Influence Of Strain Hardening Research Articles

Ductile rupture under cyclic loadings at high triaxiality: The influence of strain hardening and elasticity

Previous works (Devaux et al., 1997; Cheng et al., 2017) have emphasized the effects of strain hardening and elasticity upon ductile rupture of metals under cyclic loading conditions. This work pursues the study and modelling of these two effects by distinct theoretical methods, each coupled with micromechanical finite element simulations of the behaviour of some “representative cell”. For the effect of strain hardening, we employ Morin et al. (2017)’s approach, based on the theory of sequential limit-analysis (Yang, 1993; Leu, 2007; Leblond et al., 2018). This approach is applied to various types of hardening of the metallic matrix: isotropic, linear kinematic, nonlinear kinematic with one or two kinematic variables (Armstrong and Frederick, 2007) , and even a simplified version of Chaboche (1991)’s model accounting for complex cyclic effects. Numerical micromechanical simulations of a hollow sphere made of elastic–plastic materials obeying the various hardening laws considered, and subjected to cyclic loadings at high triaxiality, fully confirm the predictions of the model developed, provided elasticity is made negligible by using an artificially high value of Young’s modulus. When a realistic value is employed, however, the agreement between theoretical predictions and numerical results is degraded, thus emphasizing again the importance of the effect of elasticity in cyclic ductile rupture. To deal with this effect we derive, apparently for the first time, an evolution equation of the porosity accounting for (compressible) elasticity. However, numerical micromechanical simulations reveal that simply using this new evolution law, while keeping all other aspects of the model unchanged, remains insufficient to get a good match of theoretical and numerical results. Such a match is achieved by introducing the ad hoc hypothesis that the yield criterion and flow rule derived from sequential analysis still apply in the presence of elasticity, but with some “effective porosity” slightly differing from the true one through some heuristic, adjustable factor.

Experimental and Numerical Investigation on Manufacturing-Induced Pre-Strain on the Load-Bearing Capacity of Clinched Joints

Background. Clinching is a conventional cold forming process in which two or more sheets can be joined without auxiliary parts. A pre-forming of the parts to be joined, which is introduced by previous manufacturing steps, has an influence on the joining result. When considering the suitability for joining with regard to the formability of the materials, the influence of the preforming steps must be taken into account. The influences of strain hardening and sheet thickness on the joining properties must be investigated. In this context, a Finite Element Method (FEM) based metamodel analysis of the clinching process was carried out in [1] to investigate the robustness of the clinching process with respect to the different material pre-strains. In [2], the method was extended to the load bearing simulation.Procedure. The metamodel from preliminary work based on various FE models, which predicts the load-bearing capacity of a clinched joint influenced by pre-straining, is compared here with experimental data and the accuracy of the metamodel prediction is discussed. For this purpose an experimental procedure was further develop which allows the preforming of metal sheets from which joining specimens can be separated with a certain degree of unidirectional deformation. In the study, the procedure for preparing the joint specimens and the results of the loading tests are presented. Different possible relevant pre-strain combinations are investigated and compared with the simulation results, to validate the FE models and choose suitable metamodel.

The influence of strain hardening and surface flank angles on asperity flattening under subsurface deformation at low normal pressures

Characterisation of model asperity flattening under longitudinal subsurface elongation is presented with a variety of normal pressure, flank angle and strain hardening behaviour. A systematic investigation outlines an optimal specimen design to ensure a homogenous deformation field in the workpiece under stress-strain conditions, which are typical in sheet metal forming. Asperity flattening increases with normal pressure, and the longitudinal subsurface strain reduces the necessary yield pressure and promotes asperity flattening. When the flank angle is increased, the longitudinal stress component due to elongation gets smaller in the asperity, reducing the effect of longitudinal straining. Strain hardening decreases the asperity flattening rate as strain hardening extends the deformation field further into the underlying material, which results in less asperity flattening.

