Strain-hardening Exponent Research Articles

Softening behaviour of Fe-6.5%Si steel during warm deformation process

To investigate the softening behaviour during warm deformation process, thermal compression experiment of Fe-6.5%Si silicon steel was conducted. To study the relationship between stress and strain at different strain rate, the investigation of the microstructure, hardness as well as ordered phase constituent of the rolled parts was carried out, respectively. At strain less than or equal to 0.3, micro-hardness was observed to increase with increasing strain. For strain greater than 0.3, the micro-hardness decreased with increasing strain. Indentation morphology of Vickers hardness reveals that the sink-in deformation occurs as the steel has a higher strain-hardening exponent, while pile-up deformation takes place at a lower strain-hardening exponent. Brittle B 2 (FeSi) and DO 3 (Fe 3 Si) ordered phases exists in Fe-6.5%Si steel. With the increasing strain, the diffraction spot strength of B 2 and DO 3 ordered phase is decreased, resulting in the softening behaviour of the Fe-6.5%Si steel during warm deformation process.

Investigation of plastic eta factors for clamped SE(T) specimens based on three-dimensional finite element analyses

Three-dimensional finite element analyses of clamped single-edge tension (SE(T)) specimens are performed to evaluate the plastic eta factors (i.e. ηpl) for computing the J-integral. The analysis covers both plane-sided and side-grooved specimens with a wide range of specimen configurations (a/W from 0.2 to 0.7 and B/W equal to 1 and 2) and strain hardening exponents (n=5, 8.5, 10, 15 and 20). Based on the analysis results, a set of expressions for ηpl are proposed.

J-CTOD relationship for clamped SE(T) specimens based on three-dimensional finite element analyses

Three-dimensional (3D) finite element analyses (FEA) of clamped single-edge tension (SE(T)) specimens are performed to evaluate the plastic constraint factors (m) that are used to relate the crack tip opening displacement (CTOD) and the J-integral (J). The analysis covered both plane-sided and side-grooved specimens with a range of specimen configurations (a/W=0.2 to 0.7 and B/W=1 and 2) and strain hardening exponents (n=5, 8.5, 10, 15 and 20). Based on the analysis results, a new empirical m-factor equation is proposed as a function of a/W, B/W, the yield-to-tensile strength ratio and the loading level.

Unified Solution of Burst Pressure for Defect-Free Thin Walled Elbows

In order to study the mechanical properties of defect-free thin walled elbows (TWE), and evaluate impacts of the intermediate principal stress effect, tension/compression ratio, and strain-hardening of materials into logical consideration, this research, in the framework of finite deformation theory, derived the computational formula of burst pressure for defect-free TWE according to unified strength theory (UST). In addition, influences of various factors on burst pressure were analyzed, which include strength disparity (SD) effect of materials, intermediate principal stress, curvature influence coefficient, strain-hardening exponent, yield to tensile (Y/T) and thickness/radius ratio. The results show that the greater the tension/compression ratio is, the higher the burst pressure is. The influence of the SD effect of materials is more obvious with the increase of elbow curvature and intermediate principal stress. The intermediate principal stress effect can bring the self-bearing capacities and strength potential of materials into a full play, which can achieve certain economic benefits for projects. Moreover, the burst pressure of defect-free TWE increases with the growth of yield ratio and thickness/radius ratio, while decreases with the rise of curvature influence coefficient and strain-hardening exponent. It is also concluded that the Tresca-based and Mohr–Coulomb-based solutions of TWE are the lower bounds of the burst pressure, the twin shear stress (TSS)-based solution is the upper bound of the burst pressure, and the solutions based on the other yield criteria are between the above two. The unified solution in this paper is suitable for all kinds of isotropous materials which have the SD effect and intermediate principal stress effect. As the deduced formula has unified various burst pressure expressions proposed on the basis of different yield criteria for elbows of any curvature (including straight pipelines), and has established the quantitative relationships among them, its applicability is broader. Therefore, the unified solution is of great significance in security design and integrity assessment of defect-free TWE.

