Hollomon Analysis Research Articles

Effect of grain size and strain rate on tensile work hardening behavior of two different FCC metals

The present work aims to investigate the effect of grain size and strain rate on tensile work hardening behaviour of two single-phase FCC metals having different stacking fault energy (SFE); commercially pure polycrystalline Cu and pure Al. Different heat treatment processes were employed to produce different grain sizes in the materials. The samples with different grain sizes were then subjected to uniaxial tension test with strain rates in the ranges 10−4 to 10−1 s−1. The work hardening behaviour was analysed using two different approaches: Hollomon analysis and Kocks-Mecking analysis. The Kocks-Mecking analysis proves to be a better assessment technique of the work hardening behaviour of the two investigated materials as compared to the Hollomon analysis. A clear difference in work hardening behaviour between Cu and Al is noted from Kocks-Mecking analysis. Further, the Hollomon analysis doesn’t show any effect of grain size and strain rate on the work hardening behaviour. Whereas, Kocks-Mecking analysis revealed that both grain size and strain rate affect the 2nd and 3rd stage of work hardening behaviour in the case of quenched Cu. An important component of hardening in Kocks-Mecking analysis: the athermal component of strain hardening rate (θh) is found to be approximately equal to the average work hardening rate at the initial stage (stage I) of plastic deformation for both Cu and Al.

Explaining the drop of work-hardening rate and limitation of transformation-induced plasticity effect in metastable stainless steels during tensile deformation

While the occurrence of the transformation-induced plasticity effect in metastable austenitic stainless steels has been adequately explained, the reason behind the fall of work-hardening rate after the maximum value remains largely unknown. In the present work, via extensive work-hardening analysis and examination of the mechanical properties and strengthening mechanisms by the Hollomon analysis, Hall-Petch law, and rule-of-mixtures, it is revealed that the yielding of the deformation-induced martensite leads to the drop of work-hardening rate and limits the strengthening effect of strain-induced martensitic transformation and tensile ductility.

Strengthening Mechanisms and Strain Hardening Behavior of 316L Stainless Steel Manufactured by Laser‐Based Powder Bed Fusion

The microstructure–properties relations and strengthening mechanisms of additively manufactured 316L stainless steel are comprehensively investigated in this work. The orientation dependency and the strain hardening are studied by tensile testing of as‐built specimens fabricated by laser‐based powder bed fusion (LPBF) in different directions. The results are compared with those obtained for wrought material. The microstructure of the wrought and the LPBF materials are also comprehensively investigated. Equiaxed grains with random orientation and relatively uniform size (≈30 μm) are observed in the wrought material, where the LPBF samples show columnar grains inside as well as fine equiaxed grains in the bottom of the molten pool. A bimodal grain size distribution, higher values of geometrically necessary dislocations density (≈25–32%), and lower fractions of high‐angle grain boundaries (≈24–28%) are observed in LPBF 316L. A significant yield strength and considerable ultimate strength improvement without remarkable elongation decrease are obtained for the LPBF tensile specimens, resulting in a high strength‐elongation balance (up to 26 122 MPa%). Two‐stage strain hardening is depicted in both wrought and LPBF samples. This is successfully predicted with two‐stage Hollomon analysis. However, the LPBF samples illustrate lower strain hardening exponents in comparison with the wrought ones.

The effect of cold-rolling prior to the inter-critical heat treatment on microstructure and mechanical properties of 4340 steel with ferrite – Martensite microstructure

