Plastic Strain Levels Research Articles

Effects of Hydroforming Process on Fatigue Life of Reinforced S-Shaped Bellows

Reinforced s-shaped bellows, which can withstand high pressure, is a kind of typical reinforced metal bellows. The reinforced s-shaped bellows mainly uses the hydroforming process, and the forming process is a severe plastic deformation process. The hydroforming process and its effects on the fatigue life of reinforced s-shaped bellows were discussed in the present study. Different levels of plastic strain and wall thickness thinning were detected in the hydroforming process. The maximum plastic strain can reached 32%, while the maximum wall thickness thinning ratio is 20%, which occurs on the wave peak. Mechanical characteristics of reinforced s-shaped bellows were discussed considering the effects of hydroforming process. The maximum stress appears on the upper and lower ends, which is the weak part of the structure. Fatigue life of the reinforced s-shaped bellows was analyzed based on the modified Manson-Coffin method. Mechanical properties of related materials, which can be more accurate consideration the effects of hydroforming process, were tested under the pre-plastic deformation. Fatigue life analysis of reinforced s-shaped bellows was carried out and the effects of hydroforming process were discussed. The hydroforming process will lead to a decline in fatigue life, which needs to be considered well in the structural design and analysis. Keywords: Reinforced s-shaped bellows, Hydroforming process, Fatigue life, Mechanical characteristics.

Deformation field interaction in sequential circular indentation of a strain hardening material

ABSTRACTAn experimental study was made to characterise and model the deformation field in sequential circular indentation of a model strain hardening material. Digital image correlation was used to measure the evolving subsurface deformation field in terms of displacement, strain rate and strain as a function of indentation spacing and depth. These measurements were used to validate a finite element model for complementary simulations. The results identify relationships between sequential indentation parameters and overlap of subsurface strain distributions, maximum subsurface strains and indentation loads. Maximum strain and the degree of strain field overlap in the deformed subsurface were maximised when the ratio of indentation spacing (S) to projected indentation contact length (L) was approximately S/L = [1.1, 1.2]. Also discussed are the implications for understanding process-scale considerations for indentation-based mechanical surface treatments, including energy dissipation and relationship of surface coverage measures to subsurface strain overlap. Relative differences in energy expended were found for conditions that produce similar levels of subsurface plastic strain and strain field overlap. Finally, the role of sequential indentation parameters on strain path changes and path reversals in the deformed subsurface is investigated and discussed in the context of heterogeneous mechanics and corresponding effects on subsurface microstructure evolution.

Continuum damage mechanics-based ductile behavior and fatigue life estimation of low carbon steels: AISI 1020 and AISI 1030

This paper presents an experimental estimation of the ductile behavior and low-cycle fatigue life for widely used structural steels AISI 1020 and AISI 1030 based on continuum damage mechanics approach. This method identifies the deterioration in stiffness of a material arising from micromechanisms of formation, growth, and coalescence of microvoids. This helps the characterization of the ductile flow behavior of metals through a damage variable D, evaluated via load–unload cyclic tensile test. The influence of strain hardening exponent, commonly treated as a constant in ductile flow characterization, is also explored in the current investigation. Its determination uses the Hollomon constitutive relation. Estimated D at different strain levels defines the corresponding effective stress. Application of this stress to the strain equivalence theory then enables the prediction of the stress–strain curve. The model-based results closely approximate the experimental stress–strain curve up to the onset of necking. The agreement of experimental results for fatigue life of the materials from low-cycle fatigue tests with damage-based low-cycle fatigue model demonstrates the correctness of the experimental findings. The damage-based model additionally helps in the prediction of microcrack nucleation and crack propagation life separately. Fractographic examinations of test specimen exhibit usually observed morphology of involved failure mechanisms. The present study emphasizes the experimental means of damage-based ductile flow assessment involving strain hardening exponent term and also the low-cycle fatigue life estimation. The significance of varying strain hardening exponent is further expressed in terms of the corresponding damage magnitude. The material data obtained from this study depicts the damage state at different levels of plastic strain that may serve as a useful information for metal-forming process design.