New Equation for the Plastic Correction Factor η for J-Integral Determination from Test Results of Three-Point-Bend Specimens

Abstract When material yielding occurs, the stress intensity factor, K, no longer correctly characterizes the magnitude of the stress field around the crack tip. For significant amounts of yielding, the J-integral approach is applied as an advanced tool. In practice, for many engineering applications, the non-linear plasticity effects are of importance and therefore material behavior beyond yield needs an accurate description for input to tools for assessment. This work presents J-integral values of two different steel grades (1006 and 4340) using a newly developed analytical approach for the correction factors ηpl, which takes into account the elastic–plastic properties of the material. The evaluation approach is based on absorbed energies in a Charpy-sized specimen during the elastic and plastic deformation phases. Values of these energy terms were obtained via numerical simulation of 1006 and 4340 steel Charpy-sized specimens loaded in three-point-bending. This work highlights the effect of materials plastic properties on the J-integral. Different steel grades show different amounts of plasticity defined by the strain-hardening exponent and the strain-hardening constant and these influence the fracture parameters. Application of the plastic correction factor ηpl to Charpy-sized specimens, considering the respective plastic properties of the materials, leads to values of ηpl equal to 2.286 for 1006 steel and 2.621 for 4340 steel.

Effect of Partial Replacement of Si with Al on the Microstructures and Mechanical Properties of 1000 MPa TRIP Steels

Two newly synthesized C-Mn-Si-Mo-Nb transformation-induced plasticity (TRIP) steels with and without Al addition were designed in order to achieve significant improvements in the mechanical properties. The effect of substitution of Si by Al on tensile properties and the microstructure of cold-rolled C-Mn-Si TRIP steel was investigated under different heat treatments. It was shown that a complex ultrafine microstructure composed of different phases was formed and two types of morphology for ferrite were detected (equiaxial and polygonal). The distribution of alloying elements was observed by using electron probe microanalysis. It was clear that C was concentrated in the retained austenite (RA) and small M/A (austenite/martensite) islands. The Al addition facilitated the formation of polygonal ferrite and increased the stability of the RA. The strain-hardening behavior was studied in detail. All the investigated specimens showed a very high strain-hardening exponent (instantaneous n) but their strain dependence was different. For the C-Mn-Si-Mo-Nb TRIP steel, the maximum n value was achieved when the strain was only about 0.04, while the n value of the Al substituted TRIP steel increased gradually until strains in the range of 0.07-0.10 were reached and the maximum value was achieved. As a result, the elongations of the steel with Al addition increased considerably without obvious deterioration of strength. It was the first time to find microtwinned martensite located between ferrite and bainitic ferrite after tensile deformation in the low alloy TRIP steel with Al.

Processing, microstructure and properties of ultrasonically processed in situ MgO–Al2O3–MgAl2O4 dispersed magnesium alloy composites

AZ91 alloy matrix composites are synthesized by in situ reactive formation of hard MgO and Al2O3 particles from the addition of magnesium nitrate to the molten alloy. The evolved oxygen from decomposition of magnesium nitrate reacts with molten magnesium to form magnesium oxide and with aluminium to form aluminium oxide. Additionally, these newly formed oxides react with each other to form MgAl2O4 spinel. Application of ultrasonic vibrations to the melt increased the uniformity of particle distribution, avoided agglomeration, and decreased porosity in the castings. Ultrasound induced physical phenomena such as cavitation and melt streaming promoted the in situ chemical reactions. Well dispersed, reactively formed hard oxides increased the hardness, ultimate strength, and strain-hardening exponent of the composites. Presence of well-dispersed hard oxide particles and stronger interface resulting from cavitation-enhanced wetting of reactively formed particles in the AZ91 alloy matrix improved the sliding wear resistance of the composites.

Influence of Dual-Phase Microstructures on the Properties of High Strength Grade Line Pipes

The influence of dual-phase microstructures on mechanical properties of X70, X80, and X90 line pipes is investigated. It is found that the line pipes with dual-phase microstructures possess both larger uniform elongation and higher hardening exponent, especially for high grade steel X90. The tensile deformation of dual-phase line pipe does not follow the trend predicted by the Hollomon formula, and a stable strain-hardening exponent is not found. This stress-strain behavior is different from the normal line pipe. In the initial stage of plastic deformation, the strain-hardening capacity of dual-phase line pipe increases rapidly. However, it reaches a stable stage after 2.0% total strain. The dual-phase pipeline steel is composed of soft phase (polygonal ferrite) and hard phase (bainite), and thus the relatively soft ferrite is good for its deformability. Besides, the fraction of large angle grain boundaries in the dual-phase microstructures is greater than that of the normal line pipe, which is proven to be critical for improving the resistance to plastic deformation and crack propagation.

