Strain-hardening Material Research Articles

Microstructure based modeling of the strain rate history effect in wear resistant Hadfield steels

The strain rate history dependency of Hadfield steel is investigated by numerical modeling. A crystal plasticity model is employed to study the effect of strain rate jump/drop on the material's strain hardening and twinning propensity. Single crystal orientations are first examined to assess the importance of the strain rate and its history effects. Then a representative 3D microstructure aggregate is used to investigate the effects of strain rate history in a polycrystalline structure. It was found that strain rate affects the evolution of deformation twins in the microstructure, generating a strain rate history dependent deformation and hardening response. A Hadfield steel used in mineral crushing conditions is also characterized to provide details of the deformation and hardening behavior of the material under realistic low/high strain rate loading conditions. The importance of strain rate changes to strengthening and increasing the hardness of the polycrystal microstructure is discussed and considered from the wear resistance point of view.

Analysis of the hot deformation of ZK60 magnesium alloy

Abstract Hot deformation of cast-homogenized and extruded (in both the extrusion and transverse directions) ZK60 magnesium alloy was conducted using the Gleeble® 3500 thermal-mechanical simulation testing system. A new approach to model the high temperature constitutive behavior of the alloy was done using two well-known equations (i.e. hyperbolic sine and Ludwig equations). For this approach, the deformation conditions were divided into regimes of low and high temperature and strain rate (four regimes). Constitutive model development was conducted in each regime and the material parameters (P) were evaluated as strain, strain rate and temperature-dependent variables; P ( e , e ˙ , T ) . Using this approach, the flow curves were predicted with high accuracy relative to the experimental measurements. Moreover, detailed information on the evolution of hot deformation activation energy was obtained using the modified hyperbolic sine model. Using the modified Ludwig equation, details of strain hardening and strain rate sensitivity of the ZK60 material during hot deformation were obtained.

An analytical approach to prediction of internal defects during the flat rolling process of strain-hardening materials

In this paper, the upper bound method has been used in analysis of the flat rolling process and prediction of internal defects for a strain-hardening material. The arc of contact has been replaced by a chord. The inlet shear boundary of the deformation zone has been assumed as an exponential curve and the boundary at the exit has been assumed as a cylindrical surface. A kinematically admissible velocity field has been proposed and internal, shear and frictional power terms have been derived. By minimizing the total power with respect to the neutral point position and the shape of the inlet shear boundary, the rolling torque has been determined. A criterion has been presented to predict the occurrence of the internal defects for given rolling conditions. Comparison of the analytically developed approach for rolling torque and internal defects with published theoretical and experimental data shows generally good agreement.

A modified Johnson-Cook model for 10%Cr steel at elevated temperatures and a wide range of strain rates

A modified J-C model of 10%Cr steel, based on the original J-C model, is further developed to consider not only the coupling effects of strains, strain rates and temperatures, but also the mechanism of the hardening and the flow softening during whole deformation processes. The model can simulate multi-deformation processes including work hardening, recovery and recrystallization at the high temperature for use as the nuclear power equipments. To establish this new model, the compression tests at different temperatures (950–1250°C) and strain rates (0.001s−1−0.01s−1) were conducted and the observations of microstructure under various conditions were performed. The results indicate that the influences of the strain, strain rate and temperature on the strain hardening of material are not independent of each other, while many of them interact. Moreover, Compared with the original J-C model and experimental data, the modified J-C model has good predictability of the hot deformation behavior of material.

Influence of material modeling on simulation accuracy of aluminum stampings

The best practice in modeling material yield, strain hardening and anisotropic behavior in plastic deformation has been analyzed for an AA 6016 aluminum alloy. The investigation was based on the extensive material property testing, stamping benchmarking and AutoForm simulations. For the material property testing, both the uniaxial tensile test and the hydraulic bulge test were conducted. The elliptic punch test and the cross die test served as the benchmarks to validate the simulation results. In the simulations, the material characteristics was modeled with the combinations of four strain-hardening models and three yield criteria. By comparing the simulation results with the experimental measurements, the influence of material modeling on aluminum stamping simulation accuracy was evaluated. It was concluded from this study that the yield criterion is the key factor in controlling the simulation accuracy. The simulation with the BBC2005 yield model predicts the most accurate results. It was also shown that the combined Swift/Hockett-Sherby strain-hardening model is most suitable to describe aluminum strain hardening behavior.