Effect of Test Method on Stress-Relaxation Behavior of Alloy 718

The stress-relaxation behavior of alloy 718 was established at 991 K (718 °C) using two contrasting test protocols. For this purpose, compression and tension samples extracted from two subscale forgings were first solution treated and cooled to room temperature. Each sample was then reheated to 991 K (718 °C), compressed or pulled isothermally to a total strain between 0.006 and 0.02, and then allowed to relax after locking either (i) the extensometer attached to the dies (compression tests) or reduced section (tension tests) or (ii) the ram itself. For the tests in compression, the stress dropped in a monotonic fashion under locked-extensometer conditions, while the locked-ram mode gave rise to a short stress drop, a broad hardening stage, and finally softening at long times. For the tension stress-relaxation tests, monotonic stress drops whose magnitudes varied for the two test modes were observed. The various behaviors were ascribed to the specific level of plastic strain imposed during the different types of tests, its quantitative effect on the level of dynamic strain aging, and thus the increment in hardening which counterbalanced stress-relaxation per se.

The effect of pre-twinning on the mechanical behavior of free-end torsion for an extruded AZ31 magnesium alloy

In this paper, the effect of pre-twinning on the mechanical behavior of free-end torsion (FET) for an extruded AZ31 Mg alloy was investigated via pre-compression along extruded direction with 1.5%, 3.5%, 5.5% and 6.5% plastic strain levels. After pre-compression, torsion was performed at room temperature. The yield strength was enhanced remarkably during FET test after 3.5% pre-compression. However, the change of yield strength is small during FET with pre-compression (PRC) greater than 3.5%. Refinement hardening induced by twinning contributes to the enhancement of yield strength for PRC 3.5 specimen. With pre-strain increasing, the change of yield strength is ascribed to dislocation hardening. The stage II and stage III of strain hardening were observed during pure torsion and FET test after 1.5% pre-compression. In contrast, the stage II is suppressed and the stage III only occurs during FETs after 3.5%, 5.5% and 6.5%. The pre-twinning favor the activation of prismatic slip under torsion, which enhances multiple slip and dynamic recovery. The transition of deformation mechanisms from basal slip to multiple slip leads to the change of strain hardening during FET after different pre-strain levels.

Dislocation evolution at a crack-tip in a hexagonal close packed metal under plane-stress conditions

Understanding the stress state and microstructural features at a growing crack-tip is critical to understanding the failure mechanisms of engineering structures. To investigate the strain and dislocation evolution at a crack-tip, electron backscatter diffraction and geometrically necessary dislocation analysis were performed on fully annealed zirconium foils at room temperature. Different levels of macroscopic plastic strain were applied: 0.0%, 0.22%, 0.84%, 1.2%. Based on their different Burgers vectors and line vectors, prismatic <a>, basal <a>, screw <a>, screw <c+a> and pyramidal <c+a> geometrically necessary dislocation densities were estimated during crack blunting and subsequent propagation. Most of the plastic deformation was accommodated by screw <a> and pyramidal <c+a> dislocations. Screw <a> dislocations were found to be dominant over the <c+a> as might be expected. Instead of twinning, pyramidal slip accommodated the strain along the c-axis caused by contraction at the crack-tip. Dislocation densities at the crack-tip were plotted according to the angle relative to the applied tension direction and the distance from the tip, and were compared with plastic strains simulated from a 3D static finite element model. Crack-tip singularity was observed and total geometrically necessary dislocation densities were in qualitatively good agreement with the equivalent plastic strain distribution predicted by the finite element method (FEM).

A viscoplastic model based on a variable strain rate sensitivity index for superplastic sheet metals

This paper presents a new phenomenological model for describing the main features of the viscoplastic behavior of superplastic sheet metals, namely, strain hardening, softening, and damage. The proposed model is based on a variable strain rate sensitivity index (m-value) measured from uniaxial tensile tests at different strain rates under constant temperature. In this study, the uniaxial tensile tests were carried out at three strain rates (i.e., 10−3, 10−2, and 10−1 s−1) on a superplastic grade AA5083 aluminum sheet alloy. In addition, the volume fractions of cavities at different plastic strain levels were assessed using X-ray microtomography. The performance of the model was investigated by comparing its predictions with the experimental data. In addition, the model was validated with two sets of reference data for AA5083 aluminum alloy and AZ31 magnesium alloy. In particular, it was observed that the new model could predict the flow behavior of these metals more successfully compared with two reference models; nevertheless, it requires minimal experimentation and calculation efforts.