Strain hardening exponents and strength coefficients for aeroengine isotropic metallic materials – a reverse engineering approach

AbstractThe strain hardening exponent and strength coefficient of the Ramberg-Osgood flow rule are required for the accurate design analysis of the materials of aeroengine components. A direct method of deriving these parameters involves the processing of the complete raw data of tensile testing as per ASTM E-646. More often, a first design effort of aeroengine components is made using catalogue data, as the evaluation of material tensile properties is a time-consuming process that takes place concurrently. Catalogue-supplied data on the monotonic loading typically contains elastic modulus, 0.2% proof stress, and ultimate tensile stress along with other data for various temperatures. A methodology was evolved in this work to construct the Ramberg-Osgood flow rule with these three parameters and was validated with laboratory test results and published data through a comparison with ASTM E-646. The strain hardening exponents and strength coefficients were established for a family of aeroengine metallic materials for various temperatures, which can serve as a first design effort input.

Probabilistic Force Prediction in Cold Sheet Rolling by Bayesian Inference

A primary factor in manufacturing high-quality cold-rolled sheet is the ability to accurately predict the required rolling force. Rolling force directly influences roll-stack deflections, which correlate to strip thickness profile and flatness. Accurate rolling force predictions enable assignment of efficient pass schedules and appropriate flatness actuator set-points, thereby reducing rolling time, improving quality, and reducing scrap. Traditionally, force predictions in cold rolling have employed deterministic, two-dimensional analytical models such as those proposed by Roberts and Bland and Ford. These simplified methods are prone to inaccuracy, however, because of several uncertain, yet influential, model parameters that cannot be established deterministically under diverse cold rolling conditions. Typical uncertain model parameters include the material's strength coefficient, strain-hardening exponent, strain-rate dependency, and the roll-bite friction characteristics at low and high mill speeds. Conventionally, such parameters are evaluated deterministically by comparing force predictions to force measurements and employing a best-fit regression approach. In this work, Bayesian inference is applied to identify posterior probability distributions of the uncertain parameters in rolling force models. The aim is to incorporate Bayesian inference into rolling force prediction for cold rolling mills to create a probabilistic modeling approach that learns as new data are added. The rolling data are based on stainless steel types 301 and 304, rolled on a 10-in. wide, 4-high production cold mill. Force data were collected by observing load-cell measurements at steady rolling speeds for four coils. Several studies are performed in this work to investigate the probabilistic learning capability of the Bayesian inference approach. These include studies to examine learning from repeated rolling passes, from passes of diverse coils, and by assuming uniform prior probabilities when changing materials. It is concluded that the Bayesian updating approach is useful for improving rolling force probability estimates as evidence is introduced in the form of additional rolling data. Evaluation of learning behavior implies that data from sequential groups of coils having similar gauge and material is important for practical implementation of Bayesian updating in cold rolling.

Computational Analysis of Compressive Strain Hardening Exponents of Bimetal with Pearlitic Steel and Low Carbon Steel

The compressive strain hardening behaviour of a novel bimetal with pearlitic steel and low carbon steel was investigated by computational analysis based on the isothermal compression tests in a wide range of deformation temperature and strain rate. The Hollomon’s equation was employed to calculate the strain hardening exponent (SHE) with the assistance of mathematical manipulation. The result shows that the logarithmic relationship between the flow stress and plastic strain of the bimetal is highly non-linear, which results in the variation of the SHE of the bimetal. This variation reflects the dynamic competition between the strain hardening and softening mechanism by the varying value of the SHE in the range of 0.4 to-0.4. Furthermore, the influences of deformation temperature and strain rate on the SHE are significant. With decreasing temperature and increasing strain rate, the strain hardening of the bimetal was enhanced, while the dynamic recrystallisation was activated under the opposite conditions with the evidence of negative SHE value.

