficient of restitution follows power-laws with respect to normalized values of the impact velocity. Interestingly, the tangential coefficient of restitution follows a linear relationship with impact velocity. Together, these results provide a semi-empirical set of equations predicting oblique impact rebounds (both velocity and trajectory) for a wide range of conditions and material properties, with which experimental results can be rapidly interpreted. Laser-Induced Particle Impact Test (LIPIT) data are also presented for aluminum particles impacting aluminum substrates, at impact angles of 25° and 40°; the results compare favorably with the model and validate the general use of such models for the analysis of experimental data.

On elastoplastic behavior of porous enamel–An indentation and numerical study

The micro/nano pores in natural mineralized tissues can, to a certain extent, affect their responses to mechanical loading but are generally ignored in existing indentation analysis. In this study, we first examined the void volume fraction of sound and caries lesion enamels through micro-computed tomography (micro-CT). A Berkovich indentation study was then carried out to characterize the effect of porous microstructure on the mechanical behavior of the human enamels. The indentation tests were also modeled using the nonlinear finite element analysis technique to simulate indentation load-displacement curves, which showed reasonable agreement with the experimental measurements. From the simulation results, the extent of densification in the plastic zone was identified and the corresponding stress and contact pressure evolutions were quantified. Further, a conventional elastic-perfectly plastic material model without considering micropores was also developed to investigate the compaction effect of the porous structure. The simulation results reveal that conventional elastic perfect-plastic constitutive models become less reliable to model the mechanical behavior of carious lesion enamel with increasing loss of mineral content as it underestimates the yield stress and plastic energy dissipation. This study divulges the importance of compaction of porous enamel structure beneath the indented area. Note that understanding the effect of porous microstructures on plastic behavior is vital as the involved inelastic deformation mechanism associated with irreversible processes, such as wear and localized microcracking, has a significant bearing on wear and fatigue behavior of enamel. Statement of significanceBased on micro-CT and nano-indentation characterization, a numerical model was developed aiming to precisely describe the deformation behavior of naturally porous enamel. Inelastic properties and energy dissipation characteristics of porous enamel were investigated in detail. This work demonstrated that the existence of micro-pores in White Spot Lesions (WSLs) contributes to mechanical stability, which can mitigate the reduction in Young's modulus and fracture toughness resulting from loss of mineral components. The knowledge gained from this study can be used to explain the mechanisms related to irreversible processes, such as contact induced cracking and wear, and strengthen understanding of the mechanical behavior of porous mineralized tissues.

Performance of Pile–Wall System Adjacent to Footings

The performance of a retaining wall is dependent on multiple factors including lateral earth pressure, which results from backfill soils and adjacent footings located behind a retaining wall. The prediction of a retaining wall’s performance in a footing–soil–wall system (FSPS) must incorporate the influences caused by the movement of a retaining wall. This study examines the performance of a retaining wall formed by driven, precast, concrete piles located adjacent to a concrete footing using two- and three-dimensional finite element analysis (2D and 3D FEA) by ANSYS 13.0 software. Both soil and concrete are assumed to behave as non-linear, elastic-perfectly plastic and rate-independent materials in compliance with the upper-bound model of Drucker–Prager yield criterion. Three backfill and foundation soils are considered: kaolin, silty clay, and kaolin–sand. Various conditions of soil type, footing shape ratio, pile width, and footing–pile distance through 180 FEA runs are investigated. The effects of 2D and 3D FEA on the behavior of the pile–wall system are compared. The lateral deflection and pressure distribution profiles along the pile–wall are studied and presented. Two empirical equations predicting lateral deflections at the pile toe and pile head and useful for pile structural design are developed under the ultimate pressure of the adjacent footing.