This study investigates the effect of cold rolling prior to inter-critical annealing on microstructure and mechanical properties of ferrite-martensite dual phase steel. Samples were heated to 850 °C for 1 h followed by oil quenching, then the steel sheet were cold rolled by 0%,10%,15% and 20% reduction in thickness. The inter-critical annealing treatment (750 °C, 120min) was performed to generate a ferrite-martensite microstructure. Microstructural studies showed that increasing the applied cold rolling, leading to increase in volume fraction of martensite and decrease in ferrite grain size. Mechanical properties of dual phase steel were measured by tensile, impact and hardness tests. Results showed that ultimate tensile strength, yield strength, micro-hardness and toughness (e.g. total elongation, uniform elongation and impact energy) increased with increasing the applied cold rolling. Improvement of mechanical properties were related to increase in martensite volume fraction and ferrite grain refinement. Analysis of strain hardening behavior of DP steels, by Hollomon analysis, showed two stages of strain hardening corresponding to ferrite deformation and co-deformation of ferrite and martensite, respectively. The strain hardening exponent of first stage (nI) increased with increasing volume fraction of martensite. The energy absorption capacity (UE × UTS) increased with increasing cold rolling deformation.

On the thermal and mechanical stability of reverted austenite by intercritical tempering

The study provides new sights on thermal and mechanical stability of reverted austenite, which interestingly were modulated by intercritical heat treatment in a low alloy low carbon steel. Thermal and mechanical stability of reverted austenite was strongly governed by the intercritical tempering temperature during the second step of heat treatment and decreased with the increase of temperature. Hollomon analysis indicated that reverted austenite grains experienced martensitic transformation and the tensile strength was significantly enhanced. Furthermore, thermal stability studied by low temperature magnetic experiments suggested that Ms and Mf of reverted austenite generated by intercritical tempering at 720℃ were −97.5℃ and −120.5℃ respectively, and the transformation product was twinned martensite.

Effect of martensite volume fraction on abnormal work hardening behavior of a low carbon low alloy ferrite–martensite dual-phase steel

Abstract This paper investigates the work hardening behavior of a low carbon low alloy steel under various ferrite-martensite dual-phase (DP) microstructures. For this purpose, several DP microstructures containing 23- 87% martensite volume fraction (MVF) were developed by application of inter-critical annealing heat treatment processes. The Hollomon analysis was employed in conjunction with mechanical testing and electron microscopy observation to describe the work hardening behavior of DP samples. The experimental results indicated that the DP specimens containing lower than 36% MVF were associated with a ‘single stage’ of work hardening behavior while those of higher than 36% of martensitic microconstituents were related to a ‘double stage’ of work hardening pattern. With increasing the MVF from 23 to 87%, the strain hardening exponent for the first stage of work hardening showed a peak value of 0.111 at MVF = 73%, while those for the second stage of strain hardening exponents were continuously increased from 0.162 to 0.197. This abnormal trend of strain hardening exponents with MVF was correlated with the variable hardening responses of ferrite and martensite microconstituents.

Microstructure, Mechanical Properties, and Strain‐Hardening Behavior of V–N Microalloyed Pipeline Steels Consisted of Polygonal Ferrite and Acicular Ferrite

A novel V–N microalloying method is adopted to produce pipeline steels using a two‐stage thermomechanical controlled processing involving relaxation process and accelerated cooling. The main objective of the current work is to study the novel practice in terms of microstructure, mechanical properties, and strain‐hardening behavior. The microstructure of the experimental steels consists of polygonal ferrite (PF), quasi‐polygonal ferrite (QF), acicular ferrite (AF), and granular bainite (GB). Mechanical properties including strength, ductility, and low‐temperature toughness of V–N microalloyed steels meet the requirements of X80 pipeline steels. Yield strength, tensile strength, total elongation, and −20 °C impact energy are 639 MPa, 761 MPa, 21.0%, and 283 J when the volume fraction of PF is 9.1%, and 603 MPa, 724 MPa, 24.1%, and 214 J when the volume fraction of PF increases to 30.4%. The V–N microalloyed steels exhibit high strain‐hardening ability, and the values of strain‐hardening exponent are 0.12 and 0.11 based on Hollomon analysis.