Electromagnetic-assisted calibration for surface part of aluminum alloy with a dedicated uniform pressure coil

Springback is an inevitable defect of aluminum alloy sheet after conventional stamping process, which directly has an influence on the forming accuracy of part. For a surface part of aluminum alloy, the stamping process was used to complete the preforming process, and then the electromagnetic forming was adopted to calibrate the shape and improve the forming accuracy. A dedicated uniform pressure coil was proposed to quasi-uniformly impose the impulse magnetic pressure on the whole part. The effect of discharge voltage on the springback phenomenon was experimentally and numerically investigated. It was found that the springback defect of surface part was significantly reduced with the discharge voltage increasing. The forming accuracy of surface part was remarkably improved under the discharge voltage of 5 kV. It can be attributed to two aspects: on the one hand, the effective plastic strain level at the bottom of surface part was greatly elevated, and on the other hand, the gap between the tensile stress on the exterior surface and the compressive stress on the interior surface was well decreased.

A diffusion-based approach for modelling crack tip behaviour under fatigue-oxidation conditions

Modelling of crack tip behaviour was carried out for a nickel-based superalloy subjected to high temperature fatigue in a vacuum and air. In a vacuum, crack growth was entirely due to mechanical deformation and thus it was sufficient to use accumulated plastic strain as a criterion. To study the strong effect of oxidation in air, a diffusion-based approach was applied to investigate the full interaction between fatigue and oxygen penetration at a crack tip. Penetration of oxygen into the crack tip induced a local compressive stress due to dilatation effect. An increase in stress intensity factor range or dwell times imposed at peak loads resulted in enhanced accumulation of oxygen at the crack tip. A crack growth criterion based on accumulated levels of oxygen and plastic strain at the crack tip was subsequently developed to predict the crack growth rate under fatigue-oxidation conditions. The predicted crack-growth behaviour compared well with experimental results.

On the damage mechanisms in a continuous casting mold: After-service material characterization and finite element simulation

Abstract A mold is a part of a continuous casting plant where the molten steel starts to solidify. The inner surface of the mold undergoes a cyclic thermal load. In fact, service conditions are characterized by a high thermal flux, which vanishes when the plant is switched off. The highest temperatures occur in the area just beneath the free level of liquid steel (meniscus). The same area is typically characterized by thermal fatigue cracks when the mold is inspected after service. This work presents the characterization of the material of a copper mold after it had been used in the plant. The aim was to understand the damage and cracking mechanism, and our analysis confirmed that a network of cracks was present on the inner mold surface in the meniscus area, which experienced the maximum temperature gradients. Metallurgical examination demonstrated the transgranular characteristics of cracks, thus suggesting that thermal fatigue was the main cause of the damage observed. The location of the thermal fatigue cracks corresponded to the area experiencing the highest levels of plastic strains, as confirmed by the results of a finite element analysis simulating the mold in-service conditions.

Effect of strain path on forming limits and retained austenite transformation in Q&P 1180 steel

Forming limits and retained austenite (RA) transformation in Q&P 1180 steel are quantified as a function of plastic strain levels for three different strain paths. In-plane uniaxial tension testing was performed in a standard test frame, while limiting dome height tooling was employed for out-of-plane biaxial and plane strain tension experiments. Sheet specimens were tested incrementally for each strain path, and the RA content at each level of strain was measured using electron backscatter diffraction (EBSD). The biaxial tension strain path resulted in the greatest effective strain prior to necking at 0.355, compared to 0.123 for plane strain and 0.142 for uniaxial tension. EBSD measurements for various levels of plastic strain reveal a clear dependence of RA rate of transformation on strain path for the three linear strain paths that were employed in this work. Thinning strains appear to provide a slightly better correlation to RA transformation than effective strain levels, where biaxial tension achieved the greatest level just prior to necking, followed by plane-strain tension, and then uniaxial tension.