Micro-Asperity Contact Area Considering Strain Hardening for Metallic Materials

Abstract A novel micro-asperity contact area model, which considers influences of strain hardening, is proposed to describe contact area between a deformable sphere and a rigid flat for metallic materials. First, a generalized formula considering work-hardening behaviors (Pilling-up or Sinking-in) between contact area and interference is proposed for fully plastic regime based on the definition of plastic contact area index. Then a relationship to calculate the critical interference at the inception of fully plastic deformation is derived. In order to incorporate the transition from elastic regime to fully plastic regime, a quadratic rational form formula is proposed based on volume conservation model for mixed elastoplastic regime. Therewith a modification is conducted to ensure continuity of contact area model at critical interference for fully plastic regime. Ultimately several representative models and experiment results are exhibited to analyze the availability of the present model. It is noted considering work-hardening fully plastic contact area index is not a constant value of two for any metallic materials, which is a function of strain hardening exponent. Demonstration testifies that smoothness constraint is not necessary at the critical interferences. The prediction data of present model are consistent with experiment results contrasting that of other models. Current generalized contact area model considering influence of work-hardening results in a better understanding of the contact area between a deformable sphere and a rigid flat and indicates a probability to analyze contact characteristics of two mating rough surfaces accurately.

Influence of Strain Hardening and Annealing Effecton the Prediction of Welding Residual Stresses in a Thick-Wall 316 Stainless SteelPipe

Influence of Strain Hardening and Annealing Effecton the Prediction of Welding Residual Stresses in a Thick-Wall 316 Stainless SteelPipe

Machining simulation of Ti6Al4V using coupled Eulerian-Lagrangian approach and a constitutive model considering the state of stress

The accuracy of a machining model depends on the capability of this model to describe the physical phenomena associated to the real machining system. This includes the material constitutive model and the approach used to describe the field flow of the material in cutting. In this paper, a model of high speed machining (HSM) of Ti6Al4V titanium alloy is developed. This cutting model includes the proposed constitutive model considering the influence of strain hardening, strain-rate, temperature, and state of stress (e.g., stress triaxiality and Lode parameter) in the material plasticity and damage. Finite Element Method (FEM) using Coupled Eulerian-Lagrangian (CEL) approach is used to simulate the cutting model. A sensitivity analysis of the influence of the mesh topography on the chip geometry and cutting force is performed resulting in the determination of the optimal element size and element orientation. Simulation results obtained using the CEL approach are compared with those obtained using the Lagrangian one. Moreover, simulated cutting force and chip geometry obtained using the proposed constitutive model are compared with those obtained using the Johnson-Cook (J-C) model, and experimental data. Both chip geometry and cutting force predicted by the proposed constitutive model is closer to the experimental one than the J-C constitutive model. The CEL approach combined with the proposed constitutive model can simulate material side flow, which results in a larger width of chip compared to the width of cut, and in the formation of lateral burr on the workpiece. It also permits simulating the cyclic variation of the plastic strain and topography of the machined surface along the cutting direction, observed experimentally.

Influence of Strain-Hardening and Dynamic Recovery on DDRX Steady State

Relationships between macroscopic and microscopic constitutive parameters associated with steady state DDRX are derived for a material in which strain-hardening and dynamic recovery are described by the Yoshie-Laasraoui-Jonas equation. First examples are given for illustration.

Numerical analysis of the robustness of clinching process considering the pre-forming of the parts

Clinching is a conventional cold forming process in which two or more sheets of materials can be joined without any auxiliary parts. To achieve the required geometrical characteristics of the joint, it is essential to use the desired joining tools. The motivation of this study is to investigate the influence of forming steps prior to the joining process on the joint quality. The influences of strain hardening and the variation of sheet thickness on the joint characteristics are to be studied. In this regard, a metamodel-based analysis of the clinching process is performed to investigate the robustness of the clinching process with respect to the different material pre-stains. Three different material combinations made of steel and aluminium sheets (HCT590x; t = 1.5 mm, EN AW-6014, T4; t = 2.0 mm) are examined to illustrate the influence of different material properties on the joint characteristics. The numerical FEM-Simulation is used to predict the geometrical properties of the joint during the simulation of clinching process. For this purpose, an optimization software is used to conduct varieties of simulations and to create a meta-model, which is able to describe the relationship between the pre-straining and the quality relevant parameters of the clinched joint. To validate the model, the results of simulation and experiment are compared. It is shown that there is a good agreement between the simulation and the experiment concerning the geometrical parameters and force-displacement diagram. Finally the joinability of the investigated material-geometry combinations with regard to a tolerable pre-forming is described.