Investigation of pile-up during a rigid ball sliding on coated surface based on elastic–plastic analysis

A three-dimensional finite element model (FEM) is used to study the development of pile-up and contact situation during nano-indentation and sliding indentation of elastic–plastic coated solids. The FEM results were verified by nano-indentation and sliding indentation tests which were carried out on TiN specimens. Then, the influence of elastic–plastic deformation, penetration depth, contact friction and strain hardening on pile-up was investigated for a wide range of materials with different elastic modulus, yield stresses, strain-hardening exponents and friction coefficients. The results indicated that the pile-up/sink-in geometry depends on the relative amounts of elastic and plastic deformation characterized by (E/σy), in a way that pile-up grows by increasing (E/σy). At small non-dimensional penetration depth (h/R), the deformation is only elastic, then by increasing the load, the plastic zone grows and spreads upward and the sink-in diminishes. It was found that friction severely enhances pile-up only in small amounts of strain hardening exponent. In addition, the influence of a unified parameter on pile-up was utilized to investigate some parameters simultaneously for various strain hardenings which depicted that increasing strain hardening exponent leads to smaller pile-up. The finite element results may be used as a first estimate of the pile-up/sink-in behavior if the material parameters are known.

Tensile properties and strain-hardening behaviour of friction stir welded SiCp/AA2009 composite joints

3mm thick rolled 17vol%SiCp/AA2009 composite sheet in T351 condition (with 15% deformation) was subjected to friction stir welding (FSW). Tensile properties and work hardening behaviour of FSW joints were studied at strain rates from 1×10−2 to 1×10−5s−1. The FSW joints tended to fracture in the heat-affected zone, which exhibited the lowest hardness. Joint efficiencies of about 77% were achieved at various strain rates. As the strain rates increased, the yield strength, ultimate tensile strength and elongation decreased slightly, but the effect of strain rate on the elongation became weaker after FSW. The dependence of the strain-hardening exponents on the strain rate was weak in both the base metal (BM) and the FSW joint. Compared to the BM, the FSW joint exhibited higher strain-hardening rates and strain-hardening exponents, as well as a stronger hardening capacity; about three times that of the BM.

Comparative study of analytical expressions for the modelling of stainless steel behaviour

During the last decades, various material models have been proposed describing stainless steel nonlinear behaviour through different parameters. The differences among these models are analysed herein using experimental data of different stainless steel types. An interactive computer programme, usable for any series of experimental data, is developed and presented: the procedure for the determination of Young׳s modulus (E0) is pointed out and the least-square adjustment to optimize the strain-hardening exponents of different material models is described. Different expressions for the calculation of the parameters, proposed by several authors and used in a variety of codes, are analysed and new ones are proposed.

Constitutive prediction of the defect susceptibility of tensile properties to microporosity variation in A356 aluminum alloy

The aim of this study is to verify the physical meaning of the defect susceptibility of tensile properties to microporosity variation in terms of the constitutive law for tensile deformation. Additionally, it aims to investigate the contributions of plastic constraint factors describing the geometric array of eutectic Si particles and micro-voids as well as of strain-related factors to the defect susceptibility of tensile properties through theoretical prediction and systematic experiments on T4-treated A356 alloy. The empirical relationship proposed in previous studies to describe defect susceptibility can be theoretically described in terms of the constitutive law, which takes into account the strain-hardening exponent, strain rate sensitivity and microporosity terms. The modified constitutive model can very accurately predict the defect susceptibility of tensile elongation, far more accurately than the original Ghosh model. The strain-hardening exponent has practical significance, affecting the defect susceptibility of tensile elongation to microporosity variation because of its additional contribution to the plastic constraint factor, whereas the strain rate sensitivity has a minor effect on the variation of defect susceptibility. The plastic constraint factor of eutectic Si particles has a relatively lower contribution to the defect susceptibility than the plastic constraint factor of micro-voids, rather slightly increasing the defect susceptibility by increasing the maximum elongation in the defect-free condition.