Damage identification parameters of dual-phase 600–800 steels based on experimental void analysis and finite element simulations

In this work, the damage behavior of cold-rolled zinc-coated dual-phase steel sheets 600 and 800 grades was evaluated by means of standard uniaxial tensile testing, microstructural characterization and finite element modeling. The void formation in both steels was investigated as a function of the plastic strain level from digital image processing of scanning electron micrographs to quantify the average void size and to determine the corresponding measures of void density, void area fraction and void aspect ratio. Based on the void analysis and the experimental uniaxial tensile test data, a four-step procedure is proposed to identify the parameters of the Gurson–Tvergaard–Needleman (GTN) damage model. Bearing in mind the non-uniqueness of the GTN model parameters, 3D finite element simulations using a single element and an 1/8 symmetry uniaxial tensile specimen model were performed in a systematic manner to investigate the role of both nucleation and failure parameters on the uniaxial behavior. At low straining levels, most of the void initiated by debonding of globular aluminum-oxide inclusions identified by EDS in both dual-phase steels. At higher straining levels, the void density evolution is found to be more pronounced in DP600 steel owing to the faster void nucleation rate at the ferrite grain boundaries. A good agreement between predictions and experimental load-elongation is achieved allowing for the identification of the full set of GTN damage model parameters of both DP600 and DP800 steels. The proposed damage calibration of dual-phase steels can be very helpful in simulations of practical sheet metal forming processes.

Low cycle fatigue behavior and microstructure evolution of a novel 9Cr–3W–3Co tempered martensitic steel at 650 °C

A series of uniaxial strain-controlled fatigue tests were performed at 650 °C to explore the high-temperature low cycle fatigue (LCF) behavior and corresponding microstructure evolution of a novel 9Cr–3W–3Co martensitic G115 steel. The fatigue test results showed that the steel exhibited a cyclic softening behavior and the degree of softening S increased with the total strain amplitude, which was related to the decrease of dislocation density and subgrain development. Further, statistical analysis of the subgrain size after LCF tests at different strain amplitudes showed that the development of subgrain or cell depended on both the plastic strain level and cycles, among which the effect of plastic strain level is dominant. The variation of degree of softening ΔS was used to make comparison between G115 steel and P92 steels to evaluate the effects of the strain amplitudes on the respective S. The G115 steel experienced the minimum relative increment compared with P92 steel. This resulted from the strengthening by fresh and fine Cu-rich precipitates. The number density of Cu-rich particles increased with the total strain amplitude and that weakened the effect of strain amplitude on degree of softening. SEM was employed to investigate the fracture morphology; representative images of the G115 steel after the LCF tests showing three regions: fatigue crack initiation sites, stable crack growth region, and rupture region. Larger the strain amplitude was, more the crack initiation sites formed, which corroborates the significant decrease in fatigue life with increase in the total strain amplitude. In addition, a modified plastic strain energy approach based non-Masing behavior of G115 steel is proposed to predict the fatigue life.

Tensile properties and deformation microstructure of highly neutron-irradiated 316 stainless steels at low and fast strain rate

Post-irradiation deformation behavior of solution-annealed (SA) and cold-worked (CW) 316 austenitic stainless steel irradiated to doses from 9 to 39 dpa is examined as a function of strain rate and irradiation conditions (neutron spectrum, temperature). Tensile properties are found to be significantly higher for lower irradiation temperature and for CW material, for similar irradiation levels. The effect of strain rate on tensile properties is shown to be weak in the range [10−8s−1; 10−4s−1]. TEM investigations after deformation for levels of plastic strain of about 1% show on SA 316 the presence of deformation bands corresponding to one or even a mixture of twins, extended stacking faults, α′-martensite islands and ε-martensite nanobands. Bundles of crisscrossing bands, found to be a composite of overlapping stacking faults, nanotwins and ε-martensite nanolayers, are observed at TEM foils edges near the grain boundaries with α′-martensite islands decorating these edges. Except observation of a slight decrease of the number of deformation bands in the specimen deformed at slower strain rate, no qualitative microstructural differences appear between specimens tested at slow and fast strain rates.

