Plastic Material Behavior Research Articles

The influences of temperature on the macroscopic elastoplastic behaviors of heterogeneous materials

The microstructure of heterogeneous materials affects importantly their macroscopic mechanical behavior. For a thermal-mechanical coupling problem, the temperature also has a significant effect. Firstly, the effect of temperature on the elastic behavior of heterogeneous material has been investigated in the present work with the consideration of its microstructure. Then, an explicit expression of the macroscopic yield criterion has been derived for the plastic behavior of porous material by using the homogenization approach. This yield criterion takes into account explicitly and simultaneously the influence of porosity and the effect of temperature on its overall mechanical behavior. To consider the pressure sensitivity of the matrix, the Drucker–Prager type criterion is adopted at the microscopic scale. After that, the heterogeneous material with a matrix reinforced by rigid inclusions has been studied. The microstructure information, such as the inclusion content, matrix property and the temperature have been considered explicitly in the obtained yield function. The influences of temperature and the confining pressure on the macroscopic material strength are captured by the obtained criterion. Then, the obtained result is applied to describe the temperature-dependent mechanical behaviors of sandstone.

Through-thickness Work Hardening Variation in Thick High Strength Steel Plates: A Novel Inverse Characterization Method

Due to the production process, thick high strength steel plates potentially exhibit inhomogeneous plastic material behavior through the thickness. For example, the initial yield stress and work hardening behavior might vary through the plate thickness. In order to establish a reliable plasticity model that can be used in finite element simulations to optimize forming processes or to investigate the structural integrity of large structures, this material behavior needs to be characterized. A straightforward characterization method consists of slicing the thick high strength steel plate and conducting standard tensile tests. However, this approach comes with a large experimental effort. A novel specimen is proposed enabling to inversely identify the work hardening behavior at distinct locations through the thickness of a thick steel plate. To this end, a tensile specimen with circular pockets at different depths is used. The strain fields within the pockets are captured using digital image correlation (DIC). finite element model updating (FEMU) is used to inversely identify a predefined strain hardening law for each pocket. First, the procedure is optimized and numerically verified using virtual experiments generated by a finite element model with a known variation of the work hardening behavior. Finally, the procedure is experimentally validated by characterizing the strain hardening behavior of a 10 mm thick S690QL grade.

Identification of hardening and fracture behaviors of titanium alloy by a hybrid digital image correlation and finite element method

The reliable identification of deformation and fracture behaviors of titanium alloys is essential for accurate numerical simulation in sheet metal forming, cutting process and crash. In this study, an inverse method is proposed to identify both strain hardening and fracture behavior of titanium alloys by a hybrid experimental-finite element analysis. Uniaxial and notched tensile specimens are tested on the additively manufactured and cold rolled sheet Ti6Al4V alloys. The distributions of displacement and strain on the specimen surface during the loading are measured by digital image correlation method. An identification strategy, considering the stress–strain curve, surface strain evolution and variation of specimen width, is proposed to identify the strain hardening model parameters at large strain range. Finite element simulations are performed to update the model parameters by using the iterative inverse method. The parameters of fracture model are determined through experiments on tensile specimens in combination with numerical simulation. The experimental and simulation results show the feasibility and effectiveness of the proposed identification method, that it can be further used to characterize the plastic and fracture behaviors of other metallic materials in practice.

A covariant formulation for finite strain modelling of orthotropic elasticity and orthotropic plasticity with plasticity-induced evolution of orthotropy: Application to natural fibres

We introduce a rate-independent model for orthotropic elastic and orthotropic plastic material behaviour in a hyper-elasto-plastic framework at finite strains. The model is based on the postulate of covariance and does not rely on a multiplicative decomposition of the deformation gradient. Furthermore, a plastic-deformation-induced evolution of orthotropy is considered, similar to the notion of plastic spin. We propose that the orthotropic strain energy function and the orthotropic yield criterion are guided by identical structural tensors that evolve with plasticity. The modelled material behaviour is significant for natural fibres such as flax, hemp, or pulp fibres. Our formulation has three findings. Firstly, the covariant formulation of plasticity provides rate equations for the plastic variables and the structural tensors suitable for reproducing stress–strain diagrams of natural fibres. Secondly, the introduction of plastic-deformation-induced evolution of orthotropy in the proposed covariant setting results in a non-associative plasticity algorithm. Thirdly, the covariant setting allows the incorporation of suitable constitutive equations for the structural tensors to evolve orthotropy. The latter successfully models the stiffness increase in stress–strain diagrams of cyclic tensile tests of natural fibres.

Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests.

Indentation is a versatile method to assess the hardness of different materials along with their elastic properties. Recently, powerful approaches have been developed to determine further material properties, like yield strength, ultimate tensile strength, work-hardening rate, and even cyclic plastic properties, by a combination of indentation testing and computer simulations. The basic idea of these approaches is to simulate the indentation with known process parameters and to iteratively optimize the initially unknown material properties until just a minimum error between numerical and experimental results is achieved. In this work, we have developed a protocol for instrumented indentation tests and a procedure for the inverse analysis of the experimental data to obtain material parameters for time-dependent viscoplastic material behavior and kinematic and isotropic work-hardening. We assume the elastic material properties and the initial yield strength to be known because these values can be determined independently from indentation tests. Two optimization strategies were performed and compared for identification of the material parameters. The new inverse method for spherical indentation has been successfully applied to martensitic steel.

Transverse failure prediction of unidirectional carbon fiber reinforced polymer composites subjected to uniaxial and biaxial loading by stress-triaxiality-dependent computational micromechanics

Accurate characterizing the mechanical behavior of the component materials is crucial for failure predicting of unidirectional carbon fiber reinforced polymer (UD CFRP) composites. A stress-triaxiality-dependent micromechanics model is developed for the transverse failure prediction of the composites in this study, in which the stress triaxiality is innovatively adopted to define the plastic hardening behavior of the matrix material. Therefore, diverse hardening behaviors generated by heterostructures, accurate confirmation of biaxial failure, as well as hardening behavior evolution caused by stress status changes during loading process can be considered. The accuracy performance of the micromechanics model is provided by comparing the predicted results (stress–strain curves, RVE profiles and failure points) with existing experimental data and failure envelopes of failure criterion. The comparison results show that the micromechanics model can accurately capture the failure phenomenon and failure evolution mechanism of the composite under uniaxial and biaxial loadings.

Mechanical mechanism of specimen size effect on impact toughness of Al 6061: Experiment and simulation

Impact toughness has a strong size effect, which restricts the accurate evaluation of material toughness and safety of structural design. However, our understanding of the internal mechanical mechanism that influences the size effect remains incomplete. To fill this gap, this paper adopts the method of combining experiment, theory, and simulation. From the point of view of the dependence of plastic and fracture behavior of material on stress state, the internal mechanical mechanism of the size effect of impact toughness (αk) was studied. Firstly, the Charpy impact tests of different sizes were carried out on Al 6061. αk was divided into cracking initiation toughness (αini) and cracking growth toughness (αgro). The variation of αini and αgro with specimen size was analyzed. Then, through a series of tests, the influence of stress state on the plastic and fracture behavior of Al 6061 was studied. To simulate the whole process of the Charpy impact test, an uncoupled 3D fracture model was proposed. Subsequently, a stress state dependent yield function, modified Voce hardening law, and the proposed fracture model were used to simulate the Charpy impact tests. The predicted results were in good agreement with the tests. Finally, the internal mechanical mechanisms of the size effects of αini and αgro were analyzed. The results show that: (1) The αini and αgro have significant size effects, and there are significant differences between them. (2) The internal mechanical mechanism of the size effect of αini was revealed; that is, the dependence of the plastic behavior of the material on the stress state is the internal root cause of the dependence of αini on the specimen size. (3) The internal mechanical mechanism of the size effect of αgro was revealed; that is, the dependence of the plastic behavior of the material on the stress state and the fracture behavior of the material under ultra-high stress triaxiality is the internal fundamental reason affecting the size effect of αgro. (4) This study reveals the internal complex and intimate relationships between plastic behavior, fracture behavior, toughness behavior, stress state, and the size effect, providing a valuable reference for accurate and comprehensive understanding, evaluation, and selection of metal materials.