A precise theoretical model for laterally crushed hexagonal tubes

Hexagonal thin-walled structures are widely used in protective engineering and the precise prediction of their collapse behavior is very important for their crashworthiness design. In this paper, a precise theoretical model is proposed to predict the collapse behavior of hexagonal tubes under lateral compression. The rigid-linear strain hardening constitutive relation is adopted for the hexagonal tubes. A deep insight into the in-plane deformation mechanism of hexagonal tubes is presented. Comparisons of the present model with the finite element analysis, existing experiments, and conventional rigid-perfectly plastic model are conducted. It is demonstrated that the present model shows a good agreement with both the numerical simulations and the experiments. The influences of strain hardening and tube wall thicknesses on the crushing behavior are discussed. Based on the theoretical analyses, a nearly constant force-displacement plateau is obtained by selecting appropriate strain hardening modulus and wall thickness of the hexagonal tubes. The present study will pave an effective way to clearly understand the large plastic deformation of thin-walled structures with various cross sections. • A precise theoretical model for the large plastic deformation of laterally compressed hexagonal tubes is established. • Influences of strain hardening on the strengthening of materials in the plastic deformation region and geometry of the deforming tube are considered. • The deformation patterns of the tube walls are depicted in detail. • The energy absorption mechanism of the hexagonal tube is explored deeply. • A nearly constant force-displacement plateau can be obtained when the hexagonal tube is properly designed.

Ductile failure as a constitutive instability in porous plastic solids

A criterion for ductile rupture is derived using Rice’s theory for macroscopic strain localization, and a constitutive relation for porous plastic solids that accounts for inhomogeneous yielding at the mesoscale. At the microscopic scale, it is assumed that failure occurs by void coalescence along a band of voids. An approximate, parameter-free closed form expression for the failure criterion is derived as a function of a single scalar damage variable –the porosity– and the macroscopic stress state, characterized by the stress triaxiality and Lode parameters. For practical applications, an uncoupled approach is developed whereby the failure criterion is supplemented with a damage-free plasticity model and a loading path dependent damage evolution law. The predictive capabilities of the approach are illustrated by comparisons with finite element cell model studies. In particular, the influence of strain hardening is investigated in some detail.

Effects of stress concentration and occurrence of limit states under high speed loading in low temperature operating conditions

Due to the fact that the processes of fracture of machine parts and structural components usually initiate in the zones of stress and strain concentrations, the problems of assessment of stress-stain response and limit states of the material in these zones become the most critical. The capacity of the structural components to sustain load and resist fracture depends on the strain rate and temperatures. One should also take into consideration the increase of stress triaxiality in the notch zones that cause local plasticity reduction and the increase of the yield stress value. The approximate analytical approach was developed to address the problem. The effect of stress and strain concentration in a wide range of applied strains is described using a modified Neuber equation. The influences of strain hardening and strain rate are described by power law equations. Temperature is accounted for using exponential relationships

Strain Hardening Analysis for M-P Interaction in Metallic Beam of T-Section

This paper derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering strain hardening idealisations. Two models for strain hardening – Linear and parabolic have been considered, the parabolic model being closer to the experiments. The interaction relations can predict strains, which is not possible in a rigid, perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-section has been considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations have been suggested. The influence of strain hardening in the interaction study has been highlighted. The strains and hence the strain rates due to bending and an axial force can be separated only for the linear-elastic case because the principle of superposition is not valid for the nonlinear case. The difference between the interaction curves for linear and parabolic hardening for the particular material is small.

Formability Limits, Fractography and Fracture Toughness in Sheet Metal Forming.

This paper is focused on the utilisation of double edge notched tension, staggered and shear tests to determine fracture toughness and the formability limits by fracture in principal strain space. The experiments were performed in test specimens with different geometries and ligament angles, and the influence of strain hardening was taken into consideration by selecting two materials (aluminium AA1050-H111 and pure copper), with very different strain hardening exponents. Results are plotted in principal strain space, and the discussion is focused on the link between formability limits, fracture toughness and macroscopic fractography characteristics of the specimens that fail by mode I, mode II or mixed-mode.