The Effect of the Use of Technological Lubricants Based on Vegetable Oils on the Process of Titanium Sheet Metal Forming

Abstract The paper evaluates the drawability of titanium sheet metal Grade 2, with the focus on friction conditions that are present in the sheet metal forming process. The study aims to present the results of the examinations of the friction coefficient during a strip drawing test. The focus of the experiment was on lubricants based on vegetable oils i.e. rapeseed oil, sunflower oil and olive oil. Boric acid was used to improve the lubricating properties of vegetable oils. The results of numerical simulations of the process of forming a cover with stiffening components made of grade 2 titanium sheet metal was also presented. The numerical simulation was carried out using the FEM method with PAMStamp 2G software. The effect of conditions of friction between the sheet metal and tool parts and pressure force of the blank holder on the forming process were investigated. Numerical calculations were performed with consideration for the phenomenon of material strain hardening and anisotropy of plastic properties of the sheet metal formed. The analysis of the deformations and reduction in wall thickness of the drawn parts can be used for determination of the effect of changes in selected parameters on the process of drawn part forming. The quality of drawn parts was assessed based on the shape inaccuracy determined during simulation of forming. The inaccuracy depended on the conditions of the process and strength properties of the titanium sheet metal.

New load-line-displacement based η factor equation to evaluate J-integral for SE(B) specimen considering material strain hardening and no-crack displacement effect

The η factor plays an important role in the experimental evaluation of J-integral and J-R curve. While for a deeply cracked SE(B) specimen, established η factor value is available; for shallow cracked specimen, there is a variation in the η values proposed by different researchers. Although, it has been found that η factor depends on the material strain hardening behavior, most of the available equations are derived based on elastic-perfectly plastic material behavior. Additionally, almost all the existing η factor solutions do not consider the subtraction of no-crack displacement while calculating the strain energy although basic definition demands it. Hence effort has been made in this work to cover these gap areas. Plastic η factors (ηpl) have been calculated for a wide range of relative crack depth (a/W) and Ramberg-Osgood material strain hardening exponent ‘n’ with the help of elastic-plastic FE analysis. Calculated results are validated using literature values. The variation of ηpl with a/W and ‘n’ has been studied considering the effect of no-crack displacement. Based on these analyses, a closed-form equation has been proposed which is applicable for a wide range of a/W and material strain hardening exponents. The ηpl was shown to be independent of applied load level and various R-O parameters.

Determination of Failure Pressure Modes of the API Specification 12F Shop-Welded, Flat-Bottom Tanks

Shop–welded, flat-bottom tanks for storage of production liquids are designed and fabricated in specific dimensions and capacities for internal pressures close to atmospheric pressure in accordance with the API 12F specification. This study addresses the failure pressure on the eleven (11) current API 12F shop-welded steel tanks as well as two proposed sizes through finite element and stress analysis of more than 350 different tank models. An elastic analysis was carried out to determine the yielding pressure of the shell-to-bottom and roof-to-shell joints. An elastic buckling analysis and a post-buckling analysis including imperfections was performed to determine the buckling modes of the equipment. The redistribution of stresses due to inelastic deformations and plastic collapse were evaluated through a plastic stress analysis considering the stress–strain hardening of the ASTM A36 mild steel material. Moreover, the design pressure increase to failure pressure or 24 oz/in2 (10.3 kPa) was investigated regarding the stress levels and bottom uplift of the 13 flat-bottom tanks. The presented research provides meaningful insights and engineering calculations to evaluate the current design of the API 12F shop-welded, flat-bottom tanks as well as to establish new design internal pressures guaranteeing a safe performance of the equipment.