Generalized diagrams and equations of recrystallization of cold-deformed steel St

The recrystallization processes in steel St.3 inthe ferrite state were studied. Samples with diameter of 8 mmand with height of 10 mmwere deformed by compression at 20 °Cfor 20 to 80 %, annealed at 400 – 735 °Cfor a period from 5 minutes to 10 hours, and cooled in the air. On the samples, the grain size was determined in longitudinal sections (with respect to the compression axis). After separation of the entire array of experimental data (degree of deformation ε, temperature T and time τ of annealing, grain size D) into 3 groups (no recrystallization, beginning and end of the primary recrystallization), the equations of hyperplanes best sharing these groups were found by the method of discriminant mathematical analysis. Recrystallization is not observed if the temperature is below 465 °C, or if the degree of deformation is lower than 20 % for any combination of other parameters. The deformed structure completely recrystallizes if the experimental points are in the parameter range: T > 550 °C, ε > 40 %, τ > 30 min. The largest grain refinement (up to 7 – 10 μm) was obtained after deformation with a maximum degree (80 %). The first critical (physical) degree of deformation, after which the size of the recrystallized grain is larger than the original one, is absent. The second critical (technical) degree of deformation is 25 – 35 % for temperatures of 530 – 735 °C. At such degrees grain refinement was observed in comparison with the initial deformed state. Mathematical relation between the size of the recrystallized grain and the experiments’ parameters was analyzed in two ways: according to Arrhenius in the form D=AεNτMexp (-Q/RT) , and according to Hollomon with linear temperature dependence (D ~ T). The Arrhenius solution gave the following equation: log(D) = 2,08 – 0,33log(ε) + 0,023log(τ) – 967,31 1/T. Therefore, activation energy of the recrystallization process is found to be ~18,000 J/mol. In case of the Hollomon analysis, it was proposed to use the function РН = T/1000 [СН – log(τ) + log(ε)] as the Hollomon parameter, and the Hollomon constant of CH should be found by numerical methods. For these conditions, the equation D = –21,317 – 0,034T + 0,0032log(τ) T – 0,0032log(ε)T was obtained. The accuracy of both descriptions, defined as the sum of deviations squares of the measured grain sizes from calculated, is equal to ~3,3 μm or (when normalized to an average value) ~20 %.

Recrystallization behavior in a low-density high-Mn high-Al austenitic steel undergone thin strip casting process

The recrystallization behavior of a high-Mn high-Al lightweight steel (Fe-28.4Mn-8.3Al-1.27 C (wt%)) with 50% cold rolling deformation is investigated at the annealing temperature of 800 °C, 900 °C and 1000 °C. The detailed microstructure evolution is characterized by optical microscopy (OM), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), X-ray diffraction (XRD), electron probe micro-analyzer (EPMA) and transmission electron microscopy (TEM). The partial recrystallized bimodal austenite grains and κ-phase (Fe, Mn)3AlC form at 800 °C, while fully recrystallized austenite grains without κ-phase appear at 900 °C and 1000 °C. With the increase in annealing temperature, the increased frequency of annealing twin boundaries reduces the average austenitic grain size and the dispersion of the austenite grain size effectively. The effect of austenite grain size on the tensile properties is discussed. The strain hardening behavior is also investigated by Hollomon analysis and C-J analysis, and the later one is better to explain the strain hardening behavior in different four stages. The recrystallization behavior significantly improves the tensile toughness from 59 MJ/m3 to 436 MJ/m3 at the expense of tensile strength decrease from 1460 MPa to 890 MPa, due to the homogenous fine austenite grains and high frequency of high misorientation angle. The steel with fully recrystallized austenite grains of 10.0 µm annealed at 900 °C exhibits the optimum mechanical properties with excellent tensile strength of 965 MPa, ductility of 48.3%, and good toughness of 400 MJ/m3.

Effect of volume fraction of bainite on strain hardening behavior and deformation mechanism of F/B multi-phase steel

Five ferrite/bainite (F/B) multi-phase experimental steels with different volume fraction of bainite were processed by thermo-mechanical controlled processing (TMCP). The strain hardening behavior and deformation mechanism of F/B multi-phase steel were studied by modified C-J analysis, Hollomon analysis and numerical simulation method. The study indicates that the deformation mechanism in stage I and stage II are directly related to elastic-plastic deformation of ferrite and uniform strain (deformation) of ferrite and bainite, respectively. As the volume fraction of bainite increases, the deformation mechanism of ferrite and bainite changes from incoordinate deformation to coordinate deformation, which will cause the strain difference between ferrite and bainite being lessened gradually, as well as might be the reason for the transition from three-stage to two-stage in modified C-J analysis. The deformation mechanism was verified experimentally. Moreover, the effect of volume fraction of bainite on yield stress/tensile stress ratio (yield ratio), strain hardening exponent and uniform elongation were explained by the division and strain hardening capability of the stages in modified C-J analysis.