Numerical Investigation of the Seismic-Induced Rocking Behavior of Unbonded Post-Tensioned Bridge Piers

It is essential and convenient to use accurate and validated numerical models to simulate the seismic performance of post-tensioned (PT) rocking bridge piers, with a particular emphasis on accurately capturing rocking behavior. The primary contribution of this study is a comparison of the effectiveness of four commonly used numerical base rocking models (namely, the lumped plasticity (LP) model and the multi-contact spring (MCS) models with linear elastic (MCS-LE), bilinear elastic–plastic (MCS-EP) and nonlinear plastic (MCS-NP) material behavior, respectively) in modeling both the cyclic and seismic responses of PT rocking bridge piers. Also, this study validates the 3D contact stiffness equation for numerical models and assesses the differences between the dynamic and static stiffness values of the contact springs. Both quasi-static and shaking table tests of typical PT rocking piers are adopted to calibrate/validate these numerical models. These models describing the PT rocking piers’ seismic performance are formulated and calibrated, showing good agreement with test results for test specimens. Additionally, the suggested values of model spring stiffness for dynamic and quasi-static analyses are identified by parametric analysis. All base rocking models can predict the pier’s cyclic and seismic behavior after the calibration of contact spring stiffness values. The recommended contact stiffness for the dynamic analysis of PT rocking piers is smaller than that used for the quasi-static analysis. The results and findings provide a valuable reference and solution for the numerical simulation of PT rocking piers.

A model for physical dislocation transmission through grain boundaries and its implementation in a discrete dislocation dynamics tool

The mechanical behavior of most metals in engineering applications is dominated by the grain size. Physics-based models of the interaction between dislocations and the grain boundary are important to correctly predict the plastic deformation behavior of polycrystalline materials. Dislocation-grain boundary interaction is complex and a challenge to model. We present a model for simulating the physical transmission of dislocations through grain boundaries within Discrete Dislocation Dynamics tools. The properties (glide plane, Burgers vector, initial length) of the transmitted dislocation are chosen based on geometric criteria as well as a maximization of the resolved shear stress of the transmitted dislocation. Additionally, stress and displacement transparency as well as the discontinuity are ensured via a grain boundary dislocation – a butterfly-like geometry in the general case – whose properties are selected to minimize the residual Burgers vector at the interface. This additional ‘grain boundary dislocation’ allows a direct comparison as well as a calibration of the model with experiments on the macroscale particularly for neighboring grains with a high dislocation density contrast. Two basic examples illustrate the model and an application to a 40-grain polycrystal demonstrates the scalability of the approach.

Elevated-temperature material properties and fracture behavior of fire-resistant steel FR355

Fire-resistant steel (FRS) has been increasingly used in engineering structures due to their advantages of excellent earthquake and fire resistance properties. Accurately characterization of material properties and limit states of steel material is very important for structural-safety design and finite element (FE) simulation. This paper presents the results of experimental and numerical investigations on the elevated-temperature performance of FRS in terms of material properties, full-range true stress-strain curve, ductile fracture behavior, which has not yet been reported. The experimental part of the present paper includes the steady-state tensile testing of conventional structural steel (CSS) and FRS at temperatures up to 800 °C. Hollomon law and weighted average method were adopted to derive full-range true stress-strain behavior of the investigated steels at elevated temperatures, which is required for ductile fracture simulation in ABAQUS. Ductile fracture of tensile coupon specimens was modelled using the stress-modified critical strain model (SMCS). To verify the accuracy and application of the proposed true stress-strain and fracture models, finite element (FE) simulations of tensile coupon tests were performed using ABAQUS/explicit. It shows that the FE simulation incorporating proposed material plastic behavior and ductile fracture model provides accurate predictions for fracture response of the tensile coupons.