Large deformation response of additively-manufactured FCC metamaterials: From octet truss lattices towards continuous shell mesostructures

Starting with the statically-determinate solid octet truss lattice, the large strain compression response of different metamaterial architectures is analyzed through finite element analysis and compression experiments on additively-manufactured stainless steel specimens. Simulation results clearly demonstrate that for a relative density of 20% the conventional solid octet-truss lattice has a lower specific energy absorption capability than some simple periodic shell structures. The analysis of the closed-packed hollow sphere assembly subject to hydrostatic compression reveals that the constituent hollow spheres initially transform into rhombic dodecahedra, which results in significant strengthening at the macroscopic level. Unlike the octet-truss with solid struts, hollow octet truss structures remain stable for hydrostatic, confined and uniaxial compression at the lowest relative density considered. Its strength, in particular at small plastic strains, is substantially improved when substituting the geometric hollow truss joints for hollow spheres. The continuous shell mesostructures defined by the Hybrid (hollow) Truss-Sphere (HTS) and the hollow octet truss assembly exhibited the highest strength and energy absorption potential at 20% relative density for the high and low strain-hardening materials considered, respectively. Moreover, it is found that the HTS metamaterial exhibits the highest relative Young's and bulk moduli among all four architectures considered. It is also shown computationally that hollow rhombic dodecahedral mesostructures could provide nearly twice the strength and energy absorption of the conventional octet truss.

Structural behavior of a lightweight, textile-reinforced concrete barrel vault shell

Textile-reinforced concrete (TRC) as a novel composite material offers a wide range of capabilities and flexibility in the manufacturing of thin-walled, lightweight structures. The application of textile reinforcement in fine aggregate high-performance concrete has enabled the dimensioning of structural concrete in very small thicknesses. This possibility allows for the fabrication of thin-walled TRC shell structures with complex geometries. On the other hand, structural planning and construction require new modeling approaches to comprehend the structural behavior of such forms. In this paper, we present the fabrication procedure of a large-scale TRC vault shell, together with the performed experimental study. The shell structure was tested under a two-step loading scenario to study the load-bearing behavior. The particular focus of the paper is on the analysis of the structural behavior by means of an anisotropic strain-hardening material model specifically developed for the simulation of TRC shells. The prediction obtained using the nonlinear finite element simulation has been compared with the test results to validate the modeling approach. The performed studies are used to evaluate and discuss the structural redundancy included in the applied linear ultimate limit state assessment procedure.

Direct numerical simulation of ductile spall failure

Large-scale direct numerical simulations of void growth and coalescence from 3-dimensional distributions of void nucleating particles are used to investigate the effect of material strain hardening and strain rate sensitivity on spall response. The computational model spans multiple particle spacings in the in-plane directions, and several finite elements span the initial particle diameters in the mixed-zone Arbitrary Lagrange–Eulerian (ALE) simulations. The matrix material is represented by traditional plasticity models in which material failure is not permitted. The 1000 $$+$$ particles are represented by the same material model as the surrounding matrix except the particles have low tensile strength to permit fracture, which is used to simulate particle cracking or decohesion. Voids grow and coalesce naturally in the ALE framework, and the simulations produce dimpled failure surfaces similar to those observed experimentally in spalled samples. The strain hardening and strain rate sensitivity of the matrix material are altered to explore their influence on the void growth and coalescence processes and on the simulated free surface velocity. The details available from the computational model permit association of the longitudinal stress evolution with features on the free surface velocity profile.

A rigid projectile perforation model for metallic targets with the free-surface and fracture effects

The metallic targets are regarded as the compressible power-law strain-hardening materials, and the resistance function coefficients for three kinds of steel and 11 kinds of aluminum targets are obtained based on the spherical cavity-expansion theory. Then, an explicit expression for projectile impact resistance is proposed by curve-fitting, which is simple to use without performing the complex numerical solution. For the projectile perforating on the finite thickness plate, the free-surface effect is realized by multiplying a decay function with the above explicit resistance. Furthermore, a new phenomenological perforation model considering the projectile entry and exit phases, compressibility, rear free-surface and fracture effects of target is established, which is sufficiently verified by comparing with the existing 19 sets of projectile perforation tests and two typical theoretical models. Finally, the influence of the impact velocity on the rear free-surface effect is discussed.