Influence of manganese content on ε-/α′-martensitic transformation and tensile properties of low-C high-Mn TRIP steels

Low carbon steels containing 15–19 wt% Mn were processed to study the influence of Mn content on the thermally induced and deformation-induced ε-/α′-martensitic transformation and tensile properties of high-Mn TRIP steels. The stability of austenite and ε-martensite was studied in terms of thermodynamics, and the work hardening behavior during tensile deformation was divided into two stages using Hollomon analysis. The results indicated that Mn increased the stability of austenite and ε-martensite and austenite grain refinement had a larger effect on γ → ε than γ → α′ transformation. During early stages of tensile deformation, the steel having ~15 wt% Mn continued the γ → ε, ε → α′ and γ → α′ transformation because deformation energy compensated the Gibbs free energy required for phase transformation. But α′-martensitic transformation was difficult in steel having ~19 wt% Mn even after fracture because of the high stability of ε-martensite. On account of high density of dislocations in α′-martensite, the dynamic strain aging process was obvious when deformation-induced α′-martensitic transformation occurred in steel. The significant α′-martensitic transformation and intense dynamic strain aging improved work hardening exponent and ultimate tensile strength of steel, while the coordinated transformation of γ → ε and ε → α′ during tensile deformation was beneficial to improve ultimate elongation.

Influence of original austenite grain size on tensile properties of a high-manganese transformation-induced plasticity (TRIP) steel

Original austenite grain size and stacking fault energy (SFE) of a high-Mn transformation-induced plasticity (TRIP) steel were varied by annealing at different temperatures. The microstructural evolution during cooling and tensile deformation were investigated to explain the work hardening behavior. The study suggested that the amount of ε-martensite was increased with annealing temperature. When SFE was greater than 13.3mJ/m2, twin may form in austenite on cooling; and ε-martensite cannot be thermally induced in austenite once its SFE was higher than 20.6mJ/m2. Work hardening behavior of the steel annealed at different temperatures could be divided into two stages using Hollomon analysis. The grain refinement strengthening and deformation induced γ → ε transformation rendered 800°C annealed sample to have the largest work hardening exponent in Stage-I, in this case ultimate tensile strength was also highest. In Stage-II, significant deformation-induced ε → α′ transformation in samples annealed at high temperatures resulted in greater improvement of work hardening exponent. The elongation of the steel was also improved with annealing temperature because local stress concentration was effectively released by ε → α′ transformation.

The formability investigation of CNT-reinforced aluminum nano-composite sheets manufactured by accumulative roll bonding

There is an increasing demand for materials with outstanding mechanical properties for many applications. Ultrafine-grained (UFG) materials as a path for improving the base materials and composite materials as a media for combining the superior properties of different materials are the current solutions for the demanded properties. Severe plastic deformation can be used for manufacturing UFG materials with nano-structure. In this research, accumulative roll bonding (ARB), as a severe plastic method, is utilized for manufacturing aluminum matrix composites reinforced with carbon nano-tubes (CNT). An experimental platform is used to investigate the mechanical properties of ARB-ed AA1200 nano-composites with 2, 6, 32, and 128 layers. Tensile deformation via the Lankford parameter is used to study the anisotropy of the samples. It is observed that this parameter is a function of the number of ARB cycles and increases significantly by increasing the ARB cycles. Moreover, the Hollomon analysis is used to investigate the strain-hardening behavior of the samples. The results showed that the strain-hardening exponent of ARB-ed AA1200 sheets reinforced with CNT decreases by increasing the number of ARB cycles. The formability of the ARB-ed AA1200 nano-composite samples is investigated analytically by the Marciniak–Kuczinsky model and experimentally using the Erichsen tests. The results revealed that the tensile properties are enhanced and more homogenous structures are obtained; however, formability is reduced. In order to obviate this issue, annealing the samples for 30 min at 250 °C was adapted. As a result, formability is improved at the cost of a slight reduction in strength. The obtained results can be due to recrystallization and grain growth alongside the dissolving of the brittle intermetallic oxides at the interface of the layers after annealing. Annealing is used as a mediator to reach a balance between strength, ductility, and formability, so an appropriate formability is achieved at the end.