Initial grain size effect on mechanical properties and springback behavior of thin metal sheets with varying rolling reduction ratios

The aims of this study were to investigate the effect of initial grain size on mechanical properties of thin stainless steel sheet (SUS304) with an initial thickness of 1 mm underwent varying reduction ratios by roll forming and to analyze the effect of grain refinement on springback behavior in micro V-bending process. Specimens were carried out the annealing treatment to obtain different initial grain sizes in a range of 15.1 to 30.2 mm. The annealed specimens were rolled with varying reduction ratios. All specimens were conducted the tensile test for measuring the Young’s modulus, strength coefficient and strain-hardening exponent. The rolled specimens with varying reduction ratio were carried out V-bending with an angle of 90o. Furthermore, the springback behavior was simulated using finite element method and compared the springback amount with that of the experimental result. Consequently, larger initial grain size induced higher ductility but decreased ultimate tensile strength and lower yielding strength. Although grain refinement induced brittle behavior with higher elastic modulus and smaller plasticity, high elastic modulus may contribute the higher springback amount.

A Study on the Effect of Tempering Temperature on Tensile Properties of P92 Steel by Automated Ball Indentation Technique

P92 steel was normalized at 1353 K for 30 minutes followed by air cooling and subs equently tempered at 1013, 1033 and 1053 K for 60 minutes each followed by air cooling. The effect of tempering temperatures on the tensile properties of P92 steel has been investigated using automated ball indentation technique (ABI) at different test temperatures in the range of 300 K-923 K. The yield strength (YS), ultimate tensile strength (UTS) and strength coefficient (K) were determined and these were found to decrease with increase in tempering and test temperatures. The decrease in strength was attributed to the increase in M 23C6 precipitate size and lath width with higher tempering temperatures. The strain hard ening exponent (n) decreased with increase in the test temperature which is confirmed by increased pile up around indentation. The ABI results were in good agreement with the results obtained from conventional tensile tests.

Research on Formability of AZ31B Magnesium Alloy at Room Temperature

Tensile tests and a cold deep drawing process were developed at room temperature to estimate the stamping formability of AZ31B magnesium alloy sheet. The results show that AZ31B magnesium alloy sheet has poor formability at room temperature with the total elongation of ~ 20%, the yield ratio is about 0.6 and the strain-hardening exponent is 0.18, while the plastic strain ratio is 1.58, and the earing ratio is-0.55.Thus, AZ31B magnesium alloy sheet can not suffer server plastic deformation. It was found that comparatively shallow magnesium alloy cups were satisfactorily formed at room temperature without heating when the punch fillet radius 6mm and the die fillet radius10mm with a 1mm thickness sheet with limit drawing ratio of 1.25.

The Effect of Magnesium Addition on the Microstructure & Compressive Deformation Behavior of Al-Ca Alloy

The Al-Ca-Mg alloys containing varying amount of Mg are used to study the effect of Mg addition on their microstructure and deformation behavior at varying strain rate (0.01/s, 0.1/s, 1/s). The material is prepared using stir casting technique. The yield stress, flow stress and elastic limit are measured from the true stress-strain graph. The strain rate sensitivity and strain-hardening exponent were also determined for each material at different strain rates. The elastic limit decreases with increases in strain rate. The strain rate sensitivity m is found to be negative at a flow strain and invariant to the strain rate. Its microstructure reveals that the microstructural characteristics changes with Mg addition. The variation of microstructural features primarily leading to the variation of deformation behavior.

Three-dimensional finite element analysis of crack-tip fields of clamped single-edge tension specimens – Part I: Crack-tip stress fields

A systematic study has been carried out based on three-dimensional finite element analyses to investigate the impact of the in-plane and out-of-plane dimensions on the crack-tip stress fields of clamped SE(T) specimens. Both plane-sided and side-grooved specimens with a wide range of thickness-to-width ratios (B/W=1/2, 1, 2 and 4), crack lengths (a/W=0.3, 0.4, 0.5, 0.6 and 0.7) and strain hardening exponents (n=5, 10 and 20) are included in this study. The through-thickness distributions of J and CTOD as well as the distribution of the opening stress (σθθ) ahead of the crack tip at different crack front locations are presented. The distributions of J and CTOD over the crack front and those of σθθ ahead of the crack tip are impacted by a/W, B/W, n and the type of specimens (i.e. plane-sided or side-grooved). In addition, the empirical equation for calculating CTOD from J for SE(T) specimens developed by Shen and Tyson based on two-dimensional plane-strain finite element analyses is found inadequate to be applied to three-dimensional SE(T) specimens except for the plane-sided specimens with n=10 and side-grooved specimens with n=5.