Effects of Vibration Assistance on Surface Residual Stress in Grinding of Ti6Al4V Alloy

Titanium alloy Ti6Al4V is widely used in aerospace, biomedicine, and marine industries due to its high strength-density ratio and corrosion resistance property. Grinding is used to achieve final surface quality of the component, in which the surface residual stress plays an important role in the fatigue life of the component. This study presents the investigation of surface residual stress in vibration assisted grinding of Ti6Al4V. A finite element model is developed to predict the surface residual stress in both Conventional Grinding (CG) and Vibration Assisted Grinding (VAG). The effect of progressive strain hardening of the workpiece material due to multiple grit passes is considered to analyse the surface residual stress. The model is validated through 1-D and 2-D vibration assisted grinding experiments. The surface residual stress is measured through 2-D X-ray diffraction technique. It is observed that implementing vibration assistance results in increased compressive residual stress due to the indentation effect, which enhances the fatigue life of the component.

Investigation of Lubricated Die/Billet Interface in Hydrostatic Extrusion Process Using Upper Bound Theorem

The objective of this paper is to investigate numerically the existence of thermal minimum film thickness at the die-billet interface in the inlet in the hydrostatic extrusion of aluminum alloy by incorporating the viscous heat dissipation in the lubricating film. Governing equations (Reynolds equation, energy equation, Roelands viscosity relation, and film thickness geometry relation) have been solved herein using lobatto quadrature technique. Predicted minimum film thickness, temperature, and pressure at the exit of inlet zone have been used as boundary conditions in the work zone analysis. In the proposed work zone analysis, heat transfer by convection along the lubricating film, conduction across the film, uniform billet heating by plastic deformation and strain hardening of billet material have been accounted. Drastic reduction in thermal minimum film thickness has been observed in the inlet zone with respect to the isothermal minimum film thickness of inlet zone. However, about 4 to 5 times less thermal minimum film thickness has been achieved respect to the corresponding isothermal minimum film thickness at the exit of the inlet zone.

Analysis of compressibility behavior and development of a plastic yield model for uniaxial die compaction of sponge titanium powder

Uniaxial die compaction of Sponge Ti with a maximum particle size of 3mm and irregular spongy particle morphology was conducted with the Gleeble® 3500 thermal-mechanical simulation testing system at room temperature. The compressibility behavior of the powder was studied using the Heckel equation. It was observed that the behavior of the material could be analyzed in two compaction pressure regimes. In the low pressure regime (<100MPa) the powder exhibited high compressibility, while; in the high pressure regime (>100MPa) lower compressibility of the Sponge Ti was observed. A pressure-dependent plastic yield model was employed to develop the yield criterion of the powder. In this model both geometric hardening of the powder and strain hardening of the incompressible material was considered. The model was validated by comparing the experimental and modeled results.

Rifle bullet penetration into ballistic gelatin

The penetration of a rifle bullet into a block of ballistic gelatin is experimentally and computationally studied for enhancing our understanding of the damage caused to human soft tissues. The gelatin is modeled as an isotropic and homogeneous elastic-plastic linearly strain-hardening material that obeys a polynomial equation of state. Effects of numerical uncertainties on penetration characteristics are found by repeating simulations with minute variations in the impact speed and the angle of attack. The temporary cavity formed in the gelatin and seen in pictures taken by two high speed cameras is found to compare well with the computed one. The computed time histories of the hydrostatic pressure at points situated 60 mm above the line of impact are found to have "two peaks", one due to the bullet impact and the other due to the bullet tumbling. Contours of the von Mises stress and of the effective plastic strain in the gelatin block imply that a very small region adjacent to the cavity surface is plastically deformed. The angle of attack is found to noticeably affect the penetration depth at the instant of the bullet tumbling through 90°.

Springback analysis in sheet metal forming by using the Ramberg–Osgood stress–strain relation

The Ramberg–Osgood stress–strain relation is used to perform a theoretical springback analysis in the problem of bending of a narrow rectangular strip made of a strain-hardening material. The maximum strip thickness is 5 mm, and its length is significantly greater than the thickness. Based on the elasticity and plasticity deformation theory and also on the Tresca and von Mises yield criteria, an expression for the springback ratio is derived. The springback ratio depends on the ratio of the yield stress to Young’s modulus, Poisson’s ratio, strain hardening coefficient, and sheet thickness.