Design and validation of a new ring hoop plane strain test for characterizing the anisotropic plastic behavior of tubular materials

The accurate characterization of the plastic behavior of tubular materials is challenging due to the difficulties in acquiring proper specimens for mechanical testing. In this study, we propose a novel testing technique, namely the ring hoop plane strain Test (RHPST), as a supplementary test for characterizing materials experiencing distinct strain paths compared to standard uniaxial tensile tests. To design a suitable ring specimen’s geometry that satisfies the necessary plane strain conditions, we developed a meta-modelling approach merging response surface method (RSM) and the finite element method (FEM). Experimental tests are conducted on RHPST specimens, and 3D digital image correlation (DIC) technique is used to monitor the strain fields within the specimen's gauge section. However, observations indicate the presence of edge effects on the gauge specimen. These edge effects significantly influence and limit the homogeneity of the plane strain field. To tackle this limitation, a correction procedure is developed for separating the authentic plane strain area, constituting approximately 78% of the RHPST specimen's width. Furthermore, we successfully fabricated a novel grooved ring specimen (GRHPST), which exhibits a wider region of the plane strain state encompassing up to 90% of the gauge width, while minimizing the impact of edge effects. The true stress-true strain curve obtained from the GRHPST specimen exhibits exceptional agreement with the curve predicted using the Hill48 yield criterion. Notably, no additional corrections are required for the measured true stress-true strain curve, thereby affirming the efficacy of the GRHPST specimen as an adept test for characterizing the anisotropic plastic behavior of AA6063 tubes.

Analysis of Plastic Deformation of Pipes Due to Deflagration to Detonation Transition Using Static Equivalent Pressure

Abstract Explosions of premixed gases with deflagration to detonation transition (DDT) are a risk in the process industry with potentially catastrophic consequences. Robust and simple design methods are required for industrial use. Such a simplified design method based on finite element analysis is proposed to model the dynamic behavior of pipes loaded by gas explosions of premixed gases including DDT. The focus is on so-called long pipes, where the DDT is not affected by reflections at blind flanges. First, it is reviewed how the pressure load of the gas explosion and the resulting material behavior has been modeled in previous publications. The analytical equations are then extended for describing the pressure load as a function of time and location by considering the leading compression wave as it affects the pressure load of the overdriven detonation. The extended analytical equations are parameterized using Chapman-Jouguet conditions and experimental results from publications for both static equivalent pressure and the location of the DDT. To describe the plastic material behavior at high strain rates, the well-known Johnson-Cook plasticity model is used. The material parameters of the model are derived from simple experiments, which are available in an industrial environment. The comparison of a finite element simulation with experimental data shows that the concept of equivalent static pressure can be extended to an finite element analysis, which in the future will allow the sizing of complete pipe systems including tees, bends, and flanges while considering plastic deformation.

Compression-Shear Specimen Stress-State Response and Distribution Characteristics with Wide Stress Triaxiality.

Conventional methods for studying the plastic behavior of materials involve uniaxial tension and uniaxial compression. However, in the metal rolling process, the deformation zone undergoes a complex loading of multidirectional compression and shear. Characterizing the corresponding plastic evolution process online poses challenges, and the existing specimen structures struggle to accurately replicate the deformation-induced loading characteristics. In this study, we aimed to design a compression-shear composite loading specimen that closely mimics the actual processing conditions. The goal was to investigate how the specimen structure influences the stress-strain response in the deformation zone. Using commercial finite element software, a compression-shear composite loading specimen was meticulously designed. Five 304 stainless steel specimens underwent uniaxial compressive loading, with variation angles between the preset notch angle (PNA) of the specimen and compression direction. We employed digital image correlation methods to capture the impact of the PNA on the strain field during compression. Additionally, we aimed to elucidate the plastic response resulting from the stress state of the specimen, particularly in relation to specimen fracture and microstructural evolution.