The Influence of Plastic Deformation on the Low-Cycle Fatigue During the Burnishing of Holes in Flat Specimens of D16chT Steel

The paper deals with one of the most important problems of such closely related industries as mechanical engineering and aircraft manufacturing, involving the determination of the service life of components and structures operating under cyclic loading conditions. The presence of local structural and manufacturing stress concentrators greatly complicates the determination of the predicted life of components and structures at their design stage. The burnishing technique, namely, the method of plastic deformation of walls of the hole, aimed at achieving the amount of the residual plastic strain on their surface, is used to strengthen components with holes. The results of low-cycle fatigue tests conducted in repeating tension are presented for flat laboratory specimens of an aircraft aluminum alloy D16chT with a central cylindrical manufacturing hole hardened by burnishing. The burnisher geometry that ensures the required value of the residual plastic strain level (1, 2, and 3%) on the hole surface is calculated. The cyclic tensile loading of specimens at the stresses in a pulsating load cycle was performed in the range of 150 to 270 MPa at a frequency of 3 Hz using the equipment Bi-02-112. The influence of the amount of plastic strain in the burnished hole of the specimen on its cyclic life and fracture as a function of the load value is observed. It is found that due to plastic strain hardening of the surface of manufacturing holes, a local area of compressive residual stresses occur, causing the stress concentration around the manufacturing hole to decrease and the level of limit loads to increase. It is shown that the specimen, having a manufacturing hole hardened by burnishing (up to a plastic strain of 3%) and being cyclically loaded by a tensile stress to 170 MPa, failed not at the hole (the stress concentrator). Both the onset of the microcrack initiation and its further propagation take place in a solid region of the specimen. This is indicative that with a certain amount of residual stresses in the burnished hole, the specimen fracture under low-cycle fatigue becomes insensitive to the presence of this concentrator.

Rheological Behavior, Optimized Processing Interval, and Microreplication of a Zr‐Based Bulk Metallic Glass

Bulk metallic glass (BMG) is a novel advanced material developed since 1980s. In this paper, the Zr35Ti30Be27.5Cu7.5 BMG is prepared and its thermoplastic forming (TPF) tests at various strain rate with different temperatures in supercooled liquid region (SCLR) are conducted. According to differential scanning calorimetry (DSC) curve and the transformed Kissinger equation, the normally processable temperature window (588–731 K) and continuous heating transformation (CHT) curve are obtained, respectively. And the isothermal annealing experiments without deformation are performed at 663, 683, 703, and 713 K with various holding times, respectively, results of which obviously suggest that the deformation during TPF can induce crystallization. Notably, from CHT curve and TPF tests, the optimized processing interval is subsequently revealed. All evidence indicates that this alloy presents good superplastic‐like behavior with a relatively low level of flow stress and large plastic strain under the temperature ranging from 643 to 703 K and the strain rate of 1 × 10−2 s−1–5 × 10−4 s−1. Furthermore, the successful microreplication and molding of several coins and microparts under the condition of strain rate of an order of 10−3 s−1 at 663 K also provides us with the full proof for extremely good thermoplastic formability in this alloy.

A case study investigation into the effects of spatially dependent convection coefficients on the fatigue response of a power plant header component

Societal and environmental pressures are forcing thermal power plant operators to deviate greatly from the generation strategies of the past. The application of high frequency start up/shut down/partial load cycles to components that may well be outside their design life makes research into the long-term integrity of at risk assets paramount. Decoupled thermal/mechanical analyses have been used in the literature to estimate anisothermal fatigue in header components, with convective boundary conditions typically assumed for internal surfaces in order to determine heat fluxes and hence a temperature field. In reality, convective coefficients are heavily dependent upon local velocity profiles. In the present work, computational fluid dynamics is used in order to better approximate the steam flow in a real power plant header, leading to a convection coefficient field that is used to solve the thermal problem. Anisothermal fatigue analysis is finally conducted using a Chaboche type model. The results of computational fluid dynamics have illustrated that heat transfer coefficient values can vary (spatially) by a factor of 5.49 over the internal header wall, with noticeable hot spots in the wake of the stub penetrations. Peak differences of 6.47% in accumulated plastic strain levels have been observed between simulations conducted with constant (simplified) and variable (computational fluid dynamics derived) thermal boundary conditions.