Numerical investigation of the influence of transverse welds on the strength of aluminum alloy I-shaped members – Columns

This paper presents a numerical investigation, using finite element analysis, of the effects of transverse welds on the structural behavior of aluminum-alloy compression members. A non-linear finite element (FE) model was developed, and validated using experimental tests, to simulate the behavior of 6061-T6 aluminum-alloy columns with an I-shaped AW6×4.03 section geometry. The FE model included different material properties for the heat-affected zone (HAZ) that occurs in the proximity of the weld and the remaining base material, and incorporated both geometric and material nonlinearities. A parametric study of 80 columns with and without transverse welds was conducted, which investigated ten unbraced lengths, three weld centerline locations along the member length, and two types of post-yield material stiffness models, including elastic-perfectly plastic and strain hardening materials. The FE results provide clear evidence of the significance of the HAZ strength reduction on the load carrying capacity of welded aluminum-alloy columns. Numerical results were compared with those obtained using the provisions within the Aluminum Association’s Specification for Aluminum Structures, and they were used to develop proposed modifications to these provisions, which can remove the degree conservatism observed. A similar study on beams is presented in a companion paper.

Second-order improved refined plastic hinge method with implementation of continuous strength method

Stainless steel, aluminium alloy, and cold-formed steel structures have been increasingly used as the main load-bearing components in civil engineering. However, owing to the rounded stress-strain response of the materials with significant strain hardening, the traditional plastic hinge model based on elastic-perfect plastic material response is not applicable, and the strength reduction of slender cross-sections by local buckling is also not considered. This paper proposed an improved refined plastic hinge method that can apply to different materials and fully consider the strain hardening and local buckling effect. A beam-column element was proposed, in which the second-order effect between axial load and bending moment was incorporated in the stiffness matrix formulation by using the approximate sixth-order polynomial function. The continuous strength method was introduced to the refined plastic hinge model to consider the strain hardening effect of non-slender and the local buckling effect of slender cross-sections by controlling the strength and deformability of the sections. Combining the elastic and plastic limit state criteria, the stiffness degradation function for SHS and RHS was obtained. The accuracy and efficiency of the proposed method were verified by the experimental results for stainless steel, aluminium alloy, and cold-formed steel columns of SHS and RHS under axial and eccentric compression. Finally, the proposed method was used for the design of frames for the materials, the results indicated that it was an effective tool that was ready for design practice.

PROGRESSIVE DAMAGE ANALYSIS OF STEEL-REINFORCED CONCRETE BEAMS USING HIGHER-ORDER 1D FINITE ELEMENTS

The present work investigates progressive damage in steel-reinforced concrete structures. An elastic-perfectly plastic material response is considered for the reinforcing steel constituent, while the smeared-crack approach is applied to model the nonlinear behavior of concrete. The analysis employs one-dimensional numerical models based on higher-order finite elements derived using the Carrera unified formulation (CUF). A set of numerical assessments is presented to study the mechanical response of a steel-reinforced notched concrete beam loaded in tension. The predictions are found to be in very good agreement with reference experimental observations, thereby validating the numerical approach. It is shown that CUF allows for the explicit representation of the constituents within the composite beam, resulting in accurate solutions in a computationally efficient manner.

System Reliability of a Semi-Submersible Drilling Rig Considering the Effects of the Main Nodes

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

Plasto-elastohydrodynamic lubrication of heterogeneous materials in impact motion

The analysis of plastic evolution and material inhomogeneity is required for an accurate description of lubrication under impact loading. This work develops a semi-analytical model for heterogeneous materials in impact motion under plasto-elastohydrodynamic lubrication (PEHL) with limited inlet oil. A plasticity loop is proposed to obtain the accumulative plastic strain iteratively based on the analysis of the stress state. The inhomogeneous inclusion within the materials is homogenized with unknown eigenstrains according to the equivalent inclusion method. The surface displacements induced by the plastic strains and eigenstrains are introduced into the gap between the contact bodies to update the lubrication film thickness until the convergence is achieved. The consideration of plastic strains and eigenstrains makes the model more realistic for PEHL under impact loading. The responses including the pressure, film thickness, starvation parameter, residual deformation, temperature, and subsurface elastoplastic fields during the impact–rebound process are discussed. After the model validation against the reference data, the effects of material inhomogeneity and strain hardening on the lubrication response, as well as the typical features of elastic perfectly-plastic materials, are investigated to provide guidance for material reliability analysis.