Influence of a Static Reversible Loading on Mechanical and Elastic Properties of Polycrystalline Aluminum Alloy AMg6

The paper presents results from experimental studies on the influence of loading–unloading processes on the mechanical, linear, and nonlinear properties of the strain-hardening polycrystalline aluminum alloy AMg6 (Rus). The stress–strain curve is measured for AMg6 samples under high-cycle loading–unloading up to fracture of a sample. The microhardness of the sample is measured before and after its fracture. It has been found that the loading–unloading process leads to strain hardening of the AMg6 alloy. The influence of strain hardening of AMg6 on its linear and nonlinear elastic properties is studied by an ultrasonic method. To study the nonlinear elastic properties for different domains of the loading curve, we used the Thurston–Brugger method and spectral method by studying the efficiency of second acoustic harmonic generation. The experimental results are discussed.

13.03: Bending‐shear interaction of steel I‐shaped cross‐sections: Statistical investigation

ABSTRACTClause 6.2 of EN 1993‐1‐1 covers the cross‐sectional resistance of steel sections. The bending‐shear interaction design rules for I‐shaped cross‐sections make use of a reduced yield stress for the web area. On this basis, a reduced design plastic resistance moment allowing for the shear force is presented. The effect of shear on the bending resistance may be neglected if the shear force is less than half of the plastic shear resistance of the cross‐section. Plasticity in the Eurocode is described by the well‐known Von‐Mises yield criterion, however, the formula used for the reduced yield stress deviates from this criterion, resulting in sometimes greater and sometimes smaller values. The background of the Eurocode formula for reduced yield stress can be found in a publication by Drucker. The purpose of the present research is to investigate the influence of shear on the bending resistance of I‐shaped steel cross‐sections with as result a possible reconsideration of the Eurocode design rules.At Eindhoven University of Technology an experimental investigation on bending‐shear interaction in rolled steel I‐shaped sections was performed. A numerical model was developed in Abaqus Finite Element software to simulate the experiments. With the validated numerical model a larger database of numerical ‘test’ results was generated, which was subsequently used in a statistical analysis following Annex D of EN 1990 as further developed in the RFCS project Safebrictile. The statistical distributions of the steel properties recommended by Safebrictile were adopted.This paper presents the results of the statistical analysis and safety assessment of the strong axis bending‐shear interaction design rule currently present in Eurocode 3. The parametric test group consists of HEA, HEM and IPE sections in the steel grades S235, S355 and S460: in total 180 numerical simulations with increasing amount of shear. A stress‐strain model including strain hardening was used in the numerical simulations, since the influence of strain hardening is also largely present in the experimental test program. Based on strain hardening material behavior it is show in this paper that the current partial factor is un‐conservative for shear dominated beams and should be increased. Alternatively, the design rule should be modified.

Meshless microscale simulation of wear mechanisms in scratch testing

Scratch testing is an inexpensive technique used for determining the mechanical/wear properties of materials and coatings. In contrast to instrumented indentation, where quantitative relations have been established, only few studies are devoted to quantitatively understanding the material response during scratch testing. Most modelling approaches rely on the finite element method, which is particularly suitable for calculating stresses during plastic deformation, but cannot straightforwardly reproduce gross deformations or material detachment. The present work relies on smooth particle hydrodynamics (SPH) for overcoming this issue. SPH approximates a continuous field using a set of kernel functions centred about so-called particles. These carry the physical properties of the system, e.g. mass, internal energy, or velocity, thus discretising the set of underlying partial equations. By using a discrete method, material detachment is intrinsically taken into account. A parameter study was undertaken on the basis of the elastic-viscoplastic material model of Johnson-Cook. The aim of this work is to investigate the role of material/wear properties and load on the scratch behaviour via a parameter study. The influences of strain hardening, yield strength and Young's modulus on the scratch behaviour are pointed out. The results of the scratch simulations are in good agreement with experimental data for single phase alloys. Relaxation phenomena known from scratch experiments are reproduced for the first time using a numerical method.