Effect of mechanical pre-loadings on corrosion resistance of chromium-electroplated steel rods in marine environment

Providing high hardness, low friction coefficient, as well as, relatively good corrosion resistance, chromium-plated coatings (∼20 μm) are widely used for steel cylinder rods in marine environment. However, the standardized corrosion test method (ISO 9227, NSS) used to evaluate efficiency of this type of coatings does not take into account in-service mechanical loadings on cylinder rods. Nevertheless, the uniform initial network of microcracks in chromium coating is changing under mechanical loadings. Propagation of these microcracks explains premature corrosion of the steel substrate. The aim of the study was to evaluate relationship between mechanical loadings, propagation of microcracks network and corrosion resistance of chromium coatings. After monotonic pre-loading tests, it was demonstrated by microscopic observations that the microcracks propagation started at stress levels higher than the substrate yield stress (520 MPa). The microcracks become effective, i.e. they have instantly undergone through the whole coating thickness to reach the steel substrate. The density of effective microcracks increases with the total macroscopic level, i.e. the intercrack distance goes from 60 ± 5 μm at 1% of total strain to approximately 27 ± 2 μm at 10%. Electrochemical measurements have shown that the higher the plastic strain level applied during mechanical loading, the more the corrosion potential of the sample decreased until reaching the steel substrate value of approximately −0.65 V/SCE after 2 h of immersion. The polarization curves have also highligthed an increase in the corrosion current density with the strain level. Therefore, electrochemical measurements could be used to realize quick and comprehensive assesment of the effect of monotonic pre-loadings on corrosion properties of the chromium coating.

A nonlinear CDM based damage growth law for ductile materials

A nonlinear ductile damage growth criterion is proposed based on continuum damage mechanics (CDM) approach. The model is derived in the framework of thermodynamically consistent CDM assuming damage to be isotropic. In this study, the damage dissipation potential is also derived to be a function of varying strain hardening exponent in addition to damage strain energy release rate density. Uniaxial tensile tests and load-unload-cyclic tensile tests for AISI 1020 steel, AISI 1030 steel and Al 2024 aluminum alloy are considered for the determination of their respective damage variable D and other parameters required for the model(s). The experimental results are very closely predicted, with a deviation of 0%–3%, by the proposed model for each of the materials. The model is also tested with predictabilities of damage growth by other models in the literature. Present model detects the state of damage quantitatively at any level of plastic strain and uses simpler material tests to find the parameters of the model. So, it should be useful in metal forming industries to assess the damage growth for the desired deformation level a priori. The superiority of the new model is clarified by the deviations in the predictability of test results by other models.

Effect of mechanical (monotonic and cyclic) stress on the corrosion resistance of chromium-plated steel rods

Providing high hardness, low friction coefficient, as well as, relatively good corrosion resistance, chromium-plated coatings are widely used for steel cylinder rods in marine environment. Nevertheless, a uniform network of microcracks in chromium coating is evolving under mechanical loadings during the service-life of cylinder rods. The propagation of these microcracks is in the origin of the premature corrosion of the steel substrate. The aim of the study was to evaluate the relationship between mechanical stresses, the evolution of the microcracks network and the corrosion resistance of chromium coatings. After monotonic pre-loading tests, it was demonstrated by microscopic observations that the microcracks propagated for stress levels higher than the yield stress of the substrate (520 MPa) and have passed instantly through the whole thickness of the coating and reached the steel substrate. The density of microcracks increases with the level of total strain, the inter-crack distance go from 80 µm at 1% of total strain to approximately 65 µm at 5%. Electrochemical measurements have shown that the higher the level of plastic strain applied during the mechanical loading, the more the corrosion potential of the sample decreases until reaching that of the steel substrate of approximately -0.65 V/ECS after 2 hours of immersion. The polarization curves also evidenced an increase in the corrosion current density with the strain level. Moreover, we note the absence of the characteristic passive region of the reference samples that have not undergone any loading. After cyclic loadings, no microcracks propagation was observed after 104 cycles when maximal stress was lower than the yield stress. However, a decreasing of the corrosion potential was observed for samples which were submitted to a cyclic loading. Nevertheless, the current density and the characteristic passive region were not modified.