A Practical Analysis Framework for Assessment of Printed Circuit Heat Exchangers in High-Temperature Nuclear Service

Abstract Printed circuit heat exchangers (PCHEs) have high thermal efficiency because of the numerous minuscule channels. These minuscule channels result in a high thermal exchange area per unit volume, making PCHE a top contender for an intermediate heat exchanger (IHX) in high-temperature reactors. Thousands of minuscule channels make finite element analysis of the PCHE computationally infeasible. A two-dimensional analysis is usually performed for the PCHE core, which cannot simulate the local channel level responses reasonably because of the absence of global constraint influence. At present, there is no analysis technique available in the ASME Code or literature that is computationally efficient and suitable for engineers to estimate PCHE local responses. A novel but practical two-step analysis framework is proposed for performing PCHE analysis. In the first step, the channeled core is replaced by orthotropic solids with similar stiffness to simulate the global thermomechanical elastic responses of the PCHE. In the second step, local submodel analysis with detailed channel geometry and loading is performed using the elastic-perfectly plastic (EPP) material model. The proposed two-step analysis technique provides a unique capability to estimate the channel corner responses to be used for PCHE performance assessment. This study first developed a methodology for calculating the elastic orthotropic properties of the PCHE core. Next, the two-step analysis is performed for a realistic size PCHE core, and different issues observed in the results are scrutinized and resolved. Finally, a practical finite element analysis framework for PCHEs in high-temperature nuclear service is recommended.

Behaviour and design of welded stainless steel beams with compact sections under flexure and shear

The present study explores the flexural and shear behaviour of welded stainless steel beams with compact sections. A total of eleven specimens fabricated with austenitic, duplex and lean duplex stainless steel were tested under four-point and three-point loading strategies to obtain their failure modes, bearing capacities and ductility performance. Three-dimensional finite element models were then developed and validated with experimental results to numerically investigate the flexural and shear performance of the compact stainless steel beams. The obtained results from tests and numerical simulations were synthesised to comprehensively assess the applicability of existing codes of practice in terms of the bending, shear and moment-shear interaction design. It is found that the current design guidance for stainless steel beams adopts the elastic-perfectly plastic material model and conservatively predicted the bending, shear, as well as combined moment-shear strength. Accordingly, revised design methods considering the strain hardening effect of stainless steel beams were proposed.

Transient thermal fatigue crack propagation prediction in a gas turbine component

In this study, the thermal fatigue life of the detected crack on the edge of the pinhole of the hot gas path seal of a gas turbine engine under the elastic-perfectly plastic material behaviour is investigated. The component was made by a solid-solution IN625 Ni-based alloy. The non-destructive fluorescent penetration inspection (FPI) method was used to determine the crack position and direction. Stress distribution based on the thermal gradient of the seal was calculated by using a finite element method in accordace with the gas turbine work cycle. The thermal fatigue life was predicted using the ZENCRACK fracture mechanic code. The stress intensity factors (SIFs) were obtained using J-integral and CTOD methods; then, the Paris & NASGRO equations were used to predict fatigue life. Good agreement can be observed between the FE model results and the real cracked components, and the thermal fatigue life under the term of elastic-perfectly plastic material behaviour, in this case, was properly predicted.

Experimental and numerical investigations of aluminium-timber composite beams with bolted connections

This paper presents an investigation of aluminium-timber composite (ATC) beams subjected to bending. In the proposed ATC beam, a timber slab was connected to an aluminium beam using bolts. ATC beams are a relatively new civil engineering solution and they are still being developed. The authors conducted push-out tests of the bolted connections and bending tests of the ATC beams. The slip moduli k0.4 and k0.6, and the load-carrying capacity of the connection were determined experimentally. Furthermore, the short-term behaviour, load carrying-capacity, mode of failure, load-deflection and load-slip response of the ATC beams with bolted connections were investigated. What is more, the authors used a calculation procedure for steel-concrete composite elements to calculate the load-carrying capacity of the ATC beams. The results from the analytical estimations were compared with the results from the laboratory tests. In addition, two non-linear finite element models of the tested composite beam were developed and verified against the experimental results. In the three-dimensional finite element model, laminated veneer lumber was described as an elastic-perfectly plastic material, and, as a consequence, this model did not need many input parameters. In the two-dimensional finite element model, laminated veneer lumber was described as an orthotropic material and its failure was captured using the Hashin damage model. It was an advanced model which needed many input parameters. The numerical results were similar to the experimental results.

The elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect

Pressure vessel is a kind of special equipment which is involved in various industries. Once it is damaged, it will cause great loss to people’s life and property. The traditional elastic modulus reduction method for upper bound limit analysis of pressure vessels adopts the elastic-perfectly plastic material model. This method will result in waste of materials without considering the material strain hardening effect. So the material strain hardening effect is introduced into upper bound limit analysis. Firstly, the equivalent yield strength considering material strain hardening effect is established. Then, the formula of limit load multiplier which is expressed by the equivalent yield strength is derived based on the upper bound theorem. Combined with the strategy for elastic modulus adjustment, the elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect is constructed. The limitation of the elastic-perfectly plastic model for the upper bound analysis method is eliminated by the method proposed in this paper. The result calculated by this method is closer to the true limit load of pressure vessels.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Internal Pressure and Bending Moments

Abstract In this paper, the stress compensation method (SCM) adopting an elastic-perfectly plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely, the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle, and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analyzed. The present method is incorporated in a commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of piping elbows.

Effect of plastic deformation on the elastic stress field near a crack tip under small-scale yielding conditions: An extended Irwin's model

The effective stress intensity factor derived from Irwin’s model is greater than the linear elastic counterpart. This is in contradiction to the shielding effect of crack-tip plastic zone. Besides, the classic Irwin’s model underestimates the size of the crack-tip plastic zone compared with Dugdale’s model and FE analysis. In this paper, an extended Irwin’s model for elastic perfectly-plastic material under small-scale yielding conditions is developed through imposing static equivalence between the plasticity-affected stress field and linear elastic stress field in the plasticity-affected zone. The extended Irwin’s model is capable of quantifying the effect of the crack-tip plastic zone on the crack-tip elastic stress field. It reduces to the classic Irwin’s model in the limiting case. This new version of Irwin’s model provides new insights in elucidating the effect of the crack-tip plastic zone on fracture behavior.

Nonlinear deflection analysis of helical spring in elastic–perfect plastic material: Application to the plastic extension of piano wire spring

A mechanics-of-materials theory of the nonlinear deflection of helical spring within and beyond the elasticity limit was developed. The theory examined the nonlinearity due to the combined stresses of the torsion and bending of spring element by assuming the elastic–perfect plastic material obeying Tresca yield criterion. Free rotation of spring around the spring axis was taken into account. It was shown in experiment that the stress–strain curve of a piano wire was close to elastic–perfect plastic one. The outcome of the theory was compared with the experimental result of nonlinear load–deflection curves in plastically extended helical spring made of the piano wire.

Finite element analysis to determine the role of porosity in dynamic localization and fragmentation: Application to porous microstructures obtained from additively manufactured materials

In this paper, we have performed a microstructurally-informed finite element analysis on the effect of porosity on the formation of multiple necks and fragments in ductile thin rings subjected to dynamic expansion. For that purpose, we have characterized by X-ray tomography the porous microstructure of 4 different additively manufactured materials (aluminium alloy AlSi10Mg, stainless steel 316L, titanium alloy Ti6Al4V and Inconel 718L) with initial void volume fractions ranging from ≈0.0007% to ≈ 2%, and pore sizes varying between ≈ 6 μm and ≈110 μm. Three-dimensional analysis of the tomograms has revealed that the voids generally have nearly spherical shape and quite homogeneous spatial distribution in the bulk of the four materials tested. The pore size distributions quantified from the tomograms have been characterized using a Log-normal statistical function, which has been used in conjunction with a Force Biased Algorithm that replicates the experimentally observed random spatial distribution of the voids, to generate ring expansion finite element models in ABAQUS/Explicit (2016) which include actual porous microstructures representative of the materials tested. We have modeled the materials behavior using von Mises plasticity, and we have carried out finite element calculations for both elastic perfectly-plastic materials, and materials which show strain hardening, strain rate hardening and temperature softening effects. Moreover, we have assumed that fracture occurs when a critical value of effective plastic strain is reached. The finite element calculations have been performed for expansion velocities ranging from 50 m/s to 500 m/s. A key point of this investigation is that we have established individualized correlations between the main features of the porous microstructure (i.e. initial void volume fraction, average void size and maximum void size) and the number of necks and fragments formed in the calculations. In addition, we have brought out the effect of the porous microstrucure and inertia on the distributions of neck and fragment sizes. To the authors’ knowledge, this is the first paper ever considering actual porous microstructures to investigate the role of material defects in multiple localization and dynamic fragmentation of ductile metallic materials.