Study on the applicability of a modified strain approach to predict the fatigue life of HFMI-treated transverse stiffeners under variable amplitude loading

AbstractThis paper analyses the applicability of a modified strain approach to predict the fatigue life of HFMI-treated transverse stiffeners under variable amplitude loading (VAL) with random load sequences of a p(1/3) and linear shaped spectrum. Local stresses are determined using linear-elastic finite element analyses. The measured weld geometry and component imperfections are considered. From the hardness of the HFMI-treated zone and the base material, the elastic–plastic material behaviour and Coffin-Manson parameters to describe the damage parameter Woehler curve are estimated. Based on a hysteresis counting method (HCM), the damage for each closed hysteresis is calculated. The applied notch strain approach includes the impact of residual stresses and the influence of surface roughness. Thus far, the application of similar approaches has only been validated for welded components with comparatively low residual stresses and HFMI-treated welds subjected to constant amplitude loading. To validate the accuracy of the approach for HFMI-treated welds under variable amplitude loading, the approximated fatigue life is compared to the number of cycles derived from experimental investigations. In this study, it is shown in conjunction with experimental results that it is essential to consider the strength of the base material near the weld when assessing the service life. This area can be more critical than the HFMI-treated weld toe.

Strain-life behavior of thick-walled nodular cast iron

Abstract For the design of thick-walled cast iron components used for wind energy turbines, large machines, presses, and engine parts made of nodular cast iron, the assessment of fatigue life of critical component areas is a crucial point to consider. Importance increases with the demand to safe resources by applying a lightweight design in combination with a certain resistance against extreme loads and misuse situations. Moreover, this gets more important when notches or deviations in the local microstructure are present. Nevertheless, due to accessibility, a lack in the description of the local strain-based material behavior still exists. Especially new cast iron grades such as ADI are not well investigated but offer an often-discussed potential for a lightweight design of the structure or to increase the highest admissible load on the structure. To determine the cyclic material behavior of nodular cast iron, different grades EN-GJS-400-18LT, EN-GJS-450-18, EN-GJS-500-14, EN-GJS-600-3, EN-GJS-700-2, and ADI in different wall thicknesses were investigated concerning their elastic–plastic material behavior under strain control. Moreover, new possibilities for the trilinear description of the strain-life and the stress–strain curve and the statistical and technological size effect are discussed in the following based on cyclic stress–strain and strain-life curves.

Study of deformation behavior of plastic metal materials during laser-assisted micro-imprinting formings

When a large taper angle diamond taper indenter is used for micro-imprinting plastic metals, the stagnation zone is caused by excessive extrusion and friction within the material at the tip of the indenter, which in turn affects the flow characteristics of the material and the quality of the processed surface. In this study, the formation of laser-assisted diamond indenter micro-imprinting stagnation zone mechanism was proposed. The deformation behavior when processing plastic-metal materials using this technique is revealed by numerical simulation. And observed this phenomenon through the hardness distribution of the micro tapered hole cross-section. The results show that when the taper angle of the diamond indenter is greater than 105°, a significant stagnation zone occurs in the material. The initial morphology is jug-shaped, showing periodic changes due to the hard substrate. The average hardness in this region is 91.5 HV, which is significantly lower than the rest of the material. When P = 30 W, the height of the stagnation zone is reduced by 43 μm and the first presence time is extended by 90 μm. The reduction in the friction coefficient leads to a reduction in the width of the interfacial stagnation zone.