The Role of Second Phase Intermetallic Particles on the Spall Failure of 5083 Aluminum

5083 aluminum alloy is a light-weight and strain-hardened material used in high strain-rate applications such as those experienced under shock loading. Symmetric real-time (in situ) and end-state (ex situ recovery) plate impact shock experiments were conducted to study the spall response and the effects of microstructure on the spall properties of both 5083-H321 and 5083-ECAE + 30 % cold-rolled (CR) aluminum alloys shock loaded to approximately 1.46 GPa (~0.2 km/s) and 2.96 GPa (~0.4 km/s). The results show that mechanically processing the 5083-H321 aluminum by Equal Channel Angular Extrusion (ECAE), followed by subsequent CR significantly increases the Hugoniot Elastic Limit (HEL) by 78 %. However, this significant increase in HEL was at the expense of spall strength. The spall strength of the 5083-ECAE + 30 % CR aluminum dropped by 37 and 23 % when compared to their 5083-H321 aluminum counterpart at shock stresses of approximately 1.46 and 2.96 GPa respectively. This reduction in spall strength is attributed to the cracking and re-alignment of the manganese (Mn)–iron (Fe) rich second phase intermetallic particles during mechanical processing (i.e., ECAE and subsequent CR), which are consequently favorable to spallation.

Effect of Equal Channel Angular Pressing on the Microstructure and Mechanical Properties of Hybrid Metal Matrix Composites

Objectives: The objective of the present study is to prepare Al6061-Gr-SiChybrid composites by stir casting route and the effect of Equal Channel Angular Pressing (ECAP) on the microstructure and mechanical properties of Al6061-Gr-SiC hybrid composites will be evaluated. Methods: In the present study, Al6061 is selected as matrix material. The reinforcement materials chosen are graphite (Gr) and Silicon carbide (SiC) particles of 10-30 μm size. The hybrid composites have been prepared by stir casting route in which the amount of Gr particles are kept at 3wt% and SiC particles are varied from 2-10wt% in steps of 2wt% . The cast hybrid composites are subjected to annealing treatment at 400oC for 4 hours and specimens have been prepared from these composites for ECAP process. The ECAP process was carried out at room temperature using a die with channel angle of 120o and Bc route was adopted for successive passes. The influence of ECAP on microstructure and mechanical properties of Al-Gr-SiC hybrid composite was evaluated. Findings: The microstructural study revealed that the composites are free from defects and also the distribution of reinforcement particles in the matrix are fairly uniform. Significant improvement in micro hardness and tensile strength was observed as the wt% of SiCp increases in as cast Al6061-Gr- SiC hybrid composites. After ECAP process, the size and distribution of the reinforcement particles are not changed but significant reduction in the grain size of the matrix alloy was observed. The micro hardness and tensile test results revealed that, there is a significant improvement in the micro hardness and the Ultimate tensile strength of ECAP processed hybrid composites. The enhancement in mechanical properties are mainly attributed to the grain refinement of the matrix alloy and strain hardening of hybrid composite materials by ECAP process. Applications: The ECAP process had a profound effect in enhancing the mechanical properties of hybrid composites. These composite materials have great impact in automobile, military and aerospace industries.

Effect of Reverse Yielding on the Residual Contact Pressure in Tube-to-Tubesheet Joints

The analytical prediction of the contact stress in tube-to-tubesheet joints subjected to hydraulic expansion is conducted without any consideration to reverse yielding that can occur inside the tube. Most existing models consider the tube and tubesheet to unload elastically when the expansion pressure is released. These models are therefore less conservative as they overestimate the contact pressure. An analytical model that considers strain-hardening material behavior of the tube and tubesheet and accounts for reverse yielding has been developed. The model is based on Henckey deformation theory and the Von Mises yield criteria. The paper shows that reverse yielding that is present in tubes during hydraulic expansion unloading makes the joint less rigid and causes a decrease in the contact pressure depending on the gap clearance and the materials used. A good correlation between the analytical and finite elements results is obtained on different treated cases which gives confidence on the developed model.