Correlation of Tensile Properties and Strain Hardening Behavior with Martensite Volume Fraction in Dual-Phase Steels

In the present study, tensile properties, strain hardening and fracture behavior of dual-phase (DP) steels were correlated with martensite volume fraction (V M ). A series of DP steels with different amounts of V M (28–50 %) were produced by cold rolling and subsequent intercritical annealing of a ferrite-pearlite starting structure. Hardness and tensile tests results of DP steels showed that variation of hardness, uniform elongation and total elongation with V M was linear and obeyed the rule of mixtures, whereas yield strength and ultimate tensile strength exhibited a nonlinear variation with V M . Analysis of strain hardening behavior of DP steels by the Hollomon analysis showed two stages of strain hardening corresponding to ferrite deformation and co-deformation of ferrite and martensite, respectively. The strain hardening exponent of first stage (n I ) increased with increasing V M , while the strain hardening exponent of second stage (n II ) as well as transition strain between the deformation stages decreased.

On the study of tensile and strain hardening behavior of a thermomechanically treated ferritic stainless steel

Ferritic stainless steels, having a lower price than their austenitic counterparts, can compete and be replaced with some austenitic grades in some particular applications if their properties could be enhanced both chemically and mechanically. The main purpose of this work is to investigate the mechanical properties of fine-grained AISI 430 ferritic stainless steel treated by an advanced thermomechanical process. Intense cold-rolling of the specimens up to 95% reduction in thickness followed by annealing at temperatures of 700°C and 800°C for 20s and 120s at each temperature, led to significant changes in the properties compared to the unprocessed specimen. The microstructural observations showed that by this thermomechanical treatment, the grain size reduced to nano-size scale (by a factor of 660). The important improvements in yield and tensile strengths up to about 1000 and 1200MPa, respectively, showed the capability of this alloy to attain nomination as an ultrahigh strength steel. Strain hardening behavior of the samples based on Hollomon analysis indicated that the logarithmic variation of stress versus strain is not linear and obeys a two-stage strain hardening mechanism. Although all the specimens had the similar trend of strain hardening rate, more intense variations in the strain hardening rates were seen as the annealing temperature decreased. Ductile fracture mode was also characterized from the tensile fracture surfaces in all the specimens.

Mechanical Behavior and Microstructure Characteristics of Directionally Solidified TWIP Steel

The mechanical behavior and microstructure characteristics of three high Mn austenitic steels prepared by directional solidification at withdrawal rates of 60, 120, and 240 μm s−1 were investigated and compared with common TWIP steel with equiaxed grains. For each steel, the Hollomon analysis, differential C–J analysis, and modified C–J analysis as an alternative method to describe the work-hardening behavior were studied. The directionally solidified samples (DS samples) exhibited higher mechanical properties along the axis, five stages (A, B, C, D, and E) divided on the plot of stain hardening rate vs true strain, and a more stable and uniform deformation feature with larger strain-hardening coefficients when the true strain is over 0.25, in comparison with the common TWIP steel. The modified C–J analysis was found to be the best one for revealing the strain-hardening behavior characterized by several different stages with a definite work-hardening exponent n. In the case of DS samples, the dendrite spacings increase but the morphology becomes simple when decreasing the withdrawal rate. The larger volume fraction of twins and prevalent activation of twin systems, together with the fragmentations of the original grains in a sample solidified at a withdrawal rate of 120 μm s−1, lead to the best mechanical behavior in a medium-to-large strain range.