The Influence of Reverse Yielding on the Plastic Conditioning of Interference Fits in Power Transmission Engineering

Interference fits are very common shaft–hub connections due to their low manufacturing costs and excellent technical properties. The Plastic Conditioning of this machine element is a new and not very well-known method. During the development of this method, it was discovered that Reverse Yielding occurs in certain applications and has a negative impact on the result. This paper examines the effects of Reverse Yielding on the technology of Plastic Conditioning of interference fits in Power Transmission Engineering. Based on the Shear Stress Hypothesis (SH), the Plane Stress State (PSS), and the ideal plastic behavior of materials, established stress–mechanical relationships are used to find the influencing parameters of Reverse Yielding on the technology of Plastic Conditioning and their limits. As a result, a new computational concept is developed that allows the user to maximize Plastic Conditioning while avoiding Reverse Yielding. Analytical calculation suggestions and diagrams for practical application are provided. Furthermore, the deviations in the obtained results, taking into account other material models such as the Von Mises Yield Criterion (VMYC) and material hardening, as well as the Bauschinger effect, are examined in comparison with our own numerical results from the development of Plastic Conditioning, and the resulting need for further research is defined. In addition, the method of Plastic Conditioning of interference fits is introduced and its basic principles are briefly explained.

Study of effect of loading rate on mechanical properties of SS316LN and evaluation of parameters of Johnson-Cook model using parametric FE analysis and experimental data

The objective of this work is to evaluate the parameters of strain rate dependent Johnson-Cook material model using a hybrid procedure which uses finite element analysis as well as experimental data. The large strain rate tests were conducted to using split Hopkinson pressure bar test setup, whereas the quasi-static test was carried out using conventional testing machines. Johnson-Cook material model has been used to simulate the plastic deformation behavior of material under the high strain loading. This model provides the flow stress of the material as a function of equivalent plastic strain, plastic strain rate and temperature. The parameters, i.e., A, B, n, C and m of the model have been determined using a hybrid procedure as mentioned earlier. One of the important issues in split Hopkinson pressure bar testing is the variation of strain rate during the duration of loading. Due to decrease in reflected strain magnitude, the strain rate continuously decreases (as strain rate is proportional to reflected strain signal) and it is a characteristic of the above test method. However, this creates problem in evaluation of parameters of Johnson-Cook material model using conventional procedure. In this work, a modified procedure has been developed in order to take into account of this variation in strain rate as function of applied strain. The results of the method has been validated with experimental data. The parameters have been evaluated only for room temperature data and the effect of temperature shall be studied in future.

The structural strain method for fatigue evaluation of welded components: closed-form solutions

A consistent and unified analysis framework is proposed in this paper for extending the early traction-based structural stress method to low-cycle fatigue regimes in fatigue evaluation of welded structures through a novel structural strain method. Instead of local strain or notch strain, the structural strain here refers to a through-thickness strain distribution that satisfies plane-remains-plan conditions under elastic–plastic deformation conditions. This paper provides closed-form solutions to structural strain distributions corresponding to loading and unloading, structural strain range, an equivalent structural strain range, and the structural stress–strain relation by considering elastic-perfectly plastic material behavior. Both finite element method (FEA) simulations and in-house modeling tools confirm the accuracy of these closed-form analytical solutions. Although these solutions are derived based on elastic-perfectly plastic material assumption, the resulting structural strain range, as a unique fatigue damage parameter for welded components, is shown essentially the same as those obtained numerically by considering a modified Ramberg-Osgood material model under pulsating loading condition, i.e., stress ratio equals zero. Good data correlation between the equivalent structural strain range predicted results and the test results obtained for a welded steel structure under the same loading condition is achieved. Finally, the structural strain range-based parameter is proven effective in correlating a large number of both low-cycle and high-cycle fatigue test data of welded structures made of several structural materials into a narrow scatter band demonstrating the universality of the structural strain method.

Unveiling the mechanical properties of near-surface microstructures in tribological contacts via in-situ micro-bending tests

This study demonstrates the application of the in-situ V-notched micro-cantilever bending method in tribology by analyzing three distinct cases of near-surface microstructures occurring in common tribological contacts. The brown etching layer region of a rail wheel from service shows predominant plastic material behavior. Significant variations in material response and crack initiation are revealed in distinctive regions of a roller bearing's near-surface microstructure and a self-lubricating laser cladding. Qualitative analysis and stress-displacement graphs highlight the method's potential for gaining high-resolution insights into material behavior, contributing to our understanding of microstructural changes affecting friction, wear, and component failure in tribosystems.