Hardening Exponents Research Articles

Strain rate sensitivity and fracture mechanism of AlSi10Mg parts produced by Selective Laser Melting

Implementation of Additive Manufacturing (AM) parts in the growing applications within the automotive and aerospace industries encourages further investigations of the material behavior under various strain rates, spanning from quasi-static to the high strain rate regimes. Although mechanical properties of AM-Selective Laser Melting (SLM) AlSi10Mg parts under a static regime have been investigated, the strain rate sensitivity of these materials, to the best of our knowledge, has not been discussed in the literature. In this work, the properties of AM-SLM AlSi10Mg material were systematically investigated under a wide range of strain rates, spanning from 2.77×10−6 to 2.77×10−1 S−1. The AM-SLM AlSi10Mg alloy, as opposed to Al alloys fabricated by conventional methods, was found to be strain rate sensitive with significant changes to the flow stress and strain hardening exponents with an increase in strain rate. The fracture mechanisms of these specimens, built in different orientations, are discussed.

On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test

A novel methodology is proposed for estimating the strain hardening exponent of a metal single crystal directly from the spherical indentation test, without the need of solving the relevant inverse problem. The attention is focused on anisotropic piling-up and sinking-in that occur simultaneously in different directions, in contrast to the standard case of axial symmetry for isotropic materials. To correlate surface topography parameters with the value of material hardening exponent, a finite-element study of spherical indentation has been performed within a selected penetration depth range using a finite-strain crystal plasticity model. It is shown how the power-law hardening exponent can be estimated from the measured pile-up/sink-in pattern around the residual impression after indentation in a (001)-oriented fcc single crystal of a small initial yield stress. For this purpose, a new parameter of surface topography is defined as the normalized material volume displaced around the nominal contact zone, calculated by integration of the local residual height (positive or negative) over a centered circular ring. That indicator can be easily determined from an experimental topography map available in a digital form. Comparison is made with the estimates based on measurements of the contact area and the slope of the load–penetration depth curve in logarithmic coordinates. The proposed methodology is extended to estimation of the hardening exponent simultaneously with the initial yield stress when the latter is not negligible. Experimental verification for a Cu single crystal leads to promising conclusions.

쇄빙선 강재의 내충격 특성에 관한 실험적 연구: 제1부 강재 특성

This paper presents a study on the crashworthiness of the scaled-down stiffened panels used on a Korean icebreaker. In order to validate the crashworthiness of the panels, this paper provides various mechanical properties such as the results of a CVN test, quasi-static tensile test, and high-speed tensile test at arctic temperatures. Two types of steels (EH32 and FH32) were chosen for the material tests. CVN tests revealed that the two steels were equivalent up to −60℃ in terms of their impact energy absorption capacity. However, the toughness of FH32 was significantly superior to that of EH32. EH32 showed slightly higher flow stresses at all temperature levels compared to FH32. The improvement ratios of the yield strengths, tensile strengths, plastic hardening exponents, etc. for FH32, which were obtained from quasi-static tensile tests, showed an apparent ascending tendency with a decrease in temperature. Dynamic tensile test results were obtained for the two temperatures levels of 20℃ and −60℃ with two plastic strain rate levels of 1 s^−1 and 100 s^−1. A closed form empirical formula proposed by Choung et al. (2011;2013) was shown to be effective at predicting the flow stress increase due to a strain rate increase.

A simple method to estimate elastic follow-up factors for transient creep parameter C(t) under secondary stress

In this article, a semi-analytical method to estimate elastic follow-up factor as input to estimate the transient creep C( t) parameter under secondary loading is presented and validated against finite element results for a cracked two-bar structure under constant displacement loading. Predicted values of C( t) agree well with the finite element results for both elastic-creep cases and for elastic-plastic cases with the same creep and plastic hardening exponents. For elastic-plastic-creep cases with different creep and plastic hardening exponents, the proposed method gives good predictions at long time but can under- or over-predict C( t) at short time.

A Flow Stress Model for High Strength Steels with Low Carbon Bainite Structure

Two kinds of steels (YP960 and YP690) with low carbon bainite structure were designed, and their flow stress and strain hardening exponents were studied. The results showed that, when Hollomon relation was applied to describe the flow stress, there were significant errors between the experimental and calculated points in specimens tempered below 400 °C, while a high precision was observed in samples tempered above 400 °C. Whereas, the modified Voce relation could effectively predict the flow stress as well as the strain hardening exponent at different tempering temperatures, which was verified by unbiased estimators such as maximum relative error (MRXE) and average absolute relative error (AARE). Besides, the modified Voce relation was also applied to estimate the maximum uniform strain, and the correlation coefficients (R) between the experimental data and calculated maximum uniform strain were more than 0. 91. The high correlation coefficients indicated that the modified Voce relation could effectively predict the uniform deformation ability of high strength steels with low carbon bainite structure at different tempering temperatures.