The influence of strain hardening of a base material on the effective characteristics of a topocomposite

The mechanics of contact interaction between a rigid sphere and a two-layered elastoplastic half-space (topocomposite) which imitates a surface hardened with the thin protective coating has been studied. The behavior of contact parameters of the deformation force, as well as its effective characteristics (load-carrying ability, yield point and compositional hardness) against the cost of the deformational hardening of the layered body base material has been investigated.

Effect of residual stress shakedown on stiffened plate strength and behaviour

Numerical simulation is used to study the influence of welding-induced residual stress in welded, tee-stiffened plates focusing on the effect of shakedown. Welding is simulated using 3D thermo-elasto-plastic finite element analysis. The influence of strain hardening and number of load cycles on residual stress shakedown is then investigated. Load versus end-shortening curves are used to characterise the strength and behaviour of stiffened plates under axial compression both before and after shakedown. Results show that the reduction in residual stress due to shakedown occurs entirely during the first load cycle provided that the magnitude of that load is not subsequently exceeded. Both the tensile and compressive welding residual stresses in the plates are reduced by as much as 40% when the applied load causes an average stress equal to 50% of the yield stress. This level of shakedown increased the ultimate strength of tee-stiffened plates by as much as 6% in some cases, but the potential for increase in ultimate strength as a consequence of shakedown was found to depend on the failure mode.

Influence of Strain Hardening 1% by Torsion on the Behavior of a Single Crystal Alloy (Cu–at.9% Al) in Internal Friction at High Temperature

The purpose of this study is to highlight the influence of the strain hardening on internal friction behaviour of a copper single crystal alloy Cu-Al (9% at.) using Isothermal Mechanical Spectroscopy (IMS) technique. To do this, the sample was cold worked about 1% by torsion and tested at different stabilized levels of temperatures. Thus the specimen have been progressively heated to 1179 K and then cooled down to room temperature. The advantage of IMS experiments is to allow to compare the isothermal internal friction spectra obtained during heating (in this case, the annealing temperature (TA) is equal to the temperature of measurement (TM) with the measurements performed at various temperatures during cooling after annealing at 1179 K (TM< TAin this case). The results obtained in increasing temperature step by step (TA= TM) show the existence of two (02) independent relaxation peaks from 914 K to 1179 K. The first one, called here P1(at about 0.7 TMeltat 1Hz), decreased with increasing the annealing temperature, while a new relaxation peak P2(at about 0.9 TMeltat 1Hz) progressively developed. However for high temperature annealing, IMS tests (TA> TM) does reveal only one peak P2. It appears, therefore, clearly that the strain hardening is responsible for the P1existence. To monitor the evolution of P1and P2with the temperature, a method of peaks decomposition already published was applied. The relaxation parameters, deduced from the Arrhenius plots, were thus accurately determined. The mechanism responsible of the P1and P2peaks appearance has been attributed to the movement of dislocation segments inside the sample microstructure.

A Study of the Influence of Strain Hardening and Precipitation Hardening Sequence on Development of Mechanical Properties of AlMgSi Conductor Alloys

The paper focuses on 6xxx series AlMgSi conductor alloys. Such alloys are used for manufacturing of conductors for power transmission. Since the most current standards define as many as seven types of wires with various mechanical and electrical specifications, the existing philosophy of AlMgSi wires manufacturing technology for electrical applications has to be revised. Strength specifications of precipitation hardened AlMgSi alloys may be enhanced by strain and by precipitation hardening. Therefore from the scientific point of view identification seems to be relevant of the impact of the sequence of these mechanisms on development of final wire properties. In particular, this paper tries to answer the following question: Does the sequence of hardening mechanisms affect the development of mechanical properties of AlMgSi alloy wires? The paper presents results of a study of the impact of artificial ageing parameters of 6201 grade AlMgSi alloy wires on their final properties. The study results are presented and discussed in two parts. The first part addresses the impact of artificial aging temperature and duration on the strength properties of AlMgSi (grade 6201) alloy wire rod. The second part is focused on hardening development in the process of drawing of a AlMgSi wire made of the same alloy grade, subjected to different thermal treatments, the parameters of which have been selected based on analysis of the results of the first, wire-rod related, part of the study.