Effects of grain size and dislocation density on strain hardening behavior of ultrafine grained AA1050 processed by accumulative roll bonding

In this work, the effects of grain size and dislocation density on strain hardening behavior of ultrafine grained (UFG) AA1050 produced by 9-cycle accumulative roll bonding (ARB) process were studied. Transmission electron microscopy (TEM) micrographs indicated that UFG structure with the average grain size of 270 ± 11 nm achieved after nine cycles of ARB. The dislocation density which was measured by microhardness value increased with an increase in the number of ARB cycles. The dislocation density increased from about 7 × 1012 m−2 for annealed sample to above 2 × 1013 m−2 after nine cycles ARB. Tensile tests results revealed that with increasing the number of ARB cycles, mechanical properties of the samples improved. The Hollomon analysis was used to investigate the strain hardening behavior of AA1050 samples. The results showed that the strain hardening exponent decreased with increasing the number of ARB cycles. All ARBed samples showed high strain hardening rate in initial stage of deformation, which increased with increasing dislocation density and grain refinement.

Strain hardening behavior of ARMCO iron processed by ECAP

The strain hardening behavior of an ARMCO iron processed by ECAP at room temperature up to sixteen passes following route Bc was investigated through Hollomon and differential Crussard-Jaoul models. Results indicate that the Hollomon analysis shows some deviations from the experimentally determined true stress – true strain curves while the differential Crussard-Jaoul analysis based on the Ludwik equation and the modified Crussard- Jaoul analysis based on the Swift equation fit better when two work hardening exponents are considered. As expected, the strength of the material increased with the number of ECAP passes. Indeed the ultimate tensile stress reached a maximum of ~900MPa after 16 passes, which is more than three times higher than the UTS of the annealed material. Nevertheless, the strain hardening capacity of the material was reduced in comparison with the material without severe plastic deformation. For that reason the tensile ductility was also reduced at increasing ECAP passes. The increase in strength was attributed to the reduction of the grain size through refined sub-grains with high density of dislocations. After sixteenth passes the original grain size (namely 70 mm) was reduced down to 300 to 400 nm observing a good correspondence with the Hall-Petch relationship. The microstructural analysis, carried out by EBSD, showed an increasing amount in the fraction of high Angle Grain Boundaries (HAGB) after 1 pass due to the regeneration of the microstructure with a smaller grain size.

Effect of Microalloying Elements (B, Nb, V and Ti) on the Strain Hardening Behavior of High-Manganese TWIP Steels.

ABSTRACTThe present research work analyses the influence of microalloying elements (B, Nb, V and Ti) on the tensile strength and the strain hardening behavior of a high-manganese TWIP steel. The analysis was carried out by means of true stress-true strain curves derived from uniaxial tension tests. The work hardening exponent was determined by using the Hollomon and differential Crussard-Jaoul models. Metallographic characterization was carried out to determine the metallurgical changes associated with n values. The results indicate that the Hollomon analysis results in strain hardening exponent values up to 0.46. On the other hand, the differential Crussard-Jaoul analysis establishes a clear distinction of n value for two stages of plastic deformation which are determined by a sharp slope change in the plot of ln(dσ/dε)-lnε.

Characterization of different work hardening behavior in AISI 321 stainless steel and Hadfield steel

In order to distinguish the difference between AISI 321 stainless steel and Hadfield steel in work hardening behavior, both the Hollomon analysis and the differential Crussard–Jaoul analysis were used to determine the strain hardening exponent as a function of the strain. The results showed that the differential Crussard–Jaoul analysis characterized the discrepancy between AISI 321 steel and Hadfield steel in work hardening behavior more accurately than the Hollomon analysis. The work hardening of AISI 321 stainless steel resulted mainly from interactions of dislocations. When the true strain was rather low, the work hardening of Hadfield steel also resulted mainly from interactions of dislocations. At high strains, twinning would occur in Hadfield steel. It was the occurrence of twins that led to unusual work hardening at larger strains in Hadfield steel.