Identifying Deformation and Strain Hardening Behaviors of Nanoscale Metallic Multilayers Through Nano-wear Testing

In complex loading conditions (e.g., sliding contact), mechanical properties, such as strain hardening and initial hardness, will dictate the long-term performance of materials systems. With this in mind, the strain hardening behaviors of Cu/Nb nanoscale metallic multilayer systems were examined by performing nanoindentation tests within nanoscratch wear boxes and undeformed regions (as-deposited). Both the architecture and substrate influence were examined by utilizing three different individual layer thicknesses (2, 20, and 100 nm) and two total film thicknesses (1 and 10 µm). After nano-wear deformation, multilayer systems with thinner layers showed less volume loss as measured by laser scanning microscopy. Additionally, the hardness of the deformed regions significantly rose with respect to the as-deposited measurements, which further increased with greater wear loads. Strain hardening exponents for multilayers with thinner layers (2 and 20 nm, n ≈ 0.018 and n ≈ 0.022, respectively) were less than that determined for 100 nm systems (n ≈ 0.041). These results suggest that single-dislocation-based deformation mechanisms observed for the thinner systems limit the extent of achievable strain hardening. This conclusion indicates that impacts of both architecture strengthening and strain hardening must be considered to accurately predict multilayer performance during sliding contact across varying length scales.

Experimental Research on Hysteretic Characteristics of Steel Plates Artificially Corroded by Neutral Salt Spray

This paper aims to study the hysteretic characteristics of the steel plates artificially corroded by neutral salt spray. Salt spray was applied to accelerate the corrosion on the steel plates; specimens of varying degrees of corrosion were obtained in this manner. And each specimen was subject to cyclic loading test to get the hysteretic curve. Then the experimental results were extensively discussed, focusing on strength and ductility, hysteretic energy, the skeleton curve, and unloading and loading curve. After that, the hysteretic constitutive model of corroded steel was established based on the first time loading criterion, unloading criterion, cycle skeleton criterion, and reloading curve criterion. The result of the experiment showed that, with the increase of the degree of corrosion, the mechanical properties and seismic energy dissipation performance of seismic energy of the steel decreased; the deterioration of ductility got aggravated. On the other hand, the skeleton curve and the Ramberg-Osgood model were well matched, and the coefficient of circular enhancement showed a decreasing trend; the variation of cyclic hardening exponent did not have an obvious pattern. Meanwhile, the hysteretic constitutive model of corroded steel and the results of the experiment were well matched.

Analysis of Welding Properties in FSW Aluminium 6351 Alloy Plates Added with Silicon Carbide Particles

In the present investigation, properties of the Friction Stir Welded (FSW) Aluminium 6351 alloy plates added with SiC particles in the weld zone was studied. The qualities of welds were determined in two conditions of as-weld condition and annealed condition. In addition, the hardening parameters were calculated to evaluate the quality of friction stir welds of Al 6351 alloy plates. Using swift hardening law, strength coefficient (k) and strain (ε) values were calculated keeping hardening exponent (n) as constant for Al 6351 alloy. The calculated values of strength coefficient and strain were found to be present within the theoretical design limits for both as-weld and annealed conditions. Thus the process ensures the quality of friction stir welded joints of Al 6351 alloy plates with SiC particles in the weld region both in theoretical and experimental aspects.

Cyclic Constitutive Response and Effective S–N Diagram of M50 NiL Case-Hardened Bearing Steel Subjected to Rolling Contact Fatigue

A combined experimental and numerical method is developed to estimate the continuously evolving cyclic plastic strain amplitudes in plastically deformed subsurface regions of a case-hardened M50 NiL steel rod subjected to rolling contact fatigue (RCF) over several hundred million cycles. The subsurface hardness values measured over the entire plastically deformed regions and the elastoplastic von Mises stresses determined from the three-dimensional (3D) Hertzian contact finite element (FE) model have been used in conjunction with Neuber's rule to estimate the evolved cyclic plastic strain amplitudes at various points within the RCF-affected zone. The cyclic stress–strain plots developed as a function of case depth revealed that cyclic hardening exponent of the material is greater than the monotonic strain-hardening exponent. Effective S–N diagram for the RCF loading of the case-hardened steel has been presented and the effect of compressive mean stress on its fatigue strength has been explained using Haigh diagram. The compressive mean stress correction according to Haigh diagram predicts that the allowable fatigue strength of the steel increases by a factor of two compared to its fatigue limit before mean stress correction, thus potentially allowing the rolling element bearings to operate over several hundred billion cycles. The methodology presented here is generalized and can be adopted to obtain the constitutive response and S–N diagrams of both through- and case-hardened steels subjected to RCF.

A novel method for determining surface residual stress components and their directions in spherical indentation

Abstract

Loading and unloading of a power-law hardening spherical contact under stick contact condition

The loading and unloading process of a deformable sphere pressed by a rigid flat is a primary problem in contact mechanics. This work studies the contact of an elastic–plastic sphere with a rigid flat under stick condition during loading and unloading process by the finite element method. The sphere material is assumed isotropic with power-law hardening. The contact load and contact area are calculated at various Poisson׳s ratios and strain hardening exponents, with the sphere material properties varying from purely elastic to elastic-perfectly plastic. Analytical dimensionless expressions of the contact load, contact area and the residual interference after fully unloading for the power-law hardening materials in the elastic–plastic case are proposed for a wide range of interferences.