Theoretical Local Buckling Behavior of Thin-Walled UHPC Flanges Subjected to Pure Compressions.

To enhance structural performance of concrete and reduce its self-weight, ultra-high-performance concrete (UHPC) with superior structural performance has been developed. As UHPC members with 180 MPa or above of the compressive strength can be designed, a rational assessment of thin-walled UHPC structural member may be required to prevent unexpected buckling failure that has not been considered while designing conventional concrete members. In this study, theoretical local buckling behavior of the thin-walled UHPC flanges was investigated using geometrical and material nonlinear analysis with imperfections (GMNIA). For the failure criteria of UHPC, a concrete damaged plasticity (CDP) model was applied to the analysis. Additionally, an elastic-perfectly plastic material model for steel materials was considered as a reference to establish differences in local buckling behavior between the UHPC and steel flanges. Finite element approaches were compared and verified based on test data in the literature. Finally, this study offers several important findings on theoretical local buckling and local bending behavior of UHPC flanges. The inelastic local buckling behavior of UHPC flanges was mainly affected by crack propagation due to its low tensile strength. Based on this study, possibility of the local buckling of UHPC flanges was discussed.

Design of Initial Shotcrete Lining for a Mine Shaft Using Two-Dimensional Finite Element Models Considering Excavation Advance Rate

Shotcrete is widely used as a temporary support element in the construction of underground mine excavations, tunnels, and shafts. It is sprayed on the excavation walls to provide safe working conditions for mine personnel and equipment until the permanent support is installed. Therefore, the ability of the shotcrete liner to resists falls of ground is of paramount importance. In this paper, a two-dimensional finite element program is used to simulate a three-dimensional excavation advance and a shotcrete liner that is used as temporary support in a mine shaft. The mechanical properties of the shotcrete are determined based on existing empirical equations by considering the shaft advance rate. The study uses three methods to analyze the stability of the initial shotcrete liner. The first method pertains to the calculation of the load factor of safety based on the convergence confinement method. In the second method, the shotcrete liner is simulated using a structural element with elastic properties, and its stability is analyzed using support capacity diagrams. In the third method, a material model is used to explicitly simulate the shotcrete liner with elastic perfectly-plastic material behavior. This method allows for capturing the progressive yielding of the shotcrete liner during the excavation advance. The results of numerical simulations are then used to calculate a strain factor of safety for the shotcrete liner by dividing the lateral strain capacity of the shotcrete by the radial strain of the liner due to the shaft convergence. The study infers that the strain factor of safety for the 100 mm shotcrete liner is greater than unity although its load factor of safety is less than unity. Therefore, it is concluded that the 100 mm shotcrete liner can be used as temporary support until the installation of the final concrete liner.

Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method. Soil is modeled as a three-dimensional spatially varying medium, where its parameters (cohesion, friction angle, unit weight, etc.) are considered as fuzzy variables that maintain some membership functions. Soil is idealized as an elastic-perfectly plastic material obeying the Mohr-Coulomb failure criterion, where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing. The spatial variability of the soil is incorporated for both isotropic and anisotropic fields, which are determined by the values of scales of fluctuation in both the horizontal and vertical directions. A new parameter namely, limiting applied pressure at zero failure probability is proposed, and it indirectly predicts the failure probability of the footing. The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed, and it is observed that the effect is significant. Furthermore, the effect of the scale of fluctuation on the probability of failure is investigated, and the necessity for considering spatial variability in the reliability analysis is well proven.