Mechanism of grain refinement and its effect on Adiabatic Shear Bands in 4340 steel and pure copper during impact

Pre-deformation and post-deformation microstructure characterization was conducted on tempered 4340 steel and commercial pure copper specimens under impact to determine the microstructural changes and the mechanism of grain refinement that occur during the evolution of ASBs. It was observed that the movement and multiplication of dislocations, elongation of grains, breaking of elongated grains, rotation, carbide fragmentation and boundary refinement of broken grains occur simultaneously during the evolution of ASBs in the impacted 4340 steel specimens. The extent of these mechanisms depends on the imposed local strain and strain rate. Extensive grain refinement coupled with high density of dislocations results in the shear band structures being more susceptible to crack nucleation and propagation. In copper, it was observed that sequential occurrence of emergence of dislocations, dislocation cell formations with varying cell boundaries and cell interiors, dynamic recovery and extensive micro-twinning results in the formation of the shear bands. The structure within the evolved shear bands becomes less brittle after the onset of dynamic recovery and micro-twinning. The differences in the mechanism of grain refinement and evolution of the shear bands in both materials is attributed to the differences in the mobility of dislocations, the rate of strain hardening and strain hardening exponents in both materials studied.

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.

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.

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.

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.

Modeling approach and plastic deformation analysis of 6063 aluminum alloy during compression at elevated temperatures

In this study, the elevated temperature deformation behavior of AA6063 alloy has been investigated within the temperature range 625–725K at constant compression-head speeds, 0.5, 2, 5, 10 and 20cm/min of test machine respectively. To evaluate the flow stress of AA6063 alloy in hot working processes, a formula is derived by analyzing the stress–strain curves obtained from tests at various temperatures and head speeds. The stress–strain curves were divided into two ranges as work hardening part and flow softening part, limited pick strain, εp. Since all the curves showed different hardening and softening exponents, used in σ=σp(ε/εp)n formula, σp and n exponent have expressed depending on Zener–Hollomon parameter and test temperature respectively. It is demonstrated that a linear equation of the logarithmic Z fits the flow stress of the alloys at elevated temperatures. Obtained model curves were compared with experimental curves and as a result, work hardening and flow softening parts in equations were generally in a good agreement with experimental counterparts.

Tensile properties of duplex UNS S32205 and lean duplex UNS S32304 steels and the influence of short duration 475 ºC aging

Duplex stainless steels are high strength and corrosion resistant steels extensively used in the petrochemical and chemical industries. The aging at 475 °C for long periods of time provokes embrittlement and deterioration of corrosion resistance. However, short duration aging at 475 °C may be used as heat treatment to improve mechanical resistance with small decrease in the other properties. In this work the flow stress curves of lean duplex UNS S32304 and duplex UNS S32205 steels were modeled with Hollomon’s equation and work hardening exponents (n) were determined. The analyses were conducted in specimens annealed and heat treated at 475 °C for short periods of time. The aging at 475 °C for 4 hours, 8 hours and 12 hours promoted significant hardening with small decrease of ductility. The work hardening exponents of both steels were compared, being higher in the duplex steel than in the lean duplex grade.

Cyclic deformation behavior of a super-vacuum die cast magnesium alloy

Magnesium alloy as a lightweight structural material has recently kindled considerable interest in the automotive and aerospace industries, since lightweighting is considered as one of the salient strategies in reducing fuel consumption and anthropogenic greenhouse gas emissions. The structural applications of magnesium alloys inevitably involve fatigue resistance. This study was aimed at evaluating cyclic deformation behavior and fatigue life of a super-vacuum die cast (SVDC) AM60B alloy using strain-controlled low cycle fatigue tests at two strain ratios of Rs = −1 and Rs = 0.1. The SVDC AM60B alloy exhibited a superior fatigue resistance to the conventional die cast AM60 alloy especially in the high-cycle fatigue region. Fatigue life was longer at Rs = −1 than at Rs = 0.1 at lower strain amplitudes. With increasing total strain amplitude, cyclic stress amplitudes increased, hysteresis loops exhibited a clockwise rotation despite the symmetry in tension and compression at Rs = −1, and fatigue life and psuedoelastic modulus decreased at both strain ratios. Cyclic hardening increased with increasing strain amplitude and strain ratio due to the formation of more twins and their interaction with dislocations. Two types of twins (wider lenticular extension twins and narrower banded contraction twins) were observed in some favorably oriented large α-Mg cells near the fracture surface. Mean stress relaxation occurred mainly within the initial 10–30% of fatigue life. Cyclic hardening exponent was higher than monotonic hardening exponent. Fatigue crack initiation occurred from the specimen surface or near-surface defects, and crack propagation was mainly characterized by fatigue striations coupled with some secondary cracks and